Local Ensemble Transform Kalman Filter with Cross Validation

Abstract

Abstract Many ensemble data assimilation (DA) approaches suffer from the so-called inbreeding problem. As a consequence, there is an excessive reduction in ensemble spread by the DA procedure, causing the analysis ensemble spread to systematically underestimate the uncertainty of the ensemble mean analysis. The stochastic EnKF used for operational NWP in Canada largely avoids this problem by applying cross validation, that is, using an independent subset of ensemble members for updating each member. The goal of the present study is to evaluate two new variations of the local ensemble transform Kalman filter (LETKF) that also incorporate cross validation. In idealized numerical experiments with Gaussian-distributed background ensembles, the two new LETKF approaches are shown to produce reliable analysis ensembles such that the ensemble spread closely matches the uncertainty of the ensemble mean, without any ensemble inflation. In ensemble DA experiments with highly nonlinear idealized forecast models, the deterministic version of the LETKF with cross validation quickly diverges, but the stochastic version produces better results, nearly identical to the stochastic EnKF with cross validation. In the context of a regional NWP system, ensemble DA experiments are performed with the two new LETKF-based approaches with cross validation, the standard LETKF, and the stochastic EnKF. All approaches with cross validation produce similar ensemble spread at the first analysis time, though the amplitude of the changes to the individual members is larger with the stochastic approaches. Over the 10-day period of the experiments, the fit of the ensemble mean background state to radiosonde observations is statistically indistinguishable for all approaches evaluated.