Theory of the optical properties of lake ice

A radiative transfer model is developed to illustrate the processes which determine the spectral albedo and transmission of lake ice. The calculated spectral albedo is dominated by specular reflection from the ice surface in the near infrared, whereas multiple scattering by bubbles below the surface dominates the visible albedo. Adding a snow cover to lake ice will normally increase the visible albedo, but may reduce the albedo in some regions of the near infrared if the sun is low, by reducing the specular reflection. In a preliminary test of the model, spectral albedo was measured on the natural ice cover of a frozen lake. The measurements are explained using the radiative transfer model applied to the air bubble size distribution measured in the same ice. The uncertainty in measurement of bubble size distribution leads to uncertainty in the theoretical albedo which is much larger than the error due to approximations used in derivation of the model.