Dynamically Weighted Hybrid Gain Data Assimilation: Perfect Model Experiments.

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 recent proposed hybrid approaches is called Hybrid Gain (HG). It obtains the final analysis from a linear combination of two analyses: the ensemble mean analysis and the variational system, which uses the same ensemble mean analysis as the background. 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 3DVar 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 3DVar analysis. For this purpose, we define the weighting factor alpha, which multiplies the 3DVar analysis, as the normalized spread for each variable at each level. Then, (1-alpha), which decreases with increasing spread, becomes the factor that multiplies the LETKF analysis. The results are very encouraging: the original HG and new Weighted HG analyses have similarly high quality and are better than both 3DVar and LETKF. However, the dynamically Weighted HG analyses are significantly more balanced than the original Hybrid Gain 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.