Recently, the attention to the ice season in lakes has been growing remarkably amongst limnological communities, in particular, due to interest in the response of mid- and high-latitude lakes to global warming. We review the present advances in understanding the governing physical processes in seasonally ice-covered lakes. Emphasis is placed on the general description of the main physical mechanisms that distinguish the ice-covered season from open water conditions. Physical properties of both ice cover and ice-covered water column are considered. For the former, growth and decay of the seasonal ice, its structure, mechanical and optical properties are discussed. The latter subject deals with circulation and mixing under ice. The relative contribution of the two major circulation drivers, namely heat release from sediment and solar heating, is used for classifying the typical circulation and mixing patterns under ice. In order to provide a physical basis for lake ice phenology, the heat transfer processes related to formation and melting of the seasonal ice cover are discussed in a separate section. Since the ice-covered period in lakes remains poorly investigated to date, this review aims at elaborating an effective strategy for future research based on modern field and modeling methods.

Physics of seasonally ice-covered lakes: a review

A multi-model approach to evaluating target phosphorus loads for Lake Erie

Nearshore dynamics and coastal processes : theory, measurement, and predictive models

. Thermokarst lakes are typical features of the northern permafrost ecosystems, and play an important role in the thermal exchange between atmosphere and subsurface. The objective of this study is to describe the main thermal processes of the lakes and to quantify the heat exchange with the underlying sediments. The thermal regimes of five lakes located within the continuous permafrost zone of northern Siberia (Lena River Delta) were investigated using hourly water temperature and water level records covering a 3-year period (2009–2012), together with bathymetric survey data. The lakes included thermokarst lakes located on Holocene river terraces that may be connected to Lena River water during spring flooding, and a thermokarst lake located on deposits of the Pleistocene Ice Complex. Lakes were covered by ice up to 2 m thick that persisted for more than 7 months of the year, from October until about mid-June. Lake-bottom temperatures increased at the start of the ice-covered period due to upward-directed heat flux from the underlying thawed sediment. Prior to ice break-up, solar radiation effectively warmed the water beneath the ice cover and induced convective mixing. Ice break-up started at the beginning of June and lasted until the middle or end of June. Mixing occurred within the entire water column from the start of ice break-up and continued during the ice-free periods, as confirmed by the Wedderburn numbers, a quantitative measure of the balance between wind mixing and stratification that is important for describing the biogeochemical cycles of lakes. The lake thermal regime was modeled numerically using the FLake model. The model demonstrated good agreement with observations with regard to the mean lake temperature, with a good reproduction of the summer stratification during the ice-free period, but poor agreement during the ice-covered period. Modeled sensitivity to lake depth demonstrated that lakes in this climatic zone with mean depths > 5 m develop continuous stratification in summer for at least 1 month. The modeled vertical heat flux across the bottom sediment tends towards an annual mean of zero, with maximum downward fluxes of about 5 W m−2 in summer and with heat released back into the water column at a rate of less than 1 W m−2 during the ice-covered period. The lakes are shown to be efficient heat absorbers and effectively distribute the heat through mixing. Monthly bottom water temperatures during the ice-free period range up to 15 °C and are therefore higher than the associated monthly air or ground temperatures in the surrounding frozen permafrost landscape. The investigated lakes remain unfrozen at depth, with mean annual lake-bottom temperatures of between 2.7 and 4 °C.

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Thermal processes of thermokarst lakes in the continuous permafrost zone of northern Siberia - observations and modeling (Lena River Delta, Siberia)

The implications of climatic change on Lake Constance are studied by long-term hydrodynamic model simulations. In contrast to earlier studies that mostly have applied one-dimensional models, this investigation utilizes a three-dimensional hydrodynamic model and thus profits from the advantages of a spatial representation of lake bathymetry and hydrophysical processes. Model adaptation and validation are based on half a century of vertically resolved temperature recordings (1961 to 2011). Three different horizontal grid layouts are used to test the sensitivity of the thermal stratification and effective vertical turbulent diffusivities (D V ) determined with the heat-budget method to grid resolution. D V calculated from observations and from simulations with different grid resolutions agree rather well. However, in the deep water simulated D V are overestimated if the basin is resolved only by few grid cells. The investigation of the effect of climatic changes on Lake Constance is focused on the effects of altered air temperatures and wind velocities on deep-water renewal. Numerical tracers are used as indicators of the winter vertical transport and mixing. Effects on stratification and mixing strongly depend on the seasonal course of the climatic changes. Warmer winter temperatures result in reduced deep-water exchange and more frequent years with incomplete mixing. Increased air temperatures in summer have almost no effect on deepwater renewal in winter but increase water-column stability during summer and autumn. Increased wind speeds influence vertical mixing and surface heat fluxes and cause higher deep-water temperatures if wind speeds are higher during the summer. The application of numerical models to investigate the consequences of changes in physical forcing for dynamic processes in lakes has become an established methodology in limnology. Models are chosen according to the questions addressed but also with respect to the limitations of

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Effect of climatic changes on stratification and deep-water renewal in Lake Constance assessed by sensitivity studies with a 3D hydrodynamic model

An ice-formation algorithm is implemented in the three-dimensional Estuary and Lake Computer Model, to allow simulation of hydrodynamics and the thermal structure beneath the ice during winter. The one-dimensional governing equation of heat conduction among the three layers of white ice, blue ice, and snow is solved for the formation of ice cover considering the heat flux through air and water. This algorithm is applied independently in each grid cell within the simulation domain, allowing for spatially variable ice formation. The model was validated against observed data from both a large and a small Canadian mid-latitude lake (Lake Ontario and Harmon Lake, respectively). The lake surface temperature and the distribution and thickness of ice cover on Lake Ontario were predicted successfully during the 2006–2007 winter period. The model also accurately simulated spring 2007 temperature profiles, as typically used for the initial conditions for a summer simulation. The variation of ice and snow thickness, and vertical temperature profiles, were well-simulated for Harmon Lake during winter 1990–1991. These comparisons demonstrate the applicability of the model for year-round simulation of mid-latitude lakes of varying size.

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Three-dimensional simulation of lake and ice dynamics during winter

Three-dimensional winter modeling and the effects of ice cover on hydrodynamics, thermal structure and water quality in Lake Erie

A Two-Dimensional Horizontal Wave Propagation and Mud Mass Transport Model on Muddy Coastal Regions

A model of the three-dimensional hydrodynamics, transport and flushing in the Bay of Quinte

The present study offers a two-dimensional horizontal wave propagation and morphodynamic model for muddy coasts. The model can be applied on a general three-dimensional bathymetry of a soft muddy coast to calculate wave damping, fluid mud mass transport and resulting bathymetry change under wave actions. The wave propagation model is based on time-dependent mild slope equations including the wave energy dissipation due to the wave-mud interaction of bottom mud layers as well as the combined effects of the wave refraction, diffraction and breaking. The constitutive equations of the visco-elastic–plastic model are adopted for the rheological behavior of fluid mud. The mass transport velocity within the fluid mud layer is calculated combining the Stokes’ drift, the mean Eulerian velocity and the gravity-driven mud flow. The results of the numerical model are compared against a series of conducted wave basin experiments, wave flume experiments and field observations. Comparisons between the computed results with both the field and laboratory data reveal the capability of the proposed model to predict the wave transformation and mud mass transport.

Ali Oveisy

Papers

Three-dimensional simulation of lake and ice dynamics during winter

Three-dimensional winter modeling and the effects of ice cover on hydrodynamics, thermal structure and water quality in Lake Erie

A Two-Dimensional Horizontal Wave Propagation and Mud Mass Transport Model on Muddy Coastal Regions

A model of the three-dimensional hydrodynamics, transport and flushing in the Bay of Quinte

A two-dimensional horizontal wave propagation and mud mass transport model