Implementation of a Modified Adaptive Covariance Inflation Scheme for the Big Data-Driven NLS-4DVar Algorithm

Abstract

The adaptive inflation scheme is critical for avoiding underestimation of ensemble-estimated error variances. In this study, we expanded a spatially and temporally varying adaptive inflation scheme proposed within the framework of the local ensemble transform Kalman filter to a global version to facilitate its application in four-dimensional ensemble-variational (4DEnVar) data assimilation methods. We adopted an efficient local correlation matrix decomposition approach to enhance its computation efficiency and then implemented the modified adaptive inflation scheme using the big data-driven nonlinear least squares 4-D variational (BD-NLS4DVar) data assimilation method to improve its robustness. The ensemble analysis scheme of the BD-NLS4DVar method with the modified adaptive inflation scheme was able to adjust the ensemble spreads and error covariances more accurately. Several groups of observing system simulation experiments based on 2-D shallow-water equations demonstrated that the BD-NLS4DVar method implemented with the modified adaptive inflation scheme provides some performance improvement over the standard BD-NLS4DVar method with no inflation.