Limitations of triple-angle radiometric geosurface measurements from high altitude to mitigate low-absorption atmospheric effects

The remote measurement of geosurface radiances using microwave and thermal infrared radiometers from satellite platforms has been an attractive and challenging goal. A significant impediment is data corruption by the intervening atmosphere. Attempts to correct for the atmosphere apparently have not been reported at microwave frequencies, but have been addressed at thermal infrared wavelengths. For thermal infrared, papers have been written reporting on multi-spectral and multi-angle measurements to infer the absolute value of geosurface temperature. A dual-angle radiometric technique to measure sea-surface temperature from an aircraft has been reported by Saunders. His technique made measurements at zenith angles near 0° and 60°, and the reported absolute accuracies are 0.2 degree C. Since the path length was short with small path loss and insignificant path radiance, two unknowns are involved and measurements at two angles were sufficient for solution. As the platform altitude is increased, the number of significant factors increases, such as upwelling radiance from a lossy atmosphere and downwelling radiance scattered from the surface. With an increase in the number of significant factors, the number of independent measurements must also increase for solution. In this paper, an attempt is made to examine the utility of a triple-angle measurement method on the same area or pixel to extend the earlier dual-angle measurement technique. It is assumed that the next significant factor for some examples maybe the radiance from the intervening path. The purposes of the present approximate analysis are to quantify the surface radiance and its uncertainty due to measurement limitations. It is believed that there are scenarios within limited latitudinal zones, local times, and seasons where the assumed path characteristics are reasonably valid, and the error would be a small bias term to the calculated values