An adaptive covariance relaxation method for ensemble data assimilation

For ensemble filters, accounting for unrepresented errors by inflating the ensemble perturbations can help improve filter performance. However, tuning the inflation factor can be costly, thus demanding adaptive covariance inflation (ACI) algorithms that give an online estimate of a temporally varying inflation factor. Additionally, a spatially varying inflation factor should be used to account for an irregular observation network. Anderson's adaptive inflation method offers a spatially and temporally varying inflation factor estimated from innovation statistics using a hierarchical Bayesian approach. In this study, we propose an alternative adaptive covariance relaxation (ACR) method that estimates a relaxation parameter online. Instead of treating inflation parameters as spatially varying random variables as in Anderson's method, the relaxation-to-prior-spread method provides an ensemble spread reduction term that serves as a spatial mask to account for an irregular observation network. We demonstrate with a set of experiments using the 40-variable Lorenz model that the ACR method is able to improve filter performance with the presence of sampling/model errors over a range of severity. Its reliability and ease of implementation suggest potential for future applications with atmospheric models.