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Weather & Climate
EXERCISES for
NINTH EDITION
Solutions for
Greg Carbone University of South Carolina – Columbia
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1 Vertical Structure of the Atmosphere 1 2 Earth–Sun Geometry 5 3 The Surface Energy Budget 9 4 The Global Energy Budget 12 5 Atmospheric Moisture 14 6 Saturation and Atmospheric Stability 18 7 Cloud Droplets and Raindrops 21 8 Atmospheric Motion 23 9 Weather Map Analysis 30 10 Mid-Latitude Cyclones 35 11 Weather Forecasting 40 12 Thunderstorms and Tornadoes 45 13 Hurricanes 48 14 Climate Controls 52 15 Climate Classification 55 16 Climatic Variability and Change 57 17 Simulating Climate Change 60 Appendix A Dimensions and Units 62 Appendix B Earth Measures 64
Contents
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1 Vertical Structure of the Atmosphere
1. Height (km) % of atmosphere above 22.4 6.25 16.8 12.5 11.2 25 5.6 50
2. & 3.
4. 25% 250 mb 58.4% 584 mb
5. 210 mb
6. 123 mb 58.4% 69 mb 33%
3
2
02468
10121416182022242628303234
0 10 20 30 40 50 60 70 80 90 100
Hei
ght A
bove
the
Sur
face
(km
)
Percentage of the Atmosphere Above
Pressure (mb)0 100 200 300 400 500 600 700 800 900 1000
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Solutions for Exercises for Weather & Climate
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7. Ozone absorbs solar radiation (particularly in the ultraviolet portion of the electromagnetic spectrum). This absorption leads to warming in the stratosphere.
8. 2000 4000 6000 8000 10,000 2.0°C –11°C –24°C –37°C –50°C
9. & 11.
10. a. Key West b. Key West c. Fairbanks
11. See 9 above.
12. Key West tropopause: ~16,000 m, ~ –75°C; Fairbanks tropopause: ~10,000 m, ~ –53°C;
13. The greater the average temperature, the higher the tropopause. Our example suggests that vertical mixing is greater when temperature is warmer.
14. 170 mb
15. 92 mb
16. Because of greater air density in the lower layer, the pressure drop between 2 and 4 km is nearly double that between 8 and 10 km.
17. 182 mb
18. Air pressure decreases with height because there is less atmosphere to exert downward force. The pressure drop will be greatest when air density is highest because the mass of the atmosphere above decreases at a faster rate.
19. California desert: 1003.9 mb; Michigan UP: 1018.6 mb; New Brunswick: 1003.7 mb.
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
-80 -60 -40 -20 0 20 40
Key West
Fairbanks
standard atmosphere
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Lab 1 Solutions
20. The Michigan and New Orleans stations have the same pressure (1018.6 mb), but a 30°F temperature difference. The New Brunswick and southern California stations have similar low pressures (1003.7 mb and 1003.9 mb), but a 30°F temperature difference.
21. The ideal gas law shows that pressure is proportional to the product of density times temperature. Therefore, to have a similar pressure, but be 30°F warmer, New Orleans must have a lower density.
22. The Michigan and New Brunswick stations have higher air density than the other two.
23. The 1.4 g/kg mixing ratio in Fairbanks is considerably smaller than that at the surface of Key West (16 g/kg) on the same day. In fact the surface moisture value at Fairbanks is as low as the mixing ratio value 10 km above Key West.
24. The atomic weight of hydrogen equals 1; the atomic weight of oxygen equals 16. Therefore, the atomic weight of H2O is 1 g/mol + 1 g/mol +16 g/mol = 18 g/mol.
25. The solution to the previous question shows that water vapor, at 18 g/mol, is lighter than dry air (28.6 g/mol).
26.
27.
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1960 1970 1980 1990 2000 2010280
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diox
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conc
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ppm
)
J F M A M J J A S O N D
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Solutions for Exercises for Weather & Climate
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28. Minimum atmospheric CO2 concentrations occur during the northern hemisphere’s late fall at which time CO2 has been taken up by vegetation for the previous 6–8 months. Atmospheric CO2 concentrations occur in April/May after many months of leaf decay and just before spring green-up in the Northern Hemisphere.
Review Questions1. Air pressure and density decrease exponentially with height above Earth’s surface. This is because gas molecules are
concentrated near the surface and a given height increase at these lower levels means passing through more molecules than the same height increase at higher elevations. Temperature also decreases with height in the troposphere. This rate of decrease varies, but is typically linear compared to pressure or density.
2. The thickness of the troposphere is a function of temperature. Warmer temperatures in tropical regions create mixing to greater depths, pushing the tropopause higher.
3. Pressure changes much faster vertically than it does horizontally. It drops 100 mb in the lowest kilometer of the atmosphere.
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2 Earth–Sun Geometry
1. March 21
March 21 profile view
June 21
June 21 profile view
23.5° S0°30° N66.5° NSN
47° 66.5°83.5° 43°
23.5° S 0° 30° N 66.5° NS N
66.5° 90° 60° 23.5°
30°
23.5°
66.5°
0
90°
Sun’s rays
Sun’s rays
23.5°
S
30°
23.5°
66.5°
0°
90°D
Solutions for Exercises for Weather & Climate
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2. 63.5°; December 21
3. 26.5°
4. a. 0° (equator) b. 23.5° N c. 0° (equator) d. 23.5° S e. [variable]
5. New Orleans Helsinki a. 60° 30° b. 83.5° 53.5° c. 60° 30° d. 36.5° 6.5° e. [variable] [variable]
6. [variable]
7. Answer is date dependent. Example for 34° N latitude on February 1, a two-meter pole casts a shadow measuring 2.52 meters.
tan Θ =
Θ = tan−1 (0.7937) Θ = 38.44°
8. [variable]
9. 60° N December 22
30° N June 21 60° N June 21
length of polelength of shadow
1 unit
Sun’s rays
8.83 units
Zenith angle83.5°
Sun angle 6.5°
1 unit
Sun’s rays
Sun angle 83.5°
Zenith angle6.5°
1.01 units
1 unit
Sun’s rays
Zenith angle 36.5°
1.24 units
Sun angle 53.5°
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Lab 2 olutions
10. Summer temperature is highest because solar radiation is more concentrated. During the winter, it’s cooler as the solar beam is spread over a greater surface area.
11. There is a much greater seasonal range in daylight hours in polar regions than in tropical regions.
12. 30° N 60° N June solstice 14 18 Equinoxes 12 12 December solstice 10 6
13. 60° N
14. The steepness of the curves suggests that daylight hours increase and decrease faster from one day to the next near the equinoxes, and change slower from one day to the next near the solstices.
15.
16. On the December solstice, the sun rises a bit south of east and sets a bit south of west. On the June solstice, the sun rises in the northeast and sets in the northwest. At 60° N, this shift is even more dramatic.
4:59 AM
7:04 PM
6:03 AM
6:12 PM
6:52 AM
5:05 PM
Latitude: 30° N
June
March
December
W
E
SN
5:58 AM
6:06 PM
6:04 AM
6:10 PM
5:54 AM
6:02 PM
DecemberMarch
June
Latitude: 0°
W
E
SN
5:11 AM6:41 AM
5:22 PM
6:04 AM
6:10 PM 6:46 PM
December
March
June
Latitude: 23.5° S
W
E
SN9:02 AM2:36 AM
9:28 PM
5:58 AM
6:17 PM
2:54 PM
December
March
June
Latitude: 60 N
W
E
SN
Solutions for Exercises for Weather & Climate
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17.
18. The seasonal difference in solar intensity (beam spreading) and daylight hours is greater at 60° N than at 30° N.
19. The difference in beam spreading between 60° N and 30° N is very large in winter and not very different in summer. Furthermore, 60° N has a shorter daylight period than 30° N in winter, while in summer the daylight hours are actually greater at 60° N.
20. Most direct rays: 1 unit beam = 1.000 surface units; Date: March 21, September 22 Least direct rays: 1 unit beam = 1.090 surface units; Date: June 21, December 21
21. 9%
22. [variable]
23. [variable]
24. The higher the latitude, the greater the seasonal range in solar intensity. This results in a larger annual temperature range at high latitudes than in the tropics.
25. December Solstice June Solstice 60° N 8.834 1.244 50° N 3.521 1.117 40° N 2.241 1.043 30° N 1.681 1.006 20° N 1.379 1.002
26. The solar intensity gradient across the mid-latitudes is much greater in winter and contributes to a greater temperature gradient.
Review Questions1. A given change at low sun angles is much more effective than the same change at higher sun angles. Therefore, the
seasonal shift of sun angle from 36.5° to 83.5° at New Orleans results in less change in solar intensity than the shift from 6.5° to 53.5° at Helsinki.
2. A greater range in solar intensity and daylight hours will result in a greater range in solar radiation received and temperature.
0
5
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45
Tota
l dai
ly s
olar
inso
latio
n (M
joul
es p
er s
quar
e m
eter
)
J F AM M SA O N DJ J
0°
30°
60°
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