Adaptive Prior Inflation for Ensemble Filters: Application to a Large-Scale Atmospheric Model

Most ensemble assimilation schemes suffer from loss of variance due to sampling errors. The limited ensemble size in addition to the neglected model error are factors that often lead to such sampling errors. Prior covariance inflation is one possible way to counter the variance deficiency. Different adaptive forms of prior inflation have been proposed within the assimilation literature. These follow a Bayesian update scheme given the distance between the prior state distribution and the observation likelihood. Recently, few studies proposed to apply inflation on the posterior ensemble instead of the prior. The idea is to relax the uncertainty of the posterior back to the prior spread or perturbations. Here, we propose a spatially and temporally adaptive posterior inflation algorithm that is fully Bayesian and uses analysis-minus-observation type innovations to update the inflation values. In addition, we also discuss some improvements to current adaptive inflation schemes such as the use of non-Gaussian prior distributions. The usefulness of prior and posterior inflation to mitigate different sources of errors, during both the forecast and the analysis, will be investigated. The performance of the inflation schemes will be tested using twin experiments with (i) the Lorenz-96 system and (ii) a low-order atmospheric model. We will also show results for numerical weather prediction using the Community Atmosphere Model (CAM) assimilating wind and temperature observations from radiosondes, ACARS and aircraft along with GPS radio occultation observations.