Suitable Background Error Covariances for Radar Reflectivity Direct Assimilation in the Rapid Refresh Forecast System (RRFS)

Radar reflectivity data assimilation (DA) is important for improving short-term precipitation forecasts. In the Rapid Refresh Forecast System (RRFS), which is the next-generation regional ensemble forecast system being developed by NOAA and the wider UFS Community, reflectivity observations are directly assimilated by adding the reflectivity as a state variable to calculate the ensemble-based background error covariances (BECs; Wang and Wang 2017, MWR). In addition, scale-dependent and variable-dependent localization (SDLVDL) are developed to achieve simultaneous multiscale assimilation of synoptic/mesoscale in-situ and reflectivity observations (Wang and Wang 2023, JAMES). However, hybridized BECs may be unable to properly estimate the uncertainties of reflectivity without properly constructed static BECs. In particular, the impact of reflectivity DA is zero when the observed reflectivity is missed in all ensemble forecasts.

In this study, the following two static BECs related to the reflectivity are tested: (i) conventional static BECs evolved in time by the ensemble-based tangent linear model (ETLM, Yokota et al. 2023, 28th Conference on NWP) and (ii) newly created convective-scale static BECs (Wang and Wang 2021, MWR). The former enables traditional static BECs without reflectivity as the control variable and with cross-variable covariance between reflectivity and the atmospheric control variables in the ETLM. If low-pass filtered ensemble perturbations are used in the ETLM, displacement of the precipitation forecast is also accounted to a certain extent. The latter extends the static BECs to include reflectivity, hydrometeors, vertical velocity, and cross-variable covariance between control variables. Since the BECs are defined and applied independently of the forecasted storm intensity, reflectivity is efficiently assimilated even at points where the reflectivity is not forecasted. In this conference, we will show if these static BECs improve forecasts of both precipitation and other atmospheric variables, and discuss what kinds of BECs are suitable for radar reflectivity direct DA in RRFS.