An efficient adjustable-layering thermodynamic sea-ice model formulation for high-frequency forcing

Recent observations suggest that high-frequency forcing events have profound influence oil the air-sea-ice interactions in the polar region. Studying these events with sea-ice models requires close examination of the model sensitivity that may arise from the high-frequency variability of the forcing. We show that the maximum layer thickness is dictated by the time-scale of the forcing variability and that the computation of the surface temperature develops enhanced sensitivity at high-frequency forcing. We resolve these constrains by developing all "adjustable-layering" thermodynamic formulation for ice and snow that re-computes the number of layers required each time-step to satisfy this maximum thickness, which preserves the total enthalpy and general internal thermal gradients. The conservation equations form a tri-diagonal system ideal for a Fast and efficient implicit solution. Furthermore, we resolve the issue of the high sensitivity of the surface flux balance by solving the linearized version of the flux boundary condition simultaneously with the overall conservation system. In this paper we develop the analyses specifying the model requirements, describe the model system and test its algorithmic implementation.