SELF v1.0: A Minimal Physical Model for Predicting Time of Freeze-up in Lakes

Predicting the freezing time in lakes is achieved by means of complex mechanistic models or by simplified statistical regressions considering integral quantities. Here, we propose a minimal model (SELF) built on sound physical grounds that focuses on the pre-freezing period that goes from mixed conditions (lake temperature at 4 'C) to the formation of ice (0 'C at the surface) in dimictic lakes. The model is based on the energy balance involving the two main processes governing the inverse stratification dynamics: cooling of water due to heat loss and wind-driven mixing of the surface layer. They play opposite roles in determining the time required for ice formation and contribute to the large interannual variability observed in ice phenology. More intense cooling does indeed accelerate the rate of decrease of lake surface water temperature (LSWT), while stronger wind deepens the surface layer, increasing the heat capacity and thus reducing the rate of decrease of LSWT. A statistical characterization of the process is obtained with a Monte Carlo simulation considering random sequences of the energy fluxes. The results, interpreted through an approximate analytical solution of the minimal model, elucidate the general tendency of the system, suggesting a power law dependence of the pre-freezing duration on the energy fluxes. This simple yet physically based model is characterized by a single calibration parameter, the efficiency of the wind energy transfer to the change of potential energy in the lake. Thus, SELF can be used as a prognostic tool for the phenology of lake freezing.