Using radar reflectivity as a state variable in DART: Is it optimal?

Many previous radar reflectivity data assimilation studies using an ensemble adjustment Kalman filter approach have added radar reflectivity to the set of variables directly updated during each assimilation cycle. Traditionally, these variables included prognostic variables such as temperature, pressure, humidity, wind and hydrometeor concentrations. The advantage of adding reflectivity is that the resulting reflectivity in the posterior analysis fields will agree very well with observations. Also, this method allows for the reflectivity to be computed using the correct microphysics formula included within WRF for each scheme rather than a simplistic reflectivity calculation present in the default radar forward operator in the DART software. However, this technique also introduces several potential problems. The first occurs when introducing another high resolution data set such as satellite cloud radiances or retrievals. Satellite data are also correlated to reflectivity and will update that variable accordingly through the covariance matrix generating a different reflectivity than would otherwise be the case when assimilating reflectivity alone. Also, the nature of the covariances between satellite data or reflectivity and hydrometeor variables can easily result in updated hydrometeor mixing ratios and number concentrations that are inconsistent with the updated reflectivity. Since reflectivity is a diagnostic variable within WRF, its value at a particular time has no impact on later forecasts, but using an inconsistent reflectivity analysis for interpretation and verification is also not optimal. The solution to this problem is to include advanced microphysics definitions in the radar forward operator itself. Both satellite radiance and retrieval forward operators contain the necessary microphysics information to relate observations back to prognostic variables. Thus, no satellite state variables are required. It would not be practical to include state vectors for all potential high resolution data sets that may be available in the future. This research will analyze the suitability of reflectivity as a state vector by comparing several data assimilation experiments for a severe weather event occurring on 24 May 2011. One will test the difference due to removing reflectivity from the state variables and using the default DART forward operator. Another will use an updated forward operator that includes full Thompson microphysics. Finally the effects on combined reflectivity and satellite cloud retrievals will be analyzed with and without reflectivity as a state vector. It will be shown that significant differences arise, and that using reflectivity in this manner may not be optimal.