Speed and accuracy in theoretical radiative transfer

 
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 integro-differential 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 sub-problems, 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

 

 

 

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