A Method of Improving Error Covariances in EnKF and Its Application to Data Assimilation

In the ensemble Kalman filter (EnKF), the forecast error covariance matrix is estimated as the sampling covariance matrix of the forecast ensemble. However, previous studies suggest that the sampling error resulting from finite-size ensembles may make such estimations far from the true forecast error covariance, and finally degrade the performance of EnKF. A common way to address this problem is covariance inflation with a time-constant inflation factor. A time-dependent infiation approach on forecast error covariance matrix (i.e., MLE method) is developed based on the maximum likelihood estimation theory, so as to improve estimates of forecast error covariances. At Delgertsgot (DGS) Station in the Mongolian Plateau reference site, point observations of ground temperature and soil temperature at the depth of 10 cm are assimilated into the Common Land Model (CoLM) with a frequency of every 12 hours, using two assimilation algorithms (EnKF method and MLE method), in order to test the effectivity of MLE in practical assimilation. In this way, a soil temperature assimilation system is constructed on the point scale.Results indicate that MLE method performs better than EnKF method for ground temperature and soil temperatures at most depths (especially for soil temperatures at deeper depths). Moreover, considering differences between soil temperatures at shallower depths and those at deeper depths, different inflation factors are adopted to them when implementing MLE method. Compared to results of MLE using a single scalar inflation factor, it shows that multiple-factor inflation is able to alleviate the unreasonable inflation of soil temperatures at deeper depths and therefore get better assimilation results. In addition, the leaf area index (LAI) in the CoLM is updated dynamically by MODIS LAI products, and results derived using MODIS LAI are compared to those derived using LAI computed by experiential formula, so as to study the effect of the LAI accuracy on simulated and assimilated soil temperatures. It shows that using MODIS LAI can get better simulation of soil temperature at depths of 0 cm and 3 cm, as well as more accurate assimilation of soil temperature at most depths.The inflation factor is set to be variable in time, but constant in space. However, variables such as soil temperature and soil moisture behave quite differently at shallow surfaces and deep depths, and observations may be unevenly distributed in space in regional assimilation researches. Therefore, it is necessary to adopt different inflation factors to different variables or to the same variable at different locations. In the future, it is necessary to develop a time-and-space dependent inflation method and test its capability in real applications.