Spatially and temporally varying adaptive inflation algorithms have been developed to combat the loss of variance during the forecast due to various model and sampling errors. The adaptive Bayesian scheme of Anderson uses available observations to update the Gaussian inflation distribution assigned for every state variable. The likelihood function of the inflation is computed using model-minus-data innovation statistics. A number of enhancements for this inflation scheme are proposed. To prevent excessive deflation, an inverse gamma distribution for the prior inflation is considered. A non-Gaussian distribution offers a flexible framework for the inflation variance to evolve during the update. The innovations are assumed random variables, and a correction term is added to the mode of the likelihood distribution such that the observed inflation is slightly larger. This modification improves the stability of the adaptive scheme by limiting the occurrence of negative and physically intolerable inflations. The enhanced scheme is compared to the original one in twin experiments using the Lorenz-63 model, the Lorenz-96 model, and an idealized, high-dimensional atmospheric model. Results show that the proposed enhancements are capable of generating accurate and consistent state estimates. Allowing moderate deflation is shown to be useful.
