Geoscience Reference
In-Depth Information
as those that move latent heat vertically, and that these are equally effective in each
case. Recognizing the need to express temperatures in terms of virtual potential
temperature when describing flow in a hydrostatic atmosphere (see Chapter 3), the
rate of vertical sensible heat flow between two levels is assumed to be proportional
to the difference in atmospheric heat content at these two levels, i.e., proportional
to the difference in (
r
a
c
p
q
v
). Similarly, the rate of water vapor flow between the
same two levels is assumed to be proportional to the difference in humidity content
between the two levels, i.e., proportional to the difference (
r
a
q
), and latent heat
flow is then proportional to this difference multiplied by
. Consider two levels
where the potential temperatures are
q
v
1
and
q
v
2
, respectively, and the specific
humidities are
q
1
and
q
2
, respectively. If the processes for the transfer of heat and
water vapor are the same between these levels, then
λ
β
is given by:
⎡
2
1
⎤
(
rq rq
c
)
−
(
c
)
⎣
⎦
apv
apv
b
=
(7.3)
⎡
2
1
⎤
(
rl
q
)
−
(
rl
q
)
⎣
⎦
a
a
Substituting for
q
using Equation (2.9), this equation can be rewritten as:
Δ
==
Δ
q
H
E
b
g
v
(7.4)
l
e
where
e are the differences in virtual potential temperature and vapor
pressure between levels 1 and 2, respectively, and
Δθ
v
and
Δ
is the psychrometric constant
defined by Equation (2.25). Because the sum and the ratio of the sensible heat and
latent heat fluxes are known, individual values of these two fluxes can be calcu-
lated by combining Equations (7.2) and (7.4) to give:
γ
A
l
=
(7.5)
(
)
1
+
b
and:
HAl
=−
(7.6)
Measuring the difference in air temperature and humidity between two heights
required to calculate the Bowen ratio from Equation (7.4) can be difficult if these
differences are comparable in size with systematic errors in the instruments used.
But field systems have been designed to minimize the effect of sensor errors; one
approach (Fig. 7.7) is to regularly interchange pairs of temperature and humidity
sensors between the two levels. In practice, measuring the difference in humidity
is usually more difficult than measuring the difference in temperature and an
effective way to minimize the effect of humidity measurement errors is to duct air
alternately from the two levels to a common humidity sensor (Fig. 7.8). The effect
of any instrumental offset error then cancels out in the measured difference.
