125 years of radiative transfer: 
enduring triumphs and persisting misconceptions 

Michael I. Mishchenko
NASA Goddard Institute for Space Studies

      The radiative transfer theory (RTT) was introduced 125 years ago by the German 
mathematician and physicist Eugene Lommel and the Russian physicists Orest Chwolson. The 
heuristic concept of radiance was formulated in 1906 by Max Planck and was supplemented by 
the seemingly obvious concept of a directional (well-collimated) radiometer. Since then, 
measurements with directional radiometers and calculations based on the radiative transfer 
equation (RTE) have been at the very heart of atmospheric radiation, remote sensing, and 
astrophysics. 
      Yet from the fundamental-physics perspective, both the discipline of directional 
radiometry and RTT have been based on phenomenological notions many of which are profound 
misconceptions. It has been demonstrated that contrary to the widespread belief, a directional 
radiometer does not, in general, measure the flow of electromagnetic energy along its axis, while 
the radiance cannot be interpreted as quantifying the amount of electromagnetic energy 
transported in a given direction. 
      It is thus fundamentally important to understand why RTT and directional radiometry 
have often ÒworkedÓ in the practical sense and determine the range of their applicability. The 
ultimate way to achieve this key objective is via a microphysical approach that is based directly 
on the Maxwell equations and clarifies the physical nature of measurements with directional 
radiometers and the physical content of RTE. This approach has recently been developed and has 
demonstrated that the radiance has no fundamental physical meaning besides being a 
mathematical solution of RTE. Only under certain circumstances can it be used to compute the 
time-averaged local Poynting vector as well as be measured by a directional radiometer. These 
firmly established facts make the combination of RTE and a directional radiometer useful in 
some well-defined circumstances and help ÒrescueÓ the majority of documented applications of 
the phenomenological RTT. However, outside the range of validity of RTT the practical 
usefulness of measurements with directional radiometers remains uncertain.   
      The purpose of this lecture is to outline the main milestones of the 125-year long history 
of radiative-transfer research (Lommel, Chwolson, Schuster, Planck, Schwarzschild, Eddington, 
Gans, Ambartsumian, Chandrasekhar, Rozenberg, Ishimaru, etc.) and the emergence of a new 
paradigm based on the direct and self-consistent use of the Maxwell equations. This paradigm 
solves the long-standing problem of establishing the fundamental physical link between RTT and 
phenomenological radiometry on one hand and the Maxwell equations on the other. It also 
establishes the link between RTT and the spectacular effect of weak localization of 
electromagnetic waves in particulate media. As a result, it becomes possible to clarify the 
physical content of measurements with directional radiometers and their relation to the solution 
of RTE. It also turns out that in many cases the reading of a directional radiometer must be 
modeled using a more sophisticated approach than RTT and that the use of directional 
radiometers in quantifying the energy budget of the EarthÕs climate system can be problematic 
and requires a detailed first-principle analysis.