A Hybrid Kalman Filter Algorithm for Large-Scale Atmospheric Chemistry Data Assimilation

Abstract

In the past, a number of algorithms have been introduced to solve data assimilation problems for large-scale applications. Here, several Kalman filters, coupled to the European Operational Smog (EUROS) atmospheric chemistry transport model, are used to estimate the ozone concentrations in the boundary layer above Europe. Two Kalman filter algorithms, the reduced-rank square root (RRSQRT) and the ensemble Kalman filter (EnKF), were implemented in a prior study. To combine the best features of these two filters, a hybrid filter was constructed by making use of the reduced-rank approximation of the covariance matrix as a variance reducer for the EnKF. This hybrid algorithm, complementary orthogonal subspace filter for efficient ensembles (COFFEE), is coupled to the EUROS model. The performance of all algorithms is compared in terms of residual errors and number of EUROS model evaluations. The COFFEE results score somewhere between the EnKF and RRSQRT results for less than approximately 30 model evaluations. For more than approximately 30 model evaluations, the COFFEE results are, in all cases, better than the EnKF and RRSQRT results. The results of the COFFEE simulations with more than about 60 model evaluations proved to be significantly better than all the EnKF and RRSQRT simulations (even better than those with 100 and 200 modes or ensemble members). The performance of both the EnKF- and RRSQRT-type filters is affected by the nonlinear properties of the model and observation operator, because both rely on linearization to some extent. To further study this aspect, several measures of nonlinearity were calculated and linked with the performance of these algorithms.