EPA/600/A-95/127
ON THE USE OF AUTOMATIC DIFFERENTIATION FOR
SENSITIVITY ANALYSIS IN EMISSION CONTROL PROCESS
Dongming Hwang
Environmental Programs
MCNC, Information Technologies Division
Research Triangle Park, North Carolina
Daewoo W. Byun*
Atmospheric Sciences Modeling Division
Air Resources Laboratory
National Oceanic and Atmospheric Administration
Research Triangle Park, North Carolina
1. INTRODUCTION
Air quality models simulate the fate of atmospheric
pollutants using a set of algebraic and differential
equations based upon the physical laws of science. Air
quality models require meteorological inputs, emission
inputs, and initial and boundary condition concentration
fields. Theoretically, if all the inputs are completely
specified, the governing set of equations allows us to
predict the details of air flow and chemical
transformations. However, it is impossible in practice
to describe all the inputs and model parameters precisely
because they have to be estimated from stochastic
atmospheric motions. Model performance is inevitably
influenced by errors and uncertainties introduced into the
model by the parameterization schemes and the input
data. Among all input data and parameters, emissions
have received great attention because of their critical role
in the decision making process.
Knowledge of the complex chemical interactions
characterizing the photochemistry of tropospheric ozone
production has significantly increased in the past but
there exists no clear scientific consensus on the best
strategy for reducing ozone. The role of volatile organic
compounds and oxides of nitrogen in the production of
tropospheric ozone has long been recognized. Elevated
tropospheric ozone levels have proven to be much more
difficult to control than other pollutants that have shared
the focus of recent control efforts. A fundamental
complicating factor relates to the fact that ozone is not
directly emitted, but formed in the atmosphere by
reactions involving reactive hydrocarbons and nitrogen
oxides. Because of the nonlinearities in the relationships
between ozone and its precursor species, it is not at all
simple to prescribe the requisite precursor emission
Corresponding author address: Dongming Hwang, MCNC-
NCSC, P.O. Box 12889, 3021 Comwallis Rd„ Research
Triangle Park, NC, 27709; E-mail: dongming@mcnc.org
•On assignment to the National Exposure Research
Laboratory, U.S. Environmental Protection Agency
reductions necessary to reduce ozone concentrations to a
given level. Sensitivity analysis of emitted species will
provide important insights for emission control
strategies for reducing ozone. We will present a
preliminary result of sensitivity analysis in the
emission control process by using an automatic
differentiation technique.
2. METHOD
We will use an automatic differentiation technique,
ADIFOR, (Automatic Differentiation in FORtran)
(Bischof et al. 1992) in this work. ADIFOR is based on
a source translator paradigm and was designed from the
outset with large-scale codes in mind. ADIFOR
provides automatic differentiation for programs written
in FORTRAN-77. To apply ADIFOR to a given code,
the user need only specify which variables correspond to
independent and dependent variables with respect to
differentiation. ADIFOR then generates new
FORTRAN-77 code for the computation of the original
function evaluation as well as the associated derivatives.
This technique has been demonstrated to be applicable
and efficient for sensitivity analysis in air quality
models (Hwang and Byun, 1995).
A 3-dimensionaI model with only vertical
diffusion, emission, and deposition processes is used for
this study:
dC  E^l and a = l if E<1 for high emission level h
and low level /. Note that there will be no control if

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at - a2 -1 and this become uniform control if
h = i = 0. We will calculate the sensitivity of model
output to emission control factor, dC / da .
3. RESULT
We applied the sensitivity model of the diffusion-
emission process for a two-day period, OOGMT,
September 7 to 00 GMT, September 9, 1983 on
northeastern United States. We have run four test cases
among which three of them are uniform control cases
and the last one is a nonuniform control case. The
emission control parameters used for the four cases are;
(A) (a,.cr2)= (1. I), (B) (a1,o2)= (0.75, 0.75), (C)
(a„o2)= (0.5, 0.5), and (D) (a„ct2)= (0.5, 0.75) for
(M)= (5000 g/sec, 3000 g/sec). As an example, we
show the sensitivity analysis results for species S02.
The sensitivity ( dC I da) of case A is given in Figure
1 and the differences of sensitivity of case A and case D
is given in Figure 2. Figure 1 shows that the cells
potentially sensitive to an emission control coincide
with the high SO2 emission cells. Figure 2 shows
cells that are more susceptible to change to the specific
emissions control strategy, case D.
The peak values of sensitivity and concentrations
all occur at cell (19,30) and are summarized in Table 1.
It shows that the sensitivities of uniform control cases
change linearly with the control factor changes and the
concentrations are proportional to the emissions input
The nonuniform control case shows sensitivity and
concentration values in between those of cases B and C
as expected.
September *9,1983 CMXWX)
Peak = 0.1182
VoB« = 0.0000.
0
Figure 1: Sensitivity of concentration'to control factor
in case A, (a1,a2)=(l, 1), after 48 hours simulation.
Table 1: Peak values of sensitivity of concentration to
control factor after 48 hours simulation.
Case
dC / da (ppm)
Concentrations (ppm)
A
0.1182
0.1260
B
0.0887
0.0964
C
0.0591
0.0669
D
0.0631
0.0709
DISCLAIMER
This paper has been reviewed in accordance with the
U.S. Environmental Protection Agency's peer and
administrative review policies and approved for
presentation and publication. It has also been approved
for publication by MCNC. Mention of trade names or
commercial products does not constitute endorsement or
recommendation for use.
REFERENCES
Bischof, C., A. Carle, G. Corliss, A. Griewank, and P.
Hovland, 1992, ADEFOR—Generating Derivative
Codes from FORTRAN Programs, Scientific
Programming i: 11 -29.
Hwang, D., and D. Byun, 1995, Application of
Automatic Differentiation for Studying the
Sensitivity of Numerical Advection Schemes in Air
Quality Models, Proceedings of High Performance
Computing 1995 "Grand Challenges in Computer
Simulation," Society for Computer Simulation,
Phoenix, A2, pp. 52-57.
September *9,1963 IWXfcOO
Peck = 0.05:1
Volley = 0.CCCC
0
Figure 2: Differences of sensitivity of concentration to
control factor in case A, (a,,o2)=(l, 1) and case D,
(ait<*i)=(0.5,0.75) after 48 hours simulation.

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TECHNICAL REPORT DATA
1. REPORT NO.
EPA/600/A-95/127
2 .


4. TITLE AND SUBTITLE
On the use of Automatic Differentiation for
Sensitivity Analysis in Emission Control
5.REPORT DATE
6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
Hwang, D. j, and D. W. Byun2
8.PERFORMING ORGANIZATION REPORT
NO.
9. PERFORMING ORGANIZATION NAME AND ADDRESS
1	MCNC - North Carolina Supercomputing Center, 3021
Cornwallis Road, RTP, NC 27709
2	Same as Block 12
10.PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO.
12. SPONSORING AGENCY NAME AND ADDRESS
U.S. Environmental Protection Agency
Office of Research and Development
National Exposure Research Laboratory
Research Triangle Park, NC 27711
13.TYPE OF REPORT AND PERIOD
COVERED
Proceedings, FY-95
14. SPONSORING AGENCY CODE
EPA/600/9
15. SUPPLEMENTARY NOTES
16. ABSTRACT
Knowledge of the complex chemical interactions characterizing the photochemistry of tropospheric ozone production has significantly
increased in the past but there exists no clear scientific consensus on the best strategy for reducing ozone. The role of volatile
organic compounds and oxides of nitrogen in the production of tropospheric ozone has long been recognized. Elevated tropospheric ozone
levels have proven to be much more difficult to control than other pollutants that have shared the focus of recent control efforts. A
fundamental complicating factor relates to the fact that ozone is not directly emitted, but formed in the atmosphere by reactions
involving reactive hydrocarbons and nitrogen oxides Because of the nonlinearities in the relationships between ozone and its precursor
species, it is not at all simple to prescribe the requisite precursor emission reductions necessary to reduce ozone concentrations to a
given level. Sensitivity analysis of emitted species will provide important insights for emission control strategies for reducing ozone.
We will present a preliminary result of sensitivity analysis in the emission control process by using an automatic differentiation
technique.
17. KEY WORDS AND DOCUMENT ANALYSIS
a. DESCRIPTORS
b.IDENTIFIERS/ OPEN ENDED
TERMS
c.COSATI



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