Effects of mis-specified time-correlated model error in the (ensemble) Kalman Smoother.

Data assimilation is often performed under the perfect model assumption. Although there is an increasing amount of research accounting for model errors in data assimilation, the impact of an incorrect specification of the model errors on the data assimilation results has not been thoroughly assessed. We investigate the effect that an inaccurate time correlation in the model error description can have on data assimilation results, deriving analytical results using a Kalman Smoother for a one-dimensional system.

Time-correlated model error in the (ensemble) Kalman smoother.

Data assimilation is often performed in a perfect-model scenario, where only errors in initial conditions and observations are considered. Errors in model equations are increasingly being included, but typically using rather adhoc approximations with limited understanding of how these approximations affect the solution and how these approximations interfere with approximations inherent in finite-size ensembles. We provide the first systematic evaluation of the influence of approximations to model errors within a time window of weak-constraint ensemble smoothers.