Evapotranspiration → Energy Balance Method

The input variables for the Energy Balance method of estimating losses due to evaporation are defined as follows:

QSW = net shortwave radiation [W / m2]
QLW = net longwave radiation [W / m2]
Tair = air temperature [deg C]
Tsurf = surface (snow) temperature [deg C]
Tsoil_x = soil temperature at depth x [deg C]
x = reference depth in soil [m]
Ksoil = thermal conductivity of soil [W / (m deg_C)]
uz = wind velocity at height z [m / s]
z = reference height for wind [m] (above land surface)
z0 = surface roughness height [m] (with no snow)
h0snow = initial snow depth [m]
ρair = density of the air [kg / m3]
cair = specific heat capacity of air [J / (kg deg_C)]
Lv = latent heat of vaporization, water [J / kg] (2500000)
g = gravitational constant, Earth = 9.81 [m / s2]
κ = von Karman's constant = 0.41 [unitless]

Note: If net total radiation has been measured, it can be entered as QSW and then QLW can be set to zero. Any meteorological variables entered here (such as Tair) are automatically shared with other other processes, such as Snowmelt and Precipitation.

Snow depth is tracked internally, and can increase from snowfall or decrease by melting, starting from its initial value. In the current version there is no mechanism for redistribution of snow.

For each variable, you may choose from the droplist of data types. For the "Scalar" data type, enter a numeric value with the units indicated in the dialog. For the other data types, enter a filename. Values in files must also use the indicated units.

Single grids and grid sequences are assumed to be stored as RTG and RTS files, respectively. Time series are assumed to be stored as text files, with one value per line. For a time series or grid sequence, the time between values must coincide with the timestep provided.


Equations Used by the Energy-Balance ET Method

ET = (1000 * Qet) / (ρwater * Lv) = evaporation rate [mm / sec]
Qet = (QSW + QLW + Qc + Qh) = energy flux used to evaporate water [W / m2]
Qc = Ksoil * (Tsoil_x - Tsurf) * (100 / x) = conduction energy flux [W / m2] (between surf. and subsurf.)
Qh = ρair * cair * Dh * (Tair - Tsurf) = sensible heat flux [W / m2]
Dn = uz * κ2 / LN[(z - hsnow) / z0air]2 = bulk exchange coeff. (neutrally stable conditions) [m / s]
Dh = Dn / [1 + (10 * Ri)],     (Tair > Tsurf) = bulk exchange coeff. for heat [m / s] (stable)
= Dn * [1 - (10 * Ri)],     (Tair < Tsurf) = bulk exchange coeff. for heat [m / s] (unstable)
Ri = g * z * (Tair - Tsurf)   /
     [uz2 (Tair + 273.15)] = Richardson's number [unitless]


Notes on the Equations

Wherever (d > 0), evaporation results in a reduction in the surface flow depth. Wherever (d = 0), water is removed from subsurface storage. If the 1D Richards' equation is used for infiltration, then the evaporation rate is applied as a surface boundary condition and alters

In the equation for computing Dn, the reference height, z, is reduced by the computed snow depth, hsnow. It follows that z must be chosen so as to be greater than any possible snow depth.


References

Brutsaert, W. (1975) On a derivable formula for long-wave radiation from clear skies, Water Resources Research, 11, 742-744.

Dingman, S.L (2002) Physical Hydrology, 2nd ed., Prentice Hall, New Jersey. (see Chapter 7, pp. 285-299)

Schlicting, H. (1960) Boundary Layer Theory, 4th ed., McGraw-Hill, New York, 647 pp.

Zhang, Z., D.L. Kane and L.D. Hinzman (2000) Development and application of a spatially-distributed Arctic hydrological and thermal process model (ARHYTHM), Hydrological Processes, 14, 1017-1044.