Radiation transport in cloudy and aerosol loaded atmospheres Item Type Thesis Authors Kylling, Arve Download date 04/10/2021 15:20:36 Link to Item http://hdl.handle.net/11122/9381 INFORMATION TO USERS This manuscript has been reproduced from the microfilm master. UMI films the text directly from the original or copy submitted. Thus, some thesis and dissertation copies are in typewriter face, while others may be from any type of computer printer. The quality of this reproduction is dependent upon the quality of the copy submitted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleedthrough, substandard margins, and improper alignment can adversely affect reproduction. In the unlikely event that the author did not send UMI a complete manuscript and there are missing pages, these will be noted. Also, if unauthorized copyright material had to be removed, a note will indicate the deletion. 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Order Number M25174 Radiation transport in cloudy and aerosol loaded atmospheres Kylling, Arve, Ph.D. Univertity of Alwka F urbish, 1992 UMI 300 N. Zccb Rd. Ann Aibor, MI 48106 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. RADIATION TRANSPORT IN CLOUDY AND AEROSOL LOADED ATMOSPHERES A THESIS Presented to the Faculty of the University of Alaska Fairbanks in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY By Arve Kylling , Cand. Scient. Fairbanks, Alaska December 1992 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. RADIATION TRANSPORT IN CLOUDY AND AEROSOL LOADED ATMOSPHERES by Arve Kylling RECOMMENDED: APPROVED: Di. Paul 6 . Reichardt, Dean, College of Natural Sciences f- J ttn u_________________________________________ l _____________________________ Dr. Edward C. Murphy, Chancellpr’s Faculty Associate for Graduate Studies II b&ksYi'hv M 2 - ___________________ Date Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Abstract The equation for radiation transport in vertical inhomogeneous absorbing, scattering, and emitting atmospheres is derived from first principles. It is cast in a form amenable to solution, and solved using the discrete ordinate method. Based on the discrete ordinate solution a new computationally efficient and stable two-stream algorithm which accounts for spherical geometry is developed. The absorption and scattering properties of atmospheric molecules and particulate matter is discussed. The absorption cross sections of the principal absorbers in the atmosphere, H2O, CO3 and O3, vary erratically and rapidly with wavelength. To account for this variation, the correlated-A distribution method is employed to simplify the integration over wavelength necessary for calculation of warming/cooling rates. The radiation model, utilizing appropriate absorption and scattering cross sections, is compared with ultraviolet radiation measurements. The comparison suggests that further experiments are required. Ultraviolet (UV) and photosynthetically active radiation (PAR) is computed for high and low latitudes for clear and cloudy skies under different ozone concentrations. An ozone depletion increases UV-B radiation detrimental to life. Water clouds diminish UV-B, U V-A and PAR for low surface albedos and increase them for high albedos. The relative amount of harmful UV-B increases on overcast days. The daily radiation doses exhibit small monthly variations at low latitudes but vary by a factor of 3 at high latitudes. Photodissociation and warming/cooling rates are calculated for clear skies, aerosol loaded at­ mospheres, and atmospheres with cirrus and water clouds. After major volcanic explosions aerosols change O 3 and NOj photodissociation rates by 20%. Both aged aerosols and cirrus clouds have little effect on photodissociation rates. Water clouds increase (~ 100%) photodissociation rates that are sensitive to visible radiation above the cloud. Solax warming rates vary by 50% in the stratosphere due to changing surface albedo. Water clouds have a similar effect. The net effect of cirrus clouds is to warm the troposphere and the stratosphere. Only extreme volcanic aerosol loadings affect the terrestrial warming rate, causing warming below the aerosol layer and cooling above it. Aerosols give increased solar warming above the aerosol layer and cooling below it. iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Contents Abstract.................................................................................................................................................. iii List of F ig u r e s ...................................................................................................................................... viii List of T a bles ......................................................................................................................................... xvi Acknowledgements................................................................................................................................... xvii 1 Introduction..................................................................................................................................... 1 2 Radiation transport in the earth’s atmosphere ...................................................................... 6 2.1 The radiative transfer eq u a tion .......................................................................................... 6 2.1.1 Spherical geom etry................................................................................................... 7 2.1.2 The streaming term pertinent to the calculation of mean intensities .... 10 2.1.3 The source t e r m ...................................................................................................... 12 2.1.4 The one dimensional radiative transfer equation ............................................... 13 2.1.5 Layering of the atm osphere................................................................................... 15 2.2 Discrete ordinate s o lu tio n ................................................................................................... 15 2.2.1 Homogeneous solu tion ............................................................................................ 16 Homogeneous solution in the two-stream approximation....................... 18 2.2.2 Inhomogeneous solu tio n ......................................................................................... 19 Inhomogeneous exponential-linear solution in the two-stream approx­ imation......................................................................................... 23 The g, X o(/m) and ■X'i(Mi) coefficients in Eq. 2 .5 4 .................................. 24 2.2.3 Boundary conditions................................................................................................ 25 2.3 Verification of the solution m e th o d .................................................................................... 27 2.3.1 Results pertinent to the mono-directional beam pseudo-source ...................... 27 2.4 S u m m a ry................................................................................................................................ 28 3 Optical properties of the atmosphere ...................................................................................... 30 iv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V 3.1 Molecular absorption of radiation........................................................................................ 31 3.1.1 The Schrddinger eq u a tion ....................................................................................... 31 3.1.2 First-order perturbation theory ............................................................................... 32 3.1.3 Fermi’s golden rule ...................................................................................................... 33 3.1.4 The Hamiltonian and the absorption r a te ............................................................ 34 3.1.5 The absorption cross section in the electric dipole approxim ation................. 35 3.1.6 The correlation function and the fluctuation-dissipation theorem .................. 37 3.1.7 Impact approximation and the Lorentz line shape..............................................