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# Energy budget for open lake evaporation

The energy transferred from the water by the energy for evaporation $Q_ {ve}$ equals:

$Q_{ve}= Q_e*c* \frac {\left ( T_s-T_b\right )} {L}$

where $c$ is the specific heat capacity of water (cal/gm/°C) and $T_b$ is an arbitrarily chosen base temperature, in general 0 degrees Celsius, while $L$ is the latent heat of vaporization (590 cal/gm).

Re-combining the first two equations, we obtain:

$Q_{e}=\frac {Q_s-Q_{rs}-Q_{lw}+Q_v-Q_{\theta} } {1+R+c*(T_s-T_b)/L }$

with $Q_s$ incoming solar radiation and $Q_{rs}$ reflected solar radiation and $Q_{lw}$ net long wave radiation from the water body to the atmosphere, $Q_v$ net energy advected into the lake by flows of water, $Q_{\theta}$ change of energy storage in the lake. R is the Bowen Ratio.

As the total amount of energy used for evaporation is:

$E_o = \frac {Q_e} {L*\rho}$

where $\rho$ is the density $g/cm^3$, evaporation from an open water surface can be expressed in terms of the energy balance components and conditions at the lake surface:

$E_{o} = \frac {Q_s-Q_{rs}-Q_{lw}+Q_v-Q_{\theta} } { \rho * \left [ L*(1+R)+c*(T_s-T_b) \right ] }$

**References**
Dunne, T. & Leopold, L. B. (1978). Water in Environmental Planning. New York: Freeman and Company.