United States Environmental Protection Agency Office of Policy, Planning and Evaluation Washington, DC 20460 EPA-23O08-8S035 Statistical Policy Branch ASA/EPA Conferences on Interpretation of Enviionmental Data Sampling and Site Selection In Environmental Studies May 14-15, 1987 n ------- DISCLAIMER This document has not undergone final review within EPA and should not be used to infer EPA approval of the views expressed. ------- PREFACE This volume is a compendium of the papers and commentaries that were presented at the third of a series of conferences on interpretation of environmental data conducted by the American Statistical Association and the U.S. Environmental Protection Agency's Statistical Policy Branch of the Office of Standards and Regulations/Office of Policy, Planning, and Evaluation. The purpose of these conferences is to provide a forum in which professionals from the academic, private, and public sectors exchange ideas on statistical problems that confront EPA in its charge to protect the public and the environment through regulation of toxic exposures. They provide a unique opportunity for Agency statisticians and scientists to interact with their counterparts in the private sector. The conference itself and these proceedings are primarily the result of the efforts of the authors and discussants. The discussants not only provided their input to the proceedings but also reviewed the papers for the purpose of suggesting changes to the authors. The coordination of the conference and of the publication of the proceedings was carried out by Mary Esther Barnes and Lee L. Decker of the ASA staff. The ASA Committee on Statistics and the Environment was instrumental in developing this series of conferences. The views presented in this conference are those of individual writers and should not be construed as reflecting the official position of any agency or organization. Following the first conference, "Current Assessment of Combined Toxicant Effects," in May 1986, and the second conference, "Statistical Issues in Combining Environmental Studies," in October 1986, the third conference, "Sampling and Site Selection in Environmental Studies," was held in May 1987. One additional conference, "Compliance Sampling," was held in October 1987. A proceedings volume will also be published from this conference. Walter Liggett, Editor National Institute of Standards and Technology Hi ------- INTRODUCTION The eight papers and accompanying discussions in these proceedings are about drawing conclusions in environmental studies. These papers provide valuable guidance in the planning of future environmental studies. The papers address many aspects of environmental studies. The studies discussed involve air, water, ground water, and soil. These studies are aimed at specific goals as diverse as the effect of a regulatory intervention, the design of a remediation effort, the spatial distribution of a hazardous material, the validity of an environmental model, and the impact of a power plant. Some studies emphasize in addition the planning of the field work and of the chemical analyses in the laboratory. The studies employ techniques from various statistical areas such as probability sampling, response surface analysis, optimal design of experiments, time series analysis, spatial prediction, power transformations, and the analysis of variance. In the planning of an environmental study when almost all options are still open, most of these aspects are potentially relevant. These proceedings are intended for statisticians involved in the planning of environmental studies. Statistical planning is based on anticipation of the statistical analysis to be performed so that the necessary data can be collected. These proceedings should help the statistician anticipate the analysis to be performed. In addition, the papers discuss implications for planning new studies. No general prescriptions for planning are offered; none may be possible. The emphases in these papers are quite different. No two authors have chosen the same aspect of environmental studies to examine. This diversity among authors who have all invested considerable time and effort in environmental studies suggests a major challenge. The challenge is to consider carefully each study aspect in the planning process. Meeting this challenge will require a high degree of professionalism from the statistician involved in an environmental sutdy. Walter Liggett, Editor National Institute of Standards and Technology iv ------- INDEX OF AUTHORS Bailey, R. Clifton 73 Cressie, Noel A.C 25 Englund, Evan J 31 Folsom, Ralph E 41 Hudak, G 1 Jernigan, Robert W 54 Johnson, W. Barnes 23 Liu, Lon-Mu 1 Livingston, Richard A 55 Peterson, Bruce 70 Splitstone, Douglas E 15 Stewart-Oaten, Allan 57 Thrall, Anthony D 52 Tiao, George C 1 Warren, John 40 ------- TABLE OF CONTENTS Preface 111 Introduction. WALTER S. LIGGETT, National Institute of Standards and Technology iv Index of Authors v I. THE STATISTICAL BASIS: RANDOMIZATION AND PROCESS CONTROL A Statistical Assessment of the Effect of the Arizona Car Inspection/ Maintenance Program on Ambient CO Air Quality in Phoenix, Arizona. LON-MU LIU, G. HUDAK, GEORGE C. TIAO, University of Chicago 1 Sampling Design: Some Very Practical Considerations. DOUGLAS E. SPLITSTONE, IT Corporation 15 Discussion. W. BARNES JOHNSON, U. S. Environmental Protection Agency 23 H. INFERENCE ON CONTINUOUS SPATIAL DISTRIBUTIONS Spatial Prediction and Site Selection. NOEL A. C. CRESSIE, Iowa State University 25 Spatial Autocorrelation: Implications for Sampling and Estimation. EVAN J. ENGLUND, U. S. Environmental Protection Agency 31 Discussion. JOHN WARREN, U. S. Environmental Protection Agency 40 ffl. DESIGNS BASED ON AUXILIARY INFORMATION Sampling and Modeling Pollutant Plumes: Methods Combining Direct Measurements and Remote Sensing Data. RALPH E. FOLSOM, Research Triangle Institute 41 "Validation" of Air Pollution Dispersion Models. ANTHONY D. THRALL, Electric Power Research Institute 52 Modeling Pollutant Plumes. ROBERT W. JERNIGAN, The American University and Statistical Policy Branch, Environmental Protection Agency 54 Estimating the Spatial Uncertainty of Inferred Rates of Dry Acidic Deposition. RICHARD A. LIVINGSTON, University of Maryland 55 IV. STATISTICAL COMPARISON OF SITES Assessing Effects on Fluctuating Populations: Tests and Diagnostics. ALLAN STEWART-OATEN, University of California-Santa Barbara 57 Comparisons with Background Environment: Strategies for Design. BRUCE PETERSON, CH2M Hill 70 Discussion. R. CLIFTON BAILEY, U. S. Environmental Protection Agency 73 Appendix A: Program 75 Appendix B: Conference Participants 77 vii ------- A STATISTICAL ASSESSMENT OF THE EFFECT OP THE ARIZONA CAR INSPECTION/MAINTENANCE PROGRAM ON AMBIENT CO AIR QUALITY IN PHOENIX, ARIZONA Lon-Mu Liu G. Hudak G. C. Tiao University of Chicago, Graduate School of Business, 1101 E. 58th Street, Chicago, IL 60637 1. INTRODUCTION AND SUMMARY OF FINDINGS This paper presents a statistical analysis of ambient carbon monoxide concentrations over the period 1971 to 1982 at three air Monitoring sites in the state of Arizona. All three sites (Phoenix Central, Sunnyslop*, and Phoenix South) are located in the Phoenix area where a vehicle inspection and maintenance (I/H or VEI) program has been in effect since January 1977. The principal objectives of this study are to assess the trend in the CO concentrations which can be associated with the Federal Motor Vehicle Emission Control Program to determine whether or not the I/M program in the Phoenix area has had a positive impact on the concentration level. A summary of our principal findings is given in this section. Section 2 provides a description of the nature of the carbon monoxide, traffic and meteorological data used in the analysis. In Section 3 a preliminary trend analysis based on the CO readings alone is given. In Section 4 diurnal models relating CO to traffic and meteorological factors are constructed. Such models serve to identify the major exogenous variables affecting CO. In Section 5, time series intervention models for monthly means of CO readings are given. Traffic volume and relative humidity (a proxy for mixing height) are used as exogenous variables, and appropriate functional forms to model the effects of Federal emission standards and the I/M program are constructed. Finally in Section 6, a summary of the main results in trend analysis together with an assessment of the impact of the I/M program is presented. Our principal findings are as follows: (i) At all three sites one can observe a reduction in ambient CO concentration levels. The decrease at Phoenix Central is the largest. Considering the CO concentrations alone, this decrease is about 3.6% per year over the period 1973-1982. Further, the reduction at Phoenix Central is higher in the winter months, 5.7% per year, than in the summer months, 2.3% per year. (ii) Based on models for the monthly means of CO at Phoenix Central which adjust for the effects of traffic changes and meteorological variations, the winter trend reduction is estimated at about 7.1% per year while the summer reduction is about 2.3% per year. (ill) Yearly percentage changes in CO (based on adjusted monthly readings) at Phoenix Central are compared with two sets of emission factors derived from MOBILE3 analysis. One set of factors includes the expected effects of the I/M program and the other does not. It is found that, over the period 1973-1982, the year to year changes in CO concentrations in the winter months are in good agreement with changes in the set of emission factors which includes the effects of the I/M program. Provided that the emission factors are accurate, there is then some evidence from the observed ambient CO concentration levels to support the hypothesis that the I/M program has had a positive impact on ambient CO levels. (iv) Analyses of diurnal models of CO over the period 1977-1982 produced trend estimates largely consistent with estimates based on monthly averages. 2. Data Base 2.1 The Arizona Inspection and Maintenance Program The United States Clean Air Act Amendments of 1977 require that certain states implement vehicle inspection and maintenance programs (I/M programs) in certain of their major cities to reduce hydrocarbon (HO and carbon monoxide (CO) emissions from gasoline powered vehicles. Arizona Revised Statutes $36-1772, which established the Vehicle Emissions Inspection (VEI) Program, requires that gasoline powered vehicles pass an annual inspection to ensure that their exhaust emissions meet standards established by the Department of Health Services (DHS). This program was initiated in 1976 on a trial basis in the Phoenix and Tucson areas, and repairs became mandatory in January 1977. The inspection requirment applies generally to gasoline powered vehicles which are less than 14 years old and located within designated portions of Pima and Maricopa Counties which do not meet the carbon monoxide standards of the Federal Clean Air Act. According to the VEI program vehicles are tested annually to ensure that carbon monoxide and hydrocarbons in their exhaust emissions meet standards established by DHS. Motorists whose vehicles fail to meet these standards must repair their vehicles and submit to a retest. Data on the annual number of inspections and failure rates obtained from the Arizona DHS. Generally speaking, the monthly failure rates between 1977 and 1983 range between 15 and 25 percent, and they are higher in 1979 and 1980 than in other years. 2.2 Carbon Monoxide Data (COj The data consists of hourly CO concentrations (ppm) recorded at three Phoenix sites. The Phoenix CO measurment locations ares Phoenix Central (at 1845 B. Roosevelt in downtown). Sunny9lope (at 8531 N. 6th Street), and Phoenix South (at 4732 S. Central). live hourly data on CO concentrations at these three stations vary in length: Phoenix Central (71/1 - 82/12), Sunnyslope (74/10 - 82/12), and Phoenix South (74/10 - 82/12). Missing data occur at all three sites. Phoenix Central has one month (January, 1979) in which data are completely missing, the other two sites have several months completely missing. ------- 2.3 Traffic (TR) Many studies have shown that ambient CO concentrations are approximately proportional to traffic (Tiao, Box and Hamming (1975), Tiao and Hillmer (1978), Ledolter and Tiao (1979b), Tiao, Ledolter and Hudak (1982)). It is, therefore, necessary to incorporate changes in traffic into the trend analysis. Ideally, one would want to use traffic data recorded throughout the area affecting CO measurement sites over the entire period under study. Unfortunately, such detailed data are not available for this study. Estimates of relative traffic volume per day in the vincinity of Phoenix and Central and Phoenix South between 1970 and 1983 were provided by the Bureau of Air Quality Control (BAQC), Arizona Department of Health Services. These figures are listed in Table 2.1 Adjustment fractions for different months of a year, different days of a week, and different hours of a day were also provided by the Bureau of Air Quality Control and are listed in Table 2.2. 2.4 Meteorological Data Apart from traffic, variations in ambient CO concentrations are to a large extent affected by meteorological conditions: (a) wind speed and wind direction affect the transport and difussion of CO emissions (with low wind speed resulting in high CO levels); (b) inversion (mixing heights) affects the volume of air available for dilution of CO emissions; (c) temperature, solar intensity and relative humidity are related to the duration and intensity of temperature inversions and the degree of vertical mixing; (d) meteorological variables (such as temperature) influence the efficiency factors of car engines (cold starts leading to higher CO levels). Thus, one should consider incorporating these variables as exogenous factors in a trend analysis of CO. Meteorological data were obtained from the National Climatic Center (NCC) for the monitoring station of the -National Weather Service in Phoenix (near Phoenix Central). Data on wind speed (WS, knots), wind direction (HO, tens of degree), temperature (TP, °F), relative humidity (RH, percent) and precipitation frequency (PREC, 0-60) were obtained for the time period 1971/1 1982/12. Unfortunately, mixing height data were not available. A closely related variable whose data was available is delta temperature (AT). -The AT variable is the difference in temperature readings recorded at different heights. Since AT is a measure of atmospheric stability, it may be used as a proxy for mixing heights. Hourly AT measurements were made by the BAQC at the 6th Street and Bultler, where AT - temperature (°F) at 30 feet - temperature (°F) at 8 feet The hourly AT data are available between 77/5 - 82/12 but with many missing days and months. 3. Preliminary Trend Analysis of CO The primary objective of this study is to assess statistical evidence of the impact of the Arizona I/M program on the ambient CO concentration levels. Our approach to this problem is as follows. We first present in this section a preliminary trend analysis based on the CO data alone. The effects of traffic changes and the influences of meteorological variables are then considered in the next two sections (Sections 4 and 5) where various models relating CO at Phoenix Central to these exogenous factors are constructed. Finally, in Section 6, we compare the model-based trend estimates with the expected reduction in CO emissions based on EPA MOBILES analysis applied to the Phoenix Central location with and without the I/M program. 3.1 Preliminary CO Trend Analysis for Phoenix Central Figure 3.1 shows monthly means of CO at Phoenix Central. It is seen that there was an apparent down trend in CO over the period 1973-1982. (We have been informed by the DHS that CO data for the period 1971/1 - 1972/3 received by us are incorrect and hence -they have not been used in our analysis.) As a first approximation, if we assumed a linear time trend operating from 1973-1982, then the estimated CO reduction in the yearly means would be about 3.6% per year. Further study of the data shows that the percentage reduction is higher in the winter months (Oct. - Feb.) than in the summer months (April - August). Specifically, over the period 1973- 1982, the decrease is about 2.3% per year in the summer months and 5.7% per year in the winter months. 3.2 Preliminary CO Trend Analysis for Sunnyslope and Phoenix South For the Sunnyslope location, Figure 3.2 shows that over the period 1974-1982 there are many months for which data were missing. If we exclude the four years containing months of missing data (i.e., 1974, 1979, 1980 and 1982), we see that the reduction in CO is smaller than that at the Phoenix Central location. In particular, the estimated reduction in the yearly means of CO here is about 2.6% per year. Similarly, for the Phoenix South site, we see from Figure 3.3 that there are gaps of missing data. Excluding the three years 1974, 1979 and 1980, the estimated reduction in the yearly means of CO is about 2.4% per year, which is again smaller than that at the Phoenix Central site. 3.3 General Remarks The preliminary trend calculations were based on the CO readings alone. Recall from Table 2.1 that the traffic volume increased steadily over the years 1970-1982 in the Phoenix area. Thus, the estimated reduction in CO emissions would be higher than the figures given above when the traffic increases are factored into the analysis. Also, the preceding analysis did not take into account the influence of meteorological variables. We now turn to discuss various moels relating CO ------- to exogenous traffic and meteorological factors. In view of the fact that the Phoenix Central site has the longest and most complete data record on CO and that the concentration level is also much higher there than those of the two other sites, we shall confine ourselves to the Phoenix Central data in our modeling study. 4. Diurnal Models of CO The focus of this section is on modeling the diurnal behavior of CO which serves to identify the main factors affecting CO, and thus motivates the trend models discussed in Sections 5 and 6. As mentioned in Section 2, detailed traffic information, such as hourly traffic counts, was not available for the area influencing the CO measurement sites. In what follows, we use the estimated relative traffic volume over 1971-1982 pertaining to Phoenix Central and the adjustment fractions for different months, day and hours of a day provided by BAQC (see Tables 2.1 and 2.2). We have found that analyses using logarithmic transformation of the variables seem to be more meaningful than those using the original variables. The following notations will be employed: Carbon Monoxide LCO - In(CO + 0.25) Traffic LTR - ln(TR) Inverse of Wind Speed LIW - ln(l/(WS + 0.25)) Temperature LTP » ln(TP) Relative Humidity LRH - ln(RH) Delta Temperature LAT - In (AT + c), c - 2.0 for winter seasons c • 4.0 for summer seasons 4.1 Formulation of the Models In general, we can write a' model relating CO to the input traffic and meteorological variables as CO - g(TR)f(met.) where g(TR) is a function of the input traffic and f(met.) is a function of meteorological •variables. The function g(TR) will depend, among other things, on the units of measurements of CO and TR. As an approximation it seems reasonable to suppose *"" 8(W - k TR«- ».!)' where k Is a constant measuring the CO emissions and BI measures the percentage change in CO due to a one percent change in TR. Upon studying the diurnal diagrams of CO vs , various meteorological variables, we have found that the major meteorological factors influencing the diurnal behavior of CO are AT and the wind speed (WS) -or its inverse IW^JS'1. We may also approximate the function ftmet.) as f(met.) - c(AT)e2 (IW)S3 so that we have a model of the-multiplicative form CO - <* T* (4.3) where ui - ck. For trend assessment, we can make the constant k to be dependent on time, and in particular, we mav write * k • k. «-h«T where kg is a constant, T measures the time unit (year) under consideration and kj^ the percentage change in CO emissions per unit time. We are thus led to a model of the multiplicative form CO - « TR8«UT)Bl(IW)9»u where u is the error term, and upon taking logarithms, LCD - 00 * BfLTR + BjLAT + 32UW + « (4.4) where 0 - ln(o>) and e - ln(u). For diurnal data, let t stands for the t-th hour of the day, t»l,...,24. Because of the dynamic nature of the traffic and meteorological effects, we would expect that LCD could be related to some linear aggregates of the past values of these exogenous variables and also that the error term efc would be serially correlated. As an approximation, we consider the diurnal model *«t-1 + »t where at's are .- • . *. «».=*.« «£ a are white noisjs with zero means and common variance o . tg\ IT*,., • (l-*)[lT»t_| * «i.THt.j + ^LTHt.j + ...] —— (A) frill and similarly for UATt., and LIW^.,. For parameters estimation, we can write (4.5) in the alternative form - BO* (4.6) where 8-j* - B-jUr*), j - 0,..., 3. This is in the form of a linear" regression model and hence the parameters 6j*'s and * can be estimated from standard least squares' routines. To distinguish the behavior of CO between the summer and the winter, we have estimated the model (4.6) separately for each of these two seasons employing all available data, over the years. For each season, we let LCO(Y) LTR< ', LAT(iJ, LIW(i> represent the average readings of these variables at the.. t-th hour for the i-the year, and let B(l' be a separate constant for each of °the years considered. Thus LCO is the diurnal traffic pattern listed in Table 2.2 divided by the annual traffic volume in that year, and then multiplied by the annual traffic volume in 1972 for normalization. For the summer diurnal model, data from 1977 to 1982 are complete. Note that in model (4.7), the term 60. may vary from year to year, but the coefficient ------- Thus the model in (4.7) "can be written as. iCOt(" - «o + Bjaliw, + . (fc.S) Note that from (4.3), here we have i»T, kj* - k !------- 00) (5.5) I t-1.2.... (5.6) where Yt: LCOt, logarithm of fCCy- 0.25), or LCO*, logarithm of ((COt+ 0.025)/TR(i)) •208.275, i - 1972,...,1982 WNt: winter months (October-February) indicator, i.e., WNt « 1 if it is a winter month (i) * ° otherwise IDSt :summer months (April-August) indicator for the i-th year, i.e., IDSt :- 1 if it is a summer month in the i-th year « 0 otherwise i-1 for 1974,..., i-9 for 1982 IDV»t3 s winter month indicator for the j-th year, i.e., IDW^ - 1 if it is a winter month in the j-th year • 0 otherwise j - 1 for 1973/74,..., j-9 for 1981/82 TSt: summer trend TSt « 1 for all summer months in 1973 TSt - 2 for all summer months in 1974 . . . TSt .- 10 for all summer months in 1982 TSt - 0 otherwise TOt: winter trend Wt » 1 for all winter months in 1972/1973 TOt - 2 for all winter months in 1973/1974 TO « 10 for all winter month in 1981/1982 TO «• 0 otherwise In the above two models. Model (5.5) provides more detailed information of the change of CO concentrations from year to year. Specifically, a^ measures the effect (percentage change) of CO in the i-th summer compared with that for the base year 1973, and a2j the effect (percentage change) of CO in the j-th winter compared with that of the 1972/73 winter. Instead, Model (5.6) assumes linear time trends and 8± and 92 represent the percentage reductions of CO concentrations per year in the summer and winter respectively. 5.2 Model Estimation The parameters in models (5.5) and (5.6) are fitted to monthly averages of CO, CO* and RH using the SCA statistical system (Liu et al, 1983). The estimation results for Phoenix Central are listed in Table 5.1 for LCOt and Table 5.2 for LO>t. 5.3 Trend Analysis for Phoenix Central For LCOt (without normalization by the traffic volumes), Figuere 5.1(a) gives a plot of the estimated effects a2j ' (compared with the based year, winter of 1972/73) for the winters of 1973/74 to 1981/82, and Figure 5.l(b) presents a plot of o. . (compared with the base year, summer of 19737 for the summers of 1974 to 1982. Similarly, Figures 5.2 (a) and (b) give the corresponding, plots of LCo£ (after traffic normalization). From these figures and the estimates in Tables 5.1 and 5.2, we make the following observations: (i) Both in the winters and in the summers, the down trend in CO is more pronounced after traffic normalization. This is, of course, to be expected since the traffic volume was steadily increasing throughout the period 1973-1982 considered. (ii) By comparing Figures 5.Ha) with 5.2(a), and Figures 5.Kb) with 5.2(b) we see that the relative changes in the yearly effects are in fact much closer between LCOt and LCOt from 1976 onward compared with the changes before 1976. This is also reasonable since the annual percentage increase in traffic volume was much larger before 1976 - see Table 2.1. Thus, normalization by traffic volume has its major impact on the trend movement during the early, part of the data period considered. (iii) For the normalized LCO*. data, model (5.6) yields an estimated down trend of 7.1% per year in the winter season over the en.tire period 1972/73 to 1981/82. The magnitude of the percentage reduction in the summer season is much smaller, 2.3% per year. Also, figures 5.2(a) and (b) show that the summer effects exhibit considerably more variability than the winter effects do from year to year. In Section 6, we shall compare these estimated effects with the expected reduction in' emissions from EPA MOBILES analysis. 6. Summary of Trend Analysis and Assessment of the Impact of the I/M Program at Phoenix Central In Sections 3-5, we have performed several types of trend analyses on the CO concentration levels. Our main focus has been on CO at Phoenix Central where the readings are substantially higher than those at the other two sites. Sunnyslope and Phoenix South, and also where . the data span is the longest and most complete of these three locations. The main results at Phoenix Central can be partially summarized as follows: (i) Over . the time period April 1972 to December 1981 studied,' there is clear evidence of a down trend in the CO concentrations (ii) The down trend is more pronounced and smoother in the winter months (October- February), while considerably higher variability exists in the trend movement in------- the summer months (April-August). Note that CO concentration levels are substantially higher in the winter. (iii) For the winter months over the period 1972/1973 to 1981/1982: (a) preliminary analysis of monthly averages of CO readings alone yields an estimated trend reduction of 5.6% per year (b) after allowing for traffic and meteorological changes, our analysis of the monthly CO averages shows an reduction of about 7.1% per year. (iv) Over the four winters 1977/78, 1979/80, 1980/81 and 1981/82, our diurnal model relating CO to traffic and meteorological factors yield an estimated reduction of 15% per year. 6.1 Assessment of the Impact of the I/M Program Empirical assessment of the impact of the Arizona I/M program on CO concentration levels is made difficult by (i) the confounding between the expected effect of Federal emission standards and that of the I/M program and (it) the lack of a comparable "control" site without the I/M program. One approach to this problem would be to construct a time series model of the monthly averages of CO with a linear time function .characterizing the general down trend in the data and an additional term representing possible change in level of slope at the inception of the I/M program. For examples, we may contemplate the models C0t -ao*ait + « or C0t - (6'2) .,t*^(t.«.}.tct-»* k signifies the inception of the 'I/M " ,<'•>.}' "- (1 tit. Nt us the noise term which could be auto- correlatated. In (6.1) ' 03 measures ' the level change and in (6.2) a2 measures the slope change associated with the I/M program. One may then estimate the a's from the data and test the significance of a, . This approach has been adopted by McCleary and Nienstedt (1983) in their study of the Arizona DO data, and they have concluded that the I/M program has had no impact because the estimated a2 from models of the form (6.1) or (6.2) is not statistically significant. Their results can be largely seen from the plots of the estimated yearly effects of ' LCO^ in Figure 5.2. Consider, for example, the winter situation. Clearly there is little evidence from these yearly effects to support either a change of level or slope beginning in 1977/78. In the absence of any information about the magnitude of expected effects of either the Federal Emission standard and/or the I/M program, and assuming that the linear time functions in (6.1) and (6.2) aresuitable approximations to the shapes of the expected impacts of these two types of control measures, the above approach would be useful. On the other hand, when accurate information about the magnitude of the expected effects is available, other formulations of the problem are possible. Table- 6.1 lists the CO emission .factors from 1972 to 1982 with and without the I/M program for the central area of Phoenix supplied to us by the DHS. These factors were derived from EPA MOBILES analysis with adjustment for vehicle tampering/misfueling and varying speed over years. The yearly factors correspond to estimates for January 1 of the years. Assuming that these factors accurately represent the expected effects of the Federal emission standards and the expected impact of the I/M program, we can then employ the CO readings to assess to what extent trends in the emission factors with and without I/M are compatible with evidence from the data. For this analysis, we shall use monthly averages of the CO readings as discussed in Section 5. Figure 6.1(a) shows plots of the logarithms of the emission factors over time where a dot " " corresponds to the situation without I/M and a cross "x" to the situation with I/M effects included. The points in this figure then represent the percentage changes in emissions from year to year with and without the effects of the I/M program. Superimposed in the same figure by the circles "0" are the yearly effects of LCo£ for the winter months estimated from model (5.5) and shown earlier in Figure 5.2(a). It is clear that the trends in the estimated yearly effects are in reasonable agreement with emission factors with the I/M program. In a similar way. Figure 6.Kb) shows logarithms of the emission factors together with the yearly effects of LCO* for the summer seasons shown earlier in Figure 5.2(b). In this case, the estimated yearly effects are in better agreement with emission factors without the I/M program. However, it should again be noted that CO readings in the winter months are substantially higher and that the fluctuations in the summer yearly effects are much larger. To formalize the analysis, we let f.(t) be a function whose values are given by the logarithms of the emission factors with the I/M program (i.e., dots from 1972 to 1977 and crosses afterwards) and fQ |