Implementing the sub-grid boundary layer turbulent effects into variational constraints trough machine learning and its impact on typhoon assimilation

Incorporating appropriate physical constraints to data assimilation is of great significance for the assimilation of disastrous weather data assimilation and numerical forecasting. Generally, model constraints are often difficult to describe complex sub-grid physical processes with strong nonlinearity and discontinuity, due to difficulties in developing the tangent linear and adjoint. In 4DVar, simplified physical process schemes are often used instead. With the development of artificial intelligence (AI) technology, complex sub-grid physical processes can be probably considered in variational constraints. On the basis of momentum equation constraints, this study introduces sub-grid boundary layer turbulent friction effects through machine learning (ML) and adds them into momentum equation constraints. Firstly, a deep neural network model is used to train the horizontal momentum tendency simulated by the YSU boundary layer parameterization scheme of WRF model. Secondly, under the Ensemble-Var framework of WRFDA, the momentum tendency of the boundary layer is introduced into the weak constraint of the horizontal momentum equation of variational method. The boundary layer turbulent friction term is implemented by embedding a deep neural network model, and its tangent and adjoint operators are developed to construct a ML-DA scheme. Finally, a physical constraint scheme considering the turbulent friction effect of boundary layer is established for data assimilation. The new assimilation scheme is applied to the radial wind assimilation of coastal radar. Numerical simulation experiments on different typical landing typhoons show that the new scheme better described the boundary layer four-force balance during the data assimilation process. Assimilating the direct-observed wind field, the thermal fields such as pressure and temperature are also improved. The new scheme plays a positive role in typhoon intensity and structure forecasting.