The Optimization of GRAPES Global Tangent Linear Model and Adjoint Model

Adjoint models are widely applied in numerical weather prediction. For instance, in four-dimensional variational data assimilation (4DVar), they are the best method to efficiently determine optimal initial conditions. The minimization of the 4DVar cost function is solved with an iterative algorithm and is computationally demanding. Though the minimization is usually performed with a much lower resolution than in forecast model, obtaining the optimal model state requires dozens of iterations, and the model parallel efficiency must be fast enough. However, the parallel efficiency of GRAPES global tangent linear model and adjoint model version 1.0 based on GRAPES global non-linear model 1.0 is so low that it seriously impacts the development of GRAPES_4DVar. In order to reduce the computational cost, a new tangent linear model and adjoint model version 2.0 are re-designed and re-developed based on GRAPES global model version 2.0. By optimizing the program structure of tangent linear model, the calculating time of GRAPES tangent linear model can be best controlled within 1.2 times of GRAPES non-linear model's consumption with only dynamic framework. And by methods transferring the model base state and trajectory to the adjoint model, the calculating time of GRAPES adjoint model can be best controlled within 1.5 times of GRAPES non-linear model's consumption. Therefore, the new GRAPES tangent linear model and adjoint model version 2.0 are very successful in terms of computational efficiency to speed up the development of GRAPES_4DVar.In practical applications, the tangent linear model and adjoint model is run at a lower resolution than the non-linear model, since the dynamics is already simplified through the reduction in horizontal resolution, the linearized physics doesn't necessarily need to be exactly tangent to the full physics. In principle, physical parameterizations can already behave differently between non-linear and tangent-linear models due to the change in resolution. In order to reduce computational cost, it is often necessary to select different set of simplified linearized parameterizations with the full physical processes of GRAPES forecast model. By decoupling base states calculation in GRAPES and the perturbation calculation in the tangent linear and adjoint model, the computational cost of GRAPES tangent and adjoint model with simplified physical parameterizations increases only a little than no physical parameterizations versions, and the computational efficiency is higher than GRAPES forecast model with full physical parameterizations.