Heat Balance of Open Waterbodies

From a continuum–mechanical point of view, the heat balance or the thermodynamics of a lake, reservoir, or ocean is governed by three different types of processes: surface fluxes, those through the water surface and the sediment boundary of a water body; internal heat production; and external heat supply. Whereas surface fluxes are accounted for in boundary conditions, supply and production take place in the water volume and are described as additional production terms in the equation of heat (1). Turbulent diffusion and, to a much lesser degree, molecular diffusion lead to a certain temperature stratification, usually dividing a lake into a well-mixed, upper warm layer, the epilimnion, separated from it by a transition zone a colder hypolimnion. The temperature–depth distribution can be determined from the heat balance equation and boundary conditions describing the surface fluxes into the water. In contrast to this, in a well-mixed waterbody with a homogeneous temperature distribution, for example, a polymictic lake, all heat production and flux terms are lumped together in a net thermal energy flux. In this case, the heat production terms are treated as fluxes across the surface. Using such a simple system, one can determine the equilibrium temperature of the waterbody for a certain set of meteorologic conditions, that temperature to which the mixed waterbody is driven under the same prevailing meteorologic conditions. For a stratified lake or ocean, such an approach is only of limited use because it does not account for vertical transport of heat in the waterbody. But it can be a good approximation for the surface temperature when the stratification is strong, thus separating the hypolimnion from the well-mixed epilimnion. Keywords: heat balance; heat flux; air–water interface; short-wave radiation; long-wave radiation; sensible heat flux; evaporation; latent heat flux