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Errors in Ensemble Kalman Smoother Estimates of Cloud Microphysical Parameters

AbstractIf forecast or observation error distributions are non-Gaussian, the true posterior mean and covariance depends on the distribution of observation errors and the observed values. The posterior distribution of analysis errors obtained from ensemble Kalman filters and smoothers is independent of observed values. Hence, the error in ensemble Kalman smoother (EnKS) state estimates is closely linked to the sensitivity of the true posterior to observed values. Here a Markov chain Monte Carlo (MCMC) algorithm is used to document the dependence of the errors in EnKS-based estimates of cloud microphysical parameters on observed values. It is shown that EnKS analysis distributions are grossly inaccurate for nonnegative microphysical parameters when parameter values are close to zero. Furthermore, numerical analysis is presented that shows that, by design, the posterior distributions given by EnKS and even nonlinear extensions of these smoothers approximate the average of all possible posterior analysis dist...