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

514.1

5

ti

1. Begin by computing the monthly heat index:

2. Sum the 12 monthly heat index into an annual heat index (I):514.112

1 5

m

mtI COMPACT NOTATION

i = Monthly heat index t = Mean temperature of the month

I = Annual heat indexm = Month (1 = January … 12 = December)tm = Mean temperature for month m

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:

0.49 + 1.7910-2I + 7.71110-5I2 + 6.75110-7I3

 

a

p I

tbE

10

6.1

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 energy-balance approaches (3 equations)

Penman Model

100135.0

ueeE daa

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 (miles/day @ 2 m height)

Penman Model2. Equation 2 for the available energy for latent heat and heating the surface:

H = Available net radiation (Rn)

r = Albedo of evaporating surfaceRa= Theoretical radiation intensity (no atmosphere)

n/N = Ratio of actual to possible sunshine hours = Stefan Boltzman constant 5.6710-8 W m-2 K-4 or 1.3810-12 cal cm-2 s-1 K-4

Ta = Mean air temperature (K)

ed = Saturation vapor pressure at dew point

BAH

N

nRrA a 55.018.01

N

neTB da 90.010.090.056.04

Penman Model

3. Equation 3 for computing the actual ET (Penman Equation):

= Rate of change of es with temperature

= Psychrometric constant 0.66 mb/CE = Actual ET

1

aEH

E

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

a

s

a

dap

rr

reec

H

E

1

= Density of the airc = Specific heat of the airea = Saturation vapor pressure at mean air temperature

ed = Saturation vapor pressure at dew point

rs = Total surface resistance

ra = 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