- BOA data: RE = (e-2kZ)Rb + (1 -e-2kZ)Rw??
- Bierwirth's method requires atmospheric correction to BOA data
- It can be noted that pixels display as linear clouds for the Blue and Green bands, but not quite so for the Red band
- measuring 2Kblue and 2Kgreen is straightforward
- measuring 2Kred in impossible
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- Bierwirth's Kred=0.194 m-1 ==> 2Kred=0.392 m-1 at Hamelin Pool is physically un-acceptable:??
- the red band would show bottom detection down to (ln(200)-ln(1))/0.392~=13.5 m over a very bright shallow bottom in a bright Landsat TM image, whereas it seldom exceeds ~6-7 m!
- 2Kred actually varies in the range of 0.6 m-1 to 1.0 m-1 in Jerlov's clear waters (two-ways) for in TM/ETM images
- with Kblue/Kgreen=0.85
- the measured slopes of 2Kblue=0.20 m-1 and 2Kgreen=0.26 m-1 are quite obvious from looking at Fif. 4
- although I measure 2Kblue=0.25 m-1 and 2Kgreen=0.30 m-1 with Kblue/Kgreen=0.83
- Hamelin Pool's surface waters from 0 to 4 m would have water type ~OII+0.5 of Jerlov
- with Kgreen/Kred=0.68, Hamelin Pool would have water clearer than OI of Jerlov?
- Oceanic I of Jerlov is Sargasso sea
- with Kblue/Kred=0.53, Hamelin Pool would have water type ~Coastal 4 of Jerlov?
- we observed 2Kred~=0.8 m-1 in Hamelin Pool in 2000
- All this is definitely inconsistent
- As for M=0, well what can I say?
- M=0 "standardizes the geometric mean of substrate reflectance for every pixel" Hmmmf... quite a fuzzy concept
- in equation 14, for each band i with bottom detection at the current pixel, ln(Rbi)/2Ki equals the maximum detectable depth. Therefore M is the average of all these maximum detectable depths at that current pixel
- in equation 15, we see that M is a depth offset which is specific to the actual bottom reflectances of the current pixel
- "It is important to note that, in applying the constraint which standardizes the sum of the logarithms of band substrate reflectances, we introduce errors in depth determinations. These errors are greatest for dark substrates which will resolve as deeper than true." This is particularly obvious at Hamelin Pool over the area where a dark diatom rich ooze is reported.
- Seatruth
- First source of systematic error in so-called linear methods:
- bright and dark shallow bottoms shall get an underestimated Z
- while other pixels shall conversely get an overestimated Z
- Second source of systematic error in so-called linear methods:
- Offset: this an offset which may be viewed as needing a tide height correction (~3.5 m here)
- Third source of error in so-called linear methods:
- Slope: K values may have been mis-estimated, hence a possible slope not being equal to 1 in the seatruth regression
- Fourth source of error with all methods:
- Bottom detection limit: clearly visible here: if the Red band is used beyond its bottom detection limit (at most ~6-7 m, for a very bright bottom in very clear waters), things happen!
- Bottom contrast:
- for 8 bits DNs, bottom contrast=Ls-Lsw
- bottom contrast of at least 1 DN, but quite often much more where the S/N ratio of the data is poor, is needed for a band to be enabled in the computations.
- The authors refer to clearer waters at depth for a possible explanation of the change in slope beyond seatruth depth ~4 m in this regression plot
- in other words, depths are underestimated because 2K are overestimated
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