A Multiscale Local Gain Form Ensemble Transform Kalman Filter (Mlgetkf)

A new multiscale, ensemble-based data assimilation (DA) method, multiscale local gain form ensemble transform Kalman filter(MLGETKF), is introduced. MLGETKF allows simultaneous update of multiple scales for both the ensemble mean and perturbations through assimilating all observations at once. MLGETKF performs DA in independent local volumes, which lends the algorithm a high degree of computational scalability. The multiscale analysis is enabled through the rapid creation of many pseudoensemble perturbations via a multiscale ensemble modulation procedure. The Kalman gain that is used to update the raw background ensemble mean and perturbations is based on this modulated ensemble, which intrinsically includes multiscale model space localization. Experiments with a noncycled statistical model show that the full background covariance estimated by MLGETKF more accurately resembles the shape of the true covariance than a scale-unaware localization. The mean analysis from the best-performing MLGETKF is statistically significantly more accurate than the best-performing scale-unaware LGETKF. The accuracy of the MLGETKF analysis is more sensitive to small-scale band localization radius than large-scale band. MLGETKF is further examined in a cycling DA context with a surface quasigeostrophic model. The root-mean-square potential temperature analysis error of the best-performing MLGETKF is 17.2% lower than that of the best-performing LGETKF. MLGETKF reduces analysis errors measured in kinetic energy spectra space by 30%-80% relative to LGETKF with the largest improvement at large scales. MLGETKF deterministic and ensemble mean forecasts are more accurate than LGETKF for full and large scales up to 5-6-day lead time and for small scales up to 3-4-day lead time, gaining similar to 12 h(-1) day of predictability.