Geoscience Reference
In-Depth Information
where
Although this formula looks complicated it is
actually rather simple. It is possible to split the
equation into two separate parts that conform to the
understanding of evaporation already discussed. The
available energy term is predominantly assessed
through the net radiation (
Q
*) term. Other terms in
the equation relate to the ability of the atmosphere
to absorb the water vapour (
,
ρ
,
c
p
,
e
,
,
, this is
referred to as the sensible heat transfer function) and
the rate at which diffusion will absorb the water
vapour into the atmosphere (
,
u
,
z
o
, etc.).
Figure 3.6 shows the relationship between the
saturated vapour pressure and temperature. The
slope of this curve (
Q
* = net radiation (W/m
2
)
= rate of increase of the saturation vapour
pressure with temperature (kPa/°C) (see
Figure 3.6)
ρ
= density of air (kg/m
3
)
c
p
= specific heat of air at constant pressure
(
≈
1,005 J/kg)
e
= vapour pressure deficit of the air (kPa)
= latent heat of vaporisation of water (J/kg)
(see Figure 3.4)
= psychrometric constant (
≈
0.063 kPa/°C)
r
a
= aerodynamic resistance to transport of
water vapour (s/m) given by equation 3.11.
) is required in the Penman
equation and its derivatives. This can be estimated
from equation 3.12 using average air temperature
(
T
, °C):
2
−
zd
z
u
ln
(3.11)
0
r
=
17 27
237 3
2
.
T
a
2
κ
T
+
.
(3.12)
2053 058
237 3
.
exp
∆=
and
+
(
T
. )
= Von Karman constant (
≈
0.41)
When using the Penman equation there are only
four variables requiring measurement: net radiation,
wind speed above the canopy, atmospheric humidity
and temperature, which when combined will pro-
vide vapour pressure deficit (see Figures 3.6-3.8).
u
= wind speed above canopy (m/s)
z
= height of anemometer (m)
d
=
zero plane displacement
(the height
within a canopy at which wind speed drops
to zero, often estimated at two-thirds of the
canopy height) (m)
z
o
= roughness length (often estimated at one
eighth of vegetation height) (m)
8
7
6
Table 3.3
Estimated values of aerodynamic and
stomatal resistance for different vegetation types
5
4
3
Vegetation
Aerodynamic
Canopy
2
type
resistance
resistance
(r
a
) (s/m)
(r
c
) (s/m)
1
0
Pasture
30
50
-10
0
10
20
30
40
50
Forest
6.5
112
o
Temperature ( C)
Scrub
6.5
160
Tussock
7.0
120
Figure 3.6
The relationship between temperature and
saturation vapour pressure. This is needed to calculate
the rate of increase of saturation vapour pressure with
temperature (
). Equation 3.12 describes the form of
this relationship.
Source
: from Andrew and Dymond (2007).
NB although the values of canopy resistance are
presented as fixed they actually vary considerably
throughout a day and season
