Geoscience Reference
In-Depth Information
2.6.2
The energy flux at the lower boundary of the layer
The nature of
G
and the optimal method of its determination depend on the type of
substrate layer to which the energy budget equation is applied. For a thin layer of soil,
for a vegetational canopy or for a whole lake or stream, the term
G
in Equation (2.72)
represents the heat flux into the ground. For a water surface,
G
is the heat flux into
the underlying water body. Over land covered with vegetation the daily mean value
of
G
, that is the ground heat flux, is often one or more orders of magnitude smaller
than the major terms in the energy budget,
R
n
,
H
and
L
e
E
. The main reason for this is
that positive daytime values of
G
(warming) often tend to be compensated by negative
nighttime values (cooling). Therefore, in design calculations, the daily values of
G
are
often neglected.
Measurement of the soil heat flux
Several methods are available to determine
G
for a landsurface (see Brutsaert, 1982), but
a detailed review is beyond the scope of this topic. One of the more reliable methods to
measure
G
considers changes in heat storage in the upper layer of the soil, as described by
the equation
z
2
C
s
(
z
)
∂
T
∂
t
Q
H1
−
Q
H2
=
dz
(2.83)
z
1
where
Q
H1
and
Q
H2
are the heat flux densities at levels
z
1
and
z
2
, respectively,
C
s
is the
volumetric heat capacity of the soil and
T
is the temperature in the soil. On the basis of a
compilation of thermal properties of soil components by De Vries (1963), this heat capacity
(inJm
−
3
K
−
1
) can be calculated as follows
10
6
C
s
=
(1
.
94
θ
m
+
2
.
50
θ
c
+
4
.
19
θ
)
×
(2.84)
where
θ
m
,θ
c
and
θ
are the volume fractions of mineral soil, organic matter and water,
respectively. Thus if
z
1
refers to the soil surface and
z
2
to some lower level where
Q
H2
is
known, the surface heat flux
G
=
Q
H1
, during a certain time interval, may be calculated by
numerical integration of (2.83) for measured soil temperature and moisture content profiles
at the beginning and at the end of the interval. If the depth
z
2
is large enough,
Q
H2
can be
assumed to be negligible; if it is not sufficiently large to allow this assumption, the heat
flux
Q
H2
must be determined. In the so-called combination method, suggested by C. B.
Tanner of Wisconsin,
Q
H2
is measured by means of a heat flux plate placed at a depth of
5-10 cm below the surface. The integral in Equation (2.83) is then determined from suc-
cessive temperature profile measurements above the level of the heat flux plate (see also
Hanks and Tanner, 1972).
Empirically based methods to estimate the soil heat flux
When necessary measurements are not available, the surface soil heat flux may be estimated
on the basis of empirical relationships. The simplest assumption is that it is proportional to
some other term in the energy budget equation. An obvious choice is the sensible heat flux
into the air; thus
G
=
c
H
H
(2.85)
