The ice cover on small and large lakes: scaling analysis and mathematical modelling

Lake ice cover is described by its thickness, temperature, stratigraphy and overlying snow layer. When the ratio of ice thickness to lake size is above ～10^?5, the ice cover is stable; otherwise, mechanical forcing breaks the ice cover, and ice drifting takes place with lead-opening and ridging. This transition enables a convenient distinction to be made between small and large lakes. The evolution of the ice cover on small lakes is solved by a wholly thermodynamic model, but a coupled mechanical–thermodynamic model is needed for large lakes. The latter indicates a wide distribution of ice thickness, and frazil ice may be formed in openings. Ecological conditions in large lakes differ markedly from those in small lakes because vertical mixing and oxygen renewal may take place during the ice season, and the euphotic zone penetrates well into the water column in thin ice regions. Mesoscale sea ice models are applicable to large lakes with only minor tuning of the key parameters. These model systems are presented and analysed using Lake Peipsi as an example. As the climate changes, the transition size between small and large lake ice cover will change.