Attempt to model the effect of increasing greenhouse gas concentration in Earth s atmosphere using a...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Attempt to model the effect of increasing greenhouse gas concentration in Earth s atmosphere using a simplified model as in the figure below. In this model, there is a single atmospheric layer at h₁ = 5 km altitude with temperature, TA, and known longwave emissivity, &. The surface is a perfect blackbody with temperature, Ts. The atmospheric layer, however, is not a perfect blackbody: a portion of the longwave emission from the surface, (1 - )oT, escapes directly to space, and the remainder (ɛoT) is absorbed by the atmospheric layer. The atmospheric layer is assumed to be completely transparent to solar radiation. In addition to these radiative processes, the surface also cools through convection with a convective flux, Fe, which acts to warm the atmospheric layer and maintain an atmospheric lapse rate of T = 6.5 K km-¹. Thus, T, and TA are constrained to satisfy TS-TA hA = r. (1) The solar constant is So=1362 W m-2, the Stefan-Boltzmann constant is o = 5.67 × 10-8 W m-2K-4, the planetary albedo is taken to be ap = 0.27 and the emissivity of the atmospheric layer is taken to be ε = : 0.93. For all questions below, assume that the Earth system is in a steady-state, which implies that the Earth system is in thermal equilibrium. - αp) Fc OTS EOTA εσΤΑ Atmospheric layer (5 km altitude) Earth s surface 1. (10 points.) Write an expression for the energy balance of the surface in terms of Ts, TA, Fc and the other given parameters. Keep your expression algebraic, using the notation given above. 2. (10 points.) Write an expression for the energy balance of the atmospheric layer in terms of TS, TA, Fc and the other given parameters. Keep your expression algebraic. 3. (10 points.) Combine your answers from questions 1 and 2 to eliminate Fc. Write your new expression below. Keep your expression algebraic, and simplify your expression as much as possible. 4. (10 points.) Use equation (1) to eliminate TA from the expression you obtained in question 3. Write your new expression below, and keep your expression algebraic. 5. (10 points.) Obtain an expression that solves for Ts. To help with solving for Ts, you can use the linear approximations OTOT +40T30 (Ts - Tso), o(Ts - Tha) 4 ≈o(Tso - Th₁) 4 + 40 (Ts - Th₁)³(Ts - Tso), where Tso is a reasonable guess for Ts. Keep Tso and the rest of your expression algebraic, and simplify your sion as much as possible. 6. (5 points.) Using the given parameter values, determine a numerical value for Ts. Use the freezing temperature for water as your initial guess for the surface temperature (Tso = 273.15 K). Express your answer to two decimal places in units of K. 7. (5 points.) Use your result from question 6 as a new guess for surface temperature, and obtain a better estimate for Ts. Express your answer to two decimal places in units of K. This approach is closer to how numerical models actually calculate temperature: a complicated equation is linearized and then solved iteratively until the guess and the answer are nearly the same. 8. (5 points.) An increase in greenhouse gas concentration causes the emissivity of the atmosphere to increase to 0.97. Using your answer to question 7 as your initial guess for surface temperature, obtain a new value for Ts. Express your answer to two decimal places in units of K. Compare your answer to the answer you obtained in question 7, and comment on whether the change in T, makes sense given how you expect increasing greenhouse gas concentration to impact global mean surface temperature. 9. (5 points.) Under climate change, albedo is also expected to decrease because of melting glaciers and sea ice. If in combination with the atmospheric emissivity increasing to 0.97, the planetary albedo also decreases to 0.26, what is the new value of Ts? Use your answer to question 7 as your initial guess for surface temperature. Express your answer to two decimal places in units of K. 10. (9 points.) The Clausius-Clapeyron relation predicts that for every 1 K increase in surface temperature, assuming relative humidity and near-surface wind speeds are fixed, the evaporation from the surface will increase by approximately 7%. If the global average evaporation of water is 100 cm/year in the original climate (considered in question 7), what would be the new value of evaporation with the value of T, you obtained in question 9? Express your answer in units of cm/year rounded to the nearest 1 cm/year. 11. (9 points.) Based on your answer to question 9, what are the values of global mean precipitation for the original climate (considered in question 7) and the perturbed climate (considered in question 9)? Express your answers in units of cm/year rounded to the nearest 1 cm/year. 12. (12 points.) Assume that the global mean changes in temperature and precipitation found above are applicable to Toronto. How would these changes influence the rate of physical weathering of the Toronto sidewalk pictured below? Would the rate of physical weathering be affected by changes in other types of weathering (i.e. biological and chemical weathering)? If so how? (Picture from CBC News.) Attempt to model the effect of increasing greenhouse gas concentration in Earth s atmosphere using a simplified model as in the figure below. In this model, there is a single atmospheric layer at h₁ = 5 km altitude with temperature, TA, and known longwave emissivity, &. The surface is a perfect blackbody with temperature, Ts. The atmospheric layer, however, is not a perfect blackbody: a portion of the longwave emission from the surface, (1 - )oT, escapes directly to space, and the remainder (ɛoT) is absorbed by the atmospheric layer. The atmospheric layer is assumed to be completely transparent to solar radiation. In addition to these radiative processes, the surface also cools through convection with a convective flux, Fe, which acts to warm the atmospheric layer and maintain an atmospheric lapse rate of T = 6.5 K km-¹. Thus, T, and TA are constrained to satisfy TS-TA hA = r. (1) The solar constant is So=1362 W m-2, the Stefan-Boltzmann constant is o = 5.67 × 10-8 W m-2K-4, the planetary albedo is taken to be ap = 0.27 and the emissivity of the atmospheric layer is taken to be ε = : 0.93. For all questions below, assume that the Earth system is in a steady-state, which implies that the Earth system is in thermal equilibrium. - αp) Fc OTS EOTA εσΤΑ Atmospheric layer (5 km altitude) Earth s surface 1. (10 points.) Write an expression for the energy balance of the surface in terms of Ts, TA, Fc and the other given parameters. Keep your expression algebraic, using the notation given above. 2. (10 points.) Write an expression for the energy balance of the atmospheric layer in terms of TS, TA, Fc and the other given parameters. Keep your expression algebraic. 3. (10 points.) Combine your answers from questions 1 and 2 to eliminate Fc. Write your new expression below. Keep your expression algebraic, and simplify your expression as much as possible. 4. (10 points.) Use equation (1) to eliminate TA from the expression you obtained in question 3. Write your new expression below, and keep your expression algebraic. 5. (10 points.) Obtain an expression that solves for Ts. To help with solving for Ts, you can use the linear approximations OTOT +40T30 (Ts - Tso), o(Ts - Tha) 4 ≈o(Tso - Th₁) 4 + 40 (Ts - Th₁)³(Ts - Tso), where Tso is a reasonable guess for Ts. Keep Tso and the rest of your expression algebraic, and simplify your sion as much as possible. 6. (5 points.) Using the given parameter values, determine a numerical value for Ts. Use the freezing temperature for water as your initial guess for the surface temperature (Tso = 273.15 K). Express your answer to two decimal places in units of K. 7. (5 points.) Use your result from question 6 as a new guess for surface temperature, and obtain a better estimate for Ts. Express your answer to two decimal places in units of K. This approach is closer to how numerical models actually calculate temperature: a complicated equation is linearized and then solved iteratively until the guess and the answer are nearly the same. 8. (5 points.) An increase in greenhouse gas concentration causes the emissivity of the atmosphere to increase to 0.97. Using your answer to question 7 as your initial guess for surface temperature, obtain a new value for Ts. Express your answer to two decimal places in units of K. Compare your answer to the answer you obtained in question 7, and comment on whether the change in T, makes sense given how you expect increasing greenhouse gas concentration to impact global mean surface temperature. 9. (5 points.) Under climate change, albedo is also expected to decrease because of melting glaciers and sea ice. If in combination with the atmospheric emissivity increasing to 0.97, the planetary albedo also decreases to 0.26, what is the new value of Ts? Use your answer to question 7 as your initial guess for surface temperature. Express your answer to two decimal places in units of K. 10. (9 points.) The Clausius-Clapeyron relation predicts that for every 1 K increase in surface temperature, assuming relative humidity and near-surface wind speeds are fixed, the evaporation from the surface will increase by approximately 7%. If the global average evaporation of water is 100 cm/year in the original climate (considered in question 7), what would be the new value of evaporation with the value of T, you obtained in question 9? Express your answer in units of cm/year rounded to the nearest 1 cm/year. 11. (9 points.) Based on your answer to question 9, what are the values of global mean precipitation for the original climate (considered in question 7) and the perturbed climate (considered in question 9)? Express your answers in units of cm/year rounded to the nearest 1 cm/year. 12. (12 points.) Assume that the global mean changes in temperature and precipitation found above are applicable to Toronto. How would these changes influence the rate of physical weathering of the Toronto sidewalk pictured below? Would the rate of physical weathering be affected by changes in other types of weathering (i.e. biological and chemical weathering)? If so how? (Picture from CBC News.)
Expert Answer:
Related Book For
Stats Data and Models
ISBN: 978-0321986498
4th edition
Authors: Richard D. De Veaux, Paul D. Velleman, David E. Bock
Posted Date:
Students also viewed these civil engineering questions
-
Which of the following had the effect of increasing income inequality? a. The increase in the female labor force participation rate b. The decrease in globalization of capital c. The increase in...
-
Evaluate the effect of increasing the downstream boundary condition water elevation by 2.0 ft in HEC-RAS?
-
Solar radiation at 600 W/m2 is absorbed by a black roof inclined at 30?C as shown. If the underside of the roof is well insulated, estimate the maximum roof temperature in 20?C air.GIVENInclined...
-
The following Excel output summarizes the results of an analysis of variance experiment in which the treatments were three different hybrid cars and the variable measured was the miles per gallon...
-
If an entity uses the percentage-of-credit-sales method of accounting for uncollectible accounts, what are the effects on the financial statements if the entity consistently uses too low a percentage...
-
Mickey gets a new prescription of a drug that she needs to take every day. The prescription is for 250 days. She takes the first pill of the new bottle on a Friday. What day of the week will her...
-
A company has total assets of \($1,200,000,\) a required rate of return of 12%, and operating income for the year was \($345,000.\) What is the companys residual income? a. $303,600 b. $345,000 c....
-
Logan Company manufactures several toy products. One is a large plastic truck, which requires a plastic truck body, two metal axles, and four rubber wheels. Logan currently manufactures and assembles...
-
If the volume of a cone is 487 and the height is 5, what is the approximate radius of the cone? 19.3 O 6.1 28.8 5.4
-
Refer to Exercise 12-25. Stanmore Corporation makes a special-purpose machine, D4H, used in the textile industry. Stanmore has designed the D4H machine for 2017 to be distinct from its competitors....
-
Lavage Rapide is a Canadian company that owns and operates a large automatic car wash facility near Montreal. The following table provides data concerning the company's costs: Cleaning supplies...
-
Bob Mendel is the chairman and founder of ABL Company - a food processing company in CalgaryThe company is a mid- size private enterprise corporation with great achievement and competitiveness within...
-
Are the actions of the TheDarkOverlord Solutions in this case (hacking into the schools district's servers and stealing data, sending threatening e-mails to students and parents, and demanding money...
-
Javon is in a 22% tax bracket for his federal income tax. If the amount of money that he paid for federal income tax was $16,060, what was his taxable income? Javon's taxable income was $ 5
-
Sheldon saw the same commercial that Leonard saw in Leonard v. Pepsico, Inc. He wanted the Pepsi leather jacket for 1,450 Pepsi pointswhich he could earn by purchasing 1,450 individual Pepsi bottles...
-
In June 1997, Matt decided to rob a store and asked Jeff to be his driver. Knowing that Matt had served time in prison on two-armed robbery convictions, and too afraid of Matt to refuse, Jeff drove...
-
Using the following information, compute the direct materials used. Raw materials inventory, January 1 Raw materials inventory, December 31 $15000 35000 Work in process, January 1 18000 Work in...
-
A number of years ago the United Food and Commercial Workers Union organized 800 workers of the 1035 employees at one of the Wilson Brothers food operations in Toronto, Ontario. The employees include...
-
A golfer keeps track of his score for playing nine holes of golf (half a normal golf round). His mean score is 85 with a standard deviation of 11. Assuming that the second 9 has the same mean and...
-
The table gives the numbers of passenger car occupants killed in accidents in 2011 by car type. Subcompact and Mini . 1351 Compact . 3789 Intermediate .. 4050 Full . 2627 Unknown . 164 Convert this...
-
The Environmental Protection Agency (EPA) tracks fuel economy of automobiles based on information from the manufacturers (Ford, Toyota, etc.). Among the data the agency collects are the manufacturer,...
-
What is the likely effect of international stock exchange listing status on the voluntary disclosures of MNEs? :
-
Discuss the kinds of information you would expect to see in the corporate review, the operations review, and the financial review sections of an MNEs directors report.
-
Discuss the relevance to financial analysts and investors of additional disclosures by MNEs with regard to corporate strategy and related issues.
Study smarter with the SolutionInn App