A Comparison of 3DEnVar and 4DEnVar for Convective-Scale Direct Radar Reflectivity Data Assimilation in the Context of a Filter and a Smoother

Abstract

Abstract The Gridpoint Statistical Interpolation (GSI)-based four- and three-dimensional ensemble–variational (4DEnVar and 3DEnVar) methods are compared as a smoother and a filter, respectively, for rapidly changing storms using the convective-scale direct radar reflectivity data assimilation (DA) framework. Two sets of experiments with varying DA window lengths (WLs; 20, 40, 100, and 160 min) and radar observation intervals (RIs; 20 and 5 min) are conducted for the 5–6 May 2019 case. The RI determines the temporal resolution of ensemble perturbations for the smoother and the DA interval for the filter spanning the WL. For experiments with a 20-min RI, evaluations suggest that the filter and the smoother have comparable performance with a 20-min WL; however, extending the WL results in the outperformance of the filter over the smoother. Diagnostics reveal that the degradation of the smoother is attributed to the increased degree of nonlinearity and the issue of time-independent localization as the WL extends. Evaluations for experiments with different RIs under the same WL indicate that the outperformance of the filter over the smoother diminishes for most forecast hours at thresholds of 30 dBZ and above when shortening the RI. Diagnostics show that more frequent interruptions of the model introduce model imbalance for the filter, and the increased temporal resolution of ensemble perturbations enhances the degree of nonlinearity for the smoother. The impact of model imbalance on the filter overwhelms the enhanced nonlinearity on the smoother as the RI reduces. Significance Statement The background uncertainties of rapidly changing storms suffer from fast error growth and high degrees of nonlinearities during the data assimilation (DA) period. Two variants of the ensemble-based DA method can account for such temporal evolution. The smoother uses background ensemble from multiple observation times over an assimilation period to estimate the propagation of statistics. The filter frequently calculates the statistics at multiple observation times over the same period. Current comparisons of the smoother and the filter were mostly performed using simple models; however, unknowns remain for convection-allowing forecasts with additional complexities. This study compares the filter and the smoother for the convective-scale analysis and prediction using a real-data study and finds that the comparison varies with the assimilation period and the observation interval.