Regression
Combined Depths vs Sonar Depths
RMSE=1.20 m
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Sonar Two Days seatruth depths raster
not corrected for tide
15 m GSD
see depth legend |
| Seatruth regressions
against sonar depths | | | Tide | R2 | RMSE (m) | | October | 19th-2013 | 0.00m | 0.90 | 1.20 | | November | 4th-2013 | 0.60 m | 0.91 | 1.28 | | January | 7th-2014 | 0.00 m | 0.86 | 1.76 | | February | 8th-2014 | 0.60 m | 0.89 | 1.09 | | October | 22th-2014 | 1.60m | 0.91 | 0.95 | | January | 29th-2016 | 1.70m | 0.83 | 1.38 | | March | 1rst-2016 | -0.30 m | 0.89 | 1.89 | | October | 11th-2016 | -0.20m | 0.95 | 1.64 | | October | 27th-2016 | 0.00 m | 0.99 | 2.11 | - In order to reduce the RMSE of the seatruth regressions, above tide heights have been added to Sonar data.
| - Tide height at La Paz is 0.8 m at most
- Sonar seatruth depths have not been corrected for tide.
- In order to reduce the RMSE of the seatruth regressions
- tide heights have been added to Sonar data.
- Such tide heights combine two sources of "error":
- a real tide height, which cannot be negative, and cannot exceed 0.8 m at La Paz;
- a bias on retrieved depths, which can be negative, caused by the settings applied to the Soil Line while inverting the RTE.
- Real tide height appears to average 0.1 m for seven scenes:
- variations probably represent uncertainty on tide and retrieved depth,
- rather than distinct variations in bottom greenness.
- Bias on retrieved depth:
- two scenes clearly stand out: depths have been over-estimated by up to 1.4 m;
- this obviously represents a bias: bottoms at these two scenes were distinctly less green than assumed through the Soil Line assumption.
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| Comments below need updating
for Sonar Seatruth | Comments below need updating
for Sonar Seatruth |
| operational 2K
This fuzzy regression does not prove much in this complex and variable hydrologic environment: we would need a LIDAR or MBES DTM
Still, in the 10-20 m depth range,
it demonstrates two sensitive things==>
| operational 2K
retrieved depths in meters only need a tide correction
- using Jerlov's data at WLblue and WLgreen,
- along with the observed ratio Kblue/Kgreen ,
- to interpolate 2Kblue and 2Kgreen
- yields a slope=1 in the above regression
- no need for field data for the optical calibration of the model
the PAN solution is a good operational option
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| About the Soil Line assumption
Spectral water column corrected
bottom reflectance is the main unknown for all SDB methods
Therefore, all methods resort
to some assumption in this regard
- empirical model: by using field depths for calibration of a multi-linear regression
- 4SM simplified RTE: by using the Soil Line assumption
- analytical RTE: by using a LUT of all possible end-member bottom substrates submitted to all possible variations of illumination/attenuation parameters over the whole shallow depth range
In the end, all methods yield
a more/less biased depth result:
there is no escaping that
| About the Soil Line assumption
In this study case:
(please help me ensure I have it right!)
- 5-10 m range ZDTM<ZC: most retrieved depths are over-estimated:
- this means that bottom substrates are actually less green than assumed by default in 4SM
- 10-20 m range ZDTM>CZ: most retrieved depths are under-estimated:
- this means that bottom substrates are actually greener than assumed by default in 4SM
- a good case for reddish substrates
Therefore also,
computing a seatruth linear regression
with a slope=1
becomes tricky, to say the least |
| By default in 4SM>>==>> - By default since 2016, I use knowledge acquired over the Bahamas, and indulge into extending its application to all images/sites over the whole Panchro depth range, by tweaking the Soil Line in 4SM code.
- Therefore, by default in 4SM code, all bottom substrates, from the brightest to the darkest, are treated as if they actually exhibited spectral signatures similar as those observed in the Bahamas over the RED depth range: turtlegrass everywhere in variable abundance over very bright coral/oolithic sands.
- This of course is over-simplistic, and I shall in the future have to diversify that according to depths results obtained within the RED range of bottom detection (0-~10 m) on an image-wise or site-wise basis.
| >>==>>What we see here - 0-10 m: retrieved depths are over-estimated
- 10-20 m: retrieved depths are under-estimated
- though tide correction should somehow alleviate the "dramatic" tone of this pronouncement
- so, for now, I tend to infer that these two depth ranges harbour different families of bottom substrates:
- 0-10 m: bottoms there would be less "green" than Bahamas's turtle grass bottoms
- 10-20 m: bottoms there would be "greener" than Bahamas's turtle grass bottoms. Note that by being "greener", we can expect them to also be "redder"
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| GSD 15m
Co-registration
DTM - PANsharpening, CombinedDepth and Seatruth all rest on a perfect co-registration among images and with the DTM
- Further development of 4SM code shall need to ascertain that perfect co-registration is achieved (my prefered solution, can be trickythough), at professional level,
- or the practioner shall be left with their petty COTS image pre-processing packages
| Time series |
| small ROI - Fabio's ROI is limited to San Lorenzo Channel
- If I were to limit this study case to Fabio's ROI, that would be a lost case, or I would have to take unreasonable risks
| extended ROI - Instead, I insisted that I would take a broader view
- so that I, as an informed practioner, would get a feeling of the prevailing hydrologic conditions in this area so as to inform the Soil Line assumption and the Brightest Line assumption for this scene
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| Clearest waters - In 4SM, the practioner gets an estimate of the optical properties of the clearest waters over the (extended) ROI, but can also wander in search of evidence of locally less clear waters (see La Parguera, Puerto Rico, Landsat 8).
| Clearest waters - This means that less clear waters over the ROI are not accounted for
- and therefore that the 4SM results are affected accordingly?
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| Fabio, if I may Your DTM is going to be a weak link in this story.
Just think of bathymetric lines abutting the shoreline.
| Fabio, if I may So, maybe Andy would not mind contributing a more realistic DTM from your very "fish finder" measured depths.
Sorry, I can't offer to do it myself.
When I say realistic, I mean: limited to areas which are adequately/densely informed.
I suppose you would just provide us with list of
XUTM YUTM YourMeasuredDepth
as an ASCII textfile, mentioning
Depth Datum (tide correction),
UTM Datum and Zone.
And I could also use a shapefile of this data, as. mentioned above
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