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This work is devoted to the comparison of one- (1-D) and zero-dimensional (0-D) models of sea ice thermodynamics. 1-D thermodynamics solvers imply the solution of the diffusion equation with penetrating radiation in the moving domain (moving boundary problem), while 0-D implementations neglect the heat capacity of ice and penetrating radiation, that leads to a linear temperature profile by the construction. So far, some climate models use 0-D implementation of thermodynamics in a block of sea ice, while other models use 1-D implementation with a small number of nodes. In this work we present our fully implicit 0-D and 1-D version of snow–ice thermodynamics, which relieves the model of Courant-type time step constraints. Implicitness is achieved by the relaxation method for nonlinear heat capacity and thermal conductivity coefficients with simultaneous search for the temperature that satisfies the boundary conditions. We introduce the experiment with analytical forcing to compare evolution of temperature profiles. This model experiment shows that 0-D model underestimates ice thickness and overestimates the amplitude of temperature profile variation compared to 1-D solution. Despite the large differences in thickness and internal temperatures, the surface temperatures are very close. The models were also validated on the data of the SHEBA field experiment. According to comparison with observation data, the 0-D model predicts ice thickness and spatiotemporal temperature distribution much worse compared to 1-D model, but the amplitude of error in surface temperature is slightly greater for 0-D code. It can be concluded that 0-D model of sea ice thermodynamics is a good tool for predicting surface temperature, but it gives a large error in thickness and temperature distribution.

russian journal of numerical analysis and mathematical modelling

The new sea ice thermodynamics code for the INM RAS Earth System model: The design and comparison of one- and zero-dimensional approaches with the observational data