“…Recently, a hybrid ensemble variational (EnVar) method has increasingly attracted attention with expectations of preserving benefits and eliminating limitations of the traditional variational system (Var, or its specific implementations 3DVar and 4DVar) and ensemble Kalman filter (EnKF) [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. Various hybrid EnVar methods, therefore, have been used for regional numerical weather prediction (NWP) applications [7,8,13,[15][16][17][18][19][20][21][22][23] and adopted in several operational regional modeling and prediction systems, e.g., the North American Mesoscale Forecast System (NAM [24]), the Rapid Refresh (RAP [25]), the High-Resolution Rapid Refresh (HRRR [26,27]), the NAM Rapid Refresh system (NAMRR [28]), and the operational Application of Research to Operations at Mesoscale (AROME)-France NWP system [29].…”