集合卡尔曼平滑和集合卡尔曼滤波在污染源反演中的应用

Ensemble Kalman Smoother and Ensemble Kalman Filter Approaches to the Joint Air Quality State and Emission Estimation Problem

此文目的是讨论污染源反演问题的统计方法。基于Bayes估计理论,该文将资料同化中的集合平滑、集合卡尔曼平滑和集合卡尔曼滤波应用在污染源反演问题中。在详细给出污染源反演的集合平滑、集合卡尔曼平滑和集合卡尔曼滤波的严格数学表达后,用一个简单的模型演示了集合卡尔曼平滑和集合卡尔曼滤波在污染源反演中的可行性,并且通过对比理想试验结果比较了集合卡尔曼平滑和集合卡尔曼滤波方法在反演污染源排放的效果,讨论了观测误差和污染源先验误差估计对反演结果的影响。试验结果表明在观测间隔小和观测误差小的情况下,集合卡尔曼滤波和集合卡尔曼平滑都可以有效地反演出随时间变化的污染源排放。当观测误差增大时,集合卡尔曼滤波和集合卡尔曼平滑的反演效果都有一定降低,但是反演误差的增加少于观测误差的增加,同时集合卡尔曼平滑(Ensemble Kalman smoother,简称EnKS)对观测误差比集合卡尔曼滤波(Ensemble Kalman fil-ter,简称EnKF)更为敏感。当观测时间间隔较大时,EnKF不能对没有观测时的污染源排放进行估计,仅能对有观测时的污染源排放进行较好的反演。而EnKS可以利用观测对观测时刻前的污染源排放进行反演,因此其效果明显好于EnKF,并且在观测时间间隔较大的情况下依然可以较好地反演出污染源排放。试验结果还显示污染源排放的先验误差估计对反演的结果有较大影响。

The purpose of this paper is to present some ensemble based statistical estimation methods for inversing modeling of pollution emissions. Previous studies using advanced sequential method to the joint air quality state and emission estimation problem focus on the ensemble Kalman filter （EnKF） or the discrete Kalman filter （DKF）. However at each assimilation time, EnKF and DKF cannot update the emissions at the previous time, though their information is contained in the present observations. This is a major drawback, especially in the case of the time-variant emissions. Therefore it is necessary to investigate other methods that can overcome this drawback. Based on Bayes theorem, this study presents the detailed mathematical formulations of the ensemble smoother （ES）, the ensemble Kalman smoother （EnKS） and the ensemble Kalman filter for the joint air quality state and emission estimation problem. Due to the adoption of ES and EnKS, the emission estimation at previous time can be updated by assimilating observation at the later time. A simple model is used to demonstrate the feasibility of the methods. The impacts of observational error and the prior error of the emission on estimation results are also discussed based on the experiments using the simple model. The results show that EnKS can estimate the time-variant emission well at every time step when the observations are not available at every time step, while the EnKF can only estimate the emission well at the observation time. When observations are available at every time step, EnKF and EnKS perform similarly. The larger observational errors can affect the estimation results of emission, but not very sensitively. It is also shown that overestimation or underestimation of the prior emissions uncertainty can bring larger estimation errors of emissions.