Atmosphere 2011
, 2 , 407-425; doi:10.3390/atmos2030407 

# atmosphere

ISSN 2073-4433 www.mdpi.com/journal/atmosphere

Review 

## Air Quality Response Modeling for Decision Support

Daniel S. Cohan 1, * and Sergey L. Napelenok 2

1 Department of Civil and Environmental Engineering, Rice University, 6100 Main Street MS 519, Houston, TX 77005, USA

2 U.S. Environmental Protection Agency, Research Tri angle Park, NC 27711, USA; E-Mail: napelenok.sergey@epa.gov

* Author to whom correspondence should be addressed ; E-Mail: cohan@rice.edu; Tel.: +1-713-348-5129; Fax: +1-713-348-5268.

Received: 20 June 2011; in revised form: 10 August 2011 / Accepted: 17 August 2011 / Published: 26 August 2011

Abstract: Air quality management relies on photochemical mod els to predict the responses of pollutant concentrations to changes in emissions . Such modeling is especially important for secondary pollutants such as ozone and fine par ticulate matter which vary nonlinearly with changes in emissions. Numerous techniques for probing pollutant-emission relationships within photochemical models have been developed and deployed for a variety of decision support applications. However, atmosphe ric response modeling remains complicated by the challenge of validating sensitiv ity results against observable data. This manuscript reviews the state of the science of atmo spheric response modeling as well as efforts to characterize the accuracy and uncertaint y of sensitivity results.

Keywords: sensitivity analysis; source apportionment; instru mented models; air quality modeling; review

1. Introduction

At their essence, photochemical models are tools fo r estimating the pollutant concentrations that would result from given emissions, meteorology, and other specified conditions. Those simulated concentrations are critical to forecasting future p ollution events, evaluating scientific understandin g of emission inventories and atmospheric processes, ass essing relationships between source emissions and OPEN ACCESSAtmosphere 2011
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receptor concentrations, and reconstructing atmosph eric conditions beyond the limits of available observations. The accuracy of simulated concentrati ons relative to ambient observations is a primary measure of a photochemical model’s performance [1]. However, for policy applications, it is often the r esponses of concentrations to emission changes, rather than the concentrations themselves, that mos t critically inform decision making. For example, modeling to demonstrate future attainment of U.S. a mbient air quality standards typically compares concentrations under base and proposed future emiss ions to determine the sufficiency of an attainment plan [2]. Component measures for such plans can be prioritized based on sensitivity modeling of pollutant responsiveness to various emitters [3]. O ther applications seek to apportion the origin of pollutant concentrations among precursor sources (s ource apportionment), or to quantify the benefits of a control policy. In each case, some form of atm ospheric response modeling must be used to characterize the responsiveness of concentrations t o emissions. Atmospheric response modeling is especially importa nt for secondary pollutants which form from nonlinear interactions of precursor compounds. Seco ndary pollutants such as tropospheric ozone and (secondary) particulate matter (PM) have been among the leading targets of air pollution control efforts in recent decades due to their impacts on h uman health and the natural environment [4,5]. The nonlinear formation of these pollutants [6] necessi tates considering spatially and temporally variable meteorological and chemical conditions, typically v ia three-dimensional photochemical model simulations, to predict concentration responses to emission changes [7]. Other forcings on ambient pollutant concentrations may also be of interest in policy applications, such as responses due to clim ate change and changes in land use. A major challenge in atmospheric response modeling is evaluating the accuracy of sensitivity results. While simulated concentrations can be eval uated against observations from satellites, aircraf t, and ground-based monitors, the sensitivities of con centrations to emissions are not directly observed. Dynamic evaluation seeks to evaluate concentration- emission relationships within air quality models by considering periods of substantial emission chan ges [1]. For example, studies may compare simulated and observed changes in pollutant concent rations between weekdays and weekends [8,9], or across multiple years in which substantial emission changes have been documented [10,11]. Still, evaluation of simulated sensitivities is less direc t than for concentrations, and is complicated by uncertainties in simulated emissions changes and me teorological variability. Here, various techniques that have been developed t o probe the responses of pollutant concentrations to emissions perturbations in photochemical models, and their use to inform policy applications such as control strategy development and source apportio nment are reviewed. Efforts to characterize the accuracy and uncertainty of concentration-emission sensitivity estimates are also reviewed.

2. Response Modeling Methods

A wide array of response modeling techniques has be en applied to probe relationships between concentrations and emissions in photochemical model s. Several of the most widely used methods are described here: brute-force, decoupled direct metho d, adjoint, and source apportionment.Atmosphere 2011
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2.1. Brute-Force Method

The simplest and most widely used method for charac terizing concentration response to emissions in a photochemical model is simply to rerun it with alternate emission rates. This “brute-force” (fini te difference) method computes differences between con centrations in simulations with base and perturbed rates of emissions or other parameters, t ypically with other conditions held fixed unless interactions with climate change are being investig ated. A key appeal of brute-force is its ready application in any photochemical model, without the substantial programming required to implement the other response modeling techniques. In some brute-force applications, modelers may cons truct alternate emission inventories to represent specific scenarios of interest to policy developmen t or scientific investigation. For example, scenari os may represent emission levels under control strateg ies [12], or under projected climate change [13,14]

. Other studies consider hypothetical percentage chan ges in emissions by species, source sector, or source region [15]. In those cases, it is typically assumed that the rate of concentration change per emission change can be linearly interpolated or ext rapolated to predict the impacts of emission change s smaller or larger than the level explicitly modeled . More formally, suppose concentrations C i ( x , t ) are simulated under both base ( 

## ( ) ,0 , i t E x % ) and perturbed ( 

## ( )

, , i f t E x % ) levels of the emission component of interest, where f

E % differs from 0

E % by fraction ∆

f : 

## ( ) 0 1 f f ≡ + ∆ E E % % (1) 

# ( ) 0 0 ≡ C C E % (2) 

# ( ) f f ≡ C C E % (3)
Notations for species ( i = 1,...,N), place ( x = ( x , y , z )), and time ( t ) are dropped for convenience. The brute-force method would then approximate conce ntrations

ε C under any other emission level

ε E % by linearly scaling the difference in concentration s between the perturbed and base simulations: 

## ( ) 0 1
ε ε ≡ + ∆ E E % % (4) 

# ( ) 0 0

f f ε ε ∆ ≈ + − ∆ C C C C (5)

For pollutants with a nonlinear response to emissio n rates, the accuracy of Equation 5 will tend to degrade as the fractional perturbation of interest, ∆, differs more sharply from the explicitly modeled perturbation, ∆

f . Specifically, if concentrations exhibit a saturat ing (concave down) response to precursor emissions as is typically observed for oz one, Equation 5 will tend to overestimate the benef it of emission reductions smaller than ∆ f and underestimate the benefit of larger emission r eductions, assuming an emission reduction (∆ f < 0) was simulated in the perturbation case. Howev er, the accuracy of Equation 5 is rarely examined explicitl y. Selection of perturbation levels relevant to the policy or scientific questions at hand will tend to enhance the accuracy and usefulness of brute-force results. The accuracy of brute-force sensitivities can also be improved by applying the central difference method shown in Equation 6:Atmosphere 2011
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# ( ) 0 2 f f f ε ε

− ∆ ≈ + − ∆ C C C C (6)

where f

− C are the concentrations under emission level f

− E % . However, this approach doubles the needed number of perturbation simulations, and does not address inaccuracies arising from extrapolations to input perturbations substantially larger than ∆

f . Furthermore, the brute-force method has been shown to be susceptible to numerical insta bility due to model discontinuities and roundoff errors [16–18]. Another complication of nonlinear concentration-emi ssion response is that the impacts of perturbations in multiple emission components will not be strictly additive. One approach to represent the joint impacts of simultaneous emission perturba tions is response surface modeling [19,20]. Brute-force modeling is conducted for a matrix of p erturbation scenarios, each representing different levels of perturbations in the emission components. Statistical analysis of the results is then applie d to create a response surface that estimates concentrat ions for any combination of perturbations in the emission components [19,20]. Response surface model ing was recently applied to characterize the nonlinear response of ozone to precursor emissions in China [21]. Response surfaces also have been validated to be highly accurate in “metamodeling” P M concentrations in an underlying model [20]. However, as is true for brute-force methods general ly, response surfaces require a computationally burdensome number of model simulations when many in put perturbations are of interest.

2.2. Decoupled Direct Method

Various approaches have attempted to avert the need for differencing numerous brute-force simulations by computing pollutant sensitivities di rectly within the photochemical model. Several approaches, including the coupled direct method and Green’s function method have been found to be unstable or impractical for use in comprehensive photochemical models (see Yang et al. [22] and references therein). However, the decoupled dir ect method (DDM) [23] and adjoint sensitivity analysis [24] have been shown to stably and efficie ntly compute sensitivity relationships and thus hav e been more widely implemented in three-dimensional m odels [16,17,22,25–28]. DDM operates by tracking sensitivity coefficients o f all concentrations to specified model inputs or parameters, utilizing equations derived from those representing concentrations in the underlying model to evolve sensitivities. The atmospheric diffusion equation (ADE) representing the transport and reactions of chemical compounds in photochemical mo dels can be written in simplified form as: 

## ( ) ( ) t ∂ = −∇ + ∇ ∇ + + + ∂ C uC K C R E

L (7)

where u ( x , t ) is the wind field, K ( x , t ) is the turbulent diffusivity tensor, R i ( x , t ) are the net rates of chemical production, E i ( x , t ) are the emission rates, and the ellipsis denote o ther processes represented by the model. The ADE is solved by operator splitting and is subj ect to initial and boundary conditions described elsewhere [29]. Suppose that we are interested in how concentration s vary with perturbations in targeted model inputs or parameters P j ( x , t ), which may be perturbed from their unperturbed va lues P j by scaling factors  , analogously to Equation 4:Atmosphere 2011
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# ( ) 1 j j j j j p P P ε ε = = + ∆ (8)

Since our interest here is in sensitivities to emis sions, note that each parameter p j is equivalent to an emission component E

% in the notation of the previous section. Semi-normalized sensitivity coefficients ( ) 

## ( ) 1

, , i j t S x of concentration response to p j are developed by scaling non-normalized local sensitivity coeffic ients ( ∂ C /∂P j ) by the unperturbed value P j of the parameter:

( ) 

# ( ) 1 j j j

j j

j j P P p P ε ε ∂ ∂ ∂

= = = ∂ ∂ ∂ C C C S (9)

This semi-normalization simplifies calculations by placing sensitivity coefficients into the same unit s as concentrations. For the case of sensitivity to e mission rates, DDM computes the evolution of ( ) 1 j S by substituting Equation 9 into Equation 7, yielding t he equation below [22,27]:
( ) ( ) 

# ( ) ( ) 

# ( ) ( ) 1 1 1 1 j j j i j j t ∂ = −∇ + ∇ ∇ + + + ∂ S uS K S FS E %

L (10)

where F is the Jacobian matrix ( / ik i k F R C = ∂ ∂ ) and j

E % is the base level of the emissions inventory component represented by sensitivity parameter p j . Alternate terms for representing sensitivities to parameters other than emissions, as well as initial and boundary conditions for Equation 10, are described in other references [22,26]. DDM is a dec oupled approach in that for each process sensitivities are updated separately from, and afte r, concentrations. Slightly different approaches have been taken to im plement Equation 10 in air quality models. The original DDM formulation of Dunker [23,30] appl ies the same algorithms and internal time steps for chemistry in Equations 6 and 9, whereas the “DD M-3D” variation of Yang et al. [22] factorizes the Jacobian only once per advection time step. The for mer approach maximizes the accuracy and consistency of sensitivity results, whereas the lat ter enhances computational efficiency. Nevertheless
, successful implementations of both DDM [26,31] and DDM-3D [18,22,25,27,31,32] in state-of-the-science photochemical models have been validated to yield c omputational savings and consistent results relative to brute-force. A key distinction between DDM and brute-force is th at DDM predicts local sensitivity coefficients

j ε ∂ ∂ C , representing responsiveness to infinitesimal chan ges in a parameter, whereas brute-force predicts

responses to finite changes,
ε ∆ ∆ C . Just as the accuracy of brute-force results may d egrade as
interpolated or extrapolated beyond the explicitly modeled perturbation level, linear scaling of local first-order DDM sensitivities may poorly represent the nonlinear impacts of large perturbations. Thus, for highly nonlinear relationships, first-order DDM results can be applied reliably only to characteri ze local responsiveness or the impacts of small pertur bations. Hakami et al. [27,33] showed that the applicability of DDM can b e greatly expanded by incorporating second-order sensitivity coefficients . Their High-order Decoupled Direct Method (HDDM) extended the DDM-3D algorithms to compute se cond-order or even higher-order sensitivityAtmosphere 2011
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coefficients. Second-order self-sensitivity coeffic ients ( ) 2 2

, 2 j j j ε ∂

= ∂ C S represent the curvature of concentration

response to a single parameter, whereas cross-sensi tivity coefficients ( ) 2 2

, j k j k ε ε ∂

= ∂ ∂ C S characterize how

sensitivity of concentrations to one parameter chan ges as a second parameter is varied. Validation tests confirmed the consistency of HDDM and brute-force finite differencing in estimating second-order local sensitivities [27,33] . More significantly, Hakami et al. showed that Taylor series expansions incorporating first- and s econd-order HDDM coefficients via the equation below can reliably predict ozone response to simult aneous large percentage (e.g., 50%) changes in multiple parameters [27,33]:

( ) ( ) ( ) ( ) ( ) 2 2 1 1 2 2 2 , 0
, 2 2 j k j k

j j k k j k j k j k ε ε ε ε

ε ε ε ε

∆ ∆ ≈ + ∆ + ∆ + + + ∆ ∆ C C S S S S S (11)

where

,

j k ε ε C denotes concentrations when parameters P j and P

k are perturbed by fractions j ε ∆ and

k ε ∆ respectively. Cohan et al. [25] showed that Equation 11 could even be extende d with reasonable accuracy to predict the ozone impacts of zeroing-ou t individual emission sources ( i.e. , 1 j ε ∆ = − ), providing results closer to source apportionment. W hile studies applying Equation 11 with HDDM for ozone have proliferated (e.g., [34–36]), no publish ed study has yet extended DDM to second-order for PM, although such an extension was recently describ ed in a conference presentation [37]. The majority of DDM applications have focused on th e response of pollutant concentrations to emission changes. These include quantifications and optimizations of emission control strategy impacts
, in some cases linked with consideration of control costs [38], health effects [39], or climate change [40]. Hakami et al. [33] showed that HDDM coefficients could be applie d to generate isopleths of ozone response to simultaneous changes in VOC and NO x emissions. DDM-computed sensitivities to emissions have also been applied through a variety of approaches to conduct inverse modeling of emission inventories [41–43]. Sensitivities to reac tion rate constants have been applied to assess key reactions and uncertainties in the chemical mechani sms that drive air quality models [44,45]. All of these applications, though achievable using brute-f orce methods, benefitted from the ability of DDM to efficiently compute sensitivities to numerous input parameters.

2.3. Adjoint

Brute-force and DDM each compute the sensitivities of all model outputs throughout the domain to specified model inputs and parameters. Thus, they a re well-suited for characterizing how concentrations or deposition amounts everywhere are impacted by a limited number of changes in emissions or other parameters of interest. However, for some applications, it may be desired to probe how specific model outputs are influenced by numero us model parameters. For example, one may seek to probe how pollutant concentrations or deposition rates at a single monitor are influenced by many model parameters, or how a spatially aggregated met ric of pollutant conditions is influenced by numerous emitters. As the number of emitters or inp ut parameters of interest grows, it would quickly become cumbersome to compute forward sensitivities to each parameter.Atmosphere 2011
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For cases such as these, an adjoint of a model prov ides an efficient method for calculating sensitivity of a few model outputs to numerous mode l parameters. Adjoints have been implemented to some extent in several modern regional and global p hotochemical models including CMAQ [16], CHIMERE [46], STEM [47], GEOS-Chem [17], and others . Adjoints of atmospheric models have been used in a variety of applications including at tainment studies of ozone in specific airsheds as w ell as for ozone and PM 2.5 on continental scales [28,48,49]; inverse modeling of black carbon based on ground and ship measurements [50]; long-range trans port of ozone [51] and black carbon [52]; and data assimilation of ozone and NO x measurements [47]. Mathematical description of an adjoint is simplifie d by introducing the forward tangent linear model (TLM), which is analogous to the formulation of DDM (Equation 10). Both DDM and TLM refer to the forward method for calculating sensiti vity because the perturbation is carried forward through the various model processes and in time. The ADE in operator form would be: 

## ( ) = C M p (12)
where the model output vector C is a function of the model input parameter vector p , and M is the operator matrix representing the combination of all processes in the model. Analogously, TLM (Equation 10) in operator form can be written as: 

## ( ) δ δ = C L p (13)

where L is the Jacobian of the model operator. Furthermore , specific adjoint applications require the definition of a scalar function, J , based on model outputs as:



## ( ) J J = C (14)
In a simple application of calculating a sensitivit y field of species i , J = c i , whereas in a more complex scenario of inverse modeling, J can be a cost function dependent on the difference between modeled and observed values, the difference between initial and perturbed parameters, the observation error covariance matrix, and possibly other terms [ 17]. The goal of the adjoint would then be to efficiently determine ∂J

/ ∂ p , or ∂c i / ∂ p in the simplest case. Similar to DDM sensitivities (Equation 9), it is po ssible to define the adjoint variable   as:

i i J

p λ ∂

= ∂ (15)

Then the adjoint can be defined by applying Lagrang e multipliers to Equation 10 and integrating by parts by taking into account its initial and bounda ry conditions [47] as: 

## ( ) ( ) T i i i i i t λ λ λ λ φ ∂ = −∇ − ∇ ∇ − − ∂ u K F (16)

where i φ is the forcing term dependent on specific applicat ion and the definition of J

. In practice, adjoint functions are applied to each model process in sequence, including advection, diffusion, chemistry, and aerosol processes. Two me thods exist for adjoint implementation. If the underlying functions describing a particular proces s are differentiable and can be used directly, then a continuous adjoint for that process is possible. A continuous adjoint for a particular process isAtmosphere 2011
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constructed by differentiating the underlying mathe matical equations first and then discretizing the adjoint equations of solution. On the other hand, i f such calculations are too cumbersome or impossibl e due to the complexity of the process, then the proc ess can be numerically discretized first and later differentiated to obtain a discrete adjoint. The ad vantage of the continuous adjoint is that it obtain s an exact solution that may be more useful in interpret ing the results, because it represents a physical time-dependent sensitivity behavior and explicitly assures numerical stability [53]. In contrast, a discrete adjoint may exhibit instability and yield a solution inconsistent with the forward model [54]

. However, the attraction of a discrete adjoint is th at it can often be derived using automatic differentiation tools that process the forward mode l code directly. Furthermore, discrete adjoint resu lts may be more easily validated, because the resulting gradients do not differ from the actual gradient o f the numerical cost function as can be the case with continuous adjoints [17]. In practice, both approaches are frequently used for an adjoint imple mentation within a particular forward model that is solved using operator splitting, where one method m ay be used for transport processes and another for chemistry. Hakami et al. [48] demonstrate a potential regulatory applicatio n of adjoint modeling to calculate sensitivities of a nationwide U.S. ozone national a mbient air quality standard (NAAQS) to precursor emissions of NO x and VOCs. The sensitivities are presented varying in space and time to provide a fully resolved source/receptor relationship for mod eled ozone nonattainment. Source categories and locations with the greatest impact are quickly iden tified as potential targets of control strategies.

2.4. Source Apportionment

Source apportionment seeks to quantify the contribu tions of various emission sources from specific geographic areas or emissions sources to pollutant levels at particular locations. While source apportionment in photochemical models may be conduc ted by a brute-force method zeroing out sources one by one, this may become computationally prohibitive if many emitters are of interest. Thus, a host of tools has been implemented to enabl e more efficient probing of source apportionment relationships in air quality models. Here, we focus solely on model-based source apportionment techniques, not on the wide array of observation-ba sed source apportionment techniques such as chemical mass balance and positive matrix factoriza tion [55] that characterize source contributions based on ambient data. Apportioned fractions of species are typically trac ked separately from base concentrations with the specific intent to not alter base model predictions . Source apportionment methods are typically less computationally costly than zero-out brute-force si mulations, but can be limiting in that they only tr ack a subset of all possible source and species combina tions. Typically, end-point pollutants include eith er ozone or various chemical components of particulate matter, but rarely in the same model. These method s consider secondary formation from precursor emissio ns of nitrogen oxides (NO x = NO and NO 2 ), volatile organic compounds (VOCs), sulfur dioxide ( SO 2 ), and ammonia (NH 3 ), in addition to primary emissions of the tracked species. Usually, boundary and initial conditions are also tracked separately

. Various approaches have been taken in recent years to develop source apportionment methods. These methods are generally designed to provide inf ormation of pollutant formation from predefined geographic regions and/or chemical precursors. One approach for resolving emissions sourceAtmosphere 2011
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attribution for PM species is to model the particle s as an explicit external mixture while preserving source information [56]. In this method, particulat e matter precursors from each source are injected into the model separately and their identity is pre served as they undergo the various physical and chemical transformations. Modifications to the unde rlying chemical mechanism and the accompanying solver are required to accommodate precursor specie s duplication. A similar approach has been demonstrated for resolving ozone formation from tag ged VOC sources [57]. Again, modifications to the chemistry module are required, but in this case , tracking contributions of different emissions sources to concentrations of various VOCs, alkoxy r adical (RO), peroxy radical (RO 2 ), and hydroperoxyl radical (HO 2 ) is considered. These species dictate the conversi on rate of NO to NO 2 , which in turn is used as the indicator for ozone fo rmation. Source apportionment implementation for PM and ozon e is complicated by the interaction of second-generation products from explicitly tagged p recursors with one another. Such cases are typically handled on a reaction by reaction basis a nd the products are attributed to sources according to the linkage established through their molecular str ucture. Source oriented methods are computationally demandi ng, because they greatly increase not only the number of species transported by the model, but als o the computational burden involved in solving a larger number of potentially stiff differential equ ations governing gas and aerosol chemical interactions. However, preserving emissions informa tion through the model helps to overcome one of the main challenges of source apportionment, which is accounting for the highly nonlinear and time variant nature of secondary pollutant formation. Co mputationally lighter versions of this method track only a subset of species. For example, the carbon a pportionment model has been used as a diagnostic tool to track sources of chemically inert particula te organic and elemental carbon [58,59]. Other source apportionment techniques rely on simpl ifying assumptions to reduce the size of the numerical problem. For example, the ozone source ap portionment technology (OSAT) [60] implemented within the Comprehensive Air quality Mo del with extensions (CAMx) [61] groups emissions of NO x and VOCs from each tracked source together with th e corresponding ozone formed as the result of these emissions into families, and tracks these families through the various processe s in the air quality model. OSAT adds the flexibility of apportioning ozone to NO x emissions in addition to VOCs, and does so by determining NO x - or VOC-limiting ozone formation regimes on the ba sis of the ratio of the production of peroxide (H 2 O 2 ) to the production of nitric acid (HNO 3 ) [62]. At ratios above 0.35, the ozone formed is assigned to emissio ns of NO x , and at ratios below 0.35 the ozone formed is assigned to emissions of VOCs. This metho d still accounts for different VOC reactivity as do the explicit tracking methods, but may have some limitations during instances where ozone is titrated through reaction with NO near large emissi ons sources of NO x , since instantaneous negative apportionment is not possible. As a variation on OSAT, the anthropogenic precursor culpability assessment (APCA) [61] has been implemented in the CAMx model. APCA functions simil arly to OSAT, but reallocates the ozone production that was attributed to non-controllable sources to the controllable precursor that participated in its formation. For example, in a si tuation where OSAT would attribute ozone production to biogenic emissions of VOCs, APCA woul d reassign the attribution to anthropogenic NO x even under VOC-limiting conditions. As such, this method biases towards assigning more ozone formation to NO x

emissions, in order not to assign culpability to p resumably non-controllable biogenics.Atmosphere 2011
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Also stemming from the development of OSAT in CAMx is the particulate matter source apportionment technology (PSAT) and its complement, online particulate source apportionment (OPSA) [63]. Both of these methods track primary an d secondary PM components by making the simplifying assumption that each secondary componen t links directly to one specific precursor. For example, NO x emissions lead directly to formation of particulat e nitrate. Secondary effects, such as the nonlinear chemical and thermodynamic interactions b etween species are considered through the behavior of the bulk, non-apportioned species based only on the equilibrium assumption. Both PSAT and OPSA start with the gas-phase OSAT implementati on to which PM relevant reactions are added. PSAT differs from OPSA in that it apportions the tr ansport of the tagged species based on fluxes of th e bulk in an offline way, instead of transporting the tagged species themselves as in OPSA. This introduces some error to the system, since the PSAT attributes the fluxes linearly to save on computational time spent on transport routines. The CMAQ model also has implemented methodology for particulate source apportionment in the way of tagged species source apportionment (TSSA), which tracks precursors to aerosol sulfate, nitrate, ammonium, elemental carbon, secondary orga nic aerosol, and other aerosol species [64]. Similar to the PSAT implementation in CAMx [63], th is method also applies information from bulk species for most model transformations to the tagge d species. However, gaseous chemistry is described more explicitly by modifying the underlying chemica l mechanism and adding chemical tracers relevant for aerosol formation. TSSA also employs m ass normalization routines that ensure mass conservation, as do OSAT, APCA, and PSAT. This is d one by introducing an “other” source category automatically as a tracer in addition to user speci fied geographical and chemical precursor sources. An important consideration for interpreting results of any air quality source apportionment method is that there is no unique true answer to attributi ng pollutant concentrations to precursor sources. T he contributions of various sources may not be strictl y additive, since photochemical regime and pollutan t responsiveness may change as emission rates vary. T he emission source assigned the greatest zero-out source contribution may not necessarily yield the m ost benefit from its incremental control, and its contribution may vary as other sources are controll ed. However, source apportionment results still provide a wealth of information for the purpose of control strategy development or culpability assessm ent. Other drawbacks of source apportionment techniques come from the fact that these methods try to strike a balance between computational efficiency a nd explicit treatment of all science processes done by the base model. Ozone source apportionment techn iques frequently make use of various assumptions to calculate whether or not the ozone p roducing regime is either NO x - or VOC-limited. Apportionment of inorganic particulate species is f requently done by ignoring or simplifying thermodynamic interactions between PM species. Most of the described apportionment techniques assume that secondary PM components are linked dire ctly to one precursor species. For example, secondary sulfate is traced back only to SO x emissions. Therefore, these methods are unable to capture indirect effects such as the replacement of ammoniu m sulfate with ammonium nitrate that sometimes accompanies reductions of SO 2 emissions [65], or the influences of atmospheric o xidants and their precursors on secondary organic aerosol formation [ 66]. Similar to the other response models discussed, sou rce apportionment techniques aim to generate additional information about one or more modeling e pisodes that could be used to test changes to the forcings behind the model resolved state of air qua lity without the need for additional simulation. On eAtmosphere 2011
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such application is detailed by Baker and Foley [67 ]. In their approach, the CAMx model with PSAT is used to estimate annual sulfate and nitrate formati on from emissions of precursors from 99 power plants in the eastern United States. Emissions from these plants were manually perturbed, and the apportionment model repeated to arrive at brute-for ce sensitivity of source apportionment. Finally, a nonlinear regression model was used to describe the relationship of downwind particulate matter concentrations to emissions strength and distance f rom source. This hybrid formulation of two response techniques (brute-force and PSAT) together with a statistical model allows for quick approximation for impacts of varying emissions at p articular facilities or siting a new facility in th e modeling domain.

3. Accuracy and Uncertainty of Atmospheric Response Estimates

Given the critical role of atmospheric response mod eling in informing air quality decision-making, the accuracy and uncertainty of response estimates are important to examine. All of the instrumented modeling techniques above can be validated against the forward model response to ensure that they faithfully represent pollutant-emission response wi thin the underlying model. Most validations of DDM have shown it to be highly accurate in capturin g pollutant response to small-scale emission changes. The extent local sensitivity coefficients can predict large-scale response depends on the nonlinearity of pollutant formation under the condi tions at hand; in some situations, first-order sensitivities may be sufficient to predict response for up to ±30% changes in emissions [31,68], whereas Taylor expansions including second-order HD DM coefficients can allow accurate representation of ozone response to domain-wide emission reduction of at least 50% [25,33]. Such validations assess whether a response modeling technique is reliably capturing relationships within the underlying model, but do not address the accuracy of the model itself in representing actua l atmospheric response to emission changes. Simulated pollutant concentrations are routinely evaluated against observations [1], but pollutant-emission se nsitivities are not directly measured. While consistency of simulated and observed concentration s lends confidence to model performance, it does not guarantee the accuracy of sensitivity and sourc e apportionment results. Different models or alternate settings of a single model can achieve si milar performance for pollutant concentrations despite yielding markedly different predictions of pollutant-emission response [44,69,70]. Thus, there is growing interest in the use of observational dat a to infer pollutant responsiveness to emission changes and thereby ground truth modeled sensitivit y results. The approaches described in the following three paragraphs—dynamic evaluation, obse rvational indicator ratios, and receptor-based source apportionment—provide informative though imp erfect gauges of response modeling accuracy, as each of these methods entails its own set of ass umptions and simplifications. Dynamic evaluation assesses the ability of models t o represent changes in pollutant concentrations resulting from changes in emissions or other condit ions [1]. For example, differences in pollutant concentrations on weekdays and weekends can be used to assess their responsiveness to weekly patterns in emission rates [8,9,71]. Other dynamic evaluation studies have considered how pollutant levels have responded to long-term trends in emissi on rates, such as those resulting from major emission control policies [10,11,72]. In each case, a key challenge is to accurately characterize the changes in emission rates and meteorological condit ions across the periods of interest, so that theAtmosphere 2011
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pollutant response can be effectively isolated. How ever, since characterizations of emission trends an d meteorology are inevitably imperfect, dynamic evalu ation cannot definitively determine whether mispredicted trends in concentrations arise from those imperfections or from errors in a model’s responsiveness. Another check on modeled sensitivities is provided by observational indicator ratios, which consider ambient measurements of various species to infer how ozone or secondary PM was formed. For example, ratios of species concentrations such as O 3 /NO y (NO y = NO x and its oxidation products) and H 2 O 2 /HNO 3 have been found to be effective indicators of whet her ozone formed under NO x - or VOC-limited conditions [62,73]. More quantitative e stimates of ozone responsiveness to NO x emissions can be obtained from ozone production eff iciency metrics, which quantify the number of ozone molecules produced per molecule of NO x consumed [74]. For PM, the observed ratio between free ammonia and total nitrate concentrations may i ndicate whether formation of wintertime nitrate is limited primarily by NO x or ammonia emissions [75]. Such indicator ratios a lready have a role in some source apportionment methods, but could be used fur ther for evaluation purposes. For source apportionments, various receptor-based m ethods such as positive matrix factorization and chemical mass balance have been developed for a pportioning PM based on observations of its constituent compounds [76–78]. Some studies have at tempted to compare PM source apportionments derived from receptor-based and emission-based mode ls [79], or to develop hybrid approaches combining the two methods [80]. Whereas source sign atures can be inferred from speciated PM data, such approaches are, of course, inapplicable to ozo ne and other individual gases. Apart from comparisons with observational data to g auge accuracy of response modeling, a separate line of efforts has sought to characterize the unce rtainty in response modeling that arises due to uncertain model inputs and formulations. Parametric uncertainties result from uncertain model input data and parameters, whereas structural uncertainti es result from imperfect numerical formulations of physical and chemical processes [81]. Most studies conducted numerous brute-force runs with Monte Carlo sampled inputs to characterize changes in pol lutant-emission sensitivities resulting from change s in uncertain inputs [82–84]. More recent studies ha ve introduced methods utilizing HDDM and adjoints for more efficient uncertainty characteriz ation [85–88]. In either case, Bayesian approaches could be applied to use observational data to asses s the relative likelihoods of various plausible simulations and thereby refine uncertainty estimate s [89,90].

4. Discussion

The use of response modeling methods in air quality management has increased over recent years partly due to significant improvements to the compu tational capacity of management agencies, and partly due to the need to find more creative contro l strategies in response to lower air quality stand ards. While new probing tools continue to be introduced a nd refined, a growing number of publications apply existing techniques to new air quality challe nges. As applications of response modeling proliferate th rough a wider community of users, care must be taken to ensure that the methods are applied and in terpreted in an effective manner. The use of brute-force methods tends to be straightforward. Mo re complex methods such as DDM or adjoint modeling typically require more extensive validatio n to ensure that results are consistent with theAtmosphere 2011
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forward model, both to protect against possible cod ing errors as well as to check the method’s performance in a new photochemical regime. For all methods, proper interpretation of results is crucia l. For example, extrapolations of local sensitivity co efficients or interpolations of large-scale impacts can introduce error when response is highly nonlinear. There may also be important interactions between responses not captured by sensitivities to individu al parameters. Response surface modeling and high-order sensitivity coefficients can each provid e accurate results across a range of emission perturbations, but can be more complex to apply tha n other methods. The results of multiple response modeling methods c an be highly complementary. For example, source apportionment computes the impacts of entire emission sources, whereas DDM characterizes sensitivities to incremental perturbations. Neverth eless, most studies apply only a single response modeling method, despite a handful of studies that have rigorously compared multiple methods [91,92]. Zhang et al. [92] showed that first-order DDM effectively simul ated ozone response to NO x and VOC emission changes of less than 40%; OSAT was better able to simulate source apportionment ( i.e. , 100% emission reductions), but its non-negativity failed to represent VOC-limited regions where reductions in NO x may lead to increases in ozone concentrations. Koo et al. [91] compared the results of brute-force, PSAT, and DDM characterizations of particulate matter sensitivity and source apportionment. They found that first-order DDM coul d simulate responses of inorganic secondary aerosols to emissions perturbations of 20% or more, and of organic and primary aerosols to up to 100%. PSAT yielded similar results to zero-out source app ortionment in most cases, but did not account for indirect effects such as when removal of an SO 2 emitter frees up oxidants to react with SO 2 from other sources. The response modeling methods reviewed here charact erize the responses of pollutants to emission changes, but do not necessarily explain the physica l or chemical causes of those responses. Other techniques such as process analysis [93] characteri ze the contributions of various physical and chemical processes to pollutant concentrations and formation and destruction rates. Process analysis has been applied most frequently to quantify the pr ocesses influencing tropospheric ozone [94–96]. Additional insights into the causes of atmospheric response can be gleaned by substituting alternate mechanisms or parameterizations in air quality mode ls. Ultimately, response probing methods can perform only as well as the underlying model, s o ongoing improvements to the physical and chemical representations in atmospheric models, and the scientific understanding that underpins them, remain paramount.

Acknowledgements

The work of Cohan was supported by National Science Foundation CAREER Award Grant 087386. Although this manuscript has been reviewed and appr oved for publication, it does not necessarily reflect the policy or views of the U.S. Environment al Protection Agency. The authors would like to thank Kirk Baker for helpful input on the manuscrip t.Atmosphere 2011
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