Thermodynamics and the Flow of Heat through the Climate System - Climate Dynamics - page 98

Then,

== (5.24) CcMc Z

A ρ

.

The nonequilibrium surface heat balance can be used to understand the
physical basis of continentality. Suppose there is a net heating of the surface of
20 W/m 2 , so Eq. 5.22 is

2 T

S

2

C  20 W/m . (5.25)

2 t

If this net heating is incident on the ocean, in a region where the mixed-layer
depth is 100 m, then

Cc Z 4218 J/kgK 10 kg/m ρ== [ ( $ )](

3 3

)( 100 m ) = 4.2 # 10 J/ mK

8

(

2

$ ). (5.26)

WW

Rearranging (5.25), we can estimate the time required to increase the tempera-
ture of the ocean mixed layer by 2 K as

CT
20 W/m

T

S

t  . 1167 hr 8 days.  (5.27)

T

2

If the net heating is incident over land, say, onto a dry sand surface with a heat
penetration depth of 2 cm, then

CcZ 840 J/kgK 2.65 == [ ( $ )]( # 10 kg/m

3 3

)( 210m 4.510J/m K, #

− 2

) = #

4

(

2

$ )

SS

(5.28)

and D t  1.25 hr. Thus, the land surface responds to the net surface heating
on diurnal time scales, while the ocean responds on seasonal time scales, as
indicated in Table 3.1 .

5.4 OBSERVED HEAT FLUXES

GLOBAL HEAT BALANCE CLIMATOLOGY

Figure 5.4 summarizes the flow of heat into, out of, and within the climate
system in the global and annual average. The numbers (in W/m 2 ) are rough es-
timates based on satellite observations (see Additional Reading), and they may
not be exactly the same as other estimates. The figure provides only a broad
overview of the global heat balance.
The left side of Figure 5.4 o utlines the fate of solar energy as it passes through
the atmosphere. Solar radiation of 341 W/m 2 is incident at the top of the atmo-
sphere in this estimate with 102 W/m 2 reflected back to space from the earth
system, implying that the average planetary albedo is 0.3. Much of this reflec-
tion is from clouds (~62 W/m 2 ), but backscattering from molecules and reflec-
tion from the surface also contribute (~17 W/m 2 and ~23 W/m 2 , respectively).
The remaining solar radiation, about 239 W/m 2 , fuels the climate system.
Roughly 67%, or 161 W/m 2 , of this energy passes through the atmosphere and
is absorbed by the surface. Some of this solar radiation arrives at the surface in