The optimization of SO₂ emissions by the 4DVAR and EnKF methods and its application in WRF-Chem

Emissions are essential for forecasting air quality and pollution control, but traditional emissions are often not real-time by the statistics of "bottom-up" approach due to high human resource demand. The four-dimensional variational method (4DVAR) and the ensemble Kalman filter (EnKF) are generally used to optimize emissions based on chemical transport models by assimilating observations. Although the two methods solve similar estimation problems, different functions have been developed to address the process of converting the emissions to concentrations. In this paper, we evaluated the performance of the 4DVAR and EnKF methods in optimizing SO₂ emissions over China during 23-29 January 2020. The emissions optimized by the 4DVAR and EnKF methods showed a similar spatiotemporal distribution in most regions of China during the study period, suggesting that both methods are useful in reducing uncertainties in the prior emissions. Three forecast experiments with different emissions were conducted. Compared with the forecasts with prior emissions, the root-mean-square error of the forecasts with the emissions optimized by the 4DVAR and EnKF methods decreased by 45.7 % and 40.4 %. This indicates that the 4DVAR method was slightly more effective than the EnKF method in optimizing emissions and improves the accuracy of forecasts. Furthermore, it is found that the 4DVAR method performed better than the EnKF method when the spatial and/or temporal distribution of SO₂ observations with strong local characteristics, The EnKF method showed a better performance for the condition of the large difference between prior emissions and real emissions. The results may help to design suitable assimilation algorithms for optimizing emissions and improving model forecasts. The advance data assimilation systems are beneficial for the understanding the effectiveness and value of emission inventories and air quality model.