Short wave radiation

Global radiation is partially reflected at the lake surface. At a zenith angle of 90° only little global radiation is reflected (about 1% to 6%). Reflectivity increases with decreasing solar angle, with wave activity and with the turbidity of the water and therefore changes widely during the course of a year.

H_S = (1- α)·RSW

α = reflected portion of global radiation at the water surface (lake albedo)
RSW = global radiation [W·m^-2]
 

Long wave radiation

About 97% of incoming long wave radiation is adsorbed by lakes.
Incoming long wave radiation can be of more importance than direct solar radiation when solar radiation is reduced by a heavy cloud cover (which simultaneously enhances atmospheric longwave radiation) or when the reflected portion of solar radiation is high as a result of high surface reflectance such as produced by snow cover.
Within rugged massifs like the Jöri catchment, longwave radiation balance can very widely.
Long wave emission largely depends on water temperature.

H_Le =ε_w·σ·(T_s)⁴

ε_w = black body emission coefficient = 0.97
σ = Boltzmann constant [5.67·10^-8 W·m2·K^-4]
T_s =surface water temperature [K]
 

Latent heat flux

The latent heat flux is dependent on the vapor pressure gradient across the air-water interface. The phase change of a liquid to a gas is called evaporation. Disrupting the bonds between hydrogen atoms in liquid water requires heat energy called latent heat of vaporization. Latent heat, because it does not change the temperature of the air, but the surface cools.

H_E ~-(e_s-e_a)

e_s = saturated water vapour at the lake surface [hPa]
e_a = water vapour of the atmosphere [hPa]
 

Sensible heat flux

In case of a temperature difference between surface and air, heat is transferred along the temperature gradient. Both, latent and sensible heat flux, are influenced by wind, increasing with wind speed.

H_C ~-(e_s-e_a)

e_s = saturated water vapour at the lake surface [hPa]
e_a = water vapour of the atmosphere [hPa]
 

Precipitation heat flux

Temperature differences between the precipitation and lake water surface influence the water temperature. Precipitation volumes normally are small compared to the lake volume, resulting in small temperature effects. Yet, this is different when the precipitation falls in the form of snow. At a temperature difference of 1K between precipitation and water surface, energy loss due to snowfall is 80 times higher compared with rainfall. As snowfall events are quite frequent in many alpine environments, even in summer, importance of precipitation heat flux is more pronounced compared to lowland lakes.

H_P =P·c_p·ρ·(T_a-T_s) -P·c_m·ρ

P = amount of precipitation [mm]
c_m = specific heat of ice-melt [J·kg^-1]
c_p = specific heat of water [J·kg^-1·K^-1]
ρ = density of water [kg·m^-3]
T_a = air temperature
 

Throughflow heat flux

For lowland lakes throughflow heat flux can be neglected because the temperature difference between in- and outflow is near 0°K. In high alpine lakes the inflow temperature can be more than 10°K lower, as the water often comes from snowmelt, glacier melt or cold subsurface inflows. Together with the small lake surface, this inflow can cause a substantial heat loss.

H_F = Q.c_p·ρ·(T_i-T_s)/A

Q = inflow vollume [m3·s^-1]
c_p = specific heat of water [J·kg^-1·K^-1]
ρ = density of water [kg·m^-3]
A = lake surface area [m2]
 

Sediment heat flux

Heat energy stored in sediments of shallow lakes may significantly influence lake temperatures. The sediment is heating up during warmer periods through solar radiation and conduction at the water sediment interface. The energy stored in the sediments will be released in colder periods.

H_SD = -k_s·(dT_s /dz)

ks = thermal conductivity of the sediment [W·m^-1·K^-1]