An Investigation of Adaptive Radius for the Covariance Localization in Ensemble Data Assimilation

Abstract

The covariance matrix estimated from the ensemble data assimilation always suffers from filter collapse because of the spurious correlations induced by the finite ensemble size. The localization technique is applied to ameliorate this issue, which has been suggested to be effective. In this paper, an adaptive scheme for Schur product covariance localization is proposed, which is easy and efficient to implement in the ensemble data assimilation frameworks. A Gaussian-shaped taper function is selected as the localization taper function for the Schur product in the adaptive localization scheme, and the localization radius is obtained adaptively through a certain criterion of correlations with the background ensembles. An idealized Lorenz96 model with an ensemble Kalman filter is firstly examined, showing that the adaptive localization scheme helps to significantly reduce the spurious correlations in the small ensemble with low computational cost and provides accurate covariances that are similar to those derived from a much larger ensemble. The investigations of adaptive localization radius reveal that the optimal radius is model-parameter-dependent, vertical-level-dependent and nearly flow-dependent with weather scenarios in a realistic model; for example, the radius of model parameter zonal wind is generally larger than that of temperature. The adaptivity of the localization scheme is also illustrated in the ensemble framework and shows that the adaptive scheme has a positive effect on the assimilated analysis as the well-tuned localization.

Correction: Xing et al. An Investigation of Adaptive Radius for the Covariance Localization in Ensemble Data Assimilation. J. Mar. Sci. Eng. 2021, 9, 1156

“…The taper coefficient of the localization weighting function should be zero when E C(r) 2 is less than 1 N−1 , in which the corresponding distance r is the localization radius threshold value. The localization radius can be computed adaptively with known statistical properties of sample covariances and updated with the real-time characteristics in the ensemble system.…”

Numerical experimental research on assimilation of cloud-free radiances from fengyun-3D microwave sounding observations over land surface

“…The FY-3D microwave sounding instruments don't have window channels at 23.8GHz and 31.4GHz, which makes it very difficult to obtain Cloud Liquid Water (CLW) and Total Precipitation Water (TPW). But the unique 118.75 GHz channel of FY-3D happens to be very sensitive to water condensates [2][3][4]. These are the key problems to be solved in the application of FY-3D microwave data assimilation.…”