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LAKE is an extended one-dimensional model of thermodynamic, hydrodynamic and biogeochemical processes in the water basin (lake, reservoir or section of a stream) and the bottom sediments (Stepanenko and Lykosov 2005, Stepanenko et al. 2011). The model simulates vertical heat transfer taking into account the penetration of radiation (UV, PAR, NIR and IR wavebands) in water layers (Heiskanen et al., 2015), ice, snow and bottom sediments. The model allows for the evolution of ice layer at the bottom after complete lake freezing in winter. The equations of the model are formulated in terms of quantities averaged over the horizontal section a water body, which leads to an explicit account of the exchange of momentum, heat, dissolved species and suspended particles between water and the inclined bottom. In the water column, $`k-\epsilon`$ parametrization of turbulence is applied, along with computationally cheap options like Henderson-Sellers diffusivity and convective adaptation of predicted vertical profiles. The equations of motion take into account the barotropic (Stepanenko et al., 2016) and baroclinic pressure gradient (Степаненко, 2018; Stepanenko et al., 2020). In ice and snow, a coupled transport of heat and liquid water is reproduced (Volodina et al. 2000; Stepanenko et al., 2019). In bottom sediments, water phase changes are simulated, in order to reproduce taliks in permafrost zone. The water salinity effects include contributions to water density, water freezing point, and the ice growth rate taking into account the in-ice saline pockets (Stepanenko et al., 2019). The water total budget is explicitly simulated to reproduce lake level variations, as well as associated vertical motions in the water column (Степаненко и др., 2020). The model also describes vertical diffusion of dissolved gases (CO$`_2`$, CH$`_4`$, O$`_2`$), as well as their transfer by upwelling bubbles, methane oxidation, photosynthesis and processes of oxygen consumption in water column and sediments due to decay of dead organic matter. The other biogeochemical species include particulate organic matter (both living and dead fractions; the living fraction implicitly including phyto- and zooplankton), chorophyll-a, dissolved organic carbon, dissolved inorganic phosphorus. Parameterization of methane production in sediments is included (Stepanenko et al. 2011), and for the case of thermokarst lakes, an original formulation for the methane production near the lower boundary of "talik" is implemented. Model has been tested in respect to thermal and ice regime at a number lakes in contrasting climate conditions, specifically, within the LakeMIP project (Lake Model Intercomparison Project, Stepanenko et al., 2010; Stepanenko et al., 2013; Stepanenko et al., 2014; Thiery et al., 2014). The modeled carbon dioxide and methane emissions has been reported for a number of natural and artificial reservoirs (Iakunin et al., 2020; Guseva et al., 2020; Stepanenko et al., 2011; Stepanenko et al., 2016; Степаненко и др., 2020; Lomov et al., 2024).
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LAKE is an extended one-dimensional model of thermodynamic, hydrodynamic and biogeochemical processes in the water basin (lake, reservoir or a stream section) and the bottom sediments (Stepanenko and Lykosov 2005, Stepanenko et al. 2011). The model simulates vertical heat transfer taking into account the penetration of radiation (UV, PAR, NIR and IR wavebands) in water layers (Heiskanen et al., 2015), ice, snow and bottom sediments. The model allows for the evolution of ice layer at the lake bottom after complete lake freezing in winter. The equations of the model are formulated in terms of quantities averaged over the horizontal section a water body, which leads to an explicit account of the exchange of momentum, heat, dissolved species and suspended particles between water and the inclined bottom. In the water column, turbulent closure can be chosen between sophisticated versions of $`k-\epsilon`$ model, and computationally cheap options like Henderson-Sellers diffusivity combined with convective adaptation of predicted vertical profiles. A number of semi-empirical formulations are available for background diffusivity in stably stratified portion of the water column. The equations of motion may include the barotropic (Stepanenko et al., 2016) and baroclinic pressure gradient (Степаненко, 2018; Stepanenko et al., 2020), caused by mass redistribution by currents with the structure of first horizontal seiche mode. In ice and snow, a coupled transport of heat and liquid water is reproduced (Volodina et al. 2000; Stepanenko et al., 2019). In bottom sediments, water phase changes are simulated, in order to reproduce taliks in permafrost zone. The water salinity effects include contributions to water density, water freezing point, and the ice growth rate taking into account the in-ice saline pockets (Stepanenko et al., 2019). The water total budget is explicitly simulated to reproduce lake level variations, as well as associated large-scale vertical motions in the water column (Степаненко и др., 2020). The model also describes vertical diffusion of dissolved gases (CO$`_2`$ as a part of dissolved inorganic carbon, CH$`_4`$, O$`_2`$), as well as their transfer by upwelling bubbles, methane oxidation, photosynthesis and processes of oxygen consumption in water column and sediments due to decay of dead organic matter. The other biogeochemical species include particulate organic matter (both living and dead fractions; the living fraction implicitly including phyto- and zooplankton), chorophyll-a, dissolved organic carbon, dissolved inorganic phosphorus. Parameterization of methane production in sediments is included (Stepanenko et al. 2011), and for the case of thermokarst lakes, an original formulation for the methane production near the lower boundary of "talik" is implemented. Model has been tested in respect to thermal and ice regime at a number lakes in contrasting climate conditions, specifically, within the LakeMIP project (Lake Model Intercomparison Project, Stepanenko et al., 2010; Stepanenko et al., 2013; Stepanenko et al., 2014; Thiery et al., 2014). The modeled carbon dioxide and methane emissions has been reported for a number of natural and artificial reservoirs (Iakunin et al., 2020; Guseva et al., 2020; Stepanenko et al., 2011; Stepanenko et al., 2016; Степаненко и др., 2020; Lomov et al., 2024).
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