报告摘要：Idealized models of reduced complexity are important tools to understand key processes underlying a complex system. In climate sciencein particular, they are important for helping the community improve our abilityto predict the effect of climate change on the earth system. Climate models arelarge computer codes based on the discretization of the fluid dynamics equationson grids of horizontal resolution in the order of 100 km, whereas unresolved processesare handled by subgrid models. For instance, simple models are routinely used tohelp understand the interactions between small-scale processes due to atmosphericmoist convection and large-scale circulation patterns. Here, a zonally symmetric model for the monsoon circulation is presented and solvednumerically. The model is based on the Galerkin projection of the primitive equations of atmospheric synoptic dynamics onto the first modes of vertical structure to representfree tropospheric circulation and is coupled to a bulk atmospheric boundary layer(ABL) model. The model carries bulk equations for water vapor in both the free troposphere and the ABL, while the processes of convection and precipitation are representedthrough a stochastic model for clouds. The model equations are coupled through advective nonlinearities, and the resulting system is not conservative and not necessarilyhyperbolic. This makes the design of a numerical method for the solution of thissystem particularly difficult. We develop a numerical scheme based on the operator time-splitting strategy, which decomposes the system into three pieces: a conservative part and two purely advective parts, each of which is solved iteratively using an appropriate method. The conservative system is solved via a central scheme, which does not require hyperbolicity sinceit avoids the Riemann problem by design. One of the advective parts is a hyperbolicdiagonal matrix, which is easily handled by classical methods for hyperbolic equations,while the other advective part is a nilpotent matrix, which is solved via the methodof lines. Validation tests using a synthetic exact solution are presented, and formal second-order convergence under grid refinement is demonstrated. Moreover, the modelis tested under realistic monsoon conditions, and the ability of the model to simulatekey features of the monsoon circulation is illustrated in two distinct parameterregimes.

报告主持：李美丽教授

报告语言：英语