Optimization Of The Spatio-temporal Parameters In A Dynamical Marine Ecosystem Model Based On The Adjoint Assimilation

Advancing our understanding of the structure and functioning of the global oceanecosystem, its major subsystems, and its response to physical forcing is the scientificresearcher’s common goal, so that a capability can be developed to forecast theresponses of the marine ecosystem to global change. Developing the ecosystemdynamics model is becoming an important tool for studying the complicated marineenvironment. In most previous studies, the temporal and spatial variation of primaryproductivity and the concentration of ecological variables have been studied. Someresearches realize the spatial variations of the parameters, but the temporal variationsof key parameters are always ignored or not taken into account at all. In this study, thespatial and temporal variations of the parameters are realized, which improves thesimulation precision.In this effort, the adjoint variational method is applied to a3D marine ecosystemmodel (NPZD-type) and its adjoint model, which are built on global scale based onclimatological environment provided by SODA. The numerical study and assimilationexperiments are implemented within a depth of200m.In twin experiments, model-generated data of phytoplankton in the surface layerare served as fictitious observations. When the spatially varying Vm (maximumuptake rate of nutrient by phytoplankton) is estimated alone, new strategies aredesigned to optimize the step-length which is used to adjust the parameters preferablyand the assimilation efficiency is improved. On the condition that the same step isemployed, the reduced cost function (RCF), the mean absolute error of phytoplanktonin the surface layer (MAE) and the relative error (RE) of Vm between given andsimulated values decrease obviously compared with strategy in previous work. Based on the strategy above, how would the distribution schemes of spatial parameterizationand influence radius affect the results is discussed. The simulation precision is thehighest when the rate of dependent grid distance to influence radius is1.6, whichprovides for future experiments. The influence of time step was studied then and it isfound that the assimilation recovery would not be more successful with a smaller timestep of3hours compared with6hours. So6hours is the better option, by which thecomputational efficiency is improved. On the basis of the above work, when the fivekey parameters (KP) were estimated simultaneously, the given spatial variations couldbe reproduced, and the REs are less than6%. Analysis of the results of twinexperiments by linear regression method demonstrates that the relationship betweenRE of parameters and MAE is direct ratio with a correlation coefficient of0.8, soMAE can be considered as a criterion to evaluate both simulation results andparameter estimation which is useful in practical application.Real experiments are conducted based on the conclusions above.16°N-44°N,173°E-142°W and16°N-44°N,167°W-122°W are selected as study area. One year isdivided into72periods, each of which is five days long. Spatio-temporal variation ofKP was optimized by assimilating phytoplankton data in the surface layer in eachstudy area. For each study area, the RCF and MAE in each assimilation perioddecrease obviously after assimilation. The spatially varying KP (KPS), temporallyvarying KP (KPT) and constant KP (KPC) are obtained by averaging KP of spatialand temporal variation respectively. Another type of spatio-temporal KP (KPST) isrepresented by KPS, KPT and KPC. After the correlation analysis of KP, either KPS orKPT, it is found that there is the same distribution characteristics and variation trendbetween Vm, Dz and e. The correlation coefficient can reach0.99, and the relationbetween Dp and Gm is versa. After the comparison of KPT in the two study area, it isfound that KPT anomaly is time-varying. The anomaly of Vm, Dz and e are positivevalue in winter half year and negative value in summer half year, and the anomaly ofDp and Gm is versa, which accords with the real ecological mechanism.The model is run with KPS, KPT, KPC, and KPST respectively, and it is found that MAE is the minimum when KP are spatio-temporal variation (KPST), whileMAE reaches its maximum when KP are constant (KPC). KPST, representation ofspatio-temporal variation, reduces the variable number in model calculation.Therefore the spatio-temporal variation of parameters, which is the focus of severalresearchers, is reasonable and necessary and the adjoint variational method is a usefultool for optimizing the spatio-temporal parameters in a dynamical marine ecosystemmodel.