4SM deep water reflectance

Lw at Caicos tutorial
raw TM1 prominent dark shadow hence a strong Lwblue normalized Lwblue=14.1	raw TM2 faint shadow hence a weak Lwgreen normalized Lwgreen=3.5	raw TM3 no shadow?? hence a null Lwred Lwred=0.0	raw TM4 no shadow hence a null Lwnir Lwnir=0.0

Vegetation Line

Lyzenga et al's model

Lyzenga's Lyzenga et al 2006: figure 15 for the Blue vs Green pair I have rotated this image It now shows X_blue vs X_green K_blue=0.0561 K_green=0.736 K_blue/K_green=0.762 Isobath lines are clearly curved. red points are ~2-4 m deep over a very wide range of bottom types green points are 6-8 m deep over a very wide range of bottom types blue points are 10-12 m deep over a very wide range of bottom types	4SM 4SM optical model for the Blue vs Green pair It shows X_blue vs X_green K_blue/K_green=0.76 Thick blue: the brightest pixels line is shown. All iso-bottom lines are straight and parallel to the BPL line. Star: the brightest bottom type at null depth is represented by the big star symbol.
The authors write: "Clearly, there is a wide variation of the signals within each of these depth intervals, which could be caused by variations in either the water optical properties or the bottom composition"	From right to left, isobath lines are shown for 0, 5, 10, 15, 20 and 25 m. The difference Lw_blue-Lw_green determines their curvature, even in the absence of "variations in either the water optical properties or the bottom composition".
	For the Red vs NIR case, because Lw is next to null in both bands, the Z=0 isobath goes through the origin of this plot, and all isobath lines are straight and parallel lines.

illustrations from Dry Tortugas Reef , Florida Keys
This tuning is most critical in 4SM
Please refer to 4SM summary
Please refer to 4SM reflectance

Area sampled for the bi-dimensional histograms includes Dry Tortugas and Mooney Harbor	Land areas are shown in yellow Deep water area is shown in red
Land areas in Dry Tortugas area for bands 2, 3, 5 and 6 (blue, green, red, NIR) from bright beach coral sands/rubbles to dark mangrove vegetation. Includes a small area over optically deep waters. Please note where the deep water pixels plot, relative to land pixels.	Land areas in Dry Tortugas area for bands 1, 2, 4 and 6 (purple, blue, PAN, NIR) from bright beach coral sands/rubbles to dark mangrove vegetation. Includes a small area over optically deep waters. Please note where the deep water pixels plot, relative to land pixels.
Knowing that Lsw=La+Lw Lsw_NIR=La_NIR brighter pixels are coral sand/rubble darker pixels are green vegetation: high in green low in blue low in red we now have enough information to specify the Soil Line for all pairs of bands Choosing the values for La (or Lw) is a tradeoff which must result in a consistent system in accordance with the basics of physical realities	In a bi-dimensional histogram, the Soil Line runs from a bright point LsM which represents the bright coral sand/rubble to a dark point La which represents a black body The Soil Line leaves greenish land pixels on its green side leaves blueish land pixels on its blue side etc
Optical model over Land areas in Dry Tortugas area for bands 6, 5, 3, 2 from bright beach coral sands/rubbles to dark mangrove vegetation.	Optical model over Land areas in Dry Tortugas area for bands 6, PAN, 2 and 1 Note that the PAN band is fuzzy (is it a co-registration problem?)
For OLI data, LM, La and Lw values are easily converted into RM, Ra and Rw reflectance: we get the following for this calibration: RM 0.279 0.356 0.415 0.437 0.516 0.696 0.584 this represents average coral sand in the Bahamas Rw 0.033 0.026 0.006 0.000 0.000 0.000 0.000 this may be deemed a bit low for such water, in view of published scholar knowledge, we must remember that it represents near-nadir viewing rather average cosine viewing Ra 0.097 0.075 0.049 0.048 0.033 0.017 0.014 this is available for further use in formal atmospheric correction	Use of the Soil Line Upon inversion of the simplified radiative transfer equation, he SOIL Line is used as a reference at null depth: spectrally neutral water column corrected shallow pixels shall plot on the Soil Line greenish water column corrected shallow pixels shall plot on the green side of the Soil Line etc What is important is not so much that the values adopted are exact but rather that they fit reasonably well in the overall optical picture for the specific illumination conditions of the current scene What is at stake is that the darker shallow bottoms must be modeled under reasonable conditions while the brighter shallow bottoms shall yield much more reliable results anyway is that the potential bor fottom typing is maximized
Neither the red line or the green line or any line in between shall yield optimal depth retrievals for a Blue vs Green two bands case (above), retrievals can be underestimated by up to several meters One needs to account for the fact that the Soil Line is a curve in the linearized bi-dimensional space this is what 4SM does!	For the two bands case, Lyzenga's proposition Z=A + aX₁ + bX₂ amounts to using existing depth sounding points to specify a straight Soil Line in the linearized bi-dimensional space: *X1=m0+m1X2** where Z=0 m0=-A/a m1=-b/a X₁=ln(LB₁-Lw₁) at null depth X₂=ln(LB₂-Lw₂) at null depth LB₁=LsB₁-La₁ BOA radiance LB₂=LsB₂-La₂ BOA radiance THIS IGNORES THE ROLE OF WATER VOLUME REFLECTANCE if depth points mainly represent bright bottoms, then we get the red line retrieved depths over bright bottoms shall be very good retrieved depths over dark bottoms shall be badly under-estimated if depth points mainly represent dark bottoms, then we get the green line retrieved depths over dark bottoms shall be very good retrieved depths over bright bottoms shall be badly under-estimated So, some investigators process bright bottoms and dark bottoms separately! Stumpf and Holdereid (2003) just give up altogether, and engineer an operational workaround for use by NOAA Lyons, Phinn and Roelfsema conclude in 2011 that neither Lyzenga's nor Stumpf's are suitable for seagrass bottoms
WHAT 4SM DOES Use the image to specify the radiance of the brightest shallow bottom at null depth LsM Use the image to specify the deep water radiance Use the image to split Lsw and LsM into Lsw=La+Lw LsM=La+LM Now the Soil Line is specified TOA: it runs from La to LsM BOA: it runs from 0 to LM Provided the slope and intercept of the Soil Line remain unchanged, modifying Lw or LM does not affect the retrieval of shallow depth LM can be specified to represent average coral sand reflectance: this shall yield scene-independant water column corrected reflectances in view of time series studies this is the beauty of a "ratio method"!!	WHAT IS IMPORTANT Spectral La and Lw do not need to be exact Rather, what is important is that the spectral deep water radiance Lsw be as exact as possible the slope and intercept of the Soil Line in the natural bi-dimensional space be as exact as possible.

The Vegetation Line

unlike the Soil Line which has an intercept, the Vegetation Line strikes through the origin of this plot

Path radiance La in 4SM

this is generalized to all pairs of visible bands, and used in 4SM to estimate the spectral path radiance La
- which represents the TOA radiance of a black body in a deglinted image

Water volume reflectance Lw in 4SM

therefore, the spectral Water Volume Reflectance is estimated as Lw = Lsw - La

The Soil Line in 4SM

this is where depth Z may be assumed to be null
most shallow substrates at null depth are likely to range from bright non-vegetated sands all the way to pitch dark dense vegetation, as illustrated above
so, for all pairs of visible bands, the Soil Line in 4SM idealy extends from bright non-vegetated substrates (i.e. coral sands) to black body (origin)

Vegetation Line at Caicos Bank, Bahamas