Calculation | Heat content and fluxes

Water temperature and its distribution in a lake are of great ecological importance. Energy budget calculations are suited to define the temperature conditions in a lake and they are prerequisites for any numerical lake simulation model.

In the Jöri catchment, meteorological data and water temperatures were measured during three years, and heat fluxes for lake Jöri III were calculated (Gabathuler 1999).

Components of energy budget calculations

The total heat flow H_tot from atmosphere to water is determined by the following terms:

H_tot = H_S + H_La + H_Le + H_C + H_F + H_SD + H_P

H_S : global radiation absorption
H_La: longwave radiation absorption
H_Le: longwave radiation emission
H_E : latent heat flux
H_C : sensible heat flux
H_F : throughflow heat flux
H_SD: sediment heat flux
H_P : precipitation heat flux

If H_tot is positive the lake heat content and the volume-averaged lake temperature will rise.

1 - Components of energy budget calculations

For more detailed information and formulas for calculation click here.

Heat content and heat fluxes

Measured heat content of Lake Jöri III

Over a period of 3 years, lake temperatures were measured at different depths. With these data, a mean temperature could be calculated and, together with the mean depth (10.1 m for lake III), the heat content per area (H_tot) can be expressed as:

H_tot = T_smean ·cp ·ρ·z_mean [Joule·m^-2]

T_mean = mean temperature
cp      = specific heat of water [J·kg^-1·K^-1]
ρ       = density of water [kg·m^-3]
z_mean = mean depth

The heat content of lake Jöri III varies widely between years, especially during early summer and early fall. In early summer, the differences are due to different break-up dates. Lake III was mostly or totally ice-free after 20 June 1996, 28 July 1997 and 15 July 1998. The mean temperature of a lake with a total or partial ice cover is usually below 4 °C, corresponding to a heat content of less than 175 MJ m^-2. After ice melt, the heat content rises quickly and stays at a higher level for about 2 to 3 months before strong cold fronts reduce the heat content again to 175 MJ m^-2. The lake subsequently cools down to between 1 °C and 3 °C before it finally freezes again.

2 - The calculated heat content of lake Jöri III over 3 years

Calculated heat flux for lake Jöri III

Heat fluxes from global radiation, incoming and outgoing longwave radiation, latent and sensible heat flux, and precipitation heat flux were calculated for lake Jöri III during the years 1996 to 1998.

Global radiation is the only positive heat flux during the open-water period. All other heat fluxes usually add to the cooling of the lake. Because of the decreasing zenith angle of the sun and the usually increasing albedo of lake Jöri III, the heat input form global radiation decreases dramatically from June to October. The other heat fluxes show no seasonal trend. Due to the variable meteorological conditions, the heat fluxes show large fluctuations from day to day.

The mean heat loss due to precipitation is quite small compared to the other heat fluxes for most days, and for lowland lakes it is thought to be negligible. Yet, when precipitation falls as snow, the effects may be significant in small alpine lakes, and the overall heat flux can even be dominated by precipitation heat flux like on 12 September 1998.

3 - All calculated heat fluxes in lake Jöri III in 1998

Calculated vs. measured heat flux

The day-to-day difference of the heat content (heat flux) should equal the calculated heat flux of lake Jöri III. The deviation between measured and calculated heat flux is shown in Fig.4. The dashed lines symbolize a calculation ignoring precipitation heat flux, indicating the importance of this factor in lake Jöri III.

4 - Calculated vs. measured heat flux over three years

Precipitation heat flux accounts for some of the most pronounced deviations between measurements and calculations. But there are still remarkable deviations, which can not be explained by inaccuracies of the weather sensors.

Not included in the calculations were the sediment heatflux and throughflow heatflux. The sediment heat flux is largest after a rapid change in lake water temperature, i.e. right after ice break-up and when cold fronts cool down the lake later in the summer. The pattern of the deviations between calculated and measured heat fluxes in Lake III is somewhat consistent with the assumed sediment heat flux direction, being positive after ice break-up and around zero or negative later. But the deviations are too large to be totally accounted to the sediment heat flux.

Throughflow heatflux probably plays an important role in lakes (partially) fed by glacier meltwater like lake Jöri III. But the amount of inflow changes over time and is difficult or impossible to measure.

29 August 2011
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