Geoscience Reference
In-Depth Information
changes of water. The latent heat flux is positive, that is, heat is transferred
from the surface to the atmosphere, when water evaporates from the
surface. A negative latent heat flux indicates that heat is transferred from
the atmosphere to the surface by the condensation of water onto the
surface, for example, when dew forms.
Consider a 1-kg parcel of air that contains water vapor. (The 1-kg mass of
the parcel consists of dry air plus water vapor.) The amount of energy that
was used to evaporate the water contained in the 1-kg parcel is
Lq
, where
L
is the latent heat of vaporization (the amount of energy needed to evaporate
1 kg of water) and
q
is the specific humidity (section 2.3). The value of
L
(see Appendix A) is temperature dependent. For water at 0°C,
L
2.5 10
6
J/kg-H
2
O. Multiply by the density of the moist air parcel to find the energy
required to evaporate the water contained in a parcel of unit volume. Note
the units:
mass of parcel
J
kg HO
-
J
.
2
r
Lq
+
f
p
+
f
p
f
p
3
kg HO
-
mass of parcel
3
m
m
2
Therefore, the expression for the latent heat flux analogous to Eq. 5.11 is
(5.12)
HwLq
L
=
ρ
.
To develop a more physical understanding about how turbulent fluxes work
at the atmosphere/surface interface, divide each dependent variable in Eqs.
5.11 and 5.12 into time-mean and time-varying components, denoted by over-
bars and primes, respectively:
l
l
wz t wzw zt
Tz t TzT zt
q
(, ,,)
λφ
=
( ,,)
λφ
+
( ,,,);
λφ
(, ,,)
λφ
=
( ,,)
λφ
+
( ,,,);
λφ
(5.13)
(, ,,)
λφ
z t qzq zt
=
( ,,)
λφ
+
l
( ,,,).
λφ
The time-varying component is called the (
temporal
)
perturbation
, and the
time average of the perturbation quantities is zero. This is shown mathemati-
cal
ly
by takin
g t
he time
m
ean of Eqs. 5.13. For example, since the time mean
of
w
, denoted
w
, is just
w
,
wz t wzw zt wz wz t
wz t
(, ,,)
λφ
=
( ,,)
λφ
+
l
( ,,,)
λφ
=
(, ,)
λφ
+
l
(, ,,)
λφ
(5.14)
l
(, ,,)
λφ
=
.
&
Equivalently, in integral form for a time-averaging period
P
,
P
P
P
1
1
1
#
#
#
l
wz t
(, ,,)
λφ
/
P
wz tdt
(, ,,)
λφ
=
P
wz dt
(, ,)
λφ
+
P
wz tdt
(, ,,)
λφ
0
0
0
P
1
#
=
wz
(, ,)
λφ
+
P
wz tdt
l
(, ,,)
λφ
(5.15)
0
P
1
#
P
wz tdt w zt
l
(, ,,)
λφ
=
l
( ,,,)
λφ
=
0.
&
0
