| Summary: | Abstract Ensemble‐based convective‐scale radar data assimilation commonly suffers from an underdispersive background ensemble. This study introduces a multivariate additive‐inflation method to address such deficiency. The multivariate additive inflation (AI) approach generates coherent random perturbations drawn from a newly constructed convective‐scale static background error covariance matrix for all state variables including hydrometeors and vertical velocity. This method is compared with a previously proposed univariate AI approach, which perturbs each variable individually without cross‐variable coherency. Comparisons are performed on the analyses and forecasts of the 8 May 2003 Oklahoma City tornadic supercell. Within assimilation cycles, the multivariate approach is more efficient in increasing reflectivity spread and thus has a reduced spinup time than the univariate approach; the additional inclusion of hydrometeors and vertical velocity results in more background spread for both reflectivity and radial velocity. Significant differences among AI experiments also exist in the subsequent forecasts and are more pronounced for the forecasts initialized from the earlier assimilation cycles. The multivariate approach yields better forecasts of low‐level rotation, reflectivity distributions, and storm maintenance for most lead times. The additional inclusion of hydrometeor and vertical velocity in the multivariate method is beneficial in forecasts. Conversely, the additional inclusion of hydrometeor and vertical velocity in the univariate method poses negative impacts for the majority of forecast lead times.
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