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The radar ray path and beam broadening equations are important for assimilation of radar data into numerical weather prediction (NWP) models. They can be used to determine the physical location of each radar measurement and to properly map the atmospheric state variables from the model grid to the radar measurement space as part of the forward observation operators. Historically, different degrees of approximationshavebeenmadewiththeseequations;however,nosystematicevaluationoftheirimpactexists,atleastin the context of variational data assimilation. This study examines the effects of simplifying ray path and ray broadeningcalculationsontheradardataassimilationin a3Dvariational dataassimilation(3DVAR)system. SeveralgroupsofObservationalSystemSimulationExperiments(OSSEs)areperformedtotesttheimpactof these equationsto radardata assimilation with an idealizedtornadicthunderstormcase. Thisstudyshows that the errors caused by simplifications vary with the distance between the analyzed storm and the radar. For single time level wind analysis, as the surface range increases, the impact of beam broadening on analyzed wind field becomes evident and can cause relatively large error for distances beyond 150 km. The impact of the earth’s curvature is more significant, even for distances beyond 60 km, because it places the data at the wrong vertical location. The impact of refractive indexgradientis alsotested. It is shown that the variations of refractive index gradient have a very small impact on the wind analysis results. Two time series of 1-h-long data assimilation experiments are further conducted to illustrate the impact of the beam broadening and earth curvature on all retrieved model variables. It is shown that all model variablescan beretrievedto somedegrees in all data assimilation experiments.Similarto the wind analysis experiments, the impacts of both factors are not obvious when radars are relatively close to the storm. When the radars are far from the storm (especially beyond 150 km), overlooking beam broadening degrades the accuracy of assimilation results slightly, whereas ignoring the earth’s curvature leads to significant errors.

Impacts of Beam Broadening and Earth Curvature on Storm-Scale 3D Variational Data Assimilation of Radial Velocity with Two Doppler Radars