1 J 1 B . 6 A MULTI-CASE STUDY OF ENSEMBLE-BASED ASSIMILATION OF RADAR OBSERVATIONS INTO CLOUD-RESOLVING WRF USING DART

One of the long-standing problems in meteorology is the estimation of the three-dimensional wind and thermodynamic fields for convective-scale numerical forecasting. At this scale, Doppler radars are excellent sources of volumetric information and, naturally, much research has been focused on the retrieval of state variables from Doppler radar observations. Several factors make the use of Doppler radar observations for convective-scale retrieval a very challenging task. First and foremost, the absence of balances like geostrophy between the wind and mass fields forces estimation schemes to rely solely on the dynamical information from the underlying numerical models, which causes the convective-scale estimation processes to be much more prone to systematic errors compared to their larger-scale counterparts. Second, Doppler radars only observe a limited subset of the state of the atmosphere through the aggregate reflectivity measurements for which numerical models have to rely on parameterizations of microphysical processes to establish relationships between “observed” moist variables and other unobserved dynamical variables. Due to large known systematic errors associated with microphysical parameterizations (Stoelinga et al. 2003), the reliability of the modelproduced covariance information between such observed and unobserved variables becomes questionable. Furthermore, strong nonlinearities associated with moist variables and precipitation frequently violate the Gaussian assumptions underlying many of the estimation techniques available. Finally, in addition to instrument-related errors, Doppler radar observations contain significant representativeness errors. Although this mainly arises from the resolution mismatches commonly seen between observations and models (typical convective-scale model horizontal resolutions are still on the order of a few kilometers, while Doppler radar along-beam resolutions are on the order of a few hundred meters and across-beam distances are even smaller very near the radar), contributions to reflectivity from non-modeled sources such as birds, insects, and ground clutter also add to the complexity of the representativeness problem. Over the past 30 years, various methods have been proposed for analyzing the convective-scale atmospheric state from Doppler radar observations. These range from purely kinematic considerations to sophisticated variational data assimilation schemes (see Dowell et al. [2004a] for a good historical discussion on such techniques). While variational techniques, and especially the better-established state-of-the-art fourdimensional variational assimilation (4DVAR), have demonstrated considerable success at estimating unobserved variables given Doppler radar observations (e.g., Sun 2005; Xiao et al. 2005; Weygandt et al. 2002; Gao et al. 1999; and Sun and Crook 1997), several factors associated with 4DVAR make its implementation to convective scales difficult. Among these, the high cost of developing and maintaining an adjoint model and the need to include in the adjoint highly nonlinear microphysical processes, the necessity to employ tractable and typically idealized models of background error covariance matrices, and the difficulty of the cost function minimization in the absence of balance constraints are especially relevant for convective scales. Very recently, the ensemble Kalman filter (EnKF) has been proposed as an alternative data assimilation method for the assimilation of Doppler radar data using simulated observations (Snyder and Zhang 2003; Zhang et al. 2004). First proposed by Evensen (1994) for geophysical applications, the EnKF obtains the background covariance information from an ensemble of forecasts. More specifically, an ensemble of forecasts is produced at predetermined analysis intervals, available observations at which are assimilated to produce the analysis state that becomes the initial conditions for the following forecast run. This cycle is repeated sequentially in time. As a result of its sequential nature and the affordability introduced by the sampling of covariance information, the ensemble approach to data assimilation naturally brings about the advantage of employing a flow-dependent background covariance matrix Furthermore, when observation errors are uncorrelated, observations can be assimilated serially, making the EnKF algorithms very suitable for parallelization. Finally, because the filter algorithm is sequential and serial in nature, its implementation and maintenance is quite straightforward and, except the forward operator code between the model and observation spaces, is independent of the underlying forecast model. The above-mentioned distinct differences of the EnKF in comparison to the 4DVAR make the EnKF an attractive alternative data assimilation method, as a Corresponding Author Address: Altuğ Aksoy, The National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO, 80307-3000. E-mail: aksoy@ucar.edu.