
Actinic
flux versus altitude for ‘truth’, linear interpolation
of the coarsest layering and quadratic interpolation 
The propagation
of electromagnetic radiation through the atmosphere, or neutrons
in a reactor, is described by the equation of radiative transfer.
This is an integrodifferential equation, and provides special challenges
in theoretical physics. Because the relevant “input parameters”
such as atmospheric composition, sun angle, and surface properties
are so variable, it needs to be solved millions of times around
the world for such tasks as climate modelling and atmospheric remote
sensing. This places a very high premium on computational algorithms
which are both fast and accurate.
Members of the
Atmospheric Physics group specialize in this challenge, and have
recently made a number of significant contributions. We have shown
how to make use of some information which is produced in standard
algorithms to increase the accuracy of vertical profiles of heating
rates, at no extra cost in time. We have also shown how to decompose
the lidar problem, the propagation and reflection of a laser pulse,
into two simpler subproblems, and improve both speed and accuracy
in many situations.

Direct
and diffuse radiation within a plane parallel atmosphere. 
Perhaps the
most exciting development of all is the work on the Green’s
function, which is the solution of the equation for all possible
sources of radiation. Recent theoretical analysis has led to the
creation of a computer code which computes the Green’s function
in essentially the time required to solve the equation for just
a single source. This truly is a quantum leap in efficiency and
power. Algorithms are now being developed to break some important
radiative transfer problems into smaller pieces, compute the Green’s
function of each piece, and then put the pieces together in far
more flexible ways.
Igor
Polonsky, Merlinde Kay,Yi Qin and Michael Box
