Methodology for Developing Modal Emission Rates for EPA’s Multi-Scale Motor Vehicle and Equipment Emission System

          United States         Air and Radiation       EPA420-R-02-027
          Environmental Protection                 October 2002
          Agency
vxEPA    Methodology for Developing
          Modal Emission Rates for
          EPA's Multi-Scale Motor
          Vehicle and Equipment
          Emission System
                                  > Printed on Recycled Paper

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                                                                  EPA420-R-02-027
                                                                       October 2002
                   for                                                      for
                        Assessment and Standards Division
                      Office of Transportation and Air Quality
                       U.S. Environmental Protection Agency
                               Prepared for EPA by
                 Computational Laboratory for Energy, Air, and Risk
                          Department of Civil Engineering
                          North Carolina State University
                                   Raleigh, NC
                        EPA Contract No. PR-CI-02-10493
                                    NOTICE

   This technical report does not necessarily represent final EPA decisions or positions.
It is intended to present technical analysis of issues using data that are currently available.
        The purpose in the release of such reports is to facilitate the exchange of
     technical information and to inform the public of technical developments which
       may form the basis for a final EPA decision, position, or regulatory action.

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                             TABLE OF CONTENTS
1  INTRODUCTION	1
   1.1   Objectives of this Project	3
   1.2   General Technical Approach	4
   1.3   Organization of this Report	5
2  DEVELOPMENT OF ANALYSIS DATASET	7
   2.1   Development of a Combined Database	7
   2.2   Organization of the Data for Analysis	9
   2.3   Summary	10
3  DEVELOPMENT OF A MODAL EMISSIONS MODELING APPROACH	11
   3.1   Statistical Method for Developing Binning Criteria	11
   3.2   Development of the VSP-Based Modal Approach	15
        3.2.1  Exploratory Analysis	15
        3.2.2  Considerations in Refinement of the VSP-Based Modal Approach	21
        3.2.3  Comparison of Modeling and IM240 Datasets	30
   3.3   NCSU Modal Approach: Idle, Acceleration, Deceleration, and Cruise	38
   3.4   Selection of a Binning Method	53
4  SELECTION OF AN AVERAGING TIME FOR MODEL DEVELOPMENT	55
   4.1   Methodological Approach	55
   4.2   Results for Five and Ten Second Averaging Times	55
   4.3   Evaluation of Different Averaging Times and Recommendations	63
5  COMPARISON OF EMISSION FACTOR APPROACHES AND
   EVALUATION OF THE ROLE OF REMOTE SENSING DATA	65
   5.1   Background Regarding Emission Factor Units	65
   5.2   Background Regarding Remote Sensing Data	66
   5.3   Comparison of Emission Factors and Emission Ratios Based Upon the NCSU
        Modal Approach	68
   5.4   Comparison of Emission Factors and Emission Ratios Based Upon the VSP
        Modal Approach	71
   5.5   Comparison of Variability in Emission Ratios for Selected VSP Bins for the
        Modeling and RSD Data Sets	75
   5.6   Comparison of Vehicle Activity in the RSD and Modeling Databases	77
   5.7   Comparison of Emissions Ratios and Vehicle Activity Between the RSD and
        IM240 Databases	82
   5.8   Summary and Recommendations	88
6  COMPARISON AND EVALUATION OF DATA WEIGHTING
   APPROACHES	91
   6.1   Methodological Considerations	91
   6.2   Comparison of Weighting Approaches	92
   6.3   Summary and Recommendation	114

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7  QUANTIFICATION OF VARIABILITY AND UNCERTAINTY	115
   7.1  Methodological Considerations	115
        7.1.1  Variability and Uncertainty	116
        7.1.2  Empirical Distributions	116
        7.1.3  Parametric Distributions	117
        7.1.4  Averaging Time	117
        7.1.5  Normal and High Emitters	118
        7.1.6  Uncertainty Estimates for Final Model Results	119
        7.1.7  Bottom-Up and Top-Down Approaches	121
        7.1.8  Summary of Methodological Considerations	121
   7.2  Quantification of Variability	121
   7.3  Quantification of Uncertainty in Mean Emission Rates	145
   7.4  Uncertainty Correction Factor for Averaging Time	156
   7.5  Estimation of Uncertainty in Model Results	167
        7.5.1  Estimation of Uncertainty in Total Emissions Based Upon the IM240
              Driving Cycle:  Comparison of Monte Carlo Simulation and Analytical
              Approaches	167
        7.5.2  Estimation of Uncertainty in Total Emissions of Selected Driving Cycles	172
        7.5.3  Estimation of Uncertainty in Total Emissions for Different Numbers of
              Vehicles	176
   7.6  Summary and Recommendations	176
8  FEASIBILITY OF ESTIMATING MODAL EMISSIONS FROM
   AGGREGATE BAG DATA	183
   8.1  Methodological Overview	183
   8.2  Bag-Based Modal Emissions Estimation for Four Modes (Idle, Acceleration,
        Cruise, Deceleration) and for 14 VSP Modes	184
   8.3  Bag-Based Modal Emissions Estimation for the "56-bin" VSP-based Approach	195
   8.4  Characterization of Uncertainty in Predicted Modal Emissions	211
   8.5  Summary and Conclusions	214
9  VALIDATION OF THE CONCEPTUAL MODEL	217
   9.1  Validation Case Study 1	217
   9.2  Validation Case Study 2	222
   9.3  Validation Case Study 3	227
   9.4  Preliminary Exploration of Refinements to the Modal Modeling Approach	233
   9.5  Summary and Recommendations	234
10 RECOMMENDATIONS FOR METHODOLOGY FOR MODAL MODEL
   DEVELOPMENT	235

11 REFERENCES	241

12 APPENDIX A	244
                                         11

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LIST OF FIGURES

Figure 1-1. Simplified Schematic of Project Tasks and Their Inter-Relationships 4
FIGURE 3-1. AVERAGE MODAL EMISSION RATES FOR LDGVs (SOURCE: FREYETAL., 2002) 13
FIGURE 3 -2. SAMPLE REGRESSION TREE DIAGRAM (NUMBERS REPRESENT NODE NUMBERS OF THE TREE) 14
FIGURE 3 -3. EXAMPLE OF AVERAGE DISTRIBUTION OF TIME AND EMISSIONS WITH RESPECT TO MODES
(SOURCE: FREYETAL., 2002) 15
FIGURE 3-4. EXPLORATORY ANALYSIS OF AVERAGE EMISSIONS OF CO2, NOx, HC, AND CO VERSUS
VEHICLE SPECIFIC POWER (VSP) BASED UPON THE MODELING DATABASE 16
FIGURE 3 -5. EXAMPLE OF UNSUPERVISED HTBR TREE RESULTS FOR THE MODELING DATA SET FOR
NOx EMISSIONS (G/SEC) 19
FIGURE 3-6. AVERAGE MODAL EMISSION RATES (G/SEC) FOR VSP BINS FOR CO, HC, CO2, AND NOx
BASED UPON THE MODELING DATASET 20
FIGURE 3-7. PERCENT OF TIME SPENT IN VSP MODES AND PERCENTAGE OF TOTAL CO, NOx, CO2, AND
HC EMISSIONS ATTRIBUTABLE TO EACH VSP MODE, BASED UPON THE MODELING DATA
SET 22
FIGURE 3-8. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOx EMISSIONS RATES FOR 14 VSP
BINS FOR VEHICLES WITH NET WEIGHT < 4,000 LB TO VEHICLES WITH NET WEIGHT > 4,000
LB 26
FIGURE 3-9. COMAPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOx EMISSIONS RATES FOR 14
VSP BINS FOR VEHICLES WITH ENGINE DISPLACEMENT < 3.5 LITERS TO VEHICLES WITH
ENGINE DISPLACEMENT > 3.5 LITERS 27
FIGURE 3-10. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOx EMISSIONS RATES FOR 14 VSP
BINS STRATIFIED BY ENGINE DISPLACEMENT AND ODOMETER READING 28
FIGURE 3-11. SAMPLE SIZES FOR EACH VSP MODE FOR EACH ODOMETER READING AND ENGINE
DISPLACEMENT STRATA 29
FIGURE 3-12. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOx EMISSIONS RATES BASED
UPON THE MODELING DATA VERSUS IM240 DATA FOR 14 VSP BINS FOR NET VEHICLE
WEIGHT < 4,000 LB 31
FIGURE 3-13. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOx EMISSIONS RATES BASED
UPON THE MODELING DATA VERSUS IM240 DATA FOR 14 VSP BINS FOR NET VEHICLE
WEIGHT > 4,000 LB 33
FIGURE 3-14. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOx EMISSIONS RATES FOR ENGINE
DISPLACEMENT < 3.5 LITERS AND ODOMETER READING < 50,000 MILES FOR EPA
DYNAMOMETER, EPA ON-BOARD, NCHRP, AND IM240 DATABASES 34
FIGURE 3-15. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOx EMISSIONS RATES FOR ENGINE
DISPLACEMENT > 3.5 LITERS AND ODOMETER READING < 50,000 MILES FOR EPA
DYNAMOMETER, EPA ON-BOARD, NCHRP, ANDIM240 DATABASES 35
FIGURE 3-16. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOx EMISSIONS RATES FOR ENGINE
DISPLACEMENT < 3.5 LITERS AND ODOMETER READING > 50,000 MILES FOR EPA
DYNAMOMETER AND NCHRP DATABASES 36
FIGURE 3-17. COMPARISON OF AVERAGE MODAL CO, HC, CO2, AND NOx EMISSIONS RATES FOR ENGINE
DISPLACEMENT > 3.5 LITERS AND ODOMETER READING > 50,000 MILES FOR IM240 AND
NCHRP DATABASES 37
in

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FIGURE 3-18. UNSUPERVISED HBTR RESULTS FOR NCSU ACCELERATION MODE FOR NOx EMISSIONS
(G/SEC) 39
FiGURES-19. UNSUPERVISED HBTR RESULTS FOR NCSU CRUISE MODE FOR NOx EMISSIONS (G/SEC) 39
FIGURE 3-20. PERCENT OF TIME SPENT IN NCSU MODES AND PERCENTAGE OF TOTAL CO, NOx, CO2,
AND HC EMISSIONS ATTRIBUTABLE TO EACH NCSU MODE, BASED UPON THE MODELING
DATA SET 42
FIGURE 3-21. AVERAGE MODAL EMISSION RATES (G/SEC) FOR NCSU MODES FOR CO, HC, CO2, AND
NOx BASED UPON THE MODELING DATASET 43
FIGURE 3-22. SAMPLE SIZES FOR EACH NCSU MODE FOR EACH ODOMETER READING AND ENGINE
DISPLACEMENT STRATA 44
FIGURE 3 -23. AVERAGE CO EMISSIONS (G/SEC) FOR THE NCSU IDLE, DECELERATION, ACCELERATION,
AND CRUISE MODES BY VEHICLE WEIGHT AND ODOMETER READING BASED UPON THE
MODELING DAT ABASE 49
FIGURE 3-24. AVERAGE HC EMISSIONS (G/SEC) FOR THE NCSU IDLE, DECELERATION, ACCELERATION,
AND CRUISE MODES BY VEHICLE WEIGHT AND ODOMETER READING BASED UPON THE
MODELING DAT ABASE 50
FIGURE 3 -25. AVERAGE NOx EMISSIONS (G/SEC) FOR THE NCSU IDLE, DECELERATION, ACCELERATION,
AND CRUISE MODES BY VEHICLE WEIGHT AND ODOMETER READING BASED UPON THE
MODELING DAT ABASE 51
FIGURE 3-26. AVERAGE CO2 EMISSIONS (G/SEC) FOR THE NCSU IDLE, DECELERATION, ACCELERATION,
AND CRUISE MODES BY VEHICLE WEIGHT AND ODOMETER READING BASED UPON THE
MODELING DAT ABASE 52
FIGURE 3-27. COMPARISON OF VSP AND NCSU APPROACH-BASED PREDICTIONS OF AVERAGE EMISSIONS
OF CO2, CO, HC, AND NOX FOR SELECTED DRIVING CYCLES FOR VEHICLES IN THE
MODELING DAT ABASE 54
FIGURE 4-1. PERCENT OF TIME SPENT IN FIVE SECOND AVERAGING TIME MAXIMUM VSP-BASED MODES
AND PERCENTAGE OF TOTAL CO, NOx, CO2, AND HC EMISSIONS ATTRIBUTABLE TO EACH
MODE, BASED UPON THE MODELING DATA SET 58
FIGURE 4-2. FIVE SECOND AVERAGING TIME MODAL EMISSION RATES (G/SEC) FOR MAXIMUM VSP BINS
FOR CO, HC, CO2, AND NOx BASED UPON THE MODELING DATASET 59
FIGURE 4-3. PERCENT OF TIME SPENT IN TEN SECOND AVERAGING TIME MAXIMUM VSP-BASED MODES
AND PERCENTAGE OF TOTAL CO, NOx, CO2, AND HC EMISSIONS ATTRIBUTABLE TO EACH
MODE, BASED UPON THE MODELING DATA SET 60
FIGURE 4-4. TEN SECOND AVERAGING TIME MODAL EMISSION RATES (G/SEC) FOR MAXIMUM VSP BINS
FOR CO, HC, CO2, AND NOx BASED UPON THE MODELING DATASET 61
FIGURE 4-5. COMPARISON OF SAMPLE SIZES FOR 1 SECOND, 5 SECOND, AND 10 SECOND AVERAGING
TIME-BASED MODES ESTIMATED FROM THE MODELING DATA SET 62
FIGURE 4-6. COMPARISON OF PREDICTED AVERAGE EMISSIONS OF CO2, CO, HC, AND NOx FOR
SELECTED DRIVING CYCLES BASED UPON 1 SECOND, 5 SECOND, AND 10 SECOND
AVERAGING TIME VSP BINNING APPROACHES FOR THE MODELING DATABASE 64
FIGURE 5-1. AVERAGE MODAL RATES FOR ABSOLUTE AND NORMALIZED NO EMISSIONS FOR A 1999
FORD TAURUS DRIVEN ON CHAPEL HILL ROAD IN CARY, NC (SOURCE: NCSU) 66
FIGURE 5-2. AVERAGE MODAL RATES FOR ABSOLUTE FUEL CONSUMPTION FOR 1999 FORD TAURUS
DRIVEN ON CHAPEL HILL ROAD (SOURCE: NCSU) 68
IV

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FIGURE 5-3.    AVERAGE MODAL EMISSION RATIOS FOR CO/CO2, HC/CO2, AND NOx/CO2 BASED UPON
            NCSU MODES FOR THE MODELING DATA AND REMOTE SENSING DATA	69
FIGURE 5-4.    AVERAGE MODAL EMISSION RATIOS FOR CO/CO2, HC/CO2, AND NOx/CO2 BASED UPON
            VSP MODES FOR THE MODELING DATA AND REMOTE SENSING DATA FOR VEHICLES WITH
            ENGINE DISPLACEMENT OF LESS THAN 3.5 LITERS	72
FIGURE 5-5.    AVERAGE MODAL EMISSION RATIOS FOR CO/CO2, HC/CO2, AND NOx/CO2 BASED UPON
            VSP BINS FOR THE MODELING DATA AND REMOTE SENSING DATA FOR VEHICLES WITH
            ENGINE DISPLACEMENT OF GREATER THAN 3.5 LITERS	73
FIGURE 5-6.    COMPARISON OF VARIABILITY FOR CO/CO2, HC/CO2, AND NOx/CO2 RATIOS FOR
            MODELING DATA AND REMOTE SENSING DATA FOR VSP MODE 1 WITH ENGINE SIZE LESS
            THAN 3.5 LITERS	75
FIGURE 5-7.    COMPARISON OF VARIABILITY FOR CO/CO2, HC/CO2, AND NOx/CO2 RATIOS FOR
            MODELING DATA AND REMOTE SENSING DATA FOR VSP MODE 7 WITH ENGINE SIZE LESS
            THAN 3.5 LITERS	76
FIGURE 5-8.    COMPARISON OF VARIABILITY FOR CO/CO2, HC/CO2, AND NOx/CO2 RATIOS FOR
            MODELING DATA AND REMOTE SENSING DATA FOR VSP MODE 12 WITH ENGINE SIZE LESS
            THAN 3.5 LITERS	77
FIGURE 5-9.    COMPARISON OF VEHICLE ACTIVITY, IN TERMS OF SPEED AND ACCELERATION, FOR THE
            REMOTE SENSING AND MODELING DATA SETS, FOR VSP MODE 1 FOR VEHICLES WITH
            ENGINE DISPLACEMENT LESS THAN 3.5 LITERS	79
FIGURE 5-10.  COMPARISON OF VEHICLE ACTIVITY, IN TERMS OF SPEED AND ACCELERATION, FOR THE
            REMOTE SENSING AND MODELING DATA SETS, FOR VSP MODE 7 FOR VEHICLES WITH
            ENGINE DISPLACEMENT LESS THAN 3.5 LITERS	80
FIGURE 5-11.  COMPARISON OF VEHICLE ACTIVITY, IN TERMS OF SPEED AND ACCELERATION, FOR THE
            REMOTE SENSING AND MODELING DATA SETS, FOR VSP MODE 12 FOR VEHICLES WITH
            ENGINE DISPLACEMENT LESS THAN 3.5 LITERS	81
FIGURE 5-12.  AVERAGE MODAL CO/CO2, HC/CO2, AND NOx/CO2 EMISSION RATIOS BASED UPON VSP
            BINS FOR THE MODELING DATA AND IM240 DRIVING CYCLE DATA FOR VEHICLES WITH
            ENGINE DISPLACEMENT OF LESS THAN 3.5 LITERS	83
FIGURE 5-13.  AVERAGE MODAL CO/CO2, HC/CO2, ANDNOx/CO2 EMISSION RATIOS BASED UPON VSP
            BINS FOR THE MODELING DATA AND IM240 DRIVING CYCLE DATA FOR VEHICLES WITH
            ENGINE DISPLACEMENT OF GREATER THAN 3.5 LITERS	84
FIGURE 5-14.  COMPARISON OF VEHICLE ACTIVITY, IN TERMS OF SPEED AND ACCELERATION, FOR THE
            REMOTE SENSING AND IM240 DRIVING CYCLE DATA SETS, FOR VSP MODE 1 FOR
            VEHICLES WITH ENGINE DISPLACEMENT LESS THAN 3.5 LITERS	85
FIGURE 5-15.  COMPARISON OF VEHICLE ACTIVITY, IN TERMS OF SPEED AND ACCELERATION, FOR THE
            REMOTE SENSING AND IM240 DRIVING CYCLE DATA SETS, FOR VSP MODE 7 FOR
            VEHICLES WITH ENGINE DISPLACEMENT LESS THAN 3.5 LITERS	86
FIGURE 5-16.  COMPARISON OF VEHICLE ACTIVITY, IN TERMS OF SPEED AND ACCELERATION, FOR THE
            REMOTE SENSING AND IM240 DRIVING CYCLE DATA SETS, FOR VSP MODE 12 FOR
            VEHICLES WITH ENGINE DISPLACEMENT LESS THAN 3.5 LITERS	87
FIGURE 6-1.    VARIABILITY IN NOx, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #1
            CHARACTERIZED BY EMPIRICAL AND FITTED PARAMETRIC PROBABILITY DISTRIBUTION
            MODELS FOR SECOND-BY-SECOND DATA	94

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FIGURE 6-2.   VARIABILITY IN NOx, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #7
            CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC
            PROBABILITY DISTRIBUTION FOR SECOND-BY-SECOND DATA	
	95
FIGURE 6-3.   VARIABILITY IN NOx, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #14
            CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC
            PROBABILITY DISTRIBUTION FOR SECOND-BY-SECOND DAT A	96
FIGURE 6-4.   VARIABILITY IN NOx, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #1
            CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC
            PROBABILITY DISTRIBUTION FOR TRIP AVERAGE MEANS	97
FIGURE 6-5.   VARIABILITY IN NOx, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #7
            CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC
            PROBABILITY DISTRIBUTION FOR TRIP AVERAGE MEANS	98
FIGURE 6-6.   VARIABILITY IN NOx, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #14
            CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC
            PROBABILITY DISTRIBUTION FOR TRIP AVERAGE MEANS	99
FIGURE 6-7.   VARIABILITY IN NOx, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #1
            CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC
            PROBABILITY DISTRIBUTION FOR VEHICLE AVERAGE MEANS	100
FIGURE 6-8.   VARIABILITY IN NOx, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #7
            CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC
            PROBABILITY DISTRIBUTION FOR VEHICLE AVERAGE MEANS	101
FIGURE 6-9.   VARIABILITY IN NOx, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODE #14
            CHARACTERIZED BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC
            PROBABILITY DISTRIBUTION FOR VEHICLE AVERAGE MEANS	102
FIGURE 6-10.  COMPARISON OF VARIABILITY IN NOx EMISSIONS FOR TIME-AVERAGE, TRIP-AVERAGE,
            AND VEHICLE-AVERAGE APPROACHES, CHARACTERIZED BY PARAMETRIC PROBABILITY
            DISTRIBUTIONS, FOR VSP MODES #1, #7 AND #14	105
FIGURE 6-11.  COMPARISON OF VARIABILITY IN HC EMISSIONS FOR TIME-AVERAGE, TRIP-AVERAGE, AND
            VEHICLE-AVERAGE APPROACHES, CHARACTERIZED BY PARAMETRIC PROBABILITY
            DISTRIBUTIONS, FOR VSP MODES #1, #7 AND #14	106
FIGURE 6-12.  COMPARISON OF QUANTIFIED UNCERTAINTY IN THE MEAN EMISSIONS OF NOx, HC, CO2,
            AND CO FOR VSP BINS: TIME-AVERAGE, TRIP-AVERAGE, AND VEHICLE-AVERAGE
            APPROACHES	113

FIGURE 7-1.   EXAMPLE OF A STEPWISE EMPIRICAL CUMULATIVE DISTRIBUTION FUNCTION	116
FIGURE 7-1.   VARIABILITY IN NOx, HC, CO2, AND CO EMISSIONS FOR VSP MODE #1 CHARACTERIZED
            BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC PROBABILITY
            DISTRIBUTION, TIME AVERAGE, ODOMETER READING < 50,000 MILES, ENGINE
            DISPLACEMENT< 3.5 LITERS	123
FIGURE 7-2.   VARIABILITY IN NOx, HC, CO2, AND CO EMISSIONS FOR VSP MODE #4 CHARACTERIZED
            BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC PROBABILITY
            DISTRIBUTION, TIME AVERAGE, ODOMETER READING < 50,000 MILES, ENGINE
            DISPLACEMENT> 3.5 LITERS	124
FIGURE 7-3.   VARIABILITY IN NOx, HC, CO2, AND CO EMISSIONS FOR VSP MODE #8 CHARACTERIZED
            BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC PROBABILITY
            DISTRIBUTION, TIME AVERAGE, ODOMETER READING > 50,000 MILES, ENGINE
            DISPLACEMENT< 3.5 LITERS	125
                                            VI

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FIGURE 7-4.   VARIABILITY IN NOx, HC, CO2, AND CO EMISSIONS FOR VSP MODE #12 CHARACTERIZED
            BY EMPIRICAL PROBABILITY DISTRIBUTION AND FITTED PARAMETRIC PROBABILITY
            DISTRIBUTION, TIME AVERAGE, ODOMETER READING > 50,000 MILES, ENGINE
            DISPLACEMENT> 3.5 LITERS	126
FIGURE 7-5.   COMPARISON OF FITTED PARAMETRIC DISTRIBUTION BASED UPON METHOD OF MATCHING
            MOMENT AND MAXIMUM LIKELIHOOD ESTIMATION, MODE 14 CO EMISSIONS, ODOMETER
            READING < 50,000 MILES, ENGINE DISPLACEMENT < 3.5 LITERS	138
FIGURE 7-6.   COMPARISON OF FITTED PARAMETRIC DISTRIBUTION BASED UPON METHOD OF MATCHING
            MOMENT AND MAXIMUM LIKELIHOOD ESTIMATION, MODE 13 CO EMISSIONS, ODOMETER
            READING < 50,000 MILES, ENGINE DISPLACEMENT < 3.5 LITERS	138
FIGURE 7-7.   MIXTURE DISTRIBUTION COMPRISED OF Two LOGNORMAL COMPONENTS FITTED TO DATA
            FOR MODE 14 CO EMISSIONS FOR ODOMETER READING < 50,000 MILES AND ENGINE
            DISPLACEMENT < 3.5 LITERS	139
FIGURE 7-8.   MIXTURE DISTRIBUTION COMPRISED OF Two LOGNORMAL COMPONENTS FITTED TO DATA
            FOR MODE 13 CO EMISSIONS FOR ODOMETER READING < 50,000 MILES AND ENGINE
            DISPLACEMENT < 3.5 LITERS	139

FIGURE 7-9.   QUANTIFIED UNCERTAINTY IN THE NOx AND HC MEAN EMISSIONS (G/SEC) OF VSP MODES	147

FIGURE 7-10.  QUANTIFIED UNCERTAINTY IN THE CO2 AND CO MEAN EMISSIONS (G/SEC) OF VSP MODES	148
FIGURE 7-11.  EMPIRICAL DISTRIBUTION OF BOOTSTRAP REPLICATIONS OF MEAN VALUES AND FITTED
            BETA DISTRIBUTION FOR UNCERTAINTY IN THE MEAN FOR NOx EMISSIONS (G/SEC) OF
            MODE 12, ODOMETER READING < 50,000 MILES, ENGINE DISPLACEMENT > 3.5 LITERS	155
FIGURE 7-12.  ESTIMATION OF CORRECTION FACTORS FOR THE RELATIVE STANDARD ERROR OF THE MEAN
            (SEM/MEAN) VERSUS AVERAGING TIMES OF 1, 5, AND 10  SECONDS FOR NOx, HC, CO2,
            AND CO EMISSIONS (G/SEC) FOR ODOMETER READING < 50,000 MILES AND ENGINE
            DISPLACEMENT < 3.5 LITERS	157
FIGURE 7-13.  ESTIMATION OF CORRECTION FACTORS FOR THE RELATIVE STANDARD ERROR OF THE MEAN
            (SEM/MEAN) VERSUS AVERAGING TIMES OF 1, 5, AND 10  SECONDS FOR NOx, HC, CO2,
            AND CO EMISSIONS (G/SEC) FOR ODOMETER READING < 50,000 MILES AND ENGINE
            DISPLACEMENT > 3.5 LITERS	158
FIGURE 7-14.  ESTIMATION OF CORRECTION FACTORS FOR THE RELATIVE STANDARD ERROR OF THE MEAN
            (SEM/MEAN) VERSUS AVERAGING TIMES OF 1, 5, AND 10  SECONDS FOR NOx, HC, CO2,
            AND CO EMISSIONS (G/SEC) FOR ODOMETER READING > 50,000 MILES AND ENGINE
            DISPLACEMENT < 3.5 LITERS	159
FIGURE 7-15.  ESTIMATION OF CORRECTION FACTORS FOR THE RELATIVE STANDARD ERROR OF THE MEAN
            (SEM/MEAN) VERSUS AVERAGING TIMES OF 1, 5, AND 10  SECONDS FOR NOx, HC, CO2,
            AND CO EMISSIONS (G/SEC) FOR ODOMETER READING > 50,000 MILES AND ENGINE
            DISPLACEMENT > 3.5 LITERS	160
FIGURE 7-16.  BIN ADJUSTMENT FACTORS FOR THE UNCERTAINTY CORRECTION FACTOR AT "> 10
            SECONDS" OF NOX, HC, CO2, AND CO FOR ODOMETER READING < 50,000 MILES AND
            ENGINE DISPLACEMENT < 3.5 LITERS	163
FIGURE 7-17.  BIN ADJUSTMENT FACTORS FOR THE UNCERTAINTY CORRECTION FACTOR AT "> 10
            SECONDS" OF NOX, HC, CO2, AND CO FOR ODOMETER READING < 50,000 MILES AND
            ENGINE DISPLACEMENT > 3.5 LITERS	164
FIGURE 7-18.  BIN ADJUSTMENT FACTORS FOR THE UNCERTAINTY CORRECTION FACTOR AT "> 10
            SECONDS" OF NOX, HC, CO2, AND CO FOR ODOMETER READING > 50,000 MILES AND
            ENGINE DISPLACEMENT < 3.5 LITERS	
...165
                                           vn

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FIGURE 7-19.  BIN ADJUSTMENT FACTORS FOR THE UNCERTAINTY CORRECTION FACTOR AT "> 10
            SECONDS" OF NOX, HC, CO2, AND CO FOR ODOMETER READING >50,000 MILES AND
            ENGINE DISPLACEMENT > 3.5 LITERS	
	166
FIGURE 7-20.  QUANTIFIED UNCERTAINTY IN TOTAL NOx EMISSIONS FROM THE IM240 CYCLE FOR
            VEHICLES WITH ODOMETER READING < 50,000 MILES AND ENGINE DISPLACEMENT < 3.5
            LITERS BASED UPON MONTE CARLO SIMULATION	171
FIGURE 7-21.  QUANTIFICATION OF UNCERTAINTY BASED UPON MONTE CARLO SIMULATION FOR TOTAL
            NOx EMISSION FROM 13 VEHICLES TESTED ON THE ART-EF CYCLE	177
FIGURE 8-1.    PREDICTED VERSUS OBSERVED NOx NCSU MODAL EMISSION RATES ESTIMATED FROM
            NCHRP DATA USING THE STRICT CONSTRAINTS APPROACH	188
FIGURE 8-2.    PREDICTED VERSUS OBSERVED HC NCSU MODAL EMISSION RATES ESTIMATED FROM
            NCHRP DATA USING THE STRICT CONSTRAINTS APPROACH	188
FIGURE 8-3.    PREDICTED VERSUS OBSERVED CO NCSU MODAL EMISSION RATES ESTIMATED FROM
            NCHRP DATA USING THE STRICT CONSTRAINTS APPROACH	189
FIGURE 8-4.    PREDICTED VERSUS OBSERVED CO2 NCSU MODAL EMISSION RATES ESTIMATED FROM
            NCHRP DATA USING THE STRICT CONSTRAINTS APPROACH	189
FIGURE 8-5.    PREDICTED VERSUS OBSERVED NOx MODAL EMISSION RATES BASED UPON THE 14 MODE
            VSP APPROACH ESTIMATED FROM NCHRP DATA USING THE STRICT CONSTRAINTS
            APPROACH	193
FIGURE 8-6.    PREDICTED VERSUS OBSERVED HC MODAL EMISSION RATES BASED UPON THE 14 MODE
            VSP APPROACH ESTIMATED FROM NCHRP DATA USING THE STRICT CONSTRAINTS
            APPROACH	193
FIGURE 8-7.    PREDICTED VERSUS OBSERVED CO MODAL EMISSION RATES BASED UPON THE 14 MODE
            VSP APPROACH ESTIMATED FROM NCHRP DATA USING THE STRICT CONSTRAINTS
            APPROACH	194
FIGURE 8-8.    PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES BASED UPON THE 14 MODE
            VSP APPROACH ESTIMATED FROM NCHRP DATA USING THE STRICT CONSTRAINTS
            APPROACH	194
FIGURE 8-9.    PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES
            ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE
            MODELING DATABASE: ENGINE DISPLACEMENT < 3.5 LITER AND ODOMETER READING <
            50,000 MILES	204
FIGURE 8-10.  PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES
            ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE
            NCHRP DATABASE: ENGINE DISPLACEMENT < 3.5 LITER AND ODOMETER READING <
            50,000 MILES	204
FIGURE 8-11.  PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES
            ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE
            MODELING DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING <
            50,000 MILES	205
FIGURE 8-12.  PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES
            ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE
            NCHRP DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING <
            50,000 MILES	205
FIGURE 8-13.  PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES
            ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE
                                          Vlll

-------
            MODELING DATABASE: ENGINE DISPLACEMENT < 3.5 LITER AND ODOMETER READING >
            50,000 MILES	206
FIGURE 8-14.  PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES
            ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE
            NCHRP DATABASE: ENGINE DISPLACEMENT < 3.5 LITER AND ODOMETER READING >
            50,000 MILES	206



FIGURE 8-15.  PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES
            ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE
            MODELING DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING >
            50,000 MILES	207
FIGURE 8-16.  PREDICTED VERSUS OBSERVED CO2 MODAL EMISSION RATES FOR 14 VSP MODES
            ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE
            NCHRP DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING >
            50,000 MILES	207
FIGURE 8-17.  PREDICTED VERSUS OBSERVED HC MODAL EMISSION RATES FOR 14 VSP MODES
            ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE
            NCHRP DATABASE: ENGINE DISPLACEMENT < 3.5 LITER AND ODOMETER READING <
            50,000 MILES	208
FIGURE 8-18.  PREDICTED VERSUS OBSERVED HC MODAL EMISSION RATES FOR 14 VSP MODES
            ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE
            MODELING DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING <
            50,000 MILES	208
FIGURE 8-19.  PREDICTED VERSUS OBSERVED HC MODAL EMISSION RATES FOR 14 VSP MODES
            ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE
            NCHRP DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING <
            50,000 MILES	209
FIGURE 8-20.  PREDICTED VERSUS OBSERVED HC MODAL EMISSION RATES FOR 14 VSP MODES
            ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE
            NCHRP DATABASE: ENGINE DISPLACEMENT < 3.5 LITER AND ODOMETER READING >
            50,000 MILES	209
FIGURE 8-21.  PREDICTED VERSUS OBSERVED HC MODAL EMISSION RATES FOR 14 VSP MODES
            ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE
            MODELING DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING >
            50,000 MILES	210
FIGURE 8-22.  PREDICTED VERSUS OBSERVED HC MODAL EMISSION RATES FOR 14 VSP MODES
            ESTIMATED FROM NCHRP DATA USING STRICT CONSTRAINTS ESTIMATED FROM THE
            NCHRP DATABASE: ENGINE DISPLACEMENT > 3.5 LITER AND ODOMETER READING >
            50,000 MILES	210
FIGURE 9-1.    COMPARISON OF OBSERVED AND PREDICTED AVERAGE TOTAL EMISSIONS OF CO2, CO, HC,
            AND NOx FOR THREE DRIVING CYCLES AND FOR ON-BOARD DATA FOR VALIDATION
            DATASET!	219
FIGURE 9-2.    COMPARISON OF OBSERVED AND PREDICTED AVERAGE TOTAL EMISSIONS OF CO2, CO, HC,
            AND NOX FOR THE FTP75 AND US06 DRIVING CYCLES AND FOR ON-BOARD
            MEASUREMENTS FOR VALIDATION DATASET II	224
FIGURE 9-3.    COMPARISON OF OBSERVED AND PREDICTED AVERAGE TOTAL EMISSIONS OF CO2, CO, HC,
            AND NOx FOR EIGHT UCC DRIVING CYCLES FOR VALIDATION DATASET III	229
                                           IX

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FIGURE A-l. RELATIONSHIP BETWEEN AIR CONDITION USE AND EMISSIONS 244
FIGURE A-2. RELATIONSHIP BETWEEN RELATIVE HUMIDITY AND EMISSIONS 245
FIGURE A-3. RELATIONSHIP BETWEEN AMBIENT TEMPERATURE AND EMISSIONS 246
FIGURE A-4. COMPARISON OF VARIABILITY FOR MODELING DATA AND REMOTE SENSING DATA FOR VSP
MODE? WITH ENGINE SIZE LESS THAN 3.5 LITERS AND MODEL YEAR AT 1996 247
FIGURE A-5. AVERAGE MODAL EMISSION RATES FOR VEHICLES WITH ODOMETER READINGS LESS THAN
50,000 MILES BASED UPON VSP BINS 248
FIGURE A-6. AVERAGE MODAL EMISSION RATES FOR VEHICLES WITH ODOMETER READINGS GREATER
THAN 50,000 MILES BASED UPON VSP BINS 249
FIGURE A-7. EVALUATION OF AVERAGE CO EMISSION RATES FOR 14 VSP BINS WITH RESPECT TO
ACCELERATION (LEFT PANEL) AND SPEED (RIGHT PANEL) 250
FIGURE A-8. AVERAGE MODAL EMISSION RATES FOR VSP BINS FOR ENGINE DISPLACEMENT < 3.5 LITER
AND ODOMETER READING < 50K MILES FOR Two DIFFERENT SPEED STRATA 251
FIGURE A-9. AVERAGE MODAL EMISSION RATES FOR VSP BINS FOR ENGINE DISPLACEMENT > 3.5 LITER
AND ODOMETER READING < 50K MILES FOR Two DIFFERENT SPEED STRATA 252
FIGURE A-10. AVERAGE MODAL EMISSION RATES FOR VSP BINS FOR ENGINE DISPLACEMENT < 3.5 LITER
AND ODOMETER READING > 50K MILES FOR Two DIFFERENT SPEED STRATA 253
FIGURE A-l 1. AVERAGE MODAL EMISSION RATES FOR VSP BINS FOR ENGINE DISPLACEMENT > 3.5 LITER
AND ODOMETER READING > 50K MILES FOR Two DIFFERENT SPEED STRATA 254

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LIST OF TABLES
Table 3-1. Definitions for VSP Modes 18
TABLE 3-2. UNSUPERVISED HBTR REGRESSION TREE RESULTS FOR CO FOR EACH OF 14 VSP MODES 23
TABLE 3 -3. UNSUPERVISED HBTR REGRESSION TREE RESULTS FOR CO2 FOR EACH OF 14 VSP MODES 23
TABLE 3-4. UNSUPERVISED HBTR REGRESSION TREE RESULTS FOR HC FOR EACH OF 14 VSP MODES 24
TABLE 3-5. UNSUPERVISED HBTR REGRESSION TREE RESULTS FOR NOx FOR EACH OF 14 VSP MODES 24
TABLE 3-6. DEFINITION OF NCSU DRIVING MODES 40
TABLE 3-7. UNSUPERVISED HTBR REGRESSION TREE RESULTS FOR CO EMISSIONS BASED UPON THE
NCSU MODAL APPROACH 46
TABLE 3-8. UNSUPERVISED HTBR REGRESSION TREE RESULTS FOR NOx EMISSIONS BASED UPON THE
NCSU MODAL APPROACH 46
TABLE 3-9. UNSUPERVISED HTBR REGRESSION TREE RESULTS FOR HC EMISSIONS BASED UPON THE
NCSU MODAL APPROACH 47
TABLE 3-10. UNSUPERVISED HTBR REGRESSION TREE RESULTS FOR CO2 EMISSIONS BASED UPON THE
NCSU MODAL APPROACH 47
TABLE 4-1. KEY EXPLANATORY VARIABLES FOR CO, NOx, HC, AND CO2 EMISSIONS (G/SEC)
IDENTIFIED USING UNSUPERVISED HBTR FOR FIVE AND TEN SECOND-AVERAGED DATA 56
TABLE 4-2. MAXIMUM VSP-BASED MODE DEFINITIONS FOR FIVE SECOND-AVERAGED DATA 57
TABLE 4-3. MAXIMUM VSP-BASED MODE DEFINITIONS FOR TEN SECOND-AVERAGED DATA 57
TABLE 6-1. SUMMARY OF FITTED PARAMETRIC PROBABILITY DISTRIBUTIONS FOR VARIABILITY IN NOx,
HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP BINS FOR TRIP AVERAGE MEANS 103
TABLE 6-2. SUMMARY OF FITTED PARAMETRIC PROBABILITY DISTRIBUTIONS FOR VARIABILITY IN NOx,
HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP BINS FOR VEHICLE AVERAGE MEANS 104
TABLE 6-3. COMPARISON OF MEAN EMISSIONS OF NOx, HC, CO2, AND CO EMISSIONS (G/SEC) FOR
VSP BINS: TIME-AVERAGE, TRIP-AVERAGE, AND VEHICLE-AVERAGE APPROACHES 108
TABLE 6-4. COMPARISON OF STANDARD DEVIATIONS OF VARIABILITY IN NOx, HC, CO2, AND CO
EMISSIONS (G/SEC) FOR VSP BINS: TIME-AVERAGE, TRIP-AVERAGE, AND VEHICLE-
AVERAGE APPROACHES 109
TABLE 6-5. SUMMARY OF RELATIVE 95% CONFIDENCE INTERVALS FOR NOx, HC, CO2, AND CO MEAN
EMISSIONS FOR VSP BINS FOR THE TIME-AVERAGE APPROACH 110
TABLE 6-6. SUMMARY OF RELATIVE 95% CONFIDENCE INTERVALS FOR NOx, HC, CO2, AND CO MEAN
EMISSIONS FOR VSP BINS FOR THE TRIP-AVERAGE APPROACH Ill
TABLE 6-7. SUMMARY OF RELATIVE 95% CONFIDENCE INTERVALS FOR NOx, HC, CO2, AND CO MEAN
EMISSIONS FOR VSP BINS FOR THE VEHICLE-AVERAGE APPROACH 112
TABLE 7-1. COMPARISON OF MEAN BETWEEN EMPIRICAL DATA SET AND FITTED PARAMETRIC
DISTRIBUTIONS, ABSOLUTE BASIS 128
TABLE 7-2. COMPARISON OF STANDARD DEVIATION BETWEEN EMPIRICAL DATA SET AND FITTED
PARAMETRIC DISTRIBUTIONS, ABSOLUTE BASIS 132
XI

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TABLE 7-3.    COMPARISONS OF EMPIRICAL DATA SET AND FITTED PARAMETRIC DISTRIBUTIONS,
            AVERAGE DIFFERENCE FOR GOOD FITS, FITTING BASED UPON MLE	136
TABLE 7-4.    COMPARISONS OF EMPIRICAL DATA SET, FITTED LOGNORMAL DISTRIBUTIONS BASED UPON
            MLE, AND FITTED LOGNORMAL DISTRIBUTIONS BASED UPON MoMM, FOR THE Two
            WORST MLE FITS FOR CO	136
TABLE 7-5.    RECOMMENDATION OF MIXTURE DISTRIBUTIONS FOR Two WORST FITS	137
TABLE 7-6.    SUMMARY OF SINGLE COMPONENT PARAMETRIC PROBABILITY DISTRIBUTIONS FITTED
            USING MLE FOR VARIABILITY IN VSP MODES FOR NOx, HC, CO2, AND CO FOR VEHICLES
            OF DIFFERENT ENGINE DISPLACEMENT AND ODOMETER READING	140
TABLE 7-7.    VSP MODES FOR WHICH UNCERTAINTY IN THE MEAN WAS QUANTIFIED BY BOOTSTRAP
            SIMULATION	145
TABLE 7-8.    SUMMARY OF MEAN VALUES AND RELATIVE 95% CONFIDENCE INTERVALS IN THE MEAN
            FOR NOx, HC, CO2, AND CO EMISSIONS (G/SEC) FOR VSP MODES FOR VEHICLES OF
            DIFFERENT ODOMETER READING AND ENGINE DISPLACEMENT	149
TABLE 7-9.    PARAMETERS OF PARAMETRIC PROBABILITY DISTRIBUTION FIT TO THE BOOTSTRAP
            REPLICATIONS OF THE MEANS FOR SELECTED MODES, STRATA, AND POLLUTANTS, BASED
            UPON EMPIRICAL BOOTSTRAP SIMULATION	155
TABLE 7-10.   AVERAGING TIME CORRECTION FACTORS FOR UNCERTAINTY IN VSP BINS FOR NOx, HC,
            CO2, AND CO EMISSIONS (G/SEC) FOR FOUR STRATA WITH RESPECT TO ODOMETER
            READING AND ENGINE DISPLACEMENT	162
TABLE 7-11.   BIN ADJUSTMENT FACTORS FOR CORRECTION FACTOR OF TIME ADJUSTMENT AT "> 10
            SECONDS" FOR NOX, HC, CO2, AND CO AND FOR FOUR ODOMETER READING AND ENGINE
            DISPLACEMENT STRATA	168
TABLE 7-12.   ALLOCATION OF THE STANDARD IM240 DRIVING CYCLE INTO VSP MODES WITH RESPECT
            TO TIME SPENT IN EACH MODE	168
TABLE 7-13.   INPUT ASSUMPTIONS FOR PREDICTION OF UNCERTAINTY IN TOTAL NOx EMISSIONS FOR A
            CAST STUDY OF THE IM240 CYCLE, FOR VEHICLES WITH ODOMETER READING < 50,000
            MILES AND ENGINE DISPLACEMENT < 3.5 LITERS	170
TABLE 7-14.   EXAMPLE PREDICTION OF UNCERTAINTY IN TOTAL EMISSIONS FOR NOx EMISSIONS FROM
            THE IM240 CYCLE FOR VEHICLES WITH ODOMETER READING < 50,000 MILES AND ENGINE
            DISPLACEMENT < 3.5 LITERS BASED UPON MONTE CARLO SIMULATION	170
TABLE 7-15.   ALLOCATION OF THE ART-EF, IM240, FTP (BAGS 2 AND 3) AND US06 DRIVING CYCLES
            INTO VSP MODES WITH RESPECT TO TIME SPENT IN EACH MODE	172
TABLE 7-16.   ABSOLUTE AND RELATIVE UNCERTAINTY ESTIMATES FOR MEAN TOTAL EMISSIONS OF
            NOx, HC, CO2, AND CO FOR FOUR ODOMETER READING AND ENGINE DISPLACEMENT TIER
            1 VEHICLE STRATA FOR THE IM240 CYCLE	173
TABLE 7-17.   ABSOLUTE AND RELATIVE UNCERTAINTY ESTIMATES FOR MEAN TOTAL EMISSIONS OF
            NOx, HC, CO2, AND CO FOR FOUR ODOMETER READING AND ENGINE DISPLACEMENT TIER
            1 VEHICLE STRATA FOR THE ART-EF CYCLE	173
TABLE 7-18.   ABSOLUTE AND RELATIVE UNCERTAINTY ESTIMATES FOR MEAN TOTAL EMISSIONS OF
            NOx, HC, CO2, AND CO FOR FOUR ODOMETER READING AND ENGINE DISPLACEMENT TIER
            1 VEHICLE STRATA FOR THE FTP (BAGS 2 AND 3) CYCLE	174
TABLE 7-19.   ABSOLUTE AND RELATIVE UNCERTAINTY ESTIMATES FOR MEAN TOTAL EMISSIONS OF
            NOx, HC, CO2, AND CO FOR FOUR ODOMETER READING AND ENGINE DISPLACEMENT TIER
            1 VEHICLE STRATA FOR THE US06 CYCLE	174
                                          xn

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TABLE 7-20.


TABLE 8-1.



TABLE 8-2.



TABLE 8-3.
ALLOCATION OF THE ACTUAL ART-EF DRIVING CYCLE SPEED TRACES INTO VSP MODES
WITH RESPECT TO TIME SPENT IN EACH MODE FOR 13 DIFFERENT VEHICLES	
RESULTS OF ESTIMATION OF MODAL EMISSION RATES (MG/SEC) FROM AGGREGATE DATA
FOR FOUR NCSU DRIVING MODES FOR NOx: COMPARISON OF No CONSTRAINT, BASIC
CONSTRAINT, AND STRICT CONSTRAINT SOLUTIONS	
177
187
RESULTS OF ESTIMATION OF MODAL EMISSION RATES (MG/SEC) FROM AGGREGATE DATA
FOR FOUR NCSU DRIVING MODES FOR HC: COMPARISON OF No CONSTRAINT, BASIC
CONSTRAINT, AND STRICT CONSTRAINT SOLUTIONS	187
RESULTS OF ESTIMATION OF MODAL EMISSION RATES (MG/SEC) FROM AGGREGATE DATA
FOR FOUR NCSU DRIVING MODES FOR CO: COMPARISON OF No CONSTRAINT, BASIC
CONSTRAINT, AND STRICT CONSTRAINT SOLUTIONS	187
TABLE 8-4.    RESULTS OF ESTIMATION OF MODAL EMISSION RATES (G/SEC) FROM AGGREGATE DATA FOR
            FOUR NCSU DRIVING MODES FOR CO2: COMPARISON OF No CONSTRAINT, BASIC
            CONSTRAINT, AND STRICT CONSTRAINT SOLUTIONS	187
TABLE 8-5.    RESULTS OF ESTIMATION OF MODAL EMISSION RATES (MG/SEC) FROM AGGREGATE DATA
            FOR 14 VSP MODES FOR NOx: COMPARISON OF No CONSTRAINT, BASIC CONSTRAINT,
            AND STRICT CONSTRAINT SOLUTIONS	191
TABLE 8-6.    RESULTS OF ESTIMATION OF MODAL EMISSION RATES (MG/SEC) FROM AGGREGATE DATA
            FOR 14 VSP MODES FOR HC: COMPARISON OF No CONSTRAINT, BASIC CONSTRAINT, AND
            STRICT CONSTRAINT SOLUTIONS	191
TABLE 8-7.    RESULTS OF ESTIMATION OF MODAL EMISSION RATES (MG/SEC) FROM AGGREGATE DATA
            FOR 14 VSP MODES FOR CO: COMPARISON OF No CONSTRAINT, BASIC CONSTRAINT, AND
            STRICT CONSTRAINT SOLUTIONS	192
TABLE 8-8.    RESULTS OF ESTIMATION OF MODAL EMISSION RATES (G/SEC) FROM AGGREGATE DATA FOR
            14 VSP MODES FOR CO2:  COMPARISON OF No  CONSTRAINT, BASIC CONSTRAINT, AND
            STRICT CONSTRAINT SOLUTIONS	192
TABLE 8-9.    COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:
            CO2 EMISSIONS (G/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER
            READING < 50,000 MILES	196
TABLE 8-10.   COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:
            CO2 EMISSIONS (G/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER
            READING < 50,000 MILES	196
TABLE 8-11.   COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:
            CO2 EMISSIONS (G/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER
            READING > 50,000 MILES	197
TABLE 8-12.   COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:
            CO2 EMISSIONS (G/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER
            READING > 50,000 MILES	197
TABLE 8-13.   COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES: HC
            EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER READING <
            50,000 MILES	198
                                           Xlll

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TABLE 8-14.   COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES: HC
            EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER READING <
            50,000 MILES	198
TABLE 8-15.   COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES: HC
            EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER READING >
            50,000 MILES	199
TABLE 8-16.   COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES: HC
            EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER READING >
            50,000 MILES	199
TABLE 8-17.   COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES : CO
            EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER READING <
            50,000 MILES	200
TABLE 8-18.   COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES : CO
            EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER READING <
            50,000 MILES	200
TABLE 8-19.   COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES : CO
            EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER READING
            >50,000 MILES	201




TABLE 8-20.   COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES : CO
            EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER READING >
            50,000 MILES	201
TABLE 8-21.   COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:
            NOx EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER
            READING < 50,000 MILES	202
TABLE 8-22.   COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:
            NOx EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER
            READING < 50,000 MILES	202
TABLE 8-23.   COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:
            NOx EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT < 3.5 LITERS AND ODOMETER
            READING > 50,000 MILES	203
TABLE 8-24.   COMPARISON OF MODAL EMISSION RATES ESTIMATED BASED UPON THE STRICT
            CONSTRAINTS APPROACH FOR Two DIFFERENT CONSTRAINTS VERSUS ACTUAL RATES:
            NOx EMISSIONS (MG/SEC) FOR ENGINE DISPLACEMENT > 3.5 LITERS AND ODOMETER
            READING > 50,000 MILES	203
                                           xiv

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TABLE 8-25. SUMMARY OF ANALYSIS OF UNCERTAINTY IN THE PREDICTION ERROR FOR THE NOx
MODAL EMISSION RATES (MG/SEC) ESTIMATED FROM AGGREGATE DATA FOR THE 14 MODE
VSP-BASED APPROACH 212
TABLE 8-26. SUMMARY OF ANALYSIS OF UNCERTAINTY IN THE PREDICTION ERROR FOR THE HC MODAL
EMISSION RATES (MG/SEC) ESTIMATED FROM AGGREGATE DATA FOR THE 14 MODE VSP-
BASED APPROACH 212
TABLE 8-27. SUMMARY OF ANALYSIS OF UNCERTAINTY IN THE PREDICTION ERROR FOR THE CO MODAL
EMISSION RATES (MG/SEC) ESTIMATED FROM AGGREGATE DATA FOR THE 14 MODE VSP-
BASED APPROACH 213
TABLE 8-28. SUMMARY OF ANALYSIS OF UNCERTAINTY IN THE PREDICTION ERROR FOR THE CO2 MODAL
EMISSION RATES (G/SEC) ESTIMATED FROM AGGREGATE DATA FOR THE 14 MODE VSP-
BASED APPROACH 213
TABLE 9-1. SUMMARY OF VALIDATION DATASET 1 218
TABLE 9-2. KEY CHARACTERISTICS OF THE ACTIVITY PATTERN OF THE ART-EF, FTP75 AND US06
CYCLES AND OF THE ON-BOARD MEASUREMENTS USED IN VALIDATION DATASET 1 218
TABLE 9-3. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL
EMISSIONS FOR VALIDATION DATASET I FOR CO2 221
TABLE 9-4. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL
EMISSIONS FOR VALIDATION DATASET I FOR CO 221
TABLE 9-5. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL
EMISSIONS FOR VALIDATION DATASET I FOR HC 221
TABLE 9-6. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL
EMISSIONS FOR VALIDATION DATASET I FOR NOX 221
TABLE 9-7. SUMMARY OF DRIVING CYCLES, NUMBER OF VEHICLES, NUMBER OF TRIPS, AND SAMPLES
SIZE FOR VALIDATION DATASET II 223
TABLE 9-8. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL
EMISSIONS FOR VALIDATION DATASET II FOR CO2 225
TABLE 9-9. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL
EMISSIONS FOR VALIDATION DATASET II FOR CO 225
TABLE 9-10. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL
EMISSIONS FOR VALIDATION DATASET II FOR HC 225
TABLE 9-11. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL
EMISSIONS FOR VALIDATION DATASET II FOR NOX 225
TABLE 9-12. SUMMARY OF DRIVING CYCLES, NUMBER OF VEHICLES, NUMBER OF TESTS, AND SAMPLE
SIZE FOR VALIDATION DATASET III 228
TABLE 9-13. KEY CHARACTERISTICS OF THE ACTIVITY PATTERNS OF THE DRIVING CYCLES IN
VALIDATION DATASET III 228
TABLE 9-14. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL
EMISSIONS FOR VALIDATION DATASET III FOR CO2 230
TABLE 9-15. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL
EMISSIONS FOR VALIDATION DATASET III FOR CO 230
TABLE 9-16. SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL
EMISSIONS FOR VALIDATION DATASET III FOR HC 231
xv

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TABLE 9-17.   SUMMARY OF COMPARISONS OF PREDICTED VERSUS OBSERVED VEHICLE AVERAGE TOTAL
            EMISSIONS FOR VALIDATION DATASET III FOR NOX	231
TABLE A-1.   CORRELATION AMONG PARAMETERS	255
TABLE A-2.   SUMMARY OF VEHICLES IN VALIDATION DATASET!	255
TABLE A-3.   SUMMARY OF VEHICLES IN VALIDATION DAT ASET n	258
Table A-3.   Summary of Vehicles in Validation Dataset HI	259
                                          xvi

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1 INTRODUCTION

EPA is undertaking an effort to develop a new set of modeling tools for the estimation of
emissions produced by on-road and off-road mobile sources. The product of this effort will be
the Multi-scale mOtor Vehicle & equipment Emission System, referred to as MOVES. The
design of MOVES is guided by the following four considerations:

1) the model should encompass all pollutants (e.g., HC, CO, NOX, paniculate matter, air
toxics, and greenhouse gases) and all mobile sources at the levels of resolution needed for
the diverse applications of the system;
2) the model should be developed according to principles of sound science;
3) the software design of the model should be efficient and flexible; and
4) the model should be implemented in a coordinated, clear, and consistent manner.

A critical element of MOVES is the use of data gathered using on-board emissions measurement
devices. To explore this issue, in Fall 2001 EPA issued an on-board emission analysis
"shootout" contract in order to solicit several approaches for incorporating on-board emissions
into moves. Three shootout contracts were issued to three organizations that worked
independently on the same general statement of work. These organizations were NCSU,
University of California at Riverside (UCR), and Environ. Each contractor had the flexibility to
choose any approach they preferred. NCSU pursued a modal "binning" approach in which
operational bins were defined based on speed, acceleration, and power demand, and refined the
estimates within each modal bin using regression analysis. UCR pursued a database approach,
deriving separate emissions for macroscale, mesoscale and microscale based on a database
lookup of individual vehicle and trip results. Environ based their approach on a calculation of
vehicle specific power (power per unit mass, or vehicle specific power - VSP), aggregating
results over "microtrips" (20 or more seconds, defined by endpoints of stable operation). EPA
also developed a conceptual approach based upon binning of data with respect to VSP bins.

The shootout results from NCSU, UCR, Environ, and EPA, revealed several promising
approaches for using on-board data in the development of MOVES exhaust emission rates. In
particular, the development of modal emission rates using a "binning" approach was successfully
demonstrated by NCSU and EPA in the shootout analysis. NCSU directly tackled the time series
nature of the on-board data and illustrated methods for dealing with the data to reduce the
influence of the time series. The work by Environ illustrated potential benefits to averaging or
smoothing the data. As a result of this work, the proposed design of MOVES is predicated on
emission rates defined by vehicle and modal operation "bins," and the development of emission
rates for these bins in MOVES is the ultimate purpose of the methodology that will be developed
in this project.

The philosophy for MOVES is that it should be as directly data-driven as possible. The
advantages of a data driven methodology are manifold and include the following:

• Emission rates can be developed from raw data
• Emissions estimates can be developed based upon summaries of actual data within given
bins

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   •   Emissions estimates from multiple bins can be weighted to represent any combination of
       trip and vehicle characteristics.
   •   Inter-vehicle variability and fleet average uncertainty can be easily estimated based upon
       appropriate averaging times
   •   Similar conceptual approaches can be used for different types of vehicles (e.g., on-road
       gasoline and diesel, nonroad gasoline and diesel)
   •   Similar conceptual approaches can be used for different pollutants (i.e. HC, CO, NOX,
       particulate matter, air toxics, and greenhouse gases)
   •   The development of bins can be based upon empirical evidence regarding combinations
       of factors that have the most influence on aggregate emissions
   •   A modal/binning approach  can easily support meso-scale and macro-scale analysis, and
       can also support micro-scale analysis depending on how the approach is actually
       implemented.
   •   A modal/binning approach  for light duty gasoline vehicles (LDGV), heavy duty diesel
       vehicles (HDDV) and nonroad diesel vehicles has been demonstrated by NCSU and EPA
   •   The NCSU approach for on-road vehicles is an intuitive and easy to explain  one based
       upon bins that correspond to idle, acceleration, cruise, and deceleration behaviors for
       onroad vehicles. The ability to easily explain the approach to policy makers and the
       public is an important consideration in gaining acceptance for a new modeling approach.
   •   A statistical data-driven statistical approach for developing bins, using Hierarchical Tree-
       Based Regression (HTBR)  has been demonstrated and proven by NCSU and can be used
       in the identification of appropriate binning  criteria.
   •   Methods have been demonstrated by NCSU for handling cold start emissions as part of
       the modal/binning approach.
   •   Methods have been explored and recommended by NCSU regarding estimation of modal
       emission rates from aggregate data (e.g., dynamometer driving cycle data).
   •   The modal/binning approaches have been evaluated by validating the approaches in
       comparison to real-world emission measurements.
   •   Time series analysis already performed by NCSU as part of the shoot-out establish a
       credible scientific basis for determining appropriate averaging times for the
       modal/binning approach to be developed in this project.
   •   The general framework for developing databases, analyzing the data, and developing
       modal models has already been established at NCSU, both as part of the shootout project
       and in other previous work.

A key goal of the binning methodology is to develop modal emission rates  in a manner that does
not require additional modeling analysis, such as regression modeling, and  that eliminates the
need for many correction factors common to existing models such as MobileS and Mobile6.
Ideally, the emission rates estimated for a specific bin should be based directly on the sample of
raw data falling into that bin.

On-board data is a promising means for developing tailpipe emissions estimates. However, as
noted by EPA  and as explained in the NCSU final  report from the shootout (Frey, Unal,  and
Chen, 2002), in the short-term other sources of data will continue to play an important role in
populating or evaluating MOVES.  Thus, an important step in the development of MOVES is to
evaluate the feasibility of techniques for applying the modal binning approach to data from other

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sources, such as driving cycle dynamometer data and remote sensing device (RSD) data. For
example, Frey et al. (2002) demonstrated an approach for estimating modal emission rates from
aggregate data.

The key purpose of this project is to evaluate methods for developing modal emission rates from
disparate data sources (e.g., on-board data, laboratory second-by-second data, aggregate driving
cycle data, I/M data, and RSD data) for a relatively small "pilot" dataset of light duty vehicles.
In the shootout, NCSU demonstrated that similar approaches can be applied to UDDV and to
nonroad diesel vehicles; therefore, it is reasonable to focus resources on the example of LDGVs
in this project. Furthermore, in previous work, NCSU demonstrated how to develop a bin for
cold starts. Therefore, this project will focus on hot stabilized tailpipe emissions. This project
will demonstrate at the proof-of-concept level the methodology for developing modal emission
rates in MOVES using a wide variety of data sources, including an evaluation of the applicability
of aggregate (bag) data and RSD data.

An important element of MOVES is the incorporation of uncertainty analysis as part of the
emission estimation process. EPA has proposed to characterize emission rates for each
vehicle/operating bin with a mean value, a distribution form, and standard deviation, to allow for
the development of a utility in MOVES which would apply Monte Carlo analysis to generate
uncertainty estimates of model final results. Moreover, this approach enables a change in how
normal and high emitters are characterized. In previous models, EPA has stratified data into
normal and high emitter categories. In the new approach, EPA proposes to treat all vehicles
within a bin as a continuous distribution. Thus, for a given vehicle/operating bin, the distribution
of emissions will reflect the variability of emissions among all vehicles within the bin, including
what are now referred to as normal and high emitters. This approach sets the stage for estimation
of the effect of I/M programs with respect to the characteristics of the distribution of inter-
vehicle variability in emissions. For example, an I/M program would be expected to identify
some portion of the vehicles with emissions above some value and to repair/modify the vehicles
so as to reduce their emission rates. This, in turn, would change the distribution of inter-vehicle
variability in emissions.

1.1 Objectives of this Project
The objectives of this project are as follows:

• Develop, demonstrate, and report an analytical approach for producing exhaust modal
emission rates and emission rate disitributions for MOVES from a variety of data
sources, possibly including aggregate (bag) data and RSD data.
• Develop, demonstrate, and report a methodology for estimation of model uncertainty and
variability in emissions estimates
• Validate the developed approach against an independent dataset
• Develop a recommended step-by-step methodology for generating modal emission rates
in MOVES.

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        Task la: Development of
            Analysis Data Set
                   Task Ib:  Development
                   of Binning Methodology
VSP Approach
NCSU Modal Approach
Averaging (1, 5, 10 seconds)
Units (g/sec or ratios)
Weighting (time, vehicle, trip)
                 Task Ic: Character-
                 ization of Uncertainty
                       I
            Task Id: Applicability to
                   Bag Data
         Task le: Applicability to
               RSD Data
        Task 2: Validation
       Task 3: Recommend
           Methodology
       Figure 1-1. Simplified Schematic of Project Tasks and Their Inter-Relationships

1.2    General Technical Approach
In this section, an overview is provided of the technical approach of this project. This project
was organized based upon three major tasks:

   •   Task 1. Develop Pilot Modal Emission Rates From Multiple Data Sources
   •   Task 2. Perform Validation of Developed Model Against Independent Dataset
   •   Task 3. Summarize Specific Methodologies for Developing Modal Emission Rates for
       MOVES

The first task is comprised of many specific subtasks. We subdivided Task 1 into subtasks as
follows:
   •   Task la: Development of Analysis Dataset
   •   Task Ib: Development of Binning Methodology
   •   Task Ic: Characterization of Uncertainty
   •   Task Id: Applicability to Bag Data
   •   Task le: Applicability to RSD Data

The relationship among the three major tasks, and among the subtasks of Task 1, is illustrated in
Figure 1. The key starting point of the work was the development of an analysis data set in
subtask la. The other subtasks in Task 1, including subtasks Ib, Ic, Id, and le, were dependent
upon the availability of the analysis data set, which included on-board data, second-by-second
laboratory data, EVI240 data, aggregate (bag) data, and RSD data. Task Ib included several

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considerations that are illustrated by the tie-line to a box listing the binning approaches that were
evaluated, the averaging times that were compared, the emission factor units that were compared,
and the method for weighting of data. The uncertainty analysis method in Subtask Ic depended
upon the binning approach selected as a result of Subtask Ib. However, a two-way arrow is
shown between Subtasks Ib and Ic to illustrate the iterative nature of the selection of a binning
approach and an uncertainty analysis approach. For example, the choice of averaging time and
of weighting method in Subtask Ib influenced the results obtained for the uncertainty analysis
method in Subtask Ic, and the availability of uncertainty analysis methods in Subtask Ic has
implications regarding which types of weighting methods were chosen as preferred in Subask Ib.
The applicability of bag and RSD data to the binning approach methodology also impact the
uncertainty characterization. The specifics of these kinds of interactions among subtasks and
trade-offs are addressed in more detail in the discussion of each specific subtask.

In the process of developing the tasks during the course of the project, the following key
questions emerged and were addressed:

1. What dataset should be used for the final version of the conceptual model? (Task la,
Chapter 2)

2. Which binning approach should be used? (Task Ib, Chapter 3)

3. How much detail should be included in the binning approach, in terms of how many
explanatory variables and how many strata for each variable? (Task Ib, Chapter 3)

4. What averaging time is preferred as a basis for model development? (Task Ib, Chapter 4)

5. What emission factor units should be used? (Task Ib, Chapter 5)

6. What weighting approach should be used, when comparing time-weighted, vehicle
weighted, and trip weighted? (Task Ib, Chapter 6)

7. How should variability and uncertainty be characterized? (Task Ic, Chapter 7)

8. How should aggregate bag data be analyzed to derive estimates of modal emission rates?
(Task Id, Chapters)

9. What is the potential role and feasibility of incorporating RSD data into the conceptual
modeling approach? (Task le, Chapter 5)

10. How should the conceptual model be validated and what are the results of validation
exercises? (Task 2, Chapter 9)

1.3 Organization of this Report
This report is organized on the basis of the ten motivating questions of the previous section. The
development of an analysis data set is addressed in Chapter 2. Chapter 3 presents the empirical
and statistical basis for development of modal emissions modeling approaches. The selection of

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a preferred averaging time for model development is discussed in Chapter 4. Two major topics
are addressed in Chapter 5: (1) what emission factor units should be used; and (2) evaluation of
the role of RSD data with respect to model development or model validation.  Three different
data weighting approaches based upon time, trip, and vehicle averaging are compared in Chapter
6. Methods for quantifying variability and uncertainty are presented and compared in Chapter 7.
Methods for estimating modal emission rates from aggregate driving cycle data are presented
and evaluated in Chapter 8. The conceptual modal emissions model developed in this work is
verified and validated in Chapter 9.  Chapter 10 provides a brief summary of the specific
methodology for developing modal emission rates that are recommended for future work.

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2   DEVELOPMENT OF ANALYSIS DATASET

The objective of Subtask la is to develop a combined data set for running exhaust emission rates
for LDGV based upon data provided by EPA.  The dataset included the following data:
   •   Approximately 100,000 seconds of data from 17 on-board vehicles from the "shootout"
       analysis;
   •   Approximately 75,000 seconds of data on 25 vehicles tested at EPA's lab for the Mobile6
       facility-specific driving cycles and other standard cycles;
   •   82,800 seconds on 311 vehicles tested on the EVI240 as part of the Colorado EVI program;
   •   Bag-only and second-by-second data on 74 vehicles tested over FTP (i.e., Bag 2 and Bag
       3) and US06 for development of UC Riverside's Comprehensive Modal Emission Model;
       and
   •   RSD data on 200,966 Tier 1  LDGVs collected as part of a Missouri's Gateway Clean Air
       Program.

The data sets typically contained the following information:

   •   The second-by-second datasets typically had the following data fields: time; vehicle
       speed; fuel consumption; HC, CO, NOX, and CO2 emissions; vehicle engine size;  vehicle
       weight; vehicle age; vehicle technology; vehicle mileage; road grade (for on-board data);
       ambient temperature; and ambient humidity. Some datasets, such  as from on-board data,
       typically also had data for more variables such as: engine RPM; latitude; longitude;
       altitude; mass air flow; intake air temperature; engine load; and other engine related
       variables.
   •   Bag data sets included total emissions for CO, HC, NOX, and CO2. The bag data were
       typically from standard driving cycles for which either the standardized or actual test
       second-by-second speed trace was available. Vehicle-related variables such as vehicle
       engine size, vehicle mileage, vehicle age, vehicle technology, and vehicle weight  were
       available for "bag" data  sets. Additional data were available for some "bag" data sets
       such as a/c usage, ambient temperature, and relative humidity.
   •   RSD data included instantaneous vehicle speed  and emission rates for pollutants
       normalized to CO2 emissions, such as the ratios of CO/CO2, HC/CO2, and NOX/CO2. In
       addition, vehicle-related data such as engine size and model year based upon the license
       plate number that was observed during data collection, identification of the VEST based
       upon registration data, and decoding of the VEST. However, information regarding
       vehicle mileage accumulation was not available. Additional variables such as road grade,
       ambient temperature, and relative humidity were available.

2.1    Development of a Combined Database
In performing the work for this study, our general philosophy was to make use of readily
available software tools where possible. Therefore, we made use of Visual Basic, Excel, and
SAS to a significant extent, consistent with our previous experience in working with similar
datasets.

The combined second-by-second dataset, including on-board data, laboratory dynamometer data,
and EVI240 data, was created using programs written in Visual Basic and  SAS.  For this purpose,

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Visual Basic programs that were prepared in previous studies (Frey et a/., 2001; Frey et a/.,
2002) were utilized. The first step in developing a combined dataset was to make sure that each
data file has the same data fields. Each data file represents a vehicle or a trip. A Visual Basic
code was utilized to process the data and arrange the data fields such that each file has the same
format. Formatting of the fields was conducted with Visual Basic programs that were written for
this purpose in previous studies. After completing the processing of all data files, all of the data
was in Excel with the same format. The Excel files were first exported to SAS and combined
together in SAS using codes written specifically for this purpose.

For quality assurance purposes, the data were screened to check for errors or possible problems.
A notable issue was that there were zero and negative numbers in the second-by-second
emissions data. Specifically, 13 percent of the data were comprised of zero or negative values
for CO, 12 percent for HC, 22 percent for NOX, and 0.8 percent for CC>2. Since measurements
errors could result in negative values that are not statistically significantly different from zero or
a small positive value, the data were retained as is.

Several post-processing steps were applied to the dataset. The post processing steps included:
(1) humidity corrections for NOX emissions for the on-board data; (2) adjustments to the HC data
for the on-board data; and (3) calculation of derived variables such as acceleration, power
demand, and vehicle specific power. Since the dynamometer data was already corrected for
humidity, a humidity correction was also applied to the on-board data. For this purpose, a
humidity correction factor that was reported in the on-board dataset was utilized. The on-board
measurements of HC emissions were made using NDIR, whereas the dynamometer
measurements were made using FID. In other work, the measurements of the on-board
instrument developed by Sensors that was used to collect the EPA on-board data were compared
with measurements made with a laboratory dynamometer. By comparing the total HC emissions
for specific vehicles and driving cycles, it was observed that the NDIR measurements resulted in
lower values than did the FID measurements. Based upon the available comparison data, a
correction factor of, 1.65 was utilized to adjust the on-board HC measurements to an approximate
equivalent basis. Because the adjustment factor was based upon an average of total trip
emissions, the adjustment factor does not take into account possible variability in the ratio of FID
to NDIR measurements on a second-by-second basis.

Variables such as acceleration, power demand and VSP were estimated from other variables such
as vehicle speed. Acceleration is estimated from the observed speed by taking second-by-second
differences in speed. However, to account for the effects of road grade, the estimate of
acceleration was modified. As indicated by Bachman (1999), gravity exerts a force on a vehicle
that must be counteracted. Therefore, the acceleration effect of road grade should be included in
order to estimate the effective acceleration. The effect of road grade on acceleration can be
quantified as:

Acceleration (mph/sec) = 22.15 (mph/sec)x Gradient (%) (2-1)

Power demand was estimated using the following equation:

P = vxa (2-2)

where:

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       P     =      Power Demand (mph /sec)
       v     =      Vehicle speed (mph)
       a     =      Vehicle acceleration (mph/sec)

Vehicle Specific Power (VSP) was estimated using an equation given by EPA, which is:

                VSP(kW/ton) = v[l.la + 9.8l(atan(sin(grade)))+0.132]+0.000302v3     (2-3)

The coefficients given in Equation (2-3) are specific for on-board data. However, coefficients for
dynamometer measurements were not available in this study, therefore, the same coefficients
were used for dynamometer data as well. While it is recognized that the specific estimate of
VSP is a function of vehicle weight and of the specific values of the parameters for each
individual vehicle, it was beyond the scope of this study to develop detailed vehicle-specific
estimates of VSP.

2.2    Organization of the Data for Analysis
The combined database was used to create specific databases for different analyses throughout
the project.  These databases included the following:

   •   A "Modeling" or "Calibration" database comprised of data for most of the on-board
       measurements, most of the EPA dynamometer data, and most of the NCHRP data.  This
       database was also used as "Validation Data Set 1"
   •   "Validation Data Set 2" was comprised of a small sample of vehicles from the EPA on-
       board, EPA dynamometer, and NCHRP data that were excluded from the modeling
       database.
   •   EVI240 data were used separately from the other data
   •   The NCHRP data were used in the analysis of methods for developing modal emission
       rates from aggregate bag data
   •   "Validation Data Set 3" was comprised of data obtained from the California Air
       Resources Board, and are also referred to  as "ARB data."
   •   RSD data included approximately 2,000,000 seconds of data. Of this dataset, 200,966
       data points were selected randomly for analysis, where each point represents
       measurement for one vehicle.

The data from on-board, EPA dynamometer and NCHRP dynamometer measurements were
combined into the modeling data set, and included:

   •   71,699 seconds of data from 13 on-board vehicles from the "shootout" analysis;
   •   68,482 seconds of data on 33 vehicles tested at EPA's lab for the Mobile6 facility-
       specific driving cycles and other standard cycles; and
   •   92,000 seconds of data on 49 vehicles tested over FTP and US06 for development of UC
       Riverside's Comprehensive Modal Emission Model.

Therefore, the combined database for modeling has a total of 232,181 seconds of data. The
combined database has the following data fields:  source for data (e.g., EPA dynamometer);
vehicle make; vehicle model; VIN; number of vehicle tested; number of trip tested; speed;
acceleration; ambient temperature; ambient humidity; road grade; power estimate, positive
power estimate; Vehicle Specific Power (VSP) estimate; positive VSP estimate; CO, CO2,  HC,

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NOX emissions; vehicle model year; vehicle engine displacement; number of cylinders; air
condition use; and vehicle net weight.

Validation Data Set 2 included the following data:

• 3 vehicles from EPA dynamometer data
• 3 vehicles from EPA On-board data
• 25 vehicles from NCHRP data
The validation dataset included 83,183 seconds of data. The data fields for this dataset were the
same as for the Modeling dataset.

The NCHRP dataset included 8 high-emitter vehicles as reported in a User's Manual prepared by
University of California at Riverside. In preparing Validation Dataset 1 and 2, data were selected
randomly from NCHRP data. Six of the high emitter vehicles were included in Validation
Dataset 1, and two of them were included in Validation Dataset 2.

Validation Data Set 3 included data for 17 vehicles from 11 different UCC cycles. The
validation dataset included nominal speed profiles and total emissions for 15 of the vehicles, and
actual speed profiles and second-by-second emissions for two of the vehicles. Detailed
information regarding the Validation Datasets is given in the Appendix.

Data for IM240 were utilized for comparative purposes, as described in this report, including
comparing average emission rates for the developed modes with respect to those obtained from
the calibration data. The IM240 dataset included 311 vehicles tested on the IM240 cycle, for a
total of 82,800 seconds of data. The data fields for this data set were the same as for the
Modeling dataset.

EPA obtained an RSD database from the state of Missouri that contained approximately 2
million records. Of this dataset, 200,966 data points were selected randomly for analysis. This
dataset included data fields similar to the modeling database. However, vehicle net weight was
not available and engine displacement was only available for part of the dataset. Each data point
in the RSD database used for analysis represents a unique vehicle.

2.3 Summary
Data from a variety of sources were reviewed and used to develop data bases for different
components of this project. A modeling database comprised of approximately 232,000 seconds
of data from on-board and laboratory dynamometer measurements was compiled for use in
developing a conceptual modeling approach. A separate IM240 database was developed for
comparison to the modeling data. A database comprised of RSD data was developed in order to
answer key questions regarding the potential role of RSD data in model development or model
interpretation. A database comprised of NCHRP dynamometer data was developed in order to
evaluate methods for estimating modal emissions from aggregate driving cycle data. In addition
to the modeling data set, two other databases were developed for model validation purposes,
including an independent sample of on-board and dynamometer measurements for vehicles
similar to those used in the modeling data base and a separate database obtained from CARB.
10

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3 DEVELOPMENT OF A MODAL EMISSIONS MODELING APPROACH

The objective of this section is to demonstrate the modal "bin" approach on data for "running"
hot-stabilized exhaust emission rates, and to determine the best binning approach based upon
evaluation of alternative approaches. This chapter focuses upon the use of one second data in
units of mass per time. Chapter 4 compare different averaging times and Chapter 5 compares
different emission factor units. The two most promising binning approaches identified in the
"shootout" were the VSP-based approach evaluated by EPA and the driving mode-based
approach evaluated by NCSU. These two approaches were compared in this project. A key
methodological component of this work was the use of Hierarchical Tree-Based Regression
(HTBR), using S-Plus software. This chapter focuses on answering the second and third key
questions of this project: (1) which binning approach should be used?; and (2) how much detail
should be included in the binning approach, in terms of how many explanatory variables and
how many strata for each variable? First, the methodology for developing bins based upon
statistical methods is presented. Results of analysis of the modeling data set based upon each of
the NCSU and VSP based approaches are presented. An evaluation of each approach is made,
followed by a selection of a preferred approach.

3.1 Statistical Method for Developing Binning Criteria
HBTR is a forward step-wise variable selection method, similar to forward stepwise regression.
This method is also known as Classification and Regression Trees (CARTs). Conceptually,
HTBR seeks to divide a data set into subsets, each of which is more homogeneous compared to
the total data set. At a given level of division, each of the subsets is intended to be different in
terms of the mean value. Thus, HTBR is a statistical approach for binning data. More
specifically, the method is based upon iteratively asking and answering the following questions:
(1) which variable of all of the variables 'offered' in the model should be selected to produce the
maximum reduction in variability (also referred to as deviance in HTBR methodology) of the
response?; and (2) which value of the selected variable (discrete or continuous) results in the
maximum reduction in variability (i.e., deviance) of the response? The method uses numerical
search procedures to answer these questions. The HTBR terminology is similar to that of a tree;
there are branches, branch splits or internal nodes, and leaves or terminal nodes (Washington et
al, 1997).

The iterative partitioning process is continued at each node until one of the following conditions
is met: (1) the node of a tree has met minimum population criteria which is the minimum sample
size at which the last split is performed; or (2) minimum deviance criteria at a node have been
met (Frey et al., 2002; and Unal 1999).

In developing bins, vehicle-based variables such as vehicle class, mileage, age, engine size,
vehicle weight, and technology were utilized. Vehicle operation variables such as vehicle speed,
acceleration, and surrogate for power demand (i.e., Vehicle Specific Power) were included in
this analysis. Based upon the availability of the data, external parameters such as road grade, air
condition usage, ambient temperature, relative humidity were incorporated during HTBR
analysis. S-Plus scripts that were written in previous studies were used in this study.
11

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In developing bins both "unsupervised" and "supervised" techniques were utilized. In the
"unsupervised" technique, data is provided to the HTBR with no prior specification of branches
or nodes of the regression tree. In this situation, HBTR is allowed to create whatever bins result
from direct application of HBTR. In contrast, for the "supervised" technique, HTBR is forced to
start with pre-determined modes. A partially supervised technique can often be a better approach
than a purely unsupervised technique. This is because HTBR can be sensitive to artifacts of
variability in the data that may not be important from a practical perspective, and HBTR may
give unexpected or difficult to interpret results if the unsupervised technique is used. Sometimes
HBTR will repeatedly "split" on the same subset of variables (e.g., speed and acceleration)
which may indicate the need for a new explanatory variable that is a function of the subset of
variables. For example, if HBTR splits repeatedly on speed and acceleration, it may be better to
remove speed and acceleration as criteria for creating bins and instead offer some variable that is
a combination of both speed and acceleration, such as VSP or power demand.

The two binning approaches that were evaluated are the VSP approach demonstrated by EPA
and the driving mode approach demonstrated by NCSU (Frey et a/., 2002). VSP is a surrogate
for power demand and is a function of vehicle speed, road grade, and acceleration. In an
unsupervised approach, the selection of bins would be determined by the results of application of
HBTR, rather than based upon arbitrary bin assignments, such as those made by EPA as part of
the shootout (e.g., 1 kw/ton bins from -15 to +30).

The HBTR-based approach was also applied to the driving mode definitions developed by
NCSU. As part of previous work (Frey et a/., 2001; 2002), NCSU developed a priori driving
mode definitions. Idle is defined as based upon zero speed and zero acceleration. The definition
of the acceleration mode includes several considerations. First, the vehicle must be moving and
increasing in speed. Therefore, speed must be greater than zero and the acceleration must be
greater than zero. However, vehicle speed can vary slightly during events that would typically be
judged as cruising. Therefore, in most instances, the acceleration mode is based upon a minimum
acceleration of two mph/sec. However, in some cases, a vehicle may accelerate slowly.
Therefore, if the vehicle has a sustained acceleration rate averaging at least one mph/sec for three
seconds or more, that is also considered acceleration. Deceleration is defined in a similar manner
as acceleration, except that the criteria for deceleration are based upon negative acceleration
rates. All other events not classified as idle, acceleration, or decelerations are classified as
cruising. Thus, cruising is approximately steady speed driving but some drifting of speed is
allowed. It was shown by NCSU in previous studies (Frey et a/., 2001; 2002) that emission
estimates for these driving modes are statistically significantly different from each other. An
example comparison of modal emission rates for hot stabilized driving is given in Figure 3-1.

In working with the NCSU-based approach, two specific applications of HBTR were made. In
the first, the data set was modified to include a bin category for each data point. Unsupervised
HBTR was applied to the modified database to determine whether HBTR will subdivide the data
based upon the NCSU modal definitions preferentially compared to other possible binning
criteria. Additional bins were developed using HBTR in order to further refine the binning
approach. This type of approach was demonstrated briefly in the previous shootout project (Frey
et a/., 2002) and was expanded in its application in this project.
12

-------
1000 -i
"oT 100
_o
x
.2 10 -
1 -
HC (mg/sec)
C02 (g/sec)
o.iJ
Figure 3-1. Average Modal Emission Rates for LDGVs (Source: Frey et a/., 2002)

In developing modal "bins" in HTBR it should be kept in mind that there is a trade-off between
the number of bins and the usefulness of the empirical model based upon the bins. While it is
possible to obtain additional explanatory power by increasing the number of bins, there are
diminishing returns associated with creation of an increasing number of bins. Furthermore, the
FffiTR determines bins based upon whether there are differences in the average emissions among
the possible bins. It does not determine bins based upon what portion of trip or total emissions
are explained by each bin. Therefore, it is possible to obtain a potentially large number of bins
that do not help explain a significant portion of total trip or aggregate emissions. Supervised
techniques are sometimes more useful than unsupervised techniques in helping to avoid a
proliferation of relatively useless bins. Another method for dealing with the possible
combinatorial explosion of bins is to "prune" a tree created using HBTR. For example, HBTR
could be allowed to develop a large number of bins for purposes of determining a practical upper
limit on the amount of deviance in the data set that can be explained by the bins. Then, the
number of bins can be reduced to a point where there is still good explanatory power of the
binning approach with a much smaller number of bins. This process requires some judgment and
therefore would be considered to be a supervised technique. This approach has been
demonstrated previously (e.g., Rouphail et a/., 2000; Frey et a/., 2002).

Another important issue regarding bin development is that bins that are formed under different
branches of the tree (see Figure 3-2) may not be statistically significantly different from each
other
13

-------
Figure 3-2. Sample Regression Tree Diagram (Numbers represent Node Numbers of the Tree)

when the number of bins increases. All of the data are "fed" into the HBTR process as Node 1.
HBTR will divide into separate data sets at each branch in the tree. Thus, the first split of the
data is into bins represented by Nodes 2 and 3. Then, another split is made in which the data are
further subdivided into four nodes, Nodes 4, 5, 6, and 7. A third split results in eight modes,
which are Nodes 8 through 15. Each time a split is made, the two nodes that are subdivided
based upon a higher level node are statistically significantly different from each other with
respect to the mean value. Thus, for example, Nodes 8 and 9 will have significantly different
mean values. However, Nodes 9 and 10, which result from different branches, are not
guaranteed to have significantly different means. Thus, it is possible that a larger number of
nodes could result in some overlap with respect to mean values. In other words, the creation of a
large number of bins or nodes may not substantially increase explanatory power compared to a
smaller number of bins or nodes. We evaluated the statistical significance of differences in the
average value of emissions associated with different bins and considered lack of statistical
significance of average values as a stopping criteria pertaining to the creation of additional
branches of the regression tree.

Not all modes are equally important. Some modes are more important than others since they
represent a larger share of total emissions than others. For example, in a previous study by
NCSU it was found that acceleration and cruise modes are the most important modes in terms of
total trip emissions. Figure 3-3 illustrates the distribution of time spent in each driving modes
(i.e., cold-start, idle, acceleration, deceleration, and cruise) and the corresponding percentage
contribution of each mode to total trip emissions for each of four pollutants. One key finding is
that the idle and deceleration modes contribute relatively little to total emissions for any of the
14

-------
• Cruise
D Deceleration
• Acceleration
Dldle
Cold-Start
Time
HC
CO
C02
Figure 3-3. Example of Average Distribution of Time and Emissions with Respect to Modes
(Source: Frey etal, 2002)

four pollutants compared to cruise, acceleration, and cold start emissions. Therefore, there is
likely to be little to be gained by spending resources to improve the explanatory power of the idle
and deceleration modes. In contrast, cruising, acceleration, and cold start, in a general
descending order, are the most important contributors to total emissions. Therefore, an iterative
approach was taken to develop bins. First bins were developed using the HTBR method. The
percent contribution of each mode total emissions was estimated. Based upon these results, the
definitions of the modes were revised so that no single mode contributes disproportionately to
the total emissions represented in the database.

3.2 Development of the VSP-Based Modal Approach
In developing bins based upon VSP, first step was to explore the relationship between VSP and
emissions with the help of scatter plots. Based upon exploratory analysis of the sensitivity of
emissions to VSP and other explanatory variables, a recommended approach was developed for a
modal model.

3.2.1 Exploratory Analysis
Figure 3-4 shows the relation between VSP and emissions for HC, NO, CO, and CO2. VSP data
were binned into Ikw/ton bins from -50 to +50 and the average within each bin is shown.
It is observed from these scatter plots that there is an approximately monotonic increase in
emissions for all four pollutants for positive VSP. Emissions tend to be very low for negative
VSP bins and tend to increase as VSP increases above zero. For very high values of VSP (i.e.,
VSP bins higher than 45) there is an apparent decrease for CO2 and NOX especially. The number
of data points in these bins are small, typically less than 100. Thus, the reliability of the
estimates for the very high VSP bins in question. However, one reviewer of this work indicated
that there is the possibility that emissions may actually decrease on average in the very high VSP
range.
15

-------
       o
       u
         -60  -50   -40  -30   -20   -10   0   10   20   30   40   50   60
                           Vehicle Specific Power (VSP)
i
  _60   -50   -40  -30   -20  -10   0   10   20   30   40   50   60
                      Vehicle Specific Power
                                 0.02 -i
         -60  -50   -40  -30   -20  -10   0    10   20   30   40   50   60
                           Vehicle Specific Power (VSP)
        -50   -40  -30  -20   -10   0    10   20   30   40   50   60
                      Vehicle Specific Power
Figure 3-4.  Exploratory Analysis of Average Emissions of CC>2, NOX, HC, and CO versus Vehicle Specific Power (VSP) Based Upon
                                                           the Modeling Database.
                                                                      16

-------
HBTR was applied to the modeling dataset in order to see whether VSP would be selected by
HTBR as the mot important explanatory variable. An example for this analysis is given for NO
emissions in Figure 3-5. Vehicle operating parameters as well as vehicle technology parameters
were used as possible explanatory variables. These parameters are: speed; acceleration; VSP;
temperature; engine displacement; number of cylinders; a/c usage; temperature, odometer
reading; model year; and net weight. Of all these parameters VSP was selected as the first split
by HTBR. The vertical distance depicted for each branch is proportional to the reduction in
deviance associated with each explanatory variability. In this specific case, splitting the data set
into two strata based upon a VSP criteria of 13.2 lead to a substantial reduction in deviance.
Under the second branch of the tree, a second split was made based upon vehicle net weight.
However, the reduction in deviance based upon further stratification by net weight is less than
the reduction in deviance from the first split based upon VSP. At the lowest portion of the tree, a
second split based upon VSP is observed for the smaller net weight category of data. When a
variable occurs repeatedly in the tree, such as VSP does in this case, that is evidence that the
variable plays an important role. In this case, VSP alone helps explain a substantial portion of
deviance in the data. When the data are further stratified, VSP explains additional deviance for
vehicles with a net weight less than 4,400 pounds. This result illustrates that VSP is the most
important variable and therefore could be selected as the first criteria for developing bin
definitions. Qualitatively similar results were obtained for other pollutants.

A judgment was made that it would be useful to separately analysis the role of vehicle operating
parameters (e.g., VSP) as distinct from vehicle characteristics (e.g., net weight, odometer
reading, engine size). When only vehicle operating parameters were utilized in HTBR, VSP was
again found to be the most important explanatory variable.

Because VSP was consistently identified as the most important explanatory variable, modal bins
were developed using VSP. HBTR was not used to develop the actual definitions of the bins.
While useful in identifying which variables offer the most capability to explain deviance in the
data set, an "unsupervised" approach to HBTR does not provide optimal bin definitions. For
example, it is possible that nodes that occur under different branches of the tree may have similar
average emission rates. From a practical perspective, it is not useful to have bins with similar
average emission rates, since the objective is to explain variability in emissions. Therefore, a
"supervised" approach was adopted. In the supervised approach, two key considerations were
taken into account. The first is that ideally each mode should have a statistically significantly
different average emission rate than any other mode. The second is that no single mode should
dominate the estimate of total emissions for a typical trip as represented by the database.
Therefore, to guide the selection of modal definitions, it was decided that no mode should
explain more than approximately 10 percent of total emissions. Based upon these two
considerations, VSP modes were defined. It should be noted that same modes were defined for
all the pollutants. Table 3-1 gives the VSP modal definitions.

Figure 3-6 shows average modal rates for these bins for all four pollutants. The average modal
rates are significantly different from each other for all four pollutants. In all four pollutants the
average modal rates for the first two modes, Modes 1 and 2, are higher than average rate for
Mode 3. There is an increasing trend in emissions with increase in VSP bins for Modes 4
17

-------
Table 3-1.  Definitions for VSP Modes
VSP Mode
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Definition
VSP<-2
-2<=VSP<0
0<=VSP<1
1<=VSP<4
4<=VSP<7
7<=VSP<10
10<=VSP<13
13<=VSP<16
16<=VSP<19
19<=VSP<23
23<=VSP<28
28<=VSP<33
33<=VSP<39
39<=VSP
                18

-------
                                                VSP<13.1847
                                                                         Met.Weicht<4375
                        0.001429
                                                                                              0.060080
                                               0.006328
0.013790
         Figure 3-5.  Example of Unsupervised HTBR Tree Results for the Modeling Data Set for NOX Emissions (g/sec)
Note: The vertical distance of each branch indicates the proportional explanatory benefit of each particular split, and the numbers at
                        the bottom of the branches are the average emission rates for the stratified data.
                                                            19

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Figure 3-6. Average Modal Emission Rates (g/sec) for VSP Bins for CO, HC, CC>2, and NOX Based Upon the Modeling Dataset.
                                                        20

-------
through 14 for all of the pollutants. For CO, the range in average modal emissions is more than
two orders-of-magnitude, when comparing Mode 3 and Mode 15. A similar comparison for
NOX, HC, and CC>2 implies a range of approximately one to two orders-of-magnitude.

Because each pollutant has a different sensitivity to the modal definitions, there are some cases
in which a mode may contribute approximately 10 percent to the total emissions of one pollutant
but a far lower percentage of total emissions for another pollutant, as shown in Figure 3-7. For
example, for the high VSP bins, such as Modes 12, 13, and 14, approximately 10 percent of the
total CO emissions in the calibration data set are accounted for, for a total of over 30 percent of
the total CO emissions. These four modes account for less than three percent of total travel time
in the database. Furthermore, these modes account for only approximately 15 percent or less of
total NOx, HC, and CO2 emissions. The implication is that high VSP has a more substantial
impact upon CO emissions than for the other pollutants. This seems plausible, in that high VSP
is likely to be associated with an increased frequency and duration of command
enrichment, which tends to have more effect on CO emissions than, for example, NOX emissions.
Because pollutants respond differently to activity captured by each mode, it was necessary to
have 14 modes in order that no individual mode represent more than approximately 10 percent of
the emissions of any single pollutant. Of course, the proportion of emissions in each mode is
conditional on the database used to estimate the modal emission rates.

3.2.2 Considerations in Refinement of the VSP-Based Modal Approach
In order to further improve modal definitions, parameters related to vehicle technology were
included in an analysis to determine which ones are most useful in further explaining variability
in emissions. These parameters included were: engine displacement; number of cylinders;
odometer reading; model year; and net weight. Some of these parameters are correlated with
each other. For example, odometer reading and model year tend to have a positive dependence,
and engine displacement, number of cylinders, and net weight tend to have a positive
dependence. The correlation analysis for these parameters is given in Appendix. Therefore, in the
final model, it is not expected to be necessary to include all of these. Separate HTBR trees were
fit to data in each mode for each pollutant separately. Tables 3-2 through 3-5 summarize the
results of these analyses for CO, CO2, HC, and NOX respectively.

One of the observations from Tables 3-2 through 3-5 is that both net weight and engine
displacement are important variables for all of the pollutants for most of the modes. Engine
displacement is an important variable especially for CO and CO2, whereas odometer reading is
important especially for HC. Based upon the results given in Tables 3-2 through 3-5,
improvements in the VSP modal definitions were considered based upon comparison of based
upon net weight or engine displacement. In addition, the effect of stratification of VSP bins with
respect to odometer reading was also considered.
21

-------
                                     Percent of Emissions and Time Spent in VSP Modes
30
20
                                                                                                      DTime
                                                                                                      SCO
                                                                                                       ICO2
                                                                                                       IHC
10 -•
                                                                                       i
                                                                              10
11
12
14
Figure 3-7.  Percent of Time Spent in VSP Modes and Percentage of Total CO, NOX, CC>2, and HC Emissions Attributable to Each
                                   VSP Mode, Based Upon the Modeling Data Set.
                                                       22

-------
Table 3-2. Unsupervised HBTR Regression Tree Results for CO for Each of 14 VSP Modes
Mode
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1st Cut point
E* 5.3
E 5.3
E 5.3
E 5.3
E 5.3
NW** 4400
NW 4400
NW 4200
NW 4200
NW 4200
NW 4200
NW 3800
O*** 15000
NW 3300
2nd Cut point
NW 4400




O 15000
NW 3600
O 15000
/-<#### c
C 5
C5
NW 3200

O 45000
3rd Cut point
NW 3600



NW 3600


O 24000




O 79000
O 79000
Table 3-3.  Unsupervised HBTR Regression Tree Results for CO7 for Each of 14 VSP Modes
Mode
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1st Cut point
NW 3200
NW 3200
C 5
C 5
E 2.3
E 2.3
NW 3700
NW 3700
E 3.5
E 3.5
E 3.5
E 3.5
E 3.5
E 3.5
2nd Cut point
C 5

NW 3200
NW 2700
NW 2800
E 1.95
E 1.95
E 1.95
O 46000
O 44000
O 46000
O 37000
O 23000

3rd Cut point
O 25000


NW 3600
NW 3700
C>7
E 3.9
E 3.5





O 60000
 Note: "NW" means "Net Vehicle Weight (Ibs)", "O" means "Odometer Reading (miles)",
 "C" means "Number of cylinders", "E" means "Engine Displacement (liters)". The number
 following the variables is the value of the cut point.
 Results are not shown in cases where sample size was small
                                      23

-------
Table 3-4. Unsupervised HBTR Regression Tree Results for HC for Each of 14 VSP Modes
Mode
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1st Cut point
O 77000
O 77000
O 79000
O 79000
O 78000
O 78000
O 78000
O 78000
O 78000
O 78000
O 43000
O 43000
O 43000
O 46000
2nd Cut point






O 30000
O 26000
O 33000
O 32000


O 15000

3rd Cut point

O 98000

O 98000
O 98000
O 98000
O 98000

O 95000

O 95000
NW 2800
NW 3000
NW 3000
Table 3-5.  Unsupervised HBTR Regression Tree Results for NOX for Each of 14 VSP Modes
Mode
1
2
3
4
5
6
7
8
9
10
11
12
13
14
1st Cut point
NW 3600
O 66000
O 30000
NW 4400
NW 4400
NW 4400
NW 4400
O 70000
NW 4200
NW 4200
NW 4200
O 13000
O 14000
NW 3800
2nd Cut point
O 23000


O 66000
O 66000
O 66000
O 66000
NW 2800
O 38000
O 38000
O 38000


NW 3600
3rd Cut point
NW 3800
O 83000
O 43000




NW 3800




O 95000
NW 2800
 Note: "NW" means "Net Vehicle Weight (Ibs)", "O" means "Odometer Reading (miles)",
 "C" means "Number of cylinders", "E" means "Engine Displacement (liters)". The number
 following the variables is the value of the cut point.
 Results are not shown in cases where sample size was small
                                      24

-------
Figures 3-8 and 3-9 present the effect of net weight and engine displacement, respectively, on
emissions as applied to the VSP modal bins. For Figure 3-8, the data were stratified based upon
a vehicle weight of 4,000 pounds, and for Figure 3-9, the data were stratified based upon an
engine displacement of 3.5 liters. These cut-offs were chosen based upon the results of Tables 3-
2 through 3-5 and were intended to be representative values. Although for some pollutant/mode
combinations there is no significant or substantial difference in average emissions, for other
combinations there are statistically significant differences based upon either net weight or engine
displacement. For example, for the higher VSP modes (e.g., Modes 10 to 14), average emissions
are larger for all four pollutants for the larger weight category. In the case of CC>2, the trend of
higher emissions for heavier vehicles is systematic among all of the positive VSP modes (i.e.
Modes 3 to 14); this difference is expected since heavier vehicles typically have lower fuel
economy and, hence, higher CC>2 emissions than lighter vehicles. For CO and NOX, for the most
part emissions of heavier vehicles are higher for the positive VSP modes. For HC, the trend is
slightly different than other pollutants. For the first eight modes, lighter vehicles have higher
emissions; however, for Modes 10 to 14, heavier vehicles have significantly higher emissions.
These results confirm that vehicle net weight is an important variable. The differences in
emissions between the weight categories is on the order of a factor of two to five in most cases.

The relationship between emissions and engine displacement is shown for all pollutants and
modes in Figure 3-9. Although there are some exceptions, particularly for the negative VSP
modes (e.g., Modes 1 and 2), typically vehicles with larger engine size have significantly higher
emissions by a factor of two to five. Thus, engine displacement is also shown to be a
potentially important explanatory variable. Since engine displacement and net vehicle weight
are highly correlated, there is little benefit to including both as criteria for stratification of the
data. Engine displacement was selected as the criteria for further model development, although
it is likely that similar results would be obtained if net vehicle weight were selected instead.

Aside from either engine displacement or vehicle weight, it is clear from the results of Tables 3-2
through 3-5 that odometer reading is also an important explanatory variable. The range of
cutpoints for odometer reading obtained from HBTR varies substantially from one pollutant to
another, and in some cases multiple cutpoints for odometer reading were obtained from the
analysis. However, for simplicity and for consistency with other models and analyses, a single
cutpoint of 50,000 miles was selected. This cutpoint is within the range of values obtained from
HBTR.

The average modal emission rates, and the 95 percent confidence intervals for the averages, are
shown in Figure 3-10 for the 14 VSP modes stratified with respect to two engine displacement
categories and two odometer reading categories. The sample sizes for each mode for each strata
of engine displacement and odometer reading are shown in Figure 3-11.

For the lower engine displacement category of less than 3.5 liters, represented by Strata 1 and
Strata 3 in Figure 3-10, respectively, it is typically the case that the higher mileage vehicles have
higher emissions of HC and NO, only marginally higher emissions of CO, and comparable
emissions for CO2. Similarly, for the larger engine displacement category of greater than 3.5
liters, the higher mileage vehicles have substantially higher HC and NOX emissions, marginally
25

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Figure 3-8. Comparison of Average Modal CO, HC, CC>2, and NOX Emissions Rates for 14 VSP Bins for Vehicles with Net Weight <
                                      4,000 Ib to Vehicles with Net Weight > 4,000 Ib.
                                                           26

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Figure 3-9. Comaparison of Average Modal CO, HC, CO2, and NOX Emissions Rates for 14 VSP Bins for Vehicles with Engine
                       Displacement < 3.5 liters to Vehicles with Engine Displacement > 3.5 liters.
                                                       27

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                                                                         1  2  3  4  5  6  7 8  9 10  11 12 13 14 15
     Figure 3-10.  Comparison of Average Modal CO, HC, CC>2, and NOX Emissions Rates for 14 VSP Bins Stratified by Engine
                                           Displacement and Odometer Reading.
SI: Engine Displacement <3.5 liters and Odometer < 50K miles;   S2: Engine Displacement >3.5 liters and Odometer < 50K miles;
S3: Engine Displacement <3.5 liters and Odometer > 50K miles;   S4: Engine Displacement >3.5 liters and Odometer > 50K miles.
                                                           28

-------
    35000 -i
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                           Odometer Readings > 50,000 Miles
                           Engine Displacement > 3.5 Liters
                                                                                              • ill	

                                                            VSP Mode
         Figure 3-11. Sample Sizes for Each VSP Mode for Each Odometer Reading and Engine Displacement Strata.
                                                             29

-------
higher CO emissions, and comparable CC>2 emissions for most modes. Thus, it is clearly
important to compare emissions for different odometer reading categories, especially for HC and
NOX.

When comparing engine displacement categories for a given odometer category, it is typically
the case that the larger engine size category has higher CC>2, CO, HC, and NOX emissions than
the lower engine size category. However, there are some exceptions to this trend. For example,
the lower mileage vehicles with larger engines tend to have lower NOX emissions for Modes 1
through 7 compared to any other strata, and for the higher VSP modes, the NOX emissions for the
larger engines are not substantially higher than that for the smaller engines for lower mileage
vehicles. However, among the higher mileage vehicles, those with larger engines have
substantially higher NOX emissions than those with smaller engines.

The fact that there are important differences in emissions based upon engine size and odometer
reading for many modes for each of the pollutants confirms that engine size and odometer
reading are useful explanatory variables. Therefore, the modal approach based upon 14 VSP
bins, each divided into four strata representing two engine size and two odometer reading
categories, was adopted for further analysis. This approach is referred to as the "56-bin"
approach because of the 56 bins required (14 VSP bins x 2 engine displacement strata x 2
odometer reading strata = 56 bins in total).

3.2.3 Comparison of Modeling and IM240 Datasets
In this section comparison of modal results based upon the calibration dataset and the EVI240
dataset is given based upon the preliminary VSP approach. For this purpose, the VSP bins that
were segregated via net weight are given. The EVI240 data were not used in the initial calibration
activity because EVI240 data are for a smaller range of VSP than the calibration data and because
of concern that there may be significant differences in fuel characteristics. An objective in
comparing the two data sets is to determine whether the results obtained based upon the
modeling data set are robust when the same binning criteria are applied to a different data set. In
order to make this comparison, it is important to first stratify both datasets as much as possible to
correct for variability in key factors. Based upon appropriate stratification, a more direct
comparison can be made between the data sets.

Figure 3-12 presents a comparison of modeling data and EVI240 data based upon VSP bins where
vehicle net weight is less than 4,0001b. For CO2, the results from the modeling data set and the
EVI240 data are very similar, both in terms of general trends among all modes and in terms of
comparisons of mean emission rates for individual modes. The only exception is an apparent
anomaly for Mode 1. Aside from the anomaly, the comparison suggests that on average the
vehicles in the two data sets have similar CO2 emission rates, which also indicates that they have
similar fuel economy, since the vast majority of carbon in the fuel is emitted as CO2. For the
other three pollutants, there are similarities in average emission rates for the highest VSP modes,
such as Modes 10 to 14, especially for CO and HC emissions. For NOX, the emissions appear to
differ by a factor of approximately two for these modes. The similarities for the higher modes
for CO and HC may suggest that vehicles emit similarly for these two pollutants under
conditions of high power demand and, presumably, increased occurrence and frequency of
30

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Figure 3-12.  Comparison of Average Modal CO, HC, CC>2, and NOX Emissions Rates based upon the Modeling Data versus IM240
                                Data for 14 VSP Bins for Net Vehicle Weight < 4,000 Ib.
                                                       31

-------
enrichment. For all other modes, it is generally the case that the IM240 database reveals higher
average emission rates than does the calibration database. This could be perhaps because there is
a higher proportion of high emitting vehicles, a different activity pattern of the vehicles, or
perhaps different fuel or ambient characteristics.

Figure 3-13 shows the comparison between the EVI240 and the calibration data for net weight
greater than 40001b. There are not many data points in several of the VSP bins for the EVI240
data. For Modes 11 and 12 there are less than 20 data points and for Modes 13 and 14 there are
no data points. Thus, the results for Modes 11 and 12 are subject to considerable random
sampling error. Similar to the case for the lower weight vehicles, for CC>2 there are generally not
significant differences between average modal rates for the EVI240 and calibration datasets. For
other pollutants, the EVI240 database tends to have higher average modal rates than the
calibration data, especially for the first seven modes.

Overall, these comparisons suggest important similarities between the modeling and the EVI240
datasets. The general trend of an increase in emissions from Modes 3 to 14 is common to all
pollutants and for both vehicle size categories. The results for CC>2 agree very well, especially
for the smaller vehicle size category for which there is more EVI240 data. The results for NOX
are comparable in terms of general trend and relative variation in emissions among the modes,
but the average emissions are systematically higher for the EVI240 data than for the modeling
data. For HC, the average modal emissions from the EVI240 data are substantially higher than for
the modeling data for Modes 1 through 7, but are statistically similar for the highest VSP modes.
For CO, the average modal emissions based upon the EVI240 data are higher than those based
upon the modeling data set for the lower VSP modes for both vehicle size categories. For the
smaller vehicle size category, for which there are more data, the CO emissions are similar for the
higher VSP modes. Since the EVI240 is based upon potentially different fuel than the modeling
data set, it is possible that differences in fuel may be important. However, it is also likely that
the EVI240 data set contains high emitting vehicles, and that the lower VSP modes may be more
susceptible to differences between normal and high emitting vehicles than the higher VSP
modes, which also typically represent higher emissions.

A more thorough comparison of different data sets is shown in Figures 3-14 through 3-17 for the
four engine displacement and odometer reading strata, respectively. The data sets compared
include the EPA on-board data, the EPA dynamometer data, NCHRP data, and the EVI240 data.
The first three are the constituent data of the modeling database. Not all databases could be
compared for all four strata because of lack of data in some of the strata. Generally, the CO2
results are comparable among the databases, although it appears that the NCFIRP database
represents higher average CO2 emissions than does the EVI240 database for higher mileage
vehicles with larger engines. There tends to be more agreement regarding NOX emissions
estimates compared to CO and HC. Both the on-board and dynamometer data from EPA tend to
be similar. For example, for the smaller engines and lower mileage vehicles, the CO emissions
agree well for most of the modes, and for NOX the trends are very similar even though the
averages are similar primarily only for the lower VSP modes. The on-board hydrocarbon
emissions values tend to be much higher than those of the other data sets except for the high VSP
modes, although the difference is not as pronounced for the larger engine size range. Even
though emissions are not similar when comparing some of the datasets, a likely reason for such
32

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Figure 3-13.  Comparison of Average Modal CO, HC, CC>2, and NOX Emissions Rates based upon the Modeling Data versus EVI240
                                Data for 14 VSP Bins for Net Vehicle Weight > 4,000 Ib.
                                                        33

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Figure 3-14. Comparison of Average Modal CO, HC, CC>2, and NOX Emissions Rates for Engine Displacement < 3.5 Liters and

         Odometer Reading < 50,000 miles for EPA dynamometer, EPA on-board, NCHRP, and IM240 Databases.
                                                      34

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Figure 3-15. Comparison of Average Modal CO, HC, CC>2, and NOX Emissions Rates for Engine Displacement > 3.5 Liters and
         Odometer Reading < 50,000 miles for EPA dynamometer, EPA on-board, NCHRP, and IM240 Databases.
                                                      35

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Figure 3-16. Comparison of Average Modal CO, HC, CC>2, and NOX Emissions Rates for Engine Displacement < 3.5 Liters and
                   Odometer Reading > 50,000 miles for EPA dynamometer and NCHRP Databases.
                                                     36

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                        Odometer Reading > 50,000 miles for IM240 and NCHRP Databases.
                                                     37

-------
differences is a different mix of vehicles. The differences among the data sets suggest that it is
important to obtain a good representative sample of vehicles so that the combined database will
adequately capture and represent variability in emissions. The comparison also suggests that the
VSP definitions are useful in explaining variability in emissions within any of the data sets
individually.

3.3 NCSU Modal Approach: Idle, Acceleration, Deceleration, and Cruise
This approach is based on the NCSU modal definitions that are given in previous reports.
The vehicle operating conditions were categorized into NCSU modes, which are idle,
acceleration, deceleration and cruise. In order to refine the NCSU modes, HBTR was run for
each of the NCSU modes for all pollutants. When both operating and vehicle technology
parameters were included in HBTR, VSP was typically selected as the most important
explanatory variable, except as noted below. In a refined HBTR analysis based upon only
operating parameters of speed, acceleration and VSP, VSP was again selected as the most
important explanatory variable in most cases.

It was found that for the acceleration mode, VSP is most powerful in explaining the variability in
the emission rate. For example, Figure 3-18 shows the HBTR results for the acceleration mode
for NO. The first cut point is VSP, and it accounts for a large portion of the reduction of
deviance. VSP also is used for some additional stratification, along with speed. However, the
portion of deviance explained by speed is very small compared to that explained by VSP. Thus,
VSP is identified as the single most important variable to further improve the NCSU
Acceleration mode. Therefore, data within the acceleration mode were subdivided into addition
modes based upon VSP cut-offs. The cut-offs were selected based upon the same criteria as
described for the VSP approach: (1) ideally, each newly defined mode should have a
significantly different average emission rate compared to other modes; and (2) each mode should
account for not more than approximately 10 percent of the total emissions of a single pollutant.
Based upon these criteria, six modes were defined, as summarized in Table 3-6.

For the NCSU Cruise mode, it was found that VSP and Speed are both important variables that
are picked by HBTR. For example, Figure 3-19 shows the regression tree cruise mode results for
NO. The data are first stratified with respect to VSP, resulting in a large reduction in deviance,
as indicated by the vertical length of the branches under the first split. For the high VSP data,
the data are further stratified into smaller VSP categories, suggesting that VSP alone is useful in
explaining emissions as long as the VSP is above a cut-off (in the example, the cut-off is
approximately VSP=12). For the lower VSP data, speed was found to be the most important
variable for further stratification of the data. Therefore, in defining new modes within the cruise
mode, consideration was giving to using speed to stratify data for low VSP cases, and VSP alone
was used to discriminate among the high VSP data. The specific criteria for the bins shown in
Table 3-6 were developed based upon judgment after reviewing HBTR results for all pollutants.
38

-------
Speed mph
VRP<1 9 805
I I
0.001956 0.005092
I
<3fi 1904 VRP<9!

ififiO?
Rneeri rrnl- =39 389fi
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  Figure 3-18:  Unsupervised HBTR Results for NCSU Acceleration Mode for NOX Emissions
                                         (g/sec).
                              Speed.mph< £3.9951
                                                    VSP<11 7862
              Speed.mph-
36.9932
             0.0004543      0.0008228
                                                         I
                                                     0.0014750
                                              VSP<1|95302
                                                                 0.0014010
                                                     0.0024210
 Figure 3-19.  Unsupervised HBTR Results for NCSU Cruise Mode for NOX Emissions (g/sec).

Notes for Figures 3-17 and 3-18: The vertical distance of each branch indicates the proportional
explanatory benefit of each particular split, and the numbers at the bottom of the branches are the
                         average emission rates for the stratified data
                                            39

-------
Table 3-6.  Definition of NCSU Driving Modes
ID
1
3
21
22
23
24
25
26
41
42
43
44
45
46
Definition
NCSU Idle
NCSU Deceleration
NCSU Acceleration & VSP<8
NCSU Acceleration & 840
NCSU Cruise & VSP<12 and Speed<30
NCSU Cruise & VSP<12 and 3055
NCSU Cruise & 1222
                   40

-------
For the deceleration mode, speed was the most important explanatory variable picked by HBTR
analysis. However, considering that the total emission contributed by the deceleration mode is
less than 10 percent for all four of the pollutants, it was deemed not necessary to further divide
deceleration into submodes. The idle mode was also not further refined, since idle contributes
only a small portion of total emissions.

In total, 14 modes were identified, including one idle mode, one deceleration mode, six
acceleration modes, and six cruise modes. The definition of these modes is given in Table 3-6.
The time spent in each of the 14 modes, and the emissions contributed by these 14 modes is
shown in Figure 3-20. The average emission values for each of the 14 modes for the four
pollutants are given in Figure 3-21,and the sample size for each mode is shown in Figure 3-22.
Figure 3-20 indicates that CO emissions were the binding consideration in determining the need
for six acceleration modes. Specifically, the high VSP acceleration modes (i.e. Modes 24, 25,
and 26) each represent approximately 10 percent of the total CO emissions in the database, but a
far smaller percentage of emissions of the other three pollutants. On the other hand, NOX
emissions were the binding constraint on determining the need for six cruise bins, since NOX
contributes approximately 10 percent to total NOX emissions for the high VSP cruise modes
(Modes 44, 45, and 46) and other pollutants contribute less than this percentage to their
respective totals.

The comparison of average emission rates in Figure 3-21 reveals that the lowest emission rates
for a given pollutant typically occur for idle, deceleration, and low speed cruising. As cruising
speed increases for low VSP values, as represented by Modes 41, 42, and 43, the average
emission rate increases for all pollutants. High VSP cruising results in higher average emissions
than low VSP cruising. These results tend to confirm intuitive a priori assumptions that
emissions during cruising will typically be higher at higher speeds or under conditions of higher
engine load. The ability to distinguish emissions for different types of cruising illustrates the
intuitive appeal of this particular modal binning approach: it is relatively easy to explain the
relationship between vehicle activity and emissions with this approach.

For the acceleration mode, emissions for any of the pollutants increase with VSP, as illustrated
by comparing Modes 21, 22, 23, 24, 25, and 26. For CO and HC, there is a significant increase
in emissions when comparing one mode with the next mode that has higher VSP. For both NOX
and CO2 emissions, the average emissions increase substantially with VSP for the lower VSP
modes (i.e. Modes 21, 22, 23). For Modes 24, 25, and 26, there are small increases in average
emissions as VSP increases. These results suggest that CO and HC emissions are very sensitive
to VSP throughout the entire range of acceleration events, whereas NOX and CO2 emissions are
sensitive to lower ranges of VSP of less than about 25. Above VSP=25, NOX and CO2 emissions
are less sensitive to VSP. Thus, it appears to be the case that once a VSP threshold is reached,
NOX and CO2 emissions will not change much, but that CO and HC emission rates are more
sensitive to high (or perhaps aggressive) accelerations.
41

-------
      30
      20
      10
       0
                           21     22     23     24     25     26     41     42     43     44     45
46
Figure 3-20. Percent of Time Spent in NCSU Modes and Percentage of Total CO, NOX, CC>2, and HC Emissions Attributable to Each
                                  NCSU Mode, Based Upon the Modeling Data Set.
                                                      42

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               1   3  21  22 23  24  25 26  41  42 43  44  45 46
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Figure 3-21.  Average Modal Emission Rates (g/sec) for NCSU Modes for CO, HC, CC>2, and NOX Based Upon the Modeling Dataset
                                                              43

-------
          Ddometer Readings < 50,000 Miles
          Engine Displacement < 3.5 Liters
   40000 -
   30000 -
N
C/)
03
CL
E
TO
C/)
20000 -
   10000 -
                                 Odometer Readings < 50,000 Miles
                                 Engine Displacement < 3.5 Liters
                                    .I...      III.
                                                           Odometer Readings < 50,000 Miles
                                                           Engine Displacement < 3.5 Liters
                                                             Mode Definitions:
                                                             1 = idle
                                                             3 = deceleration
                                                             21-26 = acceleration
                                                             41-46 = cruise
                                                                               111
Odometer Readings < 50,000 Miles
Engine Displacement < 3.5 Liters
  I.

                                                       NCSU  Mode

      Figure 3-22. Sample Sizes for Each NCSU Mode for Each Odometer Reading and Engine Displacement Strata.
                                                       44

-------
After defining the 14 modes shown in Table 3-6, unsupervised HBTR was applied to data for
each pollutant and each mode to identify vehicle characteristics useful in further explaining the
variability in the emission rate. The vehicle characteristics considered included net weight,
number of cylinders, odometer readings and engine displacement. Tables 3-7 through 3-10
summarize which variable was chosen for the first, second, and third cut-points in the regression
tree and also display the numerical values of the cut-offs.

There is variation regarding which variables were selected for the first stratification of the data,
implying that the choice of a preferred explanatory variable is conditional on the mode.
However, since the objective of this work is to develop modes that are both technically rigorous
but also sufficiently simple for practical application, it is preferred to identify one explanatory
variable that works well for all modes. In reviewing the results of Tables 3-7 through 3-10, it is
apparent that the odometer reading is typically the most frequently selected variable for use in
the first stratification of the data. The second most frequently selected variable for the first cut-
point is the net vehicle weight. Odometer reading and net vehicle weight are also frequently
selected as the basis for the second and third cut-points. These results suggest that both
odometer reading and net vehicle weight are important variables. Therefore, both variables were
selected as the basis for further refinement of the modal definitions.

The selection of specific cutpoint values for odometer reading and net vehicle weight was made
based upon judgment. The specific cutoffs from the HBTR analysis are different for different
modes and pollutants. However, in order to keep the modal definitions as simple as possible,
only one representative cutpoint was selected for each variable. The cutpoints for odometer
readings obtained from HBTR range from typically 12,000 to 80,000 miles. However, many
values are within a range of plus or minus 15,000 miles compared to a chosen cutpoint of 50,000
miles. The cutpoint of 50,000 miles was selected because it is representative of results from the
statistical analysis and is consistent with previous cutpoints used in other modeling work. For
net vehicle weight, a representative cutpoint of 3,500 pounds was selected, which is
representative of many of the cutpoints in the range of 3,300 to 3,800 pounds identified in the
statistical analysis.

Using the same modal definitions as given in Table 3-6, the data were further binned into four
categories:

Net Weight <= 3,500 pounds AND Odometer Reading <= 50,000 miles
Net Weight <= 3,500 pounds AND Odometer Reading > 50,000 miles
Net Weight > 3,500 pounds AND Odometer Reading <= 50,000 miles
Net Weight > 3,500 pounds AND Odometer Reading > 50,000 miles

A comparison of average modal emission rates for these four categories is given in Figures 3-23,
3-24, 3-25, and 3-26 for CO, HC, NOx, and CO2 emissions, respectively. The figures suggest
that at least for some pollutant/mode combinations that average emissions for these four
categories are statistically significantly different from each other (e.g., NO emissions for
acceleration modes 21, 22, 23, 24, and 25). In some cases, there is more sensitivity to odometer
45

-------
Table 3-7. Unsupervised HTBR Regression Tree Results for CO Emissions Based Upon the
                                 NCSU Modal Approach.
Mode
1 (Idle)
3 (Deceleration)
21 (Acceleration)
22
23
24
25
26
41 (Cruise)
42
43
44
45
46
1st Cut point
Net 3328
E 4.1
O 75432
O 66163
O 43433
E3.9
Net 3 5 87
O 43433
O 15210
O 15215
E3.45
E3.45
Net 3659
O 79022
2nd Cut point
O 79901
N5
O 15210
O 15210
O 15251



O 12798
O 12789
N5
N5
N5
O 50177
3rd Cut point
Net 3482
O 17783
O 12325

O 71964



O 75432
O 56637
O 20892
Net 2862


Table 3-8.  Unsupervised HTBR Regression Tree Results for NOx Emissions Based Upon the
                                 NCSU Modal Approach.
Mode
1 (Idle)
3 (Deceleration)
21 (Acceleration)
22
23
24
25
26
41 (Cruise)
42
43
44
45
46
1st Cut point
N5
O8785
O 58057
O 66163
O 63341
O 58560
O 58057
O 58057
O 71964
Net 3611
O 17220
O 17220
O 38353
O 83490
2nd Cut point
O 60158

O 29057
O 38353
O 22195
O 12800
Net 28 13
Net 2550
E0.75
O 57695
E3.05
O 11493
E3
O 61024
3rd Cut point
E3.45
E3.45
E2.75
O 45900
O 43433
Net 3486
E2.3

Net 3754
E4.45

Net 2531
O 83491

 Note: "Net" means "Net Vehicle Weight (Ibs)", "O" means "Odometer Reading (miles)",
 "N" means "Number of cylinders", "E" means "Engine Displacement (liters)". The number
 following the variables is the value of the cut point.
 Results are not shown in cases where sample size was small
                                      46

-------
 Table 3-9. Unsupervised HTBR Regression Tree Results for HC Emissions Based Upon the
                                 NCSU Modal Approach.
Mode
1 (Idle)
3 (Deceleration)
21 (Acceleration)
22
23
24
25
26
41 (Cruise)
42
43
44
45
46
1st Cut point
O 79022
O 74867
O 79022
O 74867
O 77495
O 43437
O 43433
O 45900
O 79022
O 77495
O 77495
O 77495
O 77495
Net 43 75
2nd Cut point
O 48626
E5.3
O 37236
O 37238
O 37326
Net 25 86
Net 2967
E2.75
E5.3
Net 3611
O 29949
O 79022
O 26082
O 43433
3rd Cut point
O 98129
Net 3613
O 48465
O 48465




O 10110
E4.9



O 90660
Table 3-10.  Unsupervised HTBR Regression Tree Results for CO2 Emissions Based Upon the
                                 NCSU Modal Approach.
Mode
1 (Idle)
3 (Deceleration)
21 (Acceleration)
22
23
24
25
26
41 (Cruise)
42
43
44
45
46
1st Cut point
N5
Net 3264
O 43433
O 43433
Net 3724
Net 3724
Net 3724
E2.1
Net 3034
Net 3551
E2.45
Net 3724
Net 3724
Net 3724
2nd Cut point
Net 2454
O 25347
E3.45
El. 55
O 4403 5
E1.95
E2.1
O 55582
Net 2246
Net 2788
Net 2983
E1.95
O 45900
Net 2446
3rd Cut point

E3.45
N5
Net 3284
Net 3 568
Net 2688
O 22358

El
E2.5
Net 3626
O 45900
O 37236

  Note: "Net" means "Net Vehicle Weight (Ibs)", "O" means "Odometer Reading (miles)",
  "N" means "Number of cylinders", "E" means "Engine Displacement (liters)". The number
  following the variables is the value of the cut point.
  Results are not shown in cases where sample size was small
                                       47

-------

-------
       10 -i
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  ta
  u>
  'E
  o
  O
  O
0.1 -
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    0.001
                Mode 1: Idle
                Mode 2: Deceleration
                Modes 21-26: Acceleration
                Modes 41-46: Cruise
                                                                    DNet_Weight<=3500 & Odometer< = 50000

                                                                    SNet_Weight>3500 & Odometer<=50000

                                                                    ^Net_Weight<=3500 & Odometer>50000

                                                                    ^Net_Weight>3500 & Odometer>50000
                           21
                             22
23
24
25      26
NCSU  Mode
41
42
43
44
45
46
Figure 3-23.  Average CO Emissions (g/sec) For the NCSU Idle, Deceleration, Acceleration, and Cruise Modes By Vehicle Weight
                               and Odometer Reading Based Upon the Modeling Database.
                                                       49

-------
         1 -I
       0.1 -
  in
  3500  & Odometer<=50000

                                                                      INet_Weight< = 3500 & Odometer>50000

                                                                      INet_Weight>3500  & Odometer>50000
                                                                           i
                            21
                              22
23
24
25      26
NCSU  Mode
41
42
43
44
45
46
Figure 3-24. Average HC Emissions (g/sec) For the NCSU Idle, Deceleration, Acceleration, and Cruise Modes By Vehicle Weight
                               and Odometer Reading Based Upon the Modeling Database.
                                                        50

-------
          1 -I
        0.1 -
       0.01 -
  in
      0.001 -
     0.0001 -
    0.00001
                    Model: Idle
                    Mode 2: Deceleration
                    Modes 21-26:  Acceleration
                    Modes 41-46:  Cruise
                        • Net_Weight<=3500 & Odometer< = 50000

                        [m!!Net_Weight>3500 & Odometer<=50000

                        ^Net_Weight<=3500 & Odometer>50000

                        ^Net_Weight>3500 & Odometer>50000
                                    22      23
24
 25      26
NCSU  Mode
41
42
43
44
46
Figure 3-25.  Average NOX Emissions (g/sec) For the NCSU Idle, Deceleration, Acceleration, and Cruise Modes By Vehicle Weight
                               and Odometer Reading Based Upon the Modeling Database.
                                                        51

-------
    100 -i
     10 -
  1/1
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  O
  O
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     0.1
               Model: Idle
               Mode 2: Deceleration
               Modes 21-26: Acceleration
               Modes 41-46: Cruise
                                        • Net_Weight< = 3500 & Odometer<=50000

                                        ls!Net_Weight>3500 & Odometer<=50000

                                        ^Net_Weight< = 3500 & Odometer>50000

                                        ^Net_Weight>3500 & Odometer>50000
                           21
22
23
24
25      26

NCSU  Mode
41
42
43
44
45
46
Figure 3-26.  Average CC>2 Emissions (g/sec) For the NCSU Idle, Deceleration, Acceleration, and Cruise Modes By Vehicle Weight
                               and Odometer Reading Based Upon the Modeling Database.
                                                        52

-------
reading than vehicle weight. For example, for HC cruise modes, vehicles with higher odometer
readings have higher emissions than those with lower odometer readings, and average emissions
for a given odometer reading are similar for the two net weight categories. In contrast, for NOX
emissions, it appears that older higher mileage vehicles generally have higher modal emission
rates than for the other three categories. However, there are also many specific comparisons that
are not statistically significantly different from each other. For example, for CO emissions the
average acceleration modal emissions rates for higher mileage vehicles are similar regardless of
vehicle weight. Thus, although the specific trends are different for different pollutants, and
although in some cases there are not significant differences among the two or more of the four
categories for a given pollutant/mode, the results suggest that there are observable differences for
many pollutant/mode combinations. Therefore, these categories may be useful in explaining
variability in emissions.

3.4 Selection of a Binning Method
The VSP and NCSU binning approaches were compared and evaluated. The criteria for
evaluating the two approaches included the utility of each method to explain variability in
emissions, the ease of development of the bins, the interpretation of the bins, the ability to
explain the approach to model developers and users, and design issues for future model
development. The choice of a preferred binning approach was made based upon the application
of both approaches to the same data sets.

A comparison of predictions made with both the NCSU-based and VSP-based approaches was
developed by using both approaches to predict the average emissions for driving cycles in the
modeling database for which there were ten or more vehicles. The comparison is shown in
Figure 3-27. The average prediction and the 95 percent confidence interval for the average
prediction is shown for each method and for each driving cycle. The 95 percent confidence
intervals of the mean predictions overlap for all of the cycles and for all pollutants, indicating
that there is no statistically significant difference in predictions for the two methods.

The development of the bins is similar for both methods. The interpretation of bins is different
for the two methods, with the NCSU approach being more intuitive to a lay person and the VSP
approach being consistent with approaches used in a variety of analyses of vehicle emissions.
The NCSU approach produces some bins that have similar average emission rates, even though
they represent different activities. For example, the lower emission acceleration and cruise
modes have similar emissions. Although neither method clearly stands out when compared to
each other, the VSP approach was selected as the basis for further analysis.
53

-------

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Figure 3-27. Comparison of VSP and NCSU Approach-Based Predictions of Average Emissions of CC>2, CO, HC, and NOX for
                             Selected Driving Cycles for Vehicles in the Modeling Database.
                                                         54

-------
4 SELECTION OF AN AVERAGING TIME FOR MODEL DEVELOPMENT

The objective of this chapter is to evaluate the potential benefits of working with data that have
been averaged over time when developing bins/modes. The effect of data smoothing on binning
was determined by comparing the bins developed with data averaged over one second to those of
longer periods. For this purpose consecutive averaging of 5 and 10 seconds was utilized and
compared with each other and with the use of 1 second data.

4.1 Methodological Approach
As part of the shootout, NCSU found that there is autocorrelation in the second-by-second on-
board tailpipe emissions data (Frey et a/., 2002). In most cases, the autocorrelation was found to
be represented by a lag of up to four or five seconds. Therefore, an averaging time of five
seconds should be sufficient to decrease the autocorrelation in the data by smoothing with
consecutive averaging. However, to provide some margin for variability in the autocorrelation,
an averaging time of 10 seconds was also evaluated. It was hypothesized that this longer
averaging time should further smooth the data and remove some of the high frequency variability
in the data.

In order to determine 5 and 10 second averages based upon the second-by-second data, a
program was written in Visual Basic. This program estimated 5 and 10 second consecutive
averages for emissions, as well as vehicle activity data, such as vehicle speed and acceleration.
In addition to estimating average vehicle activity during each activity period, peak values of
vehicle activity were estimated. For example, it was hypothesized that emissions are more
sensitive to peak accelerations or peak VSP within an averaging period than they would be to
average acceleration or average VSP.

The use of averaging times requires reconsideration of the approach for developing bins. For
example, data can be binned by average VSP or by peak VSP during the 5 or 10 second
averaging time. It is possible, for example, for a 10 second period to have an average
acceleration of, say, only 1 mph/sec but to have a peak acceleration of, say, 5 mph/sec that took
place for a short duration. The short duration, high acceleration that took place within the 10
second averaging period may in fact be associated with the largest share of emissions that took
place during the averaging time. Therefore, it may be more effective to use the peak values of
key variables, such as VSP or power demand, as a basis for binning the data, rather than using
average values of these.

The basis for selection of a preferred averaging time was based upon the presence of statistically
significant differences in average emissions among modal bins and explanatory power of the
overall modal model. In addition, approaches that resulted in less variability in emissions within
a bin would typically be preferred over approaches that have more variability in emissions within
a bin.

4.2 Results for Five and Ten Second Averaging Times
The assessment of different averaging times was performed for the VSP-based approach
identified as the preferred modeling approach in Chapter 3. For the five and ten second-averaged
data, unsupervised HBTR was applied to the data sets for each pollutant. The variables used in
55

-------
the regression tree include mean speed, maximum speed, standard deviation of the speed, mean
acceleration, maximum acceleration, standard deviation of the acceleration, mean VSP,
maximum VSP, standard deviation of VSP, mean power, maximum power and standard
deviation of power. It should be noted that there is positive dependence between VSP and power.

Table 4-1 summarizes the variables that were picked during the unsupervised application of
HBTR for the first three cut points. Maximum VSP and maximum power were frequently
selected as the most important variables. Since VSP includes power as part of the estimate, these
two variables are closely related to each other. Therefore, for simplicity and consistency with
the one second averaging time analysis, VSP was chosen as the representative variable for
developing modes, and maximum VSP was selected as the specific criteria to use in defining
modes.  The approach for defining modes using a supervised technique is the same as previously
described, based upon seeking modes with average emission rates that differ from each other and
that do not contribute more than about 10 percent to total emissions for any individual pollutant.
A total of 14 modes were defined for both 5  and 10 second-averaged data, as given in Tables 4-2
and 4-3, respectively. The time spent in each mode and the percentage of total database
emissions contributed by each mode for 5 and 10 second-averaged data are given in Figures 4-1
and 4-3, respectively. Similarly, the average modal emission rates for each mode for all four
pollutants are given in Figure 4-2 for the 5-second average data and in Figure 4-4 for the 10-
second average data.

The sample sizes for the  1-second, 5-second, and 10-second averaging times for each of the 14
modes are compared in Figure 4-5. Because the modal definitions are different for each of the
three approaches, it is not expected that there is a proportional distribution of data among the
modes when comparing the approaches.  However, it is the case that the total sample size
summed over all 14 modes for the 5-second averaging time is approximately one-fifth that of the
1-second averaging time, and similarly for the 10-second averaging time the overall sample size
is approximately one-tenth that of the 1-second  averaging time.

  Table 4-1. Key Explanatory Variables for CO, NOx, HC, and CO2  Emissions (g/sec) Identified
                 Using Unsupervised HBTR for Five and Ten Second-Averaged Data

5 Seconds Average for CO
10 Seconds Average for CO
5 Seconds Average for NOX
10 Seconds Average forNOx
5 Seconds Average for HC
10 Seconds Average for HC
5 Seconds Average for CO2
10 Seconds Average for CO2
1st Cut Point
Maximum Power
Maximum Power
Maximum VSP
Mean VSP
Maximum Power
Maximum Power
Mean VSP
Mean VSP
2nd Cut Point
Maximum VSP
Maximum VSP
Maximum VSP
Maximum VSP
Maximum VSP
Maximum VSP
Maximum VSP
Maximum VSP
3rd Cut Point
Mean VSP
Maximum Speed
Mean Power
Maximum Power
Maximum Power
Mean Power
Mean VSP
Mean VSP
                                          56

-------
Table 4-2. Maximum VSP-Based Mode Definitions For Five Second-Averaged Data
ID
1
2
O
4
5
6
7
8
9
10
11
12
13
14
Definition
MaxVSP <0
0 < MaxVSP < 2
2 < MaxVSP < 6
6 < MaxVSP < 9
9 < MaxVSP < 12
12 < MaxVSP < 15
15 < MaxVSP < 18
18 < MaxVSP < 21
21 < MaxVSP < 25
25 < MaxVSP < 29
29 < MaxVSP < 34
34 < MaxVSP < 38
38 < MaxVSP < 42
MaxVSP > 42
Table 4-3.  Maximum VSP-Based Mode Definitions For Ten Second-Averaged Data
ID
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Definition
MaxVSP < 1
1 < MaxVSP < 6
6 < MaxVSP < 9
9 < MaxVSP < 12
12 < MaxVSP < 15
15 < MaxVSP < 18
18 < MaxVSP < 21
21 < MaxVSP < 24
24 < MaxVSP < 27
27 < MaxVSP < 31
31 < MaxVSP < 35
35 < MaxVSP < 39
39 < MaxVSP < 43
MaxVSP > 43
                                  57

-------
     30
     20
     10
       0
                 Time
                 CO
                 NO
                 CO2
                 HC
                                                                        10
11
12
13
14
Figure 4-1.  Percent of Time Spent in Five Second Averaging Time Maximum VSP-Based Modes and Percentage of Total CO, NOX,
                 CC>2, and HC Emissions Attributable to Each Mode, Based Upon the Modeling Data Set.
                                                   58

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Figure 4-2.  Five Second Averaging Time Modal Emission Rates (g/sec) for Maximum VSP Bins for CO, HC, CC>2, and NOX Based
                                             Upon the Modeling Dataset.
                                                         59

-------
     30  -i
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                 CO
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                 CO2
                 HC
                                                                        10
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Figure 4-3.  Percent of Time Spent in Ten Second Averaging Time Maximum VSP-Based Modes and Percentage of Total CO, NOX,
                 CC>2, and HC Emissions Attributable to Each Mode, Based Upon the Modeling Data Set.
                                                   60

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Figure 4-4.  Ten Second Averaging Time Modal Emission Rates (g/sec) for Maximum VSP Bins for CO, HC, CC>2, and NOX Based
                                             Upon the Modeling Dataset.
                                                        61

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                                                                             D5 Second
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Figure 4-5.  Comparison of Sample Sizes for 1 Second, 5 Second, and 10 Second Averaging Time-Based Modes Estimated From the
                                            Modeling Data Set.
                                                  62

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The results share many qualitative similarities compared to the analysis of 1-second data shown
previously. For example, the contribution to total CO emissions is larger for the high maximum
VSP modes (e.g., Modes 10, 11, 12, 13, and 14) than the contribution to total emissions of other
pollutants. For modes that are based only upon positive maximum VSP, the average emission
rates increase from one mode to the next as average VSP increases, for all pollutants and for both
averaging times. The range of variability when comparing the mode with the largest average
emission rate to that with the lowest average emission rate is similar for all of the averaging
times for a given pollutant. Some of the differences that are apparent as the averaging time is
increased is that there is less specific treatment of negative VSP cases and that the average
emissions for Mode 14 for either the 5-second or 10-second averaging times are typically the
same as or perhaps even a little less than that for Mode 13. The lack of a monotonic increase
when comparing Modes 13 and 14 could be attributable in part to small sample sizes for these
two modes, but also could be attributable to the effects of averaging - for example, perhaps there
is less homogeneity in the data of Mode 14 than for other modes.

4.3 Evaluation of Different Averaging Times and Recommendations
Predicted versus actual emissions for individual trips/cycles in the modeling database were
evaluated for each of the three averaging times as a consideration to help in selecting a preferred
averaging time. For that purpose predictions for Modeling dataset are compared for the three
averaging time methods. As seen in Figure 4-6, predictions with all three averaging methods are
similar. The 95 percent confidence intervals overlap for almost all of the cycles, for all
pollutants. Overall, all three averaging times yield qualitatively similar results. Thus, it is not
readily evident that one is clearly superior to another.

The five and ten second averaging times were found to offer no advantage over the one second
averaging time in terms of predictive ability with respect to total emissions for a trip. Because it
is easier to work directly with the one second average data, the one second averaging time
approach was selected.
63

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 100000
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                                                                            D 10 Seconds
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Figure 4-6. Comparison of Predicted Average Emissions of CC>2, CO, HC, and NOX for Selected Driving Cycles Based Upon 1
           Second, 5 Second, and 10 Second Averaging Time VSP Binning Approaches for the Modeling Database.
                                                              64

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5 COMPARISON OF EMISSION FACTOR APPROACHES AND EVALUATION OF
THE ROLE OF REMOTE SENSING DATA

In this chapter, two different approaches to developing emission factors are compared and
evaluated. The objective of this chapter is to develop a recommendation for a preferred emission
factor approach, in response to the fifth key question of: what emission factor units should be
used?. The two approaches evaluated include mass per time emission factors (e.g., gram/second)
and the ratio of emissions of CO, HC, and NOX with respect to CC>2. The latter was based upon
evaluation of the molar ratio of CO/CO2, HC/CO2, and NOX/CO2. Since most of the carbon in
the fuel is emitted in the form of CC>2, the ratio approach is approximately equivalent to a gram
per gallon emission factor approach. Previous studies by others (e.g,. Singer and Harley, 1996)
have touted the potential benefits of a fuel-based approach to development of area-wide emission
inventories. However, such inventories are macro-scale in nature and would require a
representative average gram per gallon emission factor combined with good estimates of total
area wide fuel consumption. For meso-scale or micro-scale predictions, it will be necessary to
estimate emissions at a more local scale. In such instances, an understanding of the influence of
different driving modes on emission ratios is critically important. Furthermore, in order to
predict mass emissions using emission ratios, it is necessary to be able to predict mass per time
CC>2 emission rates or mass per time fuel consumption.

Since one motivation for considering emission factors is potentially to facilitate accommodation
of remote sensing data, this chapter also deals with an evaluation of the relevance of remote
sensing data for model development. The evaluation is based upon comparison of modal
emission rates calculated based upon remote sensing data and compared with those calculated
from on-board measurements and dynamometer tests. Therefore, this chapter also addresses the
motivating question: What is the potential role and feasibility of incorporating RSD into the
conceptual modeling approach?

5.1 Background Regarding Emission Factor Units
Some investigators hypothesize that gram/gallon emission factors have less inherent variability
than do mass per time or mass per distance emission factors. NCSU is currently conducting an
independent study of this hypothesis, based upon analysis of on-board second-by-second data
collected as part of a previous study (Frey et a/., 2001). Our preliminary findings do not fully
support the hypothesis. As an example, we illustrate results for modal analysis of gram per
second and gram per gallon emission factors for NO for a 1999 Ford Taurus in Figure 5-1. The
gram per gallon emission factors are approximately equivalent to the ratio of NO to CO2
emissions, since CO2 emissions are linearly proportional to fuel consumption to a very good
approximation. In this case, there is significant variability in emissions among the four driving
modes considered regardless of the emission factor units employed. For example, as shown in
Figure 5-1, the average acceleration emission rates are approximately a factor of 10 or more
greater than average idle emission rates for both emission factor units. Thus, it is clearly not the
case in this instance that emission ratios or g/gallon
65

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            10 q
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                                Site:     Chapel h
                                Vehicle: 1999 Ford
                           _              Taurus
                                n:        141
           0.1 -
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                         Grams/Gallon
                II Rd.
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 Figure 5-1. Average Modal Rates for Absolute and Normalized NO Emissions for a 1999 Ford
              Taurus Driven on Chapel Hill Road in Gary, NC (Source: NCSU)

emission factors have substantially less variability from one mode to another than do mass per
time emission factors. The results tend to vary for different vehicles and for different pollutants
based upon our preliminary study. For example, the g/gallon emission factors for HC may be
more nearly similar for different driving modes than the g/gallon emission factors for CO or NO.
CO2 emissions are almost constant regardless of the driving mode; however, this is because the
vast majority of carbon in the fuel is emitted as CO2. Thus, a g CO2/gallon emission factor is
essentially a surrogate for the carbon content of the fuel.

Even if g/gallon emission factors are the same for different driving modes, the fuel  consumption
rate is not.  Figure 5-2 illustrates the variability in fuel consumption rate on a mass  per time basis
as a function of different driving modes.  For example, the average fuel consumption rate during
acceleration mode is approximately a factor of five times greater than that during the idle mode,
and the average differences in fuel consumption rate among the modes are statistically
significant.

5.2    Background Regarding Remote Sensing Data
There are two critically important limitations of RSD data that must be acknowledged: (1) RSD
data are for a very short averaging time of approximately 1 second, with no information
regarding vehicle  activity and emissions either before or after the "snapshot" of the
measurement; and (2) RSD data support estimation of relative emission rates (e.g.,  ratios of
HC/CO2 and NO/CO2 or similar), or fuel-based emission rates (e.g., g/gallon), but cannot
directly provide g/mile or g/sec emission rates.  Secondly, one would need to estimate fuel
consumption or CO2 emissions on a mass per time basis in order to convert all other g/gallon or
                                           66

-------
ratio emission estimates to a mass per time basis. RSD data will not provide a basis for
estimating CC>2 emissions on a mass per time basis or for estimating fuel economy in order to
estimate gallon/sec fuel consumption.

Before combining RSD data with second-by-second data, it is first important to determine
whether RSD data and the second-by-second data are sufficiently consistent that a combination
of the two would be meaningful. This comparison is possible if the second-by-second data are
converted to the same basis as the RSD data. Therefore, as part of the evaluation of RSD data,
modal emission rates were calculated based upon RSD data using the modal definitions that were
applied to the modeling dataset, but taking into account the inability to stratify RSD data with
respect to odometer reading. We hypothesize that relative differences in average emission rates
among the RSD-derived estimates should be similar to those observed based upon the second-
by-second data sources. If not, then there may be some significant discrepancy in the data
sources that would caution against combining the RSD data into the model development process.

A key limitation of RSD data is that it is essentially a one second (or shorter) snapshot of
emissions at a specific location. Therefore, there is no vehicle history available from which to
estimate modal emission rates for an averaging time greater than one second. The range of inter-
vehicle variability and the range of uncertainty in average modal emissions estimated based upon
RSD data were also evaluated. For example, if the RSD data were excessively noisy (high
variability) then it may not be useful as a supplement to other data sources in developing the
modal.

The appropriateness of using RSD data for developing the model depends on what type of
weighting scheme is preferable. If a time-based weighting scheme is selected, then RSD data
will likely contribute only modestly to the estimation of average emissions within a bin, because
of the short duration of the RSD measurements. If a vehicle weighted approach is selected, then
RSD data will contribute disproportionately to the estimation of average emissions, because it is
possible to obtain measurements on thousands of vehicles per day using RSDs, but each
measurement is for less than one second (typically).

The two emission factor approaches were compared and evaluated based upon the following
criteria: (1) which approach results in a "simpler" model; (2) which approach is best able to
explain variability in emissions; (3) which approach has the least amount of residual error; (4)
which approach can best support model verification or validation; and (5) which approach offers
the most flexibility. The comparison of mass per time factors versus ratios was performed for
both the NCSU and VSP based approaches, and results for both approaches are presented. In
addition, the modal emission rates of both approaches were compared with those estimated from
RSD data. Because RSD data are based upon measurements made during less than one second,
the comparison of mass per time emission factors and emission ratios was done based only upon
the one second averaging time for the modeling database.
67

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                                                   Site:    Chapel Hill Rd.
                                                   Vehicle: 1999 Ford
                                                             Taurus
                                                   n:         141
 Figure 5-2.  Average Modal Rates for Absolute Fuel Consumption for 1999 Ford Taurus Driven
                          on Chapel Hill Road (Source: NCSU)

5.3    Comparison of Emission Factors and Emission Ratios Based Upon the NCSU Modal
       Approach
The NCSU modal definitions were applied to emission ratios calculated from the modeling
dataset. The results when applied to mass per time emission factors were previously described.
To compare with remote sensing data, the emission rates in the modeling dataset were converted
to molar ratios with respect to CC>2.  Specifically, the emission rate in g/sec was divided by the
molecule weight of the pollutant to get the emission rate in mole/sec, and was further divided by
the CC>2 emission rate in mole/sec. The molecular weight used for the HC emission rate is
assumed to be as hexane (CeH^).  Figure 5-3  gives the comparison between the modeling dataset
and remote sensing data for each NCSU mode for each pollutant.
                                          68

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                                           and Remote Sensing Data
                                                     69

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The average emission rates for the NCSU modal bins have a different sensitivity when evaluated
in terms of emission ratios compared to the previously described analysis in terms of grams per
second. For example, for the CO/CO2 ratio, there is relatively little sensitivity to the mode
definitions applied to the calibration data set when comparing the deceleration and cruise modes.
Idle is not shown because idle cannot be observed with the RSD database. However, for the
acceleration modes, and particularly Modes 23, 24, 25, and 26, there is a substantial increase in
the CO/CO2 ratio as VSP increases. Similar results are observed for the HC/CO2 ratios based
upon the calibration data set. However, for the NO/CO2 ratio, the results for the calibration data
set are qualitatively similar to those obtained for the gram/second emission factor units.
Specifically, emissions for deceleration (Mode 3) are comparatively low. Within the
acceleration mode, the emissions ratio increases as VSP increases, when comparing Modes 21
through 26. For the cruise mode, the emissions ratio increases with average speed among the
three low VSP modes (Modes 41, 42, and 43) and with VSP for the three high VSP modes
(Modes 44, 45, and 46). The results obtained with the second-by-second data help set
expectations for trends that would be expected in the RSD data set.

The results from analysis of the RSD data are qualitatively different from those obtained with the
calibration database, in at least two key respects. First, the trend for inter-modal variability in
emissions is very different for the RSD data than for the calibration database for both NOX and
HC. Specifically, there is much less variability when comparing the lowest and highest average
modal rates and the trends when comparing modes are either not as strong or are not apparent at
all. For example, for the RSD HC/CO2 ratios, there is little apparent sensitivity to VSP among
the acceleration modes, in contrast to the observation based upon the calibration database. The
average NOX/CO2 ratios estimated based upon RSD data are less sensitive to changes in VSP for
the acceleration modes, and to changes in speed and VSP for the cruise modes, than the
calibration data. Because RSDs measure HC using NDIR, it may be the case that the RSD
measurements are not responding to total HC and that the ratio of measurable HC to total HC
might vary depending on the mode. For the NOX/CO2 ratio, there has been discussion in the
literature and elsewhere to the effect that RSDs have less sensitivity to NOX than to
measurements for other pollutants; however, it is not known if this is an important factor in this
particular case.

The trends for the CO/CO2 ratio from the RSD data are more comparable to those from the
calibration data compared to the other two pollutants; however, the magnitude of the average
CO/CO2 emission estimates for the three highest VSP acceleration modes is substantially less
than that for calibration data set. This might be because of differences in the vehicle mix;
however, the RSD data used for this analysis is based upon Tier 1 vehicles, as is the calibration
data set. It is possible, perhaps, that there is a different mix of mileage accumulation or other
factors; however, since the average emission rates differ by a factor of two, and each average is
based upon a fairly large sample size, it could be the case that there are differences in the
estimates because of differences in the measurement techniques. It is possible that the RSD data
may contain a better representation of high emitting vehicles, or of high emissions episodes for
normal emitting vehicles, than does the modeling data set. These questions are revisited in the
next sections based upon comparison of emission ratios for the VSP-based approach using both
the modeling data set and the RSD data.
70

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5.4    Comparison of Emission Factors and Emission Ratios Based Upon the VSP Modal
       Approach
Emission ratios were estimated for the 14 VSP modes based upon the modeling data set and were
compared with modal emission ratios estimated from the RSD data, as shown in Figure 5-4.

The results for the emission ratios estimated based upon the modeling data set indicate that for
the CO/CO2 ratio there is relatively little sensitivity of the ratios for the low VSP modes,
including Modes 1 through 10. However, for the high VSP modes, the emission ratios increase
substantially with VSP. An almost similar trend is observed for the HC/CO2 ratio, with the
exception that Mode 3 has a higher average emission rate than the other low VSP modes.  For
the NOX/CO2 ratio, the relative trend among the average emission ratios for each mode is very
similar to that observed for the mass per time emission rates.  For example, there is a monotonic
increase in the average NOX/CO2 emissions ratio from Mode 3 through Mode 14. These results
illustrate that in order to capture variability in NOX emissions  with a model, it would be
necessary to retain approximately the same number of modes  as for the mass per time emission
factor approach. Because the implementation of a modal modeling approach is simpler from  a
software design and data management perspective if the same modal definitions are used for all
pollutants, the ability to capture variability in NOX emissions would be binding constraint
regarding a lower bound for the number of modes needed.  Thus, even though it might be
possible to have far fewer than 14 modes to adequately capture variability in CO and HC
emissions, a reduction in the number of modes applied to all pollutants would result in loss of
explanatory power for NOX.

The comparison of RSD data with the results from the modeling data set illustrates important
similarities and important differences. The key similarities are the following: (1) the average
CO/CO2 ratios are relatively small for the 10 lowest VSP modes; (2) the average CO/CO2 ratios
increase monotonically for the four highest VSP modes; and (3) the average emission ratios
agree well between the two data sources for both NOX/CO2 and HC/CO2 for Modes 12 and 13.
The key differences are: (1) there is generally less variability among the average modal emission
ratios for the RSD data than for the modeling data set; (2) the RSD data produces lower average
ratios for CO/CO2 for Modes 13 and 14; and (3) the RSD data produces much higher average
ratio estimates for both HC/CO2 and NOX/CO2 for the low VSP modes.  These differences could
be because of a different combination of fuel, vehicle characteristics, and odometer reading
(which is unobservable with RSD technology) between the two data  sets.  Presumably, the RSD
would contain better representation of on-road high emitters, and possibly such vehicles lead  to
higher emissions for the lower VSP modes more so than for the higher VSP modes.  Thus, at
best, the comparison is inclusive. However, it is not possible  to stratify the RSD by odometer
reading, which complicates the ability to refine the comparison.

In the next sections, the activity underlying the RSD data is compared to that of the modeling
data set and of the IM240 data set to obtain additional insights regarding key differences between
the RSD data and the modeling data set.
                                          71

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                                                        72

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                                                         73

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-------
5.5 Comparison of Variability in Emission Ratios for Selected VSP Bins for the
Modeling and RSD Data Sets
In this section, the variability in emission ratios for selected modes is compared for both the
modeling and RSD data sets in order to evaluate the characteristics of the RSD data. Since
odometer reading is not given in the remote sensing data, it is not possible to stratify the data by
odometer reading. However, engine displacement is available in the RSD data. Therefore, the
comparison is based upon the 14 VSP modes stratified by two engine displacement categories
with a cutpoint of 3.5 liters. Examples are shown here for three selected modes based upon
engine displacements of less than or equal to 3.5 liters.

For VSP Mode 1, a comparison is shown in Figure 5-6 of the distribution of variability for
second-by-second data of the modeling dataset and of the data in the RSD data set. Mode 1 is
based upon negative values of VSP. For both the CO/CO2 and NOX/CO2 ratios, the RSD data
generally produces higher values than does the modeling data set. Although not shown as data
values in the graphs because a log scale was used for the x-axis, the modeling data set contained
data values of less than zero, which are considered to reflect measurement error and not to be
significantly different than a true value of zero or just slightly greater than zero. For the HC/CO2
ratio, the RSD data produced a distribution with less variability than the modeling data set. Most
of the data in the modeling data set are based upon FID measurements, in comparison to the
NDIR method used in remote sensing. Therefore, the difference in the shape of the distributions
from the two datasets may reflect differences attributable to the measurement methods.
Figure 5-6. Comparison of Variability for CO/CO2, HC/CO2, and NOX/CO2 Ratios for Modeling
Data and Remote Sensing Data for VSP Mode 1 with Engine Size Less Than 3.5 Liters
75

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Figure 5-7. Comparison of Variability for CO/CO2, HC/CO2, and NOX/CO2 Ratios for Modeling
Data and Remote Sensing Data for VSP Mode 7 with Engine Size Less Than 3.5 Liters

Figures 5-7 and 5-8 show comparisons of the variability in emission ratios for Modes 7 and 12,
respectively. For the CO/CO2 and NOX/CO2 ratios, the general trends are similar to that for
Mode 1 in that the average value of the RSD data is generally larger than that of the modeling
data set. Furthermore, the entire distribution of ratios for the RSD data is toward larger values
for most of the percentiles of the distribution, when compared to the modeling data set.
However, the modeling data set typically captures a wider range of variability than the RSD data,
as indicated by comparing the range from the lowest to the highest values of the distributions.
For example, the modeling data typically span three to five orders of magnitude, whereas the
RSD data typically span approximately two to three orders of magnitude in most cases. The
upper tails of the emission ratio distributions are comparable for Modes 1 and 7 for both the
CO/CO2 and NOX/CO2 ratios. For Mode 12, the upper tail of the RSD data distributions typically
have larger values than for the modeling data set.

For the HC/CO2 ratio, the results for Mode 7 are qualitatively similar to that for Mode 1. For
Mode 12, the modeling data set produced a higher average value of the HC/CO2 ratio compared
to the RSD data set. Typically, the RSD data produced a narrower range of values and smaller
values at the upper tail of the distribution when compared to the modeling data in the case of the
HC/CO2 ratio.

When comparing the three modes illustrated in Figures 5-6 through 5-8, it should be borne in
mind that the relative difference between the RSD data and the modeling data set decrease as the
76

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Figure 5-8. Comparison of Variability for CO/CO2, HC/CO2, and NOX/CO2 Ratios for Modeling
Data and Remote Sensing Data for VSP Mode 12 with Engine Size Less Than 3.5 Liters

VSP increases. For example, the distributions for the NOX/CO2 ratios for Mode 1 are more
separated from each other than is the case for Mode 12.

5.6 Comparison of Vehicle Activity in the RSD and Modeling Databases
For the CO/CO2 and NOX/CO2 ratios when compared for VSP modes, it is typically the case that
the RSD data produces larger average emission estimates and generally has higher emission
ratios than does the modeling data set. In order to gain insight into possible reasons for these
differences, the vehicle activity in the RSD data base was compared with that of the modeling
database. The comparison was done on the basis of the distribution of speed and acceleration
within specific modes. The comparison was done for selected modes for vehicles with engine
displacement less than 3.5 liters. Because odometer reading is unobservable for RSD
measurements, it was not possible to stratify the comparison with respect to odometer reading.
Three modes were selected for the comparison: (1) Mode 1 to represent low VSP values; (2)
Mode 7 to represent moderate VSP values; and (3) Mode 12 to represent large VSP values. The
cumulative distributions of both speed and acceleration, and the joint distributions of speed and
acceleration, are shown for both the modeling data and the RSD data in Figures 5-9, 5-10, and 5-
11 for VSP Modes 1, 7, and 12, respectively, for vehicles with engine displacement less than 3.5
liters.

For Mode 1, it is clear that the RSD data have less variability in speed than the modeling data.
Furthermore, the RSD data have a larger proportion of larger acceleration rates than the
77

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modeling data. Mode 1 is based upon VSP values of less than -2 kW/ton. Although the range of
VSP values in any individual bin is constrained by the definition of the mode, there are many
different combinations of speed and acceleration that can produce a narrow range of values of
VSP. For example, large magnitudes of deceleration at low speed can produce the same VSP
estimate as a small magnitude of deceleration at higher speed. When comparing the scatter plots
of acceleration versus speed for the modeling data set and the RSD data set, it is clear that the
modeling data set addresses a much wider range of combinations of acceleration and speed than
does the RSD data. Most of the RSD data are for decelerations of greater than -3 mph/sec and
for speeds between 20 mph and 40 mph, versus decelerations of typically -5 mph/sec or greater
and speeds ranging from approximately zero to greater than 70 mph. For this mode and strata,
the RSD data produced higher average emission ratios for all three pollutants. It is clear that the
range of activity for Mode 1 is very different for the RSD data compared to the remote sensing
data.

For Mode 7, the remote sensing data have a much narrower range of speeds, from approximately
20 mph to 40 mph, compared to the modeling data, for which speed varies from approximately
10 mph to over 80 mph. However, the RSD data typically have much larger values of
acceleration, with a range from approximately 1 mph/sec to as much as approximately 4
mph/sec. The modeling data set has a large proportion of acceleration data of less than 1
mph/sec, although the upper tail of the cumulative distribution of acceleration includes a small
percentage of values greater than 4 mph/sec. When comparing the scatter plots of acceleration
versus speed, it is clear that the modeling data set has a wider range of activity. The larger
average acceleration for the RSD data set is a notable difference compared to the modeling data
set, and may be a key reason as to why the emission ratios for the RSD data tend to be larger
than for the modeling data set.

For Mode 12, the modeling data set has a remarkably wider range of variability in speed than the
RSD data, but also has a noticeably lower average value of acceleration. The RSD data have
speeds ranging typically from approximately 25 mph to 50 mph, versus a range of approximately
20 mph to 80 mph for the modeling data set. The RSD data have accelerations ranging from 2
mph/sec to 4 mph/sec, compared to a range of approximately 0 mph/sec to 4 mph/sec for the
modeling data. A comparison of the scatter plots in Figure 5-11 suggests that the modeling data
capture a wider range of variability in activity, but have a much smaller proportion of activity
associated with larger accelerations when compared to the RSD data. Thus, it is likely that these
differences in activity account for at least some of the differences in emissions.

It should be pointed out that although the statistical analysis presented in Chapter 3 identified
VSP, engine displacement, and odometer reading as the three most important explanatory
variables, there may be opportunities to further disaggregate the data in the future when working
with larger data sets than the one used in this study. For example, as shown in Chapter 9, there
are some differences in average emissions for a VSP mode when taking into account differences
in speed and/or acceleration that might help explain additional variability not captured by the
model developed in Chapter 3.
78

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                         for VSP Mode 1 for Vehicles with Engine Displacement Less Than 3.5 Liters.
                                                            79

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                                                            80

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                                                            81

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5.7 Comparison of Emissions Ratios and Vehicle Activity Between the RSD and IM240
Databases
Because the RSD data are based upon observations of a large number of on-road vehicles, and
because the EVI240 are based upon a sample of on-road vehicles that is believed to better
represent high emitters than other data sets used in this study, it was hypothesized that there may
be similarities between the EVI240 dynamometer data and the RSD data. To explore this
hypothesis, the average modal emission ratios estimated from the two data sets were compared.
The comparison was stratified based upon engine displacement since information was available
in both data sets regarding this explanatory variable. The average emission ratios based upon
both data sets are shown in Figure 5-12 for vehicles with engine displacement of less than 3.5
liters and in Figure 5-13 for vehicles with engine displacement of greater than 3.5 liters.

Figure 5-12 illustrates a general similarity between the emission ratios estimated from the two
different datasets. Particularly in the case of the HC/CO2 ratios, for 9 of the 14 modes there is
not a significant difference in the average ratios when comparing the two datasets. Both datasets
imply high emission ratios for the low VSP modes, slightly lower emission ratios for the
moderate VSP modes, and relatively high values for Mode 13. In the case of the CO/CO2 ratios,
although only 5 of the 14 modes are statistically similar to each other, the qualitative trends for
both data sets are similar. In particular, the emission ratios for Modes 1 through 10 are relatively
constant for a given data set, but the average ratios increase substantially for Modes 11 through
13. Mode 14 tends to have somewhat lower values than does Mode 13. For the NOX/CO2 ratios,
the RSD data tends to have higher average values for the lowest VSP modes, and the EVI240 data
tends to have higher average values for Modes 5 to 14.

The comparisons in Figure 5-13 are less clear than those of Figure 5-12 mainly because there are
fewer data, particularly for the EVI240 database, that fall into this particular strata, and especially
for the high VSP modes (e.g., Modes 12, 13, and 14). The results suggest that there are
similarities in the two datasets for CO and NOX, except for the highest VSP modes, and that for
HC the RSD data typically have higher ratios than the EVI240 data except for Mode 1.

Overall, based upon the results shown in Figures 5-12 and 5-13, there are important qualitative
similarities in the average emission ratios for both data sets. However, a key question is whether
the similarities in emissions are because of similarities in vehicle activity. In order to answer this
question, the distributions of each of speed and acceleration were compared, as were the joint
distributions of both speed and acceleration. These comparisons are shown in Figures 5-14, 5-
15, and 5-16 for Modes 1, 7, and 12 for vehicles with engine displacement of less than 3.5 liters.

For the Mode 1 comparison shown in Figure 5-14, the EVI240 data have a wider range of speed,
but it is apparent that the distribution of speeds for the EVI240 data are bimodal. Thus, there is a
large proportion of speeds in the range of approximately 10 to 30 mph, as well as a smaller
proportion of speeds in the range of approximately 50 to 60 mph. In contrast, as noted in the
previous section, the distribution of speeds for the RSD data is primarily between 20 mph and 40
mph. The RSD data tend to have a larger proportion of larger acceleration rates than does the
EVI240 data. A comparison of the scatter plots for acceleration versus speed indicates that the
EVI240 data captures a much wider range of variability in terms of different combinations of
82

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                                                       83

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                                                       84

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                                                             85

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                                                             86

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                    Data Sets, for VSP Mode 12 for Vehicles with Engine Displacement Less Than 3.5 Liters.
                                                            87

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speed and acceleration than does the RSD data.  The RSD data had a higher average emission
ratio for NOX but lower ratios for CO and HC for Mode 1 for vehicles with engine displacements
less than 3.5 liters.

For the Mode 7 comparison, the EVI240 data are strongly bimodal with respect to both speed and
acceleration. The EVI240 data have a wider range of values for speed and acceleration than do
the RSD data.  In particular, there is more representation of higher speeds and a similar
representation of the upper tail of the distribution of acceleration when comparing the EVI240
data to the RSD data.

For Mode 12, the EVI240 data typically represent somewhat higher speeds but also somewhat
smaller accelerations than does the RSD data. However, for Mode 12, there are relatively few
data points for the EVI240 data set in comparison to the RSD data.

Overall, although not conclusive, the comparison of vehicle activity in terms of speed and
acceleration between the EVI240 and RSD data suggests that there are substantial differences in
activity patterns between the two data sets.  Thus, although in some cases both data sets have
similar emission ratios, it is possible that such apparent similarities are actually based upon
differences in the vehicle and in the vehicle activity.

5.8    Summary and Recommendations
The key findings from the comparison of emission factor units and from the evaluation of RSD
data are briefly summarized here, followed by more detailed discussion:

   •  When comparing RSD to the modeling data:
          -  There is less variability in emission ratios of CO/CO2 and HC/CO2 for the low
             VSP bins
          -  There is substantial  variability in emissions for the high VSP bins
   •  for NOX, there is a need for a similar number of modes for the emission ratios and for
      mass per time units in order to explain variability in emissions.
   •  Need CO2 (or fuel use) on a mass per time basis anyway, which motivates the need for a
      modal approach such as that developed in Chapter 3 on a mass per time basis
   •  Because of the variability in NOX emissions even when emission ratios are used, and
      because of the need to use a mass per time approach to estimate CO2 emissions, the use
      of emission ratios instead of mass per time  emission factors for only a subset of
      pollutants does not offer any significant advantage, especially from a software/model
      design perspective.
   •  RSD data are not a strong candidate for use in model development because some key
      variables are not observable, such as odometer reading.
      The HC/CO2 emissions  data from RSD do not appear to be comparable to that from the
      modeling dataset because of the measurement techniques employed.

The results of the application of the binning methods to the modeling data set suggest that there
is less variability in emission ratios of CO/CO2 and HC/CO2 for the low VSP bins. However,
there is substantial variability in the NOX/CO2 ratio for the low VSP bins, and for all three
pollutants there is substantial variability in emissions among the high VSP bins.  Therefore, the
                                           88

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use of emission ratios instead of mass per time emission factors does not offer any advantage in
terms of reducing the number of modes needed to model emissions, if the same number of modes
are to be applied to all pollutants for simplicity of software design and data management.

The potential role of RSD data was evaluated based upon several comparisons: (1) comparison
of emission ratios for the RSD data versus the modeling data; (2) comparison of vehicle activity
for the RSD data versus the modeling data; (3) comparison of emission ratios for the RSD data
versus EVI240 data; and (4) comparison of vehicle activity for the RSD data versus the EVI240
data.  The RSD data typically lead to higher emission ratios than the modeling data, especially
for lower VSP modes (e.g., Modes 1 through  10), especially for the NOX/CO2 and HC/CO2
ratios. Although it may be tempting to conclude that such differences are because the RSD data
might have a better representation of higher emitting vehicles, or of higher emissions episodes
with normal emitting vehicles, it is important to compare the vehicle activity of both data sets.  A
comparison of the speed and acceleration distributions for both data sets revealed that the RSD
data typically had lower average speeds and higher average accelerations than the modeling data
set. As  shown in Chapter 9, it can be the case within a VSP mode that some  of the variability in
emissions can be explained in terms of speed  and/or acceleration.  Therefore, although not
conclusive at this time, it is possible that the differences in emissions between the RSD data and
the modeling data may be attributable, at least in part, to differences in activity patterns.

A comparison of the EVI240 and RSD data suggests that these two data sets have quantitatively
similar emission ratios in some cases and qualitatively similar emission ratio trends among the
modes in a number of cases. However, a comparison of the speed and acceleration distributions
of the two datasets indicates that there is a substantially different activity pattern for the two data
sets, with the EVI240 data based upon bimodal speed distributions with a wider range in
variability in speed, higher average speed, and lower average acceleration, than the RSD data.
Thus, it is possible that the apparent similarities between these two data sets in terms of average
emission ratios may be because of compensating differences in fleet mix and activity patterns, or
it is possible that the emission ratios are robust to the differences in activity patterns.

The key findings regarding the potential role of RSD data are discussed here. RSD data were not
considered to be a strong candidate for use in model development because some key variables,
particularly odometer reading, are not observable. Odometer reading has been shown in earlier
chapters to be an important predictive variable.  The HC/CO2 emissions data from RSD do not
appear to be comparable to that from the modeling  dataset, which may be because of significant
differences in the measurement technique employed.  It is also possible that there are differences
in fuel composition that may cause some of the observed differences. Finally, the differences in
emission ratios for the RSD data versus the modeling data may be attributable in part to
differences in activity patterns not yet captured by the conceptual modeling approach. This latter
issue deserves some exploration as part of future work.

It has been hypothesized that RSD data may be useful in helping to better characterize the
distribution of different emitting vehicles,  and particularly high emitting vehicles.  It should be
noted that because RSD measurements are a snapshot of typically less than one second, and
because a normal emitting vehicle can have episodes of high emissions depending on the activity
pattern,  it is not conclusive that a  single high emissions ratio measurement of a vehicle enables
                                           89

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identification of such a vehicle as a high emitter. Thus, it is possible that a high emission ratio
may be associated with a high emitting vehicle or it could be associated with a high emissions
episode for a normal emitting vehicle. A comparison of the distribution of emission ratios for
the modeling data set versus that of the RSD data set suggests that the modeling data set captures
a wider relative range of variability than does the RSD data set, while at the same time the RSD
data often had higher average values than did the modeling data set. The upper tails of the
distributions of variability for a given mode for the modeling data set often overlapped
substantially with the upper tails of the distributions for the RSD data, suggesting that the highest
emission ratios in either data set were comparable. Thus, it could be the case that the modeling
dataset does not have the same proportional representation of high emitting vehicles, or of high
emissions episodes for normal emitting vehicles, as does the RSD data. These differences were
typically more pronounced for the low and moderate VSP modes. For the higher VSP modes,
the shapes of the distributions from the modeling data set and the RSD data set were very similar
for both the CO/CO2 and NOX/CO2 ratios.

The siting of the RSD instrument plays an important role in the range of activity that is observed.
It is clear from these data that the RSD sites had a much smaller range of variability in activity
patterns than did the dynamometer data or the onboard data that comprised the modeling data
base and the EVI240 database. Since RSD's are often sited at locations that are expected to have
positive accelerations or situations in which vehicles are under load, it is possible that there is a
bias in the activity pattern of the RSD data that is perhaps in part responsible for the apparent
differences in emissions when compared to the modeling data set. In this particular case,
although the range of speeds was typically less for the RSD data than for the other data sets, the
accelerations tended to be larger on average. Given these differences, it did not seem fruitful to
try to proceed with methods for making adjustments to the modeling data set in order to better
match the emission ratios estimated from the RSD data.

It is possible that RSD data could be used indirectly as a recruiting tool to try to obtain a
representative sample of vehicles for dynamometer and on-board testing, in order to improve the
representation of differently emitting vehicles.

In brief summary, for the purposes of this study, there was no substantial advantage found for
using emission ratios instead of mass per time emission factors. In either case, it is necessary to
estimate CC>2 emission in mass per time units. Therefore, for consistency, mass per time units
are recommended for further analysis. Although there were differences in the emission ratios for
the RSD data versus the modeling data, there were also substantial differences in activity
patterns for the two data sets. Therefore, the RSD data were not used as part of model
development, but the comparisons suggest that there may be opportunities to refine the
conceptual modeling approach in the future by considering additional binning criteria based upon
speed and/or acceleration for the VSP modes.
90

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6 COMPARISON AND EVALUATION OF DATA WEIGHTING APPROACHES

The objective of this chapter is to compare and evaluate three approaches for weighting data: (1)
time-weighted; (2) vehicle weighted; or (3) trip-weighted. Based upon comparison and
evaluation of these three approaches, a preferred approach is recommended.

6.1 Methodological Considerations
In the time-weighted approach, data in each bin are averaged with respect to time. For second-
by-second data, each second of data will have equal weight. For five second average data, each
five second time period of data will have equal weight. For ten second average data, each ten
second time period of data will have equal weight. The advantage of this approach is that data
can be combined from any number of vehicles within a vehicle category and the sample sizes
within each bin can become quite large. Furthermore, the time-weighted approach can be used
to support estimation of emissions for any arbitrary averaging time larger than that of the original
data. For example, 10 second average emission estimates can be developed by averaging over
10 seconds of one second data. Therefore, it is possible to consider, for example, how cruise
emissions that take place during a one minute period of freeway cruising might vary from one
time period to another. The inter-vehicle variability and fleet average uncertainty in emission
will be a function of the desired time periods. Another advantage of the time-weighted approach
is that more weight is given to vehicles that have undergone longer periods of testing. For
example, if RSD data were to be included in the development of a model based upon one second
averaging, each vehicle measured by the RSD would typically be represented by only one second
worth of data. In contrast, a vehicle that has undergone substantial on-road emissions
measurement might be represented by tens of thousands of seconds of data. Intuitively, it seems
appropriate to give more weight to vehicles that have undergone more testing time.

In the vehicle-weighted approach, data in each bin are averaged with respect to each vehicle.
Thus, for each vehicle, a single representative estimate of emissions would be developed. For
example, the simplest vehicle-weighted approach would be to calculate an average emission rate
for each vehicle based upon data for that vehicle within a given bin. The average emission rate
for all data in the bin would then be calculated by averaging the emission rates estimated for
each vehicle represented in the bin. This approach will tend to give less weight to vehicles for
which there are many seconds (or other averaging time periods) of data, and will give
disproportionate weight to vehicles for which there are relatively few time periods of data. For
example, if there are 10 seconds of data for vehicle 1, 30 seconds of data for vehicle 2, and 50
seconds of data for vehicle 3, the average emission rate for each vehicle would first be calculated
Then, the three vehicle average values would be given equal weight to determine the average
over all three vehicles. Thus, the average emission rate for Vehicle 1 would have equal weight
to that of Vehicle 2 or Vehicle 3 even though there are three and five times, respectively, as
much data for these latter two vehicles. Of course, a minimum data requirement criterion could
be specified such that a vehicle average would be calculated only for vehicles for which there are
a minimum number of seconds of data. However, there would still be variability in the amount
of testing time for different vehicles in the database, and there would remain a potential problem
that vehicles with less testing time than others would in effect have an influence comparable to
those with more testing time.
91

-------
The vehicle weight approach offers some potential disadvantages. One is that the weight given
to different vehicles may be intuitively unappealing. For example, in the extreme case, one
second of RSD data for a vehicle could be equally weighted with many hours of on-board data
for another vehicle. Secondly, the use of a vehicle-weighted approach may complicate the
quantification of variability and uncertainty. The range of inter-vehicle variability and of fleet
average uncertainty is a function of averaging time, with the latter point illustrated quantitatively
in Chapter 7. For example, one second emissions of a vehicle varies much more from one
second to another than 10 second average emissions vary from one 10 second period to another.
With the time-weighted approach, it is possible to combine data to represent any averaging time
of interest, conditioned on assumptions regarding the structure of the database (e.g., statistical
independence). With the vehicle weighted approach, the averaging time of the analysis is
unknown and is itself variable, because the average modal emission rate for one vehicle will
typically be based upon a different time period than that for another vehicle. For example, if
there are five seconds of data in a given bin for one vehicle, and 10 minutes of data in the same
bin for another vehicle, the averages of each of the two vehicles are based upon disparate
averaging times.

The trip-weighted approach was included as an alternative to be evaluated in this study. The
term "trip" essentially refers to an averaging time selected as the basis for aggregate emissions
measurements. For example, data for each vehicle could be divided into segments representing
trips. Each set of data from the same vehicle and "trip" within a bin would be averaged to arrive
at a "trip-average" emission estimate for that vehicle. A vehicle for which there is a large
amount of on-board data might be represented by more than one such "trip". Therefore, this
approach will tend to give more weight to vehicles for which there are more data, similar to the
time-weighted approach. Unlike the vehicle-weighted approach, there is some attempt in the
trip-weighted approach to have more comparability with respect to the averaging time of the
data. However, there will still be variation in the number of averaging time periods that are the
basis for any trip average emission estimate in any given bin, since the speed profile of any given
trip will differ from any other given trip. Therefore, this approach has the same qualitative
limitations as the vehicle-weighted approach.

In the vehicle weighted and trip-weighted approach, there is no direct way to control for
averaging time. Therefore, the binned data will represent a mixture of unknown averaging times,
and any uncertainty estimate developed from these data will be of unknown pedigree with
respect to averaging time. Thus, we compared the three approaches with respect to the
characterization of uncertainty in average emission rates.

In choosing a preferred weighting method, consideration was given to the following criteria: (1)
technical rigor to support a defensible estimate of variability and uncertainty; (2) flexibility to
estimate variability and uncertainty for different averaging times; (3) practical aspects of the
performance of each method (e.g., tractability, ease of developing estimates); (4) compatibility of
the method with data availability and overall modeling objectives.

6.2 Comparison of Weighting Approaches
A component of this work that is also closely related to the issue of analysis of variability and
uncertainty is comparison of different approaches for weighting data. Specifically, time, trip,
92

-------
and vehicle-weighted approaches were compared. The analysis results reported in this section
are based upon 14 VSP bins without further binning. The quantitative results for comparison of
the three approaches with respect to the 56-bin approach are given in the Appendix.

The empirical distributions of variability and fitted parametric distributions are displayed for the
examples of VSP Modes 1, 7, and 14 for each of the four pollutants considered and for the time-
weighted approach in Figures 6-1, 6-2, and 6-3, respectively. For example, for VSP Mode 1, the
Weibull distribution fitted to the NOX data appears to adequately describe the general
characteristics of the data, including the central tendency, the upper tail, and the positive
skewness. However, there are some deviances in the fit that are noticeable, such between the 50th
and 90th percentiles. Similarly, the lognormal distribution fit to the CC>2 data offers a
qualitatively good fit, but deviates from the data in some respects, such as near the 20th percentile
and near the 65* percentile. The deviations of the fitted distribution from the data in these two
cases are not large in an absolute sense, and are likely to be acceptable. In contrast, the fitted
distributions for HC and CO for Mode 1 do not appear to offer good fits. For Mode 7, all the
distributions fitted appear to capture the key trends in the data for all four pollutants. For Mode
14, the fits are generally very good for NOx, HC, and CC>2, but in the case of CO the fitted
distribution does not agree with the data, especially above the 70th percentile. Overall, in most
cases, the fitted distributions appear to perform well. In the case of CO for Mode 14, the mean
and standard deviation of the fitted distribution are substantially different than that of the data.

In addition to the time-weighted approach, the results shown graphically in Figures 6-4 through
6-6 are for the trip-weighted approach for Modes 1, 7, and 14, respectively. Similar results are
displayed for the vehicle-weighted approach in Figures 6-7, 6-8, and 6-9 for Modes 1, 7, and 14,
respectively. For the trip-weighted approach, the parametric distributions provide a good fit to
the data for Modes 1 and 7. For Mode 14, the fits for HC and CO2 are good. The fits for NOX
and particularly CO are less than ideal, although key qualitative trends are captured by the fits.
Generally, the comparison of the parametric distributions with the data is similar for the vehicle-
weighted approach: the fits are typically good for Modes 1 and 7; the fits for HC and CO2 for
Mode 14 are good; and the fits for NOX and CO for Mode 14 are not as good. As discussed in
Chaper 7, an alternative to fitting distributions using Maximum Likelihood Estimation (MLE) is
to use the Method of Matching Moments (MoMM). In the latter method, the fitted distribution
such as a lognormal will have a mean and standard deviation the same as that of the data. This
point is further illustrated in Chapter 7.

The selected types of distributions and the parameters of the fitted distributions are summarized
for all modes and pollutants in Table 6-1 for the trip-weighted approach. A similar summary is
given for the vehicle weighted approach in Table 6-2. Similar information regarding the time
weighted approach is given in the chapter on uncertainty analysis.

A direct graphical comparison of the variability associated with the time, trip, and vehicle
weighted approaches is given in Figures 6-10 and 6-11 for NO and HC, respectively, for Modes
1, 7, and 14. It is typically the case that the time-based approach has a longer upper tail to the
right than the other approaches, which involve averaging of the data. Mode 7 for NOX offers the
clearest example of the effects of averaging the data; in this case, the upper tail of the distribution
is substantially smaller than for the time-based approach.
93

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012
C0_gpsec
Sec-By-Sec, VSP Bin 1
Pollutant
Fitted Parametric Distribution3
NO
W
HC
L
C02
L
CO
L
1N = normal; L = lognormal; W = Weibull.
                                                            Empirical CDF
                                                            Fitted Parametric Distribution
     Figure 6-1. Variability in NOX, HC, CO2, and CO Emissions (g/sec) for VSP Mode #1
  Characterized by Empirical and Fitted Parametric Probability Distribution Models for Second-
                                    by-Second Data.
                                           94

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0123
1 CO gpsec
Sec-By-Sec, VSP Bin 7
Pollutant
Fitted Parametric Distribution51
NO
W
HC
L
CO2
W
CO
L
a N = normal; L = lognormal; W = Weibull.
                                                             Empirical CDF
                                                             Fitted Parametric Distribution
         Figure 6-2. Variability in NOX, HC, CO2, and CO Emissions (g/sec) for VSP Mode #7
         Characterized by Empirical Probability Distribution and Fitted Parametric Probability
                             Distribution for Second-by-Second Data.
                                               95

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0 5 10 15
- C0_gpsec
Sec-By-Sec, VSP Bin 14
Pollutant
Fitted Parametric Distribution51
NO
W
HC
L
CO2
W
CO
L
a N = normal; L = lognormal; W = Weibull.
                                                            Empirical CDF
                                                            Fitted Parametric Distribution
       Figure 6-3. Variability in NOX, HC, CO2, and CO Emissions (g/sec) for VSP Mode #14
       Characterized by Empirical Probability Distribution and Fitted Parametric Probability
                           Distribution for Second-by-Second Data.
                                             96

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Trip Average, VSP Bin 1
Pollutant
Fitted Parametric Distribution51
NO
L
HC
L
CO2
L
CO
L
i-
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>2 CO
T,
I Empirical CDF
a N = normal; L = lognormal; W = Weibull.
  Figure 6-4. Variability in NOX, HC, CO2, and CO Emissions (g/sec) for VSP Mode #1
  Characterized by Empirical Probability Distribution and Fitted Parametric Probability
                         Distribution for Trip Average Means
                                        97

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1 meanco
Trip Average, VSP Bin 7
Pollutant
Fitted Parametric Distribution51
NO
W
HC
L
CO2
W
CO
L
a N = normal; L = lognormal; W = Weibull.
                                                             Empirical CDF
                                                             Fitted Parametric Distribution
     Figure 6-5. Variability in NOX, HC, CO2, and CO Emissions (g/sec) for VSP Mode #7
     Characterized by Empirical Probability Distribution and Fitted Parametric Probability
                            Distribution for Trip Average Means.
                                            98

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                                                              meanco
Trip Average, VSP Bin 14
Pollutant
Fitted Parametric Distribution51
NO
W
HC
W
CO2
W
CO
W
a N = normal; L = lognormal; W = Weibull.
                                                            Empirical CDF
                                                            Fitted Parametric Distribution
   Figure 6-6. Variability in NOX, HC, CO2, and CO Emissions (g/sec) for VSP Mode #14
    Characterized by Empirical Probability Distribution and Fitted Parametric Probability
                          Distribution for Trip Average Means.
                                          99

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Vehicle Average, VSP Bin 1
Pollutant
Fitted Parametric Distribution51
NO
L
HC
L
C02
L
CO
W
a N = normal; L = lognormal; W = Weibull.
                                                             Empirical CDF
                                                             Fitted Parametric Distribution
  Figure 6-7. Variability in NOX, HC, CO2, and CO Emissions (g/sec) for VSP Mode #1
  Characterized by Empirical Probability Distribution and Fitted Parametric Probability
                      Distribution for Vehicle Average Means.
                                        100

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1 meanco
Vehicle Average, VSP Bin 7
Pollutant
Fitted Parametric Distribution3
NO
W
HC
L
C02
W
CO
L
                                                             Empirical CDF
                                                             Fitted Parametric Distribution
1N = normal; L = lognormal; W = Weibull.
     Figure 6-8. Variability in NOX, HC, CO2, and CO Emissions (g/sec) for VSP Mode #7
     Characterized by Empirical Probability Distribution and Fitted Parametric Probability
                          Distribution for Vehicle Average Means.
                                           101

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                                                0 .5-
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Vehicle Average, VSP Bin 14
Pollutant
Fitted Parametric Distribution51
NO
W
HC
W
C02
W
CO
W
a N = normal; L = lognormal; W = Weibull.
                                                            Empirical CDF
                                                            Fitted Parametric Distribution
   Figure 6-9. Variability in NOX, HC, CO2, and CO Emissions (g/sec) for VSP Mode #14
    Characterized by Empirical Probability Distribution and Fitted Parametric Probability
                        Distribution for Vehicle Average Means.
                                         102

-------
  Table 6-1. Summary of Fitted Parametric Probability Distributions for Variability in NOx, HC, CO2, and CO Emissions (g/sec) for
                                                 VSP Bins for Trip Average Means
VSP Bins
1
2
3
4
5
6
7
8
9
10
11
12
13
14
NO
Fit Para.
Dista
L
L
L
W
W
W
W
W
W
W
W
W
W
W
para 1
1.1746
1.2133
1.1893
0.0021
0.0025
0.0031
0.0036
0.0046
0.0055
0.0061
0.0072
0.012
0.0129
0.0151
para 2
-7.1968
-7.222
-7.5064
1.0996
1.0771
1.039
1.0137
0.9858
0.9031
0.8227
0.6991
0.8189
0.8494
0.6942
HC
Fit Para.
Disf
L
L
L
L
L
L
L
L
L
L
W
W
W
W

1.4327
1.5103
1.5108
1.4482
1.3764
1.3421
1.3774
1.4163
1.4125
1.5656
0.0018
0.0036
0.005
0.0059
Fit Para.
Dista
-8.4431
-8.6318
-8.7568
-8.2217
-8.0443
-7.9055
-7.8134
-7.7013
-7.5305
-7.4463
0.6731
0.733
0.742
0.7189
C02
para 1
L
L
L
L
L
W
W
W
W
W
W
W
W
W
para 2
0.5305
0.5001
0.4868
0.3563
0.3256
3.9612
4.5374
5.1194
5.773
6.3325
7.5883
9.0917
10.2248
10.925
Fit Para.
Dista
0.5235
0.5467
0.3599
0.906
1.0988
3.798
3.5135
3.2378
2.9653
2.5081
2.3674
2.5755
2.679
2.1308
CO

L
L
L
L
L
L
L
L
L
W
W
W
W
W
Fit Para.
Dista
1.6843
1.6961
1.5637
1.6522
1.5545
1.5702
1.595
1.6647
1.8428
0.0283
0.0518
0.1501
0.2868
0.4011
para 1
-5.5881
-5.8367
-6.1689
-5.3273
-5.1264
-5.0068
-4.8661
-4.7747
-4.6522
0.5263
0.5148
0.5218
0.5092
0.4567
a W = Weibull; para 1 of Weibull is scale parameter and para 2 of Weibull is shape parameter;
 L = lognormal; para 1 of lognormal is 0 and para 2 of lognormal is £
 Parameters were calculated using SAS.
                                                           103

-------
  Table 6-2. Summary of Fitted Parametric Probability Distributions for Variability in NOX, HC, CO2, and CO Emissions (g/sec) for
                                               VSP Bins for Vehicle Average Means
VSP Bins
1
2
3
4
5
6
7
8
9
10
11
12
13
14
NO
Fit Para.
Dista
L
W
L
W
W
W
W
W
W
W
W
W
W
W
para 1
1.162
0.001
1.1366
0.0016
0.0023
0.0031
0.0038
0.0048
0.0059
0.007
0.0098
0.0131
0.0143
0.0185
para 2
-7.4631
0.8876
-7.6305
1.1128
1.116
1.117
1.0844
1.0523
1.0186
0.9649
0.9198
0.919
0.8884
0.7472
HC
Fit Para.
Dista
L
L
L
L
L
L
L
L
L
L
L
L
L
W

1.223
1.3677
1.313
1.2155
1.0873
1.0185
1.0469
1.1083
1.0985
1.0641
1.1483
1.199
1.2823
0.0065
Fit Para.
Dista
-8.3866
-8.7468
-8.8287
-8.3183
-7.9406
-7.6843
-7.4981
-7.2772
-7.0789
-6.8674
-6.5547
-6.1941
-5.8853
0.7644
C02
para 1
L
L
L
W
W
W
W
W
W
W
W
W
L
W
para 2
0.4726
0.4384
0.3567
2.5339
3.2985
4.0899
4.8834
5.6715
6.4881
7.2909
8.7287
10.1588
0.3453
12.7194
Fit Para.
Dista
0.2934
0.3477
0.2279
4.3527
5.0571
4.7385
4.2448
3.9835
3.7832
3.4183
3.0995
2.8832
2.2655
2.7592
CO

W
L
L
L
L
L
L
L
L
W
W
W
W
W
Fit Para.
Dista
0.0127
1.4844
1.3664
1.22
1.1426
1.1543
1.256
1.4549
1.5313
0.0886
0.1588
0.3065
0.5212
0.7882
para 1
0.9102
-5.6518
-6.0737
-5.1105
-4.7103
-4.3078
-4.0167
-3.7997
-3.5608
0.7557
0.6969
0.68
0.6373
0.5785
a W = Weibull; para 1 of Weibull is scale parameter and para 2 of Weibull is shape parameter;
 L = lognormal; para 1 of lognormal is 0 and para 2 of lognormal is <^;
 Parameters were calculated using SAS.
                                                           104

-------
         0
                                                    Bin1
                                          	Time-Avg, Wei bull
                                          	Trip-Avg, Lognormal
                                          	Vehicle-Avg, Lognormal
        0.01
                 0.02
                                    NO (g/sec)
             0.03
         0
0.02
                                                    Bin 7
                                                -Time-Avg, Wei bull
                                           	Trip-Avg, Wei bull
                                           — -  -Vehicle-Avg, Weibull
0.04         0.06
    NO (g/sec)
0.08
0.1
         0
                                                    Bin 14
                                           	Time-Avg, Weibull
                                           	Trip-Avg, Weibull
                                           	Vehicle-Avg, Weibull
         0.1
                  0.2
                                    NO (g/sec)
              0.3
Figure 6-10.  Comparison of Variability in NOX Emissions for Time-Average, Trip-Average, and
 Vehicle-Average Approaches, Characterized by Parametric Probability Distributions, for VSP
                                Modes #1, #7 and #14.
                                        105

-------
        0
                                                    Bin 1
                                         	Time-Avg, Lognormal
                                         	Trip-Avg, Lognormal
                                         	Vehicle-Avg, Lognormal
     0.02
0.04
                                    HC (g/sec)
                                   0.06
£• &^
S 0.8
f
ro 1 -.• -
of
i °'6|
£ °-4 4'
03 "
1 0.2 J
a
n -,
\
Ti mo A \/n 1 nnnnrmol

	 Trip-Avg, Lognormal
— - -Vehicle-Avg, Lognormal
        0
0.02
   0.04
HC (g/sec)
     0.06
0.08
        0
                                                     Bin 14
                                           	Time-Avg, Lognormal
                                           	Trip-Avg, Wei bull
                                           	Vehicle-Avg, Weibull
      0.2
 0.4
                                    HC (g/sec)
                                    0.6
Figure 6-11. Comparison of Variability in HC Emissions for Time-Average, Trip-Average, and
 Vehicle-Average Approaches, Characterized by Parametric Probability Distributions, for VSP
                               Modes #1, #7 and #14.
                                        106

-------
Because different types of averaging lead to different weighting of information in the database,
the mean and standard deviation will differ depending upon which weighting approach is used.
Table 6-3 summarizes how much the estimate of mean emissions changes within a mode for a
given pollutant depending upon whether a trip-average or vehicle-average approach is used. The
percentage changes shown in the table are with respect to the time-weighted mean values. The
average value for the trip weighted approach can be either larger or smaller than that of the time-
weighted approach for a given pollutant when comparing different modes. For example, the trip-
weighted average for NOX emissions for Mode 1 is 25 percent greater than for the time weighted
approach, but for Mode 8 the trip-weighted average is 20 percent less than that of the time-
weighted approach. Both the trip- and vehicle-weighted approaches have substantially different
mean estimates in specific cases compared to the time weighted approach. These differences
range from essentially no difference to an increase of over 100 percent or a decrease of as much
as -42 percent. For NOX, CO, and HC, the differences in means exceed 10 percent in magnitude
for 80 percent of the pollutant/mode combinations. In contrast, for CC>2, a difference in mean
values of more than 10 percent in magnitude occurred for only approximately 30 percent of the
modes. Thus, while mean CC>2 emission estimates are more robust to the selection of averaging
methods, the average emissions of NOX, CO, and HC are dependent upon what method is
selected.

The relative range of uncertainty in the mean modal emissions is given in Table 6-5 for time-
averages, in Table 6-6 for trip-averages and in Table 6-7 for vehicle-averages. The relative
ranges of uncertainty in the mean modal emissions for trip-averages and vehicle-averages can be
compared with the time-weighted results. Because the sample size becomes smaller as second-
by-second data are averaged, even though the variability in emissions decreases to some extent
(as indicated by the results in Table 6-4), the uncertainty in the average increases when compared
to the time based approach. For example, consider the range of uncertainty in average NOX
emissions for Mode 1. For the time-weighted approach, it is plus or minus 3 percent. For the
trip-weighted approach, it is plus or minus 15 percent. For the vehicle weighted approach, it is
plus or minus 26 percent.

The average emission rates and the 95 percent confidence intervals for the averages are
compared graphically in Figure 6-12 for each of the four pollutants and for each mode.
107

-------
Table 6-3. Comparison of Mean Emissions of NOx, HC, CO2, and CO Emissions (g/sec) for VSP Bins: Time-Average, Trip-Average,
                                                and Vehicle-Average Approaches.
Bin
1
9
3
4
5
6
7
8
9
10
11
12
13
14
NOa
Time-
Avg
mean
0.0011
0.0009
0.0006
0.0016
0.0025
0.0034
0.0044
0.0058
0.0070
0.0085
0.0112
0.0144
0.0171
0.0198
Trip-Avg
mean
0.0014
0.0014
0.0011
0.0020
0.0025
0.0031
0.0036
0.0046
0.0058
0.0068
0.0092
0.0134
0.0140
0.0193
diff.
25
53
91
21
-1
-10
-19
-20
-17
-19
-18
-7
-18
-3
Vehicle-Avg
mean
0.0011
0.0010
0.0009
0.0015
0.0022
0.0029
0.0036
0.0047
0.0059
0.0071
0.0102
0.0137
0.0152
0.0225
diff.
-3
12
53
-7
-13
-14
-18
-18
-16
-16
-9
-5
-11
13
HCa
Time-
Avg
mean
0.0007
0.0004
0.0007
0.0006
0.0008
0.0011
0.0013
0.0016
0.0019
0.0023
0.0031
0.0045
0.0060
0.0098
Trip-Avg
mean
0.0006
0.0006
0.0005
0.0008
0.0008
0.0009
0.0010
0.0012
0.0014
0.0017
0.0025
0.0046
0.0064
0.0074
diff.
-9
35
-17
21
3
-14
-21
-27
-28
-26
-19
1
6
-25
Vehicle-Avg
mean
0.0005
0.0004
0.0004
0.0006
0.0007
0.0008
0.0010
0.0013
0.0015
0.0018
0.0026
0.0039
0.0056
0.0077
diff.
-28
-6
-42
-14
-16
-22
-24
-20
-20
-20
-17
-13
-5
-21
CO2a
Time-
Avg
mean
1.6337
1.5254
1.2050
2.3308
3.0882
3.7963
4.4899
5.0543
5.6496
6.1914
7.1117
8.0558
9.2945
9.9292
Trip-Avg
mean
1.9294
1.9498
1.6322
2.6267
3.1464
3.5920
4.0968
4.6024
5.1663
5.6271
6.7425
8.0667
9.0835
9.6832
diff.
18
28
35
13
2
-5
-9
-9
-9
-9
-5
0
-2
-2
Vehicle-Avg
mean
1.4894
1.5461
1.3391
2.3142
3.0461
3.7772
4.4868
5.1861
5.9128
6.5947
7.8458
9.0446
10.2076
11.3174
diff.
-9
1
11
-1
-1
-1
0
3
5
7
10
12
10
14
coa
Time-
Avg
mean
0.0110
0.0065
0.0051
0.0114
0.0156
0.0224
0.0287
0.0413
0.0526
0.0728
0.1304
0.2712
0.4878
0.8101
Trip-Avg
mean
0.0151
0.0141
0.0088
0.0186
0.0217
0.0219
0.0258
0.0333
0.0418
0.0553
0.1047
0.2701
0.5091
0.8049
diff.
37
118
72
64
39
_9
-10
-20
-21
-24
-20
0
4
-1
Vehicle-Avg
mean
0.0134
0.0100
0.0062
0.0130
0.0177
0.0263
0.0374
0.0573
0.0766
0.1074
0.2036
0.3922
0.6891
1.1002
diff.
22
54
22
14
13
17
30
39
46
48
56
45
41
36
a Unit of mean: g/sec; Unit of diff: %.
                                                         108

-------
   Table 6-4.  Comparison of Standard Deviations of Variability in NOX, HC, CO2, and CO Emissions (g/sec) for VSP Bins: Time-
                                     Average, Trip-Average, and Vehicle-Average Approaches.
Bin
1
2
3
4
5
6
7
8
9
10
11
12
13
14
NOa
Time-
Avg
std. dev.
0.0029
0.0028
0.0020
0.0037
0.0051
0.0067
0.0079
0.0092
0.0116
0.0135
0.0174
0.0207
0.0251
0.0278
Trip-Avg
std.
dev.
0.0016
0.0018
0.0020
0.0019
0.0026
0.0033
0.0040
0.0053
0.0068
0.0086
0.0130
0.0168
0.0169
0.0305
diff.
-44
-37
0
-48
-49
-51
-49
-42
-41
-36
-25
-19
-32
10
Vehicle-Avg
std.
dev.
0.0013
0.0012
0.0013
0.0014
0.0023
0.0032
0.0040
0.0053
0.0064
0.0083
0.0120
0.0159
0.0187
0.0357
diff.
-56
-57
-34
-62
-54
-53
-49
-43
-45
-39
-31
-23
-25
28
HCa
Time-
Avg
mean
0.0030
0.0016
0.0024
0.0021
0.0025
0.0030
0.0032
0.0041
0.0041
0.0049
0.0065
0.0097
0.0118
0.0192
Trip-Avg
mean
0.0013
0.0014
0.0012
0.0016
0.0015
0.0015
0.0017
0.0020
0.0023
0.0029
0.0048
0.0093
0.0133
0.0113
diff.
-58
-11
-48
-25
-40
-49
-45
-52
-44
-40
-27
-5
12
-41
Vehicle-Avg
mean
0.0007
0.0007
0.0006
0.0009
0.0010
0.0012
0.0014
0.0019
0.0020
0.0025
0.0035
0.0052
0.0074
0.0111
diff.
-77
-59
-74
-57
-60
-60
-55
-54
-51
-50
-47
-47
-37
-42
C02a
Time-
Avg
mean
1.2557
1.1395
0.7727
1.3014
1.4529
1.6444
1.8382
2.0072
2.1765
2.4519
2.9053
3.2287
3.8763
4.8908
Trip-Avg
mean
1.0260
1.0169
1.0000
0.9097
0.9255
1.0125
1.2678
1.5369
1.8802
2.4060
3.0212
3.3547
3.6558
4.8015
diff.
-18
-11
29
-30
-36
-38
-31
-23
-14
_9
4
4
-6
_9
Vehicle-Avg
mean
0.6768
0.6415
0.5182
0.5896
0.6721
0.8341
1.0729
1.3394
1.6092
2.0248
2.6930
3.4101
3.4751
4.5328
diff.
-46
-44
-33
-55
-54
-49
-42
-33
-26
-17
-7
6
-10
-7
coa
Time-
Avg
mean
0.0642
0.0477
0.0361
0.0585
0.0982
0.1416
0.1159
0.1732
0.1976
0.2841
0.4291
0.7115
0.9704
1.4374
Trip-Avg
mean
0.0389
0.0457
0.0261
0.0409
0.0536
0.0459
0.0567
0.0836
0.1020
0.1282
0.2295
0.4418
0.7430
1.1124
diff.
-39
-4
-28
-30
-45
-68
-51
-52
-48
-55
-47
-38
-23
-23
Vehicle-Avg
mean
0.0184
0.0196
0.0121
0.0254
0.0300
0.0453
0.0667
0.1086
0.1446
0.1793
0.3122
0.5094
0.8259
1.2247
diff.
-71
-59
-67
-57
-69
-68
-42
-37
-27
-37
-27
-28
-15
-15
a Unit of diff:
                                                         109

-------
Table 6-5. Summary of Relative 95% Confidence Intervals for NOX, HC, CO2, and CO Mean Emissions for VSP Bins for the Time-
                                                    Average Approach
VSP Bins
1
2
3
4
5
6
7
8
9
10
11
12
13
14
NOa
mean
0.0011
0.0009
0.0006
0.0016
0.0025
0.0034
0.0044
0.0058
0.0070
0.0085
0.0112
0.0144
0.0171
0.0198
lower
-3
-5
-4
-3
-3
-3
-3
-3
-4
-4
-5
-6
-8
-9
upper
o
J
5
4
o
J
o
J
o
J
o
J
o
J
4
4
5
6
8
9
HCa
mean
0.0007
0.0004
0.0007
0.0006
0.0008
0.0011
0.0013
0.0016
0.0019
0.0023
0.0031
0.0045
0.0060
0.0098
lower
-5
-5
-4
-4
-4
-4
-4
-5
-5
-5
-6
-9
-11
-13
upper
5
5
4
4
4
4
4
5
5
5
6
9
11
13
C02a
mean
1.6337
1.5254
1.2050
2.3308
3.0882
3.7963
4.4899
5.0543
5.6496
6.1914
7.1117
8.0558
9.2945
9.9292
lower
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-2
-2
o
-J
upper
1
1
1
1
1
1
1
1
1
1
1
2
2
3
C0a
mean
0.0110
0.0065
0.0051
0.0114
0.0156
0.0224
0.0287
0.0413
0.0526
0.0728
0.1304
0.2712
0.4878
0.8101
lower
-6
-10
-7
-6
-8
-9
-7
-8
-8
-9
-10
-11
-11
-12
upper
6
10
7
6
8
9
7
8
8
9
10
11
11
12
Unit of mean: g/sec; Unit of lower and upper bound: %.
                                                       110

-------
  Table 6-6.  Summary of Relative 95% Confidence Intervals for NOX, HC, CO2, and CO Mean Emissions for VSP Bins for the Trip-
                                                     Average Approach.
VSP Bins
1
2
3
4
5
6
7
8
9
10
11
12
13
14
NOa
mean
0.0014
0.0014
0.0011
0.0020
0.0025
0.0031
0.0036
0.0046
0.0058
0.0068
0.0092
0.0134
0.0140
0.0193
lower
-15
-16
-21
-12
-13
-13
-14
-14
-15
-16
-20
-23
-24
-32
upper
15
16
21
12
13
13
14
14
15
16
20
23
24
32
HCa
mean
0.0006
0.0006
0.0005
0.0008
0.0008
0.0009
0.0010
0.0012
0.0014
0.0017
0.0025
0.0046
0.0064
0.0074
lower
-25
-30
-28
-25
-22
-20
-20
-21
-21
-22
-26
-36
-41
-31
upper
25
30
28
25
22
20
20
21
21
22
26
36
41
31
C02a
mean
1.9294
1.9498
1.6322
2.6267
3.1464
3.5920
4.0968
4.6024
5.1663
5.6271
6.7425
8.0667
9.0835
9.6832
lower
-7
-6
-7
-4
-4
o
-J
-4
-4
-5
-5
-6
-7
-8
-10
upper
7
6
7
4
4
3
4
4
5
5
6
7
8
10
coa
mean
0.0151
0.0141
0.0088
0.0186
0.0217
0.0219
0.0258
0.0333
0.0418
0.0553
0.1047
0.2701
0.5091
0.8049
lower
-32
-39
-36
-27
-30
-26
-27
-31
-31
-29
-30
-29
-29
-28
upper
32
39
36
27
30
26
27
31
31
29
30
29
29
28
a Unit of mean: g/sec; Unit of lower and upper bound: %.
                                                         Ill

-------
Table 6-7. Summary of Relative 95% Confidence Intervals for NOX, HC, CO2, and CO Mean Emissions for VSP Bins for the Vehicle-
                                                      Average Approach
VSP Bins
1
2
3
4
5
6
7
8
9
10
11
12
13
14
NOa
mean
0.0011
0.0010
0.0009
0.0015
0.0022
0.0029
0.0036
0.0047
0.0059
0.0071
0.0102
0.0137
0.0152
0.0225
lower
-26
-26
-31
-20
-23
-23
-24
-24
-24
-25
-26
-27
-30
-40
upper
26
26
31
20
23
23
24
24
24
25
26
27
30
40
HCa
mean
0.0005
0.0004
0.0004
0.0006
0.0007
0.0008
0.0010
0.0013
0.0015
0.0018
0.0026
0.0039
0.0056
0.0077
lower
-31
-35
-36
-35
-31
-31
-31
-32
-29
-29
-29
-30
-32
-37
upper
31
35
36
35
31
31
31
32
29
29
29
30
32
37
CO/
mean
1.4894
1.5461
1.3391
2.3142
3.0461
3.7772
4.4868
5.1861
5.9128
6.5947
7.8458
9.0446
10.2076
11.3174
lower
-10
-9
-8
-6
-5
-5
-5
-6
-6
-7
-7
-9
-8
-10
upper
10
9
8
6
5
5
5
6
6
7
7
9
8
10
coa
mean
0.0134
0.0100
0.0062
0.0130
0.0177
0.0263
0.0374
0.0573
0.0766
0.1074
0.2036
0.3922
0.6891
1.1002
lower
-30
-42
-42
-42
-37
-37
-39
-41
-41
-36
-33
-30
-29
-28
upper
30
42
42
42
37
37
39
41
41
36
33
30
29
28
 Unit of mean: g/sec; Unit of lower and upper bounds: %.
                                                         112

-------
            0.0350
          o" 0.0300 -
          01
          jn
          | 0.0250 -I
          IS
          I 0.0200 -
0.0150 -

0.0100 -

0.0050 -

0.0000
                    1   2  3  4  5  6   7   8  9  10  11  12 13 14

_ 12.0000 -
o
01
jn
S 10.0000 -
IS
c
£ 8.0000 -
HI
| 6.0000 -
'in
in
| 4.0000 -

                                                      S 0.0080 -|
                                                      ro
                                                      •a
                                                      UJ 0.0060 -
                                                                 m
0.0040 -

0.0020 -

0.0000 -
                                                                            1   2  3   4   5  6  7   8   9 10  11  12 13 14
                                                                      1.6000
                                                                   _ 1.4000 -
                                                                   o
                                                                   •|, 1.2000 -

                                                                   | 1.0000 -
                                                                   •a
                                                                   UJ 0.8000 -
                                                                   in
                                                                   •3; 0.6000 -
                                                                   2, and CO for VSP Bins: Time-Average,
                                         Trip-Average, and Vehicle-Average Approaches.
                                                               113

-------
The results for the "56-bin" approach given in the Appendix for the comparison of the three
weighting approaches are qualitatively similar to those shown in this chapter for the 14 VSP
bins.

6.3    Summary and Recommendation
The main findings from the comparison of the time, trip, and vehicle weighted approaches are as
follows:

       Compared to time-weighted approach, the means for the trip and vehicle weighted
       approaches can be either higher or lower.
   •   The standard deviation decreases for the trip weighted approach, and further for the
       vehicle weighted approach, when compared to the time weighted approach.
   •   Averaging time varies for both the trip and vehicle weighted approaches; there is no
       standard averaging time
   •   The uncertainty in the average typically increases with more averaging over time,
       because of smaller sample size.
       The trip and vehicle weighted approaches disproportionately give emphasis to trips or
       vehicles with little data

Based upon these main findings, a judgment was made that the time weighted approach is the
preferred basis for development of a conceptual emission estimation model. The time weighted
approach offers flexibility in  the future to weight the data by vehicle or trip if so desired.  The
time weighted approach is predicated upon the assumption that data for a given vehicle
stratification (e.g., odometer reading and engine displacement) are representative of that strata.
It is easier from a software design and from an analysis perspective to work with time weighted
data, and such an approach will give more weight to vehicles or trips for which there are more
data, which is intuitively appealing.
                                          114

-------
7 QUANTIFICATION OF VARIABILITY AND UNCERTAINTY

The estimation of uncertainty in the average emission rate for a mode depends upon the
variability in data for the mode, the variance within the data, and the sample size. Key issues
addressed in the analyses include the adequacy of selected parametric probability distribution
models for representing variability in data, and whether the range of uncertainty in the mean
values is sufficiently small that a normality approximately can be used to represent uncertainty in
the mean. To provide insight into these issues, results are presented of analysis of both
variability and uncertainty based upon the VSP modes for one-second average data. This chapter
includes a review of methodological considerations, quantification of variability for individual
modes, quantification of uncertainty for individual modes, and estimation of uncertainty for
driving cycles or trips.

7.1 Methodological Considerations
In uncertainty analysis, there are several sources of uncertainty that must be considered. The
first is the scenario being modeled. The second is the model itself. The third are the inputs to
the model. In practice, the term "model uncertainty" is typically understood to mean uncertainty
regarding the functional form of the model itself. Cullen and Frey (1999) address sources of
model uncertainty in detail in Chapter 3. Since MOVES is anticipated to be a data-driven model,
the uncertainty associated with model structure will be associated with the definitions of the bins.
For example, suppose that average emissions are sensitive to variation in engine displacement,
but that a bin-based approach is implemented without using engine displacement as one of the
binning criteria. Then the "model" would fail to enable prediction of the sensitivity of average
emissions with respect to different engine displacements. In this case, one could argue that there
is uncertainty associated with an incomplete formulation of the model structure. Once the model
structure is correctly specified, a technique can be applied for propagating uncertainty regarding
emissions in each bin to predict uncertainty of the final model results. This latter approach
addresses uncertainty in the inputs to the model (i.e. the data within each bin) but does not
address uncertainty associated with the model structure. The main objective this task is to focus
on a methodology for propagating uncertainty in the model input data (e.g., the data used in each
bin, and the activity data used to weight the binned data) in order to predict uncertainty in the
estimated emissions. Another consideration is that for the model predictions to be accurate,
which means free of bias when comparing the average model predictions to the true average
emissions in the real world, the model must be developed based upon a representative data set.

There are several key considerations pertaining to this task, which are briefly summarized in the
following list, with more detailed discussion in the following text:

• Variability
• Uncertainty
• Choice of empirical versus parametric probability distribution models
• Averaging Time
• Bottom-Up versus Top-Down Approaches
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7.1.1 Variability and Uncertainty
Variability refers to real differences in emissions, such as from one vehicle to another.
Uncertainty refers to lack of knowledge regarding the true value of a quantity. Sources of
variability include differences in vehicle/engine design, operating conditions, maintenance, fuel
composition, and ambient conditions (as examples). Sources of uncertainty include random
sampling error, measurement error, lack of representativeness, and lack of information. For
emission factor purposes, we are typically interested in average emissions for a particular fleet of
vehicles, rather than in trying to predict emissions for an individual vehicle. Therefore, we are
typically more interested in characterizing uncertainty in the average emission estimate than in
characterizing inter-vehicle variability in the estimate. The distinction between inter-vehicle
variability and fleet average uncertainty has been demonstrated quantitatively in many recent
studies based upon different sources of data, including dynamometer (bag) data, RSD, and on-
board data (e.g., Kini and Frey, 1997; Frey, Bharvirkar, and Zheng, 1999; Frey and Zheng, 2002;
Frey, Rouphail, Unal, and Colyar, 2001; Frey, Unal, and Chen, 2002; Frey and Eichenberger,
1997a&b; Frey, Rouphail, Unal, and Dalton, 2000).

7.1.2 Empirical Distributions
EPA has emphasized that it prefers a data-driven approach to development of MOVES.
However, there is a trade-off between a purely data driven approach versus one that includes
some abstraction and aggregation. Specifically, in the context of quantitative analysis of
variability and uncertainty, there is a choice to be made regarding whether to base the analysis
upon empirical distributions or upon parametric distributions. In the former, each data point in
the database, such as for a single bin, is assigned a probability. Typically, data are assumed to be
equally weighted but this need not be the case in all situations. Based upon the data values and
the probability assigned to each data value, a step-wise empirical cumulative distribution
function can be developed. An example of a step-wise empirical cumulative distribution
function is given in Figure 7-1 for a data set with sample size of 10. A dataset such as this might
represent inter-vehicle variability in emissions.
.1? * 1
^ 0.8 H
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02468
Example Data

Figure 7-1. Example of a Stepwise Empirical Cumulative Distribution Function
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The mean and standard deviation of the empirical distribution are calculated directly from the
data. The empirical distribution has the advantage that it is "true" to the data. However, there
are several important potential disadvantages: (1) there is no interpolation within the range of
observed data (i.e. the distribution has only discrete values corresponding to the original data set,
and there is zero probability of sampling any other value); (2) there is no plausible extrapolation
beyond the range of observed data; and (3) one must retain all of the data in order to characterize
the empirical distribution. Of these three potential disadvantages, the most important are the
second and third ones. The second one is important especially for small data sets. With any data
set, but especially smaller ones, it is unlikely that the observed highest value corresponds to the
true highest value, and that the observed lowest value corresponds to the true lowest value.
Thus, there is a possibility of failing to characterize the full range of variability. The third
potential disadvantage is that one must retain all of the original data. This is not a problem for a
very small data set, but for a very large data set this could be cumbersome.

7.1.3 Parametric Distributions
An alternative to empirical distributions is to use parametric probability distributions to represent
variability. The most commonly used parametric distributions, such as lognormal, gamma, or
Weibull, typically have only two parameters. The parameters are estimated using statistical
estimation approaches such as the method of matching moments or maximum likelihood
estimation. The distribution is fully specified once the values of its parameters are estimated.
Frey and Zheng (2002) give details of these methods, and such methods are incorporated into the
AuvTool software recently developed for EPA/ORD (Zheng and Frey, 2002). Thus, a data set of
any size can be represented based upon the type of distribution selected (i.e. lognormal, gamma,
Weibull) and the numerical values of its parameters.

Compared to empirical distributions, parametric distributions allow for interpolation within the
range of observed data, and for extrapolation to the upper and lower tails of the fitted
distribution. The latter is a potential advantage because it is likely that the observed range of
variability is less than the true range of variability as previously discussed. Because parametric
distributions provide a compact way of storing information regarding variability, the data storage
requirements will be less than if the empirical data set must be retained. However, there are
some key disadvantages to the use of parametric probability distributions in MOVES. If new
data are obtained and must be used to update the distributions for variability, then it will be
necessary to combine the new data with the previous data, and repeat the process of fitting a
parametric distribution to the data. Alternatively, one could fit a distribution to the new data, and
compare the distribution fitted to the new data with the one that was fitted to the previous data.
If the two distributions are not significantly different from each other, then there would be no
compelling need to update the previous distribution. If they are different, then one could create a
new mixture distribution. For example, if the original fitted distribution was based upon 10,000
data values, and if the new distribution was estimated from a new set of 5,000 data values, a
mixture distribution could be defined in which 2/3 weight is given to the first (older) distribution
and 1/3 weight is given to the second (newer) distribution.

7.1.4 Averaging Time
The issue of averaging time must be explicitly considering regardless of the choice of the
empirical or parametric approach to characterizing variability. The issue of averaging time is
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also closely related to Subtask Ib and is addressed in Chapter 4 and implicitly in Chapter 6. For
example, suppose that the most basic form of data in MOVES is the average over a five second
time period. Any distribution developed directly from the 5-second data would represent
variability in emissions from one 5-second averaging time to another.

The data within a bin may include multiple data values for each of many vehicles. If the
objective is to estimate inter-vehicle variability, then all of the 5-second average data values for a
given vehicle should be averaged to arrive at a best estimate of the average emissions for a 5-
second period for a given bin for that vehicle. This calculation would be repeated for all vehicles
in the bin. Then, the average values for each vehicle would be used to construct a distribution of
inter-vehicle variability within that bin. The range of variability will be influenced by the fact
that the calculations are based upon a 5-second time period. In contrast, if the objective were to
estimate variability in emissions for a 10-second time period, then the range of inter-vehicle
variability would tend to be somewhat smaller. Through simple calculations with the data, as
long as there are sufficient data and as long as the data can reasonably be assumed to be
statistically independent, it is easy to combine data for two or more averaging time periods to
construct estimates of average emissions over longer time periods.

Calculation of inter-vehicle variability for different averaging times is conceptually straight-
forward when all data are retained within a bin and if empirical distributions are employed. If
parametric distributions are employed, then it is necessary to develop an analytical procedure for
adjusting the distribution based upon different averaging times. As a conceptual example, Frey
and Rhodes (1996) illustrated that the variability in power plant efficiency decreases as the
averaging increases from one hour, to one day, to one week, and so on. By analyzing example
data sets, it is possible to develop an estimate of how the variance of the data is expected to
decrease as the averaging time increases. For example, the variance is a function of averaging
time. The mean would not change. Thus, if a distribution were fitted to 5-second averaging time
data, a new distribution could be estimated for 10-second averaging time assuming the same
mean and using the empirically-derived function of variance versus averaging time. We have
developed a conceptual example of an analytical averaging time adjustment method for the
parametric approach.

7.1.5 Normal and High Emitters
Regardless of whether empirical or parametric distributions are used, all data within a bin
represent the distribution for variability, including both "normal" and "high" emitters whose data
fall into the given bin. Thus, there is no need for a discrete approach for normal and high
emitters as has been used in the past. However, it is important to have a data set that is
representative of both normal and high emitters when developing estimates of average emissions,
of variability in emissions, and of uncertainty in average emissions. The average emission rate is
calculated based upon all of the data within the bin, and therefore takes into account both normal
and high emitters. Similarly, the standard deviation is calculated based upon all of the data
within the bin, and therefore takes into account both normal and high emitters.

EPA implies that as part of future work, the effects of I/M programs on the distribution of
emission will be evaluated, but this is not included as a task in this work. For example, an I/M
program might identify vehicles with emissions above some cut-off, and result in modification or
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repair of the vehicle so that its emissions are acceptable. The distribution of emissions can be
recalculated using numerical methods by truncating the distribution and by resampling from
within the range of acceptable emissions for those vehicles that successfully undergo repair or
modification. The numerical method can also be developed to take into account repeated failures
of some proportion of the vehicles and other considerations pertaining to EVI programs.

7.1.6 Uncertainty Estimates for Final Model Results
A key objective of MOVES is to estimate uncertainty in final model results. To illustrate an
approach for estimating uncertainty in final model results, consider a simple conceptual example.
Suppose that we wish to know the fleet average tailpipe emissions for LDGVs operating on a
particular corridor. As input assumptions, we specify information such as the typical speed
profile (e.g., an average estimate of second-by-second speed), road grade at specific locations
along the corridor, proportions of vehicles in different vehicle type categories, ambient
conditions, and proportion of vehicles in different mileage accumulation categories for each
vehicle type. Based upon this type of information, weights are calculated for each bin in the
MOVES model. If we focus on a specific vehicle type and mileage accumulation category, we
can narrow the discussion to consideration only of factors having to do with the speed profile and
the road grade. For each bin, an average emission rate can be estimated. Suppose that the
emissions are in units of grams per second. In order to estimate the total emissions associated
with a given bin, there must be an estimate of the amount of time that the vehicle spends "in" the
bin (figuratively speaking), which can be obtained based upon the known or assumed speed
profile and based upon the road grade. For example, if a VSP approach is used, the speed profile
and the road grade are used to estimate VSP, and the numerical value of VSP for a given
segment of the trip is used to determine from which bin an emission estimate is needed. Thus, in
this example, an emission estimate is a time-weighted average of the mass per time emission
rates obtained from different bins. The amount of time allocated to each of the bins will differ.

The uncertainty in the average emissions for the trip is based upon the uncertainty in the average
emission rates within each bin. Potentially, there could also be uncertainty regarding the amount
of time (or weight) assigned to each bin.

The uncertainty in the average emission rate is typically influenced by the following key
considerations: (1) random sampling error; (2) measurement error; and (3) lack of
representativeness. The first of these three can be characterized based upon the variance in the
data for variability and upon the sample size. For example, if normality conditions for the
sampling distribution of the mean are satisfied, the standard error of the mean is given the by
standard deviation for variability divided by the square root of the sample size. If normality
conditions are not satisfied, then a more accurate result can be obtained using bootstrap
simulation. For example, Frey and Rhodes (1996, 1998, 1999), Frey and Burmaster (1999),
Frey, Bharvirkar, and Zheng (1999), Frey and Bammi (2002a&b), Frey and Eichenberger
(1997b), and Frey and Zheng (2002a&b) have demonstrated the use of bootstrap simulation to
characterize uncertainty in mean emission rates in situations when data are positively skewed
and, in many cases, for small sample size. The range of uncertainty in the average emissions is
typically asymmetric when there is a large amount of variability in the data and a small sample
size. The use of a normality assumption in such situations can lead to uncertainty estimates for
the mean that predict negative emission rates, which is physically impossible. Therefore, it is
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important to employ an appropriate approach for quantifying uncertainty associated with random
sampling error. We recommend the use of bootstrap techniques where appropriate, and we will
also explore simplified solutions obtained based upon the results of bootstrap simulation. For
example, we hypothesize that it is possible to develop generic solution algorithms for estimating
asymmetric uncertainty ranges in the mean when the underlying data for variability can be fitted
reasonably well by a standard parametric distribution and when the coefficient of variation
(standard deviation divided by the mean) and the sample size of the original data are known.
Such algorithms could be used to make a rapid estimate of uncertainty in average emissions
without need to run a full bootstrap simulation in every case.

Random sampling error is typically the dominant source of uncertainty in the mean when the
sample sizes are small. Random sampling error in the mean is relatively easy to quantify in
practice because it can be inferred from the standard deviation and the sample size of the data,
which are usually known.

Measurement error is a potentially important source of uncertainty and should be considered in
developing MOVES. One drawback of estimating uncertainty based only upon random
sampling error is that for very large sample sizes, the random sampling error in the mean
becomes very small. If the measurement error has a random component, then the range of
observed variability in the data is larger than the true range of variability in the actual emissions.
Therefore, random measurement errors in the data are reflected in the range of uncertainty in the
mean emission rates estimated using techniques for random sampling error. However, if
measurement error has a systematic component (bias), statistical analysis alone will not detect
this without comparison to some benchmark. Measurement error may not be well known,
however. Therefore, this source of uncertainty can be difficult to quantify in practice. Since the
random component of measurement error influences the estimate of uncertainty in the mean
obtained from random sampling error-based estimated, the primary consideration in
incorporating measurement error more fully into the analysis is to properly distinguish random
measurement error from observed variability (e.g., Zheng, 2002) and to account for biases in
measurements.

Uncertainty because of lack of representativeness cannot be quantified based upon statistical
analysis of variation within a dataset obtained by only one method. In order to quantify
nonrepresentativeness, which relates to bias (also referred to as systematic error or lack of
accuracy), it is necessary to have a benchmark of the true value of the quantity. By using on-
board data, a key goal of MOVES is to develop emission estimates based upon real-world on-
road data. Thus, the fundamental basis of MOVES is to use representative, real world data. The
validation aspects of this project also aim at testing the representativeness of the data used for
model development. Overall, the focus of this project was on methods for quantifying
uncertainty associated with random sampling error, which also is influenced by random
measurement errors.

Monte Carlo simulation or similar numerical methods (e.g., Latin Hypercube Sampling) can be
used to propagate distributions for uncertainty in average emissions for a bin to arrive at an
estimate of uncertainty in the total emissions (e.g., Frey and Rhodes, 1996; Frey and Zheng,
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2001; Zheng and Frey, 2002). In cases with linear models in which normality assumptions are
reasonable, analytical solutions can also be used (Cullen and Frey, 1999).

7.1.7 Bottom-Up and Top-Down Approaches
In the shoot-out, NCSU illustrated both a bottom-up and top-down approach for estimating inter-
vehicle variability and fleet average uncertainty in emissions. The bottom-up approach was
based upon estimating variability or uncertainty for individual modes and using statistical
formulas to estimate the variability or uncertainty in the total emissions. The top-down approach
was based upon comparing trip emissions predictions of the model with the actual observed trip
emissions. Based upon statistical analysis of the parity plots of predictions versus observations,
a 95 percent probability prediction interval was estimated for inter-vehicle variability and a 95
percent confidence interval was estimated for uncertainty in the mean.

In principle, the bottom-up approach will be the more flexible and rigorous approach, and it will
also have an advantage of allowing for identification of which bins contributed the most to
uncertainty in the total emissions estimates. The top-down approach will typically be an easier
but less flexible approach, and it will not provide any insight regarding key sources of
uncertainty.

The primary approach explored in this chapter is the bottom-up approach. This approach is more
consistent with the EPA objective of characterizing variability in emissions within bins.
However, the top-down approach is illustrated in the validation comparisons of average driving
cycle emissions, as discussed in Chapter 9.

7.1.8 Summary of Methodological Considerations
The focus here is to demonstrate a methodology for characterizing inter-vehicle variability in the
binned data and uncertainty in the estimate of the final model result. The methodology was
demonstrated for the pilot modal emission rates. The emphasis of the work was on a parametric
distribution-based approach. The parametric approach was selected because of the attractiveness
of compactly representing large data sets within a bin using only a distribution type and a few
parameters. The adequacy of a purely parametric approach is assessed. A method for properly
characterizing the effect of averaging time on variability (and, in turn, on uncertainty) is
demonstrated.

7.2 Quantification of Variability
Parametric probability distribution models that were considered for fit to data include normal,
lognormal and Weibull distributions. These distributions were selected because they often offer
good fits to dataset. In particular, the lognormal distribution is often a good candidate for fitting
to non-negative positively skewed data, and can be theoretically justified as a descriptor of
emissions data because both emissions and the lognormal distribution are based upon
multiplicative processes. The Weibull distribution can also be used to fit to nonnegative
positively skewed data. However, the Weibull distribution has additional flexibility to take on
different shapes and often has a shorter upper tail than the lognormal distribution does, when
viewed as a cumulative distribution function. The less "tail-heavy" nature of the Weibull
distribution often provides an empirically better fit than does the lognormal distribution. The
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normal distribution often provides a good fit but is appropriate for use with non-negative data
only if the ratio of the standard deviation to the mean is sufficiently small (e.g., around 0.2 or
less). Otherwise, the normal distribution may lead to predictions of negative values with
unacceptable frequency. In general, it is usually not appropriate to use the normal distribution to
represent variability within a bin, but it is often appropriate to use the normal distribution to
describe uncertainty in the average.

The probability density function (PDF) of the normal distribution is:
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                                                            Empirical CDF
                                                            Fitted Parametric Distribution
Figure 7-1. Variability in NOX, HC, CC>2, and CO Emissions for VSP Mode #1 Characterized by
Empirical Probability Distribution and Fitted Parametric Probability Distribution, Time Average,
             Odometer reading < 50,000 miles, Engine Displacement < 3.5 liters.
                                          123
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    Figure 7-2. Variability in NOX, HC, CO2, and CO Emissions for VSP Mode #4 Characterized by
    Empirical Probability Distribution and Fitted Parametric Probability Distribution, Time Average,
                 Odometer reading < 50,000 miles, Engine Displacement > 3.5 liters.
                                              124
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  Empirical Probability Distribution and Fitted Parametric Probability Distribution, Time Average,
               Odometer reading > 50,000 miles, Engine Displacement < 3.5 liters.
                                            125
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     by Empirical Probability Distribution and Fitted Parametric Probability Distribution, Time
           Average, Odometer reading > 50,000 miles, Engine Displacement > 3.5 liters.
                                            126
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Overall, in most cases, the fitted distributions appear to compare well with the data.  Because
statistical GOF tests are too sensitive, from a practical perspective, when the sample size
becomes large, alternative criteria for evaluating goodness-of-fit were sought. One such criterion
is to evaluate the absolute difference between the mean of the data and the mean of the fitted
distribution. A second criterion is to evaluate the absolute difference of the standard deviation of
the data versus that of the fitted distribution. Therefore, these absolute differences were
calculated for each of the 14 VSP modes, for each of the four strata by engine displacement and
odometer reading reading, and for each of the four pollutants.

The distributions were fitted to the data using Maximum Likelihood Estimation (MLE). The
choice of MLE was made on the basis that MLE is commonly used and is considered to be a
more statistically efficient method than other approaches, such as the Method of Matching
Moments (MoMM) (Cullen and Frey, 2002). However, MLE has a potential disadvantage in
that the central moments of the fitted distribution (e.g., the mean and standard deviation) may not
be the same as those of the data to which the distribution was fit. In contrast, for MoMM
estimates of the distribution parameters, the fitted distribution will  have a mean and standard
deviation the  same as that of the data.  In most cases, the difference of the means and standard
deviations between fitted distributions and the data are not large in an absolute sense, as shown
in  Tables 7-1  and 7-2, respectively. For example, for VSP Bins 1101 through 1114, which
represent data for odometer reading < 50,000 miles, and engine displacement < 3.5 liters, the
largest absolute deviation in  the mean values for NOX is for Mode 12 of this strata (identified as
VSP Bin 1112 in Table 7-1), with an absolute difference of 0.0004 g/sec.  This difference is in
comparison to a mean from the data set of 0.0121 g/sec, and a mean from the fitted distribution
of 0.0125 g/sec.  Therefore, on a relative basis, this difference is only approximately three
percent of the mean of the data. For the other  13 modes for this pollutant and strata, the absolute
differences are smaller. However, in some cases, the relative differences are very large. For
example, for Mode 1104, the absolute difference is -0.00028 g/sec compared to a data mean of
0.00117. Thus, the relative difference in this case is  -24 percent. However, the absolute
difference in the mean for Mode 1104 is only 70 percent of the absolute difference for Mode
1112. Typically, the largest  absolute differences are  small compared to the highest average
emission rates among the modes for given pollutant and strata, although there are some
exceptions (e.g., Mode 1211  for CO).  The exceptions typically point to situations in which a
single component distribution cannot provide a good fit because the data are inherently some
type of mixture distributions.

Based upon a review of the results in Tables 7-1  and  7-2, criteria for discriminating good and bad
fit were proposed for different pollutants. These criteria are shown in the second column of
Table 7-3. For example, for NOX, if the absolute difference in the mean of the MLE fitted
distribution versus that of the data is larger than the magnitude of the criteria value, which is
0.001 g/sec, the fit is judged  not to be good. When the absolute differences in the mean of the
fitted distribution is less than the criteria value, the fit was also judged to be acceptable. Of the
56 modes, 49 of the modes for NOX have differences in the mean between the data and the fitted
distribution of less than the criteria value. For CO, 48 of the modes satisfy the criteria value, for
HC 54 of the  modes satisfy the critera, and for CO2 all 56 modes satisfy the criteria value.
                                           127
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         Table 7-1. Comparison of Mean between Empirical Data Set and Fitted Parametric Distributions, Absolute Basis
VSP Bin8
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1201
1202
1203
1204
N0xb
empirical
0.000901
0.000628
0.000346
0.00117
0.00171
0.00237
0.00310
0.00423
0.00507
0.00587
0.00762
0.0121
0.0155
0.0179
0.000290
0.000223
0.000174
0.000719
fitted dist
0.000714
0.000554
0.000221
0.000894
0.00167
0.00234
0.00303
0.00440
0.00509
0.00601
0.00776
0.0125
0.0152
0.0180
0.000176
0.000112
0.0000733
0.000682
diff
-0.000187
-0.0000745
-0.000124
-0.000279
-0.0000384
-0.0000288
-0.0000746
0.000162
0.0000255
0.000146
0.000135
0.000398
-0.000267
0.000167
-0.000113
-0.000111
-0.000101
-0.0000374
HCb
empirical
0.000450
0.000257
0.000406
0.000432
0.000530
0.000705
0.000822
0.000976
0.00111
0.00144
0.00206
0.00337
0.00486
0.0109
0.000548
0.000222
0.000272
0.000472
fitted dist
0.000460
0.000187
0.000290
0.000357
0.000506
0.000709
0.000947
0.00121
0.00137
0.00184
0.00200
0.00309
0.00564
0.0185
0.000161
0.0000357
0.0000441
0.000125
diff
0.0000103
-0.0000701
-0.000116
-0.0000748
-0.0000242
0.00000383
0.000124
0.000235
0.000261
0.000396
-0.0000595
-0.000285
0.000787
0.00759
-0.000387
-0.000187
-0.000228
-0.000347
CO2b
empirical
1.67
1.46
1.14
2.23
2.92
3.53
4.11
4.64
5.16
5.63
6.53
7.59
9.02
10.1
1.57
1.44
1.47
2.61
fitted dist
1.68
1.45
1.11
2.26
2.92
3.52
4.09
4.62
5.13
5.60
6.52
7.58
9.02
10.1
1.56
1.38
1.43
2.61
diff
0.00901
-0.0122
-0.0213
0.0223
0.00448
-0.00774
-0.0135
-0.0192
-0.0280
-0.0295
-0.0160
-0.00516
-0.00434
0.00887
-0.00525
-0.0685
-0.0426
-0.00628
cob
empirical
0.00781
0.00391
0.00335
0.00834
0.0110
0.0170
0.0200
0.0292
0.0355
0.0551
0.114
0.208
0.442
0.882
0.0177
0.00861
0.00848
0.0145
fitted dist
0.00644
0.00248
0.00232
0.00877
0.00693
0.0101
0.0134
0.0182
0.0230
0.0823
0.177
0.381
2.08
15.8
0.00883
0.00109
0.00219
0.00560
diff
-0.00136
-0.00143
-0.00103
0.000437
-0.00403
-0.00691
-0.00662
-0.0110
-0.0125
0.0272
0.0630
0.174
1.63
15.0
-0.00886
-0.00752
-0.00629
-0.00894
(Continued on next page).
                                                       128
-------
 Table 7-1. Continued.
VSP Bin8
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
2101
2102
2103
2104
2105
2106
2107
N0xb
empirical
0.00114
0.00159
0.00237
0.00410
0.00612
0.00731
0.0132
0.0127
0.0154
0.0203
0.00101
0.00104
0.000423
0.00161
0.00264
0.00379
0.00510
fitted dist
0.00106
0.00140
0.00234
0.00427
0.00609
0.00735
0.0133
0.0122
0.0175
0.0277
0.000933
0.000888
0.000416
0.00171
0.00270
0.00386
0.00514
diff
-0.0000757
-0.000185
-0.0000344
0.000169
-0.0000310
0.0000373
0.000155
-0.000503
0.00210
0.00742
-0.0000812
-0.000154
-0.00000691
0.0000994
0.0000615
0.0000704
0.0000440
HCb
empirical
0.000754
0.000702
0.000944
0.00144
0.00171
0.00261
0.00352
0.00765
0.00667
0.00657
0.000901
0.000901
0.000835
0.00103
0.00125
0.00166
0.00209
fitted dist
0.000261
0.000477
0.00102
0.00128
0.00163
0.00240
0.00441
0.00918
0.00664
0.00658
0.000827
0.000880
0.000936
0.00113
0.00151
0.00156
0.00209
diff
-0.000493
-0.000225
0.0000781
-0.000161
-0.0000792
-0.000207
0.000884
0.00152
-0.0000266
0.00000652
-0.0000746
-0.0000215
0.000100
0.000103
0.000262
-0.000100
-0.0000000742
CO2b
empirical
3.52
4.65
5.64
6.60
7.65
8.81
11.7
14.5
15.7
17.4
1.54
1.60
1.13
2.39
3.21
3.96
4.75
fitted dist
3.49
4.62
5.57
6.57
7.59
8.75
11.6
14.5
15.6
17.4
1.54
1.61
1.10
2.39
3.21
3.94
4.74
diff
-0.0305
-0.0306
-0.0612
-0.0311
-0.0594
-0.0629
-0.0625
-0.00549
-0.0425
0.00448
-0.00782
0.00584
-0.0352
0.00229
-0.00404
-0.0216
-0.0167
cob
empirical
0.0257
0.0252
0.0411
0.0766
0.129
0.151
0.355
0.882
0.755
0.905
0.0110
0.00872
0.00468
0.0122
0.0167
0.0233
0.0293
fitted dist
0.0125
0.0418
0.0954
0.243
0.280
0.210
1.57
0.967
0.834
0.930
0.00921
0.0155
0.00459
0.0107
0.0148
0.0209
0.0275
diff
-0.0132
0.0166
0.0543
0.166
0.151
0.0592
1.22
0.0856
0.0788
0.0256
-0.00182
0.00680
-0.0000939
-0.00149
-0.00194
-0.00236
-0.00179
(Continued on next page)
                                                         129
-------
Table 7-1.  Continued.
VSP Bin8
2108
2109
2110
2111
2112
2113
2114
2201
2202
2203
2204
2205
2206
2207
2208
2209
NOxb
empirical
0.00637
0.00766
0.00991
0.0127
0.0144
0.0160
0.0167
0.000725
0.000504
0.000661
0.00252
0.00585
0.00836
0.0106
0.0145
0.0164
fitted dist
0.00652
0.00775
0.0100
0.0130
0.0145
0.0162
0.0170
0.000619
0.000489
0.000754
0.00292
0.00695
0.00928
0.0113
0.0155
0.0175
diff
0.000146
0.0000836
0.000115
0.000290
0.000105
0.000209
0.000242
-0.000106
-0.0000148
0.0000929
0.000406
0.00110
0.000919
0.000694
0.00106
0.00110
HCb
empirical
0.00233
0.00282
0.00298
0.00379
0.00457
0.00570
0.00716
0.000863
0.000300
0.000323
0.000449
0.000818
0.00122
0.00211
0.00439
0.00464
fitted dist
0.00232
0.00280
0.00303
0.00380
0.00462
0.00569
0.00721
0.000530
0.000219
0.000266
0.000409
0.000637
0.00106
0.00200
0.00453
0.00450
diff
-0.0000162
-0.0000195
0.0000464
0.0000159
0.0000482
-0.0000096
0.0000479
-0.000333
-0.0000813
-0.0000575
-0.0000398
-0.000181
-0.000155
-0.000108
0.000134
-0.000133
CO2b
empirical
5.37
5.94
6.43
7.07
7.62
8.32
8.48
1.65
1.76
1.56
2.95
4.13
5.34
6.51
7.60
8.77
fitted dist
5.34
5.92
6.39
7.04
7.60
8.30
8.46
1.63
1.68
1.48
2.94
4.12
5.34
6.50
7.60
8.77
diff
-0.0317
-0.0168
-0.0347
-0.0240
-0.0149
-0.0204
-0.0145
-0.0178
-0.0833
-0.0815
-0.00368
-0.00309
-0.00370
-0.00441
-0.00391
-0.00112
cob
empirical
0.0369
0.0495
0.0638
0.105
0.248
0.413
0.625
0.0203
0.00818
0.00483
0.0123
0.0220
0.0451
0.0775
0.167
0.170
fitted dist
0.0344
0.0557
0.0652
0.0834
0.170
0.375
0.701
0.0216
0.00332
0.00211
0.0139
0.0209
0.0447
0.0765
0.152
0.167
diff
-0.00255
0.00617
0.00148
-0.0220
-0.0775
-0.0381
0.0762
0.00136
-0.00486
-0.00272
0.00157
-0.00115
-0.000326
-0.00100
-0.0144
-0.00262
(Continued on next page).
                                                         130
-------
Table 7-1. Continued.
VSP Bin8
2210
2211
2212
2213
2214
NOxb
empirical
0.0198
0.0305
0.0342
0.0434
0.0690
fitted dist
0.0213
0.0326
0.0341
0.0433
0.0688
diff
0.00154
0.00209
-0.0000985
-0.000115
-0.000151
HCb
empirical
0.00496
0.00663
0.0109
0.0166
0.0271
fitted dist
0.00461
0.00643
0.0107
0.0166
0.0275
diff
-0.000356
-0.000203
-0.000221
0.0000243
0.000473
CO2b
empirical
10.4
12.8
15.0
16.9
18.9
fitted dist
10.4
12.8
15.0
16.9
18.9
diff
-0.00409
-0.00133
0.00141
0.00567
0.00168
cob
empirical
0.264
0.339
0.825
1.44
2.18
fitted dist
0.248
0.363
0.823
0.242
2.40
diff
-0.0153
0.0242
-0.00141
-1.20
0.223
a First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement < 3.5 liters; 12: odometer reading <
50,000 miles and engine displacement > 3.5 liters; 21: odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22:
odometer reading > 50,000 miles and engine displacement > 3.5 liters.
b Unit of mean: g/sec; Unit of diff: g/sec.
                                                           131
-------
    Table 7-2. Comparison of Standard Deviation between Empirical Data Set and Fitted Parametric Distributions, Absolute Basis
VSP Bin8
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1201
1202
1203
1204
N0xb
empirical
0.00295
0.00256
0.00154
0.00343
0.00442
0.00567
0.00671
0.00794
0.0101
0.0110
0.0147
0.0201
0.0247
0.0277
0.00135
0.00142
0.00125
0.00228
fitted dist
0.00181
0.00155
0.000544
0.00262
0.00469
0.00629
0.00799
0.0109
0.0127
0.0142
0.0166
0.0240
0.0240
0.0304
0.000495
0.000303
0.000185
0.00217
diff
-0.00114
-0.00101
-0.00100
-0.000809
0.000269
0.000621
0.00128
0.00298
0.00259
0.00318
0.00196
0.00394
-0.000653
0.00269
-0.000858
-0.00112
-0.00107
-0.000105
HCb
empirical
0.00283
0.00112
0.00150
0.00141
0.00160
0.00237
0.00240
0.00281
0.00267
0.00369
0.00545
0.0104
0.0133
0.0249
0.00246
0.00177
0.00194
0.00246
fitted dist
0.00257
0.000921
0.00157
0.00170
0.00223
0.00308
0.00419
0.00542
0.00559
0.00845
0.00335
0.00507
0.0210
0.195
0.00102
0.0000879
0.000121
0.000475
diff
-0.000259
-0.000202
0.0000668
0.000290
0.000630
0.000714
0.00179
0.00260
0.00292
0.00477
-0.00210
-0.00534
0.00769
0.170
-0.00145
-0.00169
-0.00182
-0.00199
CO2b
empirical
1.39
1.21
0.816
1.38
1.53
1.67
1.77
1.94
2.09
2.35
2.72
2.99
3.64
5.37
0.752
0.730
0.784
1.08
fitted dist
1.27
1.20
0.832
1.48
1.52
1.68
1.79
1.97
2.13
2.40
2.66
3.00
3.64
5.35
0.775
0.990
0.862
0.981
diff
-0.118
-0.0122
0.0155
0.0925
-0.00811
0.0161
0.0204
0.0319
0.0378
0.0502
-0.0570
0.00935
-0.00180
-0.0248
0.0226
0.260
0.0785
-0.100
cob
empirical
0.0589
0.0367
0.0216
0.0519
0.0968
0.155
0.106
0.152
0.165
0.252
0.396
0.571
0.906
1.52
0.0876
0.0764
0.0697
0.0803
fitted dist
0.0873
0.0307
0.0267
0.164
0.0195
0.0291
0.0378
0.0536
0.0674
2.40
5.86
13.4
173
6426
0.240
0.00895
0.0296
0.0868
diff
0.0284
-0.00602
0.00509
0.112
-0.0774
-0.126
-0.0684
-0.0987
-0.0981
2.15
5.46
12.8
172
6424
0.153
-0.0674
-0.0401
0.00648
(Continued on next page)
                                                          132
-------
 Table 7-2. Continued.
VSP Bin8
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
2101
2102
2103
2104
2105
2106
2107
N0xb
empirical
0.00334
0.00440
0.00552
0.00813
0.0140
0.0145
0.0245
0.0230
0.0359
0.0378
0.00229
0.00257
0.00168
0.00334
0.00467
0.00658
0.00802
fitted dist
0.00345
0.00454
0.00628
0.0104
0.0138
0.0151
0.0281
0.0187
0.0766
0.122
0.00198
0.00215
0.000959
0.00442
0.00587
0.00751
0.00859
diff
0.000116
0.000145
0.000753
0.00225
-0.000243
0.000630
0.00358
-0.00433
0.0408
0.0846
-0.000316
-0.000424
-0.000724
0.00108
0.00120
0.000929
0.000563
HCb
empirical
0.00360
0.00277
0.00278
0.00722
0.00443
0.00909
0.00699
0.0117
0.00917
0.00769
0.00225
0.00228
0.00312
0.00287
0.00294
0.00377
0.00403
fitted dist
0.00121
0.00269
0.00726
0.00729
0.00691
0.0107
0.0218
0.0375
0.00937
0.00744
0.00158
0.00178
0.00689
0.00614
0.00717
0.00260
0.00317
diff
-0.00239
-0.0000782
0.00448
0.0000726
0.00248
0.00159
0.0148
0.0258
0.000205
-0.000244
-0.000666
-0.000505
0.00377
0.00327
0.00423
-0.00117
-0.000860
CO2b
empirical
1.21
1.79
2.31
2.64
2.51
2.80
3.38
2.53
1.95
2.21
1.11
1.11
0.713
1.17
1.29
1.36
1.50
fitted dist
1.32
1.86
2.44
2.75
2.66
2.94
3.45
2.36
2.02
2 22
1.09
1.05
0.870
1.18
1.33
1.44
1.57
diff
0.116
0.0780
0.132
0.110
0.155
0.138
0.0633
-0.168
0.0729
0.0116
-0.0207
-0.0655
0.157
0.00910
0.0447
0.0770
0.0697
cob
empirical
0.139
0.113
0.166
0.286
0.411
0.475
0.934
1.45
1.10
1.18
0.0471
0.0371
0.0286
0.0501
0.0669
0.0828
0.0809
fitted dist
0.260
1.19
3.05
15.5
11.4
3.65
126
2.78
1.75
1.41
0.0220
0.225
0.0477
0.0226
0.0279
0.0353
0.0424
diff
0.121
1.08
2.89
15.2
11.0
3.18
125
1.34
0.650
0.234
-0.0251
0.188
0.0191
-0.0274
-0.0390
-0.0475
-0.0385
(Continued on next page)
                                                          133
-------
Table 7-2. Continued.
VSP Bin8
2108
2109
2110
2111
2112
2113
2114
2201
2202
2203
2204
2205
2206
2207
2208
2209
NOxb
empirical
0.00901
0.0107
0.0135
0.0163
0.0166
0.0186
0.0182
0.00203
0.00137
0.00181
0.00402
0.00834
0.0117
0.0133
0.0178
0.0200
fitted dist
0.0101
0.0114
0.0145
0.0182
0.0185
0.0214
0.0213
0.00142
0.00126
0.00161
0.00713
0.0186
0.0206
0.0211
0.0287
0.0315
diff
0.00109
0.000657
0.000959
0.00187
0.00182
0.00278
0.00313
-0.000610
-0.000111
-0.000202
0.00311
0.0102
0.00890
0.00785
0.0109
0.0115
HCb
empirical
0.00355
0.00520
0.00484
0.00687
0.00707
0.00814
0.0100
0.00572
0.00132
0.00249
0.000901
0.00430
0.00249
0.00404
0.0111
0.00739
fitted dist
0.00323
0.00390
0.00420
0.00513
0.00621
0.00765
0.00945
0.00192
0.000455
0.000568
0.000634
0.00106
0.00211
0.00531
0.0172
0.00671
diff
-0.000321
-0.00130
-0.000640
-0.00175
-0.000863
-0.000490
-0.000532
-0.00380
-0.000860
-0.00192
-0.000267
-0.00324
-0.000377
0.00128
0.00608
-0.000680
CO2b
empirical
1.64
1.81
1.96
2.30
2.45
3.00
3.19
0.614
0.676
0.662
0.735
0.886
1.08
1.35
1.44
1.50
fitted dist
1.72
1.87
2.05
2.38
2.56
3.09
3.25
0.685
0.856
1.13
0.676
0.836
1.02
1.26
1.36
1.47
diff
0.0744
0.0537
0.0877
0.0775
0.101
0.0927
0.0524
0.0715
0.181
0.464
-0.0582
-0.0500
-0.0627
-0.0835
-0.0803
-0.0298
cob
empirical
0.102
0.147
0.209
0.331
0.665
0.918
1.26
0.114
0.0762
0.0835
0.0623
0.0699
0.120
0.196
0.430
0.329
fitted dist
0.0511
0.177
0.207
0.242
0.614
2.27
6.02
0.489
0.0510
0.0219
0.163
0.0493
0.102
0.157
0.294
0.270
diff
-0.0507
0.0300
-0.00169
-0.0896
-0.0508
1.35
4.76
0.375
-0.0252
-0.0615
0.101
-0.0206
-0.0183
-0.0396
-0.136
-0.0596
(Continued on next page)
                                                         134
-------
Table 7-2. Continued.
VSP Bin8
2210
2211
2212
2213
2214
NOxb
empirical
0.0261
0.0330
0.0466
0.0493
0.0572
fitted dist
0.0422
0.0521
0.0518
0.0484
0.0630
diff
0.0161
0.0192
0.00521
-0.000869
0.00582
HCb
empirical
0.00948
0.0106
0.0168
0.0179
0.0327
fitted dist
0.00751
0.00980
0.0164
0.0202
0.0406
diff
-0.00196
-0.000809
-0.000441
0.00228
0.00795
CO2b
empirical
1.83
2.14
1.62
2.39
2.10
fitted dist
1.74
2.08
1.65
2.44
2.07
diff
-0.0961
-0.0507
0.0221
0.0568
-0.0313
cob
empirical
0.651
0.706
1.29
1.43
2.05
fitted dist
0.909
1.28
1.57
0.369
3.80
diff
0.257
0.577
0.272
-1.06
1.75
a First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement < 3.5 liters; 12: odometer reading <
50,000 miles and engine displacement > 3.5 liters; 21: odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22:
odometer reading > 50,000 miles and engine displacement > 3.5 liters.
b Unit of mean: g/sec; Unit of diff: g/sec.
                                                           135
-------
   Table 7-3. Comparisons of Empirical Data Set and Fitted Parametric Distributions, Average
                         Difference for Good Fits, Fitting Based upon MLE
Pollutant
NOX
HC
C02
CO
Criteria
(g/sec)a
0.001
0.001
0.1
0.1
No.
of
good
fits
49
54
56
48
Mean
Empirical
(g/sec)
0.00812
0.00302
6.27
0.140
Abs. diff
(g/sec)
0.0000404
-0.0000192
-0.0186
0.00511
Rel.
diff
(%)
0.50
-0.64
-0.30
3.6
Standard deviation
Empirical
(g/sec)
0.0116
0.00570
1.81
0.304
Abs. diff
(g/sec)
0.00119
0.000611
0.0372
0.500
Rel.
diff
(%)
10
11
2.1
160
a A fit is good when its absolute difference in the mean is smaller than criteria value.
   Table 7-4. Comparisons of Empirical Data Set, Fitted Lognormal Distributions Based upon
           MLE, and Fitted Lognormal Distributions Based upon MoMM, for the Two Worst
                                        MLE Fits for CO.
VSP
Bin3
1113
1114
MLE
Mean
empirical
0.442
0.882
fitted
dist
2.08
15.8
diff
1.63
15.0
Standard Deviation
empirical
0.906
1.52
fitted
dist
173
6426
diff
172
6424
MoMM
Mean
empirical
0.442
0.882
fitted
dist
0.442
0.882
diff
0
0
Standard Deviation
empirical
0.906
1.52
fitted
dist
0.906
1.52
diff
0
0
a First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement <
3.5 liters.
From Table 7-3, it is apparent that the relative difference in the mean values of the fitted
distribution and the data is less than one percent for NOX, HC, and CC>2 for the vast majority of
the modes, and less than four percent for the majority of the modes in the case of CO.  The
estimated standard deviation tends to be more sensitive to deviations of the fitted distribution
from the data than does the estimated mean. For most of the modes and pollutants, the relative
difference between the standard deviation of the fitted distribution versus that of the data is less
than 10 percent, but there are some examples for CO in which the difference is substantially
larger.

In this study, MLE was used to estimate parameters of fitted parametric distributions for
representing variability in population. If MoMM was used, there would have been no difference
in the mean and standard deviation between the empirical sample data and fitted distribution, as
shown for selected examples in Table 7-4.  In these two examples, which represent the worst fits
of parametric distributions to modal data for CO, the MoMM fitted distribution is confirmed to
have the same mean and standard deviation as the original  data, whereas both the mean and
standard deviations of the distribution fitted using MLE are substantially different than the
values estimated directly from the data.  However, it is not likely that the mean and the standard
deviation of population will be exactly the same as those of sample. The basis for fitting a
distribution using MLE is to estimate a distribution from which the data were most likely to have
been a sample, which is a different criterion than that for estimating a distribution using MoMM.
                                           136
-------
           Table 7-5. Recommendation of Mixture Distributions for Two Worst Fits
Bin3
1113
1114
Pollutant
CO
CO
Dist. 1
Lognormal
Lognormal
Dist. 2
Lognormal
Lognormal
Weight
0.7878
0.6367
Dist. lb
Paral
2.3619
2.1368
Para 2
-4.7782
-5.4363
Dist. 2b
Para 1
0.6782
0.7358
Para 2
0.329
0.6043
a First two digit of VSP Bins: 11:  odometer reading < 50,000 miles and engine displacement <
3.5 liters.
b Para 1 of lognormal is 0 and Para 2 of lognormal is |.
Even though MoMM results in the same estimates of the mean and standard deviation as the
original data set, MoMM does not always provide a good fit. For example, distributions fitted
using both MLE and MoMM for the case of CO emissions for odometer reading < 50,000 miles,
and engine displacement < 3.5 Liters,  are shown in comparison to the empirical distribution of
the data for VSP Mode 14 in Figure 7-5.  A similar example is given for Mode 13, for CO for the
same odometer reading and engine displacement category in Figure 7-6. Figures 7-5 and 7-6
suggest that neither MLE nor MoMM provides an ideal fit compared to the data. When
comparing MLE and MoMM fits for these two cases, it appears that MLE provides a better fit
for the lower percentiles of the distribution and MoMM provides a better fit for the upper tail of
the distribution. However, it is also clear in these examples that the data are not well represented
by a single component parametric distribution, especially in the central portion of the
distribution.  A key question is whether occasional disagreements between fitted distributions
and data, such as these, can be tolerated in the model. Alternatively, either mixture distributions
or empirical distributions can be used to represent data such as these. For the same data as
shown in Figure 7-5, an illustration of the use of a fitted mixture distribution is shown in Figure
7-7.  Similarly, for the same data as shown in Figure 7-6, an illustration of the use of a fitted
mixture distribution is given in Figure 7-8. The parameters of the mixture distributions  shown in
Figures 7-7 and 7-8 are given in Table 7-5. The mixture distributions comprised of only two
lognormal components are shown to agree very well with the empirical data in both cases.  The
mixture distributions were estimated using MLE as described by Zheng (2002) using a modified
version of AuvTool. These example case studies illustrate that mixture distributions can be an
effective approach for achieving a good fit when a single component distribution is not adequate.
These case studies also suggest that the data in these modes may be  comprised of two or more
subpopulations that might reflect different activity patterns or  different vehicle characteristics.

Table 7-6 summarizes the type of parametric distribution and the parameters of the distribution
fitted to the data for each pollutant and mode based upon MLE approach.
                                           137
-------
                                                           Empirical
                                                     	MoMM
                                                     —  - MLE
       O
                                                                      10
                                      CO (g/sec)
 Figure 7-5. Comparison of Fitted Parametric Distribution Based upon Method of Matching
Moment and Maximum Likelihood Estimation, Mode 14 CO Emissions, Odometer reading <
                    50,000 miles, Engine Displacement < 3.5 liters.
                                                            Empirical
                                                         - -MoMM
                                                          -  'MLE
        O
                                        CO (g/sec)


 Figure 7-6. Comparison of Fitted Parametric Distribution Based upon Method of Matching
Moment and Maximum Likelihood Estimation, Mode 13 CO Emissions, Odometer reading <
                    50,000 miles, Engine Displacement < 3.5 liters
                                       138
-------
                        Lognormal + Lognormal, Weight = 0.6367
                    1.0-r
                                                      A Data
                                                          (n=344)


                                                      X  Mixture Distribution
                    o.o
                      0.0   3.4    6.9   10.3  13.7   17.1
                               CO (g/sec)
Figure 7-7. Mixture Distribution Comprised of Two Lognormal Components Fitted to Data for
Mode 14 CO Emissions for Odometer Reading < 50,000 miles and Engine Displacement < 3.5
                                         Liters.
                     Lognormal + Lognormal, Weight = 0.7878
             33  0.44-
             3
                0.2-
                0.0 I
                                                      )ata
                                                      (n=648)
                                                           Mixture Distribution
0.0   2.2    A A   c
         CO (g/sec)
                                       8.7   10.9
Figure 7-8. Mixture Distribution Comprised of Two Lognormal Components Fitted to Data for
Mode 13 CO Emissions for Odometer Reading < 50,000 miles and Engine Displacement < 3.5
                                         Liters.
                                          139
-------
 Table 7-6. Summary of Single Component Parametric Probability Distributions Fitted Using MLE for Variability in VSP Modes for
                     NOV, HC, CO,, and CO for Vehicles of Different Engine Displacement and Odometer Reading.
VSP Bin3
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
NOX
Distb
W
W
W
W
W
W
W
W
W
W
W
W
W
para 1
3.00E-04
2.00E-04
9.74E-05
3.00E-04
6.00E-04
9.00E-04
1.20E-03
1.90E-03
2.20E-03
2.80E-03
4.10E-03
7.60E-03
1.12E-02
para 2
4.58E-01
4.29E-01
4.68E-01
4.17E-01
4.29E-01
4.41E-01
4.46E-01
4.65E-01
4.64E-01
4.82E-01
5.16E-01
5.61E-01
6.54E-01
HC
Distb
L
L
L
L
L
L
L
L
L
L
W
W
L
para 1
1.86E+00
1.80E+00
1.85E+00
1.78E+00
1.74E+00
1.73E+00
1.74E+00
1.74E+00
1.69E+00
1.76E+00
1.40E-03
2.20E-03
1.64E+00
para 2
-9.42E+00
-1.02E+01
-9.85E+00
-9.52E+00
-9.10E+00
-8.75E+00
-8.47E+00
-8.24E+00
-8.02E+00
-7.85E+00
6.25E-01
6.35E-01
-6.52E+00
C02
Distb
W
W
W
L
W
W
W
W
W
W
W
W
W
para 1
1.83E+00
1.54E+00
1.22E+00
5.97E-01
3.30E+00
3.97E+00
4.62E+00
5.20E+00
5.78E+00
6.32E+00
7.34E+00
8.52E+00
1.01E+01
para 2
1.34E+00
1.21E+00
1.35E+00
6.35E-01
2.01E+00
2.21E+00
2.43E+00
2.51E+00
2.59E+00
2.49E+00
2.63E+00
2.73E+00
2.67E+00
CO
Distb
L
L
L
L
W
W
W
W
W
L
L
L
L
para 1
2.28E+00
2.24E+00
2.21E+00
2.42E+00
2.50E-03
3.50E-03
4.80E-03
6.10E-03
7.80E-03
2.60E+00
2.65E+00
2.67E+00
2.97E+00
para 2
-7.65E+00
-8.52E+00
-8.52E+00
-7.66E+00
4.29E-01
4.22E-01
4.28E-01
4.16E-01
4.18E-01
-5.87E+00
-5.23E+00
-4.52E+00
-3.69E+00
(Continued on next page).
                                                         140
-------
Table 7-6. Continued.
VSP Bin3
1114
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
NOX
Distb
W
W
W
W
W
W
W
W
W
W
W
W
W
para 1
1.25E-02
6.36E-05
4.28E-05
3.10E-05
2.00E-04
3.00E-04
4.00E-04
9.00E-04
1.90E-03
3.00E-03
4.10E-03
7.20E-03
9.20E-03
para 2
6.20E-01
4.29E-01
4.39E-01
4.60E-01
3.96E-01
3.91E-01
3.93E-01
4.41E-01
4.71E-01
4.96E-01
5.32E-01
5.22E-01
6.70E-01
HC
Distb
L
L
L
L
L
L
L
L
L
L
L
L
L
para 1
2.17E+00
1.93E+00
1.40E+00
1.46E+00
1.65E+00
1.76E+00
1.87E+00
1.99E+00
1.87E+00
1.72E+00
1.74E+00
1.80E+00
1.70E+00
para 2
-6.35E+00
-1.06E+01
-1.12E+01
-1.11E+01
-1.04E+01
-9.81E+00
-9.39E+00
-8.86E+00
-8.41E+00
-7.89E+00
-7.55E+00
-7.04E+00
-6.13E+00
C02
Distb
W
W
W
W
L
W
W
W
W
W
W
W
L
para 1
1.14E+01
1.76E+00
1.51E+00
1.60E+00
3.64E-01
3.92E+00
5.20E+00
6.29E+00
7.40E+00
8.48E+00
9.75E+00
1.29E+01
1.62E-01
para 2
1.97E+00
2.12E+00
1.41E+00
1.71E+00
8.91E-01
2.87E+00
2.67E+00
2.44E+00
2.57E+00
3.12E+00
3.28E+00
3.76E+00
2.66E+00
CO
Distb
L
L
L
L
L
L
L
L
L
L
L
L
W
para 1
3.47E+00
2.57E+00
2.06E+00
2.28E+00
2.34E+00
2.46E+00
2.59E+00
2.63E+00
2.88E+00
2.72E+00
2.39E+00
2.96E+00
3.36E-01
para 2
-3.24E+00
-8.03E+00
-8.94E+00
-8.73E+00
-7.93E+00
-7.42E+00
-6.52E+00
-5.82E+00
-5.57E+00
-4.98E+00
-4.42E+00
-3.93E+00
4.22E-01
(Continued on next page).
                                                          141
-------
Table 7-6. Continued.
VSP Bin3
1213
1214
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
NOX
Distb
L
L
W
W
W
W
W
W
W
W
W
W
W
para 1
1.73E+00
1.74E+00
5.00E-04
4.00E-04
2.00E-04
7.00E-04
1.40E-03
2.30E-03
3.60E-03
4.90E-03
6.10E-03
8.00E-03
1.06E-02
para 2
-5.55E+00
-5.10E+00
5.20E-01
4.74E-01
4.90E-01
4.53E-01
5.10E-01
5.55E-01
6.26E-01
6.66E-01
6.98E-01
7.07E-01
7.26E-01
HC
Distb
W
W
W
W
L
L
L
W
W
W
W
W
W
para 1
5.40E-03
6.20E-03
5.00E-04
5.00E-04
2.00E+00
1.85E+00
1.78E+00
1.10E-03
1.60E-03
1.90E-03
2.30E-03
2.50E-03
3.20E-03
para 2
7.22E-01
8.86E-01
5.61E-01
5.39E-01
-8.98E+00
-8.49E+00
-8.07E+00
6.28E-01
6.78E-01
7.30E-01
7.31E-01
7.34E-01
7.52E-01
C02
Distb
W
L
W
W
W
W
W
W
W
W
W
W
W
para 1
1.65E+01
1.27E-01
1.69E+00
1.79E+00
1.18E+00
2.70E+00
3.61E+00
4.41E+00
5.28E+00
5.94E+00
6.58E+00
7.11E+00
7.86E+00
para 2
9.25E+00
2.85E+00
1.43E+00
1.57E+00
1.27E+00
2.13E+00
2.58E+00
2.98E+00
3.33E+00
3.44E+00
3.52E+00
3.45E+00
3.25E+00
CO
Distb
W
W
W
L
L
W
W
W
W
W
L
L
L
para 1
4.52E-01
7.13E-01
4.20E-03
2.31E+00
2.17E+00
5.70E-03
9.10E-03
1.45E-02
2.08E-02
2.68E-02
1.55E+00
1.55E+00
1.50E+00
para 2
5.23E-01
6.78E-01
4.77E-01
-6.84E+00
-7.73E+00
5.19E-01
5.67E-01
6.21E-01
6.70E-01
6.90E-01
-4.09E+00
-3.93E+00
-3.60E+00
(Continued on next page).
                                                          142
-------
Table 7-6. Continued.
VSP Bin3
2112
2113
2114
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
NOX
Distb
W
W
W
W
W
W
W
W
W
W
W
W
W
para 1
1.27E-02
1.38E-02
1.50E-02
3.00E-04
2.00E-04
4.00E-04
1.30E-03
2.70E-03
4.70E-03
7.00E-03
9.80E-03
1.13E-02
1.24E-02
para 2
7.92E-01
7.65E-01
8.02E-01
4.92E-01
4.53E-01
5.17E-01
4.71E-01
4.43E-01
5.04E-01
5.71E-01
5.77E-01
5.88E-01
5.47E-01
HC
Distb
W
W
W
L
L
L
L
L
L
L
L
W
W
para 1
3.90E-03
4.80E-03
6.20E-03
1.63E+00
1.29E+00
1.31E+00
1.11E+00
1.15E+00
1.26E+00
1.44E+00
1.65E+00
3.50E-03
3.30E-03
para 2
7.54E-01
7.54E-01
7.72E-01
-8.87E+00
-9.27E+00
-9.09E+00
-8.41E+00
-8.02E+00
-7.65E+00
-7.26E+00
-6.76E+00
6.89E-01
6.38E-01
C02
Distb
W
W
W
W
W
W
L
L
L
L
L
L
L
para 1
8.48E+00
9.31E+00
9.50E+00
1.84E+00
1.90E+00
1.60E+00
2.27E-01
2.01E-01
1.89E-01
1.93E-01
1.78E-01
1.66E-01
1.66E-01
para 2
3.27E+00
2.92E+00
2.82E+00
2.55E+00
2.06E+00
1.32E+00
1.05E+00
1.40E+00
1.66E+00
1.85E+00
2.01E+00
2.16E+00
2.32E+00
CO
Distb
L
L
L
L
L
L
L
W
W
W
W
W
L
para 1
1.62E+00
1.91E+00
2.08E+00
2.50E+00
2.34E+00
2.17E+00
2.22E+00
9.70E-03
2.18E-02
4.28E-02
9.13E-02
1.21E-01
1.63E+00
para 2
-3.09E+00
-2.80E+00
-2.51E+00
-6.95E+00
-8.44E+00
-8.50E+00
-6.75E+00
4.81E-01
4.93E-01
5.33E-01
5.58E-01
6.44E-01
-2.73E+00
(Continued on next page).
                                                          143
-------
Table 7-6. Continued.
VSP Bin3
2211
2212
2213
2214
NOX
Distb
W
W
W
W
para 1
2.38E-02
2.61E-02
4.10E-02
7.12E-02
para 2
6.49E-01
6.78E-01
8.95E-01
1.09E+00
HC
Distb
W
W
W
W
para 1
4.90E-03
8.10E-03
1.50E-02
2.16E-02
para 2
6.75E-01
6.72E-01
8.28E-01
6.95E-01
C02
Distb
L
L
L
L
para 1
1.61E-01
1.09E-01
1.44E-01
1.09E-01
para 2
2.54E+00
2.70E+00
2.82E+00
2.94E+00
CO
Distb
L
W
W
W
para 1
1.61E+00
5.02E-01
1.85E-01
1.77E+00
para 2
-2.31E+00
5.64E-01
6.76E-01
6.53E-01
a First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement < 3.5 liters; 12: odometer reading <
50,000 miles and engine displacement > 3.5 liters; 21: odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22:
odometer reading > 50,000 miles and engine displacement > 3.5 liters.
b W = Weibull; para 1 of Weibull is scale parameter and para 2 of Weibull is shape parameter; L = lognormal; para 1 of lognormal is
and para 2 of lognormal is <^; Parameters were calculated using SAS.
                                                          144
-------
7.3  Quantification of Uncertainty in Mean Emission Rates
A particular concern in this study is whether a normality approximation can be used to represent
uncertainty in the mean.  A normality assumption is convenient because it is easy to calculate the
range of uncertainty in the mean in such situations.  When a normality assumption is not
applicable, a numerical method, known as bootstrap simulation, was used to quantify uncertainty
in the mean. Typically, the normality assumption is influenced by the sample size, sample mean,
and standard error of mean (SEM).  When either sample size n < 40, or when the SEM divided
by the mean was greater than 20, then bootstrap simulation was done to estimate the sampling
distribution of the mean. Overall, in most cases, a normality assumption was applicable.  Table
7-7 indicates situations for which a normality assumption was suspected to be inadequate. These
situations include VSP Modes 12 (NOX), 13 (NOX and CO), and 14 (All Pollutants) for odometer
reading < 50,000 miles and engine displacement > 3.5 liters, and Mode 14 (All Pollutants) for
odometer reading > 50,000 miles and engine displacement > 3.5 liters. In each of these cases,
either the sample size is less than 40 or the relative standard error of the mean is greater than 0.2.
Therefore, in these cases, bootstrap  simulation was used to quantify uncertainty in the mean.
Uncertainty estimates for all other modes and strata were based upon application of the normality
assumption.
    Table 7-7. VSP Modes for Which Uncertainty in the Mean Was Quantified by Bootstrap
                                           Simulation.
Bin3

1212

1213

1214

2214
NO
SEM
mean
n = ll
SEM
mean
n = 52
SEM-Q3Q
mean
n = 39
SEM-ou
u. it ,
mean
n = 34
HC

n/a

n/a
SEM
mean
n = 39
SEM
mean
n = 34
C02

n/a

n/a
^-(xro
mean
n = 39
SEM-ooi«
mean
n = 34
CO

n/a
SEM-^Q
mean
n = 52
SEM
U.^.1 ,
mean
n = 39
SEM-016
mean
n = 34
a First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement <
3.5 liters; 12: odometer reading < 50,000 miles and engine displacement > 3.5 liters; 21:
odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22: odometer reading >
50,000 miles and engine displacement > 3.5 liters.
                                          145
-------
The absolute range of uncertainty in the mean values for each pollutant and VSP-based mode is
given in Figure 7-9 for NOX and HC and in Figure 7-10 for CO and CC>2.  The relative range of
uncertainty in the mean values for each pollutant and VSP-based mode is given in Table 7-8.
The relative range of uncertainty is typically less than plus or minus 50 percent for most cases.
For CO2, the range of uncertainty is less than plus or minus 5 percent in nearly all cases. The
relative range of uncertainty is generally smaller for the strata which have larger sample sizes.
For example, for vehicles with engine displacement less than 3.5 liters and odometer reading less
than 50,000 miles, the typical range of uncertainty is less than plus or minus 10 percent for 12 of
14 modes for modal NOX emissions, less than plus or minus 10 percent for 10 of 14 modes for
HC, less than plus or minus three percent for CC>2 for all modes, and less than plus or minus 20
percent for all modes for CO. However, for vehicles with engine displacement greater than 3.5
liters in the same odometer reading  category, the typical range of uncertainty is plus or minus 30
percent for NOX, 40 percent for HC, 7 percent for CO2, and 40 percent for CO. The latter
category has a much smaller  sample size than the former.

In the several cases identified in Table 7-7 for which the normality assumption was suspected to
be inapplicable, it was confirmed based  upon the results of bootstrap simulation that the
sampling distributions of the means were not normal. For example, for NOX emissions for Mode
13 for odometer reading < 50,000 miles and engine displacement > 3.5 liters, uncertainty in the
mean was quantified by bootstrap simulation based upon the empirical distribution of data. The
relative 95 percent confidence interval was found to be minus 48 percent to plus 73 percent. The
confidence interval is positively skewed and the wide range of uncertainty in this case is
attributed to a large  SEM relative to the  mean.  In Table 7-8, uncertainty estimates based upon
bootstrap simulation are highlighted in bold. For the cases in which uncertainties in the means
were quantified by bootstrap simulation, parametric distributions were fit to the sampling
distributions of the means using the AuvTool software.  As an example, a graphical comparison
is given in Figure 7-11 of the empirical distribution of the bootstrap replications of the mean and
a fitted parametric distribution is given for NOX emission of Mode  12 based upon an odometer
reading < 50,000 miles and engine displacement > 3.5 liters.  A summary of parameters for
parametric distributions fitted to the bootstrap replications of the means is given in Table 7-9.

Normal, lognormal, Weibull, beta and gamma distributions were considered as possible fits for
the sampling distributions. The PDFs of the normal, lognormal, and Weibull distributions have
previously been given in Equations  (7-1), (7-2), and (7-3), respectively. The PDF of the beta
distribution is:
                     B(a,p)

The PDF of gamma distribution is:
                                                                                 (7-5)
                                           146
-------
           w    o.oi -
           W

           g
              0.0001
           8
               0.001 -
                 0.1 -
                o.oi -
               0.001 -
              0.0001
                        Odometer Reading < 50,000 miles                              Odometer Reading > 50,000 miles
Odometer Reading < 50,000 miles Engine Displacement > 3.5 Liters    Odometer Reading > 50,000 miles   Engine Displacement > 3.5 Liters
Engine Displacement < 3.5 Liters                            Engine Displacement < 3.5 Liters
                                                                        n s B
                   Figure 7-9. Quantified Uncertainty in the NOX and HC Mean Emissions (g/sec) of VSP Modes.
First two digit of VSP Bins: 11: odometerreading < 50,000 miles and engine displacement < 3.5 liters; 12: odometer reading < 50,000
 miles and engine displacement > 3.5 liters; 21: odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22: odometer
                                     reading > 50,000 miles and engine displacement > 3.5 liters.
                                                                 147
-------
               100 -i
            O
                                              Odometer Reading < 50,000 miles                             Odometer Reading > 50,000 miles
                      Odometer Reading < 50,000 miles Engine Displacement > 3.5 Liters   Odometer Reading > 50,000 miles   Engine Displacement > 3.5 Liters
                      Engine Displacement < 3.5 Liters                           Engine Displacement < 3.5 Liters
g
M
^ 10 -
c
0
c/5
'g
W
s
o
1 -

a












*










m





m














.








,






ff m FT
nnn
i













: E














1








E 7









?E






n
nn
.0. n.





















.




































,





n n n
U U U




V

























^








E









[









            .2   0.01 -
               0.0001
                    Figure 7-10. Quantified Uncertainty in the CC>2 and CO Mean Emissions (g/sec) of VSP Modes
First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement < 3.5 liters; 12: odometer reading < 50,000
miles and engine displacement > 3.5 liters; 21: odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22: odometer
reading > 50,000 miles and engine displacement > 3.5 liters.)
                                                                 148
-------
   Table 7-8.  Summary of Mean Values and Relative 95% Confidence Intervals in the Mean for NOX, HC, CO2, and CO Emissions
                      (g/sec) for VSP Modes for Vehicles of Different Odometer Reading and Engine Displacement.
VSP Bin3
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
N0xb
mean
0.000901
0.000628
0.000346
0.001173
0.001706
0.002368
0.003103
0.004234
0.005069
0.005865
0.007623
0.012149
0.015456
lower
-4
-6
-5
-4
-4
-4
-4
-4
-5
-6
-8
-10
-12
upper
4
6
5
4
4
4
4
4
5
6
8
10
12
HCb
mean
0.000450
0.000257
0.000406
0.000432
0.000530
0.000705
0.000822
0.000976
0.001112
0.001443
0.002061
0.003373
0.004857
lower
-8
-7
-4
-5
-5
-6
-6
-7
-7
-8
-11
-18
-21
upper
8
7
4
5
5
6
6
7
7
8
11
18
21
C02b
mean
1.671078
1.457983
1.135362
2.233264
2.919890
3.525303
4.107483
4.635048
5.160731
5.632545
6.534780
7.585213
9.024217
lower
-1
-1
-1
-1
-1
-1
-1
-1
-1
-1
-2
-2
-3
upper
1
1
1
1
1
1
1
1
1
1
2
2
3
C0b
mean
0.007807
0.003908
0.003347
0.008335
0.010959
0.017013
0.020026
0.029222
0.035531
0.055068
0.113824
0.207586
0.441775
lower
-10
-15
-8
-9
-14
-16
-11
-12
-13
-14
-14
-16
-16
upper
10
15
8
9
14
16
11
12
13
14
14
16
16
(Continued on next page)
                                                          149
-------
Table 7-8. Continued
VSP Bin3
1114
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
N0xb
mean
0.017863
0.000290
0.000223
0.000174
0.000719
0.001136
0.001587
0.002370
0.004098
0.006124
0.007313
0.013178
0.012179
lower
-16
-19
-28
-27
-12
-13
-13
-13
-15
-21
-22
-27
-38
upper
16
19
28
27
12
13
13
13
15
21
22
27
46
HCb
mean
0.010948
0.000548
0.000222
0.000272
0.000472
0.000754
0.000702
0.000944
0.001443
0.001708
0.002605
0.003523
0.007653
lower
-24
-19
-35
-27
-20
-22
-19
-16
-38
-24
-39
-29
-34
upper
24
19
35
27
20
22
19
16
38
24
39
29
34
CO2b
mean
10.088390
1.566819
1.443564
1.470553
2.611318
3.523681
4.650741
5.635386
6.599677
7.647334
8.808448
11.670609
14.520355
lower
-6
-2
-2
-2
-2
-2
-2
-2
-3
-3
-4
-4
-4
upper
6
2
2
2
2
2
2
2
3
3
4
4
4
cob
mean
0.882300
0.017699
0.008608
0.008479
0.014548
0.025709
0.025212
0.041130
0.076601
0.129248
0.150578
0.355223
0.881642
lower
-18
-21
-39
-31
-22
-25
-22
-22
-28
-29
-35
-39
-37
upper
18
21
39
31
22
25
22
22
28
29
35
39
37
(Continued on next page)
                                                         150
-------
Table 7-8. Continued
VSP Bin3
1213
1214
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
N0xb
mean
0.016506
0.027225
0.001014
0.001042
0.000423
0.001613
0.002638
0.003793
0.005098
0.006373
0.007664
0.009913
0.012685
lower
-48
-36
-4
-7
-7
-5
-4
-5
-5
-5
-5
-5
-6
upper
73
49
4
7
7
5
4
5
5
5
5
5
6
HCb
mean
0.006667
0.006593
0.000901
0.000901
0.000835
0.001027
0.001253
0.001664
0.002089
0.002332
0.002818
0.002985
0.003786
lower
-37
-33
-5
-7
-6
-6
-6
-6
-6
-5
-7
-6
-8
upper
37
39
5
7
6
6
6
6
6
5
7
6
8
CO2b
mean
15.653272
17.35699
1.543686
1.604406
1.130833
2.386260
3.210249
3.957732
4.752012
5.374221
5.940051
6.427506
7.065985
lower
-3
-7
-1
-2
-1
-1
-1
-1
-1
-1
-1
-1
-2
upper
3
5
1
2
1
1
1
1
1
1
1
1
2
cob
mean
1.059857
0.934715
0.011030
0.008723
0.004682
0.012154
0.016731
0.023269
0.029322
0.036942
0.049513
0.063759
0.105380
lower
-25
-36
-8
-13
-10
-9
-10
-10
-8
-9
-11
-13
-15
upper
27
44
8
13
10
9
10
10
8
9
11
13
15
(Continued on next page)
                                                         151
-------
Table 7-8. Continued
VSP Bin3
2112
2113
2114
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
N0xb
mean
0.014384
0.015967
0.016717
0.000725
0.000504
0.000661
0.002518
0.005847
0.008361
0.010582
0.014473
0.016372
0.019758
lower
-7
-10
-10
-15
-20
-14
-9
-9
-11
-11
-14
-15
-17
upper
7
10
10
15
20
14
9
9
11
11
14
15
17
HCb
mean
0.004573
0.005700
0.007164
0.000863
0.000300
0.000323
0.000449
0.000818
0.001216
0.002110
0.004394
0.004635
0.004961
lower
-9
-12
-13
-36
-32
-39
-11
-34
-16
-16
-28
-19
-25
upper
9
12
13
36
32
39
11
34
16
16
28
19
25
CO2b
mean
7.617703
8.322442
8.475028
1.649427
1.762407
1.557773
2.946419
4.127492
5.343656
6.507179
7.602431
8.773093
10.365910
lower
-2
-3
-3
-2
-3
-2
-1
-1
-2
-2
-2
-2
-2
upper
2
3
3
2
3
2
1
1
2
2
2
2
2
cob
mean
0.247810
0.413069
0.624663
0.020282
0.008183
0.004830
0.012308
0.022033
0.045073
0.077496
0.166593
0.170018
0.263544
lower
-16
-18
-19
-31
-68
-87
-28
-20
-20
-22
-28
-24
-33
upper
16
18
19
31
68
87
28
20
20
22
28
24
33
(Continued on next page)
                                                         152
-------
Table 7-8. Continued
VSP Bin3
2211
2212
2213
2214
N0xb
mean
0.030507
0.034219
0.043387
0.068743
lower
-20
-32
-31
-27
upper
20
32
31
27
HCb
mean
0.006631
0.010900
0.016573
0.027174
lower
-30
-36
-30
-35
upper
30
36
30
36
CO2b
mean
12.849389
15.030303
16.861726
18.92916
lower
-3
-3
-4
-13
upper
3
3
4
10
cob
mean
0.338962
0.824829
1.444311
2.420786
lower
-39
-36
-27
-27
upper
39
36
27
28
a First two digit of VSP Bins: 11: odometer reading < 50,000 miles and engine displacement < 3.5 liters; 12: odometer reading <
50,000 miles and engine displacement > 3.5 liters; 21: odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22:
odometer reading > 50,000 miles and engine displacement > 3.5 liters.
b Unit of mean: g/sec; Unit of lower and upper bound: %.
                                                          153
-------
-------
                           0.005        0.01        0.015

                                     NOX Emission (g/sec)
0.02
0.025
 Figure 7-11. Empirical Distribution of Bootstrap Replications of Mean Values and Fitted Beta
   Distribution for Uncertainty in the Mean for NOX Emissions (g/sec) of Mode 12, Odometer
                 Reading < 50,000 miles, Engine Displacement > 3.5 Liters.
Table 7-9. Parameters of Parametric Probability Distribution Fit to the Bootstrap Replications of
         the Means for Selected Modes, Strata, and Pollutants, Based upon Empirical Bootstrap
                                           Simulation
VSP
Bin
12
13
13
14
14
14
14
14
14
14
14
Odometer
reading (miles)
< 50,000
< 50,000
< 50,000
< 50,000
< 50,000
< 50,000
< 50,000
> 50,000
> 50,000
> 50,000
> 50,000
Engine
displacement
(liters)
>3.5
>3.5
>3.5
>3.5
>3.5
>3.5
>3.5
>3.5
>3.5
>3.5
>3.5
Pollutant
NOX
NOX
CO
NOX
HC
C02
CO
NOX
HC
C02
CO
Distribution51
Beta
Beta
Gamma
Beta
Beta
Weibull
Normal
Beta
Beta
Weibull
Gamma
First
Para.
22.275
3.431
25.328
10.482
25.413
17.169
0.895
42.992
21.873
18.658
36.591
Second
Para
1761.856
96.093
0.029
511.286
3911.552
39.735
0.191
595.202
805.28
33.446
0.058
a Beta: first parameter is a, second parameter is p; gamma: first parameter is y, second parameter
is A,; Weibull: first parameter is k, second parameter is c; Normal: first parameter is jj,, second
parameter is a.
                                          155
-------
The parametric distributions fit to the bootstrap replications of the means generally offered an
excellent fit. The use of parametric distributions to describe uncertainty in the mean offers the
key advantage of compactness and eliminates the requirement to save the bootstrap replications
of the mean. There was one case shown in Table 7-9 for which a normal distribution was found
to provide the best  fit.  However, for the other 10 cases shown, beta, gamma, or Weibull
distributions offered the best fit and captured the skewness in the sampling distributions of the
mean.

7.4  Uncertainty  Correction Factor for Averaging Time
Uncertainty in the mean emission rate based upon a 1 -second time period was quantified for each
bin. However, the  range of uncertainty varies depending upon the averaging time of the data.
The objective of this section is to demonstrate how the range of uncertainty varies with
averaging time and to demonstrate an approach for adjusting estimates of uncertainty in the mean
emission rates for a one second averaging time to other averaging times.

Uncertainty in the mean is related to the Standard Error of Mean (SEM). Therefore,  it is
convenient to develop a correction factor to adjust the SEM for different averaging times. To
evaluate the relative change of the SEM, a correction factor for a t-second time period was
defined as Equation (7-6):
       where: CFt.sec: correction factor for t-second time period, no unit
             SEMt.sec: standard error of mean for t-second time period, g/sec
             SEMj.sec: standard error of mean for 1 -second time period, g/sec

Using a relative correction factor enables a straight-forward adjustment of the uncertainty range
for different time periods.  For example, if the absolute 95 percent confidence interval of mean
for a 1-second period is minus 0.1 gram/sec to plus 0.1 gram/sec, then the absolute 95 percent
confidence interval of mean for 5-second period can be calculated as minus Q.\CF5.sec gram/sec
to plus Q.\CF5.sec gram/sec. If the correction factor has a value of 2, then the uncertainty in the
mean for the 5-second averaging time would be from minus 0.2 g/sec to plus 0.2 g/sec in this
example..

In Figures 7-12 to 7-15, for each of four vehicle strata (combinations of odometer reading
reading and engine displacement categories), respectively, the relative standard error of the mean
(or correction factor defined in Equation 7-6) is plotted with respect to averaging time. The data
for this analysis was obtained from the data set used to evaluate 10-second consecutive averages
as a basis for model development.  For each 10-second averaging time, there are two five-second
averages and ten 1-second averages that can be compared in order to evaluate the range of
uncertainty for each of these three averaging times. Each graph in each figure displays the
standard error of the mean for the five-second averaging time divided by that for the 1-second
averaging time, for each of 14 VSP modes. Similar data are shown for the 10-second averaging
time.  A simplified correction factor was estimated by fitting a polynomial regression through the
data in the graphs.  Although the analysis could be extended to averaging times longer than 10
                                           156
-------
   3.00
*  2.50
_o
y  2.00
PH
I  1.50
        o
        O
           1.00 -
           0.50 -
           0.00
                 NO
                 Odo meter < 50,000 miles
                 Ergine size < 3.5
                                      y = -0.0154x  + 0.3326x+ 0.6829
                                468
                             Averaging Time (seconds)
10
12
                        3.50 -
                        3.00 -
                        2.50 -
                        2.00 -
                        1.50 -
                        1.00 -
                        0.50 -
                        0.00 -
                      HC
                      Odometeix 50,000 miles
                      Ergine size < 3.5
                            0
                                            y = -0.0167x + 0.3638x+ 0.653
                                    468
                                  Averaging Time (seconds)
                                                                                                                     10
12
   3.00 -
n  2.50-
_o
1  2.00 -
PH
I  1.50 -
           1.00-
        u
           0.50 -
           0.00
                 C02
                 Odometer< 50,000 miles
                 Ergine size < 3.5
                                      y = -0.0186x + 0.3608x+ 0.6578
                                468
                             Averaging Time (seconds)
10
12
                        3.50 -i
                        3.00 -
                        2.50 -
                        2.00 -
                        1.50 -
                        1.00 -
                        0.50 -
                        0.00 -
                      CO
                      Odometer< 50,000 miles
                      Ergine size < 3.5
                            0
                                                                                                           y = -0.0158x + 0.3441x+ 0.6717
                                    468
                                  Averaging Time (seconds)
                                                                                                                     10
12
Figure 7-12.  Estimation of Correction Factors for the Relative Standard Error of the Mean (SEM/Mean) Versus Averaging Times of
1, 5, and 10 seconds for NOX, HC, CC>2, and CO Emissions (g/sec) for Odometer Reading < 50,000 Miles and Engine Displacement <
                                                                  3.5 Liters.
                                                                     157
-------
   3.00
*  2.50
_o
y  2.00
PH
I  1.50
        o
        O
           1.00 -
           0.50 -
           0.00
                 NO
                 OdorrEter< 50,000 miles
                 Ergine size > 3.5
                                     y = -0.0152x + 0.2935x+ 0.7217
                               468
                            Averaging Time (seconds)
10
12
                       3.50 -
                       3.00 -
                       2.50 -
                       2.00 -
                       1.50 -
                       1.00 -
                       0.50 -
                       0.00 -
                      HC
                      Odometeix 50,000 miles
                      Ergine size > 3.5
                            0
                                          y = -O.OlSlx + 0.3654x+ 0.6527
                                    468
                                 Averaging Time (seconds)
                                                                                                                   10
12



lH
_0
O
cS
PH
a
o
"o
e
o
O


3.00 -

2.50 -

2.00 -

1.50 -

1.00 -


0.50 -
n nn -

C02 •
Odometer< 50,000 miles ^
Ergine size > 3.5
^A 	 t
-t,^
*^ t
j^^"^ ^
s


y = -0.0246x2 + 0.3802x+ 0.6443

                               468
                            Averaging Time (seconds)
10
12
                                                                           PH
                                                                           a
                                                                           o
                                                                            o
                                                                           O
                                                                              10.00 n
                                                                               8.00 -
                        6.00 -
                                                                               4.00 -
                                                                               2.00 -
                                                                               0.00
                               CO
                               Odo meter < 50,000 miles
                               Ergine size > 3.5
                        y = -0.0167x2 + 0.3948x+ 0.6219
                                            468
                                          Averaging Time (seconds)
                                                            10
                                                                                                                           12
Figure 7-13. Estimation of Correction Factors for the Relative Standard Error of the Mean (SEM/Mean) Versus Averaging Times of
1, 5, and 10 seconds for NOX, HC, CC>2, and CO Emissions (g/sec) for Odometer Reading < 50,000 Miles and Engine Displacement >
                                                                3.5 Liters.
                                                                    158
-------
   3.00
*  2.50
_o
y  2.00
PH
I  1.50
        o
        O
           1.00 -
           0.50 -
           0.00
                 NO
                 Odometer> 50,000 miles
                 Ergine size < 3.5
                                      y = -0.0163x + 0.3479x+ 0.6684
                                468
                             Averaging Time (seconds)
10
12
                        3.50 -
                        3.00 -
                        2.50 -
                        2.00 -
                        1.50 -
                        1.00 -
                        0.50 -
                        0.00 -
                      HC
                      Odometer> 50,000miles
                      Ergine size < 3.5
                            0
                                           y = -0.0157x + 0.3607x+ 0.6549
                                    468
                                  Averaging Time (seconds)
                                                                                                                     10
12
   3.00 -
n  2.50-
_o
1  2.00 -
PH
I  1.50 -
           1.00-
        u
           0.50 -
           0.00
                 C02
                 Odometer> 50,000 miles
                 Ergine size < 3.5
                                       y = -0.019x + 0.3682x+ 0.6508
                                468
                             Averaging Time (seconds)
10
12
                        3.00 -i
                     *  2.50-
                     _o
                     1  2.00 -
                     PH
                     .o  1.50 -
                     o
                     O
                                                                                1.00 -
                                                                                0.50 -
                                                                                0.00
                      CO
                      Odometer> 50,000miles
                      Ergine size < 3.5
                                                    y = -0.017x + 0.3371x+ 0.6799
                                             468
                                          Averaging Time (seconds)
                                                             10
                                                                                                                              12
Figure 7-14.  Estimation of Correction Factors for the Relative Standard Error of the Mean (SEM/Mean) Versus Averaging Times of
1, 5, and 10 seconds for NOX, HC, CC>2, and CO Emissions (g/sec) for Odometer Reading > 50,000 Miles and Engine Displacement <
                                                                  3.5 Liters.
                                                                     159
-------
       PH
        a
        a
        o
        O
3.50 -
3.00 -
2.50 -
2.00 -
1.50 -
1.00 -
0.50 -
0.00
                 NO
                 Odometer> 50,000 miles
                 Ergine size > 3.5
                                      y = -0.017x2 + 0.3496x+ 0.6674
                               468
                            Averaging Time (seconds)
                                            10
12
               3.50 -
               3.00 -
               2.50 -
               2.00 -
               1.50 -
               1.00 -
               0.50 -
               0.00 -
HC
Odometer> 50,000miles
Ergine size > 3.5
                                                                        0
                    y = -0.0168x + 0.3687x+ 0.6481
                                    468
                                 Averaging Time (seconds)
                                      10
12



i-H
_0
O
cS
PH
a
o
"o
8
o
U



3.00 -

2.50 -

2.00 -


1.50 -

1.00 -


0.50 -

n nn -
C02 *
Odometer> 50,000 miles
Ergine size > 3.5 t
TL 	 ' — — -4
^^^~ 9 i
^ — » i
^S^ 9
./^ *
^^r +
s


9
y = -0.0266x + 0.398x+ 0.6286

                               468
                            Averaging Time (seconds)
                                            10
12
                                                                              3.50 -i
                                                                              3.00 -
                                                                              2.50 -
                                                                              2.00 -
                                                                              1.50 -
                                                                              1.00 -
                                                                              0.50 -
                                                                              0.00 -
                                                                          CO
                                                                          Odometer> 50,000miles
                                                                          Ergine size > 3.5
                                                                        0
                                                                                              y = -0.0191x + 0.3619x+ 0.6572
                                    468
                                 Averaging Time (seconds)
                                      10
12
Figure 7-15. Estimation of Correction Factors for the Relative Standard Error of the Mean (SEM/Mean) Versus Averaging Times of
1, 5, and 10 seconds for NOX, HC, CC>2, and CO Emissions (g/sec) for Odometer Reading > 50,000 Miles and Engine Displacement >
                                                                3.5 Liters.
                                                                    160
-------
seconds, as the averaging time increases, the sample size decreases. Therefore, for
demonstration purposes, the largest averaging time considered was ten seconds.  As an example,
Figure 7-11 shows that the correction factor increases as the averaging time increases.  However,
the marginal change becomes smaller as the averaging time increases. We hypothesize that the
correction factor may reach a plateau or a maximum at some averaging time larger than 10-
seconds; however, we also hypothesize that such a plateau or maximum may not be much larger
than the correction factor estimated at 10-seconds.  Therefore,  as an initial estimate pending
further analysis in future studies, we suggest that the correction factor applied to averaging times
greater than 10-seconds be the same as that for 10 seconds.

Of the 16 graphs shown in Figures 7-12 through 7-15,  14 of them display the same general
characteristic of a reduction in the marginal increase in the correction factor as the averaging
time increases. For only two cases, which are both for CO2 emissions for odometer reading and
engine displacement strata for which the sample size is relatively small, the correction factor
appears to reach a peak at approximately 8  seconds averaging time and decreases from 8 seconds
to 10 seconds averaging times.  Thus, for these two case, shown in Figures 7-13  and 7-15, the
correction factor for the 10 second averaging time is not substantially different from the
correction factor for the 5 second averaging time.  Although it is possible that the correction
factor for these two cases might decrease as averaging time increases beyond  10 seconds, as a
conservative assumption the value of the correction factor at 10 seconds is suggested for use for
averaging times longer than 10  seconds. For CO as shown in Figure 7-13, there appears to be
some data that may represent outliers, leading to an estimate of the correction factor for an
individual mode as large as approximately 9.0 for the 10 second averaging time.  This potential
outlier may be because of a small sample size for that particular mode.

Table 7-10 summarizes the polynomial regression models fit to the data shown in Figures 7-12
through 7-15. Also shown in the table is the value of the correction factor at the 10 second
averaging time for each pollutant and each odometer reading and engine displacement strata.
These values are recommended for use for averaging times greater than 10 seconds. For NOX,
the correction factors for 10 seconds or greater averaging time range from 2.14 to 2.54 among
the four strata. The corresponding ranges for HC, CO2, and CO are 2.50 to  2.70, 1.99 to 2.43,
and 2.35 to 2.90. Thus, a typical value of these correction factors at 10 seconds or greater
averaging time is approximately 2.5, implying that the range of uncertainty  for averaging times
of 10 seconds or more is a factor of approximately 2.5  greater than that at 1  second. This
difference is substantial and illustrates the importance of properly accounting  for averaging time
when performing uncertainty analysis.

As observed in Figures 7-12 through 7-15, there is variability in the value of the correction factor
at the  10 second averaging time when comparing results for each of the 14 modes. It was
hypothesized that perhaps a portion of the inter-mode variability in the correction factor for a
given  averaging time could be explained based upon VSP.  Therefore, the values of the
correction factors at 10 seconds were normalized with  respect to the average correction factor at
10 seconds (as shown in the last four columns of Table 7-10), and the normalized correction
factors, which are described here as "bin adjustment factors," were plotted versus mode as shown
in Figures 7-16 through 7-19 for four different odometer reading and engine displacement strata.
                                           161
-------
Table 7-10. Averaging Time Correction Factors for Uncertainty in VSP Bins for NOx, HC, CO2, and CO Emissions (g/sec) for Four
                                Strata With Respect to Odometer Reading and Engine Displacement.
Strata8
11
12
21
22
< 10 seconds'1
NOX
y = -0.0154X2 + 0.3326x + 0.6829
y = -0.0152X2 + 0.2935x + 0.7217
y = -0.0163X2 + 0.3479x + 0.6684
y = -0.017x2 + 0.3496x + 0.6674
HC
y=-0.0167x2 + 0.3638x + 0.653
y = -O.OlSlx2 + 0.3654x + 0.6527
y = -0.0157X2 + 0.3607x + 0.6549
y = -0.0168X2 + 0.3687x + 0.6481
CO2
y = -0.0186X2 + 0.3608x + 0.6578
y = -0.0246X2 + 0.3802x + 0.6443
y=-0.019x2 + 0.3682x + 0.6508
y = -0.0266x2 + 0.398x + 0.6286
CO
y = -0.0158X2 + 0.3441x + 0.6717
y = -0.0167X2 + 0.3948x + 0.6219
y = -0.017x2 + 0.3371x+ 0.6799
y = -0.0191X2 + 0.3619x + 0.6572
> 10 seconds
NOX
2.47
2.14
2.52
2.46
HC
2.62
2.50
2.70
2.65
CO2
2.40
1.99
2.43
1.95
CO
2.53
2.90
2.35
2.37
a 1 1 : odometer reading < 50,000 miles and engine displacement < 3.5 liters; 12: odometer reading < 50,000 miles and engine
displacement > 3.5 liters; 21: odometer reading > 50,000 miles and engine displacement < 3.5 liters; 22: odometer reading > 50,000
miles and engine displacement > 3.5 liters.
y, correction factor (no unit), x, time (second)
                                                        162
-------
     1.08 -
     1.06 -
     1.04 -
     1.02 -
     1.00 -
     0.98 -
     0.96 -
     0.94 -
     0.92 -
     0.90 -
  NO
  Odometer < 50,000 miles
  Engine size < 3.5

  y=-0.0084x+1.0634
          1234567
                                  Bin
                               9   10  11   12   13   14
                                                                   1.20 -i
                                                                       4
                                                                3  1.00 -
                                                                o
                                                                [S
                                                                   0.80-
                                                                   0.60-
^ 0.40 -
m 0.20 -
   0.00
                                                                                  HC
                                                                                  Odometer < 50,000 miles
                                                                                  Engine size < 3.5
                                                                                                             y=-0.0121x+ 1.0907
                                                                                 1234567
                                                                                                       9  10  11  12  13  14
                                                                                                          Bin
   1.15 -
1  1.10-
I  1.05 -
a
to
.a, i.oo -
• S  0.95 -
m
   0.90
                co2
                Odometer < 50,000 miles
                Engine size < 3.5
                                          y=-0.0074x+1.0553
1   2   3    4   5   6   7   8   9   10  11   12   13   14
                        Bin
                                                                   1.40-
                                                                   1.20-
                                                                   1.00-
                                                                   0.80-
                                                                   0.60 -
                                                                   0.40-
                                                                   0.20 -
                                                                             0.00
                                                                                    CO
                                                                                    Odometer < 50,000 mile
                                                                                    Engine size < 3.5
                                                                                                                   y=-0.0169x+1.127
                                                                                 1   2   3   4   5   6   7   8   9   10  11  12  13  14
                                                                                                          Bin
Figure 7-16.  Bin Adjustment Factors for the Uncertainty Correction Factor at "£ 10 seconds" of NOX, HC, CC>2, and CO for
                            Odometer Reading < 50,000 miles and Engine Displacement < 3.5 Liters.
                                                                  163
-------

o
1
PH

§
a
1
3p
<1
.a
PQ

1.40 -
1.20 -
1.00 i

0.80 -

0.60 -

0.40 -

0.20 -
n nn

4
* * » 4

* » »




NO
Odorreter< 50,000 rriles
Engine size > 3.5 y = -O.OOlx + 1.0078

              2   3   4  5   6  78   9   10 11  12  13  14
                                 Bin
                                                                      I
                                                                      fl
                                                                      PQ
                                                                   1.40 -
                                                                   1.20 -<~>
                                                                   1.00 -
                                                                   0.80 -
                                                                   0.60 -
                                                                   0.40 -
                                                                   0.20 -
                                                                   0.00 -
                                                                   HC
                                                                   Odometer < 50,000 rriles
                                                                   Erginesize>3.5
                                                                                                         y = -0.0394x+1.2954
                                                                        1   2   3   4   5  6   7   8  9  10  11  12  13  14
                                                                                              Bin
   a
   PQ
1.60
1.40
1.20
1.00
0.80
0.60
0.40
0.20
0.00
Odometer < 50,000 rriles
Engine size > 3.5
                                        y = -0.04x+1.3001
           1  2   3   4  5   6  78   9   10 11  12  13  14
                                 Bin
   1.20 -
 8  i.oo -
1
^  0.80 H
 fl
 a  0.60 -
 t/3
^ 0.40 -
'I  0.20 -
   0.00
CO
Odometer < 50,000 rriles
Engine size > 3.5
                                                                                           y = -0.033x+1.1125
                                                                              1234567
                                                                                                    9  10  11  12  13  14
                                                                                              Bin
Figure 7-17.  Bin Adjustment Factors for the Uncertainty Correction Factor at "£ 10 seconds" of NOX, HC, CO2, and CO for
                          Odometer Reading < 50,000 miles and Engine Displacement > 3.5 Liters.
                                                              164
-------

tH
_o
"3
1
w
«



i-H
_o
"3
cS
PH
~£H
O
^
3
f
a
m

1.10 -
1.05 -
i
1.00 -
0.95 -
0.90 -
0.85 -

y=0.0073x+ 0.9453 *
• • •
* — — "^ 	 	 ^""""^
» •
» NO
* Odometer > 50,000 miles
Engine size < 3. 5
2 3 4 5 6 7 8 9 10 11 12 13 14
Bin
1.40 -
1.20 -,
1.00 -
0.80 -
0.60 -
0.40 -
0.20 -
0.00 -


« •
• •
y=-0.0006x+ 1.0047
C02
Odometer > 50,000 miles
Engine size < 3. 5
2 3 4 5 6 7 8 9 10 11 12 13 14
Bin
                                                                        1.20 -
                                                                      ° 1.00 -,
                                                                      o
                                                                     [S
                                                                        0.80-

                                                                        0.60-
                                                                        0.40 -
                                                                     m
                                                                        0.00
HC
Odometer > 50,000 miles
Engine size < 3.5
                        y = -0.0062X+ 1.0467
                                                                             1   2   3  4   5   6   7   8   9  10  11   12  13  14
                                                                                                   Bin
                                                                        1.40-
                                                                      o 1.20 -
                                                                      | 0.80

                                                                     1 0.60
                                                                     »
                                                                     ^ 0.40
                                                                     -B
CO
Odometer > 50,000 miles
Engine size < 3.5
                                                                                                             y = Q.003X+ 0.9775
                                                                        0.00
                                                                             1   2   3  4   5   6   7   8   9  10  11   12  13  14
                                                                                                   Bin
Figure 7-18.  Bin Adjustment Factors for the Uncertainty Correction Factor at "£ 10 seconds" of NOX, HC, CC>2, and CO for
                          Odometer Reading > 50,000 miles and Engine Displacement < 3.5 Liters.
                                                              165
-------
1.40 -
S 1.20 -
"3
£ i.oo -
<3 0.80 -
6
| 0.60 -
^ 0.40 -
m 0.20 -
nnn -
1.40 -
• , » 3 1-20 -
» • -M '
• S
| 0.80 -
| 0.60 -
NO < 0.40 -
y =0.0074x+ 0.9448 Odometer > 50,000 miles -S
Engine size > 3. 5 ffl "
	 , 	 , 	 , 	 , 	 , 	 , 	 , 	 , 	 , 	 , 	 , 	 , 	 , n nn
« •
HC
Odometer > 50,000 miles
Engin-ize>3.5 y = -0.0099x+ 1.0742
         1   2   3   4   5   6  7   8  9   10  11  12  13  14
                               Bin
                                                                        1  2   3   4   5   6  7   8  9   10  11  12  13  14
                                                                                              Bin
   1.60 -
S  i-40 -
|  1.20-
"S  1.00 -
o
J3  0.80 -
W
;§> 0.60 -
^  0.40 -
«  0.20-
   o.oo -
            co2
            Odometer > 50,000 miles
            Engine size > 3.5
                                      y=-0.0425x+1.3186
         1   2   3   4   5   6  7   8  9   10  11  12  13  14
                               Bin


_o
"3
03
O
s
B
•51
•<
a
m

1.40-

1.20-

i.oo-
0.80-

0.60 -

0.40-
0.20 -
n nn

» .
*
_ ^
> ~ i » * 	 	 	 ± 	
»


CO
Odometer > 50,000 miles
Engine size > 3.5 y = -0.0129X+ 1.097

                                                                        1  2   3   4   5   6  7   8  9   10  11  12  13  14
                                                                                              Bin
Figure 7-19. Bin Adjustment Factors for the Uncertainty Correction Factor at "£ 10 seconds" of NOX, HC, CC>2, and CO for
                         Odometer Reading >50,000 miles and Engine Displacement > 3.5 Liters.
                                                            166
-------
The bin adjustment factor (BAF) for a given bin is given by:


                                  BAFk = CFw—2 emissions for vehicles with odometer reading less than 50,000 miles and
CC>2 for vehicles with odometer reading greater than 50,000 miles. It is possible that this
apparent difference for the larger engine vehicles compared  to the smaller engine vehicles
represents a real difference or possibly it could be an artifact of having smaller sample sizes for
the larger engine vehicles. In general, while the linear curve fits capture the overall trends of the
data among the 14 modes, it is clear that the variation of the bin adjustment factor with respect to
VSP mode is not truly linear in all cases. In future work, it may be worth exploring other curve
fits to these data and/or exploring the use of other explanatory variables, such as the mid point
value  of VSP for each mode instead of the mode number, in order to improve the estimation of
the bin adjustment factor.

A summary of the Bin Adjustment Factors developed based upon the data and curve fits shown
in Figures 7-16 through 7-19 is given in Table 7-11.

7.5    Estimation of Uncertainty in Model Results
In this section, two methods are evaluated and compared for estimating uncertainty in the total
emissions  for a trip or driving cycle.  These methods include the numerical method of Monte
Carlo simulation and an analytical method based upon a linear model and normality assumptions
for uncertainty in individual modes.  These two methods are illustrated for a case study example
of predicting uncertainty in total trip emissions for the EVI240 driving cycle.  This case study is
followed by  case studies for uncertainty in total emissions for several different driving cycles and
then by a case study for multiple vehicles on a selected driving cycle.

       7.5.1   Estimation of Uncertainty in Total Emissions Based Upon the IM240 Driving
              Cycle: Comparison  of Monte  Carlo Simulation and Analytical Approaches
This example demonstrates the prediction of total  emissions from EVI240 cycle. The prediction
was based upon quantified uncertainty in VSP modes in which the uncertainty was adjusted for
                                          167
-------
Table 7-11. Bin Adjustment Factors for Correction Factor of Time Adjustment at "^ 10 seconds"
         for NOx, HC, CO2, and CO and for Four Odometer Reading and Engine Displacement
                                            Strata.
Odometer
reading
(mile)
< 50,000
< 50,000
> 50,000
> 50,000
Engine
displacement
(liters)
<3.5
>3.5
<3.5
>3.5
N0xa
y = -
0.0084x +
1.0634
y = -0.001x
+ 1.0078
y = 0.0073x
+ 0.9453
y = 0.0074x
+ 0.9448
HCa
y = -
0.0121x +
1.0907
y = -
0.0394x +
1.2954
y = -
0.0062x +
1.0467
y = -
0.0099x +
1.0742
C02a
y = -
0.0074x +
1.0553
y = -0.04x +
1.3001
y = -
0.0006x +
1.0047
y = -
0.0425x +
1.3186
C0a
y = -
0.0169x +
1.127
y = -0.033x
+ 1.1125
y = 0.003x
+ 0.9775
y = -
0.0129x +
1.097
a y: bin adjustment factor (no unit); x, bin number (from 1 to 14)
averaging time using the correction factors for averaging time adjustment.  The standard EVI240
cycle contains 240 seconds. The temporal allocation of the EVI240 cycle into VSP modes is
given in Table 7-12.  Most of the time spend in the EVI240 cycle is represented by VSP modes 1
through 8. Only 10 seconds are spent in Modes 9 through 11, combined, and no time is spent in
the highest VSP modes 12, 13, or 14.
 Table 7-12. Allocation of the Standard IM240 Driving Cycle Into VSP Modes With Respect to
                                   Time Spent in Each Mode.
VSP Mode Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Total Seconds
41
24
16
37
47
19
29
17
4
O
3
None
None
None
                                         168
-------
Thus, total emissions from EVI240 cycle are calculated based upon a sum of emission from each
bin, based upon summing the products of the time spent in each mode multiplied by the
respective mode average emission rate:

       TE =  41 xEFmodel + 24 xEFmode2 + 16 xEFmode3 + 3 7 xEFmode4 +
             47xEFmode5 + 19xEFmode6 + 29xEFmode7 + 17xEFmode8 +
             4xEFmode9 + 3 xEFmodeio + 3 xEFmoden                                  (7-8)

where:
       TE:  total emissions, g
       EF:  1-second based emission factor for each VSP mode (g/sec)

As an illustrative example, uncertainty in total NOX emissions from the EVI240 cycle for a vehicle
with odometer reading < 50,000 miles and engine displacement < 3.5 liters was predicted. For
Modes 1 through 11 applied to the EVI240 cycle for this particular pollutant and vehicle strata,
the quantified uncertainty in the 1-second average modal emissions can reasonably be based
upon a normality assumption.  To estimate uncertainty in total emissions, the quantified
uncertainty in the  1-second average emissions of each mode was adjusted based upon the total
amount of time  spent in the mode using the averaging time correction factor previously
described. The  input assumptions for prediction of uncertainty in total emissions are given in
Table 7-13. These assumptions include the probability distribution assumed for uncertainty in
the mean for each mode, the mean modal emission rate, the standard deviation of the distribution
for uncertainty in the mean (i.e. the standard error of the mean), the numerical value of the
correction factor applied, and the numerical value of the bin adjustment factor applied. For
Modes 1 through 8,  10 or more seconds were spent in each mode. Therefore, the correction
factor applicable to 10 or more seconds is used for these modes.  For Modes 9, 10 and 11, less
than 10 seconds were spent in each mode. Therefore, the correction factor was estimated from
the polynomial curve fits presented in Table 7-10. For cases in which the averaging time was
less than  10 seconds, a bin adjustment factor was not applied. The correction factor and bin
adjustment factor were multiplied with the standard deviation of the modal emission rate to
arrive at a new standard deviation for the modal emission rate appropriate for the particular
averaging time of each mode. For example, for Mode 1, the corrected standard deviation was
(1.97xlQ-5 g/sec) x (2.47) x (1.0248) = 4.99xlO'5  g/sec.

Monte Carlo simulation was used to propagate uncertainty in each modal emission rate, using
Equation (7-8),  in order to estimate uncertainty in total emissions. For the Monte Carlo
simulation,  a sample size of 10,000 was selected. When performing Monte Carlo simulation, the
selection of sample size is typically based upon a compromise between the precision of the
estimated uncertainty for the model output versus the computational burden. A sample size of
10,000 is not necessary in every case.  Smaller sample sizes may provide adequate results.
Moreover, other methods aside from Monte Carlo simulation, such as Latin Hypercube
Sampling, can be used to obtain precise estimates of the distribution of a model output using
smaller sample sizes than required for Monte Carlo simulation.  Cullen and Frey (1999) and
Morgan and Henrion (1990) provide more discussion on criteria and methods for selecting
sample sizes for Monte Carlo simulation and for Latin Hypercube Sampling. The results from
Monte Carlo simulation are shown in Table 7-14  and in Figure 7-20.
                                          169
-------
 Table 7-13. Input Assumptions for Prediction of Uncertainty in Total NOX Emissions for a Cast
          Study of the IM240 cycle, for Vehicles with Odometer Reading < 50,000 Miles and
                                Engine Displacement < 3.5 Liters.

Mode
Number
1
2
O
4
5
6
7
8
9
10
11
NOX Emission Factor
Input
Distribution
Normal
Normal
Normal
Normal
Normal
Normal
Normal
Normal
Normal
Normal
Normal
Mean Modal
Emission Rate
(g/sec)
0.000901
0.000628
0.000346
0.001173
0.001706
0.002368
0.003103
0.004234
0.005069
0.005865
0.007623
Standard Deviation of
Mean Modal
Emission Rate (g/sec)
1.97E-05
2.04E-05
9.26E-06
2.46E-05
3.56E-05
5.12E-05
6.86E-05
9.44E-05
0.000141
0.00017
0.000301
Correction
Factor
2.47
2.47
2.47
2.47
2.47
2.47
2.47
2.47
1.77
1.54
1.54
Bin
Adjustment
Factor
1.025
1.03
1.033
1.033
1.031
1.027
1.02
1.011
Nonea
Nonea
Nonea
 no Bin Adjustment Factor is needed because time period is smaller than 10 seconds.
 Table 7-14.  Example Prediction of Uncertainty in Total Emissions for NOX Emissions From the
            IM240 Cycle for Vehicles with Odometer Reading < 50,000 Miles and Engine
                   Displacement < 3.5 Liters Based upon Monte Carlo Simulation
Cycle
Vehicle
Pollutant
mean3' b
Absolute 95% CIa'b
Relative 95% CIa'c
Lower
Upper
Lower
Upper
IM240
Odometer reading < 50,000 miles, engine displacement < 3.5 liters
NOX
0.45 g
-0.02 g
0.02 g
-4.4 %
4.4 %
a based upon Monte Carlo Simulation results of 10,000 runs
b unit: gram
c unit: °A
                                         170
-------
              10,000 Trials

                 1.000  -I
                                    Forecast: NO, IM240

                                       Cumulative Chart
56 Outliers

- 10000
                                                                          n
                                                                          _a
                                                                          c
                                                                          ro
                                           0.45         0.'
                                   Certainty is 95.00%from 0.43 to 0.47 gram
 Figure 7-20. Quantified Uncertainty in Total NOX Emissions from the IM240 Cycle for Vehicles
   with Odometer Reading < 50,000 Miles and Engine Displacement < 3.5 Liters Based upon
                                  Monte Carlo Simulation.

The results from the Monte Carlo simulation are a total NOX emissions mean estimate of 0.45
grams with a 95 percent range of uncertainty of plus or minus 0.02 grams, or plus or minus 4.4
percent of the mean. In this particular case, even with the correction factor for averaging time
adjustment and the bin adjustment factor applied to each mode, the range of uncertainty in the
estimated average total emissions was sufficiently narrow that a normality assumption would be
justifiable.

As an alternative  to Monte Carlo simulation, an analytical solution was developed. For a linear
model and for an  assumption of normality for uncertainty in each modal emission rate,  the
uncertainty in the total emissions can be estimated as follows:
                                                                                     (7-9)
Where:
       Utotal-  Uncertainty in the sum of the quantities (i.e. half the 95% CI)
       U{.    Uncertainties associated with each quantity, (i.e. half the 95% CI)
       W{.    Weight associated with each quantity

The weight is the fraction of total time spent in each mode.  The analytical solution for the
EVI240 cycle is that the average total emissions are 0.45 grams and the uncertainty is
approximate minus or plus 0.018 grams for a 95% confidence interval, corresponding a relative
range of minus or plus 4 percent, which is similar to numerical  simulation results.

The analytical method offers the advantage of reduced computing resources required to estimate
total uncertainty in emissions, when compared to the Monte Carlo simulation approach.
However, the analytical method is limited to situations in which there are a linear combination of
normal distributions.  Therefore, if in the future there was a need to include uncertainty in not
                                           171
-------
 Table 7-15. Allocation of the ART-EF, IM240, FTP (Bags 2 and 3) and US06 Driving Cycles
                    Into VSP Modes With Respect to Time Spent in Each Mode.
VSP Mode
1
2
O
4
5
6
7
8
9
10
11
12
13
14
Seconds Spent in Each Mode by Driving Cycle
ART-EF
85
51
196
66
40
31
18
10
5
2




IM240
41
24
16
37
47
19
29
17
4
3
O



FTP
201
119
336
294
212
105
60
27
8
5
3



US06
113
19
69
26
40
55
64
61
45
56
32
9
21
11
only the modal emission rate but also in the fraction of time spent it each mode, the analytical
method presented here would not be applicable.  Cullen and Frey (1999) provide an overview of
approximate analytical methods for propagating the standard deviation of distributions for model
inputs through a model in order to estimate the standard deviation of the model output.

       7.5.2  Estimation of Uncertainty in Total Emissions of Selected Driving Cycles
In this section, uncertainty estimates are developed for total emissions of NOX, HC, CC>2, and CO
for four selected driving cycles, including ART-EF, IM240, FTP, and US06. These four cycles
represent different ranges of VSP and of total emissions. The uncertainty in total emissions was
quantified using the analytical method explained in the previous section. The distribution of the
total time of each cycle by VSP mode is given in Table 7-15. For the ART-EF cycle, over 90
percent of the total  cycle time is spent in Modes 1 through 6, and there is no representation of
Modes 11  through 14.  As previously discussed, for the IM240 cycle most of the activity occurs
in Modes 1 through 8.   The FTP is similar to the IM240 cycle in that most of the time is spent in
Modes 1 through 8. The US06 cycle is more widely distributed over the 14 modes compared to
the other three cycles.

The results of the uncertainty analysis for the IM240, ART-EF, FTP, and US06 cycles are shown
in Tables 7-16 through 7-19, respectively.  Each table shows results for the mean total emissions,
absolute uncertainty, and relative uncertainty for NOX, HC, CC>2, and CO and for four strata
based upon odometer reading and engine displacement.
                                          172
-------
  Table 7-16. Absolute and Relative Uncertainty Estimates for Mean Total Emissions of NOX, HC, CO2, and CO for Four Odometer
                             Reading and Engine Displacement Tier 1 Vehicle Strata for the IM240 Cycle.
Odometer
reading
(mile)
< 50,000
< 50,000
> 50,000
> 50,000
Engine
displacement
(liters)
<3.5
>3.5
<3.5
>3.5
NOX
Total
Emis.a
0.45
0.35
0.68
1.3
Abs.
Lmt.b
0.018
0.042
0.030
0.15
Rel.
Lmt.c
4.0
12
4.3
11
HC
Total
Emis.a
0.14
0.24
0.33
0.32
Abs.
Lmt.b
0.0079
0.061
0.018
0.083
Rel.
Lmt.c
5.6
25
5.5
26
C02
Total
Emis.a
660
841
728
962
Abs.
Lmt.b
5.3
14
6.8
12
Rel.
Lmt.c
0.79
1.6
0.93
1.3
CO
Total
Emis.a
o o
J.J
7.9
4.6
11
Abs.
Lmt.b
0.35
1.9
0.35
2.7
Rel.
Lmt.c
11
24
7.7
25
a total emissions, grams
b absolute upper and lower limits, grams
0 relative upper and lower limits, %
  Table 7-17. Absolute and Relative Uncertainty Estimates for Mean Total Emissions of NOX, HC, CO2, and CO for Four Odometer
                            Reading and Engine Displacement Tier 1 Vehicle Strata for the ART-EF Cycle.
Odometer
reading
(mile)
< 50,000
< 50,000
> 50,000
> 50,000
Engine
displacement
(liters)
<3.5
>3.5
<3.5
>3.5
NOX
Total
Emis.a
0.53
0.34
0.77
1.3
Abs.
Lmt.b
0.021
0.040
0.032
0.13
Rel.
Lmt.c
3.9
12
4.2
9.8
HC
Total
Emis.a
0.24
0.18
0.54
0.37
Abs.
Lmt.b
0.015
0.040
0.037
0.12
Rel.
Lmt.c
6.3
23
6.9
31
C02
Total
Emis.a
969
1176
1025
1318
Abs.
Lmt.b
8.2
19
11
21
Rel.
Lmt.c
0.85
1.7
1.0
1.6
CO
Total
Emis.a
4.0
8.8
5.8
11
Abs.
Lmt.b
0.41
2.3
0.44
3.1
Rel.
Lmt.c
10
26
7.7
30
a total emissions, grams
b absolute upper and lower limits, grams
0 relative upper and lower limits, %
                                                         173
-------
  Table 7-18. Absolute and Relative Uncertainty Estimates for Mean Total Emissions of NOX, HC, CO2, and CO for Four Odometer
                       Reading and Engine Displacement Tier 1 Vehicle Strata for the FTP (Bags 2 and 3) Cycle.
Odometer
reading
(mile)
< 50,000
< 50,000
> 50,000
> 50,000
Engine
displacement
(liters)
<3.5
>3.5
<3.5
>3.5
NOX
Total
Emis.a
1.7
1.1
2.5
4.6
Abs.
Lmt.b
0.069
0.13
0.11
0.46
Rel.
Lmt.c
4.0
11
4.3
9.9
HC
Total
Emis.a
0.67
0.73
1.5
1.1
Abs.
Lmt.b
0.038
0.17
0.097
0.30
Rel.
Lmt.c
5.7
23
6.2
27
C02
Total
Emis.a
2997
3640
3209
4123
Abs.
Lmt.b
25
55
33
56
Rel.
Lmt.c
0.84
1.5
1.0
1.4
CO
Total
Emis.a
13
27
18
33
Abs.
Lmt.b
1.4
6.5
1.5
7.8
Rel.
Lmt.c
11
24
8.0
24
a total emissions, grams
b absolute upper and lower limits, grams
0 relative upper and lower limits, %

  Table 7-19. Absolute and Relative Uncertainty Estimates for Mean Total Emissions of NOx, HC, CO2, and CO for Four Odometer
                             Reading and Engine Displacement Tier 1 Vehicle Strata for the US06 Cycle.
Odometer
reading
(mile)
< 50,000
< 50,000
> 50,000
> 50,000
Engine
displacement
(liters)
<3.5
>3.5
<3.5
>3.5
NOX
Total
Emis.a
2.3
2.4
3.2
7.3
Abs.
Lmt.b
0.15
0.63
0.16
1.3
Rel.
Lmt.c
6.5
27
5.1
17
HC
Total
Emis.a
0.72
0.93
1.3
2.1
Abs.
Lmt.b
0.094
0.22
0.076
0.54
Rel.
Lmt.c
13
24
5.9
26
C02
Total
Emis.a
2334
3395
2512
3827
Abs.
Lmt.b
27
60
26
51
Rel.
Lmt.c
1.2
1.8
1.0
1.3
CO
Total
Emis.a
35
72
35
117
Abs.
Lmt.b
5.6
20
5.3
30
Rel.
Lmt.c
16
28
15
26
a total emissions, grams
 absolute upper and lower limits, grams
0 relative upper and lower limits, %
                                                         174
-------
The relative range of uncertainty, on a percentage basis in comparison to the mean total
emissions, is similar for the four cycles for a given pollutant and strata in most cases. For
example, for vehicles with odometer reading less than 50,000 miles and engine displacement less
than 3.5 liters, the relative uncertainty range is approximately 4 to 7 percent for NOX, 6 to 13
percent for HC, one percent for CC>2 and 10 to 16 percent for CO when comparing all four
driving cycles.  Within these ranges, the US06 cycle tends to have larger relative uncertainty
compared to the other three cycles. For example, for the same vehicle strata, the uncertainty in
NOX emissions for the US06 cycle is plus or minus 7 percent compared to only plus or minus 4
percent for the EVI240, ART-EF, and FTP cycles. The uncertainty estimates for the US06 cycle
are larger than for the  other three cycles for NOx for all strata and for CO for strata  11 (<50,000
miles, < 3.5 liters) and 21 (>50,000 miles, <3.5 liters).

Setting aside the differences between the US06 and the other cycles, the typical ranges of
uncertainty also vary by strata, with smaller ranges of uncertainty for those strata for which there
are more data. These include the strata for engine displacement less than 3.5 liters for both
odometer reading ranges. For these two strata, a typical range of uncertainty is plus or minus 4
percent for NOX, plus or minus 6 percent for HC, plus or minus 1 percent for CO2, and plus or
minus  10 percent for CO. For the larger engine displacement strata for both odometer reading
ranges, the typical ranges of uncertainty are plus or minus 10 percent for NOX, plus or minus 25
percent for HC, plus or minus 2 percent for CO2, and plus or minus 25 percent for CO.  The
uncertainty ranges are typically narrowest for CO2.

The relative uncertainty ranges in NOX emissions are typically larger than that for CO2 but less
than that for HC and CO. The relative uncertainty ranges for HC and CO are comparable to each
other in most cases. Thus, the key insights are that: (1) the amount of uncertainty appears to
increase as the average VSP or range of VSP of a cycle increases; (2) the amount of uncertainty
is a function of sample size; and (3) the relative amount of uncertainty is smallest for CO2,
largest for both HC and CO, and in between for NOX. Furthermore, the relative range of
uncertainty for these particular cycles is as small as only one or two percent for CO2 and as large
as 30 percent or more  for HC and CO. Thus, in some cases, the range of uncertainty in total
emissions is substantial.

The uncertainty estimates presented in this section represent uncertainty in total emissions for a
single vehicle of a given odometer reading and engine displacement.  In order to estimate
uncertainty in total emissions for a fleet of vehicles, these estimates can be multiplied by the total
number of vehicles operated on each activity pattern for each strata.  For example, suppose that
100 vehicles of odometer reading less than 50,000 miles and engine displacement less than 3.5
liters were operated on an activity  pattern similar to the US06 cycle. The total emissions and the
relative range of uncertainty would be 230  g ± 6.5% for NOX, 72 g ± 13% for HC, 233,400 g
±1.2% for CO2, and 3,500 g ± 16% for CO. Suppose in addition that there were  100 vehicles in
each of the other three odometer reading and engine displacement strata.  In this case, the results
would  be be 1,520 g ± 9.6% for NOX, 505 g ±  12% for HC,  1,207,000 g ±0.7% for CO2, and
25,900 g ± 14% for CO. Of course, the method for estimating uncertainty in total emissions can
be expanded to account for the sum of total emissions and uncertainty in total emissions when
different vehicles are operating on different activity patterns.
                                           175
-------
       7.5.3   Estimation of Uncertainty in Total Emissions for Different Numbers of
              Vehicles
The purpose of this section is to illustrate that the relative range of uncertainty in total emissions
for a particular activity pattern is not a function of the number of vehicles operating on that
pattern for a given strata. As a case study, the mean total emissions and the uncertainty in the
mean total emissions was estimated for 13 vehicles operating on the ART-EF cycle.  In this case
study, the inter-vehicle variability in the speed traces for each test is taken into account. The
allocation of the second-by-second emission data from the driving cycle tests into VSP modes is
summarized in Table 7-20.  Although on average the distribution of modes among the 13
vehicles is similar to the distribution of modes for the standard ART-EF cycle as shown in Table
Table 7-15, there  is variability in the amount of time spent in each mode from one test to another.
For example, for 12 of the tests the amount of time spent in Mode 3 varied from 191 seconds to
211 seconds, while for another test the amount of time spent in this mode was 253 seconds. For
comparison, the standard ART-EF speed trace has 196 seconds in Mode 3. Thus, it is the case
that individual tests do not exactly reproduce the standard speed trace.

As an example, the uncertainty in total NOx emissions were quantified for the 13  vehicles taking
into account inter-vehicle variability in the speed traces and uncertainty in the emission rate for
each individual mode. The average estimate of mean total NOX emission from the 13 vehicles,
based upon Monte Carlo simulation with 10,000 replications, is 7.11 grams. The  quantified
absolute 95% confidence interval is from 6.84 gram to 7.38 gram, corresponding to a relative
range of minus 3.8 percent to plus 3.8 percent. The CDF of the quantified uncertainty in the
mean total emissions is shown in Figure 7-21.

The relative range of uncertainty of plus  or minus 3.8 percent is influenced in part by the
variability in the distribution of the modes among the 13 vehicles because of the variability in the
speed traces for each test. From the previous section, the uncertainty estimated based upon the
standard speed trace for the same strata of vehicles was plus or minus 3.9 percent.  The
difference in the relative range of uncertainty of 0.1 percent is most likely attributable to the role
of inter-vehicle variability in the speed traces.  Therefore, these results illustrate that the relative
range of uncertainty in mean total emissions is relatively insensitive to the number of vehicles
tested or for which predictions are being  made, even though there may be some inter-vehicle
variability in the speed traces.

7.6    Summary and Recommendations
This chapter has demonstrated several key issues pertaining to quantification of variability and
uncertainty in vehicle emissions estimates.  With regard to characterization of variability, the key
points addressed in this work include the following:

   •   Single component distributions are often useful  and reasonably accurate for estimating
       inter-vehicle variability in emissions for most modes and vehicle strata, but they do not
       work well  for all modes and vehicle strata;
   •   Single component distributions whose parameters are estimated using Maximum
       Likelihoood Estimation (MLE) can have means and standard deviations that are
       substantially different from that of the data;
                                           176
-------
  Table 7-20. Allocation of the Actual ART-EF Driving Cycle Speed Traces Into VSP Modes

                  With Respect to Time Spent in Each Mode for 13 Different Vehicles
VSP
bin3
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
Vehicle ID
#7
74
54
206
42
43
42
19
8
8
6




#10
64
67
198
66
33
35
17
10
6
4
2



#11
74
55
200
51
41
38
20
12
7
3
1



#15
75
45
202
62
50
31
16
8
7
6




#18
68
51
211
56
38
36
18
10
9
5




#21
71
53
206
52
47
34
19
8
5
7




#22
73
59
202
50
34
42
24
7
7
4




#26
71
57
200
56
45
29
19
12
8
5




#27
67
62
202
60
36
32
22
9
6
4
2



#39
54
50
253
55
40
24
4
11
2
2
4
2
2

#42
72
56
202
56
42
38
15
9
6
6




#48
73
56
199
54
39
40
22
8
4
6
1



#50
61
69
191
99
47
16
10
5
2
2




a First two digit of VSP Bins: 11:

3.5 liters
odometer reading < 50,000 miles and engine displacement <
               10,000 Trials

                  1.000 H—
                                      Forecast: NO, ART


                                       Cumulative Chart
               TO
               J=
               O

               it
                                     44 Outliers

                                     1- 10000
                                                                          n
                                                                         .0
                                 6.90         7.10        7.30

                                    Certeinty is 95.00%from 6.84 to 7.38 g
 Figure 7-21.  Quantification of Uncertainty Based upon Monte Carlo Simulation for Total NOX

                  Emission from 13 Vehicles Tested on the ART-EF Cycle.
                                            177
-------
    •   The mean and standard deviations of fitted distribution can be forced to match those of
       the data if the Method of Matching Moments (MoMM) is used instead of MLE;
    •   In specific examples evaluated here, distributions fitted using MoMM appeared to better
       represent the upper tail of the distribution of emissions for a given mode than did
       distributions fitted using MLE;
    •   The distribution of emissions within any given mode is typically positively skewed and
       for most modes either a lognormal or a Weibull distribution could provide an adequate fit
       to the data;
    •   There were a few modes out of 56 for which single component distributions (e.g.,
       lognormal, Weibull) could not provide a good fit to the data;
    •   Case studies were developed illustrating that two component mixtures of lognormal
       distributions could be fit to data sets for which a single component distribution was a
       poor fit, and that the mixture distribution provided an excellent fit to the data.
    •   For mixture distributions, MLE is a more readily available and easily applied parameter
       estimation method than MoMM; however, the differences between these two techniques
       become less important when the fit of the distribution to the data is very good.
    •   The use of parametric distributions, whether single component or mixtures, was shown to
       be a feasible approach for characterizing variability.

With regarding to the characterization of uncertainty in mean emissions for specific modes, the
main findings of this work are as follows:

    •   The sample sizes are  sufficiently large and/or the relative standard error of the means are
       sufficiently small, in most cases, so that a normality assumption can be  applied for most
       modes when estimating uncertainty in the mean emission rates;
    •   The estimation of uncertainty in the mean emission rates can be based directly upon the
       data and need not be based upon the distributions fitted to the data to represent
       variability; therefore, any discrepancies between the fitted distributions for variability and
       the data need not influence the uncertainty analysis;
    •   For situations in which the sample size is less than 40 or the relative standard error of the
       mean is greater than 0.2, a more detailed assessment is necessary regarding whether a
       normality assumption is appropriate for estimating uncertainty in mean modal emission
       rates;
    •   The numerical  method of bootstrap simulation can be used to estimate the sampling
       distribution of the mean for situations in which a normality assumptions is suspected to
       be inaccurate;
    •   The results  of bootstrap simulation may sometimes confirm that a normality assumption
       is appropriate, or may provide a strong indication that a normality assumption is not
       appropriate;
    •   Parametric distributions, such as beta, Weibull, gamma, and lognormal, can be fit well to
       the distributions of bootstrap replications of the mean in order to compactly represent
       uncertainty in mean modal emissions even for cases in which a normality assumption is
       not valid;
    •   The range of uncertainty in mean modal  emission rates is a function of averaging time;
       therefore, it was necessary to develop an averaging time correction factor in order to
                                           178
-------
       adjust uncertainty estimates developed based upon one second averages to uncertainty
       estimates applicable for other averaging times;
    •   When comparing a 10 second average to a 1 second average, the range of uncertainty
       increases by a factor of approximately 2.5;
    •   A method was demonstrated for estimating averaging time correction factors; the results
       of analysis of data from the modeling database suggest that the rate of increase of the
       correction factor becomes small for an averaging time of 10 seconds; therefore, the
       correction factor values estimated for the 10 second averaging time are suggested for use
       for averaging times longer than 10 seconds.
    •   The averaging time correction factor has some sensitivity to average VSP within a mode;
       therefore, a "bin adjustment factor" was developed in order to produce a mode-specific
       refined estimate of the correction factor.

With respect to the estimation of uncertainty in total emissions, the key findings of this work are
as follows:

    •   Monte Carlo simulation is  a flexible method for accounting for uncertainty in not just the
       modal emission rates but also in activity data, such as the percentage of time spent in
       each mode;
    •   The computational burden of Monte Carlo simulation depends on the selected sample
       size for the numerical simulation of uncertainty; the choice of sample size can be made
       taking into account trade-offs between the precision of the  estimate of uncertainty in the
       model output versus computational time. Furthermore, techniques such as Latin
       Hypercube Sampling can be used to reduce the sample size for a given level  of precision
       in the estimated distribution for a model output;
    •   For simple models involving linear combinations of normal distributions, an analytical
       approach will give an exact solution with relatively little computational burden; however,
       in order to include uncertainty from activity data in addition to uncertainty in modal
       emission rates, the analytical approach must be modified to an approximate approach;
    •   The results obtained from Monte Carlo simulation and from the analytical solution for
       linear models based upon normality were shown to be equivalent for a case study of
       estimating uncertainty in total emissions for a standard driving cycle;
    •   Based upon case studies for four driving cycles, four pollutants, and four vehicle strata,
       the key insights are that: (1) the amount of uncertainty appears to increase as the average
       VSP or range of VSP of a cycle increases; (2) the amount of uncertainty is a function of
       sample size; and (3) the relative amount of uncertainty is smallest for CC>2, largest for
       both HC and CO, and in between for NOX.  For the specific case studies, the  uncertainty
       range was as narrow as plus or minus 1 percent for CC>2 and as large as plus or minus 30
       percent for HC and CO;
    •   Uncertainty estimates for total emissions of individual vehicles can be aggregated to
       make estimates  of uncertainty in total emissions for a fleet  of vehicles;
    •   Inter-vehicle variability in  speed traces for a standardized driving cycle had little
       influence on the uncertainty estimates for multiple vehicles for the case study of the
       ART-EF cycle;
                                           179
-------
    •   The relative range of uncertainty in total emissions for multiple vehicles is relatively
       insensitive to the number of vehicles even when there is inter-vehicle variability with
       respect to a standard speed trace, for the example of the ART-EF cycle.

The recommendations based upon this work include the following with respect to quantification
of variability:

    •   It is feasible to use parametric distributions to represent variability in emissions for
       specific modes and the use of parametric distributions is preferred over empirical
       distributions because they represent a more compact method of summarizing variability.
    •   The Method of Matching Moments appears to be a preferred method for fitting
       distributions to data because the mean and standard deviation of the fitted distribution
       will be the same as that of the data and because distributions fitted using MoMM appear
       to provide a better fit to the upper tail of the distribution, compared to MLE.  Therefore,
       the use of MoMM is recommended for additional evaluation and application.
    •   Single component distributions such as  lognormal and Weibull distributions will typically
       be able to adequately describe variability for most modes.
    •   In cases where single component distributions fail to provide an adequate fit, a two
       component lognormal  mixture distribution is recommended as a strong candidate for
       substantially improving the fit.
    •   It is not necessary for the uncertainty analysis to be conditioned on the distributions fitted
       to represent variability within modes; therefore, if there are discrepancies  between the
       fitted distributions and the data, such discrepancies need not introduce any error into the
       uncertainty analysis.

With respect to quantification of uncertainty in mean modal emission rates, the recommendations
based upon this work include  the following:

    •   The development of uncertainty estimates for mean emissions should be based directly
       upon the data if there are problems in fitting distributions for variability to the data;
       however, if the fits of the distributions for variability are good, then the uncertainty
       analysis can be based either upon the data or upon the fitted distributions for variability;
    •   A normality assumption will typically be adequate for most modal emission rates as long
       as there are sufficient data;
    •   For modes for which the sample size is  less than 40 and/or the relative standard error of
       the mean is greater than 0.2, the assumption of normality should be tested by developing
       a sampling distribution of uncertainty in the mean based upon bootstrap simulation;
    •   For cases in which a normality assumption is not valid, bootstrap simulation can be used
       to estimate a distribution of bootstrap replications of the mean, and a parametric
       distribution such as beta, Weibull, gamma, or lognormal can be fit to the distribution of
       the means;
    •   The range of uncertainty in modal emission rates must be adjusted for different averaging
       times using an approach such as the correction factor and bin adjustment factor approach
       demonstrated here.
                                           180
-------
With respect to the quantification of uncertainty in total emissions, the recommendations based
upon this work include the following:

    •   A simple analytical approach for estimating uncertainty in total emissions is adequate as
       long as the uncertainty in modal emission estimates are normal or approximately normal
       for most or all of the modes and as long as there is no need to include uncertainty in
       vehicle activity in the estimate;
    •   An analytical calculation method based upon normality can be included for comparison
       purposes even if a Monte Carlo method is also used; for example, results from the
       analytical method could be used as a quality assurance check on the Monte Carlo
       simulation results;
    •   A Monte Carlo simulation-based methods, including variants based upon Latin
       Hypercube Sampling, is recommended if the objective is to include uncertainty in activity
       as an input to the estimation of uncertainty in total emissions;
    •   In situations for which the sample sizes are small and/or the variability in data is large,
       normality assumptions will not be valid.  For such situations, a Monte Carlo-based
       method is preferable.
    •   The range of uncertainty is sufficiently large in many cases that a quantitative uncertainty
       analysis is well-justified.
                                           181
-------
-------
8   FEASIBILITY OF ESTIMATING MODAL EMISSIONS FROM AGGREGATE
    BAG DATA

The objective of this task is to evaluate a methodology for deriving modal emission rates from
data in which only aggregate emission results are available, in order to answer the key question:
How should aggregate bag data be analyzed to derive estimates of modal emission rates? The
first section provides background and theory, upon which the analyses in the later sections are
based.

8.1    Methodological Overview
In order to estimate modal emission rates, the fraction of time  spent in each mode for a driving
cycle is estimated based upon the second-by-second speed trace used for the bag measurements
(preferably the actual speed trace for the test, as opposed to the nominal  speed trace), and any
other available information regarding simulation of loads with the dynamometer. A system of
equations for the unknown modal emissions, the fraction of time in each mode, and the total
(agrgretage) emissions is developed since the average emission rate for each trip can be
represented by the fraction of time spent in each mode multiplied by modal emission rate.  For
example for four different modes for running exhaust emissions, as was the case for the shootout
project that was conducted by NCSU, the following equation was specified (Frey, Unal, and
Chen, 2002):

    X ftcs + ERidle X ftidle + ERaccel X ftaccel + ERdecel X ftdecel + ER^se X ftcraise  = ERave     (8-1)

  where,
       ER;    = emission rate for mode i (g/sec)
       ft;      = fraction of time spent in mode i
       Subscripts
              cs     = cold start mode
              idle    = idle mode
              accel  = acceleration mode
              decel  = deceleration mode
              cruise = cruise mode
              ave    = average  of all modes

From the bag data, the average emission rate for the entire bag (or trip) can be estimated. From
the speed trace, the fraction of time in each mode can be estimated.  Therefore, the unknowns are
the modal emission rates.

In order to solve systems of equations such as the one given in Equation  (8-1), there are different
methods. A system where the number of equations used is the  same as the number of unknowns
is identified as a "square" system, and has unique solutions (Kress, 1998).  For "square" systems,
an exact solution is sought by using methods such as Gaussian Elimination.

Systems which have a number of equations less than the number of unknowns are identified as
"underdetermined" systems, and the solutions of these systems of equations are not unique.
                                          183
-------
Such systems can be converted to "square" systems by adding additional equations, such as an
assumption regarding the ratio of the g/sec emission rate for one mode with respect to another.

Conditions where there are more equations than unknowns are identified as "overdetermined"
cases. In these cases, which are likely to be common with respect to the use of existing vehicle
emissions bag data, least-squares methods can be used to find solutions (Kress, 1998).

According to Kress (1998), in order to be able to solve linear systems directly, the system should
be "well-conditioned", rather than "ill-conditioned". "Ill-conditioned" systems occur when small
errors in the data of a linear system cause large errors in the solution (Kress, 1998;  Hildebrand,
1987). The minimum number of equations (i.e., one equation represents one measurement of
bag data) that are desirable in order to have a well-conditioned system will depend on number of
unknowns, which is the number of modal "bins" in this case.  Techniques for solving well-
conditioned over-determined systems include least-squares regression and constrained least-
squares. In the latter method, constraints can be included. For example, if it is known that
emissions in one mode should be less than that of other modes, this can be added as a constraint
in the system. Further, a non-negativity constraint can be included. In this study, both Least-
Squares and Constrained Least-Squares were investigated. From the previous study it was
observed that Constrained Least-Squares produced good results.

The performance of the modal emission estimation approach based upon aggregate data was
evaluated based upon application of the method to second-by-second data. Specifically, the
second-by-second data were used to estimate the fraction of time spent in each mode and the
total (or trip average) emission rate.  The calculation procedure  described above was applied to
estimate the modal emission rates.  The estimated modal emission rates were compared to the
actual modal emission rates. Uncertainty in the predictions of the solution technique were
characterized by evaluating the distribution of the differences between the predicted modal
emission rates and the actual modal  emission rates.  Ideally, if the solution method is unbiased,
the average difference between the predicted and actual modal emission rates will be zero. If the
average difference is not zero, then there is a bias. The magnitude of the bias was evaluated to
determine whether it was significant. The uncertainty in the modal emission estimates obtained
from the bag (aggregate) data must be considered in the uncertainty analysis of the emissions
model if these modal emission estimates are used in the model.

8.2    Bag-Based Modal Emissions Estimation for Four Modes (Idle, Acceleration, Cruise,
       Deceleration) and for 14 VSP Modes
The objective of this portion of the work was to develop a methodology for deriving modal
emission rates from data in which only aggregate emission results are available.  The method
was first applied to relatively simple modal emission models,  including the four basic modes of
idle, acceleration, cruise, and deceleration defined by NCSU in  previous work and the 14 VSP
modes defined in this project. The generic equation underlying the estimation process can be
specified as:

                    ERi* fti + ...+ ER;* ft; +... + ERn* ftn = ERavg                   (8-2)

Where,
                                          184
-------
              ER;:  emission rate for mode I (g/sec)
              ft;  :  fraction of time spent in mode i
       Subscripts:
              i:     mode i
              n:    total number of modes
              avg:  average of all modes

From the bag data, the average emission rate for the entire bag (or trip) can be estimated. From
the speed trace, the fraction of time in each mode can be estimated. Therefore, the unknowns are
the modal emission rates.

Initially, tests of the method were done on two preliminary versions of modal definitions,
including the four original NCSU based bins and the 14 VSP based bins developed in this
project. The NCSU approach is comprised of four driving modes: idle, acceleration,
deceleration, cruise, which are assigned mode numbers from 1 to 4 sequentially for purposes of
this analysis.

Because the equation above corresponds to one  trip and there are hundreds of trips in the data
set, the equation is an "overdetermined" square  system in which there are more equations than
unknown variables. The techniques for solving such systems include least-squares and
constrained least-squares as previously discussed. We used both of them and compared their
applicability.

The basic assumption of the least squares method is to find a curve that has the minimal sum of
the deviations squared (least square error) from  a given set of data:

              Min  y = fj(x)* fi(x) + ...+ f,(x)* f;(x)  +...  + fm(x)* fm(x)               (8-3)
Where
     fi(x) = ftu* Xl +...+ ftj* Xj +...+ ftm* xn - ERavgl
     Xj: the emission rate of mode j
     m: number of trips
     n:  number of modes
     ERavgi:  aggregated emission rate for all modes  in trip i(g/sec)
     Fty  :   fraction of time spent in mode j in trip i

For the constrained least square method, the approach is to solve the above least squares problem
additionally with some constraints which may be linear or non-linear equations or inequalities.
For example, it is known that emission rates in the acceleration mode should be larger than that
in the idle modes, from which, we can assume:  xaccei > x;die. The constrained least squares
problem is a special form of Nonlinear Programming, which is  one of the classic topics in
Operations Research. In the NLP terminology, the previous equation is an objective function
which is nonlinear and quadratic.

At first, only simple constraints were used, but results with these were not promising, so strict
constraints were created. Hence, there are 3 tests conducted respectively on each pollutant for
each binning approach: unconstrained, basic constraints, and strict constraints.  The basic
                                           185
-------
constraints just consider the order of emission rates of all the modes and their non-negative
characteristic.  For example, the following is the set of basic constraints set for the NCSU
approach used in the test:
                                  X2>X4>X3>Xi>0                            (8-4)
          Where X2: emission rate of acceleration mode
                 X4: emission rate of cruise mode
                 X3: emission rate of deceleration mode
                 X2: emission rate of idle mode
If the space of the control variables X is not sufficiently focused, it is possible that the estimated
optimal value of X* might lie in an area that is infeasible, such as negative values. Thus, the
more concentrated the effective space of X is, the more accurate the test results would typically
be. Based on this, strict constraints were developed.  To develop the strict constraints, the
emission rates of each mode for each trip were calculated as ratios with respect to the smallest
emission rate among all the modes, which is idle in the case of the NCSU approach,  and then
statistically summarized over the all the trips to get the means and confidence limits of those
ratios.  These ratios were used to develop the strict constraints.. The strict constraints also
include either explicitly or implicitly the basic constraints set. Since the form of the latter was
shown above, here just the additional strict constraints are displayed:

                                  a * Xi < Xi  < b* Xi                            (8-5)

         where  Xi: the lowest emission rate among all the modes
                 a: the low bound of confidence  limits for ratio X;/ Xi  (confidence=0.05)
                 b: the high bound of confidence limits of ratio X;/ Xi  (confidence=0.05)

Below is an example of complete strict constraints set for HC emissions based upon NCHRP
data under the NCSU bin approach:

           X2>X4>X3>Xi>0                                                   (8-6)
           56.5 *Xi< X2  <73.4*Xi
            1.8 *Xi< X3  <  7.1* Xi
            3.6*Xi< X3  <13.3*Xi
           Where    X2: emission rate of acceleration mode
                     X/j; emission rate of cruise  mode
                     X3: emission rate of deceleration mode
                     X2: emission rate of idle mode

The  SAS mathematical programming software was used to solve the above NLP problem. The
test was done based upon the NCHRP data set, which has more than one hundred trips and
92,000 observations. The results are shown in Tables 8-1 through 8-4 for NOX, HC, CO, and
CO2, respectively. The results are summarized graphically in Figures 8-1 through 8-4 for the
same four respective pollutants.  The results indicate that for the analysis of only four modes, the
accuracy of estimating the average modal emission rates is less than desirable.  For example, the
                                          186
-------
  Table 8-1. Results of Estimation of Modal Emission Rates (mg/sec) from Aggregate Data for
         Four NCSU Driving Modes for NOx: Comparison of No Constraint, Basic Constraint,
                                  and Strict Constraint Solutions.
Mode
Erl
Er2
Er3
Er4
Avg. Error
Actual
2.84
65.5
3.18
22.76

NCa
-12.3
-285
972.02
-148.98

ERRORd
-5.35
-5.35
304.94
-7.54
131.4
Cb
0
28.44
28.44
28.44

ERRORd
-1
-0.57
7.95
0.25
2.44
SCC
0.78
34.05
3.49
31.81

ERRORd
-0.72
-0.48
0.1
0.4
0.43
  Table 8-2. Results of Estimation of Modal Emission Rates (mg/sec) from Aggregate Data for
          Four NCSU Driving Modes for HC:  Comparison of No Constraint, Basic Constraint,
                                  and Strict Constraint Solutions.
Mode
Erl
Er2
Er3
Er4
Avg. Error
Actual
1.18
19.7
2.8
6.58

NCa
28.69
-207.09
295.24
-12.31

ERRORd
-23.36
11.51
-104.39
2.87
35.53
Cb
0
8.38
8.38
8.38

ERRORd
1
0.57
-1.99
-0.27
0.96
scc
0.49
27.54
3.46
4.05

ERRORd
0.59
-0.4
-0.23
0.38
0.4
  Table 8-3. Results of Estimation of Modal Emission Rates (mg/sec) from Aggregate Data for
          Four NCSU Driving Modes for CO:  Comparison of No Constraint, Basic Constraint,
                                  and Strict Constraint Solutions.
Mode
Erl
Er2
Er3
Er4
Avg. Error
Actual
20.04
2013.96
77.15
447.11

NCa
-3561.8
-3957.6
31522
-6407.3

ERRORd
178.74
2.97
-407.57
15.33
151.15
Cb
0
688.62
688.62
688.62

ERRORd
1
0.66
-7.93
-0.54
2.53
SCC
1.02
1345.18
152.54
636.76

ERRORd
0.95
0.33
-0.98
-0.42
0.67
 Table 8-4. Results of Estimation of Modal Emission Rates (g/sec) from Aggregate Data for Four
          NCSU Driving Modes for CO2:  Comparison of No Constraint, Basic Constraint, and
                                    Strict Constraint Solutions.
Mode
Erl
Er2
Er3
Er4
Avg. Error
Actual
0.89
5.76
0.98
3.29

NCa
1.67
-45.07
84.78
-5.87

ERRORd
0.87
-8.82
85.14
-2.78
24.4
Cb
0
3.4
3.4
3.4

ERRORd
-1
-0.41
2.46
0.03
0.97
scc
0.96
4.61
1.01
3.65

ERRORd
0.07
-0.2
0.02
0.11
0.1
Notes for Tables 8-1 through 8-4:
aNC: No Constraint
 C: Constraint
0 SC: Strict Constraint
d Error: (Predicted-Actual)/Actual
                                          187
-------
          ra
         •o
          o
   4.5


    4 -





    3


   2.5


    2 -\


   1.5


    1
         •o


         S

         "S 0.5


         *  o
                                                 y = 0.5048X + 0.5634

                                                     R2 = 0.6952
               01       234567


                              Observed Modal Rate (mg/sec)




Figure 8-1.  Predicted versus Observed NOX NCSU Modal Emission Rates Estimated From

                 NCHRP Data Using the Strict Constraints Approach.
     3 n



I25-
  I
     2 ^
          o>

          E.
   1.5-



     1 -



"g  0.5
          co
         •o
          o
          £
         Q.
              0
            -0.5 -I
                                         y = 1.4671X-0.2214 4

                                            R2 = 0.9669
       I)
0.5          1         1.5         2



    Observed Modal Rate (mg/sec)
                                                                    2.5
Figure 8-2. Predicted versus Observed HC NCSU Modal Emission Rates Estimated From

                 NCHRP Data Using the Strict Constraints Approach.
                                      188
-------
   160
|  140
_|  120
H  100
K
«   80 -j
1   60-
|   40-
    20-
     0
          £
         Q.
                                         y = 0.6244X + 13.451
                                             R2 = 0.9324
                          50        100        150        200
                              Observed Modal Rate (mg/sec)
                                                           250
Figure 8-3. Predicted versus Observed CO NCSU Modal Emission Rates Estimated From
                 NCHRP Data Using the Strict Constraints Approach.

         I 4
         £
         co 3 -
          £
         Q.
            1 -
                                           y = 0.7827X + 0.4207
                                               R2 = 0.9434.
              01234567
                              Observed Modal Rate (g/sec)
Figure 8-4. Predicted versus Observed CO2 NCSU Modal Emission Rates Estimated From
                 NCHRP Data Using the Strict Constraints Approach.
                                      189
-------
slopes of the best fit lines in the parity plots deviate substantially from an ideal value of 1 for all
four pollutants. However, the strict constraints do produce modal estimates that qualitatively
preserve the relative ordering among modes and that yield an acceleration mode with an
emission rate substantially higher than for the other modes.

The results based upon application to the 14 VSP-based modes are shown in Tables 8-5 through
8-8 and Figures 8-5 through 8-8 for NOX, HC, CO, and CC>2, respectively. These results are
generally more promising, with the slope of the best fit line in the parity plots closer to one than
was the case for the analysis based upon only four modes, and with coefficients of determination
for the parity plots in excess of 0.80.  The results are especially promising for CC>2.

As exspected, among three types of test, the test based on strict constraints gave the best
performance, which confirms that the focus on the effective area of the control variables X will
improve the predication accuracy.

Comparing the differences among the four pollutants, only the results for CC>2 are satisfying,
with a predication error of approximately 10% or less. A possible reason for the  superior results
with CC>2 but not for the other pollutants is that is CC>2 has  small inter-trip and inter-vehicle
variance of the modal  emission rates. Too much variability in modal emission rates from one
vehicle to another may be the source of difficulties in estimation of modal rates for the other
pollutants.
                                           190
-------
Table 8-5.  Results of Estimation of Modal Emission Rates (mg/sec) from Aggregate Data for 14
            VSP Modes forNOx: Comparison of No Constraint, Basic Constraint, and Strict
                                       Constraint Solutions.
NOX
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
4.54
4.66
4.27
13.71
20.26
25.97
34.1
48.69
61.91
86.39
123.44
173.84
176.49
201.72

NCa
357.88
109.4
154.63
-83.57
-10.52
-583.9
-423.49
-533.89
260.33
515.21
576.05
295.88
908.56
849.94

ERRORd
77.82
22.48
35.18
-7.09
-1.52
-23.48
-13.42
-11.97
3.21
4.96
3.67
0.7
4.15
3.21
15.2
Cb
11.23
0
11.23
11.23
11.23
11.23
11.23
11.23
11.23
95.29
95.29
95.29
381.74
1283.26

ERRORd
1.47
-1
1.63
-0.18
-0.45
-0.57
-0.67
-0.77
-0.82
0.1
-0.23
-0.45
1.16
5.36
1.06
SCC
2.53
2.47
1.24
8.12
11.52
12.14
12.14
29.89
48.79
66.9
80.16
93.48
118.5
211.03

ERRORd
-0.44
-0.47
-0.71
-0.41
-0.43
-0.53
-0.64
-0.39
-0.21
-0.23
-0.35
-0.46
-0.33
0.05
0.4
aNC: No Constraint
b C: Constraint
0 SC: Strict Constraint
 d Error: (Predicted-Actual)/Actual
Table 8-6.  Results of Estimation of Modal Emission Rates (mg/sec) from Aggregate Data for 14
            VSP Modes for HC: Comparison of No Constraint, Basic Constraint, and Strict
                                       Constraint Solutions.
HC
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
AvgError
Actual
3.69
2.27
1.92
4.02
5.97
6.07
7.57
11.15
13.71
17.22
28.09
50.43
73.6
98.75

NCa
130.98
0.84
23.35
2.09
-61.98
-177.83
49.79
-16.64
215.81
-169.45
110.83
-98.42
-180.59
146.08

ERRORd
34.51
56.12
66.48
31.65
21.34
20.96
16.82
11.41
9.28
7.39
4.53
2.52
1.73
1.29
20.43
Cb
0
0
5.52
0
5.52
5.52
5.52
5.52
35.33
35.33
35.33
35.33
35.33
211.99

ERRORd
-1
-1.63
-1.93
-0.92
-0.62
-0.61
-0.49
-0.33
-0.27
-0.21
-0.13
-0.07
-0.05
-0.04
0.59
scc
2.25
1.41
1.16
3.01
4.04
4.96
8.87
8.87
22.33
22.33
39.42
39.42
50.35
248.96

ERRORd
-0.39
-0.63
-0.75
-0.36
-0.24
-0.24
-0.19
-0.13
-0.1
-0.08
-0.05
-0.03
-0.02
-0.01
0.23
aNC: No Constraint
 C: Constraint
0 SC: Strict Constraint
d Error: (Predicted-Actual)/Actual
                                          191
-------
Table 8-7.  Results of Estimation of Modal Emission Rates (mg/sec) from Aggregate Data for 14
            VSP Modes for CO:  Comparison of No Constraint, Basic Constraint, and Strict
                                       Constraint Solutions.
CO
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
AvgError
Actual
149.59
124.14
83.59
273.76
338.76
307.11
393.27
608.03
755.63
1015.26
2063.31
5530.73
10336.3
16338.64

NCa
23220
-2308
-2028
-2467
-13068
-2760
-1282
7636
17311
-21646
-7639
-17753
-31840
-39599

ERRORd
154.22
-19.6
-25.27
-10.01
-39.58
-9.99
-4.26
11.56
21.91
-22.32
-4.7
-4.21
-4.08
-3.42
23.94
Cb
0
0
0
0
0
0
1716
1716
3403.35
3403.35
3403.35
3403.35
3403.35
3403.35

ERRORd
-1
-1
-1
-1
-1
-1
3.36
1.82
3.5
2.35
0.65
-0.39
-0.67
-0.79
1.4
SCC
121.22
0
36.62
179.45
179.45
310.19
595.48
1114.42
1722.36
1722.36
4262.86
7571.34
7571.34
13287

ERRORd
-0.19
-1
-0.56
-0.34
-0.47
0.01
0.51
0.83
1.28
0.7
1.07
0.37
-0.27
-0.19
0.56
aNC: No Constraint
b C: Constraint
0 SC: Strict Constraint
d Error: (Predicted-Actual)/Actual
 Table 8-8. Results of Estimation of Modal Emission Rates (g/sec) from Aggregate Data for 14
            VSP Modes for CO2:  Comparison of No Constraint, Basic Constraint, and Strict
                                       Constraint Solutions.
C02
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
AvgError
Actual
1.09
1.26
1.26
2.46
3.2
3.95
4.69
5.52
6.41
7.42
8.89
10.61
11.87
13.34

NCa
14.78
4.43
3.83
-4.37
-9.19
9.73
-2.04
-3.63
9.47
-8.69
17.11
6.73
9.74
33.77

ERRORd
12.52
2.5
2.05
-2.78
-3.87
1.46
-1.44
-1.66
0.48
-2.17
0.93
-0.37
-0.18
1.53
2.42
Cb
1.28
1.28
1.15
1.28
1.28
6.18
6.18
6.18
6.18
6.18
7.04
7.04
7.39
43.5

ERRORd
0.17
0.01
-0.08
-0.48
-0.6
0.56
0.32
0.12
-0.04
-0.17
-0.21
-0.34
-0.38
2.26
0.08
scc
1.04
1.19
1.23
2.32
3.07
3.81
4.95
5.81
6.77
7.82
9.27
10.49
11.75
13.03

ERRORd
-0.05
-0.06
-0.02
-0.06
-0.04
-0.04
0.05
0.05
0.06
0.05
0.04
-0.01
-0.01
-0.02
0.04
aNC: No Constraint
 C: Constraint
0 SC: Strict Constraint
d Error: (Predicted-Actual)/Actual
                                          192
-------
            g 250,

            -52
            "01

            £ 200
            E
            LII
            x 100
            O
            •o
               50-
                                       y = 0.8027X - 6.2648

                                          R2 = 0.8871
                            50         100        150        200

                               Observed NOx Emissions (mg/sec)
                                                         250
  Figure 8-5. Predicted versus Observed NOX Modal Emission Rates Based upon the 14 Mode

     VSP Approach Estimated From NCHRP Data Using the Strict Constraints Approach.
              8  80 n

              "Si  70

              7  60 -I


              !5CH
              •|  40
              LU
              O  30-
              x
              •o

              «
              'TS
              £
   20 -
£  10
                              y = 0.7346X + 3.2797

                                  R2 = 0.861
              • •
                                20           40           60

                                Observed HC Emissions (mg/sec)
                                                        80
Figure 8-6. Predicted versus Observed HC Modal Emission Rates Based upon the 14 Mode VSP

       Approach Estimated From NCFtRP Data Using the Strict Constraints Approach.
                                         193
-------
            IT 20000
            8!
                                              y = 0.798x + 578.3
                                                 R2 = 0.9275
                                5000         10000        15000
                                Observed CO Emissions (mg/sec)
                                                         20000
Figure 8-7. Predicted versus Observed CO Modal Emission Rates Based upon the 14 Mode VSP
       Approach Estimated From NCFIRP Data Using the Strict Constraints Approach.
IT 16
I"
g  12
1  10
            E
            LU
            0>l
            O
            O
            •o
            S
            'D
            £
            Q.
    8-
    6-
    4-
    2-
    0
                                              y = 0.9986X + 0.0482
                                                  R2 = 0.9965
                               4      6      8     10     12
                                Observed CO2 Emissions (g/sec)
                                                     14
16
  Figure 8-8.  Predicted versus Observed CO2 Modal Emission Rates Based upon the 14 Mode
     VSP Approach Estimated From NCFIRP Data Using the Strict Constraints Approach.
                                         194
-------
8.3    Bag-Based Modal Emissions Estimation for the "56-bin" VSP-based Approach
In this section, evaluation of the modal estimation method for bag data was applied to the
stratified bin approach. The original NCHRP data set was divided into 4 subsets of data in terms
of odometer reading and engine displacement, based upon cut points of 50K miles and 3.5 liters,
respectively.  For each of the four subsets, the 14 VSP modes were applied. From the previous
section, a key conclusion was that the strict-constraint method is more effective than the
unconstrained and basic-constraint methods. Thus, the focus in this section was upon the strict
constraint method.  In the previous section, the strict constraints were developed based upon
analysis of the NCHRP data set. In this section, the ranges for the strict constraints were
developed based upon the NCHRP data set and, alternatively, based upon the modeling data set.

The results of the predicted modal emission rates estimated from the aggregate data, and the
observed values, are shown in Tables 8-9 through 8-24. There are four tables for each pollutant,
with each of the four tables representing a different vehicle strata with respect to odometer
reading and engine displacement. All of the results for CC>2 based upon the strict constraints
cases are shown in Figures 8-9 through 8-16. Selected results for the modal emissions estimated
for HC are shown in Figures 8-17 through 8-22.

The results for CC>2 were generally very good, especially for the case in which the range of
values for the constraints were estimated from data in the NCHRP database. For all four vehicle
strata, the average relative error in the predicted versus observed modal emission rates was less
than 10 percent, except for the first strata (odometer reading < 50,000 miles, engine displacement
< 3.5 liters) when constraints were developed based upon the modeling database. These results
imply that when the constraints are more representative of the data from which the modes are
being estimated, the results will tend to be better.  Figure 8-11 and 8-12 illustrate that the modal
emission rates for CO2 estimated using the constraints estimated from the NCHRP data are
better than those estimated using the  constraints based upon the modeling database.  In
particular, the slope of the trend line  for the predicted versus observed modes is closer to one,
indicating a more accurate result. A  similar comparison can be observed for Figures 8-13 and 8-
14.

The results for HC were generally not as good as those for CC>2.  The average relative errors for
the modal estimates, as indicated in Tables 8-13 through 8-16, were typically 0.37 to 0.64 for the
six cases in which results could be obtained. In two cases, it was not possible to get a solution.
The predicted modal emissions tend to be low for the higher VSP modes, as illustrated in Figures
8-17 through  8-19, although there are examples in Figures 8-20 through 8-22 in which the
predictions for the higher VSP modes are relatively more accurate.

For both NOX and CO, the estimation method failed for most cases. For NOX, it was possible to
get results in only three of eight cases, and the errors in these cases ranged from 0.24 to 0.55.
For CO, it was possible to get results in  only two of eight cases, with errors of 0.48 and 0.94.

Overall, the key findings of the attempts to estimate modal emission rates for the 56-bin
approach based upon NCHRP data were: (1) the method worked well only for CO2; the method
worked for HC for most cases but the accuracy of the predictions was less than desirable; and (3)
                                           195
-------
 Table 8-9. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
         Approach for Two Different Constraints Versus Actual Rates:  CO2 Emissions (g/sec)
             for Engine Displacement < 3.5 Liters and Odometer Reading < 50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
0.94
1.06
1.2
2.21
2.86
3.53
4.19
4.92
5.74
6.67
7.82
9.49
10.89
12.08

CONSTRAINT ALLDATA
1.58
1.51
1.26
2.16
2.62
3.03
4.25
4.82
5.51
6.18
7.34
9.2
11.61
12.29

Error3
0.68
0.42
0.05
-0.022
-0.084
-0.14
0.014
-0.02
-0.04
-0.07
-0.06
-0.03
0.066
0.017
0.122
CONSTRAINT NCHRP
0.91
0.95
1.08
2
2.63
3.25
4.51
5.31
6.18
7.13
8.65
9.9
11.48
12.18

Error3
-0.03
-0.10
-0.10
-0.10
-0.08
-0.08
0.08
0.08
0.08
0.07
0.11
0.04
0.05
0.01
0.072
a Error: (Predicted-Actual)/Actual
 Table 8-10. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
         Approach for Two Different Constraints Versus Actual Rates: CO2 Emissions (g/sec)
             for Engine Displacement > 3.5 Liters and Odometer Reading < 50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
1.03
1.31
1.07
2.4
3.15
3.84
4.55
5.32
6.16
7
8.43
9.91
10.54
11.92

CONSTRAINT ALLDATA
1.24
1.4
1.08
2.29
2.85
3.46
5.07
5.81
6.56
7.55
8.66
8.66
9.15
9.9

Error3
-0.20
-0.07
-0.01
0.05
0.10
0.10
-0.11
-0.09
-0.06
-0.08
-0.03
0.13
0.13
0.17
0.09
CONSTRAINT NCHRP
1.01
1.18
1
2.17
2.9
3.58
4.86
5.68
6.6
7.54
9.07
10.54
11.27
11.27

Error3
0.019
0.099
0.065
0.096
0.079
0.068
-0.068
-0.068
-0.071
-0.077
-0.076
-0.064
-0.069
0.055
0.070
'Error: (Predicted-Actual)/Actual
                                          196
-------
Table 8-11. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
         Approach for Two Different Constraints Versus Actual Rates: CO2 Emissions (g/sec)
             for Engine Displacement < 3.5 Liters and Odometer Reading > 50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
1.5
1.53
1.66
2.93
3.88
4.94
5.95
7.05
8.23
9.64
11.13
14.24
15.84
17.47

CONSTRAINT ALLDATA
1.56
1.66
1.33
2.36
2.93
5.46
6.55
7.95
7.95
7.95
12.94
18.87
18.87
18.87

Error3
-0.04
-0.08
0.20
0.19
0.24
-0.11
-0.10
-0.13
0.03
0.18
-0.16
-0.33
-0.19
-0.08
0.15
CONSTRAINT NCHRP
1.55
1.41
1.52
2.63
3.7
4.75
6.67
7.9
9.28
9.28
12.25
15.19
15.25
15.25

Error3
-0.033
0.078
0.084
0.102
0.046
0.038
-0.121
-0.121
-0.128
0.037
-0.101
-0.067
0.037
0.127
0.080
'Error: (Predicted-Actual)/Actual
Table 8-12. Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
         Approach for Two Different Constraints Versus Actual Rates: CO2 Emissions (g/sec)
             for Engine Displacement > 3.5 Liters and Odometer Reading > 50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
1.67
1.97
1.69
3.5
4.48
5.46
6.48
7.64
8.83
10.3
12.54
14.75
16.96
18.76

CONSTRAINT ALLDATA
1.64
2.15
1.54
3
4.07
5.1
6.74
6.97
9.42
11.36
13.41
13.41
20.25
21.42

Error3
0.018
-0.091
0.089
0.143
0.092
0.066
-0.040
0.088
-0.067
-0.103
-0.069
0.091
-0.194
-0.142
0.092
CONSTRAINT NCHRP
1.64
2.15
1.54
3
4.07
5.1
6.74
6.97
9.42
11.36
13.41
13.41
20.25
21.42

Error3
0.02
-0.09
0.09
0.14
0.09
0.07
-0.04
0.09
-0.07
-0.10
-0.07
0.09
-0.19
-0.14
0.09
'Error: (Predicted-Actual)/Actual
                                         197
-------
 Table 8-13.  Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
         Approach for Two Different Constraints Versus Actual Rates: HC Emissions (mg/sec)
             for Engine Displacement < 3.5 Liters and Odometer Reading < 50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
2.18
1.67
1.82
4.11
4.16
5.37
6.56
8.82
10.52
13.25
24.06
31.79
59.91
70.41

CONSTRAINT ALLDATA
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Error3















CONSTRAINT NCHRP
3.26
0.93
1.16
2.75
3.26
7.09
7.79
7.79
7.91
26.16
27.79
27.79
27.79
27.79

Error3
-0.50
0.44
0.36
0.33
0.22
-0.32
-0.19
0.12
0.25
-0.97
-0.16
0.13
0.54
0.61
0.37
a Error: (Predicted-Actual)/Actual
 Table 8-14.  Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
         Approach for Two Different Constraints Versus Actual Rates: HC Emissions (mg/sec)
             for Engine Displacement > 3.5 Liters and Odometer Reading < 50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
4.98
2.06
0.95
3.11
5.15
5.17
6.17
7.67
13.26
15.18
24.58
44.64
70.17
116.55

CONSTRAINT ALLDATA
2.52
1.73
1.33
2.79
3.19
4.38
11.42
13.01
13.01
27.09
42.49
42.49
42.49
42.49

Error3
0.494
0.160
-0.400
0.103
0.381
0.153
-0.851
-0.696
0.019
-0.785
-0.729
0.048
0.394
0.635
0.418
CONSTRAINT NCHRP
2.37
1.27
0.91
2.18
2.73
3.73
11.65
11.65
11.65
28.75
46.4
46.4
46.4
46.4

Error3
0.52
0.38
0.04
0.30
0.47
0.28
-0.89
-0.52
0.12
-0.89
-0.89
-0.04
0.34
0.60
0.45
a Error: (Predicted-Actual)/Actual
                                         198
-------
 Table 8-15.  Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
         Approach for Two Different Constraints Versus Actual Rates: HC Emissions (mg/sec)
             for Engine Displacement < 3.5 Liters and Odometer Reading > 50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
1.58
1.45
1.84
2.39
9.17
4.72
5.48
11.3
12.66
20.14
20.14
71.33
70.54
77.97

CONSTRAINT ALLDATA
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Error3















CONSTRAINT NCHRP
0.94
0.75
2.48
2.01
4.4
5.42
5.42
27.42
27.42
27.42
42.75
91.07
91.07
91.07

Error3
0.41
0.48
-0.35
0.16
0.52
-0.15
0.01
-1.43
-1.17
-0.36
-1.12
-0.28
-0.29
-0.17
0.49
a Error: (Predicted-Actual)/Actual
 Table 8-16.  Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
         Approach for Two Different Constraints Versus Actual Rates: HC Emissions (mg/sec)
             for Engine Displacement > 3.5 Liters and Odometer Reading > 50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
10.75
7.39
5.71
8.51
15
14.76
20.53
35.71
34.84
43.06
64.77
137.02
161.42
209.61

CONSTRAINT ALLDATA
1.59
1.78
3.8
0
7.29
8.35
9.15
44.64
86.61
86.61
122.99
122.99
122.99
315.45

Error3
0.852
0.759
0.335
1.000
0.514
0.434
0.554
-0.250
-1.486
-1.011
-0.899
0.102
0.238
-0.505
0.639
CONSTRAINT NCHRP
1.59
1.78
3.8
0
7.29
8.35
9.15
44.64
86.61
86.61
122.99
122.99
122.99
315.45

Error3
0.85
0.76
0.33
1.00
0.51
0.43
0.55
-0.25
-1.49
-1.01
-0.90
0.10
0.24
-0.50
0.64
a Error: (Predicted-Actual)/Actual
                                         199
-------
 Table 8-17.  Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
         Approach for Two Different Constraints Versus Actual Rates: CO Emissions (mg/sec)
             for Engine Displacement < 3.5 Liters and Odometer Reading < 50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
144.4
86.18
82.35
284.3
283.62
300.11
393.08
625.93
749.09
1033.99
2576.85
3944.7
8785.4
12567.67

CONSTRAINT ALLDATA
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Error3















CONSTRAINT NCHRP
116.78
35.4
45.98
179.31
210.11
279.07
479.53
479.53
2438.1
2684.08
2684.08
3204.4
8891.55
8891.55

Error3
0.19
0.59
0.44
0.37
0.26
0.07
-0.22
0.23
-2.25
-1.60
-0.04
0.19
-0.01
0.29
0.48
a Error: (Predicted-Actual)/Actual
 Table 8-18.  Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
         Approach for Two Different Constraints Versus Actual Rates: CO Emissions (mg/sec)
             for Engine Displacement > 3.5 Liters and Odometer Reading < 50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
150.28
130
48.96
221.4
285.13
241.95
277.95
327.58
519.72
651.3
1249.86
6740.72
12956.1
23713.22

CONSTRAINT ALLDATA
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Error3















CONSTRAINT NCHRP
63.17
0
30.66
111.62
111.62
252.67
340.68
430.83
2103.27
2225.11
5239.32
5239.32
5239.32
22508

Error3
0.58
1.00
0.37
0.50
0.61
-0.04
-0.23
-0.32
-3.05
-2.42
-3.19
0.22
0.60
0.05
0.94
a Error: (Predicted-Actual)/Actual
                                         200
-------
 Table 8-19.  Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
         Approach for Two Different Constraints Versus Actual Rates: CO Emissions (mg/sec)
             for Engine Displacement < 3.5 Liters and Odometer Reading >50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
80.7
129.75
130.09
227.75
637.64
280.52
416.31
696.73
1094.9
1253.14
2031.25
8029.59
8933.28
12979.73

CONSTRAINT ALLDATA
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Error3















CONSTRAINT NCHRP
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Error3















a Error: (Predicted-Actual)/Actual
 Table 8-20.  Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
         Approach for Two Different Constraints Versus Actual Rates: CO Emissions (mg/sec)
             for Engine Displacement > 3.5 Liters and Odometer Reading > 50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
263.35
316.27
145.17
440.86
456.54
592.43
740.36
1305.73
1135.74
1793.1
2394.7
8240.6
13064.57
19173.19

CONSTRAINT ALLDATA
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Error3















CONSTRAINT NCHRP
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Error3















a Error: (Predicted-Actual)/Actual
                                         201
-------
 Table 8-21.  Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
        Approach for Two Different Constraints Versus Actual Rates:  NOX Emissions (mg/sec)
             for Engine Displacement < 3.5 Liters and Odometer Reading < 50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
4.4
3.85
4.41
11.8
15.52
18.17
22.95
33.86
47.21
65.22
78.39
137.34
141.33
183.97

CONSTRAINT ALLDATA
6.61
5.82
3.77
9.85
9.85
18.71
18.71
45.54
45.54
89.59
89.59
121.26
121.26
121.26

Error3
-0.502
-0.512
0.145
0.165
0.365
-0.030
0.185
-0.345
0.035
-0.374
-0.143
0.117
0.142
0.341
0.243
CONSTRAINT NCHRP
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Error3















a Error: (Predicted-Actual)/Actual
 Table 8-22.  Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
        Approach for Two Different Constraints Versus Actual Rates:  NOx Emissions (mg/sec)
             for Engine Displacement > 3.5 Liters and Odometer Reading < 50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
2.66
1.39
1.75
7.56
11.67
18.45
26.75
37.46
53.37
68.14
65.56
125.35
141.54
120.47

CONSTRAINT ALLDATA
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Error3















CONSTRAINT NCHRP
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Error3















a Error: (Predicted-Actual)/Actual
                                         202
-------
 Table 8-23.  Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
        Approach for Two Different Constraints Versus Actual Rates:  NOX Emissions (mg/sec)
             for Engine Displacement < 3.5 Liters and Odometer Reading > 50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
1.58
1.45
1.84
2.39
9.17
4.72
5.48
11.3
12.66
20.14
20.14
71.33
70.54
77.97

CONSTRAINT ALLDATA
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Error3















CONSTRAINT NCHRP
0
0
0
0
0
0
0
0
0
0
0
0
0
0

Error3















a Error: (Predicted-Actual)/Actual
 Table 8-24.  Comparison of Modal Emission Rates Estimated Based Upon the Strict Constraints
        Approach for Two Different Constraints Versus Actual Rates:  NOx Emissions (mg/sec)
             for Engine Displacement > 3.5 Liters and Odometer Reading > 50,000 Miles.
Mode
ER1
ER2
ER3
ER4
ER5
ER6
ER7
ER8
ER9
ER10
ER11
ER12
ER13
ER14
Avg. Error
Actual
8.2
9.36
8.1
32.86
57.24
82.87
109.92
155.13
173.28
229.28
362.89
490.97
485
543.47

CONSTRAINT ALLDATA
19.68
13.18
8.46
41.91
47.23
78.71
86.39
137.75
177.1
177.1
177.1
177.1
214.1
2172.47

Error3
-1.400
-0.408
-0.044
-0.275
0.175
0.050
0.214
0.112
-0.022
0.228
0.512
0.639
0.559
-2.997
0.545
CONSTRAINT NCHRP
19.68
13.18
8.46
41.91
47.23
78.71
86.39
137.75
177.1
177.1
177.1
177.1
214.1
2172.47

Error3
-1.40
-0.41
-0.04
-0.28
0.17
0.05
0.21
0.11
-0.02
0.23
0.51
0.64
0.56
-3.00
0.55
'Error: (Predicted-Actual)/Actual
                                         203
-------
-. 14

I 12

I  1°
|   8
HI
s   6
o
•o   4
              5   2
              £
              *   0
                                y = 0.9939X + 0.0154
                                    R2 = 0.9881
                                   4       6       8      10
                                 Observed CO2 Emissions (g/sec)
                                                  12
14
Figure 8-9.  Predicted versus Observed CC>2 Modal Emission Rates for 14 VSP Modes Estimated
 From NCHRP Data Using Strict Constraints Estimated From the Modeling Database: Engine
              Displacement < 3.5 liter and Odometer Reading < 50,000 Miles.
              -. 14
              o
              0)
                 10-
              HI
              3   6
              o
              •o   4
              1
              Q.
    2-

    0
                                  y = 1.062X-0.1424
                                     R2 = 0.9954
                                   4       6       8      10
                                 Observed CO2 Emissions (g/sec)
                                                  12
14
    Figure 8-10. Predicted versus Observed CO2 Modal Emission Rates for 14 VSP Modes
 Estimated From NCHRP Data Using Strict Constraints Estimated From the NCHRP Database:
           Engine Displacement < 3.5 liter and Odometer Reading < 50,000 Miles.
                                         204
-------
              -. 14
              u
              0)
                10-
              HI

              8  6
              •o  4
              1
              Q.
 2-

 0
               y = 0.8613x + 0.5484
                   R2 = 0.9629
                                  4       6      8      10
                                Observed CO2 Emissions (g/sec)
                                               12
                                        14
    Figure 8-11.  Predicted versus Observed CC>2 Modal Emission Rates for 14 VSP Modes
Estimated From NCHRP Data Using Strict Constraints Estimated From the Modeling Database:
          Engine Displacement > 3.5 liter and Odometer Reading < 50,000 Miles.
              ~ 14 n
              u
              0)
              -52
              "5)
12-
              i 10
              |  8
              LU
              oi  6 -
              8
              •o  4^
y = 1.0443X-0.0958
   R2 = 0.9892
                                  4       6      8      10
                                Observed CO2 Emissions (g/sec)
                                               12
                                        14
    Figure 8-12.  Predicted versus Observed CO2 Modal Emission Rates for 14 VSP Modes
 Estimated From NCHRP Data Using Strict Constraints Estimated From the NCHRP Database:
          Engine Displacement > 3.5 liter and Odometer Reading < 50,000 Miles.
                                        205
-------
            ~  25 -i
            u
            0)

            -
            "
•»   20
l

            O
            O

            •o
                15
     10
                        y = 1.2017x-0.8651

                           R2 = 0.9648
                              5         10         15         20


                                Observed CO2 Emissions (g/sec)
                                                            25
    Figure 8-13.  Predicted versus Observed CC>2 Modal Emission Rates for 14 VSP Modes

Estimated From NCFtRP Data Using Strict Constraints Estimated From the Modeling Database:

          Engine Displacement < 3.5 liter and Odometer Reading > 50,000 Miles.
            u
            l
            O
            O

            •o
            £
            Q.
     25




     20 -




     15-




     10




      5




      0
                                y = 0.9628X + 0.3257

                                    R2 = 0.9737
0
                              5         10         15         20


                                Observed CO2 Emissions (g/sec)
                                                            25
    Figure 8-14.  Predicted versus Observed CO2 Modal Emission Rates for 14 VSP Modes

 Estimated From NCHRP Data Using Strict Constraints Estimated From the NCHRP Database:

          Engine Displacement < 3.5 liter and Odometer Reading > 50,000 Miles.
                                         206
-------
            ~  25
            o

            I

            S  20 -]
            VI
            c


            a   15 j

            E
            LU
            o
            o

            •o

            "o


            1
            Q.
                10
y = 1.1389X-0.751

   R2 = 0.9776
                              5         10         15         20


                                Observed CO2 Emissions (g/sec)
                                            25
    Figure 8-15.  Predicted versus Observed CC>2 Modal Emission Rates for 14 VSP Modes

Estimated From NCFtRP Data Using Strict Constraints Estimated From the Modeling Database:

          Engine Displacement > 3.5 liter and Odometer Reading > 50,000 Miles.
              ~ 25
              o
              0)
              I/)
               3.5 liter and Odometer Reading > 50,000 Miles.
                                         207
-------
             -80
             o>
             (A
-=- 60
(A
C
O
'w
             LLI

             O
             I
             0)
             •4-i
             o
               20
                                                   y = 0.4202x+5.4632

                                                       R2 = 0.6422
                                20           40            60

                               Observed HC Emissions (mg/sec)
                                                            80
    Figure 8-17.  Predicted versus Observed HC Modal Emission Rates for 14 VSP Modes

 Estimated From NCHRP Data Using Strict Constraints Estimated From the NCHRP Database:
          Engine Displacement < 3.5 liter and Odometer Reading < 50,000 Miles.
              0)
              -
              E
              LU
              O

              •o
              1
              Q.
    120


    100


     80


     60


     40


     20


      0
                                         y = 0.415x + 8.4139

                                             R2 = 0.621
                           20     40      60     80     100

                                 Observed HC Emissions (mg/sec)
                                                   120
140
    Figure 8-18.  Predicted versus Observed HC Modal Emission Rates for 14 VSP Modes

Estimated From NCHRP Data Using Strict Constraints Estimated From the Modeling Database:
          Engine Displacement > 3.5 liter and Odometer Reading < 50,000 Miles.
                                        208
-------
             o
             a
             I
             LU
             O
             •o
                140 n

                120

                100
                            y = 0.4381X + 10.16
                                R2 = 0.6052
20     40      60     80     100
      Observed HC Emissions (mg/sec)
                                                               120
                                                       140
   Figure 8-19. Predicted versus Observed HC Modal Emission Rates for 14 VSP Modes
Estimated From NCHRP Data Using Strict Constraints Estimated From the NCHRP Database:
          Engine Displacement > 3.5 liter and Odometer Reading < 50,000 Miles.

             LU
             O

             •o
120 n

100

 80 -I

 60

 40

 20
                          y = 1.2275X + 2.7305
                               R2 = 0.96
            20       40       60       80      100
                Observed HC Emissions (mg/sec)
                                                                       120
   Figure 8-20. Predicted versus Observed HC Modal Emission Rates for 14 VSP Modes
Estimated From NCHRP Data Using Strict Constraints Estimated From the NCHRP Database:
          Engine Displacement < 3.5 liter and Odometer Reading > 50,000 Miles.
                                        209
-------
                                                        y = 1.2151X-0.0221
                                                            R2 = 0.8317
                    0      50     100     150     200    250     300    350
                                 Observed HC Emissions (mg/sec)

    Figure 8-21.  Predicted versus Observed HC Modal Emission Rates for 14 VSP Modes
Estimated From NCHRP Data Using Strict Constraints Estimated From the Modeling Database:
          Engine Displacement > 3.5 liter and Odometer Reading > 50,000 Miles.
                                                     y= 1.2151X- 0.0221
                    0      50     100     150     200    250    300     350
                                 Observed HC Emissions (mg/sec)

    Figure 8-22.  Predicted versus Observed HC Modal Emission Rates for 14 VSP Modes
 Estimated From NCHRP Data Using Strict Constraints Estimated From the NCHRP Database:
          Engine Displacement > 3.5 liter and Odometer Reading > 50,000 Miles.
                                        210
-------
the method failed in most cases for NOX and CO. A likely reason for the failure to obtain results
in many cases for the 56-bin approach is that the sample sizes for the stratified data sets are
smaller than for the case of the 14-mode approach in the previous section.  An implication is that
it may be necessary to have a sufficient large data set in order to estimate modal emission rates
from aggregate data.  It is also apparent that the strict constraint approach produces better results
when the bounds of the constraints are derived from data similar to that being analyzed.

8.4    Characterization of Uncertainty in Predicted Modal Emissions
The objective of this part of work is to characterize the distribution of errors in the predicted
modal emissions in order to identify whether biases in the modal estimates are statistically
significant. Because the results from the 56 bin approach were not satisfying, this work was
based upon the results obtained with the 14 VSP bin approach.

In order to characterize uncertainty in the predictions, the distribution of the error of each modal
prediction, based upon the difference between the actual value for each vehicle minus the
predicted value, was estimated. These distributions are summarized by presenting the mean,
standard deviation, 95 percent confidence interval on the mean, and skewness. The results are
presented for NOX, HC, CO, and  CO2 in Tables 8-25 through 8-28, respectively.  The
predictions are based upon the strict constraint method. The average observed and predicted rates
are given in Tables 8-5 through 8-8, respectively, for these  same pollutants.

Table 8-25 summarizes the analysis of the  distribution of prediction errors among all the vehicles
and cycles in the database for predictions of modal emissions for NOX emissions.  The mean
prediction error is given for each VSP mode along with the standard deviation, lower and upper
limit for the 95 percent confidence interval on the mean, number of data points, and skewness
estimate. The average prediction  error for each mode is slightly different than zero, indicating the
possibility that the modal predictions are biased.  For example, for VSP mode 11, average
prediction error is -0.0008. However, 95 percent confidence interval on the mean includes zero,
which indicates that at a significance  level  of 0.05, the mean prediction error is not statistically
significantly different from zero.  Furthermore, the average prediction error is not statistically
significantly different from zero for all VSP modes for NOX as well as for all other pollutants.
Thus, the results indicate that there are no statistically significant biases in the mean estimates of
the prediction error.

However, the range of the prediction  error is substantial in many cases.  For example, for NOX,
the standard deviation of the prediction error is 5.1 mg/sec for Mode  1,  compared to an observed
emission rate of 4.5 mg/sec.  Similarly, the standard deviation is 276  mg/sec versus an average
observed emission rate of 202 mg/sec for Mode 14. For NOX, HC, and CO, the standard
deviation of the prediction error is comparable to the average emission rate for each mode. In
contrast, the standard deviation of the prediction error for CO2 is approximately one third of the
mean observed emission rate for  CO2. When the standard deviation of the prediction error is
large relative to the mean emission rate, the distribution of the prediction error tends to be
positively skewed. For example, the  range of skewness of the prediction errors among the 14
VSP modes is 2.7 to 4.4 for NOX, 2.0 to 5.2 for HC, and 1.0 to 4.3 for CO.  In contrast, the
distributions of the prediction errors for CO2 tend to have only slight skewness, ranging from a
                                           211
-------
Table 8-25. Summary of Analysis of Uncertainty in the Prediction Error for the NOx Modal
      Emission Rates (mg/sec) Estimated from Aggregate Data For the 14 Mode VSP-Based
                                       Approach.
VSP bin
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Mean
0.0005
-0.0017
0.0043
0.0027
0.0013
0.0019
-0.0046
-0.0017
-0.0012
-0.0018
-0.0008
0.0038
-0.0054
-0.0016
Std Dev
5.09
5.71
4.73
18.64
28.68
37.30
48.75
65.79
79.83
104.07
165.71
220.48
215.91
276.33
N
90
90
90
90
90
90
90
90
90
90
77
45
41
37
Lower
Limit
(95%)
-1.05
-1.18
-0.97
-3.85
-5.92
-7.70
-10.08
-13.59
-16.49
-21.50
-37.01
-64.42
-66.09
-89.04
Upper
Limit
(95%)
1.05
1.18
0.98
3.85
5.93
7.71
10.07
13.59
16.49
21.50
37.01
64.42
66.08
89.04
Skewness
2.77
2.99
2.69
3.25
3.56
4.40
4.38
4.03
3.76
2.82
2.66
2.72
2.98
2.74
Table 8-26. Summary of Analysis of Uncertainty in the Prediction Error for the HC Modal
      Emission Rates (mg/sec) Estimated from Aggregate Data For the 14 Mode VSP-Based
                                       Approach.
VSP bin
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Mean
-0.00188
-0.00173
-0.00532
0.00137
-0.00490
0.00329
-0.00247
0.00304
0.00077
0.00335
-0.00135
-0.00331
0.00126
-0.00448
Std
Dev
8.41
5.03
4.07
6.75
10.49
10.98
14.32
20.38
21.18
26.06
41.84
64.50
85.35
123.3
N
90
90
90
90
90
90
90
90
90
90
77
45
41
37
Lower
Limit
(95%)
-1.740
-1.041
-0.847
-1.394
-2.171
-2.265
-2.961
-4.207
-4.375
-5.381
-9.348
-18.84
-26.12
-39.73
Upper
Limit
(95%)
1.736
1.038
0.837
1.396
2.162
2.271
2.956
4.213
4.376
5.388
9.345
18.84
26.12
39.72
Skewness
4.45
4.38
4.54
4.23
3.48
5.15
4.90
4.10
3.67
3.62
3.00
2.38
2.03
2.49
                                      212
-------
   Table 8-27. Summary of Analysis of Uncertainty in the Prediction Error for the CO Modal
         Emission Rates (mg/sec) Estimated from Aggregate Data For the 14 Mode VSP-Based
                                           Approach.
VSP
bin
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Mean
0.0028
-0.0055
0.0024
0.0021
0.0025
0.0044
-0.0005
0.0042
0.0008
0.0031
0.0036
0.0021
-0.0001
-0.0044
Std Dev
233
241
186
428
686
529
747
1250
1472
1818
3324
190
8622
12297
N
90
90
90
90
90
90
90
90
90
90
78
45
41
37
Lower
Limit
(95%)
-48.04
-49.88
-38.49
-88.51
-141.8
-109.3
-154.3
-258.2
-304.1
-375.5
-737.6
-3859
-2639
-3962
Upper
Limit
(95%)
48.04
49.87
38.50
88.52
141.8
109.3
154.3
258.2
304.1
375.5
737.6
3859
2639
3962
Skewness
2.3
2.5
3.4
2.1
4.0
3.4
4.2
3.7
4.3
4.1
2.8
1.6
1.3
1.0
   Table 8-28.  Summary of Analysis of Uncertainty in the Prediction Error for the CO2 Modal
          Emission Rates (g/sec) Estimated from Aggregate Data For the 14 Mode VSP-Based
                                           Approach.
VSP bin
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Mean
0.00336
0.00340
-0.00466
-0.00046
0.00007
-0.00262
0.00366
-0.00207
0.00160
-0.00313
0.00202
-0.00189
-0.00017
0.00237
Std
Dev
0.34
0.45
0.39
0.80
0.89
1.02
1.20
1.39
1.65
1.94
2.49
2.67
2.98
3.25
N
90
90
90
90
90
90
90
90
90
90
77
45
41
37
Lower
Limit
(95%)
-0.068
-0.089
-0.086
-0.165
-0.184
-0.213
-0.245
-0.289
-0.340
-0.405
-0.553
-0.782
-0.911
-1.044
Upper
Limit
(95%)
0.075
0.096
0.076
0.164
0.184
0.207
0.253
0.285
0.343
0.398
0.557
0.779
0.911
1.049
Skewness
0.37
0.53
0.37
0.49
0.28
0.17
0.24
0.15
0.10
0.04
-0.11
0.45
0.56
0.46
magnitude of 0.04 to 0.56 among the 14 modes.  These results illustrate that the predictions for
CC>2 are generally substantially better than those for the other three pollutants.
                                          213
-------
The range of uncertainty in the mean prediction error is typically a factor of approximately five
less than the standard deviation of the prediction error, because the 95 percent confidence
interval of the uncertainty in the mean is estimated based upon a factor of 1.96 multiplied by the
standard error of the mean, which in turn is estimated based upon the standard deviation of the
data divided by the square root of sample size. For a sample size of 90, which is typical of many
of the estimates, this amounts to a factor of 0.207 multiplier of the standard deviation to arrive at
the upper and lower ranges of the 95 percent confidence interval.  Thus, the range of uncertainty
in the mean error is comparable in many cases to a range of approximately plus or minus 25 to
50 percent of the mean observed emission rate for NOX, HC, and CO, and approximately plus or
minus 7 percent of the mean observed emission rate for CC>2. These ranges of uncertainty are
larger than the ranges of uncertainty estimated based upon the modeling database in Chapter 7.
Thus, it would be the case that incorporation of emissions estimates obtained from aggregate
data would entail additional uncertainty than estimates obtained from second-by-second data.

8.5     Summary and Conclusions
The key findings from this analysis include:

   •   The strict constraint  method gave the best results.
   •   The least squares optimization method with strict constraints worked for all of the cases
       for the four driving cycle approach (idle, deceleration, acceleration,  and cruise) and for
       the 14 mode VSP-based approach.
   •   The method worked  for the VSP 56 mode approach for CC>2 for all four vehicle strata, but
       success was more limited with the other three pollutants.
       The failures to obtain solutions or to obtain sufficiently accurate solutions for HC, CO,
       and NOX with the 56-bin approach may be attributable to small  sample sizes.
   •   The analysis of uncertainty in  modal predictions for the 14 Mode VSP-based approach
       clearly illustrates that the quality of the predictions are substantially better for CO2 than
       for the other pollutants.
       The standard deviation of prediction errors for a given mode for NOX, HC, and CO based
       upon the 14-mode VSP approach is typically of the same order  of magnitude as the
       observed mean emission rate, implying that the distribution of prediction errors are
       positively skewed.
       The standard deviation of prediction errors for a given mode for CO2 based upon the 14
       mode VSP approach are approximately one third of the observed mean emission rate,
       implying that the distribution of prediction errors are relatively  symmetric.
       The range of uncertainty in modal estimates obtained from aggregate bag data are
       substantially larger than those  obtained from second-by-second data

The key recommendations from this work are that the constrained least squares optimization
method can be effective at estimating  modal emission rates from aggregate  data as long as there
is a sufficiently large  sample size of data.  The method worked well for the  14-mode VSP case
compared to the 4-mode NCSU case.  Thus, the method appears capable of handling a relatively
large number of modes for a given data set. The predictions are generally much better for CO2
than for the other pollutants. Thus,  this technique works well for CO2 even for cases in which
solutions could not be obtained for other pollutants.  For future work, it may be worth exploring
other types of constraints than those addressed in this project. For example, the "strict
                                          214
-------
constraints" employed in this work allowed for considerable variability in the ratio of the
emission rate for a particular mode with respect to another mode.  An even stricter constraint
would be to require that these ratios be defined for much narrower ranges or that some or all
combinations of ratios be point estimates.  Of course, the more that constraints are imposed upon
the solution, the more critically dependent the solution becomes upon the accuracy of the
constraints themselves. If modal emission estimates are used in a modeling framework such as
moves, the uncertainty in those estimates must be incorporated as well, since the range of
uncertainty in modal emissions rates estimated from aggregate data will typically be much larger
than that when estimated from second-by-second data.
                                          215
-------
-------
9   VALIDATION OF THE CONCEPTUAL MODEL

This report presents three validation studies in which a VSP-based binning approach was used to
estimate hot stabilized tailpipe emissions of CC>2, CO, HC, and NOX. The VSP-based approach is
based upon 1 second data in mass per time emission factor units.

The first case study includes the data utilized for model development and is only a consistency
check in response to comments received by EPA from the FACA committee. The second
validation case study is based upon comparisons of the model with EPA dynamometer, EPA on-
board, and NCHRP dynamometer data that were withheld from the modeling dataset.  The third
validation case study is based upon an independent dataset from the California Air Resources
Board.

9.1    Validation Case Study 1
In this study, internal consistency of the modeling approach was evaluated by: (1) estimating
average modal emission rates for individual driving cycles using data only from the vehicles that
were tested on those cycles based upon data in the modeling database; and (2) making
predictions of average cycle emissions based upon the estimated modal emission rates. The
purpose of this comparison was to demonstrate that the modal  emissions approach is internally
consistent in disaggregating and re-aggregating the emission estimates for a driving cycle.  For
this purpose, three driving cycles and on-board data were selected for analysis. The three cycles
were: ART-EF; FTP; and US06.  These cycles were selected because there were ten or more
vehicles tested on these cycles in the modeling database and these three cycles different ranges
of speeds, VSP, and emissions.

In Table 9-1, number of vehicles, number of trips and number  of seconds of data associated with
each of the selected driving cycles are reported. Validation Dataset 1 includes more than 100
vehicles and 169,112 seconds of data. Key characteristics of the cycles utilized for Validation
Dataset 1 are given in Table 9-2, including average speed, maximum speed, minimum speed,
maximum acceleration, average VSP, and Maximum VSP. For the on-board data, for which
there was not a standard cycle, these statistics were calculated  based upon all of the available
data for all vehicles and trips.  The average speeds for the cycles vary between 12 mph and 47
mph, with the lowest average speed associated with the ART-EF cycle and the highest average
speed associated with the US06 cycle. The average maximum  acceleration among all the cycles
is approximately 6 mph/sec. Except for the FTP, all of the cycles have a maximum acceleration
greater than 6 mph/sec.  Two  cycles, ART-EF and FTP, have an average VSP less than 5
Kw/ton, and two cycles, ART-EF and FTP, have maximum VSP less than 50 Kw/ton.

The predicted vehicle average total emissions and the observed vehicle average total emissions
for the three driving cycles and for the on-board measurements are shown graphically in Figure
9-1.  The 95 percent confidence intervals for the means are also shown. Comparisons between
predicted and observed average total vehicle emissions are given in  Tables 9-3 through 9-6 for
CO2, CO, HC, and NOX, respectively. These tables present average observed values for each
cycle with 95 percent confidence intervals, average predicted values for each cycle with 95
percent confidence intervals.
                                          217
-------
                      Table 9-1. Summary of Validation Dataset I
Vehicle Characteristics

Engine Size < 3 5 liter
OHnmptpr < 50 000


Engine Size > 3 5 liter
OHnmptpr < SO 000


Engine Size < 3 5 liter
OHnmptpr > 50 000


Engine Size > 3 5 liter
OHnmptpr > 50 000

Cycle
ART-EF
FTP
US06
On-Board
ART-EF
FTP
US06
On-Board
ART-EF
FTP
US06
On-Board
ART-EF
FTP
US06
On-Board
Number of vehicles
12
24
22
7
0
6
4
6
0
15
11
0
0
4
4
0
Number of seconds
6024
32952
13251
36096
0
8238
2436
35603
0
20595
6010
0
0
5492
2425
0
Table 9-2. Key Characteristics of the Activity Pattern of the ART-EF, FTP75 and US06 Cycles
                 and of the On-Board Measurements Used in Validation Dataset I.

Cycle
Name
Art-EF
FTP75
US06
On-Board

Time
(s)
504
1875
622
1525
Average
Speed
(mph)
12
21
47
33
Max
Speed
(mph)
40
57
81
83
Min
Speed
(mph)
0
0
0
0
Max
Acceleration
(mph/sec)
5.8
3.3
7.4
7.4
Mean
VSP
(Kw/ton)
0.9
2.2
8.3
4.6
Max
VSP
(Kw/ton)
22.8
25.1
54.5
78.3
                                        218
-------
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                                                 On-Board
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                                                                            Art-EF
                                                                         [] Observed

                                                                         • Predicted
                                                                                         FTP
                                                                                                      US06
f
                                                                                                                 On-Board
                                                                           Art-EF
                                                                                         FTP
                                                                                                      US06
                                                                                                                 On-Board
Figure 9-1. Comparison of Observed and Predicted Average Total Emissions of CC>2, CO, HC, and NOX for Three Driving Cycles
                                       and for On-Board Data for Validation Dataset I.
                                                            219
-------
-------
Table 9-3. Summary of Comparisons of Predicted versus Observed Vehicle Average Total
                         Emissions for Validation Dataset I for CC>2


Cycles
ART-EF
FTP75
US06
On-Board
Mean
Obs.
(2)
926
2740
2790
16800

95%
CI
800 - 1000
2500 - 2900
2600 - 3000
11200-22000
Mean
Pred.
(2)
926
2740
2790
16800

95%
CI
900 - 950
2600 - 2900
2600 - 2900
12000-21000

Diff. a
(%)
0
0
0
0

CIs
Overlap
Y
Y
Y
Y
     a Diff: ((Predicted-Observed)/Observed)*100
Table 9-4. Summary of Comparisons of Predicted versus Observed Vehicle Average Total
                          Emissions for Validation Dataset I for CO


Cycles
ART-EF
FTP75
US06
On-Board
Mean
Obs.
(2)
0.49
11
78
120

95%
CI
0.30-0.80
0.29-21
60-96
60 - 170
Mean
Pred.
(2)
0.49
11
78
120

95%
CI
0.47-0.51
9.4-12
72-84
77 - 150

Diff. a
(%)
0
0
0
0

CIs
Overlap
Y
Y
Y
Y
     a Diff: ((Predicted-Observed)/Observed)*100
Table 9-5. Summary of Comparisons of Predicted versus Observed Vehicle Average Total
                          Emissions for Validation Dataset I for HC


Cycles
ART-EF
FTP75
US06
On-Board
Mean
Obs.
(2)
0.033
0.4
0.83
11

95%
CI
0.006 - 0.060
0.13 -0.67
0.55-1.1
6.4 - 15
Mean
Pred.
(2)
0.033
0.4
0.83
11

95%
CI
0.032-0.035
0.35-0.44
0.66 - 1.0
8.0-14

Diff. a
(%)
0
0
0
0

CIs
Overlap
Y
Y
Y
Y
     a Diff: ((Predicted-Observed)/Observed)*100
Table 9-6. Summary of Comparisons of Predicted versus Observed Vehicle Average Total
                         Emissions for Validation Dataset I for NOx


Cycles
ART-EF
FTP75
US06
On-Board
Mean
Obs.
(2)
0.24
1.4
2.6
21

95%
CI
0.11-0.36
0.90-2.0
1.7-3.6
11-31
Mean
Pred.
(2)
0.24
1.4
2.6
21

95%
CI
0.22-0.25
1.1-1.7
2.2-3.0
15-27

Diff. a
(%)
0
0
0
0

CIs
Overlap
Y
Y
Y
Y
     a Diff: ((Predicted-Observed)/Observed)*100
                                      221
-------
The percentage difference in predicted and observed values is presented in Tables 9-3 through 9-
6. An indication is given as to whether the confidence intervals for the predicted and observed
means overlap.

The average total emissions predictions from the model are exactly the same as the observed
values for all the cycles and for the on-board data: in all cases the percentage difference between
the mean prediction and the mean observation is zero percent, and the confidence intervals for
the predicted and observed means overlap. The three cycles and the on-board data differ
substantially in terms of total average emissions.  For example, the observed values for CO range
between 0.5 grams to 115 grams when comparing the ART-EF cycle and the on-board data,
respectively.  Thus, the performance of the modeling approach is robust over a wide range of
different emissions estimates.

The main findings from Validation Case Study 1 are:

   Percent difference in the predicted versus observed values are all zero
   There was excellent agreement between the predicted and observed CC>2, CO, HC, and NOX
   emissions over a wide range of emissions
-  The methodology for disaggregating driving cycle or trip emissions into driving modes, and
   re-aggregating the average modal emissions to make estimates of driving cycle or trip
   emissions, is demonstrated to be internally consistent, as is expected.

9.2    Validation Case Study 2
For Validation Case Study 2, model predictions were prepared based upon average modal
emission rates calibrated to the modeling data set for all vehicles, all driving cycles,  and  all on-
board data. Model predictions were made for an independent data set of emissions for vehicles
that were not included in the modeling data set.  The independent data set, referred to as
Validation Data Set 2, is summarized in Table 9-7.  This data set is comprised of 81,808  seconds
of data from EPA dynamometer, EPA on-board measurement, and NCHRP dynamometer data.
The number of vehicles, number of trips and number of seconds of data associated with each
driving cycle are reported in the table. Validation Data Set 2 includes 78 vehicles, 83 trips, and
16 different cycles, including the on-board data as a lumped category. It should be noted that the
number of vehicles tested on some cycles is very small. Specifically, except for the FTP75 and
US06 cycles, three or fewer vehicles were tested. For validation purposes, comparisons  were
made only for FTP75, US06 cycles, and On-Board data for which many vehicles and/or  many
seconds of data were available. Key characteristics of the cycles utilized for the Validation
Dataset II are given in Table 9-2. Key characteristics of vehicles in this dataset are shown in
Appendix A.

The predicted and observed average total emissions for specific cycles, and the  95 percent
confidence intervals on the averages, are shown in Figure 9-2 for total emissions of CO2, CO,
HC, and NOX.  The comparisons are summarized in Tables 9-8 through 9-11 for CO2, CO, HC,
and NOX emissions, respectively.
                                          222
-------
Table 9-7. Summary of Driving Cycles, Number of Vehicles, Number of Trips, and Samples
                              Size for Validation Dataset II
Data Source
EPA Dynamometer
EPA Dynamometer
EPA Dynamometer
EPA Dynamometer
EPA Dynamometer
EPA Dynamometer
EPA Dynamometer
EPA Dynamometer
EPA Dynamometer
EPA Dynamometer
EPA Dynamometer
EPA Dynamometer
EPA Dynamometer
NCHRP
NCHRP
On-Board Data
Cycle
ART-AB
ART-CD
ART-EF
FWY-AC
FWY-D
FWY-E
FWY-F
FWY-G
FWY-HI
LOCAL
NONFWY
NYCC
Ramp
FTP75
US06
On-Board
NO. of
Vehicles
2
2
O
2
2
2
O
2
3
2
2
O
2
24
21
O
No. of Trips
2
2
3
2
2
2
3
2
3
2
2
3
2
24
21
18
Total Seconds
1471
1255
1507
1029
809
909
1321
111
1825
1047
2693
1795
529
32950
12648
19243
                                     223
-------

j2 10000 -
o

£ 1 000
HI
tM
o
O 100
Ol
O)
ro

> 10-
1 -
D Observed
D Predicted























































































2, CO, HC, and NOX for the FTP75 and US06

                         Driving Cycles and for On-Board Measurements for Validation Dataset II.
                                                         224
-------
 Table 9-8. Summary of Comparisons of Predicted versus Observed Vehicle Average Total
                          Emissions for Validation Dataset II for CC>2


Cycles
FTP75
US06
On-Board
Mean
Obs.
(2)
2563
2596
17775

95%
CI
2480 - 2645
2505 - 2686
14367-21184
Mean
Pred.
(2)
3195
2491
19612

95%
CI
3164-3227
2440 - 2542
16083 -23142

Diff. a
(%)
25
-4
10

CIs
Overlap
N
Y
Y
      a Diff: ((Predicted-Observed)/Observed)*100
 Table 9-9. Summary of Comparisons of Predicted versus Observed Vehicle Average Total
                          Emissions for Validation Dataset II for CO


Cycles
FTP75
US06
On-Board
Mean
Obs.
(2)
10.6
75.1
328.4

95%
CI
8.3-13.0
67.7 - 82.5
161.0-495.8
Mean
Pred.
(2)
17.4
34.9
199.8

95%
CI
16.7 - 18.0
32.2-37.5
162.7-236.9

Diff. a
(%)
64
-54
-39

CIs
Overlap
N
N
Y
       Diff: ((Predicted-Observed)/Observed)*100
Table 9-10.  Summary of Comparisons of Predicted versus Observed Vehicle Average Total
                          Emissions for Validation Dataset II for HC


Cycles
FTP75
US06
On-Board
Mean
Obs.
(2)
0.69
0.93
13.17

95%
CI
0.49-0.89
0.80 - 1.06
7.49-18.85
Mean
Pred.
(2)
1.26
1.08
9.40

95%
CI
1.20-1.32
1.02-1.13
7.02-11.78

Diff. a
(%)
83
16
-29

CIs
Overlap
N
Y
Y
      a Diff: ((Predicted-Observed)/Observed)*100
Table 9-11.  Summary of Comparisons of Predicted versus Observed Vehicle Average Total
                         Emissions for Validation Dataset II for NOx


Cycles
FTP75
US06
On-Board
Mean
Obs.
(2)
2.06
2.53
16.60

95%
CI
1.61-2.51
2.09-2.97
11.57-21.62
Mean
Pred.
(2)
2.33
2.93
21.05

95%
CI
2.24 - 2.42
2.78-3.07
16.46-25.65

Diff. a
(%)
13
16
27

CIs
Overlap
Y
Y
Y
       Diff: ((Predicted-Observed)/Observed)*100
                                       225
-------
As observed in Figure 9-2, the predicted average total CC>2 emissions are close to the observed
average total CC>2 emissions, especially for the US06 cycle and the on-board data. In these latter
two cases, the  confidence intervals of the predicted and observed means overlap. The predicted
average CC>2 emissions are within 25 percent of the observed average values for the FTP75
cycle.

For CO, the qualitative trends of the model predictions are similar to that of the observed data, as
illustrated in Figure 9-2. For example, the on-board data had the highest observed total
emissions and  also had the highest predicted total emissions. Both the observed and predicted
emissions decreased when comparing the FTP75 driving cycle to the US06 driving cycle.
Except for the  FTP75 cycle, the model underpredicted the observed emissions. The
underprediction is suggestive of a different vehicle mix in Validation Data Set 2 versus the
modeling data  set. Validation Data Set 2 contains a larger proportion of smaller engine sizes and
higher mileage than does the modeling data set. Nonetheless, the model predictions were not
statistically significantly different from the observed values for the on-board data, and  were
comparable in  magnitude to the data from the two driving cycles.

Qualitatively, the model predictions perform well compared to the observations for HC
emissions.  Similar to the situation for CO emissions, the model appropriately predicts the
highest emissions for the on-board data, which have the highest observed emissions. The US06
and FTP75 cycles are predicted to have moderate emissions, comparable in magnitude to the
observed values. Furthermore, the predictions of the model were not statistically significantly
different from  the observed emissions for the US06 driving cycle and for the on-board data.

For NOX, the model performed well for all three of the comparisons. In particular, the
confidence intervals of the model predictions overlapped with the confidence interval of the
observed emissions. Thus, the model predictions were not statistically  significantly  different
than the observed values. Therefore, the average error in the model prediction ranging from 13
to 27 percent among the three comparisons are not considered significant and are within the
random error of the data.

The overall findings of this case study are:

   There is good concordance in the model predictions versus the observations in terms of the
   ordinal ranking of which cycles have the highest and lowest emissions.
   The predictions for CO, HC, and NOX tend to be better when the prediction for CO2 is also
   reasonably close. For example, the predictions for all three pollutants were very good for the
   on-board data, and the predictions of two of the three pollutants were very good for the US06
   cycle. The CO2 predictions were generally very good for these three  data sets. In contrast,
   somewhat  surprisingly, the predictions were generally not as good as expected for the FTP75
   cycle, for which the CO2 average prediction was also different from the average  observed
   value by 25 percent.
-  A comparison of CO2 predicted and observed values may be a good diagnostic tool for
   identifying systematic differences between data sets. It appears that the Validation Data Set
   2 is more heavily weighted toward vehicles with smaller engines compared to the calibration
   data set.
                                          226
-------
   The systematic differences observed here for CC>2 suggest that additional refinement may be
   warranted for the engine displacement criteria when binning data. For example, rather than
   grouping all engine displacements of less than 3.5 liters into a bin for a given VSP, it may be
   appropriate to further subdivide this bin into two or more subcategories.

9.3    Validation Case Study 3
Validation Dataset III includes California Air Resources Board (CARB) data provided by the
EPA. This dataset includes data from the following cycles: UCC17; UCC20; UCC25; UCC30;
UCC35; UCC40; UCC45; OLD UCC50; UCC50; Modified Unified Cycle (MUC); and UCC60.
The data provided by EPA did not include second-by-second speed profiles for each test.
However, nominal speed profiles for these cycles were provided. The nominal speed profiles
were used to determine the fraction of time that the vehicle was in each VSP mode. Table 9-12
summarizes Validation Dataset III. A total of 17 vehicles were tested, over 164 tests, on 11
different cycles. However, the number of vehicles tested on some cycles was small. For example,
four or fewer vehicles were tested on the MUC, UCC50, and UCC60 cycles. For comparison
purposes, only cycles for which 10 or more vehicles were tested were utilized in this study.

Key characteristics of the cycles utilized for Validation Dataset III are given in Table 9-13.
Average speeds for the cycles ranges between 13 mph and 53 mph. The lowest average speed
occurred for the UCC17 cycle and the highest average speed occurred for the UCC60 cycle.  The
lowest maximum speed of 37 mph occurred for the UCC17 cycle and the highest maximum
speed of 81 mph occurred for the UCC60 cycle.  Except for the Old UCC50 and UCC50 cycles,
all cycles have a maximum acceleration of less than 7 mph/sec. Seven of the 11 cycles have  an
average VSP of less than 5 Kw/ton.  The UCC35, Old UCC50, and UCC60 cycles have a
maximum VSP greater than 50 Kw/ton.

Since engine displacement data were not available for Validation Data Set III, it was assumed
that all vehicles in this dataset have engine displacement less than 3.5 liters based upon
discussion with EPA.

The average predicted and observed emissions, along with 95 percent confidence intervals are
shown in Figure 9-3 for all four pollutants. The comparisons are detailed in Tables 9-14 through
9-17 for CO2, CO, HC, and NOX emissions, respectively. The predictions were made using the
average modal emission rates estimated from the modeling database.

For CO2, the average model predictions are close to the average observed values as indicated by
the fact that for six of the eight cycles for which comparisons were done, the means agreed to
within 10 percent. Furthermore, for seven of the cycles, the confidence intervals of the
predictions overlapped with the confidence intervals of the observations, and for all cycles the
mean predictions were within 15 percent.  These findings imply strong agreement between the
model predictions and the observations. The model average predictions vary among the driving
cycles by a factor of approximately 8 for the largest to the smallest prediction compared to a
factor of approximately 10 for the average observations. The model appears to slightly
overpredict for the lower emissions cycles.
                                         227
-------
  Table 9-12. Summary of Driving Cycles, Number of Vehicles, Number of Tests, and Sample
                                 Size for Validation Dataset III
Data Source
ARE data
ARE data
ARE data
ARE data
ARE data
ARE data
ARE data
ARE data
ARE data
ARE data
ARE data
Cycle
UCC17
UCC20
UCC25
UCC30
UCC35
UCC40
UCC45
OLD UCC50
MUC*
UCC50
UCC60
No. of
Vehicles
17
17
17
17
17
17
17
15
4
2
2
No. of Tests
17
17
17
17
17
17
17
15
20
4
4
Total Seconds
7174
15048
15372
17712
24318
24012
23472
34663
46760
8768
11240
* MUC: Modified Unified Cycle
  Table 9-13. Key Characteristics of the Activity Patterns of the Driving Cycles in Validation
                                         Dataset III.
Cycle ID
UCC17
UCC20
UCC25
UCC30
UCC35
UCC40
UCC45
OLD
UCC50
MUC*
UCC50
UCC60
Time
(s)
422
836
854
984
1351
1334
1304
2039
2338
2192
2810
Average
Speed
(mph)
13
18
23
27
32
36
45
48
17
43
53
Max
Speed
(mph)
37
44
50
59
69
72
71
76
67
72
81
Min
Speed
(mph)
0
0
0
0
0
0
0
0
0
0
0
Max
Acceleration
(mph/sec)
4.6
5.7
5.9
5.5
5.6
5.5
5.7
8.1
6.9
7.5
6.4
Mean
VSP
(Kw/ton)
1.4
1.9
2.5
3.1
4.1
5.1
6.5
7.8
2.1
6.3
9.2
Max
VSP
(Kw/ton)
22.3
25.6
23.1
35.8
68.2
48.9
43.3
86.5
35.1
28.1
57.2
* MUC: Modified Unified Cycle
                                         228
-------
   1 4—1	!	"—I—1	'	L-1—'	!	"—i—1	'	L-1—'	'	>—i—'	!	>—i—]	^  , '	^"—I      0.1 -
      UCC17    UCC20    UCC28   UCC30   UCC35    UCC40    UCC45   Old UCC50          UCC17    UCC20    UCC28    UCC30     UCC35    UCC40    UCC45   Old UCC50
      UCC17    UCC20    UCC28    UCC30    UCC35    UCC40    UCC45   Old UCC50
                                                                           UCC17    UCC20    UCC28    UCC30     UCC35    UCC40    UCC45   Old UCC50
Figure 9-3.  Comparison of Observed and Predicted Average Total Emissions of CO2, CO, HC, and NOX for Eight UCC Driving
                                                  Cycles for Validation Dataset III.
                                                                  229
-------
Table 9-14. Summary of Comparisons of Predicted versus Observed Vehicle Average Total
                         Emissions for Validation Dataset III for CC>2
Cycles
UCC17
UCC20
UCC25
UCC30
UCC35
UCC40
UCC45
OLD
UCC50
Mean
Obs.
(2)
800
1787
2050
2407
3690
4078
4586
7856
95%
CI
722 - 879
1632 - 1941
1888-2211
2220 - 2594
3416-3963
3799-4356
4257-4916
7235 - 8477
Mean
Pred.
(2)
915
1975
2196
2617
3849
4084
4439
7252
95%
CI
902 - 929
1941-2008
2155-2237
2568 - 2666
3771-3926
3998-4171
4338-4540
7070 - 7435
Diff. a
(%)
14
11
7
9
4
0
-3
-8
CIs
Overlap
N
Y
Y
Y
Y
Y
Y
Y
      a Diff: ((Predicted-Observed)/Observed)*100
Table 9-15. Summary of Comparisons of Predicted versus Observed Vehicle Average Total
                         Emissions for Validation Dataset III for CO
Cycles
UCC17
UCC20
UCC25
UCC30
UCC35
UCC40
UCC45
OLD
UCC50
Mean
Obs.
(2)
2.9
8.6
8.3
12.8
24.3
31.2
29.5
47.7
95%
CI
0.8-4.9
3.9-13.4
4.4-12.2
7.6-18.0
11.9-36.8
18.1-44.4
16.9-42.1
22.4-73.1
Mean
Pred.
(2)
4.3
9.8
11.6
15.5
25.1
29.0
34.4
54.8
95%
CI
3.9-4.7
9.0 - 10.6
10.7-12.6
14.4-16.6
23.6-26.5
27.4-30.5
32.9-35.9
52.2-57.4
Diff. a
(%)
48
14
40
21
o
J
-7
17
15
CIs
Overlap
Y
Y
Y
Y
Y
Y
Y
Y
      a Diff: ((Predicted-Observed)/Observed)*100
                                       230
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Table 9-16. Summary of Comparisons of Predicted versus Observed Vehicle Average Total
                         Emissions for Validation Dataset III for HC
Cycles
UCC17
UCC20
UCC25
UCC30
UCC35
UCC40
UCC45
OLD
UCC50
Mean
Obs.
(2)
0.08
0.20
0.24
0.34
0.56
0.67
0.71
1.19
95%
CI
0.04-0.12
0.12-0.29
0.16-0.31
0.24 - 0.44
0.36-0.76
0.45-0.89
0.49-0.93
0.74 - 1.63
Mean
Pred.
(2)
0.29
0.62
0.68
0.81
1.20
1.28
1.40
2.21
95%
CI
0.23-0.36
0.48-0.76
0.53-0.83
0.63-0.99
0.94 - 1.46
1.01-1.56
1.10-1.69
1.71-2.71
Diff. a
(%)
263
210
183
138
114
91
97
86
CIs
Overlap
N
N
N
N
N
N
N
N
      a Diff: ((Predicted-Observed)/Observed)*100
Table 9-17. Summary of Comparisons of Predicted versus Observed Vehicle Average Total
                         Emissions for Validation Dataset III for NOx
Cycles
UCC17
UCC20
UCC25
UCC30
UCC35
UCC40
UCC45
OLD
UCC50
Mean
Obs.
(2)
0.65
1.25
1.57
1.98
3.34
4.67
4.47
9.41
95%
CI
0.29- 1.00
0.54-1.96
0.70-2.44
0.86-3.11
1.22-5.46
1.34-8.00
1.64-7.30
6.7-16
Mean
Pred.
(2)
0.59
1.36
1.62
2.00
3.09
3.46
3.99
6.54
95%
CI
0.53-0.65
1.22-1.50
1.45-1.79
1.79-2.21
2.76-3.42
3.10-3.82
3.56-4.42
5.79-7.29
Diff. a
(%)
-9
9
o
J
1
-7
-26
-11
-30
CIs
Overlap
Y
Y
Y
Y
Y
Y
Y
Y
                     a Diff: ((Predicted-Observed)/Observed)*100
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For CO and NOX, the confidence intervals overlap for all eight of the driving cycles when
comparing predicted and observed averages.  This suggests strong agreement between the model
and the observations for all of the cycles evaluated.  The CO predictions typically are larger than
the observed values and the prediction errors are as large as approximately 40 percent for the
lower emission cycles and not larger than approximately 20 percent for the higher emission
cycles. The observed CO emissions vary by a factor of 16 from the smallest to the largest
values, and the predicted CO emissions vary similarly by a factor of 13. For NOX, the prediction
errors were less than plus or minus 10 percent for five of the eight cycles, and were less than or
equal to plus or minus 30 percent for all cycles. The observed NOX emissions varied by a factor
of 15 from the smallest to the highest values, while the predictions varied similarly by a factor of
11.

For HC, the predictions were typically a factor of two to three larger than the observed values.
However, the qualitative trend of the predictions was similar to the observed values when
comparing cycles in terms of rank ordering with respect to emissions. For example, the model
predicted the lowest emission rate for the UCC17 cycle and the highest emission rate  for the Old
UCC50 cycle, which is consistent with the observations.

There is some uncertainty regarding the regulations to which some of the vehicles in the CARB
data set are subject. It is possible that some of the vehicles may be TLEV, rather than Tier 1,
vehicles,  although specific information  regarding this was not available with the data  set. TLEV
vehicles are subject to a more stringent  HC emission standard but are otherwise the same as Tier
1 vehicles. The comparison suggests that the CARB vehicles have similar CO2, CO, and NOX
emissions but lower HC emissions when compared to the predictions made based upon modal
emissions rates estimated from the modeling data set. An analysis was done for two subsets of
the CARB database: (1) vehicles believed to be subject to Tier 1 standards; and (2) vehicles
believed to be subject to TLEV standards. It turned out that these two subgroups of vehicles did
not have any statistically significant difference in emissions with each other taking into account
all four pollutants and all eight driving cycles. Thus, to the extent that TLEV vehicles may be
present in the CARB database, the specific sample of TLEVs would not appear to have different
average emissions than the specific sample of Tier 1 vehicles. It is possible, therefore, that the
predicted and observed HC emissions may differ for reasons other than emission standards, such
as perhaps because of different fuels. There was also uncertainty as to whether the HC emissions
reported in the CARB database were for total hydrocarbons or for non-methane hydrocarbons
(NMHC). The data were used assuming that they represented total hydrocarbons.  However, if
the HC data were actually for NMHC, then it would be necessary to add the estimated methane
emissions in order to calculate the total  observed hydrocarbons,  in which case the comparison
would improve. Confirmation on this point could not be obtained  during the time period of this
study.

The main findings from Validation Case Study 3 are:

-  There was excellent agreement between the predicted and observed CO2, CO, and NOX
   emissions.
   There appears to be excellent concordance between the predicted and observed HC
   emissions.
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9.4    Preliminary Exploration of Refinements to the Modal Modeling Approach
Validation Case Study II indicated that there was some disagreement between the model
predictions and the observed values particularly for the FTP75 cycle. It was observed that the
validation data set tended to have vehicles with smaller engines than did the modeling dataset.
Therefore, a refinement to the modal modeling approach was explored in which the modeling
database was stratified into more engine displacement categories than was used in the "56-bin"
approach developed in Chapter 3.  In addition, a second type of refinement was explored in
which an additional explanatory variable was sought for purposes of disaggregating each VSP
bin.  Based upon an analysis of the sensitivity of the average emissions in a VSP bin to
acceleration and to average speed,  as illustrated in Appendix A in Figure A-7, either of these two
variables was identified as potentially useful in further disaggregating the modeling database to
create additional  bins. Speed was selected as the explanatory variable for further consideration
because speed is  directly measured and because speed and acceleration are inversely related to
each other for most of the VSP bins, as illustrated by the scatter plots shown in  Chapter 5 in
Figures 5-10 and 5-11.  Thus, there is little need to include both speed and acceleration as
additional explanatory variables.

In the case of refinement of the modal modeling approach based upon additional engine
displacement categories, three levels of engine displacement were used, rather than two as in the
original VSP-approach. These levels are: engine displacement less than 2.0 liter; engine
displacement greater than 2.0 liters and less than 3.5 liters; and engine displacement greater than
3.5 liter. In this approach, there are totally 84 bins, (2 odometer reading categories, 3 engine
displacement categories, and 14 VSP modes). The average modal emission rates for this "84-
bin" approach are given in Appendix A in Figures A-5 and A-6 for vehicle with odometer
reading less than 50,000 miles and for vehicles with odometer reading greater than 50,000 miles,
respectively. Using these average modal rates, predictions were made and compared to the
observed values for Validation Dataset II.  There was no significant  improvement in the
predictions based upon the disaggregating of engine displacement into three instead of two
categories.

In the case of refinement of the modal modeling approach based upon speed, two levels of speed
were defined for  each VSP mode based upon a selected  cut point of  32 mph.  The average
emission rates for each VSP mode for the low and high speed bins are shown in Appendix A in
Figures A-8 through A-l 1 for vehicles with the following characteristics, respectively: (1)
engine displacement less than 3.5 liters and odometer reading less than 50,000 miles; (2) engine
displacement greater than 3.5 liters and odometer reading less than 50,000 miles; (3) engine
displacement less than 3.5 liters and odometer reading greater than 50,000 miles; and (4) engine
displacement greater than 3.5 liters and odometer reading greater than 50,000 miles. For the
higher speed bins, the average emission rates tend to be  higher in many cases, such as for CC>2
emissions for the lower VSP modes, for CO for most modes, for HC especially for the lowest
VSP modes, and  for NOX for low to moderate VSP modes.  The comparison of the average
modal emission rates for the two speed bins for a given VSP mode suggests that there are
opportunities to refine the estimation of emission rates by considering speed as  an additional
explanatory variable. A trade-off is that the sample size of each bin  becomes smaller, leading to
wider confidence intervals in some cases. When the speed disaggregated VSP modes were used
to make predictions of cycle emissions for Validation Case Study 2,  there was not a significant
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improvement in the prediction of total emissions compared to the predictions from the "56-bin"
approach. Thus, it may be the case that additional levels of detail at the micro scale may not lead
to substantial improvements in predictions at the macro scale.  However, it is likely that
disaggregation of VSP bins by speed will lead to more accurate predictions at the micro- or
mesoscale.

Of the two refinements to the modal modeling approach explored here, the refinement based
upon speed appears to offer promise for improving the accuracy of microscale or mesoscale
predictions, even though it may not help substantially in improving macroscale predictions, at
least for the conditions evaluated in this study.

9.5     Summary and Recommendations
The main findings from all three verification and validation case studies are:

   The modal modeling approach is internally consistent, as demonstrated by Validation Case
   Study I.  Specifically, it is possible to reproduce total trip emissions based upon proper
   estimating and combination of average emissions for individual modes.
   The model generally performs well for the higher emission cycles and for cycles or
   conditions that are represented by a large portion of the data in the modeling data set.
-  The model is highly responsive, predicting a wide range of variability in average emissions.
-  Although the model tends to ove-rpredict for low emissions cycles, such cycles may be less
   important from an inventory perspective than the high emissions cycles for which the model
   performs better.
   The model performance for the low emissions  cycles could be improved by working with
   modeling datasets that have a larger representation of such cycles, or perhaps by refining the
   modal definitions to better represent such cycles.
   A promising approach for refining the modal modeling method is to consider speed as an
   additional explanatory variable.
-  Comparisons of CC>2 emissions appear to be a  good method for determine the comparability
   of two datasets: in the case of the ARB data sets, there was excellent agreement for CC>2 and
   this extended to the other pollutants. For Validation Data Set 2, there were systematic
   differences in CC>2 for one of the  driving cycles for which comparisons were done that
   appeared to extend to at least some of the other pollutants (e.g., CO, HC).

Overall, the results of the case studies illustrate the flexibility and robustness of a modal-based
approach for making  predictions for a wide variety of driving cycles and for on-board data.
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10  RECOMMENDATIONS FOR METHODOLOGY FOR MODAL MODEL
    DEVELOPMENT

This report has explored in detail a number of key issues pertaining to the methodology for
developing a modal emissions model.  The main focus of the case studies have been with respect
to hot stabilized tailpipe emissions from Tier 1 vehicles. However, when taking in the context of
recent previous work by NCSU to develop approaches for estimating cold start emissions for
gasoline vehicles, as well as modal emission rates for heavy duty diesel vehicles, this report
combined with the previous efforts clearly demonstrates the feasibility of a modal modeling
approach.

The key questions that were addressed in this work were the following:

   1.  What dataset should be used for the final version of the conceptual model? (Task la,
       Chapter 2)

   2.  Which binning approach should be used? (Task Ib, Chapter 3)

   3.  How much detail should be included in the binning approach, in terms of how many
       explanatory variables and how many strata for each variable? (Task Ib, Chapter 3)

   4.  What averaging time is preferred as a basis for model development? (Task Ib, Chapter 4)

   5.  What emission factor units should be used? (Task Ib, Chapter 5)

   6.  What weighting approach should be used, when comparing time-weighted, vehicle
       weighted, and trip weighted? (Task Ib, Chapter 6)

   7.  How should variability and uncertainty be characterized? (Task Ic, Chapter 7)

   8.  How should aggregate bag data be analyzed to derive estimates of modal emission rates?
       (Task Id, Chapters)

   9.  What is the potential role and feasibility of incorporating RSD data into the conceptual
       modeling approach? (Task le, Chapter 5)

   10. How should the conceptual model be validated and what are the results of validation
       exercises? (Task 2, Chapter 9)

The answers to these questions are briefly summarized here, and are given in more detail  in the
respective chapters devoted to each topic.

The data set used for the conceptual model was comprised of EPA dynamometer data, EPA on-
board data, and NCHRP dynamometer data.  These data comprised the modeling database. The
modeling database was compared  to several other databases, including an EVI240 database and an
RSD database.
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The binning approach selected was a 14 mode VSP-based approach. However, it was shown that
an approach based upon driving modes of idle, acceleration, cruise, and deceleration produced
comparable predictions for total emissions.  Thus, the 14 mode VSP-based approach is not
unique in its capability to predict emissions, but it is expected to facilitate design of a modeling
system perhaps moreso than the other approach.

There is a trade-off between improving the explanatory power of a model and having a model
that becomes complicated to code or use.  Odometer reading and engine displacement were
identified as key explanatory variables. Engine displacement is highly correlated with vehicle
net weight and with the number of cylinders of the engine. Therefore, it is not necessary to
include net vehicle weight or number of cylinders if engine displacement is selected as an
explanatory variable. Odometer reading is weakly correlated with model year.  This suggests
that there might be a role for model year in future model development.  Because this study
focused upon Tier 1 vehicles, with much of the data spanning only a very limited range of model
years, it is possible that the influence of model year is understated with  respect to this  analysis
and that it may be more important for other types of vehicles. Ambient parameters such as
humidity were accounted for in correcting NOX emissions.  Ambient temperature was not found
to be a significant explanatory variable. On the other hand, as discussed in Chapter 9, there may
be an opportunity  to improve the explanatory power of the 14 mode VSP-based approach by
including either speed or acceleration as a criteria for further disaggregating the bins.

The method for selecting the specific definitions of the 14 VSP bins took into account that each
pollutant has a different sensitivity to VSP.  Thus, a "supervised" technique was used in  which
the contribution of any individual mode to total emissions for a given pollutant was considered
as a key criteria. This approach produced one set of modal definitions that worked well  for all
four pollutants.

An approach based upon "56 bins" for which the 14 VSP modes were stratified into two
odometer reading  categories and two engine displacement categories performed reasonably well
when predictions were compared to observations for independent data sets, as reported in
Chapter 9. The validation case studies thus emphasize that the modal emissions approach is
feasible. A key benefit of the conceptual  modeling approach is that it works for all four
pollutants considered, and it is not necessary to develop a separate approach for each pollutant.

Three averaging times were compared with respect to ability to make predictions  of trip
emissions. No substantial difference was found.  Thus, for simplicity, the one second  averaging
time was recommended for model development and was employed in this work. However,
although the issue of averaging time may not have a significant effect on prediction of average
emissions, there is a significant effect on the prediction of uncertainty in average emissions. As
noted in Chapter 7, the range of uncertainty in the average modal emission rates is a function of
averaging times, and the uncertainty estimates should be adjusted  appropriately when making
predictions of uncertainty.

Three weighting approaches were compared, including time, trip, and vehicle weighted
approaches.  It is clear that the average emission estimates will differ depending on which
approach is used, because each approach gives a different amount of weight to different
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subgroups of the data. For example, the time weighted approach gives equal weight to each data
point. The trip weighted approach gives each trip (or driving cycle test) equal weight, even
though trip lengths may differ and even though some vehicles may be represented by many trips
and others may be represented by only one. The vehicle weighted approach gives each vehicle
equal weight regardless of the total testing time or number of trips (or tests).  When comparing
time, trip, and vehicle weighted approaches, the standard deviation of the variability in emissions
decreases in the same order because each successive approach involves more averaging.
However, the averaging time is not standardized for the trip and vehicle weighted approaches.
Because averaging time is important to accurate estimation of uncertainty, preference was given
in this work to the time weighted approach.

With regard to emission factor units, there was no clear overall advantage for emission ratios
versus mass per time emission factors for CO, HC, and NOX. Although it is the case that there is
less variability in the averages among many of the modes for CO and HC for emission ratios
when compared to mass per time emission rates, for NOX there is substantial variability across all
modes regardless of the units used.  For software design purposes, it is simpler to use the same
approach for all pollutants. Thus, an emission ratio approach would require a similar number of
modes as the mass per time approach. In this regard, there was no clear advantage.
Additionally, it is necessary to estimate mass per time emissions of CO2, or to estimate mass per
time fuel consumption, in order to convert emission ratios for CO, HC, and NOX to mass
emission rates as would be required for an emission inventory model. Although an emission
ratio approach offers some benefits of simplicity when applied to an areawide macroscale
emission inventory based upon information such as fuel sales, an emission ratio approach
nonetheless would require modal estimates of CO2 emissions or fuel use when applied to
mesoscale emission inventories.  Thus, for consistency in the modeling approach, the preferred
strategy was to use mass per time emission rates for all pollutants and to apply the same modal
emissions approach for all pollutants.

Considerable attention was devoted in this work to methods for characterizing variability in
emission rates for individual modes, uncertainty in average emissions for individual modes, and
uncertainty in total emissions estimated based upon weighted combinations of modes. The
recommendations regarding these issues are given in more detail in Chapter 7. In brief, the
feasibility of representing variability in modal emission rates with parametric distributions was
demonstrated. In some cases, single component parametric distributions cannot provide a good
fit, but in such cases a two component mixture of lognormal  distributions provided an excellent
fit.  The Method of Matching Moments is recommended as a preferred parameter estimation
method if the objective is to have the mean and standard deviation of the fitted distributions
match those of the data.  For mixture distributions, MoMM is not considered a feasible
parameter estimation method and Maximum Likelihood Estimation is recommended.  However,
the differences in results between MoMM and MLE become smaller as the goodness-of-fit
improves. Thus, a well fitting mixture distribution will  typically have a mean and standard
deviation similar to that of the data.

The analysis of uncertainty need not be conditioned upon the assumptions made regarding the
characterization of variability based upon parametric distributions.  For example, uncertainty in
the mean can be estimated  directly based upon the data using analytical or numerical methods.  It
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is recommended that the sample size and the relative standard error of the mean of each bin
quantified. If the sample size is less than 40 and/or if the relative standard error of the mean is
greater than 0.2, then bootstrap simulation is recommended as a technique for quantifying the
sampling distribution of the mean.  In all other cases, a normality assumption will typically be
more than adequate.  Parametric distributions can be fit to sampling distributions obtained from
bootstrap simulation. Thus, for all modes, it is possible to use parametric distributions to
represent uncertainty in the mean, which will facilitate software design and model applications.

Both numerical and analytical methods for propagating uncertainty through a model were
explored.  Numerical methods such as Monte Carlo simulation or Latin Hypercube  Sampling
offer the advantage of increased flexibility to accommodate many kinds of distributions and
models, including situations in which uncertainty is quantified not only for modal emission rates
but also for vehicle activity (e.g., percentage of time spent in different modes and trip duration).
In contrast, the analytical approach offers the advantage of less computational burden but is also
less flexible.  An exact solution can be obtained for linear combinations of normal distributions,
such as when uncertainty in only modal emission rates is quantified and when all such
uncertainties are assumed to be normally distributed. Approximate analytical solutions can be
developed for other situations, such as when propagating uncertainty in both activity and
emission rates.  If this latter approach is to be further considered, the approach should be
evaluated quantitatively in comparison to a Monte Carlo approach to make sure that it will
produce sufficiently accurate results.  If a Monte Carlo approach is adopted, consideration should
be given to also including an analytical approach for use as a quality assurance  tool.

The range of uncertainty in total emissions estimates was large enough in many cases to justify
the importance of performing an uncertainty analysis.  For example, for HC and CO emissions
the range of uncertainty was as large as plus or minus 30 percent for selected vehicle groups and
for four different driving cycles.

With respect to the issue of how to  estimate modal emission rates from aggregate dynamometer
data (for which no second-by-second data are available), the results were mixed. It is possible to
develop good modal emission estimates especially for CC>2 as long as there is a sufficient sample
size and as long as sufficient constraints are specified in the least squares optimization approach.
However, the range of uncertainty in the predicted modal emission rates can be much larger than
the uncertainty in modal emission rates obtained from second by second data.  The results imply
that it is important to develop good estimates of the constraints; however, when applied to
vehicle groups for which there are no or few comparable second-by-second data, such as for
older carbureted vehicles, it may be difficult to develop good estimates of what the  constraints
should be. An alternative approach is to arbitrarily specify more stringent constraints, such as
defining ratios to be multiples of each other, in which case the estimation problem becomes
simpler but the answers obtained will be highly conditional upon such constraints.

The most critical issue in the modal modeling approach is to have a representative data set.  This
issue cannot be sidestepped regardless of the modeling approach employed. A  representative
data set should have proportional representation of vehicle emission rates and activity patterns
similar to that in the real world.  The development of such a database is resource limited and
requires considerable judgment.  In this particular work, the modeling database used for
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development and demonstration of the modal emissions concept was compared to other
databases, including IM240 and remote sensing data.  It appears to be the case that modeling
database produces lower emissions estimates for some modes and comparable emissions
estimates for others when compared to these other data sources. A possible reason for the
differences could be because of a different representation of high emitting versus normal
emitting vehicles.  However, another reason that was explored is that the activity patterns of the
modeling database are generally different than those of the EVI240 and RSD data. Thus, a key
question is not only whether the modeling database contains sufficient representation of high
emitting vehicles, but also whether the EVI240 and RSD data contain adequate or appropriate
representation of real world activity patterns from which it is useful  to make inferences regarding
emissions.  The modeling database contained some high emitting vehicles, and it was apparent
that the upper range of emission rates for a given mode of the modeling database were typically
comparable to the upper range of emission rates from these other databases. Thus, the question
is not whether the modeling database represents high emitting vehicles and/or high emitting
episodes.  Clearly, it does. The question is whether it contains a sufficient proportional
representation of such  situations. The evidence to support an answer to this question is
inconclusive given the different nature of the activity patterns for the EVI240 and RSD databases
compared to that of the modeling database,  as well as the possibility of other potential
confounding factors, such as fuel effects. From a methodological perspective, the main
implication of these comparisons in terms of future model development is to make sure that the
modeling database for future work is more comprehensive in terms of sample size and coverage
of vehicles considered to be both normal and high emitters.

Three approaches were taking toward validation of the conceptual modeling approach.  The first
was to perform a consistency check, which  demonstrated that the modal emission approach can
be applied to a dataset to disaggregate emissions into modes, and that it is possible to reaggregate
the model emissions and reproduce the total trip emissions. The second was to compare model
predictions to observed values for a set of vehicles similar to but not identical to those used in the
modeling data base.  The comparison demonstrated that differences  in vehicle mix between the
modeling database and the validation database can lead to differences when comparing predicted
and observed emissions. However, for cases in which the model and the observed values agreed
well for CC>2 emissions, they also tended to agree well for emissions of the other three pollutants.
In the future, it is worthwhile to perform similar validation studies by withholding data from the
modeling database for some of the trips made by a subset of vehicles, rather than to withhold
from the modeling database all  data for a particular set of vehicles.  Such an approach would
improve the likelihood that the vehicles in the validation data set are similar to those in the
modeling data set. The third validation case study involved prediction of emissions for an
independent set of vehicles based upon data provided by CARB. The comparison of predicted
and observed emissions was generally excellent for CC>2, NOX, and CO for eight different driving
cycles.  The model overpredicted for HC in all  cases; however, it is possible that CARB may
have reported only nonmethane hydrocarbons instead of total hydrocarbons or that there was a
fuel effect. A potential distinction between Tier 1 and TLEV vehicles in the CARB database
was explored. However, no significant difference in emissions was  found for vehicles that might
be TLEVs versus those that were Tier 1; therefore, it was not useful  to report results separately
for these two possible categories.
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A key criteria for comparison when performing validation studies is to evaluate the statistical
significance of differences between predicted and observed emissions. Emissions for individual
vehicles can vary by orders of magnitude even for the same driving cycle; therefore,
comparisons based upon a small number of vehicles will typically have wide confidence
intervals for the mean and will be less reliable than those based upon a larger set of vehicles.
Since the objective of an emission inventory model is to make accurate predictions for a fleet of
vehicles, it is important to have a quantitative understanding of the level of uncertainty
associated with mean predictions of the model, as has been demonstrated in this work.

In conclusion, this work has demonstrated the feasibility of an empirically-based method for
modal emissions model. The methods demonstrated in this work can and should be incorporated
or adapted for use in the development of MOVES and other emission estimation systems.
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Cullen, A.C., and H.C. Frey (1999). The Use of Probabilistic Techniques in Exposure
Assessment: A Handbook/or Dealing with Variability and Uncertainty in Models and Inputs.
Plenum:  New York, 1999. 335 pages.

Frey, H.C., R. Bharvirkar, and J. Zheng (1999), Quantitative Analysis of Variability and
Uncertainty in Emissions Estimation, Prepared by North Carolina State University for the U.S.
Environmental Protection Agency, Research Triangle Park, NC.  July 1999.

Frey, H.C., and S. Bammi (2002a), "Quantification of Variability and Uncertainty in Lawn and
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Frey, H.C., and S. Bammi (2002b), "Probabilistic Nonroad Mobile Source Emission Factors,"
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Frey, H.C., and D.A. Eichenberger (1997a), "Quantification of Uncertainty in Remote Sensing-
Based  School Bus CO and Hydrocarbon Emission Factors," Paper No. 97-RP143.07,
Proceedings of the 90th Annual Meeting (held June 18-13 in Toronto, Canada),  Air and Waste
Management Association, Pittsburgh, Pennsylvania, June 1997 (CD-ROM).

Frey, H.C., and D.A. Eichenberger (1997b), Remote Sensing of Mobile Source Air Pollutant
Emissions: Variability and Uncertainty in On-Road Emissions Estimates  of Carbon Monoxide
and Hydrocarbons for School and Transit Buses, FHWY/NC/97-005, Prepared  by North
Carolina State University for North Carolina Department of Transportation, Raleigh, June 1997.

Frey, H.C., and D.S. Rhodes (1996), "Characterizing, Simulating, and Analyzing Variability and
Uncertainty:  An Illustration of Methods Using an Air Toxics Emissions Example," Human and
Ecological Risk Assessment: an International Journal, 2(4):762-797 (December 1996).

Frey, H.C., and D.S. Rhodes (1998), "Characterization and Simulation of  Uncertain Frequency
Distributions: Effects of Distribution Choice, Variability, Uncertainty, and Parameter
Dependence," Human and Ecological Risk Assessment: an International Journal, 4(2):423-468
(April  1998).

Frey, H.C., and D.S. Rhodes (1999), Quantitative Analysis of Variability and Uncertainty in
Environmental Data and Models:  Volume 1.  Theory and Methodology Based Upon Bootstrap
Simulation, Report No. DOE/ER/30250--Vol. 1, Prepared by North Carolina State University for
the U.S. Department of Energy, Germantown, MD, April 1999.
                                         241
-------
Frey, H.C., N. Rouphail, A. Unal, and J. Colyar (2000), "Emissions and Traffic Control:  An
Empirical Approach," Presented at CRC On-Road Vehicle Emissions Workshop, San Diego,
CA, March 27-29, 2000.

Frey, H.C., N.M. Rouphail, A. Unal, and J.D. Colyar (2001), Emissions Reduction Through
Better Traffic Management:  An Empirical Evaluation Based Upon On-Road Measurements,
FHWY/NC/2002-001, Prepared by North Carolina State University for North Carolina
Department of Transportation, December 2001.  323 pp.

Frey, H.C., A. Unal, and J. Chen  (2002), Recommended Strategy for On-Board Emission Data
Analysis and Collection for the New Generation Model, Prepared by North Carolina State
University for the Office of Transportation and Air Quality, U.S. Environmental Protection
Agency, Ann Arbor, MI. February 2002.

Frey, H.C., and J. Zheng (2000), User's Guide for Analysis of Uncertainty and Variability in
Emissions Estimation (AUVEE), Prepared by North Carolina State University for Office of Air
Quality Planning and Standards, U.S. Environmental Protection Agency, Research Triangle
Park, NC, September 2000.

Frey, H.C., and J. Zheng (2001), Methods and Example Case Study for Analysis of Variability
and Uncertainty in Emissions Estimation (AUVEE), Prepared by North Carolina State University
for Office of Air Quality Planning and Standards, U.S. Environmental Protection Agency,
Research Triangle Park, NC, February 2001.

Frey, H.C., and J. Zheng (2002a), "Quantification of Variability and Uncertainty in Utility NOX
Emission Inventories," J. of Air & Waste Manage. Assoc., in press for September 2002 issue.

Frey, H.C., and J. Zheng (2002b), "Probabilistic Analysis of Driving Cycle-Based Highway
Vehicle Emission Factors," Environmental Science and Technology, undergoing revision for
April 2002 resubmission.

Frey, H.C., J. Zheng, Y. Zhao, S. Li, and Y. Zhu (2002), Technical Documentation of the
AuvTool Software for Analysis of Variability and Uncertainty, Prepared by North Carolina State
University for the Office of Research and Development, U.S. Environmental Protection Agency,
Research Triangle Park, NC.  February 2002.

Hildebrand, F. B. (1987), Introduction to Numerical Analysis., Dover: New York, 669 pages.

Kini, M.D., and H.C. Frey (1997), Probabilistic Evaluation of Mobile Source Air Pollution:
Volume 1, Probabilistic Modeling of Exhaust Emissions from Light Duty Gasoline Vehicles,
Prepared by North Carolina State University for Center for Transportation and the Environment,
Raleigh, December 1997.

Kress, R. (1998), Numerical Analysis,  Springer: New York, 326 pages.

Morgan, M.G., and M. Henrion (1990), Uncertainty., Cambridge University Press: New York.
1990.

Rouphail, N.M., H.C. Frey, A. Unal, and R. Dalton (2000), ITS Integration of Real-Time
Emissions and Traffic Management Systems, IDEA Project No. ITS-44, Prepared by North
Carolina State University for the IDEA Program, Transportation Research Board, National
                                         242
-------
Research Council, Washington, DC.  May 2000. (available at
www4.ncsu.edu/~frey/freytech.html).

Unal, A. (1999), "Measurement, Analysis, and Modeling of On-Road Vehicle Emissions Using
Remote Sensing," M.S. Thesis, Department of Civil Engineering, North Carolina State
University, Raleigh, NC.

Washington, S., J. Wolf, and R. Guensler (1997), "A Binary Recursive Partitioning Method for
Modeling Hot-Stabilized Emissions from Motor Vehicles," Prepared by School of Civil and
Environmental Engineering, Georgia Institute of Technology for the 76th Annual Meeting of the
Transportation Research Board, Atlanta, Georgia.

Zheng, J. (2002), PhD Dissertation, Department of Civil Engineering, North Carolina State
University, Raleigh, NC.

Zheng, J., and H.C. Frey (2002), AuvTool User's Guide, Prepared by North Carolina State
University for the Office of Research and Development, U.S. Environmental Protection Agency,
Research Triangle Park, NC. February 2002.
                                          243
-------
12  APPENDIX A
                                                                  A/CUse(0'Off; 1'On)
                              Figure A-l. Relationship between Air Condition Use and Emissions
                                                           244
-------
            20        40        60
                    Relative Humidity (%)
                                                                           Relative Humidity (%)
S

                    Relative Humidity (%)
                 Figure A-2. Relationship between Relative Humidity and Emissions
                                                   245
-------
                   90      1DO
    Ambient Temperature (F)
                                                      60       70      80      90       100
                                                               Ambient Temperature (F)
    Ambient Temperature (F)
                                                              70      80      90       100
                                                               Ambient Temperature (F)
Figure A-3. Relationship between Ambient Temperature and Emissions
                                      246
-------
                                        0.0001      0.001
                                           CO/CO2
                                                                            0.000001
                                                                                     0.00001
                                                             0.0001      0.001
                                                                 HC/C02
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                     0.8 -
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                     0.1 -
• Modeling data
 Remote Sensing
                       1E-08   1E-07
                                  0.000001  0.00001   0.0001
                                            NO/C02
                                                      0.001
                                                             0.01
                                                                    0.1
Figure A-4.  Comparison of Variability for Modeling Data and Remote Sensing Data for VSP Mode 7 with Engine Size Less Than 3.5
                                                       Liters and Model Year at 1996.
                                                                      247
-------
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                                                                 249
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                                                           254
-------
                        Table A-l. Correlation Among Parameters
Parameter
Net Weight
Odometer
Number of
Cylinders
Engine
Displacement
Model Year
Net
Weight
1




Odometer
0.35
1



Number of
Cylinders
0.76
0.18
1


Engine
Displacement
0.78
0.10
0.93
1

Model
Year
0.00
0.47
0.01
-0.02
1
                  Table A-2. Summary of Vehicles in Validation Dataset
Source
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
EPA
Vehicle
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
Year
1997
1997
1996
1997
1996
1997
1996
1996
1996
1999
1996
1997
1996
1996
1997
1998
1998
1996
1998
1999
1999
1996
1997
1996
1997
1997
1996
Net
Weight
2826
3553
3633
3650
2966
3223
3669
3279
3500
3538
3627
3699
2283
3625
3598
4216
4250
3625
3628
2827
2849
3338
2826
3633
3650
3223
3669
Engine
Size
2
3
3
3.1
2.2
2.5
3.1
3.1
2.2
3
3.1
3
1.3
3.1
3.1
4.6
6.2
3
3.1
1.6
1.8
N/A
N/A
N/A
N/A
N/A
N/A
Odomet
er
15806
58197
10102
22549
68768
17312
22000
23894
7573
19208
24798
12328
76931
17233
15248
19177
5098
18992
4983
10674
23800
30418
15768
9997
22093
17207
21951
(Continued on next page)
                                         255
-------
                                Table A-2. (Continued).
Source
EPA
EPA
EPA
EPA
EPA
EPA
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
Vehicle
28
29
30
31
32
33
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
Year
1996
1996
1997
1997
1998
1998
1995
1996
1996
1995
1995
1995
1995
1996
1994
1994
1996
1996
1995
1996
1994
1995
1996
1996
1995
1996
1995
1995
1996
1996
1996
1995
1994
1993
1994
1996
1994
1997
1994
1994
1996
Net
Weight
3279
3627
3699
3598
4250
3628
2250
4000
3500
3750
2250
2250
3000
3000
4250
2750
4000
2500
3500
2625
3000
2750
2625
2875
3500
3625
3375
3250
2875
3250
2875
2375
3500
2625
3000
2750
3250
2750
4000
3875
2875
Engine
Size
N/A
N/A
N/A
6
8
6
1.5
4.6
3.8
4
1.6
1.5
2
2
4.3
1.8
4.6
2
3.8
1.9
3
1.6
1.9
2.2
2.2
3.8
3
2.2
1.9
2.4
1.8
1.5
2.2
1.9
2.5
1.6
2.2
2
4.6
3.8
1.8
Odomet
er
23799
24708
1220
15182
5038
4829
23249
13287
22607
50541
49814
43708
21468
15096
43625
27339
16390
5312
28905
18000
49492
35291
7107
5690
29209
25877
22197
37194
13719
14212
4280
56213
56197
63125
56338
13845
57192
370
58923
54825
29480
(Continued on next page)
                                         256
-------
Table A-2.  (Continued).
Source
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
On-Board
On-Board
On-Board
On-Board
On-Board
On-Board
On-Board
On-Board
On-Board
On-Board
On-Board
On-Board
On-Board
Vehicle
36
37
38
39
40
41
42
43
44
45
46
47
48
49
1
2
3
4
5
6
7
8
9
10
11
12
13
Year
1995
1995
1994
1993
1993
1995
1994
1994
1995
1994
1996
1998
1994
1998
1998
1997
1996
1996
1998
1999
1999
1999
1997
1998
1998
1996
1996
Net
Weight
4000
2750
3125
2625
3250
3000
2875
4500
3625
2750
3250
2875
4000
3375
3550
3508
3464
3464
2553
3068
2392
2515
3318
2548
2548
2935
3508
Engine
Size
3
1.6
2.5
1.9
2.2
2.2
2.5
4.3
3
1.8
2
2.2
3
2.2
3.1
3
3
2.5
1.9
3.1
1.9
2
2
3
3
2.2
3
Odomet
er
51286
54843
56936
150139
72804
20606
72483
78060
63558
28630
105430
100250
100160
13247
44362
79984
96099
96099
37278
26288
43242
39429
71446
47439
47439
86999
94321
         257
-------
Table A-3. Summary of Vehicles in Validation Dataset
DATA
EPA
EPA
EPA
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
NCHRP
On-Board
On-Board
On-Board
Vehicle
1
2
3
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
1
2
3
Year
1996
1996
1996
1996
1996
1997
1994
1995
1994
1994
1995
1994
1994
1993
1994
1996
1993
1994
1994
1993
1994
1997
1997
1997
1995
1996
1999
1995
1998
1998
1998
GVWR
4036
N/A
N/A
3500
2625
3625
3625
2375
2625
2375
3625
3000
3875
2625
2625
2000
3500
3500
3250
2750
2625
2625
3375
3250
2625
2625
2875
2875
4721
N/A
5166
Engine
Size
2.4
3.1
1.6
3.8
1.6
3
3
1.5
1.5
1.5
3.3
2.5
3.8
1.6
1.9
1
2.2
2.5
3.1
1.8
1.5
1.6
3.1
2
1.9
1.9
3.1
2.5
3
2.2
2
Odomet
er
30669
21219
9433
22651
20975
3415
22258
52111
78056
57742
62007
57407
72691
61032
64967
32034
97869
61040
80877
102240
91045
6172
3015
23099
104890
111203
100250
100250
78187
56803
41319
                       258
-------
Table A-3. Summary of Vehicles in Validation Dataset •!
DATA
ARE
ARE
ARE
ARE
ARE
ARE
ARE
ARE
ARE
ARE
ARE
ARE
ARE
ARE
ARE
ARE
ARE
Vehicle
2
5
24
33
36
41
49
59
77
79
84
187
216
258
315
341
342
Year
1994
1997
1995
1996
1993
1995
1993
1993
1993
1994
1995
1994
1993
1995
1993
1995
1995
Net
weight
3500
3250
2750
3375
3250
2250
3500
3250
3125
2875
3125
4000
3375
2750
4000
3500
2750
Odometer
65294
23503
12698
28454
52196
6181
40626
47368
37353
23730
3188
88592
90080
32015
66932
49437
14904
                        259
-------
Table A-4. Comparison of Mean Emissions of VSP Bins, Time-Average vs. Trip-Average vs. Vehicle-Average
Bin8
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
NOb
Time-
Avg
mean
0.000901
0.000628
0.000346
0.001173
0.001706
0.002368
0.003103
0.004234
0.005069
0.005865
0.007623
0.012149
0.015456
Trip-Avg
mean
0.001097
0.001017
0.000742
0.001389
0.001684
0.002066
0.002466
0.003103
0.004166
0.004178
0.004979
0.009459
0.010298
diff.
22
62
114
18
-1
-13
-21
-27
-18
-29
-35
-22
-33
Vehicle-Avg
mean
0.000852
0.000727
0.000411
0.001039
0.00141
0.00198
0.002489
0.003235
0.004544
0.004414
0.005441
0.009449
0.010679
diff.
-6
16
19
-11
-17
-16
-20
-24
-10
-25
-29
-22
-31
HCb
Time-
Avg
mean
0.00045
0.000257
0.000406
0.000432
0.00053
0.000705
0.000822
0.000976
0.001112
0.001443
0.002061
0.003373
0.004857
Trip-Avg
mean
0.000391
0.000387
0.00035
0.000528
0.000572
0.00065
0.00077
0.000813
0.000871
0.001096
0.001673
0.003284
0.005374
diff.
-13
51
-14
22
8
-8
-6
-17
-22
-24
-19
-3
11
Vehicle-Avg
mean
0.00034
0.000337
0.000274
0.000429
0.000515
0.000666
0.000804
0.000946
0.001097
0.00133
0.0019
0.002607
0.004349
diff.
-24
31
-33
-1
-3
-6
-2
-3
-1
-8
-8
-23
-10
CO2b
Time-
Avg
mean
1.671078
1.457983
1.135362
2.233264
2.91989
3.525303
4.107483
4.635048
5.160731
5.632545
6.53478
7.585213
9.024217
Trip-Avg
mean
2.092668
2.020811
1.667869
2.552053
2.98235
3.327366
3.739047
4.121626
4.606298
4.858016
5.798515
7.097114
8.439456
diff.
25
39
47
14
2
-6
-9
-11
-11
-14
-11
-6
-6
Vehicle-Avg
mean
1.780418
1.70965
1.332954
2.338717
2.931022
3.502494
4.054487
4.52942
5.152217
5.440037
6.266617
7.671417
9.319705
diff.
7
17
17
5
0
-1
-1
-2
0
-3
-4
1
3
cob
Time-
Avg
mean
0.007807
0.003908
0.003347
0.008335
0.010959
0.017013
0.020026
0.029222
0.035531
0.055068
0.113824
0.207586
0.441775
Trip-Avg
mean
0.010418
0.007937
0.005155
0.01246
0.013319
0.014941
0.017961
0.022877
0.027536
0.03832
0.08035
0.169395
0.386715
diff.
33
103
54
49
22
-12
-10
-22
-23
-30
-29
-18
-12
Vehicle-Avg
mean
0.009971
0.007968
0.004262
0.010144
0.014101
0.021879
0.030889
0.046249
0.059231
0.086515
0.175599
0.253183
0.530003
diff.
28
104
27
22
29
29
54
58
67
57
54
22
20
                                                          260
-------
Table A-4. Continued
Bin8
1114
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
NOb
Time-
Avg
mean
0.017863
0.00029
0.000223
0.000174
0.000719
0.001136
0.001587
0.00237
0.004098
0.006124
0.007313
0.013178
0.012663
Trip-Avg
mean
0.015276
0.000571
0.000526
0.000571
0.000938
0.001304
0.001657
0.002194
0.002927
0.004377
0.00506
0.00802
0.018412
diff.
-14
97
136
227
30
15
4
-7
-29
-29
-31
-39
45
Vehicle-Avg
mean
0.018635
0.000767
0.000747
0.000899
0.001112
0.00152
0.001932
0.002551
0.00348
0.005834
0.006455
0.011761
0.018412
diff.
4
165
235
415
55
34
22
8
-15
-5
-12
-11
45
HCb
Time-
Avg
mean
0.010948
0.000548
0.000222
0.000272
0.000472
0.000754
0.000702
0.000944
0.001443
0.001708
0.002605
0.003523
0.007653
Trip-Avg
mean
0.005063
0.001243
0.001518
0.001165
0.001411
0.001704
0.001412
0.001489
0.001799
0.002151
0.002985
0.003469
0.005327
diff.
-54
127
583
329
199
126
101
58
25
26
15
-2
-30
Vehicle-Avg
mean
0.005851
0.000619
0.000704
0.000395
0.000649
0.000799
0.000809
0.000939
0.001299
0.001614
0.002385
0.003386
0.005327
diff.
-47
13
217
46
38
6
15
0
-10
-5
-8
-4
-30
CO2b
Time-
Avg
mean
10.08839
1.566819
1.443564
1.470553
2.611318
3.523681
4.650741
5.635386
6.599677
7.647334
8.808448
11.67061
14.52036
Trip-Avg
mean
8.611693
1.742827
1.883233
1.778044
2.93208
3.620842
4.399458
5.248342
6.16888
7.075418
8.096559
9.372073
14.8929
diff.
-15
11
30
21
12
3
-5
-7
-7
-7
-8
-20
3
Vehicle-Avg
mean
9.917922
1.76866
1.812724
1.767513
2.769411
3.558054
4.452864
5.270724
6.252616
7.38033
8.042326
9.594158
14.8929
diff.
-2
13
26
20
6
1
-4
-6
-5
-3
-9
-18
3
cob
Time-
Avg
mean
0.8823
0.017699
0.008608
0.008479
0.014548
0.025709
0.025212
0.04113
0.076601
0.129248
0.150578
0.355223
0.881642
Trip-Avg
mean
0.574791
0.03866
0.055898
0.034922
0.04941
0.072916
0.047817
0.059382
0.070431
0.103004
0.122169
0.168599
0.546928
diff.
-35
118
549
312
240
184
90
44
-8
-20
-19
-53
-38
Vehicle-Avg
mean
0.820496
0.019879
0.025235
0.011575
0.019972
0.026876
0.026926
0.041535
0.060221
0.103436
0.123995
0.220936
0.546928
diff.
-7
12
193
37
37
5
7
1
-21
-20
-18
-38
-38
                                                           261
-------
Table A-4. Continued
Bin8
1213
1214
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
NOb
Time-
Avg
mean
0.015387
0.020308
0.001014
0.001042
0.000423
0.001613
0.002638
0.003793
0.005098
0.006373
0.007664
0.009913
0.012685
Trip-Avg
mean
0.020783
0.041798
0.001018
0.001243
0.000793
0.002034
0.002791
0.003603
0.004579
0.005964
0.007039
0.01015
0.013099
diff.
35
106
0
19
87
26
6
-5
-10
-6
-8
2
3
Vehicle-Avg
mean
0.020783
0.041798
0.000965
0.001088
0.000858
0.001561
0.002287
0.003145
0.003967
0.005095
0.006184
0.00841
0.012178
diff.
35
106
-5
4
103
-3
-13
-17
-22
-20
-19
-15
-4
HCb
Time-
Avg
mean
0.006667
0.006574
0.000901
0.000901
0.000835
0.001027
0.001253
0.001664
0.002089
0.002332
0.002818
0.002985
0.003786
Trip-Avg
mean
0.005828
0.006035
0.000926
0.000833
0.000705
0.001237
0.001192
0.00134
0.001472
0.001585
0.002136
0.002352
0.00317
diff.
-13
-8
3
-8
-16
20
-5
-19
-30
-32
-24
-21
-16
Vehicle-Avg
mean
0.005828
0.006035
0.000607
0.000545
0.000486
0.000757
0.000865
0.000994
0.001134
0.001232
0.001654
0.001781
0.002651
diff.
-13
-8
-33
-40
-42
-26
-31
-40
-46
-47
-41
-40
-30
CO2b
Time-
Avg
mean
15.65327
17.36653
1.543686
1.604406
1.130833
2.38626
3.210249
3.957732
4.752012
5.374221
5.940051
6.427506
7.065985
Trip-Avg
mean
15.30436
17.66742
1.395048
1.656132
1.266896
2.640064
3.366473
3.973958
4.620807
5.332288
5.905244
6.722447
7.632773
diff.
-2
2
-10
3
12
11
5
0
-3
-1
-1
5
8
Vehicle-Avg
mean
15.30436
17.66742
1.330709
1.547675
1.270197
2.361957
3.10974
3.83721
4.583745
5.321404
6.043941
6.755205
7.972946
diff.
-2
2
-14
-4
12
-1
-3
-3
-4
-1
2
5
13
cob
Time-
Avg
mean
0.755155
0.904851
0.01103
0.008723
0.004682
0.012154
0.016731
0.023269
0.029322
0.036942
0.049513
0.063759
0.10538
Trip-Avg
mean
0.722783
0.909832
0.014076
0.013194
0.007685
0.021867
0.025063
0.024633
0.027876
0.033271
0.046846
0.060781
0.10403
diff.
-4
1
28
51
64
80
50
6
-5
-10
-5
-5
-1
Vehicle-Avg
mean
0.722783
0.909832
0.011779
0.009119
0.006283
0.013167
0.016411
0.02069
0.027406
0.034868
0.053282
0.071075
0.139503
diff.
-4
1
7
5
34
8
-2
-11
-7
-6
8
11
32
                                                           262
-------
Table A-4. Continued
Bin8
2112
2113
2114
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
NOb
Time-
Avg
mean
0.014384
0.015967
0.016717
0.000725
0.000504
0.000661
0.002518
0.005847
0.008361
0.010582
0.014473
0.016372
0.019758
Trip-Avg
mean
0.014329
0.01535
0.015747
0.00082
0.000937
0.000812
0.003287
0.005724
0.008287
0.010992
0.015513
0.017328
0.022928
diff.
0
-4
-6
13
86
23
31
_2
-1
4
7
6
16
Vehicle-Avg
mean
0.01417
0.015462
0.013914
0.000717
0.000607
0.000619
0.00248
0.005791
0.008562
0.010822
0.014517
0.015037
0.019472
diff.
-1
-3
-17
-1
20
-6
-1
-1
2
9
0
-8
-1
HCb
Time-
Avg
mean
0.004573
0.0057
0.007164
0.000863
0.0003
0.000323
0.000449
0.000818
0.001216
0.00211
0.004394
0.004635
0.004961
Trip-Avg
mean
0.005006
0.006377
0.009796
0.001075
0.000739
0.000571
0.000851
0.0015
0.001476
0.002053
0.003571
0.003484
0.004306
diff.
9
12
37
25
146
77
90
84
21
-3
-19
-25
-13
Vehicle-Avg
mean
0.004808
0.006267
0.009379
0.000857
0.000388
0.000298
0.000444
0.000816
0.001255
0.002082
0.004342
0.004221
0.005332
diff.
5
10
31
-1
29
-8
-1
0
3
-1
-1
-9
7
CO2b
Time-
Avg
mean
7.617703
8.322442
8.475028
1.649427
1.762407
1.557773
2.946419
4.127492
5.343656
6.507179
7.602431
8.773093
10.36591
Trip-Avg
mean
8.201694
8.290563
8.780078
1.666261
1.971398
1.688165
3.503549
4.476632
5.461154
6.480357
7.642446
8.827697
10.29987
diff.
8
0
4
1
12
8
19
8
2
0
1
1
-1
Vehicle-Avg
mean
8.694089
9.310727
9.856257
1.637489
1.729282
1.594651
2.950934
4.105545
5.347669
6.513549
7.693818
8.848806
10.33755
diff.
14
12
16
-1
-2
2
0
-1
0
0
1
1
0
cob
Time-
Avg
mean
0.24781
0.413069
0.624663
0.020282
0.008183
0.00483
0.012308
0.022033
0.045073
0.077496
0.166593
0.170018
0.263544
Trip-Avg
mean
0.367169
0.63355
1.067502
0.026335
0.031627
0.014518
0.044087
0.045654
0.059244
0.074036
0.130573
0.113574
0.17931
diff.
48
53
71
30
286
201
258
107
31
-4
-22
-33
-32
Vehicle-Avg
mean
0.504717
0.884127
1.495996
0.020063
0.009787
0.004375
0.012215
0.021965
0.046499
0.077436
0.165597
0.158411
0.271669
diff.
104
114
139
-1
20
-9
-1
0
3
0
-1
-7
3
                                                           263
-------
Table A-4. Continued
Bin8
2211
2212
2213
2214
NOb
Time-
Avg
mean
0.030507
0.034219
0.043387
0.068988
Trip-Avg
mean
0.036289
0.049097
0.0485
0.054347
diff.
19
43
12
-21
Vehicle-Avg
mean
0.03191
0.037247
0.0485
0.054347
diff.
5
9
12
-21
HCb
Time-
Avg
mean
0.006631
0.0109
0.016573
0.027066
Trip-Avg
mean
0.006477
0.013702
0.016142
0.020961
diff.
-2
26
-3
-23
Vehicle-Avg
mean
0.006673
0.011512
0.016142
0.020961
diff.
1
6
-3
-23
CO2b
Time-
Avg
mean
12.84939
15.0303
16.86173
18.94712
Trip-Avg
mean
12.53602
14.74582
16.96438
18.76208
diff.
-2
-2
1
-1
Vehicle-Avg
mean
12.83404
15.13418
16.96438
18.76208
diff.
0
1
1
-1
cob
Time-
Avg
mean
0.338962
0.824829
1.444311
2.175099
Trip-Avg
mean
0.23947
0.82406
1.306457
1.917319
diff.
-29
0
-10
-12
Vehicle-Avg
mean
0.341425
0.877657
1.306457
1.917319
diff.
1
6
-10
-12
 First two digit of VSP Bins: 11: odometer < 50,000 miles and engine size < 3.5 liter; 12: odometer < 50,000 miles and engine size > 3.5
liter; 21: odometer > 50,000 miles and engine size < 3.5 liter; 22: odometer > 50,000 miles and engine size > 3.5 liter.
b Unit of mean: g/sec; Unit of diff: %.
                                                             264
-------
Table A-5. Comparison of Standard Deviations of Variability in Original Emission Data Sets of VSP Bins, Time-Average vs. Trip-
Average vs. Vehicle-Average
Bin'
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
NOb
Time-
Avg
std.
dev.
0.0029
45
0.0025
6
0.0015
43
0.0034
0.0044
18
0.0056
74
0.0067
12
0.0079
42
0.0100
76
0.0109
91
0.0146
62
0.0200
7
0.0246
82
0.0277
26
Trip-Avg
std. dev.
0.001611
0.001587
0.001962
0.001756
0.001999
0.00236
0.002811
0.003529
0.005296
0.005133
0.007957
0.012712
0.013143
0.027707
diff
-45
-38
27
-49
-55
-58
-58
-56
-47
-53
-46
-37
-47
0
Vehicle-Avg
std. dev.
0.000963
0.000811
0.000375
0.000878
0.001167
0.001735
0.00242
0.003294
0.005013
0.004874
0.006742
0.011631
0.013583
0.032729
diff
-67
-68
-76
-74
-74
-69
-64
-59
-50
-56
-54
-42
-45
18
HCb
Time-
Avg
std. dev.
0.002831
0.001123
0.001502
0.001414
0.001599
0.00237
0.002401
0.002812
0.002673
0.003685
0.005445
0.010402
0.013267
0.024933
Trip-Avg
std. dev.
0.000566
0.000774
0.000801
0.000919
0.001047
0.00116
0.001414
0.001523
0.001854
0.002444
0.004588
0.010036
0.015286
0.008866
diff
-80
-31
-47
-35
-35
-51
-41
-46
-31
-34
-16
-4
15
-64
Vehicle-Avg
std. dev.
0.0005
0.000587
0.000534
0.000777
0.000917
0.001224
0.001481
0.001687
0.001912
0.002394
0.00348
0.003884
0.007115
0.008941
diff
-82
-48
-64
-45
-43
-48
-38
-40
-28
-35
-36
-63
-46
-64
CO2b
Time-
Avg
std. dev.
1.385471
1.212863
0.816426
1.384324
1.529625
1.667104
1.77441
1.938311
2.088216
2.35424
2.720312
2.987478
3.637198
5.372496
Trip-Avg
std. dev.
1.12253
1.132493
1.130622
0.955028
0.894469
0.902644
1.1272
1.323727
1.598809
2.112815
2.556017
2.795777
3.125796
4.190774
diff
-19
-7
38
-31
-42
-46
-36
-32
-23
-10
-6
-6
-14
-22
Vehicle-Avg
std. dev.
0.935668
0.866006
0.61943
0.767325
0.709841
0.775961
0.899522
1.138721
1.322392
1.874281
2.543511
2.773975
2.715516
3.666952
diff
-32
-29
-24
-45
-54
-53
-49
-41
-37
-20
-6
-7
-25
-32
cob
Time-
Avg
std. dev.
0.058918
0.036678
0.021594
0.051944
0.096842
0.154603
0.106224
0.15224
0.165469
0.251833
0.396332
0.570599
0.906088
1.521667
Trip-Avg
std. dev.
0.021028
0.019927
0.012754
0.028064
0.03279
0.036387
0.048599
0.077492
0.09141
0.11994
0.232956
0.300565
0.622866
0.830872
diff
-64
-46
-41
-46
-66
-76
-54
-49
-45
-52
-41
-47
-31
-45
Vehicle-Avg
std. dev.
0.014674
0.018202
0.010782
0.026506
0.031709
0.049995
0.073973
0.115758
0.150854
0.191922
0.335661
0.334399
0.689833
0.891284
diff
-75
-50
-50
-49
-67
-68
-30
-24
-9
-24
-15
-41
-24
-41
                                                           265
-------
Table A-5. Continued
Bin8
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
NOb
Time-
Avg
std. dev.
0.001353
0.001423
0.001253
0.002278
0.003336
0.0044
0.005525
0.008133
0.014025
0.014451
0.024503
0.023031
0.035852
0.037826
Trip-Avg
std.
dev.
0.001435
0.001521
0.001896
0.001665
0.002119
0.002279
0.001954
0.002694
0.005225
0.006155
0.014531
0.014183
0.020699
0.066474
diff.
6
7
51
-27
-36
-48
-65
-67
-63
-57
-41
-38
-42
76
Vehicle-Avg
std.
dev.
0.001873
0.002003
0.002485
0.002125
0.002614
0.002609
0.002196
0.002807
0.006173
0.007053
0.017887
0.014183
0.020699
0.066474
diff.
38
41
98
-7
-22
-41
-60
-65
-56
-51
-27
-38
-42
76
HCb
Time-
Avg
std. dev.
0.002465
0.001773
0.001936
0.002461
0.003597
0.002765
0.002781
0.00722
0.004432
0.009088
0.006989
0.011665
0.009166
0.007689
Trip-Avg
std.
dev.
0.003384
0.004194
0.003079
0.003694
0.003467
0.003178
0.003305
0.003196
0.003916
0.005182
0.006375
0.006219
0.005278
0.004986
diff.
37
137
59
50
-4
15
19
-56
-12
-43
-9
-47
-42
-35
Vehicle-Avg
std.
dev.
0.001711
0.002062
0.000929
0.001778
0.001681
0.001488
0.001768
0.001831
0.001976
0.003244
0.005167
0.006219
0.005278
0.004986
diff.
-31
16
-52
-28
-53
-46
-36
-75
-55
-64
-26
-47
-42
-35
CO2b
Time-
Avg
std. dev.
0.752061
0.729907
0.783702
1.080752
1.206617
1.78582
2.306199
2.635432
2.505814
2.799147
3.381765
2.530211
1.94742
2.208716
Trip-Avg
std.
dev.
0.664471
0.668691
0.697239
0.677613
0.794739
1.112786
1.366
1.781243
2.228266
2.633155
3.876705
1.692154
1.40999
1.110591
diff.
-12
-8
-11
-37
-34
-38
-41
-32
-11
-6
15
-33
-28
-50
Vehicle-Avg
std.
dev.
0.774477
0.77674
0.855793
0.628547
0.714965
0.921626
1.220852
1.570403
1.895366
2.432006
3.990195
1.692154
1.40999
1.110591
diff.
3
6
9
-42
-41
-48
-47
-40
-24
-13
18
-33
-28
-50
cob
Time-
Avg
std. dev.
0.087575
0.076393
0.069682
0.080298
0.138754
0.113237
0.16598
0.286122
0.410763
0.474955
0.933668
1.445647
1.100803
1.17728
Trip-Avg
std.
dev.
0.099099
0.141591
0.078986
0.104564
0.147007
0.093205
0.113099
0.111506
0.197293
0.196622
0.326539
0.856243
0.76091
0.932473
diff.
13
85
13
30
6
-18
-32
-61
-52
-59
-65
-41
-31
-21
Vehicle-Avg
std.
dev.
0.049412
0.068659
0.023375
0.04997
0.054372
0.042388
0.061202
0.090063
0.188263
0.166781
0.370172
0.856243
0.76091
0.932473
diff.
-44
-10
-66
-38
-61
-63
-63
-69
-54
-65
-60
-41
-31
-21
                                                          266
-------
Table A-5. Continued
Bin8
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
NOb
Time-
Avg
std. dev.
0.002291
0.00257
0.001682
0.003339
0.004665
0.006577
0.008025
0.009009
0.01072
0.013533
0.016326
0.016636
0.018636
0.018182
Trip-Avg
std.
dev.
0.001038
0.001248
0.001174
0.00162
0.002149
0.002846
0.003665
0.005018
0.005428
0.008557
0.010608
0.009201
0.009346
0.012218
diff.
-55
-51
-30
-51
-54
-57
-54
-44
-49
-37
-35
-45
-50
-33
Vehicle-Avg
std.
dev.
0.001092
0.001228
0.001481
0.001267
0.001593
0.002235
0.002943
0.003925
0.005163
0.006739
0.008615
0.009319
0.008606
0.008621
diff.
-52
-52
-12
-62
-66
-66
-63
-56
-52
-50
-47
-44
-54
-53
HCb
Time-
Avg
std. dev.
0.002249
0.002282
0.003115
0.002869
0.002939
0.003766
0.004028
0.003551
0.0052
0.004841
0.006874
0.007075
0.008143
0.009979
Trip-Avg
std.
dev.
0.001355
0.001089
0.001064
0.001942
0.00126
0.00141
0.001526
0.001595
0.001935
0.002246
0.002737
0.004083
0.005669
0.012121
diff.
-40
-52
-66
-32
-57
-63
-62
-55
-63
-54
-60
-42
-30
21
Vehicle-Avg
std.
dev.
0.000609
0.000673
0.000707
0.000965
0.000973
0.001123
0.001221
0.001195
0.001437
0.001466
0.002002
0.004147
0.004974
0.009851
diff.
-73
-71
-77
-66
-67
-70
-70
-66
-72
-70
-71
-41
-39
-1
CO2b
Time-
Avg
std. dev.
1.109149
1.114641
0.713377
1.171887
1.288537
1.360129
1.498808
1.644394
1.811788
1.959334
2.303041
2.454817
3.00003
3.192905
Trip-Avg
std.
dev.
0.522517
0.653819
0.508459
0.711085
0.823675
0.737997
0.809143
0.802907
1.301192
1.247208
2.134836
2.221742
2.826129
3.65873
diff.
-53
-41
-29
-39
-36
-46
-46
-51
-28
-36
-7
-9
-6
15
Vehicle-Avg
std.
dev.
0.492078
0.596964
0.588173
0.587889
0.613453
0.56076
0.675402
0.725539
1.036041
1.169198
1.86914
2.195417
2.735825
3.427465
diff.
-56
-46
-18
-50
-52
-59
-55
-56
-43
-40
-19
-11
-9
7
cob
Time-
Avg
std. dev.
0.04711
0.037055
0.028625
0.05007
0.066924
0.082777
0.08088
0.101806
0.146791
0.208775
0.331085
0.664957
0.917957
1.255385
Trip-Avg
std.
dev.
0.017075
0.017076
0.011217
0.026471
0.031311
0.021256
0.023906
0.029478
0.040071
0.055964
0.112855
0.508908
0.906304
1.425734
diff.
-64
-54
-61
-47
-53
-74
-70
-71
-73
-73
-66
-23
-1
14
Vehicle-Avg
std.
dev.
0.008651
0.007536
0.011063
0.013628
0.012323
0.014604
0.022786
0.028732
0.042312
0.061325
0.128683
0.587978
1.037041
1.612373
diff.
-82
-80
-61
-73
-82
-82
-72
-72
-71
-71
-61
-12
13
28
                                                          267
-------
Table A-5.  Continued
Bin8
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
NOb
Time-
Avg
std. dev.
0.002025
0.001373
0.001812
0.004017
0.008341
0.011656
0.01327
0.017788
0.019972
0.026059
0.032955
0.04661
0.049311
0.057202
Trip-Avg
std.
dev.
0.000981
0.001018
0.000953
0.004185
0.00692
0.009697
0.012669
0.01643
0.020016
0.023848
0.033371
0.04875
0.048572
0.051111
diff.
-52
-26
-47
4
-17
-17
-5
-8
0
-8
1
5
-1
-11
Vehicle-Avg
std.
dev.
0.000666
0.000437
0.000498
0.003048
0.007591
0.0106
0.013467
0.017134
0.019755
0.02638
0.032509
0.047183
0.048572
0.051111
diff.
-67
-68
-73
-24
-9
-9
1
-4
-1
1
-1
1
-1
-11
HCb
Time-
Avg
std. dev.
0.005724
0.001315
0.002487
0.000901
0.004297
0.002485
0.004035
0.011091
0.00739
0.009476
0.010611
0.016814
0.017884
0.032672
Trip-Avg
std.
dev.
0.001843
0.001012
0.000827
0.001069
0.002034
0.001831
0.002652
0.00444
0.003756
0.004503
0.007382
0.012329
0.013392
0.026775
diff.
-68
-23
-67
19
-53
-26
-34
-60
-49
-52
-30
-27
-25
-18
Vehicle-Avg
std.
dev.
0.001068
0.000366
0.000309
0.000361
0.00079
0.001041
0.001958
0.004399
0.003978
0.004976
0.006424
0.012946
0.013392
0.026775
diff.
-81
-72
-88
-60
-82
-58
-51
-60
-46
-47
-39
-23
-25
-18
CO2b
Time-
Avg
std. dev.
0.613904
0.675646
0.662243
0.7346
0.88572
1.082677
1.347016
1 .439746
1.495146
1.831227
2.135363
1.624249
2.386484
2.102866
Trip-Avg
std.
dev.
0.273568
0.401726
0.237542
0.861998
0.871532
0.935579
1.10976
1.04263
1.094696
0.851895
1.230785
1.219954
1.472577
1.50871
diff.
-55
-41
-64
17
_2
-14
-18
-28
-27
-53
-42
-25
-38
-28
Vehicle-Avg
std.
dev.
0.263742
0.118576
0.22642
0.345979
0.460997
0.745519
1.145355
1.20379
1.235369
1.134458
1.433405
0.913632
1.472577
1.50871
diff.
-57
-82
-66
-53
-48
-31
-15
-16
-17
-38
-33
-44
-38
-28
cob
Time-
Avg
std. dev.
0.114323
0.076183
0.08347
0.062257
0.069947
0.120335
0.196119
0.429698
0.329428
0.651197
0.706309
1.294249
1.427208
2.051322
Trip-Avg
std.
dev.
0.041109
0.044768
0.02829
0.052883
0.062257
0.071032
0.092674
0.191461
0.119911
0.220715
0.266176
0.671993
0.894934
1.561656
diff.
-64
-41
-66
-15
-11
-41
-53
-55
-64
-66
-62
-48
-37
-24
Vehicle-Avg
std.
dev.
0.018576
0.007651
0.005443
0.009072
0.02374
0.040804
0.073024
0.175101
0.115394
0.250122
0.297055
0.717117
0.894934
1.561656
diff.
-84
-90
-93
-85
-66
-66
-63
-59
-65
-62
-58
-45
-37
-24
'First two digit of VSP Bins: 11: odometer < 50,000 miles and engine size < 3.5 liter; 12:
odometer > 50,000 miles and engine size > 3.5 liter.
b Unit of standard deviation: g/sec; Unit of diff: %.
odometer < 50,000 miles and engine size > 3.5 liter; 21: odometer > 50,000 miles and engine size < 3.5 liter; 22:
                                                                                      268
-------