A comparison of <scp>En4DVar</scp> and <scp>4DEnVar</scp> in convective‐scale supercell data assimilation: A study of the 8 <scp>May</scp> 2003 <scp>Oklahoma City</scp> tornadic supercell

Abstract The performance of ensemble four‐dimensional variational data assimilation (En4DVar) and four‐dimensional ensemble variational assimilation system (4DEnVar) in convective‐scale data assimilation remains largely unexplored. This study evaluates their effectiveness in forecasting a tornadic supercell event in Oklahoma on 8 May 2003. A single‐observation experiment was conducted to examine how analysis increments evolve within the assimilation window, showing that En4DVar's tangent‐linear model (TLM) with simplified microphysics produces unrealistic vertical propagation of increments, while 4DEnVar better matches full nonlinear model‐propagated increments. A series of radar observation assimilation experiments indicates that 4DEnVar better fits observed 1‐km altitude reflectivity in the analysis but underestimates graupel mixing ratios at midlevels (5 km), leading to degraded reflectivity forecasts compared to En4DVar. Diagnostics suggest this degradation is due to 4DEnVar's spurious temporal correlations. Despite no solid hydrometeor increment due to the simplified physics of the TLM, cross‐variable correlations at the start of the window in En4DVar enhance graupel analysis increments, compensating for the lack of explicit solid hydrometeor microphysics, which improves storm structure representation and forecasts.