# The Greenhouse Effect

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1 The Greenhouse Effect

2 The Greenhouse Effect Solar and terrestrial radiation occupy different ranges of the electromagnetic spectrum, that we have been referring to as shortwave and longwave.

3 The Greenhouse Effect Solar and terrestrial radiation occupy different ranges of the electromagnetic spectrum, that we have been referring to as shortwave and longwave. Water vapor, carbon dioxide and other gases whose molecules are comprised of three or more atoms absorb long waveradiation more strongly than short wave radiation.

4 The Greenhouse Effect Solar and terrestrial radiation occupy different ranges of the electromagnetic spectrum, that we have been referring to as shortwave and longwave. Water vapor, carbon dioxide and other gases whose molecules are comprised of three or more atoms absorb long waveradiation more strongly than short wave radiation. Hence, incoming solar radiation passes through the atmosphere quite freely, whereas terrestrial radiation emitted from the earth s surface is absorbed and re-emitted several times in its upward passage through the atmosphere.

5 The Greenhouse Effect Solar and terrestrial radiation occupy different ranges of the electromagnetic spectrum, that we have been referring to as shortwave and longwave. Water vapor, carbon dioxide and other gases whose molecules are comprised of three or more atoms absorb long waveradiation more strongly than short wave radiation. Hence, incoming solar radiation passes through the atmosphere quite freely, whereas terrestrial radiation emitted from the earth s surface is absorbed and re-emitted several times in its upward passage through the atmosphere. The distinction is quite striking, as shown in the following figure.

6 2

7 Exercise: Calculate the radiative equilibrium temperature of the earth s surface and atmosphere assuming that the atmosphere can be regarded as a thin layer with an absorbtivity of 0.1 for solar radiation and 0.8 for terrestrial radiation. 3

8 Exercise: Calculate the radiative equilibrium temperature of the earth s surface and atmosphere assuming that the atmosphere can be regarded as a thin layer with an absorbtivity of 0.1 for solar radiation and 0.8 for terrestrial radiation. Assume that the earth s surface radiates as a blackbody at all wavelengths. Also assume that the net solar irradiance absorbed by the earth-atmosphere system is F = 241 W m 2. 3

9 Exercise: Calculate the radiative equilibrium temperature of the earth s surface and atmosphere assuming that the atmosphere can be regarded as a thin layer with an absorbtivity of 0.1 for solar radiation and 0.8 for terrestrial radiation. Assume that the earth s surface radiates as a blackbody at all wavelengths. Also assume that the net solar irradiance absorbed by the earth-atmosphere system is F = 241 W m 2. Explain why the surface temperature computed above is considerably higher than the effective temperature in the absence of an atmosphere. 3

10 Solution: 4

11 Solution: The incoming flux of solar radiation at the top of the atmosphere is F S = 240 W m 2. 4

12 Solution: The incoming flux of solar radiation at the top of the atmosphere is F S = 240 W m 2. Since the absorbtivity for solar radiation is 0.1, the downward flux of short wave radiation at the surface is 0.9 F S. 4

13 Solution: The incoming flux of solar radiation at the top of the atmosphere is F S = 240 W m 2. Since the absorbtivity for solar radiation is 0.1, the downward flux of short wave radiation at the surface is 0.9 F S. Let F E be the long wave flux emitted upwards by the surface. 4

14 Solution: The incoming flux of solar radiation at the top of the atmosphere is F S = 240 W m 2. Since the absorbtivity for solar radiation is 0.1, the downward flux of short wave radiation at the surface is 0.9 F S. Let F E be the long wave flux emitted upwards by the surface. Since the absorbtivity for terrestrial radiation is 0.8, there results an upward flux at the top of the atmosphere of 0.2 F E. 4

15 Solution: The incoming flux of solar radiation at the top of the atmosphere is F S = 240 W m 2. Since the absorbtivity for solar radiation is 0.1, the downward flux of short wave radiation at the surface is 0.9 F S. Let F E be the long wave flux emitted upwards by the surface. Since the absorbtivity for terrestrial radiation is 0.8, there results an upward flux at the top of the atmosphere of 0.2 F E. Let F L be the long wave flux emitted upwards by the atmosphere; this is also the long wave flux emitted downwards. 4

16 Solution: The incoming flux of solar radiation at the top of the atmosphere is F S = 240 W m 2. Since the absorbtivity for solar radiation is 0.1, the downward flux of short wave radiation at the surface is 0.9 F S. Let F E be the long wave flux emitted upwards by the surface. Since the absorbtivity for terrestrial radiation is 0.8, there results an upward flux at the top of the atmosphere of 0.2 F E. Let F L be the long wave flux emitted upwards by the atmosphere; this is also the long wave flux emitted downwards. Thus, the total downward flux at the surface is 0.9 F S + F L. 4

17 Solution: The incoming flux of solar radiation at the top of the atmosphere is F S = 240 W m 2. Since the absorbtivity for solar radiation is 0.1, the downward flux of short wave radiation at the surface is 0.9 F S. Let F E be the long wave flux emitted upwards by the surface. Since the absorbtivity for terrestrial radiation is 0.8, there results an upward flux at the top of the atmosphere of 0.2 F E. Let F L be the long wave flux emitted upwards by the atmosphere; this is also the long wave flux emitted downwards. Thus, the total downward flux at the surface is 0.9 F S + F L. This must equal the upward flux from the surface: F E = 0.9 F S + F L 4

18 The upward and downward fluxes at the top of the atmosphere must also be in balance, which gives us the relation F S = 0.2 F E + F L 5

19 The upward and downward fluxes at the top of the atmosphere must also be in balance, which gives us the relation F S = 0.2 F E + F L To find F E and F L, we must solve the system of simultaneous equations F L F E = 0.9F S F L + 0.2F E = F S 5

20 The upward and downward fluxes at the top of the atmosphere must also be in balance, which gives us the relation F S = 0.2 F E + F L To find F E and F L, we must solve the system of simultaneous equations F L F E = 0.9F S F L + 0.2F E = This gives the values F E = F S = 380 W m 2 F L = F S = 164 W m 2 F S 5

21 The upward and downward fluxes at the top of the atmosphere must also be in balance, which gives us the relation F S = 0.2 F E + F L To find F E and F L, we must solve the system of simultaneous equations F L F E = 0.9F S F L + 0.2F E = This gives the values F E = F S = 380 W m 2 F L = F S = 164 W m 2 Then, for the Earth s surface, we get F S σt 4 surface = F E = 380 W m 2 5

22 The upward and downward fluxes at the top of the atmosphere must also be in balance, which gives us the relation F S = 0.2 F E + F L To find F E and F L, we must solve the system of simultaneous equations F L F E = 0.9F S F L + 0.2F E = This gives the values F E = F S = 380 W m 2 F L = F S = 164 W m 2 F S Then, for the Earth s surface, we get σt 4 surface = F E = 380 W m 2 Therefore, since σ = W m 2 K 4, we have T surface = = 286 K = +13 C 5

23 For the atmosphere we have 0.8 σt 4 atmos = 164 W m2 6

24 For the atmosphere we have 0.8 σt 4 atmos = 164 W m2 whence T atmos = = 245 K = 28 C 6

25 For the atmosphere we have 0.8 σt 4 atmos = 164 W m2 whence T atmos = = 245 K = 28 C Note that the surface temperature in this case is some 31 C higher than in the case of exercise 4.6 when there was no atmosphere: T surface = +13 C T atmos = 28 C 6

26 For the atmosphere we have 0.8 σt 4 atmos = 164 W m2 whence T atmos = = 245 K = 28 C Note that the surface temperature in this case is some 31 C higher than in the case of exercise 4.6 when there was no atmosphere: T surface = +13 C T atmos = 28 C No atmosphere: T surface = 18 C 6

27 Exercise: Consider a planet with an atmosphere consisting of multiple isothermal layers, each of which is transparent to shortwave radiation and completely opaque to longwave radiation. 7

28 Exercise: Consider a planet with an atmosphere consisting of multiple isothermal layers, each of which is transparent to shortwave radiation and completely opaque to longwave radiation. The layers are in radiative equilibrium with one another and with the surface of the planet. 7

29 Exercise: Consider a planet with an atmosphere consisting of multiple isothermal layers, each of which is transparent to shortwave radiation and completely opaque to longwave radiation. The layers are in radiative equilibrium with one another and with the surface of the planet. Show how the surface temperature of the planet is affected by the presence of this atmosphere and describe the radiative equilibrium temperature profile in the atmosphere of the planet. 7

30 Solution: 8

31 Solution: Begin by considering an atmosphere comprised of a single isothermal layer. 8

32 Solution: Begin by considering an atmosphere comprised of a single isothermal layer. The effective temperature of the planet now corresponds to the temperature of the atmosphere, which must emit F units radiation to space as a blackbody to balance the F units of incoming solar radiation. 8

33 Solution: Begin by considering an atmosphere comprised of a single isothermal layer. The effective temperature of the planet now corresponds to the temperature of the atmosphere, which must emit F units radiation to space as a blackbody to balance the F units of incoming solar radiation. Since the layer is isothermal, it also emits F units of radiation in the downward radiation. 8

34 Solution: Begin by considering an atmosphere comprised of a single isothermal layer. The effective temperature of the planet now corresponds to the temperature of the atmosphere, which must emit F units radiation to space as a blackbody to balance the F units of incoming solar radiation. Since the layer is isothermal, it also emits F units of radiation in the downward radiation. Hence, the downward radiation at the surface of the planet is F units of incident solar radiation plus F units of longwave radiation emitted from the atmosphere, a total of 2F units, 8

35 Solution: Begin by considering an atmosphere comprised of a single isothermal layer. The effective temperature of the planet now corresponds to the temperature of the atmosphere, which must emit F units radiation to space as a blackbody to balance the F units of incoming solar radiation. Since the layer is isothermal, it also emits F units of radiation in the downward radiation. Hence, the downward radiation at the surface of the planet is F units of incident solar radiation plus F units of longwave radiation emitted from the atmosphere, a total of 2F units, This must be balanced by an upward emission of 2F units of longwave radiation from the surface. 8

36 and the temperature of the atmosphere is the same as the temperature of the surface of the planet in Exercise

37 and the temperature of the atmosphere is the same as the temperature of the surface of the planet in Exercise 4.6. If a second isothermal, opaque layer is added, the flux density of radiation upon the lower layer will be 2F (F units of solar radiation plus F units of longwave radiation emitted bythe upper layer). 8

38 and the temperature of the atmosphere is the same as the temperature of the surface of the planet in Exercise 4.6. If a second isothermal, opaque layer is added, the flux density of radiation upon the lower layer will be 2F (F units of solar radiation plus F units of longwave radiation emitted bythe upper layer). To balance the incident radiation, the lower layer must emit 2F units of longwave radiation. Since the layer is isothermal, it also emits 2F units of radiation in the downward radiation. 8

39 and the temperature of the atmosphere is the same as the temperature of the surface of the planet in Exercise 4.6. If a second isothermal, opaque layer is added, the flux density of radiation upon the lower layer will be 2F (F units of solar radiation plus F units of longwave radiation emitted bythe upper layer). To balance the incident radiation, the lower layer must emit 2F units of longwave radiation. Since the layer is isothermal, it also emits 2F units of radiation in the downward radiation. Hence, the downward radiation at the surface of the planet is F units of incident solar radiation plus 2F units of longwave radiation emitted from the atmosphere, a total of 3F units, which must be balanced by an upward emission of 3F units of longwave radiation from the surface. 8

40 Radiation balance for a planetary atmosphere that is transparent to solar radiation and consists of two isothermal layers that are opaque to planetary radiation. 9

41 By induction, the above reasoning can be extended to an N-layer atmosphere. 10

42 By induction, the above reasoning can be extended to an N-layer atmosphere. The emissions from the atmospheric layers, working downward from the top, are F ; 2F ; 3F :::NF and the corresponding radiative equilibrium temperatures are 255, 303, (F/Nσ) 1/4 K. 10

43 By induction, the above reasoning can be extended to an N-layer atmosphere. The emissions from the atmospheric layers, working downward from the top, are F ; 2F ; 3F :::NF and the corresponding radiative equilibrium temperatures are 255, 303, (F/Nσ) 1/4 K. To estimate the corresponding radiative equilibrium lapse rate within the atmosphere we would need to take into account the fact that the geometric thickness of opaque layers decreases rapidly as one descends through the atmosphere owing to the increasing density of the absorbing media with depth. 10

44 By induction, the above reasoning can be extended to an N-layer atmosphere. The emissions from the atmospheric layers, working downward from the top, are F ; 2F ; 3F :::NF and the corresponding radiative equilibrium temperatures are 255, 303, (F/Nσ) 1/4 K. To estimate the corresponding radiative equilibrium lapse rate within the atmosphere we would need to take into account the fact that the geometric thickness of opaque layers decreases rapidly as one descends through the atmosphere owing to the increasing density of the absorbing media with depth. Hence, the radiative equilibrium lapse rate steepens with increasing depth. 10

45 By induction, the above reasoning can be extended to an N-layer atmosphere. The emissions from the atmospheric layers, working downward from the top, are F ; 2F ; 3F :::NF and the corresponding radiative equilibrium temperatures are 255, 303, (F/Nσ) 1/4 K. To estimate the corresponding radiative equilibrium lapse rate within the atmosphere we would need to take into account the fact that the geometric thickness of opaque layers decreases rapidly as one descends through the atmosphere owing to the increasing density of the absorbing media with depth. Hence, the radiative equilibrium lapse rate steepens with increasing depth. In effect, radiative transfer becomes less and less efficient at removing the energy absorbed at the surface of the planet due to the increasing blocking effect of the greenhouse gases. 10

46 Once the radiative equilibrium lapse rate exceeds the adiabatic lapse rate, convection becomes the primary mode of energy transfer. 11

47 Once the radiative equilibrium lapse rate exceeds the adiabatic lapse rate, convection becomes the primary mode of energy transfer. In order to perform more realistic radiative transfer calculations, it will be necessary to consider the dependence of absorptivity upon the wavelength of the radiation. 11

48 Once the radiative equilibrium lapse rate exceeds the adiabatic lapse rate, convection becomes the primary mode of energy transfer. In order to perform more realistic radiative transfer calculations, it will be necessary to consider the dependence of absorptivity upon the wavelength of the radiation. The bottom panel of Fig. 4.5 shows that the wavelength dependence is quite pronounced, with well defined absorption bands identified with specific gaseous constituents, interspersed with windows in which the atmosphere is relatively transparent. 11

49 Evaporation The above models are greatly simplified. 12

50 Evaporation The above models are greatly simplified. They assume pure radiative balance. 12

51 Evaporation The above models are greatly simplified. They assume pure radiative balance. In fact, the main process balancing incoming solar radiation at the earth s surface is evaporation. 12

52 Evaporation The above models are greatly simplified. They assume pure radiative balance. In fact, the main process balancing incoming solar radiation at the earth s surface is evaporation. The water evaporated from the ocean is carried upward by convection. 12

53 Evaporation The above models are greatly simplified. They assume pure radiative balance. In fact, the main process balancing incoming solar radiation at the earth s surface is evaporation. The water evaporated from the ocean is carried upward by convection. The moisture reaches levels above the main infra-red absorbers. 12

54 Evaporation The above models are greatly simplified. They assume pure radiative balance. In fact, the main process balancing incoming solar radiation at the earth s surface is evaporation. The water evaporated from the ocean is carried upward by convection. The moisture reaches levels above the main infra-red absorbers. The latent heat is then released by condensation, from where much of it radiates to space. 12

55 End of

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