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Layden, A., MacCallum, S. N., & Merchant, C. J. (2016). Determining lake surface water temperatures worldwide using a tuned one-dimensional lake model (FLake, v1). Geoscientific Model Development, 9(6), 2167-2189.
FLake is a freshwater lake model capable of predicting the vertical temperature structure and mixing conditions in lakes of various depth on time scales from a few hours to many years. The model is intended for use as a lake parameterisation scheme in numerical weather prediction, climate modelling, and other numerical prediction systems for environmental applications. FLake can also be used as a stand-alone lake model, as a physical module in models of aquatic ecosystems, and as an educational tool.
FLake is a bulk model. It is based on a two-layer parametric representation of the evolving temperature profile and on the integral budgets of heat and kinetic energy for the layers in question. The structure of the stratified layer between the upper mixed layer and the basin bottom, the lake thermocline, is described using the concept of self-similarity (assumed shape) of the temperature-depth curve. The same concept is used to describe the temperature structure of the thermally active upper layer of bottom sediments and of the ice and snow cover. The result is a computationally efficient bulk model that incorporates much of the essential physics.
FLake incorporates (i) a flexible parameterization of the temperature profile in the thermocline, (ii) an advanced formulation to compute the mixed-layer depth, including the equation of convective entrainment and a relaxation-type equation for the depth of a wind-mixed layer, both mixing regimes are treated with due regard for the volumetric character of solar radiation heating, (iii) a module to describe the vertical temperature structure of the thermally active layer of bottom sediments and the interaction of the water column with bottom sediments, and (iv) a snow-ice module. Empirical constants and parameters of FLake are estimated, using independent empirical and numerical data. They should not be re-evaluated when the model is applied to a particular lake. In this way, FLake does not require re-tuning, a procedure that may improve an agreement of model results with a limited amount of data but should generally be avoided as it greatly reduces the predictive capacity of a physical model.
In order to compute fluxes of momentum and of sensible and latent heat at the lake surface, a parameterization scheme is developed that accounts for specific features of the surface air layer over lakes. The scheme incorporates (i) a fetch-dependent formulation for the aerodynamic roughness of the water surface, (ii) advanced formulations for the roughness lengths for potential temperature and specific humidity in terms of the roughness Reynolds number, and (iii) free-convection heat and mass transfer laws to compute fluxes of scalars in conditions of vanishing mean wind.