7. Compensating for variable water depth to improve mapping of underwater habitats: why it is necessary
Editor: Dr Alasdair.J.Edwards, University of Newcastle, UK.
Aim of Lesson
To learn how to carry out 'depthinvariant' processing in order to compensate for the effect of light attenuation in the water column (i.e. water depth) on bottom reflectance using a CASI airborne image.
Learning Objectives
 To understand the concepts underlying depthinvariant processing.
 To inspect an unprocessed image using transects to discover how depth dominates returns from the seabed.
 To learn how to carry out depthinvariant processing of a CASI airborne image.
 To compare false colour composites of the processed and unprocessed images to see the results of compensating for the effects of water depth.
In this lesson two bands of an 8waveband Compact Airborne Spectrographic Imager (CASI) image are used to introduce depth invariant processing. The image was recorded from a local Cessna at a spatial resolution of approx. 1 m^{2}, near South Caicos Island in July 1995.
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Concepts underlying depthinvariant processingWhen light penetrates water, its intensity decreases exponentially with increasing depth. The rate of attenuation differs with the wavelength. The red part of the visible spectrum attenuates more rapidly than shorter wavelength blue light and infrared light hardly penetrates water at all. The spectral radiances recorded by a sensor are therefore dependent both on the reflectance of the substrata and on the depth of the water. The influence of depth on the signal will create considerable confusion when attempting to map habitats. Since most marine habitat mapping exercises are only concerned with mapping benthic features, it is useful to remove the confounding influence of variable water depth. This lesson describes a fairly straightforward means of compensating for variable depth, which is applicable to clear waters such as those surrounding coral reef environments.  
Correcting for water depthTo compensate for the depth involves four steps.

Above: Calculating the ratio of attenuation coefficients for CASI bands 3 and 4 using a series of coral sand patches at different depths. To linearise the relationship between depth and radiance the natural logarithms of the radiances in the CASI bands have been taken. The quantities Ls3 and Ls4 are the mean deepwater radiances in each band  2 standard deviations.

Implementing the calculations in BilkoThe equation to generate one depthinvariant band from each bandpair is simple to implement as a Bilko formula document:
where Ln is the natural logarithm, L_{si} and L_{sj} are the mean deepwater radiances in bands i and j, and k_{i}/k_{j} is the ratio of their attenuation coefficients as determined from sand patches at varying depth.  
Left: Colour composite of three depthinvariant bands (bands 2/4, 3/4 and 3/5) of the CASI image of Cockburn Harbour with an automatic linear stretch. Note how the effect of water depth has been compensated for with the reef structure at 18 m depth at the south (bottom) end of the image now clearly visible. 
References
Lyzenga, D.R. 1978. Passive remote sensing techniques for mapping water depth and bottom features. Applied Optics 17 (3): 379383.
Lyzenga, D.R. 1981. Remote sensing of bottom reflectance and water attenuation parameters in shallow water using aircraft and Landsat data. International Journal of Remote Sensing 2: 7182.
Mumby, P.J., Clark, C.D., Green, E.P., and Edwards, A.J. 1998. Benefits of water column correction and contextual editing for mapping coral reefs. International Journal of Remote Sensing 19: 203210.
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