Optical calibration, bathymetry, water column correction and bottom typing of shallow marine areas, using passive remote sensing imageries

WorldView 2 image at Waimanalo Beach, Oahu, Hawaii islands
3289x3241, 2 m ground resolution, courtesy of Ron Abileah
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4SM   vs  NOAA's method

July 13th
Modeling with NOAA's log ratio method : Stumpf's method
 SHOALS DTM: five BLUE profiles and four YELLOW profiles   In 4SM, all visible bands are now used in a generalized version of Stumpf's method: if suitable bottom detection in all WV2 visible bands: Z=(   Mone[5]*((log(L[1])+log(L[2])+log(L[3])+log(L[4])) /(4*log(L[5])))   )    -Mzero[5]; In 4SM, Mzero=Mone for Stumpf's method Let Z=0 in 4SM, L1=L2=L3=L4=L5, because the Soil Line is normalized therefore ==> Mzero=Mone      sure, you'll like that! In 4SM, computed depths are used as "seatruth" to estimate a value for Mzero for Stumpf's method no need for field data and no need for segmenting the image into several bottoms substrates, like 'sand' vs 'coral', with separate calibrations sure, you'll like that! thresholds: -Lm/1.0/1.0/1.0/10.0/10.0/255/255.0/255.0 From this comparison, it is quite clear that deeper that 15-20 m here, depths become badly underestimated by Stumpf's method (some sort of assymptot) that's ~60% of maximum depth of bottom detection while 4SM yields results over the whole bottom detection depth range 4SM shall easily beat Stumpf's method even when field data are not available nothing shall (ever) beat the LIDAR in terms of accuracy on depth How about very dark bottoms? this image lacks very dark bottom substrates which should yield badly over-estimated  depths by Stumpf's method Atmospheric correction, anyone? now, who shal insist that they do require atmospheric corrections after all? or field data for that matter? Real life conditions? Well, Waimanalo Bay in Hawaii is expected to be  "very clean tropical waters": now, better think twice, as it also has its pollution problems! All this now must be documented rigorously by independent investigators, using a variety of imageries including WV2 Below are the plots for these 9 profiles by 4SM method Below are the plots for these 9 profiles by Stumpf's method Profile YELLOW by 4SM method Profile YELLOW by Stumpf's method Profile BLUE by 4SM method Profile BLUE by Stumpf's method ZC vs ZR regression by 4SM method ZC vs ZR regression by Stumpf's  method ZC - ZR ZZRegressor: Statistics of seatruth ZC-ZR on image waimanalowv2m_deg at Oahu, Hawaii N=5.609 millions pixels by Morel's 4SM method Htide=1 Smooth=1_5 Using_bands_1_2_3_4_5 cZ=1.00    1.79% pixels with depth underestimated by more than 5.0 m  4.17% pixels with depth underestimated by more than 3.0 m  6.78% pixels with depth underestimated by more than 2.0 m 13.71% pixels with depth underestimated by more than 1.0 m 35.68% pixels with depth underestimated by more than 0.0 m 25.91% pixels with depth  overestimated by less than 1.0 m  8.15% pixels with depth  overestimated by less than 2.0 m  2.27% pixels with depth  overestimated by less than 3.0 m  1.16% pixels with depth  overestimated by less than 5.0 m  0.37% pixels with depth  overestimated by more than 5.0 m 61.60% of computed depths are within  +-1.0 m of DTM depth 83.46% of computed depths are within  +-2.0 m of DTM depth 92.51% of computed depths are within  +-3.0 m of DTM depth 97.83% of computed depths are within  +-5.0 m of DTM depth over a total of 100.00% of computed depths ZC - ZR ZZRegressor: Statistics of seatruth ZC-ZR on image waimanalowv2m_deg at Oahu, Hawaii N=5.574 millions pixels by Stumpf's method HTide=1 m Smooth=1_5 Using_bands_1_2_3_4_5 cZ=1.00 4.96% pixels with depth underestimated by more than 5.0 m  8.97% pixels with depth underestimated by more than 3.0 m  9.79% pixels with depth underestimated by more than 2.0 m 17.07% pixels with depth underestimated by more than 1.0 m 25.60% pixels with depth underestimated by more than 0.0 m 26.13% pixels with depth  overestimated by less than 1.0 m  6.71% pixels with depth  overestimated by less than 2.0 m  0.66% pixels with depth  overestimated by less than 3.0 m  0.10% pixels with depth  overestimated by less than 5.0 m  0.00% pixels with depth  overestimated by more than 5.0 m 51.73% of computed depths are within  +-1.0 m of DTM depth 75.52% of computed depths are within  +-2.0 m of DTM depth 85.97% of computed depths are within  +-3.0 m of DTM depth 95.04% of computed depths are within  +-5.0 m of DTM depth over a total of 100.00% of computed depths ZC - ZR by 4SM ZC - ZR by Stumpf's method