Bathymetry and water column correction
LANDSAT 8 OLIP 
at Mulroy Bay, Ireland
Image courtesy of the U.S. Geological Survey
 
Using the Panchromatic band for water column correction
to derive water depth and spectral bottom signature:

Landsat 8 OLIP bandset used for this work
Purple=1Blue=2Green=3PAN=4Red=5NIR=6 and SWIR1=7

Work done july 2018
GSD 15 m
 
 
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HOW GOOD: Precision on Computed Depths ?

see also the 4SM error page
All computed depths are to be multiplied by a single and final correcting factor
to be derived from sea-truth when it becomes available.
Computed depths are "not intended for navigation",
although error on depth is most likely to be
by default of depth rather than by excess of depth
(that's because an excess of radiance-glints, slight turbidity-
translates into underestimation of depth).
  • Best possible: the computed depth is the best possible estimate of the actual water depth at the time of imaging that may derived from the imagery itself without the use of any field data.
  • CoefZ :all computed depths may conveniently be multiplied by a unique final depth correction factor, while the computed bottom reflectances remain totally unaffected.
  • Tide correction : computed depths may be corrected for height of tide over a specific datum by applying a tide correction, if and when such information is issued by the end-user.
  • RMS error : because of the exponential nature of the attenuation of light in water, the error on computed depth should be specified as a percentage of the actual depth in meters .

 
 
THE N-BANDS CASE: bands i, j,..., k, with Ki/Kj<~0.8
  • Bias: this error is mostly due to the fact that the bottom tends to be actually reddish or greenish at places. In such case the depth is computed too deep (reddish) or too shallow (greenish).
  • Noise: the error caused by the system noise -S/N ratio- increases from shallow to deep waters, and from bright to dark bottoms:
    • you want more photons to be captured by a cooled sensitive sensor, and radiances to be recorded as 16 bits digital numbers
  • up to ~10% : it has been predicted, and verified in favorable conditions, that the RMS error on the estimation of water depth is likely to be approximately at best up to 10% of the actual depth for a majority of shallow water pixels.
  • up to ~25%: depths computed closer to extinction of bottom reflected signal in the faster attenuated band can suffer an RMS relative error of up to 25% of actual depth: this affects the  darker bottoms first.
  • Therefore, thresholds are applied in order to prevent the output of results for pixels which exhibit a very low S/N ratio,
    • although a smart smoothing scheme helps a lot in this respect to reduce the error
THE 1-BAND CASE
  • Deeper than the above-mentioned limits for the N-bands case, the water depth can only be computed, on special request, through the choice of an arbitrary value for prevailing bottom reflectance for deeper bottoms in shallow areas .
  • Naturally, this last choice entails a very high level of error in the computed depths, as follows:
    • for bottoms actually brighter than the chosen bottom type, water depth is computed badly underestimated,
    • and vice versa.
    • this may give rise to errors well in excess of several meters.





















































 




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