Basic Concepts and Equations

HEC-HMS implements the Penman-Monteith method as derived by the United Nations Food and Agriculture Organization (FAO) (Allen et al., 1998). The Penman Monteith was adopted as the standard for reference evapotranspiration by the FAO. The reference evapotranspiration provides a standard to which evapotranspiration in different seasons or regions and of other crops can be compared.

Evapotranspiration can be derived using an energy balance or mass transfer method. Evaporation of water requires energy, either in the form of sensible heat or radiant energy. The rate of evapotranspiration is governed by the energy exchange at the vegetation surface and is limited by the amount of available energy. Therefore, the rate of evapotranspiration can be derived from a surface energy balance. Evapotranspiration can also be derived by balancing the incoming and outgoing water fluxes to the soil, or root zone. The mass transfer method is better suited for estimating ET over long time periods (on the order of weeks or more). 

The Penman Monteith method combines energy balance and mass transfer methods (Penman, 1948; Monteith, 1965). The evapotranspiration rate is represented by the latent heat flux:

where R_n is the net radiation at the crop surface, G is the soil heat flux , $//<![CDATA[ \begin{array}{l}\rho_a\end{array} //]]>$ is the mean air density at constant pressure, c_p is the specific heat of air, e_s is the saturation vapour pressure, e_a is the actual vapour pressure, e_s - e_a is the vapour pressure deficit, $//<![CDATA[ \begin{array}{l}\Delta\end{array} //]]>$ is the slope of the saturation vapour pressure temperature relationship, and $//<![CDATA[ \begin{array}{l}\gamma\end{array} //]]>$ is the psychrometric constant, and r_s and r_a are the (bulk) surface and aerodynamic resistances, respectively.

The bulk surface resistance accounts for the resistance of vapour flow through the transpiring crop (stomata, leaves) and evaporating soil surface. The aerodynamic resistance describes the upward resistance from vegetation resulting from the friction from air flowing over vegetated surfaces.

While a large number of empirical evapotranspiration methods have been developed worldwide, some have been calibrated locally leading to limited global validity. The FAO Penman Monteith method uses the concept of a reference surface, removing the need to define parameters for each crop and stage of growth. Evapotranspiration rates of different crops are related to the evapotranspiration rate from the reference surface through the use of crop coefficients. A hypothetical grass reference was selected to avoid the need for local calibration. According to FAO (Allen et al., 1998):

The reference surface closely resembles an extensive surface of green grass of uniform height, actively growing, completely shading the ground and with adequate water. The requirements that the grass surface should be extensive and uniform result from the assumption that all fluxes are one-dimensional upwards.

The reference crop is defined as a hypothetical crop with a height of 0.12 m, a surface resistance of 70 s/m, and an albedo of 0.23. The FAO's simplified equation for reference evapotranspiration is (Allen et al., 1998):

where ET_o is the reference evapotranspiration, R_n is the net radiation at the crop surface, G is the soil heat flux density, T is the mean daily air temperature at 2 m height, u₂ is the wind speed at 2 m height, e_s is the saturation vapour pressure, e_a is the actual vapour pressure, e_s - e_a is the vapour pressure deficit, $//<![CDATA[ \begin{array}{l}\Delta\end{array} //]]>$ is the slope of the saturation vapour pressure curve, and $//<![CDATA[ \begin{array}{l}\gamma\end{array} //]]>$ is the psychrometric constant.

Required Parameters

The parameterization is entirely dependent on the atmospheric conditions: solar radiation, air temperature, humidity, and wind speed measurements. Weather measurements should be made at 2 m above the ground surface (or converted to that height).