Insights into brine dynamics and sea ice desalination from a 1-D model study of gravity drainage

We study gravity drainage using a new 1-D, multiphase sea ice model. A parametrization of gravity drainage based on the convective nature of gravity drainage is introduced, whose free parameters are determined by optimizing model output against laboratory measurements of sea ice salinity evolution. Optimal estimates of the free parameters as well as the parametrization performance remain stable for vertical grid resolutions from 1 to 30 mm. We find a strong link between sea ice growth rate and bulk salinity for constant boundary conditions but only a weak link for more realistic boundary conditions. We also demonstrate that surface warming can trigger brine convection over the whole ice layer. Over a growth season, replacing the convective parametrization with constant initial salinities leads to an overall 3% discrepancy of stored energy, thermal resistance, and salt release. We also derive from our convective parametrization a simplified, numerically cheap and stable gravity-drainage parametrization. This parametrization results in an approximately 1% discrepancy of stored energy, thermal resistance, and salt release compared to the convective parametrization. A similarly low discrepancy to our complex parametrization can be reached by simply prescribing a depth-dependent salinity profile.