Chapter #8.1 Solutions - Understanding Weather and Climate - James E Burt, Edward Aguado - 7th Edition

1. Maintaining General CirculationUnceasing motion is undoubtedly the most conspicuous feature of the atmosphere. Across the planet winds ranging from gentle breezes to hurricane strength are the rule. Even when calm conditions arise in some locales, they don’t last long. This is obvious from even the most casual observation, but the reasons are not so obvious. Why must the atmosphere continually move? How are the circulation systems described in this chapter maintained? As described in this box, answers to these questions involve considering transformations of energy and momentum within the Earth–atmosphere system.The Global Atmospheric Heat EngineAt the largest scale, that of the globe, we know from Chapter 3 that energy gained by the planet from the Sun balances longwave radiation emitted by the atmosphere and surface. In particular, about 70 percent of incoming solar radiation is absorbed (238 W/m2) and an equal amount of radiation is emitted to space. (To keep the discussion simple, we are ignoring the prospect for climate change.) Atmospheric motions represent kinetic energy (KE), all of which is ultimately traceable to the input solarradiation. So, some part of absorbed solar radiation must be convertedto the energy of motion. Just as a car’s engine converts the heat of burning fuel into motion, the atmospheric heat engine converts solar radiation into motion. However, in the atmosphere transformation of heat energy to KE is far less directthanin a car engine.Recall from Chapter 2 that potential energy (PE) is energy that could possibly be converted to motion. The child in Figure 8-1-1a generates PE by tossing sand onto a sand pile. Lifting sand against the force of gravity requires energy, and that energy is stotedas PE in the sand pile. Frequently, part of the sand pile collapses and some of the sand tumbles down. These minor landslides occurwhen the difference in potential energy between sandgrains exceeds the ability of friction to prevent movement. Clearly, the PE provided by the childis converted to KE. Similar considerations regarding PE and KE apply to the atmosphere The potential energy of an air column arises partly from its temperature. A warm column has more PE than a cold column. Another part of PE, about 40 percent, arises from the vertical position of molecules in the column. To life a parcel of air against the force of gravity requires energy, and that energy is stored as PE.In the atmospheric heat engine, the Sun warms the planet and raises the potential energyof the atmosphere, just as the child raises the potential energy of the sand. If the surfaceis warmed by the Sun and heats the overlying air column, its PE increases. Not only does the temperature increase, but the column expands vertically and therefore air molecules are on average higher than before. Thus, both parts of the column’s PE increase: PE due to temperature and PE due to the molecules’ vertical position.Abouthalf of the atmosphere’s mass is below the 500 mb level and so the center of gravity for the atmosphere must be at about 5.5 km. If this leads to you think that vast amounts of PE are held in the atmosphere, you are right. However, most of a column’s PE is not available for conversion to KE, because air parcels aloft are supported by parcels below. The same is true of the sand pile; all of the grains in the interior are supported from below and cannot be moved. Only if circumstances are right can conversion to kinetic energy result. In a sandpile, movement happens on the slope, where there is a gradient in PE—and so it is in the atmosphere. Loosely speaking, if the height of the center of gravity in two adjacent columns of air is not the same, we can expect KE (and wind) to result. Or, if dense air is found above less dense air, overturning of the air column will result, again converting PE to KE.Figure 8-1-1b illustrates this production and conversion of energy in a schematic form. Energy inputs and outputs to Earth balance, maintaining a PE store of about 2600 million joules (MJ) per square meter of Earth. Only a tiny fraction of thathuge inventory, 0.23 percent, is available for conversion to KE. As seen in the figure, the rate of conversion is about 3 W/m2. This is enough to sustain all of the motions we observe, such as the huge belts of prevailing winds and ocean currents seen on the maps. It also includes all manner of “disturbances,” ranging from hurricanes and tornadoes down to the smallest puffsof wind. Notice, however, that at 3 W/m2 the average rate of energy conversion is small, roughly 1.3 percent of incoming solar radiation. Clearly, the atmosphere engine is quite inefficient.If 3 W/m2 is extracted from the store of PE, that same amount of heat energy must be returned so that planetary PE doesn’t decrease over time and so that Earth can emit the full 233 W/m2 required for energy balance. In other words, it can’t remain as kinetic energy but must be added back to the pool of PE. By the same token, kinetic energy can’t simply accumulate indefinitely, because that would lead to infinitely high winds! In other words, the store of KE must be constant, which requires losses that balance the input.The conversion back to PE is accomplished by friction. Frictional losses occur as air blows past the surface. They also occur within the atmosphere because of turbulence. If you blow hard air rushes out of your lungs, but the puff doesn’t cross the room. There is friction as it moves through the surrounding air, and that friction robs the puff of energy. Eventually the room air is as quiet as before, and the energy of motion has been converted to heat. This is called frictional dissipation and corresponds to production of PE. As seen in the figure, the average rate of frictional dissipation equals the generation of kinetic energy. Most of this occurs in the lower troposphere, where friction is especially important.Constant movement implies a pool of KE, just as there is a pool of PE. The KE store is not large compared to PE, only about 5 million joules per square meter (MJ/m2). It is interesting to think about how long that store would last if depleted at a rate of 3 W/m2. Remembering that a watt is one joule per second, the calculation is straightforward:...We see that there is enough KE present to maintain motions for about 1.6 million seconds, or just 19 days! Just as the atmosphere’s store of water is small compared to evaporation and precipitation, the store of KE is small compared to its production and loss.Momentum Exchange and Atmospheric MotionMaintaining atmospheric motion also involves momentum transfers. In this case angular momentum is the quantity in question. Imagine a basketball player spinning a ball on his or her finger. Even though the ball doesn’t move through space, it possesses momentum called angular momentum. To stop the ball from spinning or to make it go faster, we must remove or add angular momentum. Likewise, the Earth–atmosphere system has angular momentum by virtue of its rotation. Most is earth momentum, but the atmosphere contributes to the total because it spins with the surface below. Ignoring weak tidal forces from other objects in the solar system, nothing is pushing on the planet, and the total angular momentum for the planet is nearly constant.Consider locations where the average surface winds are westerly. Blowing from west to east, they are pushing in the direction of rotation, and clearly add angular momentum to the earth (Figure 8-1-2). In other words, westerly winds transfer angular momentum from the atmosphere to Earth. Easterly winds do just the opposite, transferring angular momentum from Earth to the atmosphere. Clearly, it must be that averaged over the whole planet, easterly and westerly momentum exchange must balance in order to maintain atmospheric motion. Just as there is no net energy loss or gain for the planet, total angular momentum is constant. Were that not the case, winds would either cease or increase forever.As a final point, we should emphasize that the numbers given are global averages. In some places the production of PE by solar radiation is not too different than the rate of conversion to KE, and winds are sustained on a more-or-less steady basis. The Hadley cells are one example. The fairly continuous nature of the trade winds is maintained by roughly continuous conversion of PE at a rate close to what is provided by the Sun in the tropics. This is like a playground carousel, where spinning is maintained by repeated small pushes, whose energy transfer is just large enough to offset frictional costs. On the other hand, oftentimes KE production rates in the atmosphere are thousands of times larger than solar energy input, as seen in tornado winds that move fully loaded train cars. Or, to take another example, how could a thunderstorm develop at night when the Sun isn’t even shining? Clearly, storms don’t violate energy conservation and their KE doesn’t come out of nowhere. Such disturbances are produced when available PE is concentrated in small areas and released in bursts of KE production. Just how that happens is a story of its own covered in later chapters.FIGURE 8-1-1 Potential and Kinetic Energy Conversions. (a) The child adds potential energy (PE) to the pile by raising sand grains against the force of gravity. As grains tumble down, their PE is converted to the energy of motion, kinetic energy (KE). (b) Atmospheric motion is maintained by continuous conversion of PE to KE within the Earth system. Winds eventually shed their energy through frictional heating, which helps maintain longwave emission by the planet to space.`...FIGURE 8-1-2 Angular Momentum Transfer to and from the Surface. Westerly winds blow in the direction of rotation and transfer momentum to the surface below. By contrast, easterly winds represent momentum transfer to the atmosphere....Car engines are about 20 percent efficient. How does this compare to the atmospheric heat engine? Get solution

2. Maintaining General CirculationUnceasing motion is undoubtedly the most conspicuous feature of the atmosphere. Across the planet winds ranging from gentle breezes to hurricane strength are the rule. Even when calm conditions arise in some locales, they don’t last long. This is obvious from even the most casual observation, but the reasons are not so obvious. Why must the atmosphere continually move? How are the circulation systems described in this chapter maintained? As described in this box, answers to these questions involve considering transformations of energy and momentum within the Earth–atmosphere system.The Global Atmospheric Heat EngineAt the largest scale, that of the globe, we know from Chapter 3 that energy gained by the planet from the Sun balances longwave radiation emitted by the atmosphere and surface. In particular, about 70 percent of incoming solar radiation is absorbed (238 W/m2) and an equal amount of radiation is emitted to space. (To keep the discussion simple, we are ignoring the prospect for climate change.) Atmospheric motions represent kinetic energy (KE), all of which is ultimately traceable to the input solarradiation. So, some part of absorbed solar radiation must be convertedto the energy of motion. Just as a car’s engine converts the heat of burning fuel into motion, the atmospheric heat engine converts solar radiation into motion. However, in the atmosphere transformation of heat energy to KE is far less directthanin a car engine.Recall from Chapter 2 that potential energy (PE) is energy that could possibly be converted to motion. The child in Figure 8-1-1a generates PE by tossing sand onto a sand pile. Lifting sand against the force of gravity requires energy, and that energy is stotedas PE in the sand pile. Frequently, part of the sand pile collapses and some of the sand tumbles down. These minor landslides occurwhen the difference in potential energy between sandgrains exceeds the ability of friction to prevent movement. Clearly, the PE provided by the childis converted to KE. Similar considerations regarding PE and KE apply to the atmosphere The potential energy of an air column arises partly from its temperature. A warm column has more PE than a cold column. Another part of PE, about 40 percent, arises from the vertical position of molecules in the column. To life a parcel of air against the force of gravity requires energy, and that energy is stored as PE.In the atmospheric heat engine, the Sun warms the planet and raises the potential energyof the atmosphere, just as the child raises the potential energy of the sand. If the surfaceis warmed by the Sun and heats the overlying air column, its PE increases. Not only does the temperature increase, but the column expands vertically and therefore air molecules are on average higher than before. Thus, both parts of the column’s PE increase: PE due to temperature and PE due to the molecules’ vertical position.Abouthalf of the atmosphere’s mass is below the 500 mb level and so the center of gravity for the atmosphere must be at about5.5 km. If this leads to you think that vast amounts of PE are held in the atmosphere, you are right. However, most of a column’s PE is not available for conversion to KE, because air parcels aloft are supported by parcels below. The same is true of the sand pile; all of the grains in the interior are supported from below and cannot be moved. Only if circumstances are right can conversion to kinetic energy result. In a sandpile, movement happens on the slope, where there is a gradient in PE—and so it is in the atmosphere. Loosely speaking, if the height of the center of gravity in two adjacent columns of air is not the same, we can expect KE (and wind) to result. Or, if dense air is found above less dense air, overturning of the air column will result, again converting PE to KE.Figure 8-1-1b illustrates this production and conversion of energy in a schematic form. Energy inputs and outputs to Earth balance, maintaining a PE store of about 2600 million joules (MJ) per square meter of Earth. Only a tiny fraction of thathuge inventory, 0.23 percent, is available for conversion to KE. As seen in the figure, the rate of conversion is about3 W/m2. This is enough to sustain all of the motions we observe, such as the huge belts of prevailing winds and ocean currents seen on the maps. It also includes all manner of “disturbances,” ranging from hurricanes and tornadoes down to the smallest puffsof wind. Notice, however, that at 3 W/m2 the average rate of energy conversion is small, roughly 1.3 percent of incoming solar radiation. Clearly, the atmosphere engine is quite inefficient.If 3 W/m2 is extracted from the store of PE, that same amount of heat energy must be returned so that planetary PE doesn’t decrease over time and so that Earth can emit the full 233 W/m2 required for energy balance. In other words, it can’t remain as kinetic energy but must be added back to the pool of PE. By the same token, kinetic energy can’t simply accumulate indefinitely, because that would lead to infinitely high winds! In other words, the store of KE must be constant, which requires losses that balance the input.The conversion back to PE is accomplished by friction. Frictional losses occur as air blows past the surface. They also occur within the atmosphere because of turbulence. If you blow hard air rushes out of your lungs, but the puff doesn’t cross the room. There is friction as it moves through the surrounding air, and that friction robs the puff of energy. Eventually the room air is as quiet as before, and the energy of motion has been converted to heat. This is called frictional dissipation and corresponds to production of PE. As seen in the figure, the average rate of frictional dissipation equals the generation of kinetic energy. Most of this occurs in the lower troposphere, where friction is especially important.Constant movement implies a pool of KE, just as there is a pool of PE. The KE store is not large compared to PE, only about 5 million joules per square meter (MJ/m2). It is interesting to think about how long that store would last if depleted at a rate of 3 W/m2. Remembering that a watt is one joule per second, the calculation is straightforward:...We see that there is enough KE present to maintain motions for about 1.6 million seconds, or just 19 days! Just as the atmosphere’s store of water is small compared to evaporation and precipitation, the store of KE is small compared to its production and loss.Momentum Exchange and Atmospheric MotionMaintaining atmospheric motion also involves momentum transfers. In this case angular momentum is the quantity in question. Imagine a basketball player spinning a ball on his or her finger. Even though the ball doesn’t move through space, it possesses momentum called angular momentum. To stop the ball from spinning or to make it go faster, we must remove or add angular momentum. Likewise, the Earth–atmosphere system has angular momentum by virtue of its rotation. Most is earth momentum, but the atmosphere contributes to the total because it spins with the surface below. Ignoring weak tidal forces from other objects in the solar system, nothing is pushing on the planet, and the total angular momentum for the planet is nearly constant.Consider locations where the average surface winds are westerly. Blowing from west to east, they are pushing in the direction of rotation, and clearly add angular momentum to the earth (Figure 8-1-2). In other words, westerly winds transfer angular momentum from the atmosphere to Earth. Easterly winds do just the opposite, transferring angular momentum from Earth to the atmosphere. Clearly, it must be that averaged over the whole planet, easterly and westerly momentum exchange must balance in order to maintain atmospheric motion. Just as there is no net energy loss or gain for the planet, total angular momentum is constant. Were that not the case, winds would either cease or increase forever.As a final point, we should emphasize that the numbers given are global averages. In some places the production of PE by solar radiation is not too different than the rate of conversion to KE, and winds are sustained on a more-or-less steady basis. The Hadley cells are one example. The fairly continuous nature of the trade winds is maintained by roughly continuous conversion of PE at a rate close to what is provided by the Sun in the tropics. This is like a playground carousel, where spinning is maintained by repeated small pushes, whose energy transfer is just large enough to offset frictional costs. On the other hand, oftentimes KE production rates in the atmosphere are thousands of times larger than solar energy input, as seen in tornado winds that move fully loaded train cars. Or, to take another example, how could a thunderstorm develop at night when the Sun isn’t even shining? Clearly, storms don’t violate energy conservation and their KE doesn’t come out of nowhere. Such disturbances are produced when available PE is concentrated in small areas and released in bursts of KE production. Just how that happens is a story of its own covered in later chapters.FIGURE 8-1-1 Potential and Kinetic Energy Conversions. (a) The child adds potential energy (PE) to the pile by raising sand grains against the force of gravity. As grains tumble down, their PE is converted to the energy of motion, kinetic energy (KE). (b) Atmospheric motion is maintained by continuous conversion of PE to KE within the Earth system. Winds eventually shed their energy through frictional heating, which helps maintain longwave emission by the planet to space.`...FIGURE 8-1-2 Angular Momentum Transfer to and from the Surface. Westerly winds blow in the direction of rotation and transfer momentum to the surface below. By contrast, easterly winds represent momentum transfer to the atmosphere....What role does frictional dissipation play in the heat engine? Get solution

3. Maintaining General CirculationUnceasing motion is undoubtedly the most conspicuous feature of the atmosphere. Across the planet winds ranging from gentle breezes to hurricane strength are the rule. Even when calm conditions arise in some locales, they don’t last long. This is obvious from even the most casual observation, but the reasons are not so obvious. Why must the atmosphere continually move? How are the circulation systems described in this chapter maintained? As described in this box, answers to these questions involve considering transformations of energy and momentum within the Earth–atmosphere system.The Global Atmospheric Heat EngineAt the largest scale, that of the globe, we know from Chapter 3 that energy gained by the planet from the Sun balances longwave radiation emitted by the atmosphere and surface. In particular, about 70 percent of incoming solar radiation is absorbed (238 W/m2) and an equal amount of radiation is emitted to space. (To keep the discussion simple, we are ignoring the prospect for climate change.) Atmospheric motions represent kinetic energy (KE), all of which is ultimately traceable to the input solarradiation. So, some part of absorbed solar radiation must be convertedto the energy of motion. Just as a car’s engine converts the heat of burning fuel into motion, the atmospheric heat engine converts solar radiation into motion. However, in the atmosphere transformation of heat energy to KE is far less directthanin a car engine.Recall from Chapter 2 that potential energy (PE) is energy that could possibly be converted to motion. The child in Figure 8-1-1a generates PE by tossing sand onto a sand pile. Lifting sand against the force of gravity requires energy, and that energy is stotedas PE in the sand pile. Frequently, part of the sand pile collapses and some of the sand tumbles down. These minor landslides occurwhen the difference in potential energy between sandgrains exceeds the ability of friction to prevent movement. Clearly, the PE provided by the childis converted to KE. Similar considerations regarding PE and KE apply to the atmosphere The potential energy of an air column arises partly from its temperature. A warm column has more PE than a cold column. Another part of PE, about 40 percent, arises from the vertical position of molecules in the column. To life a parcel of air against the force of gravity requires energy, and that energy is stored as PE.In the atmospheric heat engine, the Sun warms the planet and raises the potential energyof the atmosphere, just as the child raises the potential energy of the sand. If the surfaceis warmed by the Sun and heats the overlying air column, its PE increases. Not only does the temperature increase, but the column expands vertically and therefore air molecules are on average higher than before. Thus, both parts of the column’s PE increase: PE due to temperature and PE due to the molecules’ vertical position.Abouthalf of the atmosphere’s mass is below the 500 mb level and so the center of gravity for the atmosphere must be at about 5.5 km. If this leads to you think that vast amounts of PE are held in the atmosphere, you are right. However, most of a column’s PE is not available for conversion to KE, because air parcels aloft are supported by parcels below. The same is true of the sand pile; all of the grains in the interior are supported from below and cannot be moved. Only if circumstances are right can conversion to kinetic energy result. In a sandpile, movement happens on the slope, where there is a gradient in PE—and so it is in the atmosphere. Loosely speaking, if the height of the center of gravity in two adjacent columns of air is not the same, we can expect KE (and wind) to result. Or, if dense air is found above less dense air, overturning of the air column will result, again converting PE to KE.Figure 8-1-1b illustrates this production and conversion of energy in a schematic form. Energy inputs and outputs to Earth balance, maintaining a PE store of about 2600 million joules (MJ) per square meter of Earth. Only a tiny fraction of thathuge inventory, 0.23 percent, is available for conversion to KE. As seen in the figure, the rate of conversion is about 3 W/m2. This is enough to sustain all of the motions we observe, such as the huge belts of prevailing winds and ocean currents seen on the maps. It also includes all manner of “disturbances,” ranging from hurricanes and tornadoes down to the smallest puffsof wind. Notice, however, that at 3 W/m2 the average rate of energy conversion is small, roughly 1.3 percent of incoming solar radiation. Clearly, the atmosphere engine is quite inefficient.If 3 W/m2 is extracted from the store of PE, that same amount of heat energy must be returned so that planetary PE doesn’t decrease over time and so that Earth can emit the full 233 W/m2 required for energy balance. In other words, it can’t remain as kinetic energy but must be added back to the pool of PE. By the same token, kinetic energy can’t simply accumulate indefinitely, because that would lead to infinitely high winds! In other words, the store of KE must be constant, which requires losses that balance the input.The conversion back to PE is accomplished by friction. Frictional losses occur as air blows past the surface. They also occur within the atmosphere because of turbulence. If you blow hard air rushes out of your lungs, but the puff doesn’t cross the room. There is friction as it moves through the surrounding air, and that friction robs the puff of energy. Eventually the room air is as quiet as before, and the energy of motion has been converted to heat. This is called frictional dissipation and corresponds to production of PE. As seen in the figure, the average rate of frictional dissipation equals the generation of kinetic energy. Most of this occurs in the lower troposphere, where friction is especially important.Constant movement implies a pool of KE, just as there is a pool of PE. The KE store is not large compared to PE, only about 5 million joules per square meter (MJ/m2). It is interesting to think about how long that store would last if depleted at a rate of 3 W/m2. Remembering that a watt is one joule per second, the calculation is straightforward:...We see that there is enough KE present to maintain motions for about 1.6 million seconds, or just 19 days! Just as the atmosphere’s store of water is small compared to evaporation and precipitation, the store of KE is small compared to its production and loss.Momentum Exchange and Atmospheric MotionMaintaining atmospheric motion also involves momentum transfers. In this case angular momentum is the quantity in question. Imagine a basketball player spinning a ball on his or her finger. Even though the ball doesn’t move through space, it possesses momentum called angular momentum. To stop the ball from spinning or to make it go faster, we must remove or add angular momentum. Likewise, the Earth–atmosphere system has angular momentum by virtue of its rotation. Most is earth momentum, but the atmosphere contributes to the total because it spins with the surface below. Ignoring weak tidal forces from other objects in the solar system, nothing is pushing on the planet, and the total angular momentum for the planet is nearly constant.Consider locations where the average surface winds are westerly. Blowing from west to east, they are pushing in the direction of rotation, and clearly add angular momentum to the earth (Figure 8-1-2). In other words, westerly winds transfer angular momentum from the atmosphere to Earth. Easterly winds do just the opposite, transferring angular momentum from Earth to the atmosphere. Clearly, it must be that averaged over the whole planet, easterly and westerly momentum exchange must balance in order to maintain atmospheric motion. Just as there is no net energy loss or gain for the planet, total angular momentum is constant. Were that not the case, winds would either cease or increase forever.As a final point, we should emphasize that the numbers given are global averages. In some places the production of PE by solar radiation is not too different than the rate of conversion to KE, and winds are sustained on a more-or-less steady basis. The Hadley cells are one example. The fairly continuous nature of the trade winds is maintained by roughly continuous conversion of PE at a rate close to what is provided by the Sun in the tropics. This is like a playground carousel, where spinning is maintained by repeated small pushes, whose energy transfer is just large enough to offset frictional costs. On the other hand, oftentimes KE production rates in the atmosphere are thousands of times larger than solar energy input, as seen in tornado winds that move fully loaded train cars. Or, to take another example, how could a thunderstorm develop at night when the Sun isn’t even shining? Clearly, storms don’t violate energy conservation and their KE doesn’t come out of nowhere. Such disturbances are produced when available PE is concentrated in small areas and released in bursts of KE production. Just how that happens is a story of its own covered in later chapters.FIGURE 8-1-1 Potential and Kinetic Energy Conversions. (a) The child adds potential energy (PE) to the pile by raising sand grains against the force of gravity. As grains tumble down, their PE is converted to the energy of motion, kinetic energy (KE). (b) Atmospheric motion is maintained by continuous conversion of PE to KE within the Earth system. Winds eventually shed their energy through frictional heating, which helps maintain longwave emission by the planet to space.`...FIGURE 8-1-2 Angular Momentum Transfer to and from the Surface. Westerly winds blow in the direction of rotation and transfer momentum to the surface below. By contrast, easterly winds represent momentum transfer to the atmosphere....Do easterly winds add or withdraw angular momentum from the solid earth? Get solution


Chapter #17 Solutions - Understanding Weather and Climate - James E Burt, Edward Aguado - 7th Edition

1c. What happens to light if it enters a medium of higher density? Get solution 1ct. Consider the way the apparent position of the...