Radiative Transfer Modeling in the Cryosphere

Radiative transfer (RT) modeling plays a key role in interpreting the radiance measured by multispectral sensors. Glaciers respond to variations in solar irradiance. At-sensor radiance depends upon glacier surface material composition and intermixture of materials, solar and sensor geometry, and surface topography. To bridge the gap between investigative findings and spectral data, a physically based (i.e., based on first principles) linkage between properties of the observed surface and the measured electromagnetic signal should be established. Complementing the treatment of related subjects in Chap. 2 of this book by Bishop et al., in this chapter we show how RT theory can be adapted to derive radiative transfer equations (RTEs) that are commonly employed to properly describe the radiative field within, at the surface of, and above glaciers, debris fields, and glacier lakes. RTEs are derived using the basic principle of conservation of photons and are simplified to obtain equations that are more mathematically tractable. Such equations are numerically solved to compute quantities that are of interest in remote sensing (e.g., bidirectional reflectance factor, BRF, and spectral albedo) that are a function of the optical properties of the observed surface. Accurate modeling of the optical properties of single-material particles (e.g., ice or snow, water, lithic debris, and carbon soot) is critical to obtaining meaningful and accurate RT calculations. The common methods employed to determine single-scattering albedo and scattering phase function, for both single-type particles and mixtures, are discussed. In addition, although the basic conservation of photons holds for both glaciers and glacier lake water, we have marked a clear distinction between the equation of transfer for glacier surfaces and glacier lake water, as well as between the methods employed to describe their optical properties. The chapter also provides examples of RT-based calculations for both BRF and spectral albedo in scenarios typically found in the cryosphere. Five simulation sets show how remotely measurable quantities depend on the morphological and mineralogical properties of the medium (e.g., BRF for mixtures of snow and debris; spectral albedo variation for snow and carbon soot with varying grain size and particle concentration; and spectral variation of glacier lake water reflectance as a function of rock “flour” concentration).