Ice Concentration Scaling Laws for Freshwater Lakes in Numerical Weather and Climate Prediction

Abstract

If lake ice is assumed to deform and fail as a linear viscoelastic material under the action of wind stress, then a simple ice concentration scaling law can be constructed suitable for one‐dimensional lake models embedded within environmental prediction systems. Most 1‐D lake models assume no ice mechanics at all, while others adapt the viscous‐plastic rheology common in ice‐ocean models for the purpose of estimating ice fraction. Elastic buckling is generally disregarded as a significant failure mechanism in ice under low stress conditions at geophysical scales. However, by adding viscosity to the constitutive equation, the conditions for viscoelastic buckling seem quite plausible over a wide range of lake size and ice thickness. An ice concentration scaling law based on this process is evaluated here in multiannual simulations over North America and found to produce superior ice phenology statistics compared with simulations based on plastic failure or no ice mechanics.