Evapotranspiration → Penman-Monteith Method

The input variables for the Penman-Monteith 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]
RH = relative humidity [unitless] (between 0 and 1)
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)
zd = zero-plane displacement [m]
P = atmospheric pressure [mbar]
fs = shelter factor [unitless] (between 0.5 and 1)
Cleaf = leaf conductance [m / s]
LAI = leaf area index [unitless] (LAI ≥ 0)
ρair = density of the air [kg / m3]
cair = specific heat capacity of air [J / (kg deg_C)]
ρwater = density of water, 1000 [kg / m3]
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.

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 Penman-Monteith Method

ET = (M1 + M2) / M3 = evaporation rate [m / sec]
M1 = Δ(Tair) * (QSW + QLW) = term in the PM equation
M2 = ρair * cair * Catm * esat(Tair) * (1 - RH) = term in the PM equation
M3 = ρwater * Lv * [Δ(Tair) + γ*(1 + Catm/Ccan)] = term in the PM equation
esat = 6.11 * exp[(17.3 * T) / (T + 237.3)] = saturation vapor pressure [mbar, not KPa] (T in deg_C)
Δ = desat(T)/ dT = slope of esat(T) curve [mbar / deg_C] (function of T)
γ = cair * P / (0.622 * Lv) = psychometric constant [mbar / deg_C]
Catm = uz * κ2 / [LN((z - zd) / z0)]2 = atmospheric conductance, water [m / s]
Ccan = fs * LAI * Cleaf = canopy conductance [m / s]

Notes on the Equations

The Penman-Monteith method is distinguished by the fact that it does not require surface temperature measurements (by design) and also takes transpiration of plants into account. (Note that surface temperature is still needed to compute QLW, unless it has been measured.) The derivation begins with several of the same equations that are used by the Energy-Balance method but approximates the ratio [(esat(Tsurf) - esat(Tair)] / (Tsurf - Tair) with Δ(Tair), as defined above. This is basically how the equation is made to be independent of surface properties. The following equations are also used in the derivation:

ET = (QSW + QLW + Qh) / (ρwater * Lv) = evaporation rate [m / sec]
ET = KE * uz * (esurf - eair) = evaporation rate [m / sec]
Qh = KH * uz * (Tair - Tsurf) = sensible heat flux [W / m2] (notice sign here)
KH = (Catm / uz) * ρair * cair = sensible heat coefficient
eair = esat(Tair) * RH = vapor pressure of air [mbar] (definition of RH)
esurf = esat(Tsurf) = vapor pressure at surface [mbar]

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 the soil moisture profile accordingly.

100 kPa = 1 bar = 1000 mbar, so 1 kPa = 10 mbars.

The equation for saturation vapor pressure as a function of temperature in degrees Celsius, esat(T), is originally due to Brutsaert (1975).

The log term that appears in the equation for Catm and involves the von Karman constant, κ, comes from boundary layer theory (for turbulent flows) and the so-called logarithmic law of the wall. See Schlicting (1960) for details.

References

Beven, K.J. (2000) Rainfall-Runoff Modeling: The Primer, Wiley, New York. (see pp. 73-77)

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.