The world's coral reefs are a particularly sensitive indicator of global climate change, and are also adversely impacted by human activity. To further the goal of mapping and monitoring coral reef distribution and health worldwide, we have carried out a radiative transfer study to demonstrate the feasibility of remote sensing with existing satellite platforms (LANDSAT) and with a proposed instrument that would be optimized for this work. The study uses a discrete-ordinates radiative transfer model with a coupled atmosphere and ocean. The model contains a rigorous angular redistribution function to correct for the Fresnel interface between the two media. The model atmosphere is appropriate for the tropics, and includes a maritime background aerosol loading. The model ocean uses light attenuation coefficients that are appropriate for clear natural waters, and treats the reflecting coral reef as a Lambertian lower boundary at a specified depth, with spectral reflectance from field work. Two measured coral reflectance spectra are used, from samples of Montastrea cavernosa and Acropora palmata. The measured spectral signatures of sand and coralline algae are also used. This study shows that it is possible to distinguish between living coral and sand or algae using the Thematic Mapper, to a depth of at least 5 meters. To distinguish between coral species, better results are obtained by using narrower spectral intervals that are chosen for this purpose. The use of optimized spectral channels also increases the water column depth over which coral reef remote sensing is feasible. In addition, if an instrument specifically designed for coral reef remote sensing is placed on a low inclination rather than a polar orbit, a much larger number of coral reef scenes would be available within a given timeframe.