Geoscience Reference
In-Depth Information
9.2 The surface energy balance
Both the convective and stably stratified ABLs owe their distinctive structural prop-
erties to stability effects linked to the surface energy balance. That energy balance,
a first-law statement for a thin slab of the earth's surface ( Figure 9.4 ) , reads:
∂I
∂t =
C t +
R n +
C b ,
(9.5)
I
=
internal energy of the slab ,
C t =
net rate of energy input by conduction through air ,
R n =
net rate of energy input by radiation ,
C b =
net rate of energy input by conduction through soil .
For a dry surface I is proportional to the depth-averaged temperature of the
slab, so for a very thin slab Eq. (9.5) in effect determines the surface temperature.
With the near-surface air temperature and wind speed this determines the rate of
surface heat transfer, C t . As in turbulent pipe flow, Chapter 1 , this is carried by
conduction caused by the temperature gradient at the surface. The turbulent air
above minimizes the thickness of the surface sublayer and thereby minimizes the
temperature difference across it that is required to support C t (Problem 9.18) .
If the surface is warmer than the air above, C t is directed upward, making
the near-surface air unstably stratified. If the surface is cooler than the air it is
downward and the stratification is stable. Figure 9.5 shows the diurnal behavior of
the surface heat flux measured over a dry prairie in the 1968 Kansas experiments.
In general the contributions of water substance need to be included in Eq. (9.5)
and the vertical flux of virtual temperature ( Chapter 10 ) determines the stability
state of the overlying air. An evaporating surface has a positive (upward) flux of
water vapor mixing ratio; this can cause the flux of virtual temperature to be positive
even if the surface is cooler than the air.
Figure 9.4 A schematic of the surface energy balance, Eq. (9.5) .
 
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