Mid-term exam solutions

Mid-term exam solutions
Physics on Climate Phys 20054
Spring 2011
1. Provide a one sentence description or formula defining albedo, opacity, and lapse rate!
Albedo describes the fraction of incoming solar radiation spectrum reflected back into outer
space. Low albedo (water) reflects low reflection potential, high albedo (snow) reflects high
reflection potential
Opacity expresses the transparency of a material to electromagnetic radiation. Opacity depends
on the wavelength of the radiation. Material of high opacity has no transparency and vice versa.
Lapse rate is the change of temperature (or other atmospheric variables) with altitude.
2. You live presently in South Bend, Indiana (altitude of 702ft) with an average annual temperature
of 49.5 o F and an average atmospheric pressure of 1 atm. Bad fate forces you to move to
Boulder, Colorado at an altitude of 1750m. Determine the reduced atmospheric pressure
condition you are exposed to using the barometric formula and estimate the average annual
temperature from the lapse rate. Compare such derived averaged temperature with the
recorded value.
The pressure decreases exponentially according to the barometric formula
P P
0
e
z
H
P
P
Boulder
SB
e
1
H
z
z
234m
1750m
SB
Boulder
e
1
3
7.3110 m
0.812
P Boulder = 0.812 atm
The temperature decreases with the lapse rate =-9.7K/km
dT
dz
9.7K
/ km
3
z
z
282.9 9.7 10
1750
234 268. K
T
Boulder
TSB
Boulder SB
2
T Boulder = 23.1 F

3. Black bodies of a certain temperature emit electromagnetic radiation in a certain wavelength
range with maximum intensity at max . Consider Death Valley in Southeastern California with a
typical temperature of 120 o F and Nome, Alaska at winter time at a typical temperature of -
14.6 o C. Determine max for both regions assuming black body conditions. Judging by the pictures
what is the Albedo for each location.
Death Valley, California
Nome, Alaska
NommDeath Calley, california
max
2897
T
D
nm
Death Valley : T
Nome : T
259K
322K
max
max
8.966nm
40%
11.205nm
90%

4. Consider the emission temperature of the polar ocean for an incoming solar Flux of
F=1370W/m 2 . Choose the albedo and emissivity parameters for summer and winter
conditions as shown in the pictures and determine the amount of absorbed flux and
reflected energy flux.
Arctic Ocean, summertime
Arctic Ocean, wintertime
F
0
1370W
/ m
summer 7% 98%
F
ref
2
0.07 1370
96W
/ m
2
F
abs
(1 0.98) (1
0.07) F
0
27.2W
/ m
2
winter
80%
99%
F
ref
0.81370
1096W
/ m
2
F
abs
(1 0.99) (1
0.8) F
0
2.74W
/ m
2

5. The atmosphere as well as the ocean is categorized by the physical properties in the
different altitude or depth layers, respectively. Explain why the temperature in the
mixed layer of oceans is constant and why the temperature in the lower Stratosphere
(Tropopause) remains constant. What is the underlying physical process responsible for
this effect?
The temperature in the mixed layer of the ocean is determined by convection between
surface water and water in the deeper layers of the layer. This warrants rapid heat
exchange and equilibrates the temperature across the layer. The temperature in the
lower stratosphere layer (or Tropopause) is constant because the absorbed energy flux
from the thermal radiation of earth surface is balance by the emitted radiation flux .
6. Name three aerosols which affect the climate conditions or earth and explain the origin
and the impact of these aerosols in the atmosphere.
SO 2 volcanic or industrial origin, accumulates as aerosol in stratosphere reflecting solar
radiation and reduces such the heating of atmosphere
Carbon results from biomass burning and industrial production, CO 2 absorbs thermal
radiation from earth, causing greenhouse effect
Dust, water vapor reduces incoming solar flux and eventually affects the albedo and the
reflection of incoming solar energy flux

7. Consider a flux of 500 W/m 2 of visible light entering the upper layer of the Troposphere
at an altitude of 10 km. Assume an average density 500 g/m 3 . What is the flux of visible
light reaching the surface of the earth considering an absorption cross section of
sunny =10 -26 cm 2 for a sunny day and cloudy =10 -25 cm 2 for a cloudy day.
Smoky Mountains, sunny day
Smoky Mountains, hazy day
F
F e
0
(
,
x)
dx
F e
0
N
m
A
air
d
sunny :
F
W
500
m
2
e
6.02210
500
29
23
10
30
4
10
W
450
m
2
smoky:
F
W
500
m
2
e
6.02210
500
29
23
10
29
4
10
W
177
m
2
On a sunny day only 10% of the solar light is absorbed, on a foggy day more than 60% of
the incoming light is absorbed.