Lecture 10
Evapotranspiration (3)
Evapotranspiration Estimation
• General Comments
• Thornthwaite model
• Penman model
• Penman-Montieth model
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
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:
1.514
t
i 
 5
i
t
= Monthly heat index
= Mean temperature of the month
2. Sum the 12 monthly heat index into an annual heat index (I):
COMPACT NOTATION
1.514
 tm 
I   
m1  5 
12
I = Annual heat index
m = Month (1 = January … 12 = December)
tm = Mean temperature for month m
Thornthwaite Model
3. Compute monthly potential ET:
 10t 
E p  1.6b

 I 
i
I
Ep
b
a
a
= Monthly heat index
= Annual heat index
= Monthly potential ET (cm)
= (Total monthly daylight hours)/360
= Cubic function of I:
0.49 + 1.7910-2I + 7.71110-5I2 + 6.75110-7I3
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
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 energybalance approaches (3 equations)
Penman Model
1. Equation 1 for the drying power of the air
u 

Ea  0.35ea  ed   1 

 100
Ea
ea
ed
u
= Potential evaporation
= Saturation vapor pressure
= Saturation vapor pressure at dew point
= Wind speed (miles/day @ 2 m height)
Penman Model
2. Equation 2 for the available energy for latent heat
and heating the surface:
H  A B

 n 
A  1  r Ra 0.18  0.55 
 N 


 n 
4
B  Ta 0.56  0.90 ed  0.10  0.90 
 N 



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
Penman Model
3. Equation 3 for computing the actual ET (Penman Equation):
  

  H  E a 
 


E
   
   1
   
 = Rate of change of es with temperature
 = Psychrometric constant 0.66 mb/C
E = Actual ET
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
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)
Penman Monteith Equation
H 
E

c
ea
ed
rs
ra



=
=
=
=
=
=

=
=
cp ea  ed 
ra

  rs  
    1    

  ra  
Density of the air
Specific heat of the air
Saturation vapor pressure at mean air temperature
Saturation vapor pressure at dew point
Total surface resistance
Aerodynamic resistance
=
Latent heat of vaporization
Psychrometric constant
Rate of change of es with temperature
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