Geoscience Reference
In-Depth Information
In words, Equation (2.72) states that the difference between incoming and outgoing
energy fluxes is equal to the rate of increase of the energy stored in the layer under
consideration; the sign convention is such that the energy fluxes toward the layer are
taken as positive and those away from it as negative. In (2.72) the quantity
R
n
is the net
radiative flux density at the upper surface of the layer,
L
e
is the latent heat of vaporization,
L
p
is the thermal conversion factor for fixation of carbon dioxide,
F
p
is the specific flux
of CO
2
,
G
is the specific energy flux leaving the layer at the lower boundary,
A
h
is the
energy advection into the layer expressed as specific flux, and
t
is the rate of energy
storage per unit horizontal area in the layer; in the case of an ice or snow layer this last
term may include the energy consumed by fusion, and
L
e
may have to be replaced by
L
s
, the heat of sublimation. At present in the SI system all these surface energy fluxes
are commonly expressed in units of W m
−
2
.
∂
W
/∂
Example 2.1. Some features of the surface energy budget
The order of magnitude and the diurnal variation of the main terms in the energy budget
for different surfaces are illustrated in Figures 2.19-2.22. Figure 2.19 shows the terms
in an irrigated environment under clear sky in the summer. Figure 2.20a illustrates the
response of the turbulent heat fluxes in response to varying cloudiness in the course of a
spring day, whereas Figure 2.20b shows a typical clear sky situation, which is generally
similar to Figure 2.19. In contrast to what happens over land, Figure 2.21 shows how
over deep water the turbulent heat fluxes
L
e
E
and
H
do not follow the diurnal cycle of
the solar radiative energy supply; as a result of the large heat capacity of the water body,
the surface temperature tends to remain more constant, and less affected by the radiative
energy input. Figure 2.22 illustrates the gradual evolution of the three main terms of the
energy budget in natural prairie during a period of prolonged drying in the fall season
during the First ISLSCP Field Experiment. As the soil moisture content is decreasing the
evaporation rate exhibits a steady decrease. On the other hand, the sensible heat flux is
not increasing in the same steady way, as one might expect if the available energy were
constant; it is more erratic and is more responsive to the vagaries of the weather while
the radiation is steadily declining as winter approaches.
2.6.1
Net radiation
This quantity can be broken down into several components, viz.
R
n
=
R
s
(1
−
α
s
)
+
ε
s
R
ld
−
R
lu
(2.73)
where
R
s
is the (global) short-wave radiation,
α
s
is the albedo of the surface,
R
ld
is the
downward long-wave or atmospheric radiation,
ε
s
is the emissivity of the surface and
R
lu
is the upward long-wave radiation. The downward long-wave radiation is multiplied
by the emissivity
ε
s
, because this is equal to the absorptivity, which is the fraction of the
incoming long-wave radiation absorbed by the surface. The net radiation can be measured
directly, and at present fairly reliable instruments are available for this purpose. In the
absence of direct measurements, or when great accuracy is required,
R
n
can be obtained
from measurements of its components on the right-hand side of Equation (2.73). When
