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The LAKE model webpage: https://mathmod.org/lake/
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).
The current **version** of the model is 3.2
The complete **model archive** with sample input data:
* [LAKE2.0.zip](/uploads/93a0c94120a307d0fdd9bcdb069e3125/LAKE2.0.zip)
* [LAKE2.1.zip](/uploads/79b6a6772b02920f6046145580bfca91/LAKE2.1.zip) (salinity dynamics in ice cover is added)
* [LAKE2.2.zip](/uploads/ff8d297490a8c4603d037fcd42500210/LAKE2.2.zip) (input/output of control point added, minor bugs fixed)
* [LAKE2.3.zip](uploads/ef2109b0ad39f3c00715735a279e811c/LAKE2.3.zip) (commit 7d016e79 in gitlab repository, which is updated by testing at GNU Fortran 9.3.0 compiler; the model is adapted to simulate artificial reservoirs with high throughflow and water level variations; a model configuration for simulating the vertical structure of river flow is added)
* [LAKE2.4.zip](uploads/cfc05ee41701ee056bff985df3ad3f97/LAKE2.4.zip) (commit f29fb387 in repository; bugs related to $k-\epsilon$ model fixed, new b.c. options for $k-\epsilon$, Cuette-Poiseuille flow setup and turbulence closure added, methane production parameters are set specific for each sediment column, new output options)
* [LAKE2.5.zip](uploads/198e9d503e1c7438fef548e36b7618d8/LAKE2.5.zip) (commit 82350cae in repository; the code is adapted for ifort compiler, bugs fixed)
* [LAKE2.6.zip](uploads/0d22404df6562bbd5187d00ea6daae60/LAKE2.6.zip) (commit 08aa0758 in repository; new driving parameters, related to background diffusivity in thermocline, methane production and oxidation in water column, are included in setup file)
* [LAKE-LAKE3.0.zip](uploads/834e6d605925da87c858afad66eb0131/LAKE-LAKE3.0.zip) (commit
6548bc92 in repository; a number of bugs fixed, esp. related to salinity; filling missing input radiation fluxes by values computed by empirical formulae; model code improved)
* [LAKE3.1.zip](uploads/b7f18f096b38c23ffd371377bbf3b0d8/LAKE3.1.zip) (commit 16cfe649 in repository; bug in LAKE3.0 related to methane fixed, cmake compilation added)
* [LAKE3.2.zip](uploads/b0ecb4455c5340c063d1be290608e492/LAKE3.2.zip) (commit 69ba4cc1 in repository; multiple fixes and improvements in biogeochemical scheme)
When **publishing** results using please refer to:
* for LAKE2.x: Stepanenko, V., Mammarella, I., Ojala, A., Miettinen, H., Lykosov, V., & Vesala, T. (2016). LAKE 2.0: a model for temperature, methane, carbon dioxide and oxygen dynamics in lakes. *Geoscientific Model Development*, 9(5), 1977–2006. http://doi.org/10.5194/gmd-9-1977-2016
* for LAKE3.x: Lomov V., Stepanenko V., Grechushnikova M., and Repina I. (2024). Mechanistic modeling of the variability of methane emissions from an artificial reservoir. *Water*, 16(1):76. http://dx.doi.org/10.3390/w16010076; V. M. Stepanenko, M. G. Grechushnikova, and I. A. Repina (2022). Numerical simulation of methane emission from an artificial reservoir. *Izvestiya - Atmospheric and Oceanic Physics*, 58(6):649–659. http://dx.doi.org/10.1134/S0001433822060159
Any **questions** regarding LAKE model please address to Victor Stepanenko (stepanen(at)srcc.msu.ru)
**References**
* Lomov V., Stepanenko V., Grechushnikova M., and Repina I. (2024). Mechanistic modeling of the variability of methane emissions from an artificial reservoir. *Water*, 16(1):76. http://dx.doi.org/10.3390/w16010076
* Clark Jason A., Elchin E. Jafarov, Ken D. Tape, Benjamin M. Jones, and Victor Stepanenko (2022). Thermal modeling of three lakes within the continuous permafrost zone in alaska using the LAKE 2.0 model. Geoscientific Model Development, 15:7421–7448. http://dx.doi.org/10.5194/gmd-15-7421-2022
* Iakunin, Maksim, Victor Stepanenko, Rui Salgado, Miguel Potes, Alexandra Penha, Maria Helena Novais, and Gonçalo Rodrigues (2020). Numerical study of the seasonal thermal and gas regimes of the largest artificial reservoir in western europe using the LAKE 2.0 model. *Geoscientific Model Development*, 13(8):3475–3488. http://dx.doi.org/10.5194/gmd-13-3475-2020
* Heiskanen, J. J., Mammarella, I., Ojala, A., Stepanenko, V., Erkkilä, K.-M., Miettinen, H., … Nordbo, A. (2015). Effects of water clarity on lake stratification and lake-atmosphere heat exchange. *Journal of Geophysical Research*, 120(15). http://doi.org/10.1002/2014JD022938
* Gladskikh, D. S., V. M. Stepanenko, and E. V. Mortikov (2021). The effect of the horizontal dimensions of inland water bodies on the thickness of the upper mixed layer. *Water Resources*, 48(2):226–234. http://dx.doi.org/10.1134/S0097807821020068
* Golub, Malgorzata, Wim Thiery, Rafael Marcé, Don Pierson, ..., and Galina Zdorovennova (2022). A framework for ensemble modelling of climate change impacts on lakes worldwide: the isimip lake sector. Geoscientific Model Development, 15:4597–4623. http://dx.doi.org/10.5194/gmd-15-4597-2022
* Guseva, S., T. Bleninger, K. Jöhnk, B. A. Polli, Z. Tan, W. Thiery, Q. Zhuang, J. A. Rusak, H. Yao, A. Lorke, and V. Stepanenko (2020). Multimodel simulation of vertical gas transfer in a temperate lake. *Hydrology and Earth System Sciences*, 24:697–715, http://dx.doi.org/10.5194/hess-24-697-2020.
* Guseva, S., M. Aurela, A. Cortés, R. Kivi, E. Lotsari, S. MacIntyre, I. Mammarella, A. Ojala, V. Stepanenko, P. Uotila, A. Vähä, T. Vesala, M. B. Wallin, and A. Lorke (2021). Variable physical drivers of near-surface turbulence in a regulated river. *Water Resources Research*, 57(11):e2020WR027939. http://dx.doi.org/10.1029/2020wr027939
* Stepanenko, V. M., Machul’skaya, E. E., Glagolev, M. V., & Lykossov, V. N. (2011). Numerical modeling of methane emissions from lakes in the permafrost zone. *Izvestiya, Atmospheric and Oceanic Physics*, 47(2), 252–264. http://doi.org/10.1134/S0001433811020113
* Stepanenko, V. M., Martynov, A., Jöhnk, K. D., Subin, Z. M., Perroud, M., Fang, X., … Goyette, S. (2013). A one-dimensional model intercomparison study of thermal regime of a shallow, turbid midlatitude lake. *Geoscientific Model Development*, 6(4), 1337–1352. http://doi.org/10.5194/gmd-6-1337-2013
* Stepanenko, V., Jöhnk, K. D., Machulskaya, E., Perroud, M., Subin, Z., Nordbo, A., … Mironov, D. (2014). Simulation of surface energy fluxes and stratification of a small boreal lake by a set of one-dimensional models. *Tellus, Series A: Dynamic Meteorology and Oceanography*, 66(1). http://doi.org/10.3402/tellusa.v66.21389
* Stepanenko, V., Mammarella, I., Ojala, A., Miettinen, H., Lykosov, V., & Vesala, T. (2016). LAKE 2.0: a model for temperature, methane, carbon dioxide and oxygen dynamics in lakes. *Geoscientific Model Development*, 9(5), 1977–2006. http://doi.org/10.5194/gmd-9-1977-2016
* S. Guseva, V. Stepanenko, N. Shurpali, M. E. Marushchak, C. Biasi, and S. E. Lind. Numerical simulation of methane emission from subarctic lake in Komi republic (Russia). *Geography, Environment, Sustainability*, 2(9):58–74, 2016. http://dx.doi.org/10.15356/2071-9388/_02v09/_2016/_05
* Stepanenko, V. M., Repina, I. A., Ganbat, G., and Davaa, G. Numerical simulation of ice cover of saline lakes (2019). *Izvestiya - Atmospheric and Oceanic Physics*, 55(1):129–138. http://dx.doi.org/10.1134/S0001433819010092
* V. M. Stepanenko, G. Valerio, and M. Pilotti (2020). Horizontal pressure gradient parameterization for one-dimensional lake models. *JOURNAL OF ADVANCES IN MODELING EARTH SYSTEMS*, 12(2):e2019MS001906, http://dx.doi.org/10.1029/2019ms001906.
* V. M. Stepanenko, M. G. Grechushnikova, and I. A. Repina (2022). Numerical simulation of methane emission from an artificial reservoir. *Izvestiya - Atmospheric and Oceanic Physics*, 58(6):649–659. http://dx.doi.org/10.1134/S0001433822060159
* Thiery, W., Stepanenko, V., Fang, X., Jöhnk, K., Li, Z., Martynov, A., … van Lipzig, N. (2014). LakeMIP Kivu: evaluating the representation of a large, deep tropical lake by a set of one-dimensional lake models. *Tellus, Series A: Dynamic Meteorology and Oceanography*, 66. http://doi.org/doi:10.3402/tellusa.v66.21390
* Volodina, E., Bengtsson, L., & Lykosov, V. N. (2000). Parameterization of heat and moisture transfer in a snow cover for modelling of seasonal variations of land hydrological cycle. *Russian Meteorology and Hydrology*, (5), 5–14.
* Wang Mengxiao, Lijuan Wen, Li Zhaoguo, Matti Leppäranta, Victor Stepanenko, Yixin Zhao, Ruijia Niu, Liuyiyi Yang, and Georgiy Kirillin (2022). Mechanisms and effects of under-ice warming water in ngoring lake of qinghai–tibet plateau. The Cryosphere, 16:3635–3648. http://dx.doi.org/10.5194/tc-16-3635-2022
* Степаненко В.М. (2018) Параметризация сейш для одномерной модели водоёма. *Труды Московского физико-технического института*. том 10, № 1, с. 97-111.
* В. М. Степаненко, М. Г. Гречушникова, И. А. Репина. Численное моделирование эмиссии метана из водохранилища (2020). *Фундаментальная и прикладная климатология*, 2:76–99. http://dx.doi.org/10.21513/2410-8758-2020-2-76-99
<!-- **Acknowledgements**
The LAKE model webpage: https://mathmod.org/lake/
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).
The current **version** of the model is 3.2
The complete **model archive** with sample input data:
* [LAKE2.0.zip](/uploads/93a0c94120a307d0fdd9bcdb069e3125/LAKE2.0.zip)
* [LAKE2.1.zip](/uploads/79b6a6772b02920f6046145580bfca91/LAKE2.1.zip) (salinity dynamics in ice cover is added)
* [LAKE2.2.zip](/uploads/ff8d297490a8c4603d037fcd42500210/LAKE2.2.zip) (input/output of control point added, minor bugs fixed)
* [LAKE2.3.zip](uploads/ef2109b0ad39f3c00715735a279e811c/LAKE2.3.zip) (commit 7d016e79 in gitlab repository, which is updated by testing at GNU Fortran 9.3.0 compiler; the model is adapted to simulate artificial reservoirs with high throughflow and water level variations; a model configuration for simulating the vertical structure of river flow is added)
* [LAKE2.4.zip](uploads/cfc05ee41701ee056bff985df3ad3f97/LAKE2.4.zip) (commit f29fb387 in repository; bugs related to $k-\epsilon$ model fixed, new b.c. options for $k-\epsilon$, Cuette-Poiseuille flow setup and turbulence closure added, methane production parameters are set specific for each sediment column, new output options)
* [LAKE2.5.zip](uploads/198e9d503e1c7438fef548e36b7618d8/LAKE2.5.zip) (commit 82350cae in repository; the code is adapted for ifort compiler, bugs fixed)
* [LAKE2.6.zip](uploads/0d22404df6562bbd5187d00ea6daae60/LAKE2.6.zip) (commit 08aa0758 in repository; new driving parameters, related to background diffusivity in thermocline, methane production and oxidation in water column, are included in setup file)
* [LAKE-LAKE3.0.zip](uploads/834e6d605925da87c858afad66eb0131/LAKE-LAKE3.0.zip) (commit
6548bc92 in repository; a number of bugs fixed, esp. related to salinity; filling missing input radiation fluxes by values computed by empirical formulae; model code improved)
* [LAKE3.1.zip](uploads/b7f18f096b38c23ffd371377bbf3b0d8/LAKE3.1.zip) (commit 16cfe649 in repository; bug in LAKE3.0 related to methane fixed, cmake compilation added)
* [LAKE3.2.zip](uploads/b0ecb4455c5340c063d1be290608e492/LAKE3.2.zip) (commit 69ba4cc1 in repository; multiple fixes and improvements in biogeochemical scheme)
* [LAKE3.3.zip](uploads/afde6a23e58274f89778e1e4c69007ea/LAKE3.3.zip)(commit 95346103 in repository; new snow scheme, including snow (white) ice and crystal (black) ice)
When **publishing** results using please refer to:
* for LAKE2.x: Stepanenko, V., Mammarella, I., Ojala, A., Miettinen, H., Lykosov, V., & Vesala, T. (2016). LAKE 2.0: a model for temperature, methane, carbon dioxide and oxygen dynamics in lakes. *Geoscientific Model Development*, 9(5), 1977–2006. http://doi.org/10.5194/gmd-9-1977-2016
* for LAKE3.x: Lomov V., Stepanenko V., Grechushnikova M., and Repina I. (2024). Mechanistic modeling of the variability of methane emissions from an artificial reservoir. *Water*, 16(1):76. http://dx.doi.org/10.3390/w16010076; V. M. Stepanenko, M. G. Grechushnikova, and I. A. Repina (2022). Numerical simulation of methane emission from an artificial reservoir. *Izvestiya - Atmospheric and Oceanic Physics*, 58(6):649–659. http://dx.doi.org/10.1134/S0001433822060159
Any **questions** regarding LAKE model please address to Victor Stepanenko (v.stepanenko(at)rcc.msu.ru)
**References**
* Lomov V., Stepanenko V., Grechushnikova M., and Repina I. (2024). Mechanistic modeling of the variability of methane emissions from an artificial reservoir. *Water*, 16(1):76. http://dx.doi.org/10.3390/w16010076
* Clark Jason A., Elchin E. Jafarov, Ken D. Tape, Benjamin M. Jones, and Victor Stepanenko (2022). Thermal modeling of three lakes within the continuous permafrost zone in alaska using the LAKE 2.0 model. Geoscientific Model Development, 15:7421–7448. http://dx.doi.org/10.5194/gmd-15-7421-2022
* Iakunin, Maksim, Victor Stepanenko, Rui Salgado, Miguel Potes, Alexandra Penha, Maria Helena Novais, and Gonçalo Rodrigues (2020). Numerical study of the seasonal thermal and gas regimes of the largest artificial reservoir in western europe using the LAKE 2.0 model. *Geoscientific Model Development*, 13(8):3475–3488. http://dx.doi.org/10.5194/gmd-13-3475-2020
* Heiskanen, J. J., Mammarella, I., Ojala, A., Stepanenko, V., Erkkilä, K.-M., Miettinen, H., … Nordbo, A. (2015). Effects of water clarity on lake stratification and lake-atmosphere heat exchange. *Journal of Geophysical Research*, 120(15). http://doi.org/10.1002/2014JD022938
* Gladskikh, D. S., V. M. Stepanenko, and E. V. Mortikov (2021). The effect of the horizontal dimensions of inland water bodies on the thickness of the upper mixed layer. *Water Resources*, 48(2):226–234. http://dx.doi.org/10.1134/S0097807821020068
* Golub, Malgorzata, Wim Thiery, Rafael Marcé, Don Pierson, ..., and Galina Zdorovennova (2022). A framework for ensemble modelling of climate change impacts on lakes worldwide: the isimip lake sector. Geoscientific Model Development, 15:4597–4623. http://dx.doi.org/10.5194/gmd-15-4597-2022
* Guseva, S., T. Bleninger, K. Jöhnk, B. A. Polli, Z. Tan, W. Thiery, Q. Zhuang, J. A. Rusak, H. Yao, A. Lorke, and V. Stepanenko (2020). Multimodel simulation of vertical gas transfer in a temperate lake. *Hydrology and Earth System Sciences*, 24:697–715, http://dx.doi.org/10.5194/hess-24-697-2020.
* Guseva, S., M. Aurela, A. Cortés, R. Kivi, E. Lotsari, S. MacIntyre, I. Mammarella, A. Ojala, V. Stepanenko, P. Uotila, A. Vähä, T. Vesala, M. B. Wallin, and A. Lorke (2021). Variable physical drivers of near-surface turbulence in a regulated river. *Water Resources Research*, 57(11):e2020WR027939. http://dx.doi.org/10.1029/2020wr027939
* Stepanenko, V. M., Machul’skaya, E. E., Glagolev, M. V., & Lykossov, V. N. (2011). Numerical modeling of methane emissions from lakes in the permafrost zone. *Izvestiya, Atmospheric and Oceanic Physics*, 47(2), 252–264. http://doi.org/10.1134/S0001433811020113
* Stepanenko, V. M., Martynov, A., Jöhnk, K. D., Subin, Z. M., Perroud, M., Fang, X., … Goyette, S. (2013). A one-dimensional model intercomparison study of thermal regime of a shallow, turbid midlatitude lake. *Geoscientific Model Development*, 6(4), 1337–1352. http://doi.org/10.5194/gmd-6-1337-2013
* Stepanenko, V., Jöhnk, K. D., Machulskaya, E., Perroud, M., Subin, Z., Nordbo, A., … Mironov, D. (2014). Simulation of surface energy fluxes and stratification of a small boreal lake by a set of one-dimensional models. *Tellus, Series A: Dynamic Meteorology and Oceanography*, 66(1). http://doi.org/10.3402/tellusa.v66.21389
* Stepanenko, V., Mammarella, I., Ojala, A., Miettinen, H., Lykosov, V., & Vesala, T. (2016). LAKE 2.0: a model for temperature, methane, carbon dioxide and oxygen dynamics in lakes. *Geoscientific Model Development*, 9(5), 1977–2006. http://doi.org/10.5194/gmd-9-1977-2016
* S. Guseva, V. Stepanenko, N. Shurpali, M. E. Marushchak, C. Biasi, and S. E. Lind. Numerical simulation of methane emission from subarctic lake in Komi republic (Russia). *Geography, Environment, Sustainability*, 2(9):58–74, 2016. http://dx.doi.org/10.15356/2071-9388/_02v09/_2016/_05
* Stepanenko, V. M., Repina, I. A., Ganbat, G., and Davaa, G. Numerical simulation of ice cover of saline lakes (2019). *Izvestiya - Atmospheric and Oceanic Physics*, 55(1):129–138. http://dx.doi.org/10.1134/S0001433819010092
* V. M. Stepanenko, G. Valerio, and M. Pilotti (2020). Horizontal pressure gradient parameterization for one-dimensional lake models. *JOURNAL OF ADVANCES IN MODELING EARTH SYSTEMS*, 12(2):e2019MS001906, http://dx.doi.org/10.1029/2019ms001906.
* V. M. Stepanenko, M. G. Grechushnikova, and I. A. Repina (2022). Numerical simulation of methane emission from an artificial reservoir. *Izvestiya - Atmospheric and Oceanic Physics*, 58(6):649–659. http://dx.doi.org/10.1134/S0001433822060159
* Thiery, W., Stepanenko, V., Fang, X., Jöhnk, K., Li, Z., Martynov, A., … van Lipzig, N. (2014). LakeMIP Kivu: evaluating the representation of a large, deep tropical lake by a set of one-dimensional lake models. *Tellus, Series A: Dynamic Meteorology and Oceanography*, 66. http://doi.org/doi:10.3402/tellusa.v66.21390
* Volodina, E., Bengtsson, L., & Lykosov, V. N. (2000). Parameterization of heat and moisture transfer in a snow cover for modelling of seasonal variations of land hydrological cycle. *Russian Meteorology and Hydrology*, (5), 5–14.
* Wang Mengxiao, Lijuan Wen, Li Zhaoguo, Matti Leppäranta, Victor Stepanenko, Yixin Zhao, Ruijia Niu, Liuyiyi Yang, and Georgiy Kirillin (2022). Mechanisms and effects of under-ice warming water in ngoring lake of qinghai–tibet plateau. The Cryosphere, 16:3635–3648. http://dx.doi.org/10.5194/tc-16-3635-2022
* Степаненко В.М. (2018) Параметризация сейш для одномерной модели водоёма. *Труды Московского физико-технического института*. том 10, № 1, с. 97-111.
* В. М. Степаненко, М. Г. Гречушникова, И. А. Репина. Численное моделирование эмиссии метана из водохранилища (2020). *Фундаментальная и прикладная климатология*, 2:76–99. http://dx.doi.org/10.21513/2410-8758-2020-2-76-99
<!-- **Acknowledgements**
The LAKE model development was supported by Russian Science Foundation, grant 17-17-01210. -->
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