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

Abstract

[1] 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 depthdependent salinity profile.Citation: Griewank, P. J., and D. Notz (2013), Insights into brine dynamics and sea ice desalination from a 1-D model study of gravity drainage,

Sea-ice thermodynamics and brine drainage

“…The long-term trends of salt flux versus growth rate evaluated using climatological data to determine ocean and atmospheric heat fluxes [20] suggest that, when averaged over a week, a linear relationship between salt flux and growth rate, as used in current models, gives a good approximation, so the sophistication and cost of evaluating the salinity of sea ice dynamically may not be worthwhile. On the other hand, such a coarse-grained view averages over periods of rapid growth while the ice is thin and periods of rapid drainage during warming events.…”

“…On the other hand, the physics causing such a delay, that the Rayleigh number is insufficiently large, can occur in later stages of ice growth as the atmospheric and oceanic heat fluxes vary. Related to that, they can all predict enhancement or re-initiation of brine drainage during periods of warming [20]. And they all adjust their dynamics to different oceanic salinities and should work as well in the Baltic, for example, as in the central Arctic.…”

“…Griewank & Notz [20] calculate a local downflow at each level, proportional to the amount by which the local Rayleigh number exceeds a critical value, and sum these for all levels above the level in question to determine the upflow there. This is illustrated by the expression…”

“…Turner et al estimate the magnitude of convection α by equating the dynamic pressure drop along the channel with that driving a vertical return flow through the surrounding mush. Rees Jones & Worster [18] calculate α in the idealized setting explored with their CAP model but suggest that in the context of sea ice it is best treated as a tuning parameter [21], as is also done by Griewank & Notz [20]. Although various stability analyses have determined critical Rayleigh numbers in different settings, all three sets of authors treat the constant R c as a tuning parameter, which seems appropriate for use in the complex settings of real sea ice.…”

Advances in understanding and parameterization of small-scale physical processes in the marine Arctic climate system: a review

“…Based on this understanding, models are starting to simulate in a physically consistent way the evolution of the bulk salinity of sea ice from its initial formation to its complete melt. Such models range from specialized models of gravity drainage (Wells et al, 2011;Rees Jones and Worster, 2013a, b) to more applied models that present simplified parameterizations of this major desalination process for the use in large-scale models (Turner et al, 2013;Griewank and Notz, 2013). Based on these models, a more realistic representation of the interaction between the smallscale structure of sea ice and the ocean and the atmosphere has now become possible.…”