SELF v1.0: A minimal physical model for predicting time of freeze-up in lakes

Abstract

Abstract. Predicting the freezing time in lakes is pursued 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, which focuses on the pre-freezing period that, in dimictic lakes, goes from mixed conditions (lake temperature at 4 °C) to the formation of ice (0 °C at the surface). 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 an opposite role in determining the time required for ice formation and contribute to the large inter-annual variability observed in ice phenology. More intense cooling, indeed, accelerates the rate of decrease of lake surface water temperature (LSWT), while stronger wind deepens the surface layer, increasing the heat capacity, and thus reduces 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.

Novel Air2water Model Variant for Lake Surface Temperature Modeling With Detailed Analysis of Calibration Methods

“…Similar to the idea presented in [25], the role of K, and hence the parameters a11 and a12, is to choose whether the water temperature should be computed according to the version representative for warm waters, cold waters, or a mix of both. This division is important due to different stratification dynamics in colder and warmer waters [81]- [82]. Note that  does not appear in this variant of air2water model.…”