Developing estimates of the social costs of air pollutants and their uncertainty using Reduced Complexity Models (RCM)

Elisabeth A. Gilmore1,*, Jinhyok Heo2, Nicholas Z. Muller3, Christopher W. Tessum4, Jason D. Hill5, Julian D. Marshall4, Peter J. Adams6

1. Department of International Development, Community, and Environment. Clark University,

Worcester, MA., USA. gilmore@clarku.edu, 1-508-793-7292 2. Center for Atmospheric Particle Studies, Carnegie Mellon University, Pittsburgh, PA, USA

3. Tepper School of Business / Department of Engineering and Public Policy, Carnegie Mellon

University, Pittsburgh, PA, USA & National Bureau of Economic Research, Cambridge, MA, USA

4. Department of Civil and Environmental Engineering, University of Washington, Seattle, WA, USA

5. Department of Bioproducts and Biosystems Engineering, University of Minnesota, St. Paul, MN, USA

6. Department of Civil and Environmental Engineering / Department of Engineering and Public Policy, Carnegie Mellon University, Pittsburgh, PA, USA

WORKING PAPER

DO NOT CITE WITHOUT AUTHOR PERMISSION

This paper has been prepared for the Harvard Center for Risk Analysis “Risk Assessment, Economic Evaluation, and Decisions” workshop, September 26-27 2019

Abstract

Reliable estimates of externality costs—such as the costs from premature mortality from exposure to fine particulate matter (PM2.5) —are critical for policy analysis. To facilitate the consideration of the social costs of air pollution, several datasets of social costs of air quality have been produced by a set of “reduced complexity models (RCMs)," which are easier to use than the ‘state of the science' chemical transport models (CTMs). Here, we show how these models and the social cost datasets were developed and compare them to the conventional approach to air pollutant valuation. We then discuss examples of how and when to use these models for policy analysis and demonstrate how these models can be combined into ensembles for uncertainty analysis. We conclude with recommendations on how to use the RCMs for policy analysis.

1. Introduction

For air pollution, adverse human health effects – especially premature mortality from exposure to ambient concentrations of fine particulate matter (PM2.5) – result in high costs to society (United States Environmental Protection Agency (U.S. EPA), 2009). When conducting a benefit-cost analysis of rules and regulations related to the abatement (or increase) of air pollutants, it is critical to account for costs that are observed in the market as well as non-market costs, known as externalities (Baumol & Oates, 1988). To estimate these costs in its regulatory analyses, the U.S. EPA has generally employed an impact pathway assessment. This multi-step approach is as follows: first, Chemical Transport Models (CTMs) are used to estimate the impact of emissions on ambient concentrations; second, the health effects from exposure to these concentrations are quantified using concentration-response (C-R) functions; and finally, the health impacts are monetized. For premature mortality, an estimate of the willingness-to-pay to avoid this impact, known as the value of a statistical life (VSL), is used to monetize these impacts. Presently, the U.S. EPA employs a central estimate of 7.4 million in 2006 USD (U.S. EPA, 2010).

While these benefits generally exceed the costs of the abatement, characterizing, and

communicating uncertainty in these benefits is critical for sound policy (Morgan & Henrion, 1992; National Academy of Sciences, 2002). For the economic valuation of the benefits of abated air pollution, the USEPA regularly conducts an uncertainty analysis on several of the parameters in its valuation approach, namely the strength of the relationship between exposure and human health effects and the magnitude of the value of a statistical life (VSL). Uncertainty in the CTMs that transform the emissions to their equivalent ambient concentration is rarely addressed in a comprehensive manner. It is often argued that the uncertainty in the CTM is less than the uncertainty in the other parameters. However, analyses on the relative importance of uncertainty of the air quality model are not conducted as it is difficult to assign quantitative estimates to the uncertainty in the air quality model since individual models are mechanistic (e.g., Fraas & Lutter, 2013). Further, a multi-model effort could be impractical for any given regulatory analysis due to time constraints. This is in part because CTMs are the ‘state-of-the-science’ tool for predicting how much PM2.5 is formed from a given set of emissions, but the complexity of these models limits their applicability.

To improve the availability and accessibility of air quality modeling and cost estimates, the air

quality research community has produced a set of new models, known as reduced-complexity air quality models (RCMs) and associated sets of marginal social costs, i.e., monetized damages per pollutant (in USD per tonne of emission). Presently, there are three RCMs and their datasets that provide estimates of externality costs from air pollution: the Air Pollution Emission Experiments and Policy (APEEP) model (Muller & Mendelsohn, 2007) updated to AP2 (Muller et al., 2011) and now AP3 (Clay et al., (2019), the Estimating Air pollution Social Impacts Using Regression (EASIUR) model (Heo et al., 2016a; 2016b), and the Intervention Model for Air Pollution (InMAP) (Tessum et al., 2017). We select these three RCMs as they provide comprehensive

estimates covering the entire continental United States (U.S.) at relatively high spatial resolution (county-level or finer). As the three RCMs take fundamentally different approaches to the air quality modeling, they may be understood to produce largely independent estimates. Hence, comparing and quantifying the differences between the independently derived estimates of social costs from the RCMs also provides an indication of the uncertainty of how emissions are transformed into ambient concentrations. For example, using these models, we show that while the uncertainty in the air quality model is likely less than the other C-R function and VSL when aggregating values (e.g., reporting benefits at a national level), these uncertainties are more meaningful when considering the distributions of exposures and developing abatement policies to best address these exposures.

In this paper, we outline several sources of uncertainty in the air quality modeling and highlight

when and how it can make a difference in the analysis by leveraging the social cost datasets from the three RCMs. First, we review the sources of uncertainty in the impact pathway assessment, focusing on the elements in the air quality modeling and why they matter. Second, we describe the RCMs and review a model inter-comparison conducted in Gilmore et al. (2019) that shows their performance. Third, we show three examples of how these data can be used to evaluate uncertainty in the model and policy applications. We conclude with recommendations for these use of these models for the characterization of uncertainty. We restrict our analysis to PM2.5 as this species accounts for the majority of the premature mortality and thus, dominates the social cost. Characterizing and communicating uncertainty would improve the analyses that use social cost estimates (Morgan & Henrion, 1992; National Academy of Sciences, 2002). The purpose of outlining the major sources of variability and uncertainty is to make them available to the analysts who employ these social cost estimates and thus, to encourage the consideration of these dimensions and the influence in any given analysis.

2. Review of air quality modeling for economic valuation for air pollution and policies

In Figure 1, we show the impact pathway assessment for the valuation of air pollution. Importantly, each stage of this calculation imparts some uncertainty into the damage estimation: emission rates vary based on technologies and performance, dispersion and chemical transformation depend on meteorological conditions, and populations move throughout time. Further, individual responses to exposure are heterogeneous, and the value associated with risks to health depends on both observable traits (income) as well as unobservables such as innate risk preferences. It is computationally impractical, and in some cases ethically indefensible to model the full heterogeneity associated with each of these parameters. Thus, modelers typically employ sample averages (Muller, 2011; USEPA, 1999; 2011). As we will show empirically, at a national level, the analysis of the benefits is robust to the uncertainty in the air quality modeling efforts. However, this is not to imply that the models produce identical damage estimates. As the subsequent empirical analysis will show, the models indeed differ in their predictions of the cross-

sectional distribution of damage estimates. The critical difference emanates from the models’ treatment of the fate and transport of emissions. So, while there are numerous sources of uncertainty and variability in the models’ damage estimates, that which is crucial to the difference in relative damage estimates (e.g., applying the same C-R function and VSL to the same population with the same emission inventory) is the air quality modeling.

Figure 1: Impact pathways approach to developing social cost for air quality

Here, we review the chemistry and physics that describe the formation of PM2.5. We focus on

the main sources of uncertainty in the scientific knowledge that affect the fidelity by which the models can predict ambient concentrations from emissions. PM2.5 is a complex mixture of chemical species from diverse sources. Species emitted directly as PM2.5, such as primary elemental carbon (PEC), are referred to as “primary” species. However, most of the PM2.5 mass consists of “secondary” species, such as sulfate (SO4

2-), nitrate (NO3-), ammonium (NH4

+) and secondary organic aerosols (SOA) that are produced from chemical or physical transformations of gaseous precursors after being emitted and transported away from the source. The importance of secondary PM2.5 components underlines the need for a model to represent the atmospheric chemistry that governs PM2.5 formation.

First, for all pollutants, uncertainties in atmospheric transport, dispersion, and removal will affect the results. For species emitted as primary PM2.5, these processes will account for much of the observed differences. The two primary species that contribute most to the mass of the ambient concentrations are elemental carbon (PEC) and primary organic aerosol (POA). PEC is inert and non-volatile and is formed from the combustion of carbonaceous materials and broadly refers to the same material as "black carbon," although there are important differences in both definitions and measurements approaches. Until recently, POA was also treated as inert and non-volatile in models, but recent evidence strongly questions these assumptions (Robinson et al., 2007). POA consists of a complex mixture of different organic compounds; some of these compounds are more

volatile (i.e., have higher vapor pressures) and do not remain in a solid form. A significant fraction of directly emitted POA may evaporate upon dilution to cleaner atmospheric conditions (Lipsky & Robinson, 2006; Shrivastava et al., 2006). Some evaporated POA is expected to return to the particle phase after gas-phase oxidation, partly compensating for the evaporation (Robinson et al., 2007). Not all air quality models account for these processes, which themselves are subject to considerable uncertainty. As a result, current emissions inventories and models may overestimate the impact of POA on PM2.5 by assuming that some part of the POA is inert.

For secondary species which comprise about 50% of the mass of PM2.5, the chemistry is also an important source of uncertainty. Results for all secondary pollutants depend on how efficiently precursors are converted to and partitioned between gas and PM2.5 mass. The major inorganic components of PM2.5 are sulfate (SO4

2-), nitrate (NO3-) and ammonium (NH4

+), which form from emissions of sulfur dioxide (SO2), nitrogen oxides (NOx) and ammonia (NH3), respectively. Interactions between these species make it challenging to evaluate the impact of SO2, NOx, and NH3 emissions on atmospheric PM2.5. First, models must represent the efficiency with which the gas-phase precursors, SO2 and NOx, are oxidized to sulfuric and nitric acids, respectively. Second, because these two acids compete for available NH3, the resulting PM2.5 mass depends nonlinearly on the levels of all three (Ansari & Pandis, 1998; West, Ansari, & Pandis, 1999). Errors in the emissions and chemistry of any of these species necessarily affect the simulation of the others and the complex interactions among the components can make this chemistry challenging to represent in a reduced complexity model. Often, PM levels are most sensitive to just one of the pollutants, such that the social costs may be near zero in some conditions while very high in others. For example, in some cases, the effect of sulfate reductions on PM2.5 mass is canceled out by increasing in nitrate, leading to little or no change in PM mass (Pinder, Adams, & Pandis, 2007). Thus, establishing social costs requires that models correctly average over these different chemical regimes, which can shift on a daily timescale. Finally, the fact that sulfur emissions have been reduced more effectively than NOx or NH3 means that the contribution of these last two to PM has become more important over recent years, a trend that is expected to continue. Estimates for the social costs of SO2, NOx, and NH3 emissions will, therefore, need to be updated accordingly (Pinder et al., 2008; Holt et al., 2015).

For secondary organic aerosol (SOA) formation, the complex and poorly understood

atmospheric organic chemistry hinders our ability to map precursor emissions into organic PM2.5 formation. Therefore, damage estimates associated with VOC emissions must be viewed as inherently more uncertain than inorganic PM2.5 and its precursors. While our understanding of organic PM2.5 formation is advancing rapidly, there is an inevitable lag between fundamental understanding and its incorporation into the air quality models and the resulting cost estimates. All VOCs are not equal in terms of the formation of SOA, and VOC emissions may not be a good indicator of SOA formation. For example, most alkanes with a carbon number of seven or less have negligible SOA yields but comprise a significant amount of VOC emissions (Lim et al., 2009). Therefore, a more detailed representation of the chemical composition of the emissions can

be important for predicting PM2.5 formation and health damages. Traditionally, it was believed that organic aerosol was more primary than secondary, but over the past 10-15 years, a consensus has emerged that the opposite is true (Robinson et al., 2007; Zhang et al., 2007) - although CTMs are still being updated to reflect this fact. Traditionally, it was also believed that SOA was produced from the gas-phase oxidation of a relatively small number of biogenic and anthropogenic volatile organic compounds (VOCs), which produced products with low enough vapor pressure that they condensed into PM. Newer measurements techniques for OA, however, strongly suggest that there is more SOA than previously thought, and current models tend to predict much lower atmospheric SOA levels than are observed (Volkamer et al., 2006). There may be previously unrecognized VOC precursors such as intermediate volatility organic compounds (IVOCs) (Robinson et al., 2007) or isoprene (Henze et al., 2008). Alternatively, known SOA precursors may form SOA more efficiently than previously recognized.

Finally, the major removal mechanism for PM2.5 is via precipitation. Hence, PM2.5 can be

transported for several days downwind, affecting populations up to approximately 1,000 km away from the point of emission (e.g., Evans et al., 2002). On the other hand, primary PM2.5 emitted in urban areas will have a large impact in the immediate vicinity. As a result, models of PM2.5 must reproduce the behavior of a complex physical and chemical system, and they require both sufficiently high resolution near sources as well as a long-range spatial extent to capture all the health impacts of a single source.

3. Methods: Review of Reduced Complexity Models (RCM)

Predicting the impacts of emissions on ambient concentrations is usually done using a comprehensive CTMs. CTMs are three-dimensional mechanistic models that predict ambient concentrations of pollutants using mass balance principles and accounting for emissions, transport, and dispersion by winds, chemical transformations, and atmospheric removal processes. CTMs are the most scientifically detailed and rigorous tools available for linking emissions to ambient concentrations. Examples of CTMs include the Comprehensive Air Quality Model with Extensions – CAMx (ENVIRON, 2016), Community Multi-scale Air Quality Model – CMAQ (Appel et al., 2017), and Weather Research and Forecasting model coupled with Chemistry – WRF-Chem (Powers et al., 2017). Running full CTMs is intensive enough in terms of expertise, time, and resources that their usage is generally limited to air quality researchers and regulatory authorities, such as the U.S. EPA’s regulatory impact assessment for revisions to the National Ambient Air Quality Standards (NAAQS) and state agencies as part of the accompanying State Implementation Plans (SIPs). As a result, generally, one or two models are certified for any given authority, and no explicit uncertainty analysis is conducted.

To address the challenges with running CTMs, several RCMs have been developed. In this

analysis, we leverage three existing RCMs to show the implications of uncertainty in the modeling

for policy analysis. The empirical models used in the analysis include AP2 (Muller, 2011; Muller, 2014), EASIUR (Heo et al., 2015), and InMAP (Tessum, Hill, and Marshall, 2017). Each of these models features a common integrated structure that consists of five modules: emissions, air quality modeling, exposures, physical health, and environmental impacts, and monetary valuation. One of the first applications of the RCMs has been to develop marginal damage estimates, i.e., those that result from small perturbations of emissions. The results from the model, expressed in US dollars (USD) of damage per tonne of emissions, are specified at a minimum for a type of pollutant, a location, a population and at least implicitly, for a given time period (e.g., a year). All results in this manuscript are expressed in 2010 USD. For the current analysis, the models employ the same population data to tabulate exposures, the same concentration-response function controlling the relationship between PM2.5 exposure and adult mortality (Krewski et al., 2009), and the same incremental value for changes in mortality risk: the VSL used is that recommended by the USEPA in its Regulatory Impacts Analyses (RIAs), (USEPA, 2017). The models differ in their spatial resolution and in the way that emissions are used to estimate ambient concentrations. For a detailed discussion of these differences, (see Gilmore et al., 2019).

Each model predicts marginal damages by making a small change to baseline emissions:

typically one ton of a particular pollutant is added to a particular source or source location. Then, the model is run through to determine the change in air quality across space, the resulting increase in exposures, physical health effects, and monetary damages. The sum of the change in damages across space is the marginal ($/ton) damage. Since all other parameters in each model are held fixed when emissions are perturbed, the resulting change is strictly attributable to the additional ton. The models then repeat this general algorithm across pollutants and source locations over a common set of pollutants and source locations. This produces three comparable datasets.

APEEP and its updated version, AP2 (and now AP3), employs a source-receptor (S-R) matrix

framework to map emissions to ambient concentrations at the county-level (Muller & Mendelson, 2007, Muller et al., 2011). The contribution of emissions in a source county (S) to the ambient concentration in a receptor county (R) is represented as the (S, R) element in a matrix. In the module for PM2.5 formation, the model contains S-R matrices that govern how PEC, SO2, NOx, NH3, and VOC map to PM2.5. Each of these matrices accepts annual (U.S. short tons per year) emission vectors to produces predictions of annual means. For each of these matrices, the model distinguishes among emissions released at four different effective height categories: ground-level emissions, point sources under 250 meters, point sources between 250 meters and 500 meters, and point sources over 500 meters. AP2 employs the approach to estimating the NH4

+, SO42- and NO3

- equilibrium embodied in the Climatological Regional Dispersion Model (CRDM), a national-scale Gaussian dispersion model (Latimer, 1996). In the equilibrium computations, ambient NH4

+ reacts preferentially with SO4

2-. Second, ammonium nitrate (NH4NO3) is only able to form if there is excess NH4

+. To translate VOC emissions into secondary organic particulates, AP2 employs the fractional aerosol yield coefficients estimated by Grosjean and Seinfeld (1989). While APEEP was

evaluated against a 2002 annual average baseline run produced by CMAQ, AP2 predictions are tested against Air Quality System (AQS) monitoring data. Calibration coefficients are used to adjust AP2 predictions to minimize mean fractional error and mean fractional bias jointly. We use AP2 in the text to clarify that we are comparing the results from the updated version of the original APEEP.

The EASIUR model (Heo et al. 2016a; 2016b) estimates marginal social costs for four

species—inert primary PM2.5, SO2, NOx, and NH3—in a 36 km × 36 km grid covering the continental U.S. The social costs are provided for four seasons and three emissions elevations (ground-level, 150 m, and 300 m). The EASIUR model was derived by running regressions on a CTM data set consisting of small emissions perturbations occurring at 100 sample locations. CAMx was run to calculate social costs of the four species at the sample locations (randomly chosen based on population size) across the nation. Then, the resulting per-tonne social costs were regressed as a function of exposed population and atmospheric variables such as temperature and atmospheric pressures using half of the sample locations as training for the regression and half as out-of-sample evaluations. Finally, using the regression models, per tonne social costs were estimated at all the cells in the 36 km × 36 km grid. An EASIUR-based source-receptor model was also developed from the regression results (Heo et al., 2017). The source-receptor version was used to estimate concentrations for comparisons made in this study.

InMAP (Tessum et al., 2017) combines simplified representations of atmospheric chemistry

and physics with output from WRF-Chem to calculate annual-average marginal changes in concentrations of PM2.5 caused by marginal changes in emissions of SO2, NOx, NH3, VOCs, and inert primary PM2.5 using a three-dimensional spatial grid with horizontal resolution ranging between 1 km × 1 km in highly populated areas to 48 km × 48 km in unpopulated areas and over the ocean. InMAP operates independently of the underlying CTM, and InMAP users would only need to use a CTM or access the raw CTM output data if they were interested in applying InMAP to a new spatial or temporal domain (e.g., outside of the continental U.S.). We used an InMAP-based source-receptor matrix (ISRM; Goodkind et al., 2019) to predict the health impacts and to calculate social costs of emissions in every InMAP grid cell at three emission heights (ground level, low stack height point sources, and high stack height point sources) and used the social cost of emissions from each county centroid in comparisons here.

In Gilmore et al. (2019), we conducted an inter-comparison of these three RCMs. In this paper,

we assessed the RCMs in terms of their ability to predict observed PM2.5 concentrations and their composition. We compared concentration estimates against annual average concentrations provided by U.S. EPA’s Air Data (available at https://www.epa.gov/outdoor-air-quality-data) as well as to at CTM, WRF-Chem. In general, we find that all models have similar performance. These results showed some important trends, with all models, including the CTM, performing worse for NH4

+ and NO3- predictions, illustrating that some PM2.5 species are more challenging to

model and, by extension, the damage estimates for their precursors will be more uncertain. At the same time, the relative success in reconstructing PM2.5 concentrations from marginal impact estimates suggests that differences between marginal and average changes are not too large or mostly cancel out among different pollutants and locations. On balance, these comparisons boost confidence in the use of RCMs and suggest that the necessary simplifications inherent in them do not substantially degrade their performance compared to CTMs.

4. Using these data for policy and uncertainty analysis

Here, we present four examples that highlight what the RCMs can tell us about uncertainty in the models and the implications for policy analysis. Our main finding is that when aggregating the social costs to the national level or when the policymaker is interested only in which pollutant to target, the benefits are insensitive to the uncertainty in the model. However, for analysis where location matter or the spatial distribution of benefits is important (e.g., for equity or exposure to vulnerable populations), benefits can vary depending on model choice. We also use the RCMs to show how decisions in model specification on the spatial extent and grid resolution can also influence the social cost estimates.

4.1 When uncertainty in air quality modeling does not matter Our first observation is that the general uncertainty in the air quality modeling appears to be

minor when aggregated to the national level. As suggested by the overall performance of the RCMs, at an aggregated level of the emissions-weighted national average damages, there is very close agreement amongst the three RCMs (See the red dots in Figure 2). Therefore, for decision scenarios that involve nationally distributed emissions changes, damage estimates will tend to agree, within a factor of 2, regardless of which model is used. Thus, a policy that results in similar reductions in emission for any given species across the U.S. will reveal similar benefits regardless of the model.

Second, for each RCM, the rank order of species from most damaging to least damaging (per

tonne) is also robust to the different models. That is, marginal damages for PM2.5 emissions are largest relative to the other pollutants for each model. The next most harmful pollutant, on average, for each model, is NH3, followed by SO2 and then NOx. Despite these fundamental differences in model design, Figure 2 also reveals that the magnitude of the average damages is similar across models and that the rank ordering of relative harm due to the emission of each species is invariant to which model's predictions are used. This is important as it allows a policymaker to weigh reductions that target specific pollutants using different models for benefit per ton estimates, and it would not influence the relative predicted benefits. Although many factors influence a careful benefit-cost analysis of these policy options, the benefits of further reductions in the sulfur content of diesel fuel to reduce SO2 against the deployment of particle traps in the vehicle fleet to reduce primary PM2.5 will be insensitive to the uncertainty in the model.

However, we do not show results for VOCs due to these large uncertainties. Some earlier datasets provide estimates for VOC emissions, such as the benefits per ton estimates from the USEPA (Fann et al., 2009). As discussed above, there have been recent changes in the fundamental understanding of how VOCs in general and specific compounds in VOCs form organic PM2.5 which are not yet incorporated into the models. We discuss the implications of the uncertainty in the SOA values and make recommendations for how to approach these estimates in Section 5.

Figure 2: Box plot of the marginal social costs (in USD/tonne) for ground and elevated source emissions across all US counties by pollutant and by air quality model. Red dots and lines indicate emission-weighted mean and median, respectively. The left and right boxes are the 25th and 75th percentiles and the whiskers are the 2.5th and 97.5th percentiles.

4.2 Variability and uncertainty from the location of emissions can matter a lot

All three RCMs provide damage estimates that are highly spatially resolved with respect to emissions location. In Figure 3, we show the spatial distribution of the emissions across the US at a county-level. Whereas some application scenarios will involve nationwide emissions changes, others may be interested in damages from emissions in one region of the country, perhaps a single state or even a single county. Here, we begin to observe differences in the models that can influence policy analysis and the realized benefits. Overall, the models tend to predict similar cost estimates for primary PM2.5; generally within a factor of three. For primary PM2.5, which is an inert species

emitted directly as a particle, concentrations are influenced only by differences in atmospheric transport and dilution. Results for cost estimates for secondary pollutants are more variable on average and spatially. The formation of secondary PM2.5 depends on how efficiently precursors are converted to secondary species. In the atmosphere, this typically depends on chemistry, deposition rates, sunlight, and the availability of co-reactants especially atmospheric oxidants and thermodynamic interactions between inorganic ions (Ansari and Pandis 1998; West et al. 1999). Additionally, the impacts of secondary pollutants should also be more dependent on accurately predicting transport as chemical reactions can occur over longer distances and thus expose populations further from the source. Thus, the model selection has a more significant role as the estimates of impacts depends on both the representation for long-range transport and chemical processes. Since sulfate, nitrate, and ammonium concentrations depend on each other, differences in the model predictions for one species will influence the others.

For any given analysis, it is critical to select values that are as specific to the location as possible because the damage per unit emission varies by 1-2 orders of magnitude depending on the location of the emissions. Thus, the three datasets reviewed in this manuscript provide coverage at the county-level (or higher) for the US. Primarily, location determines the population exposed. Secondarily, it establishes several features that are important for characterizing the air quality chemistry (e.g., background atmospheric conditions, the meteorological conditions, and the topology of the area). The location also reveals differences between the models. While these differences can be substantial, the estimates for the impacts of air emissions can also be compared by the type of policy analysis. For many policy applications, it is appropriate to cost over many sources. In these cases, much of the uncertainty in the air quality modeling approaches is less important. Generally, for the evaluation of policies that are enacted at the national level, the total costs from all models are within a factor of two or three. For more specific applications, such as the Marcellus shale development, where NOx emissions are the dominant concern, the models may diverge more substantially. Here, it is possible to account for this variability from the model by examining the range of estimates. However, since these values are not a distribution of possible estimates, they should be input one at a time into the policy analysis model.

Additionally, many policy applications are assumed to affect emissions relatively evenly over the year such that an annual damage estimate is appropriate. However, for the secondary pollutants, meteorology – especially temperature – influences the reactions as well as whether the more volatile gases can condense. If the emissions show seasonality, then the cost estimates should also reflect the difference in seasonal conditions.

Figure 3: Marginal social costs for ground-level emissions for each US county by pollutant and by air quality model (in USD/tonne). Negative values are in shown in green.

4.3 Managing the uncertainty for policy analysis

The uncertainty in the air quality model can also be contextualized with respect to the policy under consideration. Here, we examine uncertainty that may arise due to a policy choice. Specifically, we outline a policy that aims to increase the economic efficiency of pollution abatement. Often, due to any number of constraints (e.g., ease of implementation, equity issues, prior experience with a specific policy design, capacity to analyze alternatives, etc.), regulators opt to control all pollution sources at the same degree (e.g., a single tax for all sources). However, the wide range of social cost estimates across the U.S. suggests that there are opportunities to capture benefits by "grouping" sources under different tax brackets. In Figure 4 and 5, we show an example of a policy that separates the sources into one group for sources with high damages and a separate group for sources with low damages. Since the damages for air pollutants are highly skewed, the number of sources in the top group is much smaller than the lower damage group. The optimal number of sources in the top tax bracket, however, varies by species and by model. There is a higher number of sources in top tax bracket for SO2 then for NOx. However, the number of sources by model varies less than the spatial distribution of these sources.

While the efficiency gains may appeal to the regulator, it is less clear which model to use or which sources to select. One approach may be to select all sources that fall in the top tax bracket in any given model. An alternative is to select only sources that are identified by all models. The answer to this depends on the regulators’ tolerance for uncertainty compared to their desire to maximize efficiency gains. For example, a regulator may feel more confidence in selecting sources where the model has a high agreement for SO2 than for NOx.

Figure 4: Distribution of sources of SO2 with top economic damages (~1,300 sources)

Figure 5: Distribution of sources of NOx with top economic damages (~600 sources)

4.4 Modelling choices affect the social costs

The spatial extent of the model and the spatial resolution of the emissions and exposure can also influence social costs. These choices would matter whether one opts to use a CTM or a RCM. However, they have rarely been explicitly explored for their influence on social costs. RCMs can facilitate testing of the implications of these choices. Since PM2.5 is long-lived, a significant fraction of the damages nearly always occur downwind - sometimes hundreds of km. Thus, assessing impacts based solely on population density in the immediate vicinity is inappropriate. This is especially true for SO2 and NOx emissions since the chemistry that converts them to PM2.5 occurs on a timescale of approximately one day, minimizing PM2.5 damages in the immediate vicinity. We emphasize that to represent the total damages stemming from emissions at a point typically requires modeling the impacts far beyond the emission source. We show how this can be important in Figure 6 using results from EASIUR. In some cases, most of the damages occur near the emission sources. In rural areas, however, the far-from-source impacts may also be important as the population density is generally low and more uniform over the relevant transportation distance.

In Figure 7, we examine how model resolution influences the air quality costs using results from InMAP. In part, the spatial resolution of the underlying air quality model depends on the application for social costs. Lower resolution (e.g., 36 km by 36 km and county-level) is likely justified for national averaging, although environmental justice applications will likely seek higher spatial resolution. The need for finer spatial resolution may also depend on how spatially correlated the emissions are with population density, the height of the sources (e.g., ground-level versus elevated) and the relative importance of primary versus secondary PM2.5. Specifically, primary emissions at ground level in areas with high population density will benefit from higher resolution in the model, such as diesel vehicles in urban centers. In this case, assessing impacts while disregarding the impact of near-source gradients in pollutant concentration is inappropriate. Emissions and population density are often spatially correlated, and thus, lower spatial resolution will cause a negative bias in health impact estimates. The underestimation caused by low near-source spatial resolution has been estimated as ranging from approximately 8 to 30% (e.g., Fountoukis et al., 2013). For models that generate county-level results, there may be special concerns for underestimation due to resolution in larger countries in the west. This underestimation, however, is generally less than that caused by only considering short-range transport. This is especially critical for elevated sources, such as power plants, which have more regional-scale impacts. Generally, elevated sources generally lead to lower social costs but not always; elevated emissions in very rural areas sometimes increases the pollution transported to large cities hundreds of km downwind.

Figure 6: Cumulative fraction of total damages occurring within a given distance from an emission source (blue lines) for three locations and four species emitted. Green dashed lines represent a hypothetical case where the population is distributed uniformly and are shown for reference. Values are taken from the EASIUR model.

Figure 7: The area-weighted percent difference between damages caused by emissions in each InMAP grid cell in the county compared to the damages caused by the grid cell at the county centroid. The variation in these damages within a county provides an indication of the effect of higher-resolution modeling.

5. Recommendations for using RCMs and managing uncertainty

Here, we present recommendations on how or when to employ these values compared to conducting a specific impact assessment pathway for any given analysis as well as how to manage the model selection and its relation to treating model uncertainty.

At a national level, the total social costs are relatively insensitive to the uncertainty of how we model the transformation of emissions to ambient concentrations. The more aggregated the level of analysis, the less the uncertainty in the models matters. For many analyses, we are also interested in the distribution of the damages. The RCM results show the importance of location and why we need spatially resolved values for social costs. First, location determines the population exposure level. Second, it establishes several features that are important for characterizing the air quality chemistry (e.g., background atmospheric conditions, the meteorological conditions, the topology of the area). Looking at the spatial distribution also highlights the uncertainty. While overall there is high agreement, the model show larger discrepancies for some species in some counties. Thus, at lower resolutions, there can be more model uncertainty, and it may be necessary to evaluate how sensitive analysis is to the different damage estimates.

Further, ensembles can be developed that draw upon the results of multiple models (Amann et

al., 2011; Colette et al., 2012; Spadaro & Rabl, 2008) that can provide guidance for the benefits of different policy designs. Source characteristics, namely the height of the emissions, matters. Ground-level sources will have more local impacts, while higher stacks will have more regional-scale impacts. Generally, elevated sources lead to lower social costs but not always; elevated emissions in very rural areas can "help" PM2.5 reach large cities hundreds of km downwind.

All the RCMs show that assessing impacts based solely on population density in the immediate

vicinity is inappropriate. We emphasize that to represent the total damages stemming from emissions at a point require modeling the impacts far beyond the emission source. The required spatial resolution of the underlying air quality model depends on the application for social costs. Lower resolution (e.g., 36 km by 36 km and country-level) may be fine for highly aggregated analyses. For some pollutants and locations, higher resolution is needed. Primary emissions in areas with high population density may benefit from higher resolution in the model. For models that generate county-level results, there may be problems with resolution in larger countries in the west. Environmental justice applications will likely want a higher spatial resolution.

Air quality models are still necessary for some applications. For many purposes, it is

appropriate to cost an annual average of the meteorological conditions and over many sources. In these cases, much of the uncertainty in the air quality modeling approaches will be less important. However, other emissions may only occur for short periods of time (e.g., peak electricity emissions) or there may be a non-concurrent displacement of emissions (e.g., charging of utility-scale batteries on an electricity grid) (Gilmore, Apt, Walawalkar, Adams, & Lave, 2010). These

cases may require independent air quality modeling to produce social cost estimates. Air quality models are also needed for highly non-marginal changes. More broadly, the social cost estimate for a given pollutant can be non-linear or even negative for a given increase in emissions depending on the ambient atmospheric composition and concurrent changes in other emissions. Concurrent air quality regulations that may alter the background concentrations, changes in climatic conditions, and other socioeconomic factors, such as population age and regional migration, may generate different marginal social costs.

Even for an analysis of non-marginal changes, these values from the RCMs, however, may still be appropriate for "screening purposes," especially for decision tools such as benefit-cost analysis (BCA) or a comparative lifecycle analysis (LCA). For example, in a BCA type framework, one may only need to show that the benefits exceed the costs. Here, one may calculate the costs and then evaluate the range of social costs to see if it is "plausible" given the available values do not meet the "benefits greater than costs" threshold. Taking this type of approach would also highlight cases where there is a need for more impact pathway analyses to characterize the application.

In the comparisons that we show here, we do not provide values for volatile organic compounds

(VOCs). VOCs are a very broad category of species with very different atmospheric behaviors. SOA is formed from a relatively small subset of VOCs accounting for a small fraction of total mass of VOC emissions. Therefore, one should not necessarily expect that VOC emissions are a good predictor of impacts/social costs. Different sources will have different mixes of VOCs and, therefore, different SOA/PM formation and social costs. This has not been well accounted for to date and is still poorly understood.

As Dockery and Evans (2017) expressed about the estimates for the damages from air

pollution, “we must be honest about the strengths and weaknesses of the estimates we make from even the best methods now available. Scientists will need time to resolve these uncertainties. However, decision-makers must resist the temptation to wait for perfect information before they act, because the costs in loss of life to be expected while waiting will be substantial.” (Dockery & Evans, 2017). RCMs help address this concern. With under a minor loss of fidelity to a full CTM, RCMs can be used to quickly examine several parameters that can influence the social costs estimates of air quality and explore how the uncertainty in these estimates can affect policy design.

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Acknowledgments: This publication was developed by funding from the Center for Air, Climate

and Energy Solutions under Assistance Agreement No. RD83587301 awarded by the U.S. Environmental Protection Agency. It has not been formally reviewed by the U.S. EPA. The views expressed in this document are solely those of the authors and do not necessarily reflect those of the Agency. U.S. EPA does not endorse any products or commercial services mentioned in this publication.