Spatial Structure of the Ensemble Weights in the LETKF and Its Insights

The local ensemble transform Kalman filter (LETKF) finds the optimal weights of linear combinations of the forecast ensemble to obtain the analysis ensemble, independently at each grid point. Therefore, we have spatial distributions of each element of the ensemble weights. Yang et al. previously found that spatial interpolation of the weights help improve the analysis accuracy at least in some cases, in addition to computational accelerations. They implied that smoothing out the high-frequency components of the weights due to spatial interpolation might be the reason for the improvement. Inspired by their findings, this study investigates the spatial structure of the ensemble weights more in detail, in particular, the scale dependence on the localization scales. The careful study about the structure of weights motivates adaptive weight interpolation, in which we skip computing the weights when and where it is found to be appropriate. Also, this motivates mixing weights at different scales, allowing multi-scale treatment in data assimilation.