Numerical study on spatially varying control parameters of a marine ecosystem dynamical model with adjoint method

Based on the simulation of a marine ecosystem dynamical model in the Bohai Sea, the Yellow Sea and the East China Sea, chlorophyll data are assimilated to study the spatially varying control parameters (CPs) by using the adjoint method. In this study, the CPs at some grid points are selected as the independent CPs, while the CPs at other grid points can be obtained through linear interpolation with the independent CPs. The independent CPs are uniformly selected from each 30'×30' area, and we confirm that the optimal influence radius is 1.2° by a twin experiment. In the following experiments, when only the maximum growth rate of phytoplankton (V_m) is estimated by two given types of spatially varying CPs, the mean relative errors of V_m are 1.22% and 0.94% while the decrease rates of the mean error of chlorophyll in the surface are 94.6% and 95.8%, respectively. When the other four CPs are estimated respectively, the results are also satisfactory, which indicates that the adjoint method has a strong ability of optimizing the prescribed CP with spatial variations. However, when all these five most important CPs are estimated simultaneously, the collocation of the changing trend of each parameter influences the estimation results remarkably. Only when the collocation of the changing trend of each parameter is consistent with the ecological mechanisms which influence the growth of the phytoplankton in marine ecosystem, could the five most important CPs be estimated more accurately.