Radiation transport in cloudy and aerosol loaded atmospheres

Kylling, Arve

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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, CO₂ and O₃, vary erratically and rapidly with wavelength. To account for this variation, the correlated-𝘬 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, UV-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 atmospheres, and atmospheres with cirrus and water clouds. After major volcanic explosions aerosols change O₃ and NO₂ 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. Solar 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.

Description

UAG R-319; Thesis presented to the faculty of the University of Alaska Fairbanks in partial fulfillment of the requirements for the degree of Doctor of Philosophy; December 1992.

Abstract -- List of figures -- List of tables -- Acknowledgements -- 1. Introduction --- 2. Radiation transport in the earth’s atmosphere – 2.1. The radiative transfer equation – 2.1.1. Spherical geometry – 2.1.2. The streaming term pertinent to the calculation of mean intensities – 2.1.3. The source term – 2.1.4. The one dimensional radiative transfer equation – 2.1.5. Layering of the atmosphere – 2.2. Discrete ordinate solution – 2.2.1. Homogeneous solution – 2.2.2. Inhomogeneous solution – 2.2.3. Boundary conditions – 2.3. Verification of the solution method – 2.3.1. Results pertinent to the mono-directional beam pseudo-source – 2.4. Summary -- 3. Optical properties of the atmosphere – 3.1. Molecular absorption of radiation – 3.1.1. The Schrödinger equation – 3.1.2. First-order perturbation theory – 3.1.3. Fermi’s golden rule – 3.1.4. The Hamiltonian and the absorption rate – 3.1.5. The absorption cross section in the electric dipole approximation – 3.1.6. The correlation function and the fluctuation-dissipation theorem – 3.1.7. Impact approximation and the Lorentz line shape – 3.1.8. Doppler broadening and the Voigt function – 3.1.9. The HITRAN database and line-by-line calculation - 3.1.10. The correlated-𝘬 distribution method – 3.2. The absorption and scattering of light by small particles – 3.2.1. Maxwell equations for periodic fields – 3.2.2. Solutions to the vector wave equations – 3.2.3. Solutions of coefficients from boundary conditions – 3.2.4. Cross sections – 3.2.5. An approximate scheme for Mie theory calculations for water clouds – 3.2.6. Rayleigh scattering – 3.3. Summary -- 4. Photodissociation rates – 4.1. The continuity equation and photochemical processes – 4.1.1. Definition of the photodissociation rate – 4.2. The solar spectrum, cross sections and quantum yields – 4.3. Comparison of the radiation transport model with experiment – 4.3.1. Model description – 4.3.2. Model results and discussion – 4.3.3. Summary of comparison of radiation model with experiment – 4.4. Calculation of photodissociation rates – 4.4.1. The accuracy of photodissociation rates with number of streams – 4.4.2. The importance of spherical geometry in twilight conditions – 4.5. Summary -- 5. Biologically active radiation, water cloud effects – 5.1. Introduction – 5.2. Model description – 5.3. Results and discussion – 5.3.1. UV-B, UV-A and PAR fluxes – 5.3.2. UV-B/PAR, UV-A/PAR and UV-B/UV-A ratios – 5.3.3. Daily UV-B, UV-A and PAR irradiances – 5.4. Summary -- 6. Warming/cooling rates – 6.1. Definition of warming/cooling rates – 6.2. Cooling rates – 6.2.1. Sample calculation, CO₂ in the 5000-5050 cm⁻¹ region – 6.2.2. H₂O cooling rate – 6.2.3. CO₂ cooling rate – 6.2.4. O₃ cooling rate – 6.2.5. Note on the correlated-𝘬 distribution method – 6.3. Warming rates – 6.3.1. O₃, O₂ and NO₂ warming rates – 6.3.2. H₂O warming rate – 6.4. Summary -- 7. The radiative effects of clouds and aerosols – 7.1. Cloud and aerosol models – 7.1.1. Water cloud model – 7.1.2. Cirrus cloud model – 7.1.3. Aerosol models – 7.2. Photodissociation rates – 7.2.1. Surface albedo effects – 7.2.2. The effects of clouds and aerosols – 7.3. Warming/cooling rates – 7.3.1. Surface albedo effects – 7.3.2. The effects of clouds and aerosols – 7.4. The radiative effects of clouds and aerosols on chemistry and dynamics – 7.5. Summary -- 8. Summary and suggestions for further work -- A. The existence of the α coefficient for thermal radiation.

Date

1992-12

Type

Report

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GI Reports