Dual-Scale Neighboring Ensemble Variational Assimilation Scheme to incorporate Satellite Microwave Imager brightness temperatures

Satellite Microwave Imager (MWI) brightness temperatures (TBs) give precipitation-related information globally. The goal of the present study is to develop an Ensemble-based Variational Assimilation (EnVA) scheme with sampling error damping method to assimilate MWI TBs into Cloud-Resolving Models (CRMs). This is because, in ensemble-based assimilation schemes for CRMs, sampling error is serious, in particular, for precipitation-related variables (precipitation rate, vertical wind speed) because they are confined in rainy areas.

Based on the CRM ensemble forecast error analyses for various precipitation cases, we developed the sampling error damping method that consisted of a Neighboring Ensemble (NE) method and a dual scale separation of NE (hereafter referred as dual-scale NE method). The NE method approximated the forecast error correlation using NE members within a reduced-grid box based on the spectral localization assumption. In the dual scale separation, we divided the NE forecast error into large-scale portions and small-scale deviations so as to reflect the horizontal scale differences in forecast error between precipitation-related variables and others.

In order to introduce the dual-scale NE method to the EnVA, first, we estimated the standard deviation and correlation of forecast error by this method, and prescribed the space spanned by this forecast error (the dual scale NE forecast error subspace). Then we minimized a three-dimensional cost function to obtain the optimal analysis increment for the ensemble mean, assuming that the analysis increments were subject to the dual scale NE forecast error subspace. We employed Bishop's transform matrix to calculate the analysis increments for ensemble members from the ensemble forecasts.

In order to examine the EnVA scheme, we performed observation system simulation experiments for several meteorological disturbance cases. The results show that the NE method was successful in producing plausible analyses of precipitation-related variables from the simulated surface precipitation even for grid points where less than 20 % of the ensemble members forecasted precipitation, and that the dual scale separation of NE made spatial scale changes in analysis increments in correspondence with precipitation rates. The EnVA scheme was also successful in retrieving precipitation flags and precipitation profiles from the simulated multi-channel microwave brightness temperatures that were non-linear functions of various precipitation-related variables.