Kalman filter-based air quality forecast adjustment

doi:10.1016/j.atmosenv.2012.01.032

Atmospheric Environment

Volume 50, April 2012, Pages 381-384

https://doi.org/10.1016/j.atmosenv.2012.01.032 Get rights and content

Abstract

We evaluate a Kalman Filter (KF) based adaptive regression method for the correction of deterministic air quality 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 dynamically by means of the KF technique. Basically, this method exploits the information regarding the mismatch between the deterministic forecast and observations of the prior period to calculate regression coefficients for the correction of the next forecast step.

We considered model output generated by the deterministic regional air quality model AURORA over northern Belgium for the year 2007, together with observed values at a few tens of stations. It was found that, for daily mean PM₁₀ concentrations, and averaged over the monitoring stations, the correction scheme reduced the root mean square error from 15.9 to 10.5 μg m⁻³, largely thanks to the bias reduction from 8.8 to 0.5 μg m⁻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 μg m⁻³, the bias from 7.9 to 0.2 μg m⁻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 the adaptive regression method outperformed this simpler scheme consistently, demonstrating the relevance of the dynamic KF-based method for use in the correction of deterministic air quality forecasts.

Introduction

Over the past decade, the use of data assimilation techniques to improve deterministic air quality forecasts has increased considerably. Most of these techniques aim at estimating optimal initial and boundary conditions (including emission correction factors) for a deterministic model forecast. Different sophisticated approaches exist, such as four-dimensional variational data assimilation (4DVAR) (Elbern et al., 2007, Zhang et al., 2008) and Ensemble Kalman Filtering (EnKF) (Eben et al., 2005, Barbu et al., 2009, Tang et al., 2011). Also, increasing use is made of ensemble median-based approaches (Riccio et al., 2007). While these techniques are potentially 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 ensemble members.

Conversely, in recent years rather simple bias adjustement techniques have emerged, in which the bias correction factors are estimated by means of the Kalman (1960) filter (KF) approach. Borrowed from meteorology (see, e.g., Kalnay, 2002), these techniques are applied in post-processing (i.e., off-line) mode rather than as a part of the initialization of the deterministic forecast, and they are characterized by a very low computational cost. Delle Monache et al. (2008) and Kang et al. (2008) showed that a KF-based bias adjustment scheme is very good at removing systematic errors from O₃ forecasts. Kang et al., 2010a, Kang et al., 2010b, Djalalova et al., 2010, and Borrego et al. (2011) further demonstrated the ability of these schemes to considerably improve deterministic forecasts for O₃ and PM₁₀. Finally, Garcia et al. (2010) found that simple bias correction techniques performed as well or better than more complex approaches, although it must be noted that the more sophisticated methods such as 4DVAR and EnKF are probably far from being fully exploited.

In this paper, we evaluate the suitability of the KF-based adaptive regression method for the correction of deterministic air quality forecasts in an area characterized by high levels of atmospheric pollution. As a study case, we focus on the northern part of Belgium, which has a high density of human activities, with accordingly high levels of air emissions from residences, traffic, and industry.

We apply the KF-based bias correction method to output from the deterministic regional air quality model AURORA, covering the northern part of Belgium with a resolution of 3 km, thus complementing several of the studies cited above that generally considered coarser resolutions (in the range of ten to a few tens of kilometres). Focusing on daily mean PM₁₀ and daily maximum O₃ concentrations, we calculate station-level forecast correction factors, and subsequently compare the corrected forecast concentrations to observed values from a network of monitoring stations. We also compare the results obtained with the KF method to results obtained with a conceptually (but not computationally) simpler linear regression scheme.

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

Section snippets

Method

In the description of the Kalman filter-based adaptive regression method we follow Kalnay (2002), in particular her Eqs. (C.3.5). In this method, it is assumed that improved concentration values c_k^c (superscript c for ‘corrected’ quantity) can be obtained as a linear function of the free (uncorrected) model forecast, denoted c_k^f, the index k referring to time. Considering only one predictor, that is, the forecasted concentration c_k^f itself, and accounting for both additive and multiplicative

Results

Results of the validation are provided in Fig. 1, Fig. 2, and Table 1. From this it is clear that the KF-based correction scheme improves the forecast results for all stations, though the degree of improvement varies. For daily mean PM₁₀, and when averaged over the stations, the adjustment scheme reduces the RMSE from 14.1 to 10.5 μg m⁻³, largely owing to the bias reduction from 8.8 to 0.5 μg m⁻³. The average correlation coefficient increases from a value of 0.65 to 0.73. For daily maximum O₃, the

Conclusions

We presented an application of the KF-based adaptive regression method to correct deterministic air quality forecast results. Use was made of simulated ground-level concentration fields generated by the AURORA model for the year 2007, considering in particular daily mean PM₁₀ and daily maximum O₃ concentrations. Even though use was made of retrospective model output, we ran the KF scheme as if it were in forecast mode, by only considering observations collected prior to the forecast step in the

Acknowledgements

The work described here was carried out with support of the European Commission, within the LIFE+ project ATMOSYS and the FP7 project PASODOBLE. We acknowledge the European Environment Agency and the Belgian Interregional Environment Agency (IRCEL/CELINE) for making the concentration measurements available.

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Technical noteKalman filter-based air quality forecast adjustment

Abstract

Introduction

Section snippets

Method

Results

Conclusions

Acknowledgements

Atmospheric Environment

Atmospheric Environment

Science of the Total Environment

Atmospheric Environment

Atmospheric Environment

Atmospheric Environment

Atmospheric Environment

Atmospheric Environment

Atmospheric Environment

Atmospheric Environment

A Kalman-filter bias correction of ozone deterministic, ensemble-averaged, and probabilistic forecasts

Tellus B

Modeling changes of aerosol compositions over Belgium and Europe

International Journal of Environment and Pollution

Technical note
Kalman filter-based air quality forecast adjustment