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Figure 9.8 Left: Observed versus predicted ground-level SF 6 concentrations for
CRSTER, a Gaussian-plume model, at the Kincaid power plant. Observations
are one-hour averages; predictions are ensemble means. Right: Same but for an
improved model. From We i l ( 1988 ).
A parallel analysis shows that time changes in ABL depth h can be unimportant
for the turbulence if ∂h/∂t
u . The dynamics of the entrainment of a capping
inversion typically does limit ∂h/∂t to a small fraction of u ( Chapter 11 ). Such
conditions are typically satisfied in the daytime ABL away from the early-morning
and late-afternoon transitions.
Inhomogeneity can be treated in the same way. If L x is the spatial scale of
variability in surface conditions, we expect that when L x
h the ABL
turbulence does not “feel” the inhomogeneity and so can be locally homogeneous .
Requiring L x
h can be more demanding than the quasi-steady criterion, but it
can be satisfied in some applications.
Turbulence in the stable ABL tends to have smaller spatial scales and be less
diffusive than that in the convective ABL, so we expect that the stable ABL can
be much more sensitive to terrain-related inhomogeneities such as the downslope
gravity forces on even slightly uneven terrain ( Chapter 12 ). Figure 9.9 illustrates
these differences through potential temperature contours in an earlymorning, stably
stratified ABL and in the CBL existing two hours later.
9.6 The mean-momentum equations
Under horizontal homogeneity, mean properties (except mean pressure) do not
depend on horizontal position. If so, the mean continuity equation (8.66) reduces to
∂W/∂z =
0. Since W vanishes at the surface, this says it must vanish everywhere
 
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