Researchers have been attempting to estimate depth of shallow water using remote sensing for several years (e.g. Lyzenga 1978). A common problem among most studies is that the seafloor is covered by a patchwork of organisms and substrates that have different albedos (= reflectances), ranging from very dark (e.g. coral ~0.05) to very bright (e.g. sand ~0.6). The difficulty is that a dark object strongly absorbs light and will appear to be deeper than it really is. This effect is not as severe for bright objects, which absorb less strongly. Thus, for coral and sand at the same true depth, the coral virtually always appears to be deeper than the sand.
We have developed a method for bathymetry estimation that is independent of bottom composition. Our method is based upon our knowledge of the spectral reflecting properties of reef benthic communities. Essentially, we identify a ratio of wavebands that is constant for all bottom types. Then, that ratio replaces the unknown albedo in our depth calculations.
For example, this is two wavebands plotted against each other:
Clearly, there is a high correlation between the two wavebands. We take advantage of this correlation in our depth estimates.
For an image of northern Kaneohe Bay,
we used our model to compute depth at every pixel:
We compared our results to water depth obtained from a NOS survey:
This is the result of the pixel-by-pixel comparison:
The remotely-sensed bathymetry parallels the NOS bathymetry until depths of ~8 m. The remotely-sensed depths are about 1 m offset from the 1-to-1 line. This is due to the difference in tide levels of the data sets. Also, the slope of the remote sensing data vs. the NOS data changes to travel through zero. The reason for this slope change is that NOS simply extrapolated their data from deeper water to the beach, where they assumed depth equals zero. The remote sensing data actually measures the points. There is a range of ~1 m around any given remotely-sensed depth. The variability is due mostly to somewhat inaccurate georeferencing between the two data sets. Also, waves are clearly visible in the remote sensing image, and these can add up to 2 m of water depth over a given pixel location. Finally, there is a sharp bend in the remote sensing data at ~8 m. With increasing depth, the contribution of backscatter to the remotely-sensed signal becomes more significant. The model we used in this analysis did not consider the effects of backscatter, and is thus unable to accurately predict those depths where backscatter is significant. Another reason for the bend in the data might be the increased path length that light must travel when it enters the water at an angle (path length equals vertical water depth divided by the cosine of the incident zentih angle). This path length effect is only significant at increased water depths.
To show that our model is independent of bottom composition, we can focus on a small area of the image. In the following figure, the top left image shows our remotely-sensed depth estimate, and the top right image shows the reflected intensity of the bottom for the same area. The intensity image shows a moon-shaped sand patch surrounded by a darker substrate. From experience, we know that sand gathers in depressions in the reef. Therefore, we can guess that the sand patch here is probably 1 - 2 m deeper than the surrounding bottom. The depth image agrees with our assessment, showing greater depth in the sand patch.
The scatterplot at the bottom of the figure shows estimated depth versus reflected intensity. If the bathymetry model were sensitive to bottom composition, we would expect estimated depth to decrease with increasing intensity. However, the scatterplot clearly shows increasing depth correlates with increasing intensity, confirming that the method isindependent of bottom composition.