Thermal Physics of the Atmosphere

Thermal Physics of the Atmosphere

Volumn , Issue , 2010, Pages

  Ambaum, Maarten H P ^a  

^a UNIVERSITY OF READING   (United Kingdom)

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EID: 84891583960     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1002/9780470710364     Document Type: Book

References (68)

1. Adkins, C. J. (1983) Equilibrium Thermodynamics, 3rd edn. Cambridge University Press, Cambridge.
2. Kittel, C. & Kroemer, H. (1980) Thermal Physics, 2nd edn. W. H. Freeman, New York.
3. SI stands for Systéme International d'Unitès, the internationally agreed system of units for physical quantities.
4. The number N of thermodynamic variables required to define the state of any system is given by the Gibbs' phase rule, N = 2 + C-P, with C the number of independent constituents and P the number of coexisting phases (gas, liquid, solid) in the system.
5. Not all available degrees are necessarily accessible. Quantization of energy levels implies that there is a minimum energy required to excite any degree of freedom.
6. In a more formal treatment of thermodynamics, temperature is defined to be the quantity that indicates the direction of spontaneous heat flow; so heat will flow by definition from high to low temperatures. See Baierlein, R. (1999) Thermal Physics. Cambridge University Press, Cambridge.
7. See also Kondepudi, D. & Prigogine, I. (1998) Modern Thermodynamics. J. Wiley & Sons, Chichester.
8. Fermi, E. (1956) Thermodynamics. Dover, New York.
9. A popular account is in Ruelle, D. (1991) Chance and Chaos. Princeton University Press, Princeton.
10. Although the expansion is not a reversible process, we can in principle link the initial and final state with a reversible process and thus calculate the change in state variables between the initial and final states.
11. This problem is solved in quantum mechanics, where the phase space available to molecules is made up of elementary volumes with a size equal to Planck's constant, h.
12. The configuration freedom of a system can be quantified by its information entropy, as defined by Claude Shannon. Edwin Jaynes showed how Shannon's information entropy maps onto the thermodynamic entropy we use here. See Shannon, C. E. (1948) Bell System Technical Journal 27, 379-423, 623-656
13. Jaynes, E. T. (1957) Physical Review 4, 620-630
14. Jaynes, E. T. (1965) American Journal of Physics 33, 391-398. See also Problem 4.8.
15. A monoatomic molecule is made of one atom and a diatomic molecule is made of two atoms.
16. See, for example, Kittel, C. & Kroemer, H. (1980). Thermal physics, 2nd edn. W. H. Freeman, New York.
17. The expression Uρh is really a flux density, that is, a flux per unit area. Here, and throughout the rest of this book, we will use the term 'flux' to mean either 'total flux' or 'flux density', depending on the context.
18. See Lewis, J. M. (1995) Bull. Am. Met. Soc. 76, 2433-2443.
19. Ambaum, M. H. P. (2008) Proc. Roy. Soc. A 464, 943-950.
20. For moist air, we need to replace the temperature in these equations by the virtual temperature, see Section 1.3.
21. Because in dynamic meteorology applications only gradients of the Montgomery function play a role, we normally use the dry static energy, Eq. 4.51, instead of the generalized enthalpy to define the Montgomery function for the atmosphere.
22. Tolman, R. C. (1918) Phys. Rev. 11, 261-275.
23. This requires the cylinder to be below the critical temperature, the temperature above which the gas and liquid phases become indistinguishable and no phase separation can occur no matter how high the pressure is. The critical temperature for water is 647 K.
24. This version of Tetens' formula was published in Bolton, D. (1980) Mon. Wea. Rev. 108, 1046-1053.
25. The effects of global warming on water vapour and the hydrological cycle are discussed in Boer, G. J. (1993) Clim. Dynam. 8, 225-239; Allen, M. R. & Ingram, W. J. (2002) Nature 419, 224-232; Held, I. M. & Soden, B. J (2006) J. Clim. 19, 5686-5699.
26. Pseudo-adiabatic processes are somewhat artificial for descending parcels: this would require the external provision of just enough liquid water at the right temperature to keep the parcel saturated.
27. Emanuel, K. (1994) Atmospheric convection. Oxford University Press, Oxford.
28. For accurate expressions for the wet-bulb potential temperature see Bolton, D. (1980) Mon. Wea. Rev. 108, 1046-1053.
29. In these arguments we use virtual temperature, but note that the tephigram only shows temperatures.
30. See Renno, N. O. & Ingersoll, A. P. (1996) J. Atmos. Sci. 53, 572-585.
31. The Kóhler curve itself is a weak function of temperature. However, this does not change the main argument here.
32. For a derivation of the onset of Rayleigh explosions, see Peters, J. M. H. (1980) Eur. J. Phys. 1, 143-146.
33. There is an asymmetry between positively charged ions and negatively charged ions: positively charged ions require a relative humidity of about 600%; this is presumably due to the geometry of water molecules. See Wilson, C. T. R. (1899) Proc. Roy. Soc. London 65, 289-290.
34. See Westbrook, C. D. et al. (2008) J. Atmos. Sci. 65, 206-219.
35. For further reading on cloud physics, see Mason, B. J. (1971) The physics of clouds, 2nd edn. Oxford University Press, Oxford;
36. Rogers R. R. & Yau, M. K. (1989) A short course in cloud physics, 3rd edn. Butterworth-Heinemann;
37. Pruppacher, H. R. & Klett, J. D. (1997) Microphysics of clouds and precipitation, 2nd edn. Kluwer, Dordrecht.
38. There are quite a few specialized texts on atmospheric radiation. Notable examples are Goody R. M. & Yung, Y. L. (1989) Atmospheric radiation. Theoretical basis, 2nd edn. Oxford University Press Oxford;
39. Petty, G. W. (2004) A first course in atmospheric radiation Sundog Publishing, Madison.
40. See Trenberth, K. E., Fasullo, J. T. and Kiehl, J. (2009) Bull. Am. Meteor. Soc. 90, 311-324.
41. For further reading, see James, I. N. (1995) Introduction to circulating atmospheres. Cambridge University Press, Cambridge.
42. See Manabe, S. & Strickler, R. F. (1964) J. Atmos. Sci. 21, 361-385;
43. Manabe, S. & Wetherald, R. T. (1967) J. Atmos. Sci. 24, 241-259
44. Optical depth is also often given the symbol.
45. The value of the reference irradiance Sr does not modify the outcome of the fit but does change the graphical representation of the data. The default choice of 1Wm-2 misrepresents the scatter in the data; it is better to choose Sr to be similar to S0 or typical values of Sb.
46. For more comprehensive model calculations of radiative-convective equilibrium, see Manabe, S. & Wetherald, R. T. (1967) J. Atmos. Sci. 24, 241-259;
47. Ramanathan V. & Coakley, J. A. (1978) Rev. Geoph. Space Phys. 16, 465-489
48. The present derivation is partly based on Adkins, C. J. (1983) Equilibrium thermodynamics, 3rd edn. Cambridge University Press, Cambridge.
49. We can add a constant S0 to the total entropy S by adding S0/V to the entropy density s̃ and still satisfy Eq. 9.87. By the third law, this constant is zero.
50. We have assumed that the radiation remains black during the compression.
51. For further reading see Kittel C. & Kroemer, H. (1980) Thermal physics 2nd edn. W. H. Freeman, New York;
52. Baierlein, R. (1999) Thermal physics Cambridge University Press, Cambridge.
53. The argument presented here is not complete in quantum mechanics as we ignore the ground level of each wave mode. However, this does not change the phase space density gK, which is the purpose of the quantization presented here.
54. Here we restrict ourselves to atmospheric applications. More general treatments can be found in De Groot, S. R. &
55. Mazur, P. (1984) Non-equilibrium thermodynamics. Dover, New York;
56. Woods, L. C. (1975) The thermodynamics of fluid systems. Oxford University Press, Oxford.
57. See Vallis, G. K. (2006) Atmospheric and oceanic fluid dynamics. Cambridge University Press, Cambridge;
58. Kuhlbrodt, T. (2008) Tellus 60A, 819-836.
59. See Dutton, J. A (1995) Dynamics of atmospheric motion. Dover, New York.
60. See Kondepudi, D. & Prigogine, I. (1998) Modern Thermodynamics J. Wiley & Sons, Chichester.
61. See Trenberth, K. E., Fasullo, J. T. and Kiehl, J. (2009) Bull. Amer. Meteor. Soc. 90, 311-324.
62. See Pascale et al., (2010) Clim. Dyn., doi: 10.1007/s00382-009-0781-1.
63. Paltridge, G. W. (1975) Quart. J. Roy. Met. Soc. 101, 475-484;
64. Ozawa, H. et al. (2003) Rev. Geoph. 41(4), 1-24;
65. Kleidon, A. & Lorenz, R., eds. (2005) Non-equilibrium thermodynamics and the production of entropy. Springer, Berlin.
66. There are various synonyms for exergy. The most commonly encountered synonym is availability, hence the symbol A.
67. See Bejan, A. (2006) Advanced Engineering Thermodynamics, 3rd edn. J. Wiley & Sons, Hoboken.
68. Accurate equations used to construct pseudo-adiabats are given in Bolton, D. (1980) Mon. Wea. Rev. 108, 1046-1053.