Radiative Transfer Modelling

Radiative Transfer through the Earth's atmosphere is described by the radiative transfer equation, see e.g. [Chandrasekhar, 1950], [Lenoble, 1993]. Various solvers are freely available to date, and there is general agreement that the equation of radiative transfer can be solved with state-of-the art models to an accuracy of 1% or better. The basic uncertainty is the parameterization of the input data, ranging from an appropriate description of the atmosphere over the reflectivity of the Earth's surface, to the extraterrestrial irradiance and its variations.

Different applications require different radiative transfer solvers. Mainly due to constraints of computational time, there is no radiative transfer model which would be able to answer all possible questions in a reasonable way. E.g., for calculations in a cloudless sky atmosphere, or for the special case of horizontally homogeneous clouds, a one-dimensional radiative transfer model like e.g. DISORT [Stamnes et al., 1988] is sufficient. But even for one-dimensional atmospheres, more complex models are required for certain applications, for example:

Calculations for very low sun require a correction for the sphericity of the Earth, a so-called pseudo-spherical or fully-spherical correction [Dahlback and Stamnes, 1991]. This requirement may also be necessary for sky radiance calculations even at high sun.
The accurate calculation of sky radiance requires the consideration of polarization by the model which is not taken into account by scalar models like DISORT.
Inelastic (Raman-) Scattering, the so-called Ring-Effect, has to be taken into account when the fine structure of the solar spectrum is of interest.
Even with nowadays computers, most chemistry models and all climate models cannot afford to solve the equation of radiative transfer exactly. They still depend on approximations like a two- or four-stream method.

The situation becomes even more complicated (and thus more interesting) when two- or three-dimensional effects are investigated. Possible applications for a three-dimensional model are

The investigation of the effect of structured, more realistic, clouds on the transmission, reflection, and absorption of radiation.
The effect of inhomogeneous surface albedo, e.g., due to partial snow cover.
The influence of topography on the irradiance, e.g., for the interpretation of measurements in valleys and on mountains.

For each of these applications, special models have been developed. From all today's model types, a forward Monte-Carlo model which traces individual photons through the atmosphere can probably consider the most of these requirements at the same time (like 3-D clouds, inhomogeneous surface albedo, topography, and polarization). If an average of the irradiance over a large enough area is requested, the Monte Carlo solution even works at a reasonable speed. If, on the other hand, sky radiance as a function of location is required, a different solver like e.g. SHDOM should be preferred due to its much better performance for such applications.

For the calculations in my PhD-thesis which focussed on cloudless sky, a one-dimensional model like DISORT was the appropriate solution. To be of real use, however, each radiative transfer solver requires a front-end which translates the measurable properties of the atmosphere (total ozone, aerosol properties, profiles of ozone, temperature, and pressure, etc.) into the optical properties which are required as input to the model (profiles of optical depth, single scattering albedo, and the phase function). UVSPEC by Arve Kylling, which became freely available at that time, provides a convenient way to do this. During my PhD studies I wrote a front-end for UVSPEC which allowed to use the measured atmospheric properties to simulate the spectra measured by the spectroradiometer. This resulted in a joint publication with Arve Kylling, [Mayer et al., 1997] and a completely new version of UVSPEC, now called libRadtran (library for Radiative transfer).

References

1: Chandrasekhar, S.
Radiative transfer. Oxford Univ. Press, UK, 1950.
2: Dahlback, A. and K. Stamnes.
A new spherical model for computing the radiation field available for photolysis and heating at twilight. Planet. Space Sci., 39, 671-683, 1991.
3: Lenoble, J.
Atmospheric Radiative Transfer. A. DEEPAK Publishing, Hampton, Virginia, USA, 1993.
4: Stamnes, K. S.C. Tsay, W. Wiscombe, and K. Jayaweera.
A Numerically Stable Algorithm for Discrete-Ordinate-Method Radiative Transfer in Multiple Scattering and Emitting Layered Media. Applied Optics, 27, 2502-2509, 1988.