Integration of Deep Neural Network‐Based Boundary Layer Subgrid Frictional Effects Into the Momentum Equation Constraint of WRFDA EnVar to Improve Tropical Cyclone Forecasts

Abstract The incorporation of appropriate dynamic constraints in data assimilation (DA) is highly important for improving the forecasting of disastrous weather. It is often challenging to describe subgrid physical processes with strong nonlinearity and discontinuity in dynamic constraints because of difficulties in tangent linear and adjoint development. Based on the frictionless momentum equation weak constraint within the Weather Research and Forecasting ensemble‐three‐dimensional variational (En3DVar) DA, this study incorporates the subgrid planetary boundary layer (PBL) turbulent friction effects through a machine learning (ML) approach. The new constraint is aimed at improving the coupling between dynamic and thermodynamic variables. A deep neural network (DNN) is applied to emulate the model parameterized PBL horizontal momentum tendency. The tendency is introduced into the momentum equation as a turbulent friction term. The tangent linear and adjoint of the DNN are embedded into the variational framework to construct a ML‐improved DA scheme. Sensitivity experiments for tropical cyclones (TCs) reveal that including turbulent friction effectively compensates for the insufficient pressure adjustments during wind assimilation according to the original constraint framework. Three DA experiments that involve assimilating radar radial velocities are conducted using En3DVar (EVAR), En3DVar with the original constraint (EVAR–DC) and En3DVar with the ML‐improved constraint (EVAR–MLDC) for landfalling TCs Muifa (2022) and Doksuri (2023). In response to wind increments, compared with EVAR–DC and EVAR, EVAR–MLDC produces larger pressure adjustments around the eyewall. Overall, a better description of thermodynamic states is obtained by the new scheme, which plays a positive role in TC track and intensity forecasting.