A New Scheme of Adaptive Covariance Inflation for Ensemble Filtering Data Assimilation

Abstract

Due to the model and sampling errors of the finite ensemble, the background ensemble spread becomes small and the error covariance is underestimated during filtering for data assimilation. Because of the constraint of computational resources, it is difficult to use a large ensemble size to reduce sampling errors in high-dimensional real atmospheric and ocean models. Here, based on Bayesian theory, we explore a new spatially and temporally varying adaptive covariance inflation algorithm. To increase the statistical presentation of a finite background ensemble, the prior probability of inflation obeys the inverse chi-square distribution, and the likelihood function obeys the t distribution, which are used to obtain prior or posterior covariance inflation schemes. Different ensemble sizes are used to compare the assimilation quality with other inflation schemes within both the perfect and biased model frameworks. With two simple coupled models, we examined the performance of the new scheme. The results show that the new inflation scheme performed better than existing schemes in some cases, with more stability and fewer assimilation errors, especially when a small ensemble size was used in the biased model. Due to better computing performance and relaxed demand for computational resources, the new scheme has more potential applications in more comprehensive models for prediction initialization and reanalysis. In a word, the new inflation scheme performs well for a small ensemble size, and it may be more suitable for large-scale models.