Thermodynamics and the Flow of Heat through the Climate System - Climate Dynamics - page 93

At the surface of the earth, other forms of heat and other processes of heat
transfer in addition to radiation must be considered. The exchange of heat
between the atmosphere and the surface is expressed in terms of three forms
of energy. One is radiative, including both longwave and shortwave radiative
fluxes. The other two are sensible and latent heat fluxes, denoted here by H S
and H L , respectively, and often referred to as the turbulent heat fluxes. . For
the thermal equilibrium case, and in the absence of vertical or horizontal heat
fluxes within the surface, the surface heat balance is

− −−= (5.9)

(1 − α ) S F HH 0.

SINC NET S L

Each term in Eq. 5.9 is discussed in further detail.

(1) S INC , the rate at which shortwave (solar) radiation is incident on the
surface, was defined in Eq. 4.8, and a S is the albedo of the surface material.
Therefore, (1 α− is the rate at which shortwave radiation is absorbed

by the surface, analogous to Eq. 4.9, which considered the rate at which
the incident solar radiation is absorbed by the entire earth system. Surface
albedos vary widely, from values of about 0.1 over water to values greater
than 0.8 for fresh snow. Table 5.1 lists typical albedo values for some
common surfaces.
(2) The net longwave radiative heating of the surface, F NET , is the difference
between the upward emission from the surface and the downward back
radiation from the atmosphere:

) SINC

F εσ=− T

4

F . (5.10)

NET S BACK

Here, the emissivity of the surface material has been accounted for (see Eq.
4.2). Longwave emissivities for common surface substances tend to be close
to 1 ( Table 5.1 ), but the values depend on wavelength as well as on other
factors such as the moisture content of the surface.
(3) The surface sensible heat flux, H S , is the rate at which heat is transferred
between the atmosphere and the surface by conduction . Heat conduction
is defined as the transfer of heat down a temperature gradient through the
interactions and random motions of adjacent molecules. However, in the
field of climate dynamics, sensible heating also includes the transport of
heat by incoherent motion. The term is also used to encompass the effects
of turbulence on heat transport, which refers to small-scale irregular
motion as well as to small-scale organized circulations such as thermals.

The sensible heat content of a unit mass of air at temperature T is c p T ,
where c p is the specific heat at constant pressure, or the amount of heat it takes
to raise the temperature of 1 kg of air by 1 K [

p  without
allowing the parcel to do work. Thus, c p T represents the amount of energy
(number of joules) that was “invested” to bring each kilogram of a parcel to its
observed temperature. The sensible heat content of a unit volume of air is r c p T .
A heat flux is the amount of heat crossing a unit surface area per unit time,
expressed in units of J/(m 2  s) or, equivalently, W/m 2 . In formulating a math-
ematical expression for H S , imagine that a unit volume of air moves from the
surface to a height of 1 m in 1 second, so the vertical velocity is w  1 m/s. In
this case, an amount of sensible heat given by r c p T is removed from the surface

c 004 ( J/ Kkg )]