7. Compensating for variable water depth to improve mapping of underwater habitats: why it is necessary

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.

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:

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 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.