ZComputedZRecorded Z5 only: band_5 against bands_1 to 4 
these results cover the whole area where radiance in the red band 5 is significantly higher that over deep waters 
all thresholds at minimum 
part of the error is because ZR is coded in discrete meters 
Blue tones signal underestimated depths Z5 only ZZRegressor: Statistics of seatruth ZCZR on image waimanalowv2m_deg at Oahu, Hawaii N=3.468 millions pixels E1/3289/430/3241 HTide=1.00 Smooth=1_5 Using_bands_1_2_3_4_5 cZ=1.00 9.99% pixels with depth underestimated by more than 5.0 m 12.15% pixels with depth underestimated by more than 3.0 m 9.60% pixels with depth underestimated by more than 2.0 m 18.42% pixels with depth underestimated by more than 1.0 m 32.66% pixels with depth underestimated by more than 0.0 m 16.57% pixels with depth overestimated by less than 1.0 m 0.60% pixels with depth overestimated by less than 2.0 m 0.02% pixels with depth overestimated by less than 3.0 m 0.00% pixels with depth overestimated by less than 5.0 m 0.00% pixels with depth overestimated by more than 5.0 m 49.22% of computed depths are within +1.0 m of DTM depth 68.23% of computed depths are within +2.0 m of DTM depth 77.86% of computed depths are within +3.0 m of DTM depth 90.01% of computed depths are within +5.0 m of DTM depth over a total of 100.00% of computed depths  ZComputedZRecorded Z4 only: band_4 against bands_1 to 3 
these results cover the whole area where radiance in the yellow band 4 is significantly higher that over deep waters 
all thresholds at minimum 
part of the error is because ZR is coded in discrete meters 
Blue tones signal underestimated depths Z4 only ZZRegressor: Statistics of seatruth ZCZR on image waimanalowv2m_deg at Oahu, Hawaii N=4.029 millions pixels E1/3289/430/3241 HTide=1.00 Smooth=1_5 Using_bands_1_2_3_4_5 cZ=1.00 8.01% pixels with depth underestimated by more than 5.0 m 11.19% pixels with depth underestimated by more than 3.0 m 8.71% pixels with depth underestimated by more than 2.0 m 14.04% pixels with depth underestimated by more than 1.0 m 37.37% pixels with depth underestimated by more than 0.0 m 20.11% pixels with depth overestimated by less than 1.0 m 0.52% pixels with depth overestimated by less than 2.0 m 0.05% pixels with depth overestimated by less than 3.0 m 0.01% pixels with depth overestimated by less than 5.0 m 0.00% pixels with depth overestimated by more than 5.0 m 57.48% of computed depths are within +1.0 m of DTM depth 72.03% of computed depths are within +2.0 m of DTM depth 80.79% of computed depths are within +3.0 m of DTM depth 91.99% of computed depths are within +5.0 m of DTM depth over a total of 100.00% of computed depths 
ZComputedZRecorded Z3 only: band_3 against bands_1 to 2 
these results cover the whole area where radiance in the green band 3 is significantly higher that over deep waters 
all thresholds at minimum 
part of the error is because ZR is coded in discrete meters 
Blue tones signal underestimated depths Z3 only ZZRegressor: Statistics of seatruth ZCZR on image waimanalowv2m_deg at Oahu, Hawaii N=5.593 millions pixels E1/3289/430/3241 HTide=1.00 Smooth=1_5 Using_bands_1_2_3_4_5 cZ=1.00 0.99% pixels with depth underestimated by more than 5.0 m 1.62% pixels with depth underestimated by more than 3.0 m 2.99% pixels with depth underestimated by more than 2.0 m 10.14% pixels with depth underestimated by more than 1.0 m 21.25% pixels with depth underestimated by more than 0.0 m 28.92% pixels with depth overestimated by less than 1.0 m 22.18% pixels with depth overestimated by less than 2.0 m 8.04% pixels with depth overestimated by less than 3.0 m 3.26% pixels with depth overestimated by less than 5.0 m 0.61% pixels with depth overestimated by more than 5.0 m 50.16% of computed depths are within +1.0 m of DTM depth 82.48% of computed depths are within +2.0 m of DTM depth 93.51% of computed depths are within +3.0 m of DTM depth 98.40% of computed depths are within +5.0 m of DTM depth over a total of 100.00% of computed depths  So  the pollution affects the areas where the blue tone is darkest
 it causes computed depths to be underestimated, and depth results to be produced where the shallow bottom has not even been detected!
 yellow and red bands are badly affected by the pollution
 bluegreen bands are much less affected
 it all looks like (slightly) more turbid waters tend to rest in locally deeper areas
 this "turbidity" might well be caused, not so much by "pollution" per se, but rather by a mere increase of the suspended load along the coastline
 in the Z4 case, 57.48% of computed depths are within +1.0 m of DTM depth
 this is the best result
 ?allowing for a +0.5 m uncertainty of the rounded ZR values, this indicates that 57.4% of the results in the 4bands case would be within +0.5 m of nonrounded recorded depths
 in the Z3 case, 82.5% of computed depths are within +2.0 m of DTM depth
 but only 50.2% of computed depths are within +1.0 m of DTM depth
 therefore
 band 5 is of little use: a strong threshold value on red radiance must be applied
 band 4 is more attractive, but again a strong threshold value on yellow radiance must be applied
 therefore
 a select few and very shallow pixels can benefit of the Z5 case
 then the Z4 case shall slightly reduce the error down to 36 m of depth
 then the Z3 case shall be used for the remaining vast majority of pixels down to 2530 m of depth
 this may be seen as a worst case,
 first because the SHOALS data have been rounded into discrete values of meters, thereby introducing a +0.5 m error
 then because of the extremely adverse smoothing scheme which need be applied to this very noisy dataset
it is also seen that some artifacts in the data are not accounted for: this is most obvious in the Z3 case image  gully: notice the curving of a small group of depth points in the 815 m depth range, as computed depths "saturate" at ~8 m. This occurs inthe small contorted deepblue gully,
 which actually reaches a depth of 15 m
 where turbid waters might get trapped
 where the green band cannot see through the mist
 relics of seasurface glint
 this increases the level of noise in the output
 this noise is seen to increase exponentially with depth

No need for field data! Please, note that the "mushroom" shape in the 3035 m depth range in the above regression includes  wild pixels scattered over the deep water area (glints no deep water mask used here)
 lousy pixels generated by the preliminary "deglinting" process along the borders of the image
 No need for field data! Incidentaly, this plot demonstrates that 
MIDWAVEBAND: setting wavelengths at midwaveband for the estimation of spectral K in m^{1} approximately suits the observed data 
Zfinal=0.943*ZR: but seatruth data show that a small increase of WL for the green band would not hurt, in order to increase Kgreen by a factor of 0.943 : 
Kgreen=0.123 m^{1} must be increased to Kgreen=0.130 m^{1} 
this is to be done by increasing WLgreen from 546.0 nm to 549.5 nm upon using Jerlov's data If this can be confirmed with other WV2 images, then YES, NO NEED FOR FIELD DATA when using WV2 IMAGES, EH! Getting further insight into the operational wavelength problem Please note: although I used extensively the SHOALS data in order to gain understanding of this image, the only "use" of it was to estimate a coefZ factor: Zfinal=0.943*ZR, which then translated into a slight increase of operational wavelength for the green band 
WLgreen set at 549.5 nm 61.49% of computed depths are within +1.0 m of DTM depth This now is final for the whole image  WLgreen set at 549.5 nm 61.49% of computed depths are within +1.0 m of DTM depth ZZRegressor: Statistics of seatruth ZCZR on image waimanalowv2m_deg at Oahu, Hawaii N=5.593 millions pixels E1/3289/1/3241 HTide=1.00 Smooth=1_5 Using_bands_1_2_3_4_5 cZ=1.00 1.70% pixels with depth underestimated by more than 5.0 m 3.73% pixels with depth underestimated by more than 3.0 m 5.64% pixels with depth underestimated by more than 2.0 m 11.51% pixels with depth underestimated by more than 1.0 m 29.65% pixels with depth underestimated by more than 0.0 m 31.84% pixels with depth overestimated by less than 1.0 m 11.56% pixels with depth overestimated by less than 2.0 m 3.00% pixels with depth overestimated by less than 3.0 m 1.18% pixels with depth overestimated by less than 5.0 m 0.19% pixels with depth overestimated by more than 5.0 m 61.49% of computed depths are within +1.0 m of DTM depth 84.56% of computed depths are within +2.0 m of DTM depth 93.20% of computed depths are within +3.0 m of DTM depth 98.11% of computed depths are within +5.0 m of DTM depth over a total of 100.00% of computed depths 
Profile BLUE  Profile YELLOW 
Observed error  Observed error 
Seatruth regression in the 010 m depth range over the whole image Lm/0001.0/001.0/010.0/010.0/010.0/255.0/255.0/255.0  Seatruth regression in the 010 m depth range over the whole image Lm/0001.0/001.0/010.0/010.0/010.0/255.0/255.0/255.0 RMSE error = 0.67 m  final RMSE=1.71 m over the 035 m depth range
 it then reduces to RMSE=1.21 m, as we want to subtract 0.5 m because the SHOALS data are rounded into disctere meters
 it then reduces to RMSE=0.67 in the 010 m depth range
Average error on depth = 0.36 m  avDZ=0.86 m over the 010 m depth range
 it then reduces to avDZ=0.36 m, as we want to subtract 0.5 m because the SHOALS data are rounded into disctere meters
Who knows?  Detailed DTM: who knows how these figures would further reduce over the 06 m depth range if using a detailed SHOALS DTM?
 Smart smoothing: who knows how they would further reduce if using a less glinted and less noisy image, so that a smart smoothing would be applied instead of a very punishing plain smoothing which whipes out small topographic details and sharp gradients?

Seatruth regression in the 010 m depth range over the western part of the image which is not affected by the pollution Lm/0001.0/001.0/010.0/010.0/010.0/255.0/255.0/255.0  Seatruth regression in the 010 m depth range over the western part of the image which is not affected by the pollution Lm/0001.0/001.0/010.0/010.0/010.0/255.0/255.0/255.0 The western part of the image would not seem to be affected by the "pollution", i.e. up to column 1000 RMSE error = 1.040.5 = 0.54 m Average error on depth = 0.730.5 = 0.23 m Who knows?  Detailed DTM: who knows how these figures would further reduce over the 06 m depth range if using a detailed SHOALS DTM?
 Smart smoothing: who knows how they would further reduce if using a less glinted and less noisy image, so that a smart smoothing would be applied instead of a very punishing plain smoothing which whipes out small topographic details and sharp gradients?
see this profile accross the western area 