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May 25, 2006 - (17) address the issues of ozone apportionment using sensitivity analysis. A problem common to all these methods is that when the numbe...
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Environ. Sci. Technol. 2006, 40, 4200-4210

Adjoint Sensitivity Analysis for a Three-Dimensional Photochemical Model: Application to Southern California PHILIP T. MARTIEN* AND ROBERT A. HARLEY Department of Civil and Environmental Engineering, University of California, Berkeley, California 94720-1710

An adjoint method was used to investigate the sensitivity of peak ozone at selected sites in Southern California to nearly 900 model inputs including surface emissions, reaction rate coefficients, dry deposition velocities, boundary conditions, and initial conditions. Simulations showed large changes in ozone and ozone sensitivities at three sites investigated between summers 1987 and 1997 due to emission reductions. However, only small changes in ozone and ozone sensitivities were predicted between 1997 and 2010. Sensitivities of the differences in ozone between simulations with different emission scenarios were calculated and compared to sensitivities of ozone in each simulation. In some cases, the sensitivities of ozone differences were smaller than those of ozone itself, but in other cases, such as when the sensitivity to NOx emissions changed sign, sensitivities of differences were larger. The adjoint method was most useful for determining when and where model inputs affect, or have the potential to affect, an ozone response. For example, the method was used to plot the spatial distribution of important emission source regions to 1-hour versus 8-hour peak ozone. Changes in the distribution and sign of the adjoint function for emitted species revealed changes in the area of influence of pollutant emissions on peak ozone due to emission controls. The adjoint method provides useful information complementary to that obtained from forward sensitivity analysis methods.

Introduction One of the goals of air quality modeling is to estimate the effectiveness of emission controls in reducing pollution levels. The importance of this application is evidenced by the many photochemical modeling studies that have examined changes in ozone levels with changes in emissions of precursor pollutants to evaluate the effectiveness of specific pollution control measures (1-5). Previous modeling studies have also investigated the influence of inputs and parameters other than emissions on an ozone response to estimate the importance of these model data (6-8). Some studies (6, 9) have examined first-order sensitivities to evaluate the change in model response for small changes in data. Higher-order methods have shown that changes in model data of 20% or less produce nearly linear changes in a simulated ozone response (10, 11). Often modeling is used * Corresponding author e-mail: [email protected]. 4200

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to generate differences in a target response, such as between a base year emission scenario and a future year emission scenario where the change in emissions represents a large fraction of the base year levels. In such cases, the change in response becomes the focus and one may wish to evaluate sensitivities of that response change. In past applications of 3D photochemical models, the brute-force method, whereby the model is re-run with modified data, is usually applied to estimate response changes. A forward method, such as the decoupled-direct method (DDM) (12), has also been used to generate model sensitivities (13-15). Dunker et al. (16) applied a source apportionment tool (OSAT) to identify important source types and source regions for a set of ozone responses consisting of 1-hour averaged modeled ozone at various times and locations. Cohan et al. (17) address the issues of ozone apportionment using sensitivity analysis. A problem common to all these methods is that when the number of sensitivities or, in the case of OSAT, the number of source types and regions becomes large compared to the number of useful responses, the methods become difficult to apply. Other researchers have used adjoint methods to examine sensitivities to many inputs and parameters (18). Mallet and Sportisse (19) applied an adjoint model to investigate ozone sensitivities and “sensitivity apportionments” to all emissions over western Europe. Sensitivity apportionment differs from source apportionment in that sensitivity apportionment is generally valid only for small changes in the response (about 10-20%), while source apportionment apportions the total response. However, sensitivity apportionment can reveal the response contribution of any model data, not just pollutant sources. Furthermore, as shown below, sensitivity apportionment defines source regions as part of the analysis, whereas source apportionment requires that potential source regions be defined in advance. In this paper, the adjoint sensitivity analysis procedure, or ASAP (20), is applied to Southern California and used to calculate and diagnose ozone sensitivities. Our objective was to analyze the sensitivity of peak ozone at urban and downwind sites using emission estimates for three years: 1987, 1997, and 2010. ASAP allowed us to rank sensitivities of specific ozone responses at specified locations to all emissions, reaction rate coefficients, dry deposition velocities, boundary conditions, and initial conditions. In addition to investigating sensitivities of the ozone responses themselves, we also ranked sensitivities of changes in ozone due to emission reductions between years. Finally, ASAP was used to produce actual and potential sensitivity apportionments for 1987, 1997, and 2010. As discussed elsewhere (20), sensitivity apportionments reveal when and where data perturbations contribute to a change in model response. Potential sensitivity apportionments, developed by considering additive as opposed to multiplicative source perturbations, reveal where sources could contribute to the response. The potential sensitivity apportionment can be useful, for example, for estimating the impacts of new sources in regions where no emissions currently exist.

Methods We use the CIT airshed model (21) with an extended version of the SAPRC99 chemical mechanism (15, 20, 22) applied to the meteorological conditions of the June 23-25, 1987, southern California ozone episode. Sensitivity analysis is performed using the adjoint function for three emissions scenarios (1987, 1997, and 2010) and four different target 10.1021/es051026z CCC: $33.50

 2006 American Chemical Society Published on Web 05/25/2006

TABLE 1. Anthropogenic Emission Estimates for California’s South Coast Air Basin (103 kg/day) for Typical Summer Weekday Conditions year

1987

1997

2010

emissions category

AVOC

NOx

AVOC

NOx

AVOC

NOx

on-road vehicles other anthro. total

2000 1230 3230

790 650 1440

530 730 1260

740 370 1110

200 540 740

370 310 680

responses: (1) 1-hour peak ozone at Central Los Angeles, (2) 1-hour peak ozone at Azusa, (3) 1-hour peak ozone at Rubidoux, and (4) 8-hour peak ozone at Rubidoux. Central Los Angeles was selected because it is near the downtown core with high emissions. Azusa was selected because incremental reactivities for many VOC are high there (15). This site experienced 1-hour peak ozone that approached the maximum observed in the South Coast Air Basin during this episode. Rubidoux, located further inland and downwind, was selected because the location with highest peak ozone has shifted toward there since 1987 and because it was expected to show different sensitivities to NOx emissions (23). The 8-hour peak ozone at Rubidoux was also selected as a target response to study differences in sensitivities for 1-hour versus 8-hour average ozone concentrations. The first of the three emissions scenarios represents the historical emissions for conditions appropriate to the Southern California Air Quality Study (SCAQS) from summer 1987 (24). The 1987 inventory was adjusted using measurements of on-road vehicle emissions and ambient pollutant concentration ratios (25). A more recent emissions inventory for summer 1997 is also considered here (26). The third emissions scenario is a forecast/planning inventory for summer 2010, which involves further reductions in emissions of both anthropogenic VOC and NOx relative to 1997 (26). Emission inventories were prepared by California Air Resources Board and South Coast Air District staff. Biogenic emissions were estimated by Scott and Benjamin (27) and were held constant across the three emission scenarios considered here. Different organic gas speciation profiles were used for gasoline engines and related emissions depending on the year: gasoline without oxygenates in 1987, gasoline with 11 vol % methyl tert-butyl ether (MTBE) in 1997, and gasoline with 6 vol % ethanol in 2010. Table 1 summarizes the three emission inventory scenarios used in this study; more detailed emission tabulations by source category are available elsewhere (26). Table 1 indicates that between 1987 and 1997, anthropogenic emissions of volatile organic compounds (AVOC) and nitrogen oxides (NOx) decreased by 60 and 23%, respectively, which is consistent with other findings that AVOC emissions have been reduced more than NOx (28, 29). The large reduction in on-road vehicle VOC emissions between 1987 and 1997 is consistent with on-road measurements (30). Increases in diesel NOx offset decreases in gasoline engine NOx over this same period (31). Reductions of 40% in both AVOC and NOx emissions are forecast to occur between 1997 and 2010. It will be difficult to achieve this level of NOx reduction by 2010 given the slow rate of progress in controlling NOx emissions from diesel engines (31). Each distinct emissions scenario involved a separate air quality model run. The adjoint sensitivity analysis was conducted in a two-part procedure with separate programs, referred to as ASAP1 and ASAP2 (20). For each emission scenario, each target response required an ASAP1 run to determine the adjoint function. Then, ASAP2 could be run efficiently in a scaling mode to calculate many sensitivities. In this context “scaling mode” means that perturbations in

each parameter or input were assumed to be proportional to their unperturbed value. All sensitivities are to episodewide and domain-wide changes to the parameters. Seminormalized sensitivities were sorted by absolute value in descending order and tabulated. To simplify the sensitivity analyses, it was useful to treat the NOx emissions as a single parameter and, similarly, to combine all anthropogenic VOC emissions into AVOC and combine all biogenic VOC emissions into BVOC. To derive the sensitivity of the response to combined parameters, consider a response R ) R(R1,R2) where we seek the sensitivity of R with respect to the combined data element R ) R1 + R2. For small perturbations in the data, if we assume that changes in R1 and R2 can be expressed as a single constant scaling factor applied to each, that is, if

δR1 ) λR1 and δR2 ) λR2

(1)

sR ) sR1 + sR2

(2)

then

Equation 2 expresses the result that, for the special case of constant scaling applied to each parameter, the seminormalized sensitivity of a response to the sum of parameters is the sum of the semi-normalized sensitivities of each parameter. Using this result, the semi-normalized sensitivity for NOx emissions was computed as the sum of seminormalized sensitivities to NO and NO2 emissions, and the semi-normalized sensitivities for AVOC and BVOC emissions were computed as the sum of semi-normalized sensitivities of each constituent emitted species (e.g., BVOC ) isoprene + R-pinene + other (lumped) terpenes). To investigate the sensitivity of ozone differences among years, a relation for the sensitivity of differenced responses is required. To develop this relation, we consider two responses: Rb with base-year emissions, and Rm with modified emissions. Here we allow for the possibility that the difference between the base and reduced emissions cases is not small, producing nonlinear changes in the mixing ratios of pollutant species between cases. The difference between the responses is ∆R ) Rm - Rb. It follows that

sm-b,R ) R0

∂Rm ∂Rb ∂[∆R] ) R0 - R0 ) sm,R - sb,R ∂R ∂R ∂R

(3)

Equation 3 expresses the result that the semi-normalized sensitivity of a difference between two responses is given by the difference in the semi-normalized sensitivities of the responses. This holds even when there are large data differences between a pair of responses. Note that in eq 3, the same normalization factor R0 is used for all seminormalized sensitivities. In particular, for comparing seminormalized sensitivities to emissions for different years, it was necessary to renormalize to a common year. In this study, the emissions sensitivities for years 1987 and 2010 were renormalized to year 1997 emissions. For example, the seminormalized sensitivity of ozone to NO emissions in 2010 was scaled by the ratio of the 1997 to the 2010 total NO emissions (totaled over the domain and simulation period). The 1997 date was selected for emissions normalization because it is recent and because emissions then are intermediate between 1987 levels and 2010 future levels. In addition to investigating sensitivities, we also use the adjoint function to generate both actual and potential sensitivity apportionments. For example, if ψNO represents the component of the adjoint function corresponding to species NO and eNO represents the emissions of NO, then the semi-normalized sensitivity of the response to a uniform VOL. 40, NO. 13, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 1. Ozone time series plots at Central Los Angeles (a, b), Azusa (c, d), and Rubidoux (e, f) comparing simulated and observed concentrations (left) and simulated concentrations for 1987, 1997, and 2010 emissions scenarios (right). scaling of NO emissions is given by

seNO )

∫∫ ∫ T

0

L1

0

L2

0

[ψNO eNO]x3)0 dx2 dx1 dt

normalized sensitivity of a response to a uniform scaling of the southern NO boundary condition can be found using

(4)

where x3 is the vertical dimension, and x1 and x2 are horizontal dimensions. In the integration, time varies between the simulation start (t ) 0) and its end (t ) T), while spatial dimensions x1-x3 vary between domain limits of zero and L1-L3 respectively. The height x3 ) 0 corresponds to the ground surface. The spatial distribution of the contributions to the semi-normalized sensitivity shows what regions contribute to the change in response or the sensitivity of the response to a given parameter. The sensitivity contribution apportioned to a single cell is found by integrating eq 4 over that cell. Sensitivities for 1-hour and 8-hour responses are calculated in exactly the same way but with different adjoint functions, which result from different response functions (20). A similar equation gives the sensitivity of the ozone response to boundary conditions. For example, the semi4202

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sbNOsouthern )

∫∫ ∫ T

0

L1

0

L3

0

[ψNO u2 bNO]x2)0 dx3 dx1 dt,

u2 > 0 (5)

where u2 is the horizontal component of the mean wind in the north-south direction, u2 > 0 at x2 ) 0 specifies southerly flow into the modeling domain through the southern boundary, and bNO is the boundary condition for NO. The potential sensitivity can also be obtained with the adjoint function. For example, the sensitivity of a response to a constant additive perturbation in NO emissions is defined as

S′eNO )

∫∫ ∫ T

0

L1

0

L2

0

[ψNO]x3)0 dx2 dx1 dt

(6)

The spatial distribution of the potential sensitivity shows the regions that could contribute to the change in response from

FIGURE 2. Observed trends in 1-hour peak ozone at Central Los Angeles, Azusa, and Rubidoux. a given parameter. For each model grid cell the potential sensitivity of emissions for the grid is found by integrating eq 6 over a single cell. The potential sensitivity apportionment of a parameter is independent of the actual parameter value but provides a measure of when and where the parameter has the potential to contribute to the response. The sensitivity apportionment of a parameter is a measure of when and where the parameter actually does contribute to the response. The distributions of the sensitivity apportionment and the potential sensitivity apportionment were plotted for various responses and emission scenarios.

Results and Discussion Sensitivities for 1987, 1997, and 2010 Emissions. Figure 1a, c, and e show the time series plots of simulated and observed surface-level ozone on June 25 at Central Los Angeles (1a), Azusa (1c), and Rubidoux (1e). At Central Los Angeles, observed ozone peaks at over 100 ppb between 1000 and 1100 PST and remains near that level throughout the day. Simulated ozone peaks at nearly the same time but does not reach the observed levels. At Azusa, both simulated and observed ozone peak at about 200 ppb. Ozone peaks later at Rubidoux than at Azusa, but the peak values are similar. Further model evaluation for the June 23-25, 1987, ozone episode has been presented previously (15, 32). Figure 1 also shows the time series plots of simulated ozone with 1987, 1997, and 2010 emissions on June 25 at Central Los Angeles, Azusa, and Rubidoux. Simulations show dramatic reductions in ozone between 1987 and 1997 as a result of emission reductions, primarily AVOC reductions. Between 1997 and 2010, significant emission reductions are forecast for both AVOC and NOx, with larger percentage reductions in NOx; model predictions show only minor reductions in ozone at Rubidoux and small ozone increases at Central Los Angeles and Azusa. The large reductions in ozone between 1987 and 1997 are consistent with observed ozone reductions that have in fact occurred over this period. For example, Figure 2 plots observed trends in peak ozone at these sites. Although peak 1-hour ozone is an extreme value statistic that varies from year to year depending on the meteorology of the worst-case ozone episode, Figure 2 shows a clear downward trend in peak ozone up to about 1997, after which the trend appears to flatten out. The effects of each of the reduced emission cases can be explained using results of sensitivity analysis for each ozone

TABLE 2. Top 40 Semi-Normalized Sensitivities (ppb) for Rubidoux 8-Hour Peak Ozone with 1997 Emissionsa rank

parameter

S-N Sens. (ppb O3)

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 36 37 38 39 40

eNO kHO.+NO2 kNO2+hν kO3+NO kO3+hνfO1D kO1D+H2O kO1D+M kHCHO+hνf2HO2. vdO3 bO3(southern) kHO.+CO kHO2.+NO kCCO-O2.+NO kCCO-O2.+NO2 kPAN eOLE2(lumped olefin) eisoprene eCO eethene kCH4+HO. vdNO2 eALK3(lumped alkane) kHCHO+hνfH2 eARO2(lumped aromatic) bCCHO(southern) eNO2 bCH4(southern) em-xylene kCCHO+HO. kRCO-O2.+NO bCO(southern) etoluene epropene kRCO-O2.+NO2 kRCHO+hν kHCHO+HO. kPPN kethene+HO. kALK3+HO. bNO2(southern)

-82.45 -49.43 39.22 -35.57 33.37 29.12 -29.12 18.75 -16.73 15.91 11.19 9.80 9.70 -8.75 8.07 7.26 6.86 6.32 6.05 5.91 5.91 5.61 -5.48 5.30 4.80 -4.68 4.53 4.53 4.20 4.12 3.98 3.96 3.82 -3.77 3.68 -3.62 3.56 3.54 3.24 3.23

a Top sensitivities are to emissions (e), reaction rate coefficients (k), deposition velocities (vd), and boundary conditions (b).

response. For each of four model responses with emissions from years 1987, 1997, and 2010, we applied ASAP to generate semi-normalized sensitivities for all 50 emitted species; for initial conditions of all 100 pollutant and radical species; for VOL. 40, NO. 13, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. Top 12 semi-normalized ozone sensitivities with 1987 emissions for 1-hour peak ozone at (a) Central Los Angeles, (b) Azusa, and (c) Rubidoux; with 1997 emissions for 1-hour peak ozone at the same three sites (d-f); and with 2010 emissions for 1-hour peak ozone at the same sites (g-i). AVOC ) all anthropogenic, BVOC ) all biogenic VOC emissions. boundary conditions for each lateral boundary and all species; for deposition velocities for all deposited species; and for all 246 reaction rate coefficients defined in the SAPRC99 chemical mechanism. Once ASAP1 was applied to generate the adjoint function for a given response, ASAP2 was used to efficiently calculate many sensitivities. Table 2 shows the top 40 sensitivities out of nearly 900 for 8-hour maximum ozone at Rubidoux on June 25 using 1997 emissions. For the Rubidoux 8-hour ozone response, Table 2 shows that the largest sensitivity is to NO emissions. The negative sensitivity to NO emissions indicates that the chemistry is VOC-sensitive, but the ranking of reaction rate coefficients affords additional insight into the chemical processes that produce ozone at this site. For example, the second-ranked (absolute value) sensitivity is the rate coefficient for the reaction of NO2 with a hydroxyl radical to produce nitric acidsthis is an important radical termination step when NOx is abundant. The rankings and signs of these top sensitivities indicate that NOx is abundant and that scarcity of radicals limits ozone production. 4204

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FIGURE 4. Top 12 semi-normalized sensitivities for the difference in 1-hour peak ozone at Rubidoux using (a) 1987 case minus 1997 case and (b) 1997 case minus 2010 case. All sensitivities of ozone to VOC and CO emissions in Table 2 are positive. The highest ranking among these sensitivities are species which have abundant emissions

FIGURE 5. Estimated spatial distribution of the apportionment of the semi-normalized sensitivity (ppb) of the 1-hour peak ozone on June 25 at (a) Central Los Angeles, (b) Azusa, and (c) Rubidoux to the southern ozone boundary condition, with 1997 emission estimates. upwind of Rubidoux and which most efficiently produce radicals. Ozone and NO2 dry deposition velocities (respectively ranked 9 and 21) contribute negatively to Rubidoux 8-hour peak ozone. Among the lateral boundary conditions, the southern boundary condition for ozone (bO3, rank 10) has the greatest influence. The boundary condition of acetaldehyde (rank 25) also contributes positively. Somewhat surprisingly, boundary conditions for CO and methane (respectively ranked 27 and 31), two relatively inert though abundant species, also appear in the list of top contributors. After 2 days of simulation, no initial condition is included in the list of the top 40 sensitivities. For this analysis it was necessary to select specific model responses of interest. However, it was not necessary to guess which parameters were important to study in advance. Once sensitivities to all emissions, all rate coefficients, all deposition velocities, all initial conditions, and all boundary conditions were generated, their ranking determined their overall importance. The efficiency of ASAP for generating many sensitivities makes this kind of analysis practical.

The top 12 sensitivities were plotted in Figure 3 for each emission scenario and for each of the 1-hour responses, with emissions sensitivities combined into NOx, AVOC, and BVOC categories. In Figure 3 sensitivities are color-coded. The primary photolytic cycle is in yellow outline, photolysis reactions are in green, the cycling of organic peroxy nitrates are in pink, other radical termination reactions are in red, VOC oxidation reaction rates are in gray, deposition velocities are brown, boundary conditions are dark blue, and nighttime ozone reactions are light blue. Emission sensitivities for all years are normalized to 1997 emissions since a constant normalization factor is required to make inter-year comparisons (see eq 3). Figure 3a-c plot the ranked semi-normalized sensitivities for the case of 1987 emissions. For the Central Los Angeles 1-hour peak ozone response (Figure 3a) the sensitivity to NOx emissions and to rate coefficients for radical termination reactions (rank 2 and 9) are strongly negative, while the sensitivity to AVOC emissions and to rate coefficients for photolysis reactions with radical yield and associated reacVOL. 40, NO. 13, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 6. For the 1-hour peak ozone at Azusa on June 25 with 1997 emissions: the estimated spatial apportionment of (a) the actual semi-normalized sensitivity (ppb) and (b) the potential sensitivity (ppb/kg/km2 hr) to NOx emissions (as NO2). tions are strongly positive. For example, photolysis reactions that directly and indirectly produced radicals (rank 6, 11, and 12) are particularly important at this site. Sensitivities to VOC reaction rates such as ethene + hydroxyl radical (rank 7) were all positive for this case. Semi-normalized sensitivities at Azusa (Figure 3b) are larger than those at Central Los Angeles since ozone levels are higher, but the sensitivities and their rankings are similar. One difference is that photolysis reactions that produce radicals (rank 6, 7, 8) at Azusa are higher in rank, relative to Central LA, as are those reactions that compete with radical production (rank 9). Sensitivities at both Central LA and Azusa reveal that peak ozone at these sites with 1987 emissions is VOC (or radical) sensitive. In contrast to this, sensitivities at Rubidoux (Figure 3c) reveal peak ozone at this site to be NOx sensitive. Sensitivities to emissions of both NOx (rank 8) and VOC (rank 10) are positive. Direct removal of ozone via deposition (rank 4) and nighttime chemistry losses (rank 12) are relatively more important at Rubidoux than at the other sites, while radical production is less important. The large emission changes, mostly VOC reductions, between 1987 and 1997 reduced ozone significantly and also changed sensitivity rankings. At Central LA (Figure 3d) and Azusa (Figure 3e) peak ozone still shows a large negative sensitivity to NOx emissions and large positive sensitivity to AVOC emissions. In fact, the sensitivity to AVOC emissions has moved up in rank at both sites, while sensitivity to rate coefficients for HO + NO2 and the primary photolytic cycle reactions moved down. At both sites, the sensitivity to the southern boundary condition has become more important, particularly at the Central LA site where the sensitivities to the southern boundary conditions for ozone, NO2, and NO moved up to rank 6, 8, and 10, respectively. With the reduction of AVOC, sensitivity to rate coefficients for VOC oxidation reactions dropped in ranking while that for CO rose (rank 11 at both Central LA and Azusa). At both sites ozone deposition velocity moved up to rank 12. 4206

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Even more dramatic changes in sensitivity ranking are evident at the Rubidoux site between 1987 and 1997. Ozone chemistry at Rubidoux has shifted to a VOC sensitive regime, and the sensitivity rankings have become similar to those for Azusa. At Rubidoux, the sensitivity to NOx emissions changed from positive (rank 8) to strongly negative (rank 1). Rate coefficients for photolysis reactions that produce radicals or that compete with radical production moved up significantly, while those for PAN cycling dropped out of the top 12. Biogenic emissions have become relatively more important (rank 12). Between 1997 and 2010 simulated peak ozone did not change substantially at any of the three sites (less than (10 ppb as shown in Figure 1b, d, and f). Likewise there were only small changes in the sensitivities and their rankings (Figure 3d-i). Despite significant forecast reductions in both NOx and VOC emissions, peak ozone at both central urban sites and sites downwind of these core urban areas remain VOC sensitive. Based on the sensitivities in 1987 at all three sites it is clear why the emission reductions that occurred between 1987 and 1997 were effective. Both NOx and VOC emissions were reduced, but VOC emissions were reduced more. This strategy prevented NOx disbenefits from counteracting the VOC benefits. Based on the sensitivities in 1997, an emission reduction strategy that reduces NOx in approximately equal proportion to VOC reductions is unlikely to be as effective in lowering ozone. All three sites are VOC sensitive, so NOx reductions are likely to offset benefits of VOC control. Sensitivities of Differences. The difference between responses from two simulations can reveal effects of changes in data. For example, air quality modelers commonly examine differences between a simulation with modified emissions and a base-case simulation. The sensitivity of the difference between two simulated responses can be as important as the sensitivity of the simulated responses themselves. As shown in eq 3, the sensitivity of differences between two

FIGURE 7. Estimated spatial distribution of the apportionment of the semi-normalized sensitivity (ppb) of the 1-hour peak ozone at Azusa to (a) AVOC emissions and (b) BVOC emissions, with 1997 emissions. Estimated spatial distribution of the potential sensitivity (ppb/kg/km2 hr) of (c) propene emissions and (d) isoprene emissions to the 1-hour peak ozone at Azusa. cases equals the difference in sensitivities between the cases; this is true even for large emission changes. This relation allows us to easily investigate whether and to what degree the sensitivities of differences between responses vary from the sensitivities of the responses themselves. It is often asserted that differences between simulations will be more robust with respect to uncertainties in the data, compared to absolute predictions in a single model run. The underlying assumption is that sensitivities are smaller for the differences in responses than for the responses themselves. Here we investigate the validity of that assumption. For the difference in 1-hour peak ozone at Rubidoux between the 1987 case and the 1997 case, many of the sensitivities that appear in the top 12, as shown in Figure 4a, also appear in the top 12 for the 1997 case itself. In Figure 4a, some of the sensitivities of the response difference were found to be larger than the sensitivities for either 1987 or 1997 response. For example, the NOx emissions sensitivity changed drastically between the 1987 case and the 1997 case. Whereas the sensitivity to NOx emissions was positive for the 1987 case, it is strongly negative for the 1997 case. The sensitivity of the difference between the simulated responses is therefore larger than that of either response. Thus, it is not always the case that the sensitivities of a difference are less than those of the base case. Where the sensitivities of two runs are similar, the sensitivities of the differences tend to be small. Compared to the sensitivities of the 1987 simulation, the sensitivities for the 2010 simulation were closer to those of the 1997 simulation. As a result, the sensitivities of the differences between the 1997 and 2010 emissions cases (Figure 4b) tend to be small compared the differences between 1987 and 1997 cases. When both AVOC and NOx precursors are reduced, the sensitivities of the peak ozone response are quite similar to the base-case simulation. Changes in sensitivities become pronounced when the chemical regime changes between the simulations being differenced, for example, when one response is VOC sensitive and the other is NOx sensitive.

Sensitivity Apportionment. Analyzing response sensitivities can reveal much about underlying processes and chemical regimes in an air quality simulation. It is helpful to have information about both the spatial and temporal apportionment of the sensitivities as well. For example, if boundary conditions for a pollutant are important, when are they important? And what part of the boundary is most influential? The adjoint function, suitably integrated, can provide this type of information. The potential sensitivity of an input or parameter is generated from the adjoint function alone (see eq 6). To see the actual contribution or sensitivity apportionment, the model input data or parameter must be included within the integral weighting of the adjoint function (see eq 4). The rest of this section presents potential sensitivity and sensitivity apportionment fields. In the ranked list of semi-normalized sensitivity (Table 2) the southern boundary condition for ozone was seen to be the most important of the boundary conditions. For more detailed information, the time-integrated contribution of each cell on the southern boundary can be apportioned using eq 5 (for ozone rather than NO), by mapping the contribution from each cell to the overall integral. For the 1997 emission scenario, Figure 5a plots the spatial apportionment over the southern boundary of the sensitivity of peak 1-hour ozone at Central Los Angeles to the southern ozone boundary condition. Figure 5b and c plot similar sensitivity apportionment contours for the peak ozone at Azusa and Rubidoux, respectively. In Figure 5 the vertical grid levels are plotted as dashed lines. The sensitivity apportionments for all three sites reach a maximum at about 500 m above ground level. Ozone on the southern boundary was set to 40 ppb and held constant in both time and space. The high sensitivity contributions aloft are mainly due to the fact the upper grid cells are thicker than the lower cells, providing more area for the influx of ozone. The topmost and thickest grid cell of the lateral boundary does not contribute as much as those below, due to the presence of VOL. 40, NO. 13, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 8. Estimated spatial distribution of the apportionment of the semi-normalized sensitivity (ppb) of peak ozone at Rubidoux to NOx emissions (left) and AVOC emissions (right) for (a, b) 1-hour peak ozone with 1987 emissions, (c, d) 1-hour peak ozone with 1997 emissions, (e, f) 8-hour peak ozone with 1997 emissions, and (g, h) 1-hour peak ozone with 2010 emissions. an elevated inversion layer that restricts mixing from topmost to lower layers. The main differences between sensitivity apportionments at Central LA, Azusa, and Rubidoux are that the center of the distribution is shifted progressively further to the east and the values become larger. The shift in the location of the distributions is simply due to the fact that Azusa is east of Central LA, Rubidoux is east of Azusa, and the onshore winds are fairly uniform and southwesterly. The increase in magnitude is due to the fact that simulated ozone in 1997 increases with distance inland, and the sensitivities are only semi-normalized. Figure 6a shows the spatial apportionment of peak ozone sensitivity at Azusa to NOx emissions. This plot, generated 4208

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by applying eq 4 over the simulation period for each surface cell, reveals the cells with NOx emissions that most influence ozone at Azusa. In this case, these sources are centered on the southeastern portion of Los Angeles county. As discussed earlier, the effect of small increases in NOx emissions in the 1997 simulation is to reduce ozone at Azusa. This finding is reflected in Figure 6a: all the colored contours plot negative sensitivity contributions, ranging from -0.5 ppb (light blue) to -3.5 ppb or less (dark blue). However, as shown in Figure 6b, there is a region further upwind where NOx emissions would have the potential to contribute positively to ozone at Azusa. Figure 6b plots the potential sensitivity of NOx emissions in units of ppb ozone per unit of emitted NOx flux. This plot was generated by applying eq 6 over the simulation

period for each surface cell. The region where NOx emissions would suppress ozone at Azusa is plotted in blue shades, while the region where NOx emissions would enhance the production of ozone is plotted in red shades. This analysis suggests that offshore NOx emissions (e.g., from ships) would increase ozone at Azusa. The second largest sensitivity of Azusa ozone for the 1997 scenario was to AVOC emissions. The spatial apportionment of AVOC sensitivity is plotted in Figure 7a. As for NOx emissions, the region that contributes most to Azusa AVOC sensitivity is southeastern Los Angeles county, just upwind of Azusa. All contours plotted in Figure 7a are positive. For comparison, the sensitivity apportionment of BVOC emissions is plotted in Figure 7b. (Note the change in scale between Figure 7a and b.) This comparison shows that the maximum grid contribution from BVOC is about an order of magnitude less than the AVOC contribution. This difference does not imply that the BVOC have no potential to produce ozone. In fact, potential sensitivity plots show that propene, an AVOC, (Figure 7c) and isoprene, a BVOC, (Figure 7d) emissions have similar potential to contribute. The difference in actual impact stems from differences in the amounts and the spatial distributions of AVOC versus BVOC emissions. The important source regions of precursor emissions that contribute to an ozone response can change when emission controls are implemented or when new ozone standards, and therefore modified responses, are considered. Such changes are shown in Figure 8, which plots the apportionment of sensitivities of Rubidoux 1-hour and 8-hour peak ozone for both NOx and AVOC for 1987, 1997, and 2010 emissions estimates. In the NOx sensitivity plots of Figure 8 (left column), positive semi-normalized sensitivities are shown in shades of red (0.05-0.25 ppb or greater) while negative sensitivities are shown in blue (-0.05 to -0.35 ppb or less). In the AVOC sensitivity plots (right column), all sensitivities are positive and shown in a color scale that indicates magnitude (0.11.9 ppb or greater). For comparison to other years, all emission sensitivities were renormalized to 1997 emissions. In the 1987 case, NOx emissions upwind to the southwest of Rubidoux contribute positively to peak 1-hour ozone at Rubidoux, as shown in Figure 8a. Only NOx sources in the immediate vicinity of Rubidoux suppress ozone. In 1987, the important source regions for AVOC emissions (Figure 8b) affecting Rubidoux 1-hour peak ozone have a footprint similar to that of the important NOx sources. In 1997, the NOx emissions sensitivities at Rubidoux increased in magnitude and changed sign. Figure 8c shows that except for a small region offshore, where NOx emissions from ships make a positive contribution to peak 1-hour ozone, NOx emissions sensitivities are all negative (blue contours). The distribution of important AVOC source regions in 1997 is similar to that for 1987, but the magnitude has increased as the chemical regime at Rubidoux shifted from NOx sensitive to VOC sensitive (Figure 8d). For 8-hour peak ozone, the important source regions for both NOx and AVOC have shifted further upwind (further west of Rubidoux) compared to those for the 1-hour peak (compare Figure 8e and c and Figure 8f and d). Reducing emissions in Orange county (at the coast) would have a larger effect on 8-hour peak ozone at Rubidoux than would similar reductions in Riverside county, which contains Rubidoux. The opposite was true for 1-hour ozone. Thus, control measures aimed at meeting the new federal 8-hour ozone standard may need to consider sources further upwind than measures targeting the old 1-hour standard. Despite significant reductions of both NOx and AVOC emissions between 1997 and 2010, the emissions sensitivities and the important emission source regions in 2010 appear not to have changed significantly from those for 1997. Compared to the equivalent Figure 8c and d for the 1997

emissions, Figure 8g and h for the 2010 emissions show distributions of emission sensitivities that are similar in both magnitude and extent. These analyses highlight the strengths of the adjoint sensitivity analysis procedure to reveal how multiple source perturbations affect a single receptor. This type of analysis complements forward sensitivity analysis methods, such as DDM, that are most useful for investigating how a single source perturbation affects multiple receptors.

Acknowledgments This research is an extension of work originally funded by the California Air Resources Board under contract 98-309. The statements herein are those of the authors and not necessarily those of the California Air Resources Board. We thank Paul Allen of the California Air Resources Board for providing emission inventory data files. We are also grateful to the Bay Area Air Quality Management District for leaves of absence granted to P.T.M. to allow completion of this research as part of his doctoral dissertation.

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Received for review May 31, 2005. Revised manuscript received February 21, 2006. Accepted April 6, 2006. ES051026Z