Tijana Janjic, Hans Ertel Centre for Weather Research, DWD
Conservation laws and the local ensemble transform Kalman filter
Abstract: In order to better predict the properties of nonlinear flow with numerical weather prediction (NWP) models, Arakawa (1966,1972) proposed that numerical discretization schemes preserve the most important conservation properties of the continuum system. This principle has influenced the design of climate and NWP models for many years, and many numerical models of the atmosphere in use today are able to preserve these properties. The question arises, whether data assimilation algorithms can and should incorporate some of the properties of the nonlinear flow, following the similar principle of design as NWP models.
To this end, we explore the conservation properties during assimilation using perfect model experiments with mass, total energy and momentum conserving 2D shallow water model that also conserves enstrophy for non-divergent flow. The performance with respect to nonlinear energy cascade is assessed as well. Data assimilation uses the LETKF, with varying localization radius, thinning interval, observed variable and inflation. It was found that during assimilation, the total mass remains consistent with that of nature run and that the total energy of the analysis mean converges towards the nature run value. However, enstrophy, divergence as well as spectra of energy are strongly affected by localization radius, thinning interval, and inflation and depend on variable, which is observed. Having in mind that Arakawa and Arakawa and Lamb showed that the conservation of both kinetic energy and enstrophy by momentum advection schemes in the case of non-divergent flow prevents systematic and unrealistic energy cascade towards high wave numbers, we test the effects on prediction depending on the type of errors in the initial condition. We measure nonlinear energy cascade through scalar, domain averaged, noise term. We show that the accumulated noise during assimilation and the analysis RMSE are good indicators of quality of the prediction.