A 3.5-dimensional variational method is developed for Doppler radar data assimilation. In this method, incremental analyses are performed in three steps to update the model state upon the background state provided by the model prediction. First, radar radial-velocity observations from three consecutive volume scans are analyzed on the model grid. The analyzed radial-velocity fields are then used in step 2 to produce incremental analyses for the vector velocity fields at two time levels between the three volume scans. The analyzed vector velocity fields are used in step 3 to produce incremental analyses for the thermodynamic fields at the central time level accompanied by the adjustments in water vapor and hydrometeor mixing ratios based on radar reflectivity observations. The finite element B-spline representations and recursive filter are used to reduce the dimension of the analysis space and enhance the computational efficiency. The method is applied to a squall line case observed by the phased-array radar with rapid volume scans at the National Weather Radar Testbed and is shown to be effective in assimilating the phased-array radar observations and improve the prediction of the subsequent evolution of the squall line. 1. Introduction Because the radar network provides only single-Doppler scanning over most areas in the U.S., research efforts have been undertaken to develop various methods for meteorological parameter retrievals from single-Doppler observations (Sun et al. [1]; Kapitza [2]; Qiu and Xu [3]; Sun and Crook [4]; Xu et al. [5, 6]; Laroche and Zawadzki [7]; Shapiro et al [8]; Zhang and Gal-Chen [9]; Liou [10]; Gao et al. [11]; Weygandt et al. [12]). These previous efforts, however, were focused mainly on retrievals with zero background information. By utilizing the background information provided by model predictions, some of the previous retrieval methods can be upgraded for radar data assimilation (Sun and Crook [13]; Xu et al. [14]; Gu et al. [15] Gao et al. [16]; Hu et al. [17]). This paper presents a 3.5-dimensinal variational method for radar data assimilation developed by upgrading and combining the previous retrieval methods (Qiu and Xu [18]; Xu et al. [19]; Gal-Chen [20]; Hane and Scott [21]). This method uses simplified dynamical and thermodynamical equations of a numerical weather prediction (NWP) model (in this study we use the Coupled Ocean/Atmosphere Mesoscale Prediction System or COAMPS (COAMPS is a registered trademark of the Naval Research Laboratory.), Hodur [22]) as constraints while the background information is
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