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Atmospheric Environment 50 (2012) 381e384

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Atmospheric Environment

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Technical note

Kalman filter-based air quality forecast adjustment

Koen De Ridder*, Ujjwal Kumar, Dirk Lauwaet, Lisa Blyth, Wouter LefebvreVITO, Flemish Institute for Technological Research, Boeretang 200, B-2400 Mol, Belgium

a r t i c l e i n f o

Article history:Received 20 October 2011Received in revised form6 January 2012Accepted 11 January 2012

Keywords:Air qualityDeterministic forecastKalman filterAdaptive regression

* Corresponding author.E-mail address: koen.deridder@vito.be (K. De Ridd

1352-2310/$ e see front matter � 2012 Elsevier Ltd.doi:10.1016/j.atmosenv.2012.01.032

a b s t r a c t

We evaluate a Kalman Filter (KF) based adaptive regression method for the correction of deterministic airquality forecasts. In this method, corrected forecast concentrations are obtained by linear regression,using the free model forecast values as predictors, and estimating the regression coefficients dynamicallyby means of the KF technique. Basically, this method exploits the information regarding the mismatchbetween the deterministic forecast and observations of the prior period to calculate regression coeffi-cients for the correction of the next forecast step.

We considered model output generated by the deterministic regional air quality model AURORA overnorthern Belgium for the year 2007, together with observed values at a few tens of stations. It was foundthat, for daily mean PM10 concentrations, and averaged over the monitoring stations, the correctionscheme reduced the root mean square error from 15.9 to 10.5 mgm�3, largely thanks to the bias reductionfrom 8.8 to 0.5 mgm�3. The correlation coefficient increased from 0.65 to 0.73. For daily maximum O3

concentrations, the root mean square error was reduced from 25.9 to 17.2 mgm�3, the bias from 7.9 to0.2 mgm�3, and the correlation coefficient increased from 0.60 to 0.79.

We also implemented a non-adaptive linear regression scheme to the same data. It was found that theadaptive regression method outperformed this simpler scheme consistently, demonstrating therelevance of the dynamic KF-based method for use in the correction of deterministic air quality forecasts.

� 2012 Elsevier Ltd. All rights reserved.

1. Introduction

Over the past decade, the use of data assimilation techniques toimprove deterministic air quality forecasts has increased consid-erably. Most of these techniques aim at estimating optimal initialand boundary conditions (including emission correction factors) fora deterministic model forecast. Different sophisticated approachesexist, such as four-dimensional variational data assimilation(4DVAR) (Elbern et al., 2007; Zhang et al., 2008) and EnsembleKalman Filtering (EnKF) (Eben et al., 2005; Barbu et al., 2009; Tanget al., 2011). Also, increasing use is made of ensemblemedian-basedapproaches (Riccio et al., 2007). While these techniques arepotentially very powerful, they are also highly computation-intensive, requiring either the implementation of a model adjoint,or the simultaneous integration of several tens of model ensemblemembers.

Conversely, in recent years rather simple bias adjustementtechniques have emerged, in which the bias correction factors areestimated by means of the Kalman (1960) filter (KF) approach.

er).

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Borrowed from meteorology (see, e.g., Kalnay, 2002), these tech-niques are applied in post-processing (i.e., off-line) mode ratherthan as a part of the initialization of the deterministic forecast, andthey are characterized by a very low computational cost. DelleMonache et al. (2008) and Kang et al. (2008) showed thata KF-based bias adjustment scheme is very good at removingsystematic errors from O3 forecasts. Kang et al. (2010a,b), Djalalovaet al. (2010), and Borrego et al. (2011) further demonstrated theability of these schemes to considerably improve deterministicforecasts for O3 and PM10. Finally, Garcia et al. (2010) found thatsimple bias correction techniques performed as well or better thanmore complex approaches, although it must be noted that themoresophisticated methods such as 4DVAR and EnKF are probably farfrom being fully exploited.

In this paper, we evaluate the suitability of the KF-basedadaptive regression method for the correction of deterministic airquality forecasts in an area characterized by high levels ofatmospheric pollution. As a study case, we focus on the northernpart of Belgium, which has a high density of human activities, withaccordingly high levels of air emissions from residences, traffic, andindustry.

We apply the KF-based bias correction method to output fromthe deterministic regional air quality model AURORA, covering the

K. De Ridder et al. / Atmospheric Environment 50 (2012) 381e384382

northern part of Belgium with a resolution of 3 km, thus com-plementing several of the studies cited above that generallyconsidered coarser resolutions (in the range of ten to a few tens ofkilometres). Focusing on daily mean PM10 and daily maximum O3concentrations, we calculate station-level forecast correctionfactors, and subsequently compare the corrected forecast concen-trations to observed values from a network of monitoring stations.We also compare the results obtainedwith the KFmethod to resultsobtained with a conceptually (but not computationally) simplerlinear regression scheme.

The remainder of this paper is organized as follows. Section 2gives a brief overview of the KF-based adaptive regressionmethod, and of the deterministic model and the observationsinvolved. Section 3 gives an account of the results obtained, andSection 4 formulates the conclusions.

2. Method

In the description of the Kalman filter-based adaptive regressionmethod we follow Kalnay (2002), in particular her Eqs. (C.3.5). Inthis method, it is assumed that improved concentration values ck

c

(superscript c for ‘corrected’ quantity) can be obtained as a linearfunction of the free (uncorrected) model forecast, denoted ck

f , theindex k referring to time. Considering only one predictor, that is, theforecasted concentration ck

f itself, and accounting for both additiveand multiplicative bias, this linear relation can be written as

cck ¼ Afk þ Bfkc

fk ¼

h1 cfk

i"Afk

Bfk

#hhT

kxfk; (1)

with hkT¼ [1 ck

f ] and xkf ¼ [Akf Bk

f ]T, the latter containing the forecastregression coefficients at time k.

The adaptive KF based approach consists of dynamically esti-mating these regression coefficients, using the difference betweenthe corrected forecast (ckc) and observed (cko) concentration values asa measure for the goodness-of fit in the KF least squares optimi-zation framework. The KF employs a sequential approach, making itparticularly suitable for use in a forecasting scheme. For a full

Fig. 1. Error statistics of the uncorrected (grey stacks) and corrected (black stacks) forecast dthe AURORA domain. The panels show, from top to bottom, the root mean square error, co

account of the steps involved in the implementation of the KalmanFilter, we refer to Kalnay’s (2002) Eqs. (C.3.5).

The implementation of the KF method requires the specificationof the model and observation error covariance matrices. Theregression model error covariance was specified as a diagonalmatrix (the regression coefficient errors being assumeduncorrelated)

Q k ¼"s2A 00 s2B

#; (2)

its elements sA and sB denoting the standard deviations of theregression coefficients Ak

f and Bkf , respectively. The values assigned

to these quantities are discussed below. The observation errorcovariance Rk matrix is simply a scalar with value rk, the value ofwhich is also discussed below.

We considered model output from the deterministic air qualitymodel AURORA, together with observed values, to verify theperformance of the KF-based adaptive regression technique.AURORA is a limited-area Eulerian chemistry-transport modeldescribed in Van de Vel et al. (2009). The model has been appliedand tested in several urban-/regional-scale air quality modelingstudies (De Ridder et al., 2008; Beckx et al., 2009; Lefebvre et al.,2011).

The AURORAmodel was run for the entire year 2007, generatinghourly output concentration fields of relevant pollutant species.The model was run in a triply nested configuration with respectivespatial resolutions of 25, 9, and 3 km, the latter covering the studydomain of northern Belgium. The coarsest domainwas itself nestedwithin output fields of the European-scale Eulerian chemistry-transport model BelEUROS (Deutsch et al., 2008). We used theMIMOSA4 traffic emissions model (Mensink et al., 2000; Lefebvreet al., 2011) to generate hourly emissions of relevant species,including NOx, PM10 and PM2.5, for the study domain. The non-traffic emissions for the Flemish Region were based on the emis-sion inventory compiled by the Flemish Environmental Agency(Vlaamse Milieumaatschappij, 2011). For the regions outside theFlemish Region, but still within the simulation domain, the EMAP

aily mean PM10 concentration values, for all the stations measuring this quantity withinrrelation coefficient, and mean absolute bias, respectively.

Fig. 2. As in Fig. 1, but for daily maximum O3 concentration.

Table 1Error statistics for the free (uncorrected) model forecast result (FREE), the simpleregression method (REGR), and the correction obtained with the Kalman Filteradaptive regression method (KF), for daily mean PM10 and daily maximum O3

concentrations. The table provides the root mean square error (RMSE), magnitude(absolute value) of the bias (jBIASj), and correlation coefficient (CORR), averagedover the stations.

Daily mean PM10 Daily maximum O3

FREE REGR KF FREE REGR KF

RMSE (mgm�3) 14.1 12.0 10.5 25.9 19.0 17.2jBIASj (mgm�3) 8.8 0.6 0.5 7.9 0.6 0.2CORR 0.65 0.63 0.73 0.60 0.74 0.79

K. De Ridder et al. / Atmospheric Environment 50 (2012) 381e384 383

tool (Maes et al., 2009) was used to generate gridded emissionsbased on the downscaling of European-scale EMEP emissions.Meteorological forcing fields were generated with the AdvancedRegional Prediction System (ARPS, see Xue et al., 2000), which isa non-hydrostatic mesoscale meteorological model. The ARPSsimulations were nested in 6-hourly analysis fields of the opera-tional model of the European Centre for Medium-Range WeatherForecasting (ECMWF).

We took results from this retrospective AURORA simulation, yetsetting up the correction scheme as if it were running in forecastmode, i.e., only using observed concentration values available priorto the time of the ‘forecast’, considering the uncorrected simulatedconcentration value of the next day as a one-day model forecast,then applying the KF-based correction, and comparing the result-ing corrected concentration value to the observation of that day.This exercise was done for all days occurring in the AURORAsimulation, considering daily mean PM10 and daily maximum O3concentrations.

Regression model coefficient errors in Q (see above) wereassigned depending on the pollutant, with sA¼ 10 mgm�3 andsB¼ 0.3 in the case of daily mean PM10, and sA¼ 30 mgm�3 andsB¼ 0.5 for daily maximum O3 concentrations. These values werefound by trial and error to yield a good overall performance, and theaccuracy of the results was found to be relatively insensitive to theprecise value of the specified model error. The measurement errorrk (see above) was set to 10% and 20% of the observed concentra-tions for O3 and PM10, respectively.

Observations were taken from the AirBase data archive (http://air-climate.eionet.europa.eu/databases). Given the 3-km resolutionof the AURORA simulation, we only selected background stations,excluding traffic and industrial stations as these are generally notrepresentative at the scale of a 3-km model grid cell. It must benoted that, even though the AURORA model provides full spatialcoverage within its domain boundaries, we only consider forecastcorrections for those grid cells containing a monitoring station, assuch is the restriction imposed by the method used here. This is, ofcourse, a severe restriction; a possible remedy might consist ofspatially interpolating results obtained at station level with the KF-based scheme to the entire model simulation domain, using an

existing technique such as optimal interpolation (see, e.g.,Tombette et al., 2009), and considering the corrected forecastconcentration at each station as a (synthetic) ‘observation’.

3. Results

Results of the validation are provided in Figs. 1 and 2, andTable 1. From this it is clear that the KF-based correction schemeimproves the forecast results for all stations, though the degree ofimprovement varies. For daily mean PM10, and when averaged overthe stations, the adjustment scheme reduces the RMSE from 14.1 to10.5 mgm�3, largely owing to the bias reduction from 8.8 to0.5 mgm�3. The average correlation coefficient increases froma value of 0.65 to 0.73. For daily maximum O3, the RMSE is reducedfrom 25.9 to 17.2 mgm�3, the bias from 7.9 to 0.19 mgm�3, and thecorrelation coefficient increases from a value of 0.60 to 0.79. Theseerror statistics and the improvements obtained by the KF-basedcorrection are similar in magnitude than those obtained by Kanget al. (2010b) and Borrego et al. (2011).

The method implemented here is largely based on straightfor-ward linear regression. It derives its power from the dynamicestimation of the regression coefficients by means of the Kalmanfilter. In order to assess the benefit of the Kalman filter, wecompared the KF-based results against results obtained withanother scheme, in which the regression coefficients were simplyobtained from a linear fit between the observed concentrations and

K. De Ridder et al. / Atmospheric Environment 50 (2012) 381e384384

the free deterministic forecast values for a period prior to theforecast step. By trial and error it was found that a period of twoweeks gave the best results. While somewhat easier to implement,this non-adaptive linear regression scheme is computationally onlymarginally cheaper than the KF scheme. The error statistics ob-tained with this approach and averaged over all the stations areshown in Table 1, demonstrating the better performance achievedby the KF-based method. We conclude from this exercise that theadaptive regression (i.e., dynamic estimation of the regressioncoefficients) by the Kalman filter does have a demonstrated addedvalue.

4. Conclusions

We presented an application of the KF-based adaptive regres-sionmethod to correct deterministic air quality forecast results. Usewasmade of simulated ground-level concentration fields generatedby the AURORA model for the year 2007, considering in particulardaily mean PM10 and daily maximum O3 concentrations. Eventhough use was made of retrospective model output, we ran the KFscheme as if it were in forecast mode, by only considering obser-vations collected prior to the forecast step in the analysis scheme.

The main outcome is that, for daily mean PM10 and dailymaximum O3 concentrations, and averaged over all the stationswithin our study domain, the KF-based correction yieldeda decrease in the RMSE between 26% and 34%, and an increase ofthe correlation coefficient between 12% and 32%. The bias wasreduced to almost nothing, as one would of course also expect fromthis type of correction scheme, which explicitly addresses multi-plicative and additive bias. Overall, the correction scheme wasfound to be easy to implement, very flexible (e.g., in the case oftransitions between negative and positive bias in the course ofsimulated concentration time series), and requiring a very shortspin-up period only. Moreover, when compared to results ofa simple non-adaptive linear regression-based correction scheme,the KF approach was found the more accurate scheme.

The improvement obtained in the forecast error statistics owingto the KF based correction method confirm results obtained byother workers (see references cited in the Introduction) for otherregions and periods. The ease of implementation of the method,together with the gain in accuracy, support the suitability of the KFbased method for correcting deterministic air quality forecasts.

Acknowledgements

The work described here was carried out with support of theEuropean Commission, within the LIFEþ project ATMOSYS and theFP7 project PASODOBLE. We acknowledge the European Environ-ment Agency and the Belgian Interregional Environment Agency(IRCEL/CELINE) for making the concentration measurementsavailable.

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