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

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Solutions Manual toExercises for Weather & Climate,8th ed.1Vertical Structure of the Atmosphere12Earth–Sun Geometry43The Surface Energy Budget84The Global Energy Budget105Atmospheric Moisture126Saturation and Atmospheric Stability167Cloud Droplets and Raindrops198Atmospheric Motion219Weather Map Analysis2810Mid-Latitude Cyclones3311Weather Forecasting3712Thunderstorms and Tornadoes4313Hurricanes4614Climate Controls5015Climate Classification5316Climatic Variability and Change5517Simulating Climatic Change58Appendix ADimensions and Units60Appendix BEarth Measures62Appendix CGeoClock63iii

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1.Height (km)% of atmosphere above22.46.2516.812.511.2255.6502. & 3.4.25%250 mb58.4%584 mb5.210 mb6.123 mb58.4%69 mb33%320246810121416182022242628303234010 20 30 40 50 60 70 80 90 100Height Above the Surface (km)Percentage of the Atmosphere AbovePressure (mb)0 100 200 300 400 500 600 700 800 900 1000Vertical Structure of the Atmosphere11

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27.Ozone absorbs solar radiation (particularly in the ultraviolet portion of the electromagnetic spec-trum). This absorption leads to warming in the stratosphere.8.2000400060008000100002.0°C–11°C–24°C–37°C–50°C9. & 11.10.a. Key Westb. Key Westc. Fairbanks11.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 verticalmixing is greater when temperature is warmer.14.170 mb15.92 mb16.Because of greater air density in the lower layer, the pressure drop between 2 and 4 km is nearlydouble that between 8 and 10 km.17.182 mb18.Air pressure decreases with height because there is less atmosphere to exert downward force. Thepressure drop will be greatest when air density is highest because the mass of the atmosphere abovedecreases 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.02000400060008000100001200014000160001800020000-80-60-40-2002040Key WestFairbanksstandard 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 Questions1.Air pressure and density decrease exponentially with height above Earth’s surface. This is becausegas molecules are concentrated near the surface and a given height increase at these lower levels meanspassing through more molecules than the same height increase at higher elevations. Temperature alsodecreases with height in the troposphere. This rate of decrease varies, but is typically linear compared topressure or density.2.The thickness of the troposphere is a function of temperature. Warmer temperatures in tropicalregions 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 temperatureand pressure. At the low pressure of the mid and upper troposphere, density is lower than it is at lowerelevations.4.Pressure changes much faster vertically than it does horizontally. It drops 100 mb in the lowestkilometer of the atmosphere.3

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41.June 21June 21 profile viewMarch 21Sun’s Rays231/2°NS30°23½°66½°0°90°DABCD30˚ N0˚661⁄2˚N231⁄2˚ SABCD47˚43˚831⁄2˚661⁄2˚30°23½°66½°0°90°ABCDSun’s RaysEarth–Sun Geometry2

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March 21 profile view2.631⁄2°; December 213.261⁄2°4.a. 0° (equator)b. 231⁄2° Nc. 0° (equator)d. 231⁄2° Se. [variable]5.New OrleansHelsinkia.60°30°b.831⁄2°531⁄2°c.60°30°d.361⁄2°61⁄2°e.[variable][variable]6.[variable]7.Answer is date dependent. Example for 34° N latitude on February 1, a two-meter pole casts ashadow measuring 2.52 meters.Θ =tan−1(0.7937)Θ =38.44°8.[variable]30˚ N0˚661⁄2˚N231⁄2˚ SABCD90˚231⁄2˚661⁄2˚60˚5(length of pole)(length of shadow)tanΘ =

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69.60° N Dec. 2230° N June 2160° N June 2110.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° N60° NJune solstice1418Equinoxes1212December solstice10613.60° N14.The change in daylight hours is greatest near the equinoxes (when solar declination changes aregreatest) 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 andSeptember equinoxes, it rises slightly north of east and sets slightly north of west. Between theSeptember 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 thaton the June solstice the sun rises just north of NE (45°) and sets just north of NW (315° N). On theDecember solstice, the sun rises just south of SE (135°) and sets just south of SW (225°).1 unitSun’s raysSun angle83.5°Zenith angle6.5°1.01 units1 unitSun’s rays8.83 unitsZenith angle83.5°Sun angle 6.5°1 unitSun’s raysZenith angle36.5°1.24 unitsSun angle53.5°

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16.March 21: 500 Wm–2September 22: 500 Wm–2June 21: 349 Wm–2December 22: 658 Wm–217.The seasonal difference in solar intensity (beam spreading) and daylight hours is greater at 60° Nthan 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 actuallygreater at 60° N.19.[variable}20.Most direct rays: 1 unit beam =1.000 surface units; Date March 21, September 22Least direct rays: 1 unit beam =1.090 surface units; Date June 21, December 2121.9%22.[variable]23.[variable]24.The higher the latitude, the greater the seasonal range in solar intensity. This results in a largerannual temperature range at high latitudes than in the tropics.25.December SolsticeJune Solstice60° N8.8341.24450° N3.5211.11740° N2.2411.04330° N1.6811.00620° N1.3791.00226.The solar intensity gradient across the mid-latitudes is much greater in winter and contributes to agreater 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 insolar 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 radiationreceived and temperature.7

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81.a.E= (5.67 • 10–8W m–2K–4) • (6000 K)4=73,483,200 Wm–2b.E= (5.67 • 10–8W m–2K–4) • (300 K)4= 459.27 Wm–22.a. 20b. 160,000c. 73,483,200/459.27 = 160,0003.Earth: 2898/300 = 9.66Sun: 2898/6000 = 0.484.Visible.5.Solar intensity is much greater in early February, when the zenith angle is only a few degrees, thanin 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 smoothcurves in August suggest that solar radiation is not diminished by clouds.8.110 Wm–2divided by 789 Wm–2= 13.9%.9.The Stefan-Boltzmann equation demonstrates that the magnitude of radiation emission dependson temperature. Outgoing long-wave radiation from Earth’s surface is greater, because the surface iswarmer than the atmosphere.10.Long-wave radiation emission peaks each afternoon when surface temperature is highest. Themagnitude of this peak is greater in February because surface temperature is greater than in August. Thepeak in August is later in the afternoon, suggesting that the daily maximum temperature occurs later inthe day than in February, probably because of afternoon clouds and thunderstorms during the rainymonth of February.11.The jagged net radiation curve for March illustrates how clouds influence surface radiation receiptcompared 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 agreater latent heat flux and diminished sensible and soil heat flux. When the surface is drier inSeptember, latent heat flux is drastically reduced, allowing greater sensible and soil heat fluxes.13.a. Solid curve date: September 24; Dotted curve date: March 18b. The greater temperature range (the solid curve) occurs on September 24, during the dry seasonwhen there are few clouds and water vapor is lower. March 18 is during the wet season, when cloudsThe Surface Energy Budget3

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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 diurnaltemperature 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 around4:00 PM when net radiation falls to zero.b. Winds cause more mixing, which tends to ventilate and cool surface temperatures. Winds alsocan 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 therateof increase in LW radiation with temperatureis 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 surfacetemperature increase. However, the module does not change surface temperature.Review Questions1.Shortwave (solar) radiation varies more seasonally and diurnally. It varies as a function of sunangle 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 anddiurnally.2.If a forecaster anticipated cloudy conditions, she would predict higher minimum temperatures andlower maximum temperatures than she would with clear conditions.9

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101.In the Northern Hemisphere, all latitudes north of 23.5° receive peak solar intensity and longestdaylength on one day—June 21 (45° S does so on Dec. 21). At 5° N, the sun is directly overhead twiceduring 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 onemoves from 5° N to 65° N, the seasonal range in both variables increases because variations in solarintensity and daylength are greater at higher latitudes.4.Latitudes north of 40° N have seasonal variation in snow and ice cover. During winter and earlyspring 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, orice-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° Nand 40° S have a net radiation deficit.6.Average annual poleward heat transport peaks near 50° N and 50° S latitude. This correspondsclosely 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 NorthernHemisphere has a deficit in January. The gradient across latitudes is not great in July, but quite sharpfrom the tropics to about 55° N in January.8.Outside of the tropics, the temperature gradient across the Northern Hemisphere is much sharperin 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 thepeak 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 theyextend farther south in January.11.The seasonal temperature range at 45° N is greater because there is more land mass there than at45° S. Large water bodies moderate the seasonal temperature range in the Southern Hemisphere.12.A. DurbanB. ViedmaC. Port NollothD. Punta GaleraThe Global Energy Budget4

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13.A. Bahía de CaráquezB. QuitoC. Cotopaxi14.Since all three locations are near the equator, they all have a very small seasonal range in solar radi-ation receipt and temperature.Review Questions1.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 isgreater. 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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121.50 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 equalthe 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 incorrecttemperature measurements.10.Energy was used to change phase of water from liquid to gas (evaporation). It is stored in the watervapor 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 vaporconsumedclothes drying; evaporation off a water surfaceIce→water vaporconsumedsolid air freshener; sublimation of snowWater vapor→waterreleaseddew; condensation on a soda canWater vapor→icereleasedfrost on the grass or windowWater→icereleasedfreezing ice cubes, pond, etc.14.Temp. (°C)Saturation mixing ratio (g/kg)Rel. Humidity (%)1410.14 g/kg49%1410.14 g/kg89%2419.21 g/kg26%2419.21 g/kg10%3435.13 g/kg20%Atmospheric Moisture5

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15.Even when saturated, cold air contains very little moisture. When air is heated, its relative humiditydrops since the saturation point (potential vapor pressure) increases. Humidifiers are often used tocompensate for this dry air.16.During the summer, warmer air can contain large amounts of water vapor. A cool basement has ahigh 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)Rank14°10.1409.12632014.9568.97442419.2107.68453027.69411.07813435.13410.54218.Relative humidity is temperature dependent and, therefore, often does not characterize the actualamount of atmospheric water vapor.19.Dry-bulbWet-bulbWet-bulbRelativetemperaturetemperaturedepressionhumidity32°C25°C7°C56%10°C5°C5°C43%20.[variable]21.Students should include a discussion of variables that will influence temperature or moisture suchas the nature of the land surface (naturally vegetated compared with human-made), ventilation at thesite, or degree of shade.22.22°C23.From Table 5-2, saturation mixing ratio = 35.134 g/kgMixing ratio = (35.134 g/kg)(.62) = 21.783 g/kgFrom Table 5-2 or Figure 5-4, dew point = 26°C-40-30-20-100102030400102030405060Mixing Ratio (g/kg)Temperature (°C)13

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