A comparison of En4DVar and 4DEnVar in Convective Scale Supercell Data Assimilation

Ensemble four-dimensional variational assimilation system (En4DVar) and Four-dimensional ensemble variational assimilation system (4DEnVar) are the two variants of four-dimensional variational assimilation systems that can account for the temporal evolution of the background errors in the assimilation window. En4DVar employs tangent linear (TL) and adjoint models to estimate the propagation of error statistics, while 4DEnVar utilizes a linear combination of ensemble perturbations at discrete times. While most comparisons of En4DVar and 4DEnVar have been conducted using simple and global models, uncertainties remain for convection-allowing data assimilation and forecasts. This study compares En4DVar and 4DEnVar for the convective-scale analysis and forecast of a tornadic supercell assimilating radar reflectivity and radial velocity. The results first demonstrated the inherent limitations of En4DVar in using simplified microphysical parameterization in its TL model. Despite this inherent limitation, En4DVar outperforms 4DEnVar in the supercell forecast, particularly in representing mid-level graupel mixing ratios. Single observation tests suggest that the underperformance of 4DEnVar is attributed to its sampling errors in representing temporal error correlation. En4DVar propagates cross-correlation of hydrometeors at the start of the assimilation window, especially in mixed-phase regions, which compensates for its shortcomings of using simplified microphysics scheme in the TL model.