Submitted as: model description paper 23 Aug 2021

Submitted as: model description paper | 23 Aug 2021

Review status: this preprint is currently under review for the journal GMD.

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

Marco Toffolon1, Luca Cortese1,2, and Damien Bouffard2 Marco Toffolon et al.
  • 1Department of Civil, Environmental and Mechanical Engineering, University of Trento, Italy
  • 2Eawag, Swiss Federal Institute of Aquatic Sciences, Department Surface Waters Research & Management, Kastanienbaum, Switzerland

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.

Marco Toffolon et al.

Status: open (until 18 Oct 2021)

Comment types: AC – author | RC – referee | CC – community | EC – editor | CEC – chief editor | : Report abuse
  • RC1: 'Comment on gmd-2021-234', Anonymous Referee #1, 18 Sep 2021 reply
    • AC1: 'Reply on RC1', Marco Toffolon, 16 Oct 2021 reply
  • RC2: 'Comment on gmd-2021-234', Anonymous Referee #2, 30 Sep 2021 reply
    • AC2: 'Reply on RC2', Marco Toffolon, 16 Oct 2021 reply
  • EC1: 'Invitation to proceed with response and revisions', Andrew Wickert, 01 Oct 2021 reply
    • AC3: 'Reply on EC1', Marco Toffolon, 16 Oct 2021 reply

Marco Toffolon et al.

Marco Toffolon et al.


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Short summary
The time when lakes freeze varies considerably from year to year. A common way to predict it is to use negative degree days, i.e. the sum of air temperatures below 0 °C, a proxy for the heat lost to the atmosphere. Here we show that this is insufficient because the mixing of the surface layer induced by wind tends to delay the formation of ice. To do so, we developed a minimal model based on a simplified energy balance, which can be used both for large-scale analyses and short-term predictions.