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Lyzenga's
log-linear bathymetric inversion approach
Lyzenga+depth 2006 Conger, Hochberg, Fletcher & Atkinson 2006 Arce's thesis in Puerto Rico 2005 Sagawa et al Nurlidiasari et al : bottom typing of coral reefs in Indonesia 2005 Legleiter OBRA SHOM 2012

Lyzenga+depth in 2006

This paper in 2006, by the founding father of the most widely used algorithms with two other big wigs of the US accademic scene,

elaborates on various aspects of the simplified radiative transfer model
- GREAT READING
and attempts to improve the estimation of shallow water depth
- Though reading
GREAT presentation of seatruth correlations
- using eight IKONOS images in clear waters and excellent LIDAR seatruth datasets which are used for the calibration of model parameters

Authors claim that, thanks to rather obscure refinements, their new "algorithm corrects for a range of variations in both water attenuation and bottom reflectance"

Estimation of water attenuation properties is still conditional to the use of an adequate seatruth dataset
The result is still just an estimation of water depth, and the estimation of spectral bottom reflectance is not even mentioned

Fig. 15 of Lyzenga et al.
log(Ls_green-Lsw_green) vs log(Ls_blue-Lsw_blue)

"Clearly, there is a wide variation of the signals within each of these depth intervals, which could be caused by variations in either the water optical properties or the bottom composition "
I say: Nope! Accounting for the fact that Lw_blue >> Lw_green explains nicely the curved display of these clouds of linearized pixels

Lyzenga+Depth_fig_15_flipped
Fig. 15 is flipped for comparison with 4SM illustrations
log(Ls_blue-Lsw_blue) vs log(Ls_green-Lsw_green)

Just add a "Soils Line" at null depth (Z=0 m) and this plot now becomes most familiar to a 4SM-savy reader
- isobath lines are curved lines which parallel the Soils Line (0, 5, 10, 15, 20 and 25 m isobath lines are drawn)
Just add a "Brightest Pixels Line" at LB=max, in other words a collection of pixels sampled at various depths over the brightest of shallow bottom types
- isobottom lines are straight lines which parallel the Brightest Pixels Line, with a slope of K_blue/K_green

Variable diffuse attenuation properties

what worries the authors is the curved aspect of displays of pixel clouds
authors claim that the curved fit observed is caused by some obscure variations in the diffuse attenuation properties of the water which they now undertake to estimate and account for...Hmmm!

Spectral water volume reflectance

in 4SM, we have observed that the curved aspect of isobath lines in such a scatter plot is because Lw_blue>>Lsw_green
Nothing to do, therefore, with alleged/observed variations in the diffuse attenuation properties of the water
- Fig. 13 shows them to be "uniform",
- as is the case with all faithfull images we have investigated todate in 4SM
Please refer to optical_modeling_slide47
Please refer to optical_modeling_slide79

The authors' method

is quite confusing from an operational point of view
require adequate seatruth dataset for calibration
uses just the blue and green pair of bands
only allow for "depth-invariant" images of the variations of bottom reflectance to be produced
still do not account for the water volume reflectance!!!!!!!!!! in spite of an all-out review of all aspects of the model

No sweat then: although it uses the same simplified physical approach, the 4SM approach

is much simpler on an operational point of view
does account for water volume reflectance Lw
does not require any seatruth dataset,
can use all bands with significant bottom detection (instead of just the blue and green pair)
delivers
- computed depths which should compare favorably with those in this paper
- spectral K i.e. water quality
- spectral water-column-corrected bottom reflectance

I ought to look into the sun angle aspect though, as it might explain the alleged shift in wavelength I seem to observe.

Conger, Hochberg, Fletcher & Atkinson 2006

"A New Method of Decorrelating Remote Sensing Color Bands from Bathymetry in Optically Shallow Waters"

Nice reading, keeps track of physics behind

"The goal is to remove the variability due to depth while maintaining variability due to bottom composition"
Innovates from Lyzenga's method
Needs existing bathymetric data for calibration : "this method requires a depth value for each pixel to be rotated" : uses a Quickbird image in Hawaii and SHOALS Lidar bathymetry
"There is also potential that our pseudo-color bands may be calibrated to absolute reflectance through techniques such as the empirical line method, thus allowing application of spectral classifiers built using libraries of in situ reflectance data"

I say: use 4SM

you won't need any existing depth information
for most shallow pixels, your output shall be
- a depth value
- N spectral values for 2Kd (water quality)
- N spectral values of La, the atmospheric path radiance
- N spectral values of Lw, the water volume reflectance
- N water column corrected spectral bands in units of DNs at the base of the atmosphere , that you can convert into units of reflectance if you so need , ready for bottom typing
- and a deglinted image , whether BOA or TOA

Jeanette Arce's thesis 2005

"Remote sensing of benthic habitats in SouthWestern Puerto Rico"

Preprocessing of Ikonos image
- atmospheric correction using dark pixel subtraction
- sunglint correction using Hochberg's technique
Preprocessing of Hyperion image
- destriping
- atmospheric correction using ACORN
- deglinting using Lee's "750 Normalizing" technique
- followed by supervised classifications
Water column correction using Lyzenga's technique, followed by supervised classification

This spectrum for corals (right) is remarkable,
appears locally in water column corrected data at Caicos Bank

Sagawa et al

A NEW APPLICATON METHOD FOR LYZENGA’S OPTICAL MODEL

Easy reading,
pragmatic approach to water column correction,
quite simplistic though

Bottom typing: authors only want to do bottom typing over seagrass
Lw: first time I see someone noting that the water volume reflectance is not accounted for in Lyzenga' method
- L = Ls + ar exp( − K g Z )
- authors do not mention atmospheric correction from TOA radiance to BOA radiance
Please compare their model with ours:
- TOA: Ls= La + Lw - Lw/ exp (2KZ) + LB/ exp(2KZ)
- BOA: L = Lw - Lw/ exp (2KZ) + LB/ exp(2KZ)
Jerlov and effective K: authors could have resorted to Jerlov's data in order to derive operational K, and spared the burden of using seatruth data. Particularly so as they use an existing DTM in addition to side scan sonar data
What they do is use Z and spectral K at the current pixel, so that they can solve for spectral bottom reflectance ar
- just like Malthus and Karpouzli whose paper in 2003 authors seem to have missed: how sad
"bathymetry data accuracy is of primary concern"
Their method does not work in the 0-2 m depth range: how sad!
- not because of internal reflections,
- but rather because they need to include Lw in their TOA model or apply atmospheric corrections to the image data
Blue vs Green: so they do not use the Red band at all
Posidonia on sand: that's an easy binary task indeed

see Coral reefs in East Kalimantan, Indonesia (thesis)

NURLIDIASARI et al water column correction and bottom typing

Work done in 2004 at ITC, Enschede, the Netherlands, on a QuickBird image

elaborate process to calibrate the data into BOA reflectance
elaborate process to estimate spectral deep water radiance, based on field work
elaborate process to estimate ratios K_i/K_j for Lyzenga's algorithm for water column correction
- variance and covariance
- Kblue/Kgreen~=0.74, quite neat
- Kgreen/Kred ~=0.60, lousy
Linearization : at the base of the atmosphere X_i = ln(L_i) should actually be X_i = ln(L_i - Lw_i)
Depth-invariant indexes
Bottom typing for 6 classes, using only the Blue/Green depth-invariant image
- this is equivalent to shades of grey, from brightest to darkest
Water column correction improves the acuracy of the bottom typing by 22% for patchy seagrass, patchy reef, sand and algae

With 4SM

Image preparation and full processing is quite simple in comparison
- no need for field data
- no need for conversion into BOA calibrated radiances
- a same-day process
Bayhymetric map and Bottom typing map are prepared ahead of any field work
- Computed depths still need some seatruthing Zfinal= bias + slope*Zcomputed
  - bias accounts for the tide height correction
  - slope accounts for real atenuation coefficients in the Blue and Green bannds
- Bottyom typing map only needs
  - possibly binning of classes
  - a label for each class
Field work much easier,
- using pre-classified image and detailed bathymetric map

Legleiter : the OBRA approach 2009

River bathymetry using Hyperspectral images
Calibrate a optimal band ratio using existing depths : Optimal Band Ratio Analysis
An extension of the "linear approach"