Ensemble filtering and low-resolution model error: Covariance inflation, stochastic parameterization, and model numerics

The use of under-resolved models in ensemble data assimilation schemes leads to two kinds of model errors: truncation errors associated with discretization of the large-scale dynamics and errors associated with interactions with subgrid scales. Multiplicative and additive covariance inflation can be used to account for model errors in ensemble Kalman filters, but they do not reduce the model error. Truncation errors can be reduced by increasing the accuracy of the numerical discretization of the large-scale dynamics, and subgrid-scale parameterizations can reduce errors associated with subgrid-scale interactions. Stochastic subgrid-scale parameterizations both reduce the model error and inflate the ensemble spread, so their effectiveness in ensemble assimilation schemes can be gauged by comparing with covariance inflation techniques. The effects of covariance inflation, stochastic parameterizations, and model numerics in two-layer periodic quasigeostrophic turbulence are compared on an f plane and on a ß plane. The stochastic backscatter schemes used here model backscatter in the inverse cascade regime of quasigeostrophic turbulence, as appropriate to eddy-permitting ocean models. Covariance inflation improves the performance of a benchmark model with no parameterizations and second-order numerics. Fourth-order spatial discretization and the stochastic parameterizations, alone and in combination, are superior to covariance inflation. In these experiments fourth-order numerics and stochastic parameterizations lead to similar levels of improvement in filter performance even though the climatology of models without stochastic parameterizations is poor.