Geoscience Reference
In-Depth Information
Penman's (see below). There are also problems with
using Thornthwaite's model in areas of high poten-
tial evaporation. The empirical nature of the model
means that it has been calibrated for a certain set
of conditions and that it may not be applicable out-
side these. The Thornthwaite model has been shown
to underestimate potential evaporation in arid and
semi-arid regions (e.g. Acheampong, 1986). If the
model is being applied in conditions different
to Thornthwaite's original calibration (humid tem-
perate regions) it is advisable to find out if any
researcher has published different calibration curves
for the climate in question.
pressure (which can be derived from relative
humidity) and net radiation and gives the evap-
oration in units of mm per day. All of these can
be obtained from meteorological measurement (see
p. 49). It is normal to use daily averages for these
variables, although Shuttleworth (1988) has sug-
gested that it should not be used for time steps of
less than ten days. There are several different ways
of presenting this formula, which makes it difficult
to interpret between texts. The main difference is in
whether the evaporation is a flux or an absolute rate.
In the equation above terms like 'net radiation' have
been divided by the amount of energy required to
evaporate 1 mm of water (density of water (
ρ
)
multiplied by the latent heat of vaporisation (
)) to
turn them into water equivalents. This means the
equation derives an absolute value for evaporation
rather than a flux.
Penman continued his work to consider the evap-
oration occurring over a vegetated surface (Penman
and Scholfield, 1951), while others refined the work
(e.g. van Bavel, 1966). Part of this refinement was
to include a term for aerodynamic resistance (
r
a
) to
replace
E
a
(equation 3.9).
Aerodynamic resistance
is a term to account for the way in which the water
evaporating off a surface mixes with a potentially
drier atmosphere above it through turbulent mixing.
The rougher the canopy surface the greater degree
of turbulent mixing that will occur since air passing
over the surface is buffeted around by protruding
objects. As it is a resistance term, the higher the
value, the greater the resistance to mixing; therefore
a forest has a lower value of
r
a
than smoother pasture.
Some values of aerodynamic resistance for different
vegetation types are given in Table 3.3.
Substituting the new aerodynamic resistance
term into the Penman equation, and presenting the
results as a water flux (kg of water per m
2
of area),
the evaporation estimation equation can be written
as equation 3.10.
Penman
Penman was a British physicist who derived a
theoretical model of evaporation. Penman's first
theoretical model was for open water evaporation
and is shown in equations 3.8 and 3.9 (Penman,
1948):
∆
*
γ
γ
+
+
QE
(3.8)
a
E
=
o
∆
where an empirical relationship states that:
u
(3.9)
E
=
26
.
δ
1
+
a
e
1 862
.
and
Q
* = net radiation (in evaporation equivalent
units of mm/day)
= rate of increase of the saturation vapour
deficit with temperature (kPa/°C see
Figure 3.6)
e
= vapour pressure deficit of the air
(kPa)
≈
= psychrometric constant (
0.063 kPa/
°C)
u
= wind speed at 2 m elevation (m/s)
In his original formula Penman estimated net radia-
tion from empirical estimates of short- and long-
wave radiation. The formula given here requires
observations of temperature, wind speed, vapour
+
⋅ ⋅
( )
ρδ
(3.10)
c
r
ρ
e
Q
*
∆
a
=
PE
λγ
∆
