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Bilko Module 7

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

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To learn how to carry out 'depth-invariant' 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

  1. To understand the concepts underlying depth-invariant processing.
  2. To inspect an unprocessed image using transects to discover how depth dominates returns from the seabed.
  3. To learn how to carry out depth-invariant processing of a CASI airborne image.
  4. 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 8-waveband 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 m2, near South Caicos Island in July 1995.

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Concepts underlying depth-invariant processing

When 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.

Right: Raw colour composite (bands 2, 3 and 4) of a CASI image of Cockburn Harbour with an automatic linear stretch. Note how the water steadily darkens from the shore (north of image) to the deeper reef at around 18 m depth at the south (bottom) end of the image.

Correcting for water depth

To compensate for the depth involves four steps.

  1. Removal of scattering in the atmosphere and external reflection from the water surface
    The first step is a crude atmospheric correction based on the 'dark pixel subtraction' method. (If a full atmospheric correction had already been carried out this step would not be needed.)

  2. Linearise relationship between depth and radiance
    In relatively clear water, the intensity of light will decay exponentially with increasing depth. If values of light intensity (radiance) are transformed using natural logarithms (ln), this relationship with depth becomes linear.

  3. Calculate the ratio of attenuation coefficients for band pairs
    Two bands are selected and a bi-plot made of (log transformed) reflectances for the same substratum (in this case sand) at differing depths. Since the effect of depth on measured radiance has been linearised and the substratum is constant, pixel values for each band will vary linearly according to their depth, with the slope representing the ratio of the attenuation coefficients of the two bands.

  4. Generate a depth-invariant index of bottom type
    If reflectance values for other habitats are added to the bi-plot, similar lines with the same slope will be obtained, with each differing in position (and intercept at the y-axis) according to the reflectances of the different habitats. Each pixel can be converted mathematically to its intercept value (or depth-invariant index) to remove the effect of depth.

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Regression line

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.

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Implementing the calculations in Bilko

The equation to generate one depth-invariant band from each band-pair is simple to implement as a Bilko formula document:

Depth invariant equation

where Ln is the natural logarithm, Lsi and Lsj are the mean deepwater radiances in bands i and j, and ki/kj is the ratio of their attenuation coefficients as determined from sand patches at varying depth.

Left: Colour composite of three depth-invariant 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.


Lyzenga, D.R. 1978. Passive remote sensing techniques for mapping water depth and bottom features. Applied Optics 17 (3): 379-383.

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: 71-82.

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: 203-210.

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