Comparing hybrid data assimilation methods on the Lorenz 1963 model with increasing non-linearity

Abstract

We systematically compare the performance of ETKF-4DVAR, 4DVAR-BEN and 4DENVAR with respect to two traditionalmethods (4DVAR and ETKF) and an ensemble transform Kalman smoother (ETKS) on theLorenz 1963 model. We specifically investigated this performance with increasing non-linearity and using a quasi-static variational assimilation algorithm as a comparison.Using the analysis rootmean square error (RMSE)as a metric, thesemethods have been compared considering (1) assimilation window length and observation interval size and (2) ensemble size to investigate the influence of hybrid background error covariance matrices and non-linearity on the performance of the methods. For short assimilation windows with close to linear dynamics, it has been shown that all hybrid methods show an improvement inRMSEcompared to the traditionalmethods. For long assimilation window lengths inwhich non-linear dynamics are substantial, the variational framework can have difficulties finding the globalminimum of the cost function, so we explore a quasi-static variational assimilation (QSVA) framework. Of the hybrid methods, it is seen that under certain parameters, hybrid methodswhich do not use a climatological background error covariance do not need QSVA to perform accurately. Generally, results show that the ETKS and hybrid methods that do not use a climatological background error covariance matrix with QSVA outperform all other methods due to the full flow dependency of the background error covariance matrix which also allows for the most non-linearity.