Geoscience Reference
In-Depth Information
εσ
T
S
4
(1 -
α
S
)
S
INC
F
BACK
H
S
H
L
δA
ρ
S
,
α
S
, T
S
, c
F
H
Z
F
V
Figure 5.3 A volume,
V
, of surface material exchanging heat
with the atmosphere as well as with adjacent surface material.
Consider the volume d
V
Z
d
A
of surface material (land or water) drawn
in
Figure 5.3.
The surface of the volume exchanges heat with the atmosphere
across a unit surface area d
A
. This surface has an albedo a
S
. The density of the
surface material is r
S
, and it is assumed to be isothermal at temperature
T
S
. The
depth of the volume,
Z
, can be interpreted as the mixed-layer depth for a heat
balance calculation over the ocean or the depth to which heat penetrates the
soil over land.
If the components of the heat budget do not balance, the surface will heat or
cool at a rate
Tt
22
determined by
2
T
S
4
C
=− +−−−−−
(
1
α
)
S
F THHFF
εσ
(5.22)
2
t
S
INC
BACK
S
S
L HV
where
C
is the
heat capacity
of the surface material, defined as the amount of
heat required to raise the temperature of the volume by 1 K.
F
H
and
F
V
are
the net horizontal and downward heat fluxes out of the volume, respectively.
For example, if the volume is in the ocean
F
H
captures the effects of horizontal
ocean currents transporting energy out of (or into) a volume of water. The term
F
V
can account for the effects of downward diffusion of heat within soil or
water, and upwelling and downwelling in the ocean.
The value of the heat capacity,
C
, depends on two factors. One is the specific
heat capacity,
c
, usually called just the specific heat, of the surface material.
This is the amount of heat required to raise the temperature of 1 kg of the
surface material by 1 K. (See Appendix A for specific heats of some substances
relevant to the climate system.)
The other factor that determines
C
is the mass of material associated with a
unit surface area, that is, the mass heated by the net energy absorbed across the
surface area d
A
. Denoted by
M
A
, with units of kg/m
2
, this mass is
mass of the volume
ρ
V
S
M
=
=
=
ρ
Z
.
(5.23)
A
δ
A
S
surface area of the volume
