Modeling of Intra-System Relationships in the Adaptive Model of the Marine Environment Biochemical Processes
Purpose. Complexity of biochemical processes in marine environment entails the problem of parameterizing their interactions in constructing the marine ecosystem mathematical models. The aim of the investigation is to simplify solution of this problem by applying the concept of the ecosystem stationary state and the hypothesis on balance of the processes' mutual influence based on the matter balances of biochemical reactions in substance transformations. Methods and Results. To simplify the
... o simplify the ecosystem model, applied is the method of the adaptive balance of causes which now is being developed by the authors. The method equations contain negative feedbacks between the ecosystem model variables and the velocities of their change. These feedbacks stabilize the equations' solutions and make the model adaptive to the external effects on the ecosystem. The concept of the solutions' convergence to the stationary state permitted to propose a simple methods (based on the normalized relationships between their average values) for estimating the coefficients of the processes' mutual influences. To test these methods, the adaptive model of the Sevastopol Bay ecosystem was constructed. The data of multi-year observations of the chemical processes in the bay were used for assimilating the observations of the nitrate and ammonia concentrations in the model. The data were assimilated both through their reducing to the dimension and scales of the variability corresponding to the model variable, and their including to the right parts of the model equations as the additional sources and sinks. The numerical experiments carried out using the integral model of the Sevastopol Bay ecosystem showed that application of the normalized relationships between their average values as the estimates of the processes' mutual influences permitted to reproduce the scenarios of all the processes in the ecosystem based on the limited observational data. The model response to the external effects at the constant and varying normalizing factors in the model coefficients is studied. It shows that the variable factors provide the model with higher sensitivity to the external effects. Conclusions. The adaptive models of marine ecosystems constructed by the method of the adaptive balance of causes provide fast solutions' convergence to the stationary state. According to the laws of the matter balances' conservation in the biochemical reactions in substance transformations, the adaptive model tends to establishing dynamical balances in the external and intra-system influences. Therefore the proposed methods of estimating the intra-system relationships' coefficients in the marine ecosystem adaptive model permit to reconstruct the scenarios of those processes in which only their average values are known. Keywords: ecosystem stationary state, adaptive balance of causes, variable normalization factors, marine ecosystem integral model, Sevastopol Bay, observation data assimilation. Acknowledgments: the work was carried out on theme "Complex interdisciplinary investigations of the oceanologic processes conditioning functioning and evolution of the Black and Azov seas' coastal zones". Numerical experiments using the model of the Sevastopol Bay ecosystem were performed at financial support of RFBR and the Sevastopol Administration, grant 18-47-920001 "Investigation of the principles of constructing the adaptive models of ecological-economic systems and digital information technologies for managing the scenarios of sustainable development of economic complexes in the Sevastopol region".