Self-shading correction for oceanographic upwelling radiometers.

We present the derivation of an analytical model for the self-shading error of an oceanographic upwelling radiometer. The radiometer is assumed to be cylindrical and can either be a profiling instrument or include a wider cylindrical buoy for floating at the sea surface. The model treats both optically shallow and optically deep water conditions and can be applied any distance off the seafloor. We evaluate the model by comparing its results to those from Monte Carlo simulations. The analytical model performs well over a large range of environmental conditions and provides a significant improvement to previous analytical models. The model is intended for investigators who need to apply self-shading corrections to radiometer data but who do not have the ability to compute shading corrections with Monte Carlo simulations. The model also can provide guidance for instrument design and cruise planning.