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Solution Manual for Exercises for Weather and Climate, 8th Edition

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    Solutions Manual to Exercises for Weather & Climate, 8th ed. 1 Vertical Structure of the Atmosphere 1 2 Earth–Sun Geometry 4 3 The Surface Energy Budget 8 4 The Global Energy Budget 10 5 Atmospheric Moisture 12 6 Saturation and Atmospheric Stability 16 7 Cloud Droplets and Raindrops 19 8 Atmospheric Motion 21 9 Weather Map Analysis 28 10 Mid-Latitude Cyclones 33 11 Weather Forecasting 37 12 Thunderstorms and Tornadoes 43 13 Hurricanes 46 14 Climate Controls 50 15 Climate Classification 53 16 Climatic Variability and Change 55 17 Simulating Climatic Change 58 Appendix A Dimensions and Units 60 Appendix B Earth Measures 62 Appendix C GeoClock 63 iii

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    iv

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    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 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 0 10 20 30 40 50 60 70 80 90 100 Height Above the Surface (km) Percentage of the Atmosphere Above Pressure (mb) 0 100 200 300 400 500 600 700 800 900 1000 Vertical Structure of the Atmosphere 1 1

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    2 7. Ozone absorbs solar radiation (particularly in the ultraviolet portion of the electromagnetic spec- trum). This absorption leads to warming in the stratosphere. 8. 2000 4000 6000 8000 10000 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. 20. The Michigan and New Orleans stations have the same pressure (1018.6 mb), but a 30°F tempera- ture 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. 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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    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. Review Questions 1. 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. The higher its relative density, the more likely air is to sink. Density is influenced by temperature and pressure. At the low pressure of the mid and upper troposphere, density is lower than it is at lower elevations. 4. Pressure changes much faster vertically than it does horizontally. It drops 100 mb in the lowest kilometer of the atmosphere. 3

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    4 1. June 21 June 21 profile view March 21 Sun’s Rays 23 1/2 ° N S 30° 23½° 66½° 0° 90° D A B C D 30˚ N 0˚ 66 1 ⁄ 2 ˚ N 23 1 ⁄ 2 ˚ S A B C D 47˚ 43˚ 83 1 ⁄ 2 ˚ 66 1 ⁄ 2 ˚ 30 ° 23½° 66½° 0 ° 90 ° A B C D Sun’s Rays Earth–Sun Geometry 2

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    March 21 profile view 2. 63 1 ⁄ 2 °; December 21 3. 26 1 ⁄ 2 ° 4. a. 0° (equator) b. 23 1 ⁄ 2 ° N c. 0° (equator) d. 23 1 ⁄ 2 ° S e. [variable] 5. New Orleans Helsinki a. 60° 30° b. 83 1 ⁄ 2 ° 53 1 ⁄ 2 ° c. 60° 30° d. 36 1 ⁄ 2 ° 6 1 ⁄ 2 ° 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. Θ = tan − 1 (0.7937) Θ = 38.44° 8. [variable] 30˚ N 0˚ 66 1 ⁄ 2 ˚ N 23 1 ⁄ 2 ˚ S A B C D 90˚ 23 1 ⁄ 2 ˚ 66 1 ⁄ 2 ˚ 60˚ 5 ( length of pole ) ( length of shadow ) tan Θ =

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    6 9. 60° N Dec. 22 30° N June 21 60° N June 21 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 change in daylight hours is greatest near the equinoxes (when solar declination changes are greatest) and smallest near the solstices. 15. a. At 30° N, the sun rises due east and sets due west on the equinoxes. Between the March and September equinoxes, it rises slightly north of east and sets slightly north of west. Between the September and March equinoxes, it rises slightly south of east and sets slightly south of west. b. The same general pattern is found at 60° N, but it is more extreme. In fact, the figure shows that on the June solstice the sun rises just north of NE (45°) and sets just north of NW (315° N). On the December solstice, the sun rises just south of SE (135°) and sets just south of SW (225°). 1 unit Sun’s rays Sun angle 83.5° Zenith angle 6.5° 1.01 units 1 unit Sun’s rays 8.83 units Zenith angle 83.5° Sun angle 6.5° 1 unit Sun’s rays Zenith angle 36.5° 1.24 units Sun angle 53.5°

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    16. March 21: 500 Wm –2 September 22: 500 Wm –2 June 21: 349 Wm –2 December 22: 658 Wm –2 17. The seasonal difference in solar intensity (beam spreading) and daylight hours is greater at 60° N than at 30° N. 18. The difference in beam spreading between 60° N and 30° N is greater in winter. 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. 19. [variable} 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 Questions 1. 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. 7

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    8 1. a. E = (5.67 • 10 –8 W m –2 K –4 ) • (6000 K) 4 = 73,483,200 Wm –2 b. E = (5.67 • 10 –8 W m –2 K –4 ) • (300 K) 4 = 459.27 Wm –2 2. a. 20 b. 160,000 c. 73,483,200/459.27 = 160,000 3. Earth: 2898/300 = 9.66 Sun: 2898/6000 = 0.48 4. Visible. 5. Solar intensity is much greater in early February, when the zenith angle is only a few degrees, than in early August when the zenith angle is 36–38°. 6. Scattering and reflection by the atmosphere reduce the amount of solar radiation reaching the sur- face. 7. The jagged curves in February show the effect of clouds reducing solar radiation. The smooth curves in August suggest that solar radiation is not diminished by clouds. 8. 110 Wm –2 divided by 789 Wm –2 = 13.9%. 9. The Stefan-Boltzmann equation demonstrates that the magnitude of radiation emission depends on temperature. Outgoing long-wave radiation from Earth’s surface is greater, because the surface is warmer than the atmosphere. 10. Long-wave radiation emission peaks each afternoon when surface temperature is highest. The magnitude of this peak is greater in February because surface temperature is greater than in August. The peak in August is later in the afternoon, suggesting that the daily maximum temperature occurs later in the day than in February, probably because of afternoon clouds and thunderstorms during the rainy month of February. 11. The jagged net radiation curve for March illustrates how clouds influence surface radiation receipt compared to the smooth net radiation curve for September, a month with little cloudiness and rainfall. 12. During the wet month of March, more surface energy is used to evaporate water, resulting in a greater latent heat flux and diminished sensible and soil heat flux. When the surface is drier in September, latent heat flux is drastically reduced, allowing greater sensible and soil heat fluxes. 13. a. Solid curve date: September 24; Dotted curve date: March 18 b. The greater temperature range (the solid curve) occurs on September 24, during the dry season when there are few clouds and water vapor is lower. March 18 is during the wet season, when clouds The Surface Energy Budget 3

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    reduce surface heating during the day, and clouds and water vapor reduce the loss of long-wave radia- tion to space, making surface temperatures warmer at night. These two things will moderate the diurnal temperature range on March 18, relative to September 24. 14. There is a net loss of radiation until approximately 8:00 AM. 15. a. Based on net radiation data only, the maximum temperature should have occurred around 4:00 PM when net radiation falls to zero. b. Winds cause more mixing, which tends to ventilate and cool surface temperatures. Winds also can advect cold air into a location. 16. Incoming SW radiation: 1053 Wm –2 . 17. Atmospheric scattering, absorption, and reflection reduce the amount reaching the surface. 18. Here’s one combination that reduces incoming SW radiation to 527 Wm –2 : high clouds: 3/10; medium clouds: 3/10; low clouds: 7/10. 19. Middle clouds seem to reduce SW radiation the most. Low and high clouds have the same effect. 20. Even on December 21, the solar radiation is more than half (605 Wm –2 ) of the June 21 amount. North of 35° N, you would be able to reduce the solar radiation by more than half. 21. Time: 7:45 or 16:15 (519 Wm –2 ). 22. Increasing albedo decreases the net radiation at the surface as more incoming radiation is reflected. 23. Long-wave radiation from Earth increases with temperature. 24. The Stefan-Boltzmann equation shows that the rate of increase in LW radiation with temperature is greater at higher temperatures. 25. Incoming LW radiation increases with increasing cloudiness. Lower clouds seem to affect incom- ing LW radiation more than higher clouds. 26. Water vapor concentrations, thermal advection, emission of LW radiation from the surface. 27. When you increase clouds, you increase the incoming LW radiation, which should make surface temperature increase. However, the module does not change surface temperature. Review Questions 1. Shortwave (solar) radiation varies more seasonally and diurnally. It varies as a function of sun angle above the horizon, which influences intensity of the solar beam striking the surface. By contrast, long-wave radiation, which depends on the temperature of emission, varies much less seasonally and diurnally. 2. If a forecaster anticipated cloudy conditions, she would predict higher minimum temperatures and lower maximum temperatures than she would with clear conditions. 9

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    10 1. In the Northern Hemisphere, all latitudes north of 23.5° receive peak solar intensity and longest daylength on one day—June 21 (45° S does so on Dec. 21). At 5° N, the sun is directly overhead twice during the year (April 4 and September 9). 2. There is a greater seasonal range in solar radiation at 45° S than at 45° N. 3. The tropics have very little seasonal range in solar radiation and, therefore, temperature. As one moves from 5° N to 65° N, the seasonal range in both variables increases because variations in solar intensity and daylength are greater at higher latitudes. 4. Latitudes north of 40° N have seasonal variation in snow and ice cover. During winter and early spring months, such surface cover reflects more solar radiation. The tropics have no such seasonal varia- tion, and most of the Southern Hemisphere has no such variation. It is either snow-free year-round, or ice-covered (i.e., Antarctica). The only exception is at 65° S where there is seasonal variation in sea ice. 5. Latitudes equatorward of 40° N and 40° S have a net radiation surplus; those poleward of 40° N and 40° S have a net radiation deficit. 6. Average annual poleward heat transport peaks near 50° N and 50° S latitude. This corresponds closely to the steepest net radiation gradient found between 50° and 65° N and 50° and 65° S latitude. 7. The entire Northern Hemisphere has a surplus of radiation in July; nearly the entire Northern Hemisphere has a deficit in January. The gradient across latitudes is not great in July, but quite sharp from the tropics to about 55° N in January. 8. Outside of the tropics, the temperature gradient across the Northern Hemisphere is much sharper in January than in July. The greatest range in seasonal temperature occurs near 65° N latitude. 9. There is far more poleward energy transport in January than July. There is a northward shift in the peak energy transfer from January to July. 10. The latitudinal gradient of net radiation and of temperature causes the poleward transport of heat, moving surplus energy to areas of deficit. The greater magnitude and more southerly location of pole- ward heat transport reflect the fact that the net radiation and temperature gradient are greater, and they extend farther south in January. 11. The seasonal temperature range at 45° N is greater because there is more land mass there than at 45° S. Large water bodies moderate the seasonal temperature range in the Southern Hemisphere. 12. A. Durban B. Viedma C. Port Nolloth D. Punta Galera The Global Energy Budget 4

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    13. A. Bahía de Caráquez B. Quito C. Cotopaxi 14. Since all three locations are near the equator, they all have a very small seasonal range in solar radi- ation receipt and temperature. Review Questions 1. Poleward heat transport occurs because certain parts of the globe have energy surpluses. Therefore, poleward heat transport will increase when the difference in energy across latitudes is greater. The location will correspond closely with the steepest gradient in net energy across latitudes. 2. Students should think of the controls that affect temperature in their hometown (e.g., latitude, proximity of large water bodies, geographic position on a continent, ocean currents, and mountains). 11

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    12 1. 50 calories • (Hot-water temperature – Final temperature). 2. 50 calories • (Ice-water temperature – Final temperature). 3. Answer #1 should equal answer #2 since the heat lost by the hot water should approximately equal the heat gained by the cold water. 4. 50 calories • (80°C – Temperature after melting). 5. 50 calories • (Ice-water temperature – Temperature after melting). 6. (Answer to #4) – (Answer to #5). 7. This energy was used to melt the ice. 8. Answer to #6 ÷ 25 grams. 9. Dependent on student results. Possible sources of error are incorrect weighing of ice, or incorrect temperature measurements. 10. Energy was used to change phase of water from liquid to gas (evaporation). It is stored in the water vapor produced. 11. The dry surface should have the higher air temperature because less energy was used for evapora- tion of water from the grass. More energy can be used to heat the dry surface. 12. 4 grams x 600 calories per gram = 2400 calories. 13. Water → water vapor consumed clothes drying; evaporation off a water surface Ice → water vapor consumed solid air freshener; sublimation of snow Water vapor → water released dew; condensation on a soda can Water vapor → ice released frost on the grass or window Water → ice released freezing ice cubes, pond, etc. 14. Temp. (°C) Saturation mixing ratio (g/kg) Rel. Humidity (%) 14 10.14 g/kg 49% 14 10.14 g/kg 89% 24 19.21 g/kg 26% 24 19.21 g/kg 10% 34 35.13 g/kg 20% Atmospheric Moisture 5

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    15. Even when saturated, cold air contains very little moisture. When air is heated, its relative humidity drops since the saturation point (potential vapor pressure) increases. Humidifiers are often used to compensate for this dry air. 16. During the summer, warmer air can contain large amounts of water vapor. A cool basement has a high relative humidity because of the high actual water vapor content in relatively low temperatures. 17. Temp. (°C) Saturation mixing ratio (g/kg) Actual mixing ratio (g/kg) Rank 14° 10.140 9.126 3 20 14.956 8.974 4 24 19.210 7.684 5 30 27.694 11.078 1 34 35.134 10.54 2 18. Relative humidity is temperature dependent and, therefore, often does not characterize the actual amount of atmospheric water vapor. 19. Dry-bulb Wet-bulb Wet-bulb Relative temperature temperature depression humidity 32°C 25°C 7°C 56% 10°C 5°C 5°C 43% 20. [variable] 21. Students should include a discussion of variables that will influence temperature or moisture such as the nature of the land surface (naturally vegetated compared with human-made), ventilation at the site, or degree of shade. 22. 22°C 23. From Table 5-2, saturation mixing ratio = 35.134 g/kg Mixing ratio = (35.134 g/kg)(.62) = 21.783 g/kg From Table 5-2 or Figure 5-4, dew point = 26°C -40 -30 -20 -10 0 10 20 30 40 0 10 20 30 40 50 60 Mixing Ratio (g/kg) Temperature (°C) 13

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