Chapter 2 - Basic State Variables and the Radiative Transfer Equation

Summary

Introduction

In this book we are mostly concerned with the flow of radiative energy through atmospheres and oceans. We will ignore polarization effects, which means that we disregard the Q, U, and V components of the Stokes vector and consider only the first (intensity) component I. This approach is known as the scalar approximation, in contrast to the more accurate vector description. In general, this approximation is valid for longwave radiation where thermal emission and absorption dominate scattering processes. However, at shorter wavelengths where scattering is important, the radiation is generally partially polarized. For example, polarization is a basic part of a description of scattering of sunlight in a clear atmosphere or in pure water (so-called Rayleigh scattering). Generally, a coupling occurs between the various Stokes components, and an accurate description requires the full Stokes vector representation.

Of central importance in the theory is the scalar intensity, which plays as central a role in radiative transfer theory as the wave function plays in quantum theory. Its full specification as a function of position, direction, and frequency variables conveys all of the desired information about the radiation field (except for polarization).

In this chapter, we define the basic state variable of the theory, the scalar intensity. We first review the most basic concepts of geometrical optics, those of pencils and beams of light. We then define the various state variables in a transparent medium, involving flow of radiative energy in beams traveling in specific directions and over a hemisphere.