Estimation of Linearized Vertical Diffusion Scheme in GRAPES Model

Four-dimensional variational data assimilation (4DVAR) is an optimal method to obtain a best estimate of the initial conditions for a forecast model. A cost function is defined that involves a model trajectory as compared with three-dimensional variational data assimilation. The minimization requires an adjoint model in order to solve the problem at a reasonable computing cost. A four-dimensional variational data assimilation system (GRAPES 4DVAR) based on regional GRAPES model is developed by Chinese Academy of Meteorological Sciences. There are only several 4DVAR systems based on the non-hydrostatic model as GRAPES worldwide. GRAPES 4DVAR also has the ability to assimilate the observations, including the new non-conventional satellite and radar data. For the operational implementation in the future, GRAPES 4DVAR system is designed in the incremental formulation. The tangent-linear and adjoint model are both required to calculate the cost function and its gradient in the inner-loop. As the starting point, an adiabatic version of the linerized model is developed in 2005. Recently, much more effort is spent in the development of the linerized physical parameterization scheme for the application in GRAPES 4DVAR system. The linearization of vertical diffusion scheme used in GRAPES model is discussed.MRF nonlocal boundary layer scheme is used by GRAPES model to describe the vertical diffusion within and above the mixed boundary layer. The vertical diffusion scheme for the free atmosphere is linearized. After the straightforw ard linearization of vertical diffusion scheme, the standard tests are carried out to check the correctness of the tangent-linear model with vertical diffusion. It is well known that all physical processes are characterized by discontinuities and nonlinearities by which the departures of their linearied schemes can be significantly increased. To evaluate the validity of tangent-linear approximation for vertical diffusion scheme, twentyone cases during August 7—27, 2005 are run to calculate the mean departure between the tangent-linear model and the nonlinear model. It is found that the discontinuity resulted from the "on-off" switch has little influence on the mean departure between the tangent-linear model and the nonlinear model. Indeed, significant departures caused by the nonlinearity of vertical diffusion scheme may be lead to by a straightforward linearization of vertical diffusion scheme. This is a clear demonstration of the possible detrimental impact on the perturbed pressure and wind fields. The problem is solved by neglecting the perturbation of the surface flux for momentum. After the simplification, a better agreement between the tangent-linear model and the nonlinear GRAPES model with full physics for all variables is resulted in by the inclusion of the linearized vertical diffusion scheme. In conclusion, the results are encouraging, and the linearized vertical diffusion scheme is applicable in GRAPES 4DVAR systems. More linearized physics parameterization schemes will also be developed in the near future.