Thermodynamics of Atmospheres and Oceans
Practice Exam III
1. Compare the conductive heat flux, Fc, for a slab of snow with thickness 10 cm thick
and a temperature gradient of 5°C across this distance for snow of the following
characteristics:
a) new snow,  = 100 kg m-3
b) wind packed snow,  = 400 kg m-3
Which type of snow will have the largest conductive heat flux? Explain.
Recall, Fc= κs *(dT/dz ) and κs=aρ2 this indicates that the dense wind packed snow while
have a greater conductive heat flux.
2. A decrease in atmospheric water vapor will (increase, decrease, not change) the
downwelling surface longwave radiation flux.
3. A decrease in atmospheric water vapor will (increase, decrease, not change) the
downwelling surface shortwave radiation flux.
4. Clouds (increase, decrease, not change) the downwelling surface longwave
radiation flux relative to clear sky conditions.
5. Clouds (increase, decrease, not change) the downwelling surface
shortwave radiation flux relative to clear sky conditions.
6. A decrease in air temperature will (increase, decrease, not change) the
downwelling surface longwave radiation
7. A decrease in air temperature will (increase, decrease, not change) the
downwelling surface shortwave radiation.
8-9. During summer, alpine snowfields disappear (faster, slower) on a calm humid day
than on a dry windy day with the same air temperature and insolation. Explain.
Alpine snowfields disappear slower on a calm humid day than on a dry windy day
because sensible and latent heat fluxes are both proportional to wind speed. Additionally,
the latent heat flux is also a function of humidity so that on a calm humid day the transfer
of both sensible and latent heat fluxes will be less than it would be for windy and dry
conditions.
10-11. On a clear still night over land, the surface temperature usually (increases,
decreases) if a low cloud moves overhead. Explain.
Low clouds tend to insolate the surface by reducing OLR. The cloud will allow the
radiation leaving the surface to be absorbed at its base and re-radiated to the surface.
Thus increasing the surface longwave flux via thermal emission from the cloud.
12-13. Consider two adjacent land regions on a clear night. In the early part of the
evening, one of the regions received 10 cm snowfall, while the other region has no snow
(the land surfaces and atmospheric conditions are identical prior to the snowfall). The
region with the snow cover tends to (increase, decrease) the surface temperature relative
to the region that has no snow. Explain briefly.
For this problem you don’t need to consider the albedo effect of the snow because these
are nighttime conditions. Snow will insulate the underlying surface preventing this
warmer surface radiation from escaping into the atmosphere. As a consequence of
changes in the upward longwave flux, which is less for the snow covered conditions, the
surface air temperature will tend to decrease in comparison to the region without any
snow/insolation.
14-15. At high latitudes the latent and sensible heat flux from the oceans is much larger
during winter than during summer. Explain briefly.
In winter, the ocean temperature is warmer than the overlying atmosphere. Strong
temperature and moisture gradients between the ocean surface and overlying atmosphere
allow moisture and heat to be readily transferred from the ocean surface. During summer,
the gradients are weaker.
16-17. The lowest winter temperatures in the northern hemisphere are found over Siberia
rather than at the pole. Explain.
Energy Balance is a function of the incoming solar radiation, planetary albedo, OLR, etc.
Although both of these regions have snow cover, Siberia has less cloud cover which leads
to more OLR/surface cooling.
20-21. Summers are cooler in the polar regions than in middle latitudes despite the fact
that there is greater incoming solar radiation in the polar regions. Explain.
Although there is more incoming solar radiation in the polar regions, much of this energy
is reflected back to space because of the high surface albedo. On average more incoming
solar radiation is absorbed in middle latitudes for summer time conditions. This produces
warmer summers for mid-latitudes.
23-27. Write expressions for the change with surface temperature of
a) the upwelling longwave flux from the surface (assume black body radiation). Would
this contribute to positive or negative feedback?
b) the surface sensible heat flux (assume u, Ta remain unchanged), dFSH/dT.
this contribute to positive or negative feedback?
Would
Consider the following for 28-33.
Table 14.6: Values of equivalent black body planetary temperature, Te, as a function
of the planetary solar constant, S, and planetary albedo, p, and optical thickness of the atmosphere n.
Planet
Mercury
Venus
Earth
Mars
p (%)
5.8
71
33
17
S
(W m-2)
Te (K)
9200
2600
1370
600
442
244
254
217
T0
n
K
452
740
288
223
0.09
84
0.65
0.12
We derived the following expression for the Earth’s radiative energy balance
under conditions of radiative equilibrium
S 1 –  p r 2 =  T 4e 4  r
(12.1a)
28-29. If there were no clouds on Earth, the planetary albedo would be about 10%. Under these
conditions (and relative to the current Earth conditions), the black body planetary temperature
would (increase, decrease, remain the same). Briefly explain.
The net effect of clouds is to cool the planet. So by creating clear conditions worldwide, we
should be increasing the amount of shortwave radiation flux @ the surface and hence increasing
the blackbody planetary temperature.
30-31. During the early solar system history, the solar luminosity was believed to be 30% less.
Under these conditions, relative to the current conditions, the planetary temperatures would be
(briefly explain):
a) 30% higher
b) 30% lower
c) none of the above
If solar luminosity was less this would decrease the shortwave radiation flux @ the surface and
planetary temperatures would be lower. However, the temperature would not be lower by 30%.
For example, take data for Venus; so that we decrease S by 30%. As indicated below, the
temperature has not changed by 30%.
S 1   p  / 4  T 4
4
1820(1  .71)
 T  219.638K
4
32-33. Under the conditions described in 30-31, which planet would show the greatest surface
temperature change? Briefly explain.
a) Venus
b) Earth
c) Mars
d) all would show the same temperature change
Not considering n.
TVo = 244K TVc = 219.6K
TEo = 254K TEc = 230.7K
TMo = 217K TMc = 198.0K
However, even if you consider the effect of n, Venus would still have the greatest
temperature change.
41-45. As warming occurs, continental glaciers are often observed to gain mass owing to
increased snowfall. Accumulating glaciers are often used as evidence that warming is not
taking place. How do you reconcile the observations that the surface is warming, and the
glaciers are also accumulating mass? Explain.
As the surface warms, there will be a flux of moisture from the surface to the atmosphere
(via evaporation). Additionally, from the the Clausius-Clayperon relation we know that
warmer air can hold more moisture. As this warm moist air is transferred poleward to
balance the meridional temperature gradients, the moisture in this air will eventually
precipitate out as snow (once it reaches the poles) and result in the growth/accumulation
of glaciers.

d 
d
dz – dz
g
N2 = 0
adv
ent
rad
SH
LH
PR
F net
Q0 – F Q0 – F Q0 = F Q0 + F Q0 + F Q0 + F Q0
ent
 adv
F net
s0 – F s0 – F s0 = –  l P r –  s Ps + E – R s 0 +  i
dh i
s0 – si
dt
net
FB0 = g  c F net
Q0 –  F s0
0 p
T

F net
Q0 =   z
T
2 T
 i ci i =  i 2i + F z
t
z
S 1 –  p r 2 =  T 4e 4  r
dI j

F rad
TOA
f = Go

I
j
j dT 0

 F rad 1
f = Go
W v g
Wv =

0
p0
0
H L lv
ws T d  H +
  dT 0 T R T 2
v
v dz
dp L lv p
=
dT Rv T2
cp
dwl,ad =
   s dz
L lv d
 3Wl
* =
 ext
2l re
dp