Radiative Transfer Modelling
Radiative Transfer through the Earth's atmosphere is described by
the radiative transfer equation, see e.g.
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:
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
- Calculations for very low sun require a correction for the
sphericity of the Earth, a so-called pseudo-spherical or
[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.
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.
- The investigation of the effect of structured, more realistic,
clouds on the transmission, reflection, and absorption of
- The effect of inhomogeneous surface albedo, e.g., due to partial
- The influence of topography on the irradiance, e.g., for the
interpretation of measurements in valleys and on mountains.
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
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).
Radiative transfer. Oxford Univ. Press, UK, 1950.
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.
Atmospheric Radiative Transfer. A. DEEPAK Publishing, Hampton, Virginia, USA, 1993.
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.