Optical calibration, bathymetry, water column correction and bottom typing of shallow marine areas, using passive remote sensing imageries
Busy? 4SM in 10 lines
Review of some papers collected on the net
 
As it turns out, this review shows that most of those
go through formal atmospheric correction and  calibration  to reflectance 4SM does not
are mostly stuck with either Lyzenga's model or Stumpf's model 4SM innovates
need existing depth sounding to yield water depth 4SM does not
don't even mention water column correction and bottom typing 4SM does it all
       Your comments are invited                   See you on 4SM blog    
4SM errors
4SM conclusions
 
 

reviews and comparisons
Jared Kibele 2017  Submerged_habitats_from_space_Increasing_map_production_capacity_with_new_methods_and_software
Zoffoli et al 2014 : water column correction for coral reef studies
Dekker et al 2011 : Intercomparison of shallow water bathymetry... 
Cowley Beach bathymetry trial
4SM vs DigitalGlobe    
 4SM vs ALUT on CASI at Heron Island
  4SM performance 

Hogrefe   see Hogrefe_Thesis.pdf 2008 
 
see also "Derivation and Integration of Shallow-Water Bathymetry:
Implications for Coastal Terrain Modeling and Subsequent Analyses"
KYLE R. HOGREFE, DAWN J. WRIGHT, AND ERIC J. HOCHBERG,
Marine Geodesy, 31: 299–317, 2008


an operational nightmare: see Hogrefe_cookbook at
ftp://ftp.soest.hawaii.edu/pibhmc/website/webdocs/documentation/Cookbook_042108.pdf
steps 2, 3, 4, 5, 7 and 7bis are all integrated in 4SM


see Hochberg et al,  poster presented at the October 2007 NOAA PRIDE meeting in Honolulu, Hawaii
can process several tens of bands
How can anyone be satisfied of such poor performances?
They all rely on fancy statistics using existing seatruth data and loose control of the physics behind:
their statistically derived parameters get out of hand
  • a, b, c, etc for the "linear method" of Lizenga
  • m0 and m1 for the non-linear method of Stumpf
  • spectral K, M=0 for Bierwirth's method

Su et al (2008) get more reasonable results
using either linear or non-linear approches,
I wish to add 4SM results to this kind of figure!


 

4SM versus ALUT
ALUT stands for
Model Inversion by Adaptive Linearized Look-up Trees
see CASI demonstration at Heron Island
This is a follow-up of my work on CASI at Heron Island

see also 4SM versus DigitalGlobe

see also 4SM where's the catch? 

 

It is fair to stress that
4SM cannot account for variable water optical properties
unlike semi-analytical methods

 

review Hedley et al's ALUT paper       doi:10.1594/PANGAEA.779522
"Efficient radiative transfer model inversion for remote sensing applications" 
John Hedley, Chris Roelfsema, Stuart R. Phinn, 2009

 
ALUT
Forward Semi-analytical
Model Inversion
does not use depth points for calibration
requires formal atmospheric correction
  • LUT building: in Hedley et al's ALUT work on Heron CASI, the semi-analytical method first builds a LUT to describe
    • 78 pair combinations of 13 end-member spectral reflectance signatures (bottom types),
    • over a variety of inherent water optical properties (absorbtion, backscatter, etc, from litterature),
    • and over a "depth parameter subdivision structure" (depth increments)
    • that's in excess of 5 million combinations
    • this requires exhaustive knowledge of the spectral properties of all bottom types at the scene, and of their possible combinations
  • Spectral matching search algorithm: then each shallow pixel's spectral remote sensing reflectance is compared to each of the 5 millions combinations until the best match is achieved: this spectral matching search algorithm requires 1.5 milliseconds of the computer used (likely to be more intimidating than my four years old 4GB RAM I3core Toshiba Satellite Ubuntu laptop).
  • Spectral matching limited to the Blue/Green range
  • This then is open to further "unmixing" of end-members


 
4SM
Backward Simplified Model Inversion

does not use depth points for calibration
does not require formal atmospheric correction
  • Soil Line parametrization: optical calibration uses land areas of the image to specify the Soil Line at the base of the atmosphere (BOA in DNs).
    • this does not require any knowledge of the bottom types at the scene
  • Water Type parametrization: using ratio Ki/Kj observed in the image at wavelengths WLi and WLj, a water type is interpolated using Jerlov's optical classification of marine waters, spectral 2K is specified for the whole scene (assuming homogeneous waters)
  • Spectral matching search algorithm:  approx 15 optimized iterations using a ~0.04 m depth increment are enough to correct
    • from pixel's BOA spectral signature in DNs at depth Z 
    • to BOA bottom spectral signature in DNs at null depth (at the Soil Line). 
  • Spectral matching limited to the Blue/Green range
  • This then is open to further "unmixing"
ALUT performance
As I understand it, Hedley's Adaptive LUT method attempts
to reduce the horrendous computing time for processing an hyperspectral image
using semi-analytic forward modeling

 
  • LUT per-pixel inversion time from 580 ms, to 25 ms, then to 1.1 ms
    • that's ~24 hours at best for 60 million pixels using the Detailed Depth ALUT process,
    • that's 1.5 ms per pixel, at best

 
In comparison, this work shows that
the 4SM backward inversion
using an image-based empirical method
is 40 times faster than ALUT
  • 32 bits laptop: 4SM per-pixel inversion time is 82 minutes for 36 millions pixels of the same CASI image on my 32 bits laptop
    • that's 0.14 ms per pixel, or ten times faster than the fastest ALLUT process, with a finer precision
  • 64 bits laptop: 4SM per-pixel inversion time is 20 minutes for 36 millions pixels of the same CASI image on my new 64 bits laptop
    • that's 0.035 ms per pixel, or 40 times faster than the fastest ALLUT process, with a finer precision
see also 4SM performance

It is fair to stress though
that 4SM cannot account for variable water optical properties
unlike semi-analytical methods


 
Discretization and limitation:
"depth parameter subdivision structure"
  • ALUT uses as much computer memory as available: "ALUTs of 5 × 106 spectral space points"
    • this severely limits the "depth parameter subdivision structure", which is seen to be fairly coarse
    • and it imposes a maximum modeling depth of 20 m here
  • 4SM uses a "depth parameter subdivision structure" which is much finer in comparison, as the concept of using end-members in the forward inversion  is replaced by the concept of the Soil Line in the backwards inversion.
    • it involves a 750 even increments "depth parameter subdivision structure" from 0 m to 30 m maximum depth for this scene.
  
Red profile is ALUT retrieved depth
Black profile is 4SM retrieved depth
Coloured profiles are 4SM water column corrected BOA bands 1, 3 and 7 in scaled image DNs



 

 
 
 
 


Mobley: Moreton Bay Hyperspectral

Algorithm comparison

 
  • LUT approach by quite a big wig:
    • it will be a while before the LUT catters for all possible combinations of "known water, bottom, and external environmental conditions".
  • 4SM can get the desired result without any LUT:
    • the Brightest Pixels Line and Soils Line assumptions do the trick using raw data in DNs.



 

Intercomparison of shallow water bathymetry, hydro-optics, and benthos mapping techniques
in Australian and Caribbean coastal environments

Arnold G. Dekker, Stuart R. Phinn, Janet Anstee, Paul Bissett, Vittorio E. Brando, Brandon Casey, Peter Fearns,
John Hedley, Wojciech Klonowski, Zhong P. Lee, Merv Lynch, Mitchell Lyons, Curtis Mobley, Chris Roelfsema

Limnol. Oceanogr. Methods 9:396-425 (2011) | DOI: 10.4319/lom.2011.9.396

ABSTRACT

Science, resource management, and defense need algorithms capable of using airborne or satellite imagery to accurately map bathymetry, water quality, and substrate composition in optically shallow waters. Although a variety of inversion algorithms are available, there has been limited assessment of performance and no work has been published comparing their accuracy and efficiency. This paper compares the absolute and relative accuracies and computational efficiencies of one empirical and five radiative-transfer-based published approaches applied to coastal sites at Lee Stocking Island in the Bahamas and Moreton Bay in eastern Australia. These sites have published airborne hyperspectral data and field data. The assessment showed that (1) radiative-transfer–based methods were more accurate than the empirical approach for bathymetric retrieval, and the accuracies and processing times were inversely related to the complexity of the models used; (2) all inversion methods provided moderately accurate retrievals of bathymetry, water column inherent optical properties, and benthic reflectance in waters less than 13 m deep with homogeneous to heterogeneous benthic/substrate covers; (3) slightly higher accuracy retrievals were obtained from locally parameterized methods; and (4) no method compared here can be considered optimal for all situations. The results provide a guide to the conditions where each approach may be used (available image and field data and processing capability). A re-analysis of these same or additional sites with satellite hyperspectral data with lower spatial and radiometric resolution, but higher temporal resolution would be instructive to establish guidelines for repeatable regional to global scale shallow water mapping approaches.

I wish 4SM was offered the opportunity to contribute to this intercomparison

4SM depth results on such "ideal" hyperspectral datasets
should compare favorably  with those illustrated in Figure 5 of this paper
for just a fraction of the effort and cost




4SM modeling performance

100 minutes at 2.13 GHz on my Intel I3 Core Toshiba laptop
from reading raw data
to writing Z and spectral LB output

  This is 31300 pixels per second

on a 7432*25260 8-bands WV2 image
compare with Table 1 of Mobley in 2011



It is fair to stress though
that 4SM cannot account
for variable water optical properties
unlike semi-analytical methods
see 4SM vs ALLUT


 


Cowley Beach
THE COWLEY BEACH BATHYMETRY TRIAL

 
Rapid Environment Assessment
An in depth review of Maritorena's and Stumpf's methods
for the military by CSIRO, Australia
  Great reading!
Sambuca

 
Theory of water remote sensing
Bathymetry from multispectral and hyperspectral imagery
Band ratio methods
Philpot's algorithms
Semi analytical models
The neural network approach
Maritorena et al's algorithm
Stumpf et al.'s algorithm
Ikonos and HyMap
Inherent and apparent water optical properties
  
  • OBJECTIVE 1: TO COMPARE TWO TECHNIQUES FOR MULTISPECTRAL AND HYPERSPECTRAL DATA TO INVESTIGATE IF ONE FORM OF DATA OR TECHNIQUE PROVIDES IMPROVED MAPPING OVER THE OTHER
  • OBJECTIVE 2: TO UNDERSTAND THE LIMITATIONS OF THESE TECHNIQUES TO REMOTELY SENSE BATHYMETRY
  • OBJECTIVE 3: TO GAIN A SENSE OF HOW PASSIVE REMOTE SENSING OF BATHYMENTRY MIGHT BE USED OPERATIONALLY, I.E. CAN THEY BE READILY/EASILY INTEGRATED INTO THE WORK FLOW FOR THE PLANNING OF AMPHIBIOUS OPERATIONS?
  • OBJECTIVE 4: TO UNDERSTAND THE IMPACT OF THE INHERENT AND APPARENT OPTICAL PROPERTIES ON BATHYMETRIC TECHNIQUES
     
  • "The Maritorena et al., (1994) technique requires a considerable amount of a priori  knowledge  which may not always be readily available."
  • "The Stumpf et al., (2003) method also has a significant limitation.  It requires a small number of known depths so that the method can be tuned."
  • "Both techniques require a priori information to work"
  • in the end, CISRO's complex and computationaly intensive SEMI-ANALYTICAL MODEL FOR BATHYMETRY, UN-MIXING AND CONCENTRATION ASSESSMENT (SAMBUCA) is mentioned as very attractive.
 
 
By contrast,
apart from Jerlov's table of attenuation coefficients of marine waters,
4SM does not require a priory knowledge or known depths,
does not need proper atmospheric corrections,
and can proceess hyperspectral data as well as multispectral data
at Cowley Beach
within a very tight time constraint.
 
 
 



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