[p1] NonGaussianity and nonlinearity
[p117] 
4DEnVAR with iterative calculation of nonlinear model

S. Yokota (Meteorological Research Institute), M. Kunii (Meteorological Research Institute), K. Aonashi (Meteorological Research Institute), and S. Origuchi (Fukuoka Aviation Weather Station) 
Abstract 
4DEnVAR is a useful ensemblebased variational data assimilation method, which does not use adjoint matrices of tangent linear observation operator (H) and forecast model (M). However, 4DEnVAR analyses are generally worse than Hybrid 4DVAR probably because 4DEnVAR does not iteratively calculate nonlinear H and M. Yokota et al. (2016, SOLA) developed 4DEnVAR with observation space localization that iteratively calculates nonlinear H, and showed that this method can make better analyses than 4DLETKF. In this study, we improved this 4DEnVAR to iteratively calculate M as well as H (hereafter, 4DEnVARM), and showed the advantage of 4DEnVARM with singleobservation assimilation experiments and observation system simulation experiments (OSSEs) using a lowresolution AGCM. In the singleobservation assimilation experiments, 4DEnVARM analyses were closer to the observations than 4DEnVAR analyses without iterative calculation of M. In the OSSEs, observations of zonal and meridional winds, temperature, relative humidity, and surface pressure were created by adding random errors to "true" values (results of freerun simulation) and assimilated. Biases and root mean square errors from "true" values were smaller in the forecasts from 4DEnVARM analyses than those from 4DEnVAR analyses without iterative calculation of M. Therefore, iteratively calculating M is likely to be effective to make better analyses. 