• 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 ZC-ZR
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

• 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 ZC-ZR
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

• 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 ZC-ZR
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

• the pollution affects the areas where the blue tone is darkest
• it causes computed depths to be under-estimated, 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
• blue-green 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 4-bands case would be within +-0.5 m of non-rounded 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 3-6 m of depth
  • then the Z3 case shall be used for the remaining vast majority of pixels down to 25-30 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

• gully: notice the curving of a small group of depth points in the 8-15 m depth range, as computed depths "saturate" at ~8 m. This occurs inthe small contorted deep-blue 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 sea-surface 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 30-35 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

1. MID-WAVEBAND: setting wavelengths at mid-waveband for the estimation of spectral K in m^-1 approximately suits the observed data

2. 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 :

3. Kgreen=0.123 m^-1 must be increased to Kgreen=0.130 m^-1

4. 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!

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

Observed error

Seatruth regression in the 0-10 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 0-10 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 0-35 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 0-10 m depth range

• avDZ=0.86 m over the 0-10 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

• Detailed DTM: who knows how these figures would further reduce over the 0-6 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?

The western part of the image
would not seem to be affected by the "pollution",
i.e. up to column 1000

 

RMSE error                       = 1.04-0.5 = 0.54 m
Average error on depth = 0.73-0.5 = 0.23 m

 

• Detailed DTM: who knows how these figures would further reduce over the 0-6 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