1. Lecture 10 Evapotranspiration (3)
Evapotranspiration Estimation
General Comments
Thornthwaite model
Penman model
Penman-Montieth model

2. General Comments
ET is the basic hydrological components needed for many purposes
ET is affected by many factors, and formulae with various complexities are needed for different applications
ET can be measured with large efforts, but can also be modeled accurately in most cases

3. Thornthwaite Model
Developed by Warren Thornthwaite in 1948 to estimate PET
Generally applicable to arid areas like Central and eastern USA
1. Begin by computing the monthly heat index:
i = Monthly heat index
t = Mean temperature of the month
2. Sum the 12 monthly heat index into an annual heat index (I):
COMPACT NOTATION
I = Annual heat index
m = Month (1 = January … 12 = December)
tm = Mean temperature for month m

4. Thornthwaite Model 3. Compute monthly potential ET:
i = Monthly heat index
I = Annual heat index
Ep = Monthly potential ET (cm)
b = (Total monthly daylight hours)/360
a = Cubic function of I:
10-2I 10-5I 10-7I3

5. Characteristics of theThornthwaite Model
Purely empirical
Used where data are limited. Relatively little data required
Criticism for using air temperature justified because of the fixed relationship between the portion of Rn used for heating and that portion used for evaporation under PET conditions (full water availability)
An indirect reference to the radiation balance
Model adopted for use in North America (temperate and continental climate) – Temperature and radiation are highly correlated
Downfall: over the course of a year, air temperature tends to lag behind radiation

6. Penman Model
Developed by Howard Penman in 1948 (later modified by John Monteith et al. to yield the Penman–Monteith model)
Much greater demands on data than the Thornthwaite model
Well established and a basis for further theoretical development in the field of evaporation research
Basically a combination of turbulent transfer and energy-balance approaches (3 equations)

7. Penman Model 1. Equation 1 for the drying power of the air
Ea = Potential evaporation
ea = Saturation vapor pressure
ed = Saturation vapor pressure at dew point
u = Wind speed 2 m height)

8. Penman Model
2. Equation 2 for the available energy for latent heat and heating the surface:
H = Available net radiation (Rn)
r = Albedo of evaporating surface
Ra= Theoretical radiation intensity (no atmosphere)
n/N = Ratio of actual to possible sunshine hours
 = Stefan Boltzman constant 5.6710-8 W m-2 K-4 or 1.3810-12 cal cm-2 s-1 K-4
Ta = Mean air temperature (K)
ed = Saturation vapor pressure at dew point

9. Penman Model
3. Equation 3 for computing the actual ET (Penman Equation):
 = Rate of change of es with temperature
 = Psychrometric constant 0.66 mb/C
E = Actual ET

10. Characteristics of Penman Model
Originally designed for evaporative computations from free water surfaces (Eo)
Can be related to extensive, short, green vegetated surfaces by multiplying by a constant:
ET = f  Eo
where, f averages 0.75, but is influenced by seasons etc.
Various modifications and substitutions of this “base” model are possible
Heat conduction in soil is ignored

11. Penman-Monteith Model
The Penman model does not consider surface resistances or atmospheric resistances
John Monteith et al. modified the Penman equation to perhaps its most popular format to incorporate these resistances
The model considers the vegetation canopy as one isothermal leaf (not a set of individual leaves)

12. Penman Monteith Equation
 = Density of the air
c = Specific heat of the air
ea = Saturation vapor pressure at mean air temperature
ed = Saturation vapor pressure at dew point
rs = Total surface resistance
ra = Aerodynamic resistance
l                   = Latent heat of vaporization
 = Psychrometric constant
 = Rate of change of es with temperature

13. Characteristics of Penman-Monteith Model
Due to data requirements, the model is used more widely in conceptual ways rather than in physically determining potential evapotranspiration
“Big leaf” model is geared towards homogeneous canopies
Considers a bulk canopy conductance equal to the parallel sum of the individual leaf stomatal conductances
Various authors have compared these techniques, indicating the superiority of the Penman-Monteith model – as a comparison, the Thornthwaite model tends to underestimate potential evapotranspiration