• 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

• 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

• 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.