Abstract
Hybrid systems have become the state of the art among data assimilation methods. These systems combine the benefits of two other systems that are traditionally used in operational weather forecasting: an ensemble-based system and a variational system. One of the most recently proposed hybrid approaches is called hybrid gain (HG). It obtains the final analysis as a linear combination of two analyses, assuming that the innovations (i.e. the forecast and the set of observations used) between the two data assimilation methods are identical. A perfect model experiment was performed using the HG in the SPEEDY model to show a new methodology to assign different weights to the two analyses, LETKF and 3D-Var in the generation of the final analysis. Our new approach uses, in the assignment of the weights, the ensemble spread, considered to be a measure of uncertainty in the LETKF. Thus, it is possible to use the estimation of the uncertainty of the analysis that the LETKF provides, to determine where the system should give more weight to the LETKF or the 3D-Var analysis. For this purpose, we define a geographically varying weighting factor alpha, which multiplies the 3D-Var analysis, as the normalised spread for each variable at each level. Then, (1-alpha), which decreases with increasing spread, becomes the factor that multiplies the LETKF analysis. The underlying mechanism of the spread–error relationship is explained using a toy model experiment. The results are very encouraging: the original HG and the new weighted HG analyses have similar high quality and are better than both 3D-Var and LETKF. However, the dynamically weighted HG analyses are significantly more balanced than the original HG analyses are, which has probably contributed to the consistently improved performance observed in the weighted HG, which increases with time throughout the 5-day forecasts.
Acknowledgements
The authors thank Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for the Sandwich scholarship and PhD scholarship. We also thank the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for the PhD scholarship.
Disclosure statement
No potential conflict of interest was reported by the authors.