Simulation-based investigation of the generality of Lyzenga's multispectral bathymetry formula in Case-1 coral reef water

Lyzenga's multispectral bathymetry formula has attracted considerable interest due to its simplicity. However, there has been little discussion of the effect that variation in optical conditions and bottom types—which commonly appears in coral reef environments—has on this formula's results. The present paper evaluates Lyzenga's multispectral bathymetry formula for a variety of optical conditions and bottom types. A noiseless dataset of above-water remote sensing reflectance from WorldView-2 images over Case-1 shallow coral reef water is simulated using a radiative transfer model. The simulation-based assessment shows that Lyzenga's formula performs robustly, with adequate generality and good accuracy, under a range of conditions. As expected, the influence of bottom type on depth estimation accuracy is far greater than the influence of other optical parameters, i.e., chlorophyll-a concentration and solar zenith angle. Further, based on the simulation dataset, Lyzenga's formula estimates depth when the bottom type is unknown almost as accurately as when the bottom type is known. This study provides a better understanding of Lyzenga's multispectral bathymetry formula under various optical conditions and bottom types.