Boundary Layer Coupling to Charney-Phillips Vertical Grid in GRAPES Model

It is an important challenge in numerical weather and climate prediction to obtain accurate coupling between physical parameterization and high resolution dynamic framework. Increased resolution in models and the use of large time-steps in semi-Langrangian advection stress the need for an equally accurate computation in time of the corresponding physical parameterizations and the physics-dynamics coupling on the temporal aspects. Physics-dynamics coupling on spatial aspects also plays a very important role on the accuracy of model predictions, for there is a choice for how to vertically arrange the predicted variables, namely, the Lorenz and Charney-Phillips grids.The physics-dynamics coupling on spatial aspects in GRAPES model is studied. As the Charney-Philips grid is used, the horizontal velocity is staggered relative to potential temperature, which means potential temperature and water substances are calculated at full levels, while horizontal velocity is calculated at half levels. In Lorenz physics scheme, all variables are set at half levels and the correspondent tendencies are estimated at half levels. The interpolation has to be used between full and half levels in physics-dynamics coupling before and after physics scheme package is called. The interpolation error is unavoidable and an unexpected zigzag noise appears because of the second-order difference in PBL (planetary boundary layer) scheme.In C-P PBL scheme, the momentum diffusivity K_M is required at full levels and the heat diffusivity K_H is required at half levels. It is easy to compute K_M and K_H in unstable PBL because K_M and K_H depend on the PBL height and surface variables. For local scheme in stable PBL and free convective atmosphere, diffusivities are functions of local Richardson number which has relation with both potential temperature and horizontal velocity. Here potential temperature gradient is averaged so that Richardson number is calculated at full levels. K_M can be calculated at the full level and K_H can be averaged at the half level. The boundary condition is given by the surface flux according to the constant flux layer. C-P PBL parameterization is developed to assure the accurate coupling of PBL physics and vertical Charney-Phillips grid.Improvements are detected using C-P PBL parameterization spatial physics-dynamics coupling in GRAPES_GFS model. The zigzag noise of temperature and moisture in PBL is removed and the correspondent profiles appear to be smooth with C-P PBL parameterization. The accuracy of PBL and dynamics coupling is improved, and an overall enhancement is found in the forecast of height and temperature.