Adjoint Sensitivity Analysis of Ozone Nonattainment over the

Adjoint sensitivity analysis has long been used for variational data assimilation ..... Air Quality System database of monitoring stations (formerly k...
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Environ. Sci. Technol. 2006, 40, 3855-3864

Adjoint Sensitivity Analysis of Ozone Nonattainment over the Continental United States A M I R H A K A M I , † J O H N H . S E I N F E L D , * ,† TIANFENG CHAI,‡ YOUHUA TANG,‡ GREGORY R. CARMICHAEL,‡ AND ADRIAN SANDU§ Departments of Chemical Engineering and Environmental Science and Engineering, California Institute of Technology, Pasadena, California 91125, Center for Global and Regional Environmental Research, University of Iowa, Iowa City, Iowa 52242 and Department of Computer Science, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061

An application of the adjoint method in air quality management is demonstrated. We use a continental scale chemical transport model (STEM) to calculate the sensitivities of a nationwide U.S. ozone national ambient air quality standard (NAAQS) nonattainment metric to precursor emissions for the period July 1 to August 15, 2004. The model shows low bias and error (-4 and 24%, respectively), particularly for areas with high ozone concentrations. The nonattainment metric accounts for both 1-h and 8-h ozone standards, but is dominated by the 8-h exceedances (97% of the combined metric). Largest values of sensitivities are found to be with respect to emissions in the south and southeast U.S., Ohio River Valley, and California. When nonattainment sensitivities are integrated over the entire U.S., NOx emissions account for the largest contribution (62% of the total), followed by biogenic and anthropogenic VOCs (24% and 14%, respectively). For NOx emissions, point/area and mobile sources account for 54% and 46% of the total sensitivities, respectively. We also provide a state-by-state comparison for the nonattainment magnitude, nonattainment sensitivity, and emission magnitudes to explore the influence of interstate transport of ozone and its precursors, and policy implications of the results. Our analysis of the nationwide ozone nonattainment metric suggests that simple capand-trade programs may prove inadequate in achieving sought-after air quality objectives.

Introduction Air quality models are an indispensable tool in air quality policy-making and regulatory processes. Chemical transport models (CTM) describe the physical and chemical mechanisms that affect pollutant formation and transport and, therefore, are best suited to evaluate the effectiveness of potential pollution abatement strategies, a task generally accomplished by means of sensitivity analysis. Federal and local environmental agencies, as well as research communi* Corresponding author phone: (626)395-4635; fax: (626)796-2591; e-mail: [email protected]. † California Institute of Technology. ‡ University of Iowa. § Virginia Polytechnic Institute and State University. 10.1021/es052135g CCC: $33.50 Published on Web 05/11/2006

 2006 American Chemical Society

ties, routinely use model sensitivity analysis for diagnostic and prognostic purposes. Various methods have been developed and employed for formal sensitivity analysis in CTMs. In most cases, atmospheric sensitivity analysis is carried out in the forward mode, in which a perturbation in one or multiple inputs (such as emissions, dry deposition velocities, etc.) is propagated forward in time, resulting in calculation of derivatives at multiple receptors with respect to the perturbed parameters (1-3). Forward sensitivity analysis is inherently a source-oriented approach and is most efficient when sensitivities of multiple outputs with respect to few inputs are required. Adjoint sensitivity analysis has long been used for variational data assimilation in meteorology and oceanography. In adjoint (backward) analysis, a perturbation in a receptor-based metric (e.g., concentration at a receptor, or an observation-based cost function) is propagated backward in time, leading to the calculation of its sensitivities with respect to a multitude of inputs (4-7). In contrast to the forward analysis, backward sensitivity analysis is efficient when sensitivities of a limited number of outputs (or metrics) to a large number of inputs are to be calculated. The contrast between the ranges of computational efficiencies for the forward and backward sensitivity analyses makes the methods complementary and provides flexibility in addressing a wide spectrum of questions. Although most applications of the adjoint method in CTMs have been intended for inverse modeling and data assimilation (8-10), more direct sensitivity analysis applications have also received attention. Vukicevic and Hess (11) developed an adjoint version for the model HANK and conducted sensitivity analysis for concentrations of a tracer with respect to various inputs and model parameters. Vutard et al. (12), Menut (13), and Schmidt and Martin (14) have used the adjoint version of the chemical transport model CHIMERE and conducted sensitivity analysis of urban and regional scale ozone. Sandu et al. (15) developed computational tools for chemistry adjoint code generation and implemented the method in STEM, a regional CTM (16). Increased ground-level concentrations of ozone are associated with adverse human health effects (worsened chronic respiratory illnesses, increased emergency room visits, etc.) (17). Also, short-term exposures (weekly) to higher ozone concentrations have been shown to be associated with increased daily mortality rates in numerous urban communities (18-21). As of the end of 2004, 474 counties in the U.S., with nearly 160 million inhabitants, were in some degree of nonattainment with respect to the 8-h national ambient air quality standard (NAAQS) for ground-level ozone (80 ppbv). Currently, state agencies are responsible to devise state implementation plans (SIPs) that ensure attainment with ozone standards. However, atmospheric lifetimes of ozone and its precursors are sufficiently long that they can be transported far from emission sources and across state boundaries. Owing to its significant policy implications, longrange transport of ozone has been the subject of extensive scientific and regulatory modeling studies (22, 23). As a result of these studies, states are also responsible for developing SIPs (also referred to as NOx SIP Call) to reduce regional transport of ozone in the eastern U.S. (In absence of adequate state planning, the U.S. Environmental Protection Agency may be required to develop a Federal Implementation Plan for reducing interstate transport of ozone.) In recognition of the importance of interstate transport, the Clean Air Interstate Rule (CAIR) was promulgated by the U.S. E.P.A. in March 2005. CAIR is promulgated on the basis of section 110 (a) (2) (D) of the 1990 Clean Air Act that prohibits states “ ...from VOL. 40, NO. 12, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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emitting any air pollutant in amounts which will contribute significantly to nonattainment in, or interfere with maintenance by, any other state with respect to any such national primary or secondary ambient air quality standard”. CAIR regulates only the emissions of NOx and SO2 from Electric Generating Units (EGUs) for states that interfere with the attainment of ozone and/or PM2.5 standards in other states. Currently, of 28 eastern states and the District of Columbia covered by CAIR, 25 states and the District of Columbia are recognized as significant contributors to interstate ozone nonattainment. CAIR requires an emission budget for each state but also recommends an EPA-sponsored interstate capand-trade program (at the discretion of the state). In other words, states are required to meet the gradually declining emissions caps, but sources within a state are allowed to participate in emissions trading with EGUs from other states. The conceptual expectation in the cap-and-trade program is that more stringent national (or regional) caps will eventually lead to more geographic homogeneity in emissions and address high regional emission densities. Consequently, the underlying premise in the program is that emissions can be treated equally regardless of their spatial distribution; i.e., regional specificities do not play a major role in the ozone (or PM2.5) formation potential of precursors. This assumption inherent in current cap-and-trade programs has been explored in previous works (24, 25). These studies, due to their source-oriented nature, focus on specific cases (emissions from select power plants) and do not provide information about all precursor sources of different types. The receptor-oriented nature of adjoint sensitivity analysis makes it particularly attractive for policy applications. The strength of the adjoint analysis (in the context of 3-D atmospheric modeling) lies in its computational efficiency for calculation of sensitivities (of a scalar, like a species concentration) with respect to a spatially (and temporally) variable input field (e.g., emissions). Here, we employ the adjoint method for sensitivity analysis of a national ozone nonattainment metric. We use a continental-scale CTM, STEM (26, 16), and demonstrate that the adjoint analysis provides a powerful, flexible, and scientifically robust method for addressing policy questions.

Methods The core of a CTM is the atmospheric diffusion equation (27, 28):

∂Ci ) -∇‚(uCi) + ∇‚(K∇Ci) + Ri(C1, C2,...,Cn) + Ei ∂t

(1)

where Ci is the concentration of species i, u is the vector wind field, K is the diffusivity tensor, the term Ei represents elevated emissions, and Ri is the net rate of production of species i by chemical reactions. This set of coupled nonlinear differential equations is integrated subject to specific initial and boundary conditions, resulting in the time evolution of concentrations from an initial state (t ) t0) to a final time (t ) tF). The surface-level boundary condition is

K

∂Ci -vd,iCi + EiS ) 0 ∂z

(2)

where z is the vertical coordinate, vd,i is the species i dry deposition velocity, and EiS is its ground-level emission rate. In adjoint sensitivity analysis, an auxiliary set of differential equations that contain the adjoint variables are applied to the forward model, i.e., to eq 1. Adjoint variables contain sensitivity information about a scalar function M, usually referred to as the cost function (or objective function). For sensitivity analysis of concentrations, the cost function is simply set to the concentration of species of concern at a 3856

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specific location/time. In data assimilation, the cost function is observation-based and represents an integrated measure of model prediction errors over various measurement locations/times. In this study, we define the local ozone nonattainment function m as

m(ω,t) ) f1h{max[0,(C1h - γ1h)]}2 + f8h{max[0,(C8h - γ8h)]}2 (3) where C is the simulated 1-h or 8-h (ozone) concentration (ppb), and γ is the corresponding nonattainment threshold. The spatially and temporally variable function m is calculated by eq 3 over the continental U.S. and is zero elsewhere. The nationwide nonattainment metric (M) is an integration of the local nonattainment function over time (duration of the modeled episode) and space (continental U.S.)

M)

∫∫ t

Ω

m(C(t,ω)) dω dt

(4)

where ω is a generalized coordinate variable over the domain Ω. The nationwide nonattainment metric, M, is the scalar cost function the sensitivity of which is to be calculated in adjoint analysis. The nonattainment thresholds in eq 3 can be considered to be the NAAQS for ozone (80 and 120 ppb, for 8-h and 1-h averaging times, respectively); however, to allow a margin for the uncertainties in the model and inputs (and consequent errors in model predictions), we use values of 70 and 100 ppb for 8-h and 1-h thresholds, respectively. Values below the standards are weighted by the risk factors f:

f1h ) min {max [0,(C1h - γ1h)/20 (ppb)],1}

(5a)

f8h ) min{max[0,(C8h - γ8h)/10 (ppb)],1}

(5b)

Therefore, all concentrations (1-h or 8-h) below the threshold are assigned a weight factor of zero, while the weight factor for the concentrations above the standard is unity. Concentrations between the threshold and standard are weighted linearly between those limits. It should be noted that different definitions can be used in calculation of the nationwide nonattainment metric M. The definition used here is inspired by variational data assimilation applications and is deemed appropriate as its quadratic nature ensures pronounced representation of high-concentration events. The adjoint system corresponding to eq 1 is [thorough derivation of the adjoint equations can be found in Sandu et al. (16)]

∂λi ) u‚∇λi + ∇‚(K∇λi) + JiTλ + φi ∂t

-

(6)

where λ is the vector of the adjoint variables, and Ji is the ith column of the Jacobian for the chemical reaction rates (Jij ) ∂Ri/∂Cj). The boundary conditions for the adjoint system at the surface are

∂λi - vd,i λi ) 0 ∂z

K

(7)

The system of adjoint equations is driven by the forcing term φi

φi ) ∂m/∂Ci

(8)

Areas and periods of significant nonattainment cause larger forcing terms in the adjoint system. Note that the forcing term, for our definition of the cost function (nonattainment), is always positive (i.e., only exceedance above

FIGURE 1. Computational domain and spatial distribution of the ozone nonattainment metric. The values are integrated over the simulation period (46 days), normalized to the nationwide nonattainment metric, and represented in percent. For example, a value of 1% at a grid cell indicates that 1% of the nationwide nonattainment during the simulation period has occurred in that grid cell.

TABLE 1: Model Performance Statistics for Ozone Predictiona mean normalized bias (MNB)b (%) mean normalized error (MNE)b (%) average daily (1-h) unpaired peak prediction accuracy (UPPA)b (%) days with unpaired peak prediction accuracy within (25% (%)

a

Bias and error are calculated for a 70 ppb concentration cut-point.

b

MNE )

|Pi - Oi| 1 , MNB ) N i)1 Oi N 1

N

∑

domainwide

rural

urban/suburban

-3.7 23.9 -7.5 4.4 96 83

-4.4 24.3

-3.4 23.7

western U.S. eastern U.S. western U.S. eastern U.S.

Pi - Oi Ppeak - Opeak , UPPA ) where O and P are observations and model predictions, respectively. O Opeak i i)1 N

∑

the threshold causes nonattainment). Also, our study only considers ozone nonattainment, and therefore, ozone is the only species that may have nonzero forcing terms. However, as most species are coupled through the chemistry, a nonattainment event (and consequently nonzero forcing terms for ozone) can result in nonzero adjoints for multiple species. The negative sign for the time derivative term in eq 6 indicates that the adjoint equations are integrated backward in time from tF to t0, and the wind field in the adjoint system is also reversed. Equations 6 and 7 (as well as other initial and boundary conditions not shown here) uniquely define the adjoint variables. The choice of the adjoint equations and boundary conditions is made such that the adjoint system of equations is independent of partial derivatives of the state variables (concentrations). However, because of the nonlinearities of the gas-phase chemistry, the adjoint equations are coupled to the system equations (eq 1) through the Jacobian of the reaction rates. Therefore, integration of the adjoint equations backward in time requires knowledge of the concentrations from the forward integration of the CTM. Equation 6 is in continuous form and can be solved numerically. Alternatively, one may solve an adjoint system of equations for the discretized form of eq 1. The latter method (referred to as discrete adjoint) is model-specific as it depends on the discretization schemes used in each CTM. The two methods may produce slightly different results as the adjoint and discretization operators are not necessarily commutable. Here, for the sake of generality, formulation of nonattainment

sensitivity analysis is presented in the continuous form. However, STEM uses a discrete implementation for integration of the adjoint equations (for details, see 16), and the results presented here are based on discrete adjoints. The adjoint variables carry sensitivity information about the nationwide nonattainment metric M, and once calculated (in the continuous or discrete form), the information can be used to calculate the sensitivities (gradients) of M with respect to various model parameters. For the implementation in a three-dimensional CTM, the normalized sensitivities with respect to emissions (ground-level or elevated) are calculated as (10):

∂M ˜ 1 ) ∂i M ∂M ˜ 1 ) ∂iS M

∫∫

Ei(ω,t)λi(ω,t)dω dt

(9a)

∫∫

EiS(ω,t)λi(ω,t) dω dt

(9b)

t

t

Ω

Ω

where  is an emission scaling factor such that ∂M ˜ /∂ ) (E/M)(∂M/∂E). For each species, the integration is carried out for all times over the simulation period (t0 e tetF) and all sources in the domain; alternatively, the nonattainment sensitivities can be integrated for a specific source category, over a subdomain (e.g., a state), during a specified period, or evaluated at a particular grid cell and time. Normalized sensitivities calculated in eq 9 are dimensionless and represent the fractional (or percentage) change in the VOL. 40, NO. 12, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 2. Nonattainment sensitivities from various species emissions. Sensitivities are integrated for the duration of the episode and are normalized to the nationwide nonattainment metric (presented as percentage). For example, a 1% value in one location indicates that 100% reduction in the emissions of that species in that location will result in 1% reduction in nationwide nonattainment metric. nonattainment metric as a result of a specified change in the emission strengths. For instance, consider a case in which the nonattainment sensitivities are integrated with respect to the NOx emissions over individual states, where a single emission scaling factor () is assigned to all the NOx emissions within each state. For this case, a normalized statewide nonattainment sensitivity of 0.1 (or 10%) for one state 3858

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indicates that R% reduction in the NOx emissions in that state will produce a reduction of 0.1R% in the nationwide ozone nonattainment metric. Such statewide analysis can provide quantitative insight about the relative effectiveness of emission controls in various states for reducing the nationwide nonattainment metric. The same type of analysis can be conducted to calculate the normalized sensitivities

at each grid cell, or by integrating those sensitivities over particular periods of time (e.g., weekends), or for specified species. Normalized sensitivities represent marginal contributions from various emission sources to the nationwide nonattainment metric at the base case (current emissions). Since the nonattainment metric and the governing equations for the time evolution of the concentrations are nonlinear, these marginal contributions (sensitivities) are expected to change as the emissions vary from the base case (e.g., with the implementation of future emission control measures). Still, these sensitivities represent, to a first-order approximation, contributions to the overall nonattainment metric from various sources. The assumption of linearity (i.e., first-order approximation) is likely to be valid for small ranges of change in emission strengths (less than ∼30%) that are expected in policy applications.

Results and Discussion We employ here the adjoint version of STEM-2k1 CTM (26, 16) for sensitivity analysis of ozone nonattainment. Parallel implementation of the adjoint equations using the communication and parallelization library of PAQMSG (29) and its evaluation is discussed elsewhere (16). In the parallel mode, the domain is divided into horizontal and vertical slices that are processed by different computational nodes. The model uses efficient two-level checkpointing storage, as the state vector (concentrations) is required for the backward integration of the adjoint variables. The SAPRC-99 (30) chemical mechanism (94 species, 235 chemical reactions, 30 photolytic reactions) represents the gas-phase chemistry. The modeling domain covers the continental United States and portions of Canada and Mexico (Figure 1). The horizontal domain is composed of 97 × 62 grid cells with 60 km resolution; the vertical domain consists of 21 terrain-following layers in sigma-pressure coordinates. For this study, we conduct forward and backward calculations for 46 days (July 1 to August 15, 2004). Meteorological fields over the domain are simulated using the PSU/NCAR mesoscale model, MM5. The emission inventory for NOx, CO, SO2, NH3, and 30 explicit or lumped VOCs is prepared based on the 2001 National Emission Inventory and includes emissions from mobile, point, area, nonroad mobile, and fire sources. Model performance for ozone prediction is evaluated against the U.S. E.P.A.’s Air Quality System database of monitoring stations (formerly known as AIRS). Acceptable performance is achieved, particularly for areas with ozone concentrations at the upper end of the distribution, with mean normalized bias and error of -4 and 24%, respectively. A cut-point of 70 ppb is used for performance evaluation, as it is the concentration threshold for the nonattainment metric evaluation. Regional peak concentrations are predicted well both in the western and eastern U.S. (Table 1). Model performance for nighttime ozone is poorer than the daytime predictions; however, these low-concentration periods have little significance for this study. On a regional basis, the model has slight low bias (underpredictions) in California and Texas, and high bias (overpredictions) in the southeast. The grid resolution employed in this study is too coarse to resolve individual urban areas; however, no distinct difference is noticed between the performance of the model against rural or urban/suburban monitors (Table 1). Figure 1 shows the spatial distribution of the nonattainment metric (percent, normalized to the nationwide metric) integrated over the simulation period. The nationwide nonattainment metric is the summation of nonattainment values in Figure 1 over the continental U.S. During the simulation period, the highest concentrations are predicted in the southeast U.S. and California. Overall, ozone concentrations during this period were lower than typical values

TABLE 2: Contributions of Various Source Types to the Overall Anthropogenic Nonattainment Sensitivities in the United States for the Simulation Period mobile sources point and area sources

NOx

VOCs

46% 54%

44% 56%

in other years, e.g., high concentrations in Texas (particularly the Houston-Galveston area) did not occur as regularly as expected. During this period, the metric (as defined by eqs 3 and 4) is dominated by the 8-h nonattainment (97% of the total metric). This result is expected, as the 8-h standard is a considerably more stringent attainment criterion than the 1-h standard. An important point to be emphasized is that the nonattainment metric, M, is entirely model-based and does not include any observations. This is in contrast with, and different from, the observation-based criteria used for regulatory determination of nonattainment. In other words, the metric presented in this paper does not correspond to the regulatory definition of the term “nonattainment”. Nonattainment Sensitivities. Adjoint variables contain information on the sensitivity of the nonattainment metric with respect to concentrations at various locations and times. Integrating the adjoint variables according to eq 9 yields normalized sensitivities of the nonattainment metric with respect to emission sources at each grid cell [∂M ˜ /∂(ω,t) in eq 9]. These sensitivities can be calculated separately for various emitted species or source categories. Figure 2 shows the spatial distribution of the total (integrated over all times and vertical layers for each grid cell) normalized sensitivities with respect to VOC (anthropogenic and biogenic) and NOx emissions. The nonattainment sensitivities in Figure 2 are normalized and dimensionless (expressed in percent) and are integrated over the simulation period (46 days). For instance, a sensitivity of 1% to NOx emissions at a grid cell indicates that 100% reduction in the emissions in that grid cell will, to first-order approximation, reduce the nationwide nonattainment by 1%. Note that normalized sensitivities calculated in eq 9 can add up to a total greater than 100%. Over the entire continental U.S., the total amount of normalized sensitivities with respect to NOx and VOC emissions amounts to 530%; i.e., the summation of the nonattainment sensitivities with respect to all the precursor emissions in the U.S. is more than five times the magnitude of the nationwide nonattainment metric. In other words, 20% uniform reduction in emissions of NOx and VOCs will, by a first-order approximation, result in attainment. However, in reality larger reductions may be needed due to nonlinearity in the nonattainment metric and in the response of ozone with respect to precursor emissions. As expected, on a nationwide basis, the largest contributions (sensitivities) are from NOx emissions (62% of the total sensitivities from all species). For VOCs, biogenic emissions show more significant contributions than anthropogenic emissions (24% and 14% of the total sensitivities, respectively), as most of the nonattainment events during the simulated period occur in regions with substantial biogenic emissions. Areas in proximity to major cities (Los Angeles, Detroit, etc.) show negative sensitivity with respect to NOx emissions in Figure 2. Negative sensitivity of ozone with respect to NOx emissions is expected in the NOx-inhibited urban plumes in the vicinity of these cities. However, the sensitivities calculated here are those of the nationwide nonattainment metric and are not limited to the NOx-inhibited urban areas. Therefore, the results in Figure 2, indicating a potential increase in the nonattainment metric as a result of reduced urban emissions seem counterintuitive and warrant further explanation. In general, an urban plume is NOx-inhibited VOL. 40, NO. 12, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 3. Spatial distribution of contributions from mobile and point/area sources of NOx emissions. Sensitivities are normalized to the nonattainment metric. immediately downwind of the city, but as a result of dilution and/or fresh VOC emissions becomes NOx-limited farther downwind. As NOx availability is by far the single most influential parameter affecting ozone, the maximum concentration will usually occur when/where sensitivity of ozone to NOx emissions/availability is close to zero (3, 31), i.e., the region where transition from NOx-inhibited (negative ozone sensitivity to NOx) to NOx-limited (positive sensitivity) regime occurs. Either side of the peak location may have concentrations sufficiently high to affect the nonattainment metric. Therefore, the overall sensitivity of the nationwide nonattainment metric to urban NOx emissions will depend on the relative spatial/temporal coverage of the NOx-inhibited and NOx-limited sides. The overall effect of urban NOx emissions on nonattainment is too complicated to predict and will depend on VOC availability, vertical mixing, wind speed, spatial and temporal distribution of the sources along the path of the air mass, etc. (Obviously, in an NOx-limited environment such as the southeast U.S., nonattainment sensitivity with respect to NOx emissions is invariably positive.) On one hand, the NOx-limited regime may be more significant, as very close to the source ozone production is suppressed and nonattainment will not occur. On the other hand, the NOx-inhibited side could be more influential, because closer to the source precursor emissions are more 3860

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likely to affect the surface layer where nonattainment is evaluated. The overall effect also depends on the level of peak ozone concentration. On average, the air mass is likely to reach peak ozone level at about the same distance from the source (barring significant changes in wind speed, vertical mixing, or emission profiles). In other words, the spatial length of NOx-inhibited side is not a strong function of the peak level. However, if the peak level is very high (or equivalently if the nonattainment threshold is too low), the air mass will continue to contribute to the overall nonattainment metric in the NOx-limited regime for an extended length of time/space. If the nonattainment is only marginal, the NOx-limited side will be short in length, and the upwind portion (negative sensitivity) will be more important on a relative basis. Most importantly, it should be noted that the nonattainment metric is only integrated over 48 continental states. It is more likely for a portion of the NOx-limited side to fall outside the 48 states (e.g., over the ocean or in Canada). In that case, contributions from that regime (positive sensitivity) to the overall nonattainment sensitivity are diminished. It is worth noting that all grid cells with negative nonattainment sensitivities in Figure 2 are located close to bodies of water or U.S. borders. Finally, there is another potential source, albeit small, for negative nonattainment sensitivities with respect to urban NOx emissions. Most

FIGURE 4. Average (over 46 days) daily contribution of NOx emissions to the nonattainment metric in weekdays and weekends. Sensitivities are normalized to the value of nationwide nonattainment metric. advection schemes, including that used in this study, produce small numerical dispersion and cause slight overshoots and undershoots (ripples) at either tail of the advected signal. As the baseline of the signal in the adjoint field is zero, these ripples will result in small negative numbers that can get transported backward to the source regions and produce negative sensitivities. This effect is small and will be masked by the main signal; however, it could slightly exaggerate the magnitude of negative sensitivities. The nonattainment sensitivities can also be integrated on the basis of the emission source category, as shown in Table 2. Mobile and point/area sources contribute almost evenly to the NOx nonattainment sensitivities. These contributions (for NOx emissions) are in accordance with the contributions to the emissions. Figure 3 shows spatial distribution of mobile and point/area source contributions to the nationwide nonattainment (M). Point sources have largest contributions in the southeast and along the Ohio River valley, while mobile NOx emissions produce largest sensitivities in the southeastern states and California. The emission inventory used for this study distinguishes between weekdays and Saturdays and Sundays. Figure 4 shows the average daily sensitivity of total NOx emission sources for weekdays and weekends. On average, weekdays have a larger contribution, mainly a result of larger mobile emissions,

which, in turn, leads to higher concentrations, and therefore, larger adjoint variables. During this simulation period, the difference is small in the western U.S. but is significant in the NOx-limited southeastern/southern states of Georgia, Alabama, and Mississippi. The difference in the south may be coincidental and due to the fact that during this period some of the highest ozone concentrations in this region occurred on Thursdays and Fridays in the week. Implications for Interstate Transport. The power of the adjoint method lies in linking the response of the receptorbased nonattainment metric to spatially resolved input parameters such as emissions. In so doing, the adjoint method provides a direct way to identify (a) the source categories, and (b) the locations that contribute most significantly to nonattainment. The same analysis can be applied for environmental exposure or risk assessment. Furthermore, this method provides policy-makers with a robust tool to address the issue of interstate (or transboundary) transport of pollution. Figure 5 illustrates an example of such application, where states’ shares/contributions in the nationwide nonattainment, emissions, and nonattainment sensitivity are shown. There are important differences among parts a-c of Figures 5; particularly notable is that between the emissions and nonattainment sensitivities. The disparities between the three plots in Figure 5 demonstrate the nature VOL. 40, NO. 12, 2006 / ENVIRONMENTAL SCIENCE & TECHNOLOGY

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FIGURE 5. State shares (%) in nationwide (a) nonattainment, (b) emissions (NOx), and (c) nonattainment sensitivities for the duration of analysis. Values in Figure 5c are, to first-order approximation, contributions of states to nationwide nonattainment metric. of the controversy surrounding the issue of interstate transport of ozone (or other pollutants). Part of the controversy stems from the duality associated with the costs and benefits of interstate controls (32, 33). While these controls mostly benefit the states with a large share in the nonattainment metric (Figure 5a), the costs are mainly imposed on those states with largest shares in emissions (Figure 5b). Physical and chemical processes that control ozone formation and transport further complicate the issue of “responsibility” and its quantification. As a result, there is often a less than desirable correlation between the first measure of responsibility (i.e., emissions) and scientifically 3862

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more robust estimates (nonattainment sensitivities) at the state level. A closer examination of such disparities is possible in Table 3, where state ranks in terms of shares in nonattainment, NOx emissions, and nonattainment sensitivities with respect to NOx emissions are shown. For example, Alabama is ranked 11th in NOx emissions; however, its contribution from NOx emissions to the nationwide ozone nonattainment is ranked second during the simulation period. This is mostly a result of the fact that, during this period, the downwind state of Georgia had the largest share in the nonattainment metric. Conversely, Illinois has a significantly higher rank in its emissions than its contribution

TABLE 3: State Ranks in Share/Contribution to the Nationwide Metrics of Nonattainment, NOx Emissions, and Nonattainment Sensitivitiesa Alabama Arizona Arkansas California Colorado Connecticut Delaware Florida Georgia Idaho Illinois Indiana Iowa Kansas Kentucky Louisiana Maine Maryland Massachusetts Michigan Minnesota Mississippi Missouri Montana Nebraska Nevada New Hampshire New Jersey New Mexico New York North Carolina North Dakota Ohio Oklahoma Oregon Pennsylvania Rhode Island South Carolina South Dakota Tennessee Texas Utah Vermont Virginia Washington West Virginia Wisconsin Wyoming

emissions

nonattainment

sensitivity

11 16 22 2 24 43 45 7 6 37 3 9 28 20 17 8 42 39 31 5 27 25 23 36 18 40 46 35 33 13 12 38 10 19 41 4 48 21 44 15 1 34 47 14 30 29 26 32

3 4 28 2 10 29 44 15 1 36 38 30 45 23 25 22 20 31 26 42 47 13 39 37 21 6 32 34 24 14 9 40 16 12 43 5 47 8 33 11 7 18 35 19 41 17 46 27

2 8 13 1 10 33 47 22 3 31 25 15 39 23 11 12 42 38 28 32 41 5 27 29 30 17 45 37 26 36 18 44 9 6 34 21 48 14 35 7 4 24 46 19 43 16 40 20

a For each state these metrics are integrated for the duration of the episode (46 days).

to the nonattainment metric. In other words, even though the NOx emissions in the state of Illinois are considerably higher than those in Alabama, the effect of NOx emissions in Alabama on the nationwide nonattainment metric is about 10 times as large. This issue has significant policy implications. As part of the cap-and-trade program endorsed in CAIR, states may allow interstate emission trading, as the nationwide emission-based caps are gradually reduced. However, nondiscriminatory trading of the emissions between states with significantly differing contribution potentials (nonattainment sensitivities) may compromise benefits from the reduction in the nationwide cap. Also, the original caps are based on the estimated emission levels in each state, which, as shown in Table 3, are not necessarily true indicators of the influence each state has on the nationwide nonattainment metric. The question of (state) responsibility needs to be addressed in a manner in which atmospheric processes are fully accounted for. The adjoint method has the ability to link benefits

(corresponding to Figure 5a), costs (correlated to Figure 5b), and effectiveness (Figure 5c) of possible ozone control measures. The goal of this paper is to demonstrate the adjoint analysis as a scientifically robust and flexible tool to address the ultimate issue in air quality management, i.e., attainment of air quality standards. It is not the intent of the authors, nor should it be that of the reader, to draw definitive policy conclusions from the results presented here, especially since we present results only for 46 days in July and August 2004. There are limitations in this study that need to be addressed in future work. 1. The choice of the nonattainment metric should be made with thorough consideration and input from policy-makers, air quality managers, air pollution epidemiologists, and air quality scientists. However, we believe it is unlikely that the choice of the metric will have significant effect on the relative contributions from various sources/species/states. 2. The grid resolution employed in this study is coarser than that required to resolve urban areas. Continental-scale modeling of photochemistry with a detailed chemical mechanism usually entails coarser horizontal resolution than that used in urban/regional simulation. The cost of adjoint calculations also adds to the computational limitations. Nevertheless, conclusive application of this method for nonattainment studies requires finer resolution over urban areas. However, on the basis of the model performance, employing finer resolution would likely not have caused a significant change in the results presented here. 3. The results shown here are specific to the period July 1 to August 15, 2004. Ideally, one would consider a larger number of ozone episodes, encompassing a wider range of environmental and meteorological conditions. These episodes should be sufficiently long to allow long-range transport to manifest itself fully. 4. The analysis in this paper is focused on ozone nonattainment. The method can be adapted for multipollutant nonattainment sensitivity analysis and/or sensitivity analysis of population exposure or associated health risks. Such ability will be invaluable in an integrated approach toward combined nationwide ozone and particulate matter nonattainment analysis. Such extension requires development of adjoint models for aerosol processes.

Acknowledgments This work was supported by National Science Foundation award NSF ITR AP&IM 0205198.

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Received for review October 26, 2005. Revised manuscript received March 20, 2006. Accepted April 5, 2006. ES052135G