Data assimilation experiments with transformed ensemble Kalman filter

Using simulated observations of radial velocity and radar reflectivity factor the behavior of the transformed EnKF for convective-scale data assimilation is tested. The mesoscale weather prediction model used is a US NAVY COAMPS (Hodur, 1997). The model has a total of eleven variables including three Cartesian velocity components (u,v,w), five mixing ratios (cloud, rain, snow, graupel and water vapor), potential temperature th, perturbation exner function pi and turbulence kinetic energy e. The model solves the nonhydrostatic equations in a domain of 72 km by 72 km with grid resolution of 2 km in the horizontal directions and 35 vertical layers with variable resolution. The model time step used in this study is 6 s. The reference simulation begins with a warm, moist bubble in a horizontally uniform environment; that is, u, v, th and mixing ratios vary only with height outside the bubble, and w is zero. The perturbation potential temperature inside the bubble is formulated by simple analytical function of coordinates with the initial amplitude of the bubble A=2K. The reference simulation then produces a sequece of integrations as a necessary part of a perfect-model design. Simulated observations of radial velocity were produced during reference model run in a way similar to the work of Snyder and Zhang (2003). In our experiments two different environmental soundings are used. One is based on the Wallops Island VA US sounding from 1200 UTC 09 May 2003 and the second on the Legionowo Poland sunding from 0000 UTC 21 Jul 2004. In control runs simulated observations of radial velocity were assimilated using the ensemble transform Kalman filter (ETKF) formulation (Bishop et. al 2001). This is a variant of ensemble based Kalman square-root filters with the forecast and analysis covariance matrices being represented by k ensemble forecast and k analysis perturbations. For a given set of forecast perturbations Z^f at time t, the analysis perturbations Z^a are solved from the Kalman filter equation. The number of ensemble members is limited by the computer resources and is too small compared with a space of the model state. For a given number of ensembles, it is important to estimate analysis error covariances properly. In our experiments we focused on an inflation and localization of the analysis covariance matrix.

Bishop, C.H., B.J. Etherton and S.J. Majmudar, 2001: Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Mon. Wea. Rev., 129, 420-436.\\ Hodur, R., 1997: The Naval Research Laboratory's Coupled Ocean/Atmosphere Mesoscale Prediction System (COAMPS). Mon. Wea. Rev. 125, 1414-1430.\\ Snyder, C., and F. Zhang, 2003: Assimilation of simulated Doppler radar observations with the ensemble Kalman filter. Mon. Wea. Rev., 131, 1663-1677.