<b>Geographic-dependent Parameter Optimization based on A-4DEnVar: Simulation with an </b><b>Idealized 2-D </b><b>Coupled Model</b>

Coupled climate models integrate multiple components including atmospheric, oceanic, and land submodels, while the uncertainty of model parameters from different parameterization schemes or empirically derived inevitably introduces systematic biases. Coupled parameter optimization (CPO) can reduce the systematic biasesin coupled model and enhance its capability for weather forecast and climate prediction. However, the implementation of CPO involves in dealing with strong nonlinear processes inherent in a coupled model. The analytical four-dimensional ensemble variational (A-4DEnVar) data assimilation methodretains the nonlinear processing capability of the four-dimensional variational (4D-Var) data assimilation methodbut gets rid of the dependence on the adjoint model. In this study, a novel dynamic independent point (DIP) scheme combined with a sample-space variable replacement algorithm, which enhances the convexity of the cost function, reduces computational dimensionality, and further expands the parameter subspace, is introduced to A-4DEnVar. Based on the improved A-4DEnVar, a series of geographic-dependent CPO experiments with an idealizedatmosphere-ocean-land coupled modelare carried out. The results show that,despite the strong nonlinear influence from the coupled model, A-4DEnVar can still accurately capture the geographical characteristics of model parameters, and exhibit high-quality performance in geographic-dependent optimization of cross-component parameters. This provides a new perspective when a coupled general circulation model is used for climate estimation and prediction.Additionally, the DIP scheme presents significant advantages compared to the static independent point scheme, especially with fewer independent points. In the case of only 90 independent points, satisfactory geographic-dependent CPO can be achieved.