Using the (Iterative) Ensemble Kalman Smoother to Estimate the Time Correlation in Model Error

Numerical weather prediction systems contain model errors related to missing and simplified physical processes, limited resolution. While it has been widely recognized that these need be included in the data assimilation formulation, providing prior estimates of their spatio-temporal characteristics is a hard problem. We follow systematic path estimate parameters error specifically time-correlated errors. This problem more difficult than standard parameter estimation because are only visible through random realisations. By concentrating on linear nonlinear low-dimensional systems, we able highlight many aspects this problem, using state augmentation an ensemble Kalman smoother (EnKS) its iterative variant (IEnKS). It not possible one window enough information gathered see errors, even when every time step observed. If estimated one-dimensional system EnKS works well, but try two method fails. An IEnKS find correct values for system. For highly logistic map can get stuck local minima, with careful tuning length iterations transformation solution space found. The main conclusion estimating –even systems– via reformulation practical solutions