Displaced Ensemble variational assimilation to incorporate microwave imager brightness temperatures into a cloud-resolving model for Typhoon Conson

Satellite Microwave Imager (MWI) brightness temperatures (TBs) give precipitation-related information around Tropical Cyclones (TCs). The goal of the present study is to develop a method to assimilate MWI TBs into Cloud-Resolving Models (CRMs). To address the non-linear relationship of TBs to the state variables of CRM and the flow-dependency of the CRM forecast error covariance, we adopted an Ensemble-based variational data assimilation method. There often exist large-scale displacement errors of rainy areas between the observation and the CRM forecasts, in particular, around TCs over ocean. In such cases, Ensemble-based data assimilation can give erroneous analysis, particularly for observed rain areas without forecasted rain. In order to solve this problem, we propose the Ensemble-based assimilationthat uses Ensemble forecast error covariance with displacement error correction. Based on this idea, we developed a data assimilation method that incorporates the MWI TBs into the CRM developed by the Japan Meteorological Agency (JMANHM). This method consisted of a displacement error correction scheme and an Ensemble-based variational assimilation scheme. In the displacement error correction scheme, we obtained the optimum displacement that maximized the conditional probability of TB observation given the displaced CRM variables. In the assimilation scheme, we derived a cost function in the displaced Ensemble forecast error subspace. Then, we obtained the analyses of CRM variables by non-linear minimization of the cost function. We applied this method to assimilate TMI (TRMM Microwave Imager) low-frequency TBs (10, 19, and 21 GHz with vertical polarization) for the Typhoon Conson case around Okinawa (9th June 2004). In this case, TBs calculated from the CRM Ensemble forecasts had large-scale displacement errors, in particular over south-east and east of the Typhoon. The results of the assimilation experiments showed that the assimilation of TMI TBs alleviated the large-scale displacement errors and improved the CRM forecasts. The displacement error correction scheme and the Ensemble-based variational assimilation scheme contributed to this alleviation by moistening the mid- to lower-troposphere and inducing updraft in the mid-troposphere in the observed rain areas, respectively. The displacement error correction also increased the number of Ensemble members with precipitation comparable to the observation. This reduced the sampling error in the analysis of the Ensemble-based variational assimilation.