There is interest in the prediction of the top-of-the-atmosphere (TOA) reflectance of the ocean–atmosphere system for in-orbit calibration of ocean color sensors. With the use of simulations, we examine the accuracy one could expect in estimating the reflectance ρ T of the ocean–atmosphere system based on a measurement suite carried out at the sea surface, i.e., a measurement of the normalized sky radiance ρ B and the aerosol optical thickness (τ a ), under ideal conditions—a cloud-free, horizontally homogeneous atmosphere. Briefly, ρ B and τ a are inserted into a multiple-scattering inversion algorithm to retrieve the aerosol optical properties—the single-scattering albedo and the scattering phase function. These retrieved quantities are then inserted into the radiative transfer equation to predict ρ T . Most of the simulations were carried out in the near infrared (865 nm), where a larger fraction of ρ T is contributed by aerosol scattering compared with molecular scattering, than in the visible, and where the water-leaving radiance can be neglected. The simulations suggest that ρ T can be predicted with an uncertainty typically ≲1% when the ρ B and τ a measurements are error free. We investigated the influence of the simplifying assumptions that were made in the inversion-prediction process, such as modeling the atmosphere as a plane-parallel medium, using a smooth sea surface in the inversion algorithm, using the scalar radiative transfer theory, and assuming that the aerosol was confined to a thin layer just above the sea surface. In most cases, these assumptions did not increase the error beyond ±1%. An exception was the use of the scalar radiative transfer theory, for which the error grew to as much as ~2.5%, suggesting that the use of ρ B inversion and ρ T prediction codes that include polarization would be more appropriate. However, their use would necessitate measurement of the polarization associated with ρ B . We also investigated the uncertainty introduced by an unknown aerosol vertical structure and found it to be negligible if the aerosols were nonabsorbing or weakly absorbing. An extension of the analysis to the blue, which requires measurement of the water-leaving radiance, showed significantly better predictions of ρ T because the major portion of ρ T is the result of molecular scattering, which is known precisely. We also simulated the influence of calibration errors in both the Sun photometer and the ρ B radiometer. The results suggest that the relative error in the predicted ρ T is similar in magnitude to that in ρ B (actually it was somewhat less). However, the relative error in ρ T induced by error in τ a is usually much less than the relative error in τ a . Currently, it appears that radiometers can be calibrated with an uncertainty of ~±2.5%, therefore it is reasonable to conclude that, at present, the most important error source in the prediction of ρ T from ρ B is likely to be error in the ρ B measurement.
© 1996 Optical Society of America
Original Manuscript: January 30, 1996
Revised Manuscript: June 3, 1996
Published: November 20, 1996
Howard R. Gordon and Tianming Zhang, "How well can radiance reflected from the ocean–atmosphere system be predicted from measurements at the sea surface?," Appl. Opt. 35, 6527-6543 (1996)