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A Comparison of Statistical Techniques for

Combining Modeled and Observed Concentrations

to Create High-Resolution Ozone Air Quality

SurfacesValerie C. Garcia

a, Kristen M. Foley

a, Edith Gego

b, David M. Holland

a& S.

Trivikrama Raoa

a

U.S. Environmental Protection Agency, Office of Research and Development,National Exposure Research Laboratory, Research Triangle Park, NCbGego Associates, Idaho Falls, ID

Version of record first published: 24 Jan 2012.

To cite this article:Valerie C. Garcia, Kristen M. Foley, Edith Gego, David M. Holland & S. Trivikrama Rao (2010): AComparison of Statistical Techniques for Combining Modeled and Observed Concentrations to Create High-Resolution

Ozone Air Quality Surfaces, Journal of the Air & Waste Management Association, 60:5, 586-595

To link to this article: http://dx.doi.org/10.3155/1047-3289.60.5.586

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A Comparison of Statistical Techniques for CombiningModeled and Observed Concentrations to Create High-Resolution Ozone Air Quality Surfaces

Valerie C. Garcia and Kristen M. FoleyU.S. Environmental Protection Agency, Office of Research and Development, National Exposure

Research Laboratory, Research Triangle Park, NC

Edith GegoGego Associates, Idaho Falls, ID

David M. Holland and S. Trivikrama RaoU.S. Environmental Protection Agency, Office of Research and Development, National Exposure

Research Laboratory, Research Triangle Park, NC

ABSTRACTAir quality surfaces representing pollutant concentrationsacross space and time are needed for many applications,including tracking trends and relating air quality to hu-man and ecosystem health. The spatial and temporalcharacteristics of these surfaces may reveal new informa-tion about the associations between emissions, pollutionlevels, and human exposure and health outcomes thatmay not have been discernable before. This paper pre-sents four techniques, ranging from simple to complex, tostatistically combine observed and modeled daily maxi-mum 8-hr ozone concentrations for a domain coveringthe greater New York State area for the summer of 2001.Cross-validation results indicate that, for the domain andtime period studied, the simpler techniques (additive andmultiplicative bias adjustment) perform as well as or bet-ter than the more complex techniques. However, the spa-tial analyses of the resulting ozone concentration surfacesrevealed some problems with these simpler techniques inlimited areas where the model exhibits difficulty in sim-ulating the complex features such as those observed in theNew York City area.

INTRODUCTION

Air pollutant concentrations across space and time areused in a multitude of applications, including tracking

trends and relating air quality to human and ecosystem

health. Changes in air quality attributable to emission

reductions stemming from control policies are often weak

signals within the overall changes in observed or modeled

concentrations. This signal can be further confounded

when investigating the impacts of emission reductions on

human health. Although air quality observations taken at

various locations represent the ground truth, these ob-servations are often limited in terms of spatial and tem-

poral coverage. Air quality models can predict pollutant

concentrations over a given spatial domain, but the mod-

eled values are uncertain because of model input errors

and the models inability to perfectly simulate the variousphysical and chemical processes occurring in the atmo-

sphere. To alleviate these problems, four techniques that

statistically combine air quality measurements with

model output to produce high-resolution ambient pollut-

ant concentrations are considered here to better charac-

terize air quality in a study area encompassing New YorkState (NYS) for the 2001 ozone season. These improved air

quality surfaces may reveal associations between pollu-tion levels and health outcomes not discernable before.1

Several investigators27 have applied techniques (e.g.,

the Kalman filter and ensemble approaches) to adjust

forecasted meteorological variables and air pollution con-centrations using observations. Gego et al.8 and Hogrefe

et al.9 applied bias-adjustment approaches to predict air

pollutant concentrations for use in health studies. Hirst et

al.10 used a hierarchical modeling approach to combine

measured and modeled deposition values to estimate

long-range transport of air pollutants in Europe by mod-eling the underlying (unobserved) true deposition pro-

cess as a function of two stochastic components: one

nonstationary and correlated over long distances, and theother describing variation within a grid square. Fuentes

IMPLICATIONS

Linking emission control actions to human health impacts is

important in determining whether the regulations that have

been implemented are reducing air pollution as intended.

Measurements of pollutant concentration levels are often

spatially sparse, and modeled outputs are only an estimate

of the true pollutant concentration levels, hampering the

ability to detect a relatively small signal of change embed-

ded in ambient concentrations. This paper assesses four

techniques to combine the strengths of modeled and ob-

served data to provide high-resolution ozone concentration

surface maps for use in human health studies and assess-

ing whether regulatory control actions have had the in-

tended impact.

TECHNICAL PAPER ISSN:1047-3289 J. Air & Waste Manage. Assoc. 60:586595DOI:10.3155/1047-3289.60.5.586Copyright 2010 Air & Waste Management Association

586 Journal of the Air & Waste Management Association Volume 60 May 2010


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and Raftery11 used a Bayesian approach to combine ob-served and modeled dry deposition pollutant concentra-tions to improve spatial predictions, evaluate the model,and remove the model bias. Similar to Hirst et al.,10 Fu-entes and Raftery11 assumed that the model output and

available observations can be represented as a function ofan unobserved ground truth plus error and bias terms.McMillan et al.12 defined an approach used in this study(discussed later in the paper) that again applies a hierar-chical Bayesian approach to predict ozone concentrationsbut extends the model to include a temporal dimensionusing an autoregressive structure.

Although varying in their approach, the intent ofthese statistical data combination techniques is to retainthe strongest components of each data type (i.e., obser-vations and model outputs) to best represent the pollut-ant of concern. For example, observations are the bestrepresentation of the true pollutant concentration value

at a given site and time; however, depending on thenetwork and the chemical being measured, the spatialand temporal extent may be limited. Classical interpola-tion of observed concentrations helps to fill-in the spa-tial and temporal gaps but tends to produce overlysmoothed results. Three-dimensional deterministic airquality models (e.g., the Community Multiscale Air Qual-ity [CMAQ] model13) can estimate pollutant concentra-tions across a uniform spatial and temporal scale. How-ever, the accuracy of these estimates is based on theuncertain understanding of the physical and chemicalprocesses underlying the formation, interaction and fateof atmospheric pollutants, and errors in the model input

(e.g., emissions, meteorology, boundary conditions).Even a perfect model with perfect model input cannot

exactly reproduce the observations because random vari-ations embedded in the observations taken at individualmonitoring locations are not explicitly estimated in cur-rent regional-scale models. Thus, an observation reflects asingle event out of a population, whereas the modeled

concentration represents the population average. More-over, the predictions from a deterministic model repre-sent the volume-averaged concentration for the grid cell,whereas observations at a given monitoring location re-flect point measurements.14

Figure 1 illustrates some of the strengths and weak-nesses inherent in the modeled and observed data used inthis study by displaying the modeled, observed, and inter-polated (kriged) ozone 8-hr daily max surfaces for the do-main encompassing NYS for June 13, 2001. On this day, theinterpolated observations appear to be overly smooth andmiss the hot spots generated by emissions from significantsources of ozone precursor chemicals captured by the

model. The modeled surface shows the effects of titration inthe area of New York City (NYC) where high nitrogen oxide(NO) emissions scavenge ozone, creating areas of lowozone concentrations around the emission source. If theselocal features are measured, kriging tends to smooth themout. The model captures this important feature but mayoverestimate the extent of the titration effect. Thus, captur-ing hot spots and other spatial gradients that may besmoothed out by kriging, yet correcting the bias that mayexist in model estimates, may produce improved air qualitysurface concentrations critical to detecting health impacts.In this study, statistical combination techniques are appliedthat integrate the observed concentrations with the

model estimates to optimize the strengths of each dataset.Focus is on the summer of 2001 for the NYS domain as a

Figure 1. Ozone 8-hr MDA (ppb) for June 13, 2001: (a) modeled, (b) observed, and (c) kriged observations. Kriging smoothes the hot spots,

whereas the model may overpredict titration in NYC.

Garcia, Foley, Gego, Holland, and Rao

Volume 60 May 2010 Journal of the Air & Waste Management Association 587


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pilot study to demonstrate the use of these enriched airquality data in an epidemiological health study and riskassessment for NYS.

APPROACHFour techniques ranging from relatively simple to com-plex are investigated here for combining observed andmodeled ozone concentrations for a domain in thegreater NYS area from June 1 to August 31, 2001 (Figure2). The focus of this investigation is on providing thedaily maximum 8-hr ozone concentrations to state health

assessors for their use in investigating relationships be-tween air quality and human health end points (e.g.,respiratory-related hospital admissions) across multipleyears. The daily maximum 8-hr ozone concentrationsused in the study were calculated from observations andfrom CMAQ model predictions. Four statistical combina-tion techniques were applied to the observed and mod-eled data to produce combined daily maximum 8-hrozone concentration surfaces on a 12- by 12-km spatialgrid for a total of 92 days in the summer of 2001. Thesecombined surfaces were quantitatively compared throughcross-validation and qualitatively compared throughanalysis of the spatial surfaces produced by each of the

methods.

ObservationsHourly ozone observations for June 1 through August 31,2001 were obtained from (1) the U.S. Environmental Pro-tection Agencys (EPA) Air Quality System (AQS) database(http://www.epa.gov/oar/data/aqsdb.html) and Clean AirStatus and Trends Network (CASTNet; http://www.epa.gov/castnet), and (2) the Canadian EnvironmentalAssessment Agencys National Air Pollution SurveillanceNetwork (NAPS; http://www.etc.-cte.ec.gc.ca/publica-tions/napsreports_e.html). All monitoring networks pro-vided hourly concentrations for each day in the summer

with a total of 200 sites (139 AQS sites, 52 NAPS sites, and9 CASTNet sites). Information on the quality assurance

conducted for each network can be found at the websitesprovided above. The daily maximum 8-hr ozone concen-trations were calculated by applying an 8-hr moving win-dow to the hourly time series and selecting the 8-hr timewindow with the highest ozone concentration value (re-ferred to as the 8-hr maximum daily average [MDA]throughout the paper). Only those days having morethan 20 hr of data were used for computing the MDA.

Model OutputOzone 8-hr MDAs were calculated from the hourly con-centration values simulated by EPAs CMAQ model, ver-sion 4.5. Specifically, the simulated concentrations for

June 1 through August 31 were extracted from the 2001annual simulation with 12- by 12-km horizontal gridcells. The meteorology and emissions inputs for this sim-ulation were from the Fifth Generation National Centerfor Atmospheric Research/Penn State Mesoscale Model(MM5) and EPAs 2001 National Emissions Inventory,respectively. The 12-km simulation encompassed most ofthe eastern United States and was nested within a 36- by

36-km horizontal grid simulation covering the contigu-ous United States using the same model configuration asthe 12-km nested simulation. Boundary conditions forthe 36-km simulation were provided by a global chemi-cal transport model (GEOS-CHEM).15 Several evalua-tions1621 have been done of the CMAQ model. In partic-ular, Appel et al.22 evaluated the CMAQ annual simula-tion used in this study and found that the medianobserved and predicted ozone concentrations correspondwell between 10:00 a.m. and 6:00 p.m., which are thehours that typically makeup the 8-hr MDA. Appel et al.22

also report that the model consistently overestimated lowconcentrations and underestimated high concentrations

of ozone. Additional details on the CMAQ simulationused in this study and the evaluation of the simulationresults can be found in Byun and Schere13 and Appel etal.,22 respectively.

Statistical Combination TechniquesThe four techniques investigated for combining the ob-served and modeled values were additive bias adjustment,multiplicative bias adjustment, weighted average, and hi-erarchical Bayesian. The application of each of these tech-niques resulted in a spatial surface (12-km horizontal res-olution) of 8-hr MDA ozone concentrations (parts perbillion [ppb]) for each day of the summer in 2001. In

general, the bias-adjustment approaches modify the mod-eled surface concentration values by accounting for biasin the modeled ozone concentrations. The weighted-average approach uses weights for the interpolated obser-vations and modeled surfaces on the basis of a relativeaccuracy of each surface at each grid cell, and the hierar-chical Bayesian approach treats the observations and themodel concentrations as representing a true surface andcalculates model parameters using a Markov Chain/Monte Carlo technique.

Interpolated Observations. In addition, 8-hr MDA ozoneobservations were interpolated with a kriging approach

that applies a Matern spatial correlation function23 toproduce daily 12- by 12-km maps. For each day of the

Figure 2. Domain and observations used in this study. Solid circles

show location of AQS sites, triangles show NAPS sites, and squares

show CASTNet sites. Open circles highlight sites clustered in urban

areas.




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RMSE for the four combination techniques and krigedobservations were within 1.4 ppb of each other, and themean bias values were within 1.05 ppb of each other. R2

ranged from 85 to 88%. The metrics also indicated that allfour combination techniques substantially improved themodeled surface (R2 of 60%).

However, the percentile rank-ordered analysis revealedinteresting differences among the combination techniquesand the interpolated observations. Figure 4 displays scatter-plots (predicted vs. observed), highlighted by color code todepict the percentile range. Note that the weighted-averageand HBM techniques correct the model bias fairly well at thelower percentiles but follow the scatterplot pattern of theraw modeled output at the higher percentiles. The additiveand multiplicative bias techniques follow the one-to-oneline closely, indicating that a simple correction of the modelbias may be effective for improving the spatial characteriza-tion of ozone concentrations.

Although cross-validation often favors kriging of the

ozone observations (because of the concept discussed ear-

lier of randomly selecting cross-validation data from clus-

tered monitoring sites), the bias-adjustment techniques

produce slightly better results than kriging at the higher

percentiles. This same difference is evident in the error

plots in Figure 5. The tendency of the CMAQ model to

overestimate low ozone values and underestimate high

ozone values can be clearly seen. Similar to the scatter-

plots, the weighted-average and HBM techniques appear

to correct this overestimation at the lower ozone concen-

trations but do not do as well at reproducing the observed

ozone concentration levels at the higher percentiles. (It

should be noted that the HBM technique was designed to

provide Bayesian predictions over large national spatial

scales rather than the small regional domain of this

study.) The additive and multiplicative bias-adjustment

approaches appear to perform best across all percentiles,

slightly outperforming the kriging of the observations at

the higher percentiles as noted earlier. Although it is

recognized that inferences from the smaller sample sizesin the higher percentile bins must be done with caution

(sample size ranges from 370 to 123 site-days for the three

highest percentile bins), the sample sizes range from

515% of the total sample size of 2454 site-days, provid-

ing credence to the results discussed above.

In addition, the spatial texture seen with the com-

bined surfaces indicates that model-based spatial informa-

tion seen in CMAQ is retained with the combined sur-

faces. Figure 6 shows 8-hr MDA ozone values for the (a),

Table 1. Cross-validation results for ozone 8-hr MDAs.

RMSE

(ppb)

Mean Bias

(ppb) R2

n 2454

CMAQ only 11.70 0.88 0.60

Kriged observations 6.40 0.49 0.88

Additive bias adjustment 6.80 0.33 0.86Multiplicative bias adjustment 6.80 0.05 0.86

Weighted average 6.70 0.50 0.88

Hierarchical Bayesian 7.80 1.10 0.85

Figure 4. Observed (y-axes) and predicted (x-axes) 8-hr MDA ozone (ppb) binned by percentile for cross-validation sites for (a) modeled, (b)

kriged observations, (c) additive bias, (d) multiplicative bias, (e) weighted average, and (f) HBM. Black 050%, red 5175%, orange 7690%, blue 9195%, green 96100%.




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CMAQ model, (b) kriged observations, and (c) multiplica-

tive bias adjusted values for two representative days on

June 7 and July 19, 2001. Note the overly smooth surface

inherent in the interpolated observations and the influ-

ence of the model in the spatial texture of the combined

surface. Figure 7 shows the mean concentration values for

each grid cell. The model estimates of the ozone titration

effect near NYC and Boston can clearly be seen in the

modeled surface. The measurements in these same areas

also show low ozone concentration values; however,

these low values are averaged out by the interpolation. In

addition, the model predicts high ozone values over the

Great Lakes and the Atlantic Ocean because of lower plan-

etary boundary layer heights, stable atmospheric condi-

tions, and reduced turbulence and depositionall physi-

cal processes known to exist over large waterbodies.

Ozone measurements taken over Lake Michigan and air-

craft observations over the coastal areas of the Northeast

indicate the presence of high ozone concentrations over

large waterbodies, which the model seems to cap-

ture.24,25

Similar to titration in the urban core, theinterpolated observations do not show this physical

phenomenon. Because the purpose of this study is to

provide improved air quality data for health studies, the

difference in the estimation of titration is particularly

relevant because this physical phenomenon can occur

in highly populated areas.

The coefficient of variation (Figure 8) calculated for

all days at each grid cell reveals a problem introduced by

Figure 5. Mean error (binned by percentile) between modeled,

kriged, and the four combination techniques vs. mean observed

concentrations for all cross-validation sites. Circles represent aver-

age mean for each binned percentile; lines are for identification of

technique but do not represent linear relationships between aver-

aged points.

Figure 6. Contribution of spatial information from model in combined surface of 8-hr MDA. Column a represents modeled surface, column b

represents interpolated observations, and column c represents multiplicative adjusted bias. Top panels are for June 7, 2001 and bottom panelsare for July 19, 2001.




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the large standard deviation values (relative to the mean)produced by the titration effect in the additive and mul-tiplicative bias-adjustment approaches. For example, thecoefficient of variation is high for the multiplicative biassurface near Staten Island and Boston, for which themodel predicts low ozone concentration values because of

titration. These high coefficient of variation values are theresult of large differences between the modeled and ob-served concentrations that result in very large observed-to-modeled ratios (eq 4; Figure 9a). Kriging the ratios andmultiplying them by the model surface creates highozone concentrations in the nontitrated area surrounding

Figure 7. Mean 8-hr MDA ozone concentrations across all days for (a) modeled, (b) kriged observations, (c) multiplicative bias, (d) additive

bias, (e) weighted average, and (f) HBM.

Figure 8. Coefficient of variation calculated for 8-hr MDA ozone concentrations across all days for (a) modeled, (b) kriged observations, (c)multiplicative bias, (d) additive bias, (e) weighted average, and (f) HBM.




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the titrated area (Figure 9b). Although selection of a cross-validation site in one of the impacted areas may have

changed the results, this effect occurs for less than 0.03%of the total number of estimated values and for only 3days during the total 92-day study time periods. In addi-tion, the high observed-to-modeled ratios do not produceexcessively high ozone concentrations except for over theocean outside of Staten Island where the population islow.

SUMMARYThe cross-validation results of this pairwise comparisonusing standard statistical metrics did not reveal a largedifference among the four combination techniques, butdid reveal that all techniques provide improved estimates

of 8-hr MDA ozone concentrations as compared with themodel surface alone. The percentile analysis of the cross-validation results revealed interesting results not dis-cerned by the all-day/all-site metrics alone. The percentileanalysis indicated that the additive and multiplicativebias-adjustment techniques tended to improve the com-bined 8-hr MDA ozone concentrations at the higher per-centiles as compared with the other techniques, includingkriging the observations. Further analysis of the resultingspatial surfaces revealed problems with the additive andmultiplicative bias-adjustment approaches introduced bythe modeled titration effect, yielding artificially highozone concentration values in adjacent cells. However,

this problem occurred for less than 0.03% of the totalconcentrations on only 3 days of the total summer andprimarily over waterbodies where the population is low.The qualitative spatial analysis performed supported thatthe combination techniques added spatial informationfrom the model as compared with kriging the observa-tions alone. In the case of this study, the intended appli-cation of the combination approach is to provide im-proved air quality surface maps for conductingepidemiology studies in NYS. The additive and multipli-cative bias-adjustment approaches are considered appro-priate for this application because (1) accurately repre-senting days of high-ozone concentration is important for

the health study of interest, and the additive and multi-plicative bias-adjustment approaches outperformed the

other methods at the higher ozone concentration percen-tiles; (2) the additive and multiplicative bias-adjustment

approaches are relatively simple and can readily be ap-plied by the state health community; and (3) to date,estimates of predicted error produced by the HBM andweighted-average approaches are not generally used inhealth studies. However, as epidemiology studies movetoward the use of predictive distributions, more complexapproaches such as HBM may be needed to estimate pre-diction error. Finally, these results are limited in applica-bility to the domain, pollutant, and time period studied.

ACKNOWLEDGMENTSThe authors thank Drs. Steven Porter, Christian Hogerefe,and Jenise Swall for many helpful discussions on the datafusion techniques. Although this paper has been reviewedand approved for publication, it does not necessarily re-flect the views and policies of EPA.

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adjusted bias approach.




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About the Authors

Valerie Garcia is chief of the Atmospheric Exposure Inte-gration Branch, Atmospheric Modeling and Analysis Divi-

sion (AMAD), within EPA. Dr. Kristen Foley is a statistician

within AMAD, Dr. David Holland is a senior statistician with

the National Exposure Research Laboratory within EPA,

and Dr. S. Trivikrama Rao is Director of AMAD. Edith Gego

is a consultant with Gego Associates in Idaho Falls, ID.

Please address correspondence to: Valerie C. Garcia, U.S.

Environmental Protection Agency, MD: E243-02, 79 T.W.

Alexander Drive, Research Triangle Park, NC 27711;

phone: 1-919-541-2649; fax: 1-919-541-1379; e-mail:

[email protected].



a comparison of statistical techniques for combining modeled and observed concentrations to create...

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