Geoscience Reference
In-Depth Information
where the last equality sign is based on the assumption that the aerodynamic resis-
tances for water vapour and trace gas X are equal. Then, by measuring simultaneously
at the same height the concentrations of water vapour and the gas under consider-
ation, the mass Bowen ratio can be determined. In combination with a separate obser-
vation of
E
(either with the Bowen ratio method, or otherwise) this will give the trace
gas lux
F
X
.
Note that although Eq. (
7.4
) is an elegant deinition for a mass Bowen ratio that
seems dimensionless, strictly speaking it is not. The dimensions of
q
X
are kilograms of
gas X per kilogram air, and those of
q
are kilograms of water vapour per kilogram of
air. Hence the dimensions of
β
X
are kilograms of gas X per kilogram of water vapour.
This ratio is not dimensionless. Therefore, a Bowen ratio involving, for example,
F
X
and the sensible heat lux (and hence the vertical differences of
q
X
and temperature)
would be an equally valid approach (and useful if an independent observation of
H
is
available and an observation of
L
v
E
is not).
Question 7.2:
Given the following observations:
Quantity
Value at
5 m height
Value at
2 m height
Value at
surface
Unit
Net radiation
500
W m
-2
Surface soil heat lux
50
W m
-2
Air temperature
28.5
28.8
°C
Density of dry air (
ρ
d
)
1.155
1.154
kg m
-3
Water vapour density (
ρ
v
)
10.0·10
-3
10.5·10
-3
kg m
-3
CO
2
density (
ρ
c
)
600·10
-6
597·10
-6
kg m
-3
a) Compute the sensible and latent heat luxes using the Bowen ratio method. (Use
c
p
= 1013 J kg
-1
K
-1
).
b) Compute the CO
2
lux density using the mass Bowen ratio.
7.2 Penman-Monteith Equation
For the Bowen ratio method, observations at two levels are needed, which are often
not routinely available. The Penman-Monteith equation is a way to use observations
at only one level, and treat the lowest level (the surface) only implicitly (i.e., no sur-
face temperature or humidity information is needed).
First the Penman equation (valid for wet surfaces) will be derived (
Section 7.2.1
).
Then the concept of the 'big-leaf' approach is presented, and used to derive the Pen-
man-Monteith equation, which describes the transpiration from dry vegetation (
Section
7.2.2
)
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