Geoscience Reference
In-Depth Information
Problems
9.1
Calculate the temperature gradient at the surface at midday in the Kansas
experiment, given that the surface temperature flux (
Figure 9.5
)
is due to
molecular diffusion. Explain physically why this gradient is so large. (Recall
our discussion of the wall fluxes in pipe flow,
Chapter 1
.)
9.2
The convective ABL is sometimes modeled as a mixture of updrafts and
downdrafts of area fractions and vertical velocities
f
u
,w
u
and
f
d
,w
d
respectively. Interpret physically the statements
f
u
f
d
1
,w
u
f
u
w
d
f
d
+
=
+
=
0
.
Two additional equations are
(w
u
)
2
f
u
(w
d
)
2
f
d
w
2
,(w
u
)
3
f
u
(w
d
)
3
f
d
w
3
.
+
=
+
=
Interpret these as well. Solve the set and discuss the solution.
9.3
Use estimates of temperature fluctuations, mean temperature gradients, and
other quantities as needed to show why the ABL is seldom apt to be in a
neutral state (i.e., be unaffected by buoyancy).
9.4
Reconcile the notions of quasi-steadiness and local homogeneity (
Section
9.5
) and the sensitivity of the mean momentum balance to time changes and
horizontal inhomogeneity (
Section 9.6
).
9.5
Discuss how variation of the horizontal pressure gradient with
z
changes
the nature of the mean momentum balance in a quasi-steady, horizontally
homogeneous ABL. Which term would you expect to balance most of this
height variation under very convective conditions? Explain. Sketch the ver-
tical profiles of the three terms in the momentum balance in this limiting
case. Contrast the situation with the case where the pressure gradient is
independent of height.
9.6
Sketch the profile of vertical temperature flux in a quasi-steady convective
ABL capped by an inversion.
9.7
Confirm that the Ekman solution
(9.23)
satisfies the steady, hori-
zontally homogeneous mean-momentum equations with a constant-
K
closure.
9.8
A radiosonde is a standard instrument for measuring vertical profiles in the
lower atmosphere. Sensorsmounted belowa lighter-than-air balloonmeasure
temperature and water vapor along its rising path and transmit signals back
to earth. Discuss the utility of such data in numerical modeling.
9.9
Generalize the Ekman solution
(9.23)
to the case with geostrophic wind
varying linearly with height. Is the solution physical?
