## Abstract

An analysis of the errors due to multiple scattering which are expected to be encountered in application of the current Coastal Zone Color Scanner (CZCS) atmospheric correction algorithm is presented in detail. This was prompted by the observations of others that significant errors would be encountered if the present algorithm were applied to a hypothetical instrument possessing higher radiometric sensitivity than the present CZCS. This study provides CZCS users sufficient information with which to judge the efficacy of the current algorithm with the current sensor and enables them to estimate the impact of the algorithm-induced errors on their applications in a variety of situations. The greatest source of error is the assumption that the molecular and aerosol contributions to the total radiance observed at the sensor can be computed separately. This leads to the requirement that a value *∊*′(λ,λ_{0}) for the atmospheric correction parameter, which bears little resemblance to its theoretically meaningful counterpart, must usually be employed in the algorithm to obtain an accurate atmospheric correction. The behavior of *∊*′(λ,λ_{0}) with the aerosol optical thickness and aerosol phase function is thoroughly investigated through realistic modeling of radiative transfer in a stratified atmosphere over a Fresnel reflecting ocean. A unique feature of the analysis is that it is carried out in scan coordinates rather than typical earth–sun coordinates allowing elucidation of the errors along typical CZCS scan lines; this is important since, in the normal application of the algorithm, it is assumed that the same value of *∊*′ can be used for an entire CZCS scene or at least for a reasonably large subscene. Two types of variation of *∊*′ are found in models for which it would be constant in the single scattering approximation: (1) variation with scan angle in scenes in which a relatively large portion of the aerosol scattering phase function would be examined by the sensor in the single scattering approximation and (2) variation with aerosol optical thickness in a manner that increases with increasing solar zenith angle. In the worst case examined, the error associated with the variation of *∊*′ with scan angle was found to be 2.7–5.4 counts in Band 1 (depending on the turbidity of the atmosphere) for a marine aerosol, while the error associated with the variation of *∊*′ with aerosol optical thickness was at most 3 counts but would be reduced to negligible values when *∊*′ could be determined in regions of high aerosol optical thickness. Since the water-leaving radiance must be determined with an accuracy of ≈1–2 digital counts for maximum usefulness, these worst-case errors indicate that typically the algorithm will perform with the required accuracy in the case of CZCS, if limited to subscenes which are not too large. However, since for a variety of reasons it is highly desirable to be able to estimate the value of *∊*′ at each pixel, computations were performed to determine how accurately the algorithm would perform in retrieving the water-leaving radiance in the blue, assuming that it was known in the green and red. It is found that the simple expediency of decreasing the derived value of *∊*′ in the blue by 5% was sufficent to decrease the error in the retrieved water-leaving radiance to <2 counts for a variety of aerosol phase functions and aerosol optical thicknesses (including mildly absorbing aerosols) and for several orbit geometries. Thus we conclude that in situations where *∊*′ can be estimated at each pixel, this modification will result in water-leaving radiances with the desired accuracy in most cases.

© 1987 Optical Society of America

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