Local ensemble transform Kalman filter with realistic observations

Abstract

The main goal of my research is to improve the performance of the EnKF in assimilating real observations in order to accelerate the development of EnKF systems towards operational applications. A Local Ensemble Transform Kalman Filter (LETKF, Hunt et al. 2007) is used as an efficient representative of other EnKF systems. This dissertation has addressed several issues relating to the EnKF for assimilating real data.

The first issue is model errors. We assimilated observations generated from the NCEP/NCAR reanalysis fields into the SPEEDY model. The performance of the LETKF without accounting for model errors is seriously degraded compared with that in the perfect model scenario. We then investigated several methods to handle model errors including model bias and system-noise. Our results suggest that the pure bias removal methods (DdSM and LDM) are not able to beat the multiplicative or additive inflation schemes that account for the effects of total model errors. By contrast, when the bias removal methods (DdSM+ and LDM+) are supplemented by additive noise for representing the system-noise, they outperform the inflation schemes. Of these augmented methods, the LDM+, where the constant bias, diurnal bias and state-dependent errors are estimated from a large sample of 6-hour forecast errors, gives the best results.

The other two issues addressed are the estimation of the inflation factor and of observation error variance. Without the accurate observation error statistics, a scheme for adaptively estimating inflation alone does not work, and vice versa. We propose to estimate simultaneously both the adaptive inflation and observation error variance. Our results for the Lorenz-96 model examples suggest that the simultaneous approach works perfectly in the perfect model scenario and in the presence of random model errors. For the case of systematic model bias, although it underestimates the observation error variance, our algorithm produces analyses that are comparable with the best tuned inflation value. SPEEDY model experiments indicate that our method is able to retrieve the true error variance for different types of instrument separately when applied to a more realistic high-dimension model.

Our research in this dissertation suggests the need to develop a more advanced LETKF with both bias correction and adaptive estimation of inflation within the system.