Validation of shallow-water reflectance model for remote sensing of water depth and bottom type by radiative transfer simulation

Abstract Lyzenga proposed a shallow-water reflectance model that describes the exponential relationship between the remote-sensing reflectance ( R ) and water depth [ Appl. Opt. 17, 379 383 (1978)]. The model has been widely used in remote sensing of water depth to estimate the depth from R , and in remote sensing of bottom type to remove the effect of depth from R . Although it was derived from radiative transfer theory ignoring internal reflection at the water surface, no study has quantitatively validated it following the theory. In this study, we examine its accuracy under various conditions using Monte Carlo radiative transfer simulations. Although internal reflection contributed significantly to R in some cases, the model, if fitted to (calibrated with) data covering the entire target depth range, described the relationship between R and depth reasonably accurately ( R 2 > 0.9935 ). This was because the internally reflected component of R , as well as the other component, decreases exponentially with depth. However, because the sum of two exponentially decreasing functions is not strictly exponential, the model does not accurately estimate the depth using R when the calibration data did not cover the entire depth range of interest: the model significantly underestimated the depth when used for extrapolation.

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