A coupled thermodynamic system of sea ice and its parameter identification

In this paper, we deal with a coupled thermodynamic system of sea ice and its parameter identification problem. Based on the characteristics of the sea ice temperature distribution, we construct a thermodynamic system of sea ice coupled by the snow, the sea ice and the ocean mixed layer. Then taking the thermodynamic parameters (density, specific heat and thermal conductivity) of snow, ice and ocean mixed layer as the control variable and the minimal error of the temperature obtained from the system and the observed temperature data of sea ice as the performance criterion, an optimal control model with state constraints is given. We also prove the dependency relationship between state and control variables, and discuss the existence of the optimal control. Finally necessary conditions for optimality are derived.