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

Abstract

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.

Diatoms abound in ice-covered Lake Erie: An investigation of offshore winter limnology in Lake Erie over the period 2007 to 2010

“…Wind-driven resuspension during isothermal conditions could bring silt to the surface and there is evidence that vertical circulation features such as Langmuir cells (Dethleff and Kempema, 2007) and release of positively buoyant anchor ice (Kempema et al, 2001) can lead to sediment entrainment in ice. Large lakes with discontinuous ice cover are also likely to experience frazil ice formation (Leppäranta and Wang, 2008), wherein particles (e.g. silt, phytoplankton [ Table 4]) serve as nucleation sites for ice formation in super-cooled water in open leads on the lake surface that frequently form in large lakes.…”

Surface Water Temperature and Ice Cover of Tatra Mountains Lakes Depend on Altitude, Topographic Shading, and Bathymetry

“…Besides the direct influence of solar radiation, a potentially important factor in heating the water of shallow lakes can be high sediment heat storage (Golosov et al, 2007). Together with the fact that a thin and snow-free ice layer is vulnerable to solar radiation (Leppäranta, 2010;Leppäranta and Wang, 2008), the above-mentioned factors could easily eliminate the temporary ice cover of shallow lakes.…”

Lake ice phenology in Berlin-Brandenburg from 1947–2007: observations and model hindcasts

“…Most recently used ice models carry the heat transfer equation solved on a finite difference grid, where the number of grid points and the grid spacing differ depending on the application. With regard to ice thermodynamics, the model is broadly similar to most other models developed to date (Launiainen and Cheng 1998;Patterson and Hamblin 1988;Leppäranta 1993;Duguay et al 2003;Leppäranta and Wang 2008). The unified bulk treatment of the ice -water column -sediment system makes FLake an attractive tool in climate research applications, where numerical efficiency and a minimum number of tunable parameters are desirable ( Table 3).…”

“…Climate change studies based on ice phenology have been conducted for many North American lakes (Futter 2003;Jensen et al 2007;Liston and Hall 1995;Magnuson et al 2000a;Stefan and Fang 1997;Vavrus et al 1996), but for only a few European lakes (Adrian and Hintze 2000;George 2007; Leppäranta and Wang 2008;Livingstone and Dokulil 2001). The sensitivity of ice phenology to climate variability and change has been investigated using observations from ground and remote sensing, and simulation data from computer models and regression models (e.g., Jeffries et al 2005).…”

“…Many long time-series of field observations, taken at coastal stations and during field trips, are available for different regions of North America (northern USA and Canada; e.g., Liston and Hall 1995;Ménard et al 2002;Stefan and Fang 1997;Vavrus et al 1996). Since the 1970s, observations by aerial surveys or satellites have provided passive microwave images to study lake ice phenology (Kouraev et al 2008;Leppäranta and Wang 2008). Single and multiple variable regression analyses were used to develop regression models that require observed ice data and a few correlated input data to predict ice phenology and ice thickness (Gao and Stefan 1999;George 2007;Livingstone 1997;Palecki and Barry 1986;Williams et al 2004).…”