Simultaneous state estimation and attenuation correction for thunderstorms with radar data using an ensemble Kalman filter: tests with simulated data

Abstract A new approach to dealing with attenuated radar reflectivity data in the data assimilation process is proposed and tested with simulated data using the ensemble square‐root Kalman filter. This approach differs from the traditional method where attenuation is corrected in observation space first before observations are assimilated into numerical models. We build attenuation correction into the data assimilation system by calculating the expected attenuation within the forward observation operators using the estimated atmospheric state. Such a procedure does not require prior assumption about the types of hydrometeor species along the radar beams, and allows us to take advantage of knowledge about the hydrometeors obtained through data assimilation and state estimation. Being based on optimal estimation theory, error and uncertainty information on the observations and prior estimate can be effectively utilized, and additional observed parameters, such as those from polarimetric radar, can potentially be incorporated into the system. Tests with simulated reflectivity data of an X‐band 3 cm wavelength radar for a supercell storm show that the attenuation correction procedure is very effective—the analyses obtained using attenuated data are almost as good as those obtained using unattenuated data. The procedure is also robust in the presence of moderate dropsize‐distribution‐related observation operator error and when systematic radar calibration error exists. The analysis errors are very large if no attenuation correction is applied. The effect of attenuation and its correction when radial velocity data are also assimilated is discussed as well. In general, attenuation correction is equally important when quality radial velocity data are also assimilated. Copyright © 2009 Royal Meteorological Society