4SM summary

THE 4SM BATHYMETRY MODELING PROCESS

SUMMARY

What RSP and 4SM stand for
4SM is original
4SM is a "ratio method" What is optical modeling? a summary of 4SMprocess
How can it possibly work? a detailed account of 4SM process
Why does 4SM possibly work? an answer to current objections
4SM References

"4SM" stands for "Self-calibrated Spectral Supervised Shallow-water Modeler"

4SM is an implementation of the principles of passive multispectral bathymetry modeling.
It caters for multi/hyperspectral imagery, up to several tens of wavebands.
For the calibration of the optical model, 4SM only uses dry land and marine areas in the imagery itself along with Jerlov's table of spectral attenuation coefficients of marine waters worldwide.
Therefore, in most cases, field data are neither required nor used.

"RSP" stands for "Remote Sensing Production"

Same Day: we want that the water column correction of a worthy 4-bands image should be achieved same day
- operationality and ergonomy are wanted
RSP Ltd: if/when appropriate, I should establish a place of business to be called something like RSP Ltd, in order to manage licensing fees

4SM is original
in that it uses only the image itself, as it is in raw DNs,
to "frame" the optical properties of the shallow water body. This means that no field data are needed.

All shallow pixels lie between"Brightest Pixels Line" and the "Soils Line".
This allows to compute depth and spectral bottom reflectance of shallow pixels.
Using a value K _i/K _jobserved in the image, operational two-way spectral attenuation coefficients are interpolated from Jerlov's table of diffuse attenuation coefficients for downwelling irradiance: this allows to compute depths in meters.

All this can be done ahead of any field work.
For a proper "finish", all computed depths then need to be multiplied by a final adjustment factor which can only be derived from some sea truth when available, while spectral bottom reflectances remain unaffected.

The 4SM process is a "ratio method" derived from the concepts behind "passive multispectral bathymetry modeling"

Passiverefers to natural sun light.
Multispectralrefers to RS imagery comprised of N wavebands in the visible range (N>=2).
Modelingrefers to the estimation of the desired information using simplifying assumptions in order to operate the very complex physical model of radiative transfer of light through water for an applied purpose.

Although modeling may not be presented in simple plain terms, it is necessary to present its nature and detail its limitations in respect of the services offered.

WHAT IS OPTICAL BATHYMETRY MODELING?

A summary of the 4SM process

4SM is an existing operational radiative transfer model process which

uses multispectral or hyperspectral remote sensing imagery
to achieve water column correction of spectral radiance (~="a low tide view ")
andyield an estimate of water depth (="a digital terrain model ") at each shallow pixel ,
withoutthe use of any field data.

Applications to Remote Environment Assessment and Coastal Zone Management.

A widely accepted simplified
operational radiative transfer model for a shallow bottom is

Ls= La + Lw - Lw/ exp (KZ) + LB/ exp(KZ) top of the atmosphere (TOA )

which may be rewritten L = Lw + (LB-Lw)/exp(KZ) base of the atmosphere (BOA)
where, at any given wavelength in the visible to near infra-red range,

La is the atmospheric path radiance
Lw is the BOA water volume backscattering radiance over optically deep water
Lsw=Lw+La is the TOA radiance over optically deep water

K(in m ^-1) is an operational two-way attenuation coefficient for remote sensing radiance
Z(in m) is the depth of the shallow bottom

L is the BOA radiance for the shallow bottom at depth Z
Ls=L+La is the TOA radiance for the shallow bottom at depth Z

LB is the BOA water column corrected radiance for the shallow bottom (i.e. if Z=0)
LsB=LB+La is the TOA water column corrected radiance for the shallow bottom (i.e. if Z=0)

Please notice:

Physical units of radiance :
Radiance terms in this model do not need to be specified in physical units of radiance. Radiances may be raw digital numbers.

Atmospheric correction to BOA reflectance:
If K, La and Lsw are assumed to be constant over the remote sensing scene and may be estimated from the image, then the image does not need to be corrected to BOA reflectance for atmospheric path radiance

Ratio method:
Using a band ratio method to derive both Z and spectral LB only requires that spectral LB meets a certain condition.

Like most existing operational propositions,
the 4SM process assumes that
the deep water radiance Lsw
may be estimated from the imagery itself.

Unlike all current methods,
the calibration of the optical properties
of the model in 4SM

accounts for the color of the water column,
and does not need or use any field data.

In an innovative approach in 4SM:

The concept of the "soil line" (SL)
uses the bare land areas of the image to derive an average spectral model of the desired water column corrected image: a spectral bottom reflectance reference model at null depth.
This shall be used to specify the above mentioned required condition on spectral LB, which, among other things,eliminates the need for a spectral library of bottom type end-members to be collected on site. This is a distinct improvement of Polcyn et al.'s work (1970).

Estimating the path radiance La
The soil line also allows for the estimation of the spectral atmospheric path radiance La, and therefore of the spectral water volume backscattering radiance Lwin Lsw=La+Lw, thus permitting a first order atmospheric correction of the imagery at the base of the atmosphere. This is a distinct improvement of Polcyn et al.'s work (1970).
The concept of the "brightest pixels line" (BPL)
uses the shallow bright bottom areas of the image to derive a set of consistent ratios of operational attenuation coefficients K _i/K _jfor all pairs of spectral wavelengths i and j. This is a distinct improvement of Lyzenga's work (1978).

The Brightest Pixels Line and the Soil Line

Calibrating spectral K in units of m ^-1 Using one of these ratios and Jerlov's published data on marine optics (1976), and in line with Kirk's statement that " a family of curves, of progressively changing shape, determined mainly by phytoplancton concentration, is observed. Thus, for any given oceanic water, specification of the ratio of radiances or radiance reflectances at any two wavelengths should, in effect, specify the whole radiance reflectance curve, and therefore the optical character of the water ", one then derives one seed K value, either K _ior K _j, which then is enough for specifying all required spectral K values across the whole visible range (400-700 nm).
This avoids the need for field calibration data, and is enough to "ballpark" the optical calibration very closely. Interestingly, the estimated spectral K values are very close to sea-truth derived values.

Using Jerlov's classification for specifying spectral K

Now that all model parameters are specified:

Z and spectral LB are then derived at each shallow pixel in the image by inversion of the above model , assuming that, for the assumed depth Z, the average spectral water column corrected bottom signature LB must approximately match the spectral soil line.

The output are a DTM of the shallow water area, and also " a low-tide view of the scene in units of radiance" ready for shallow bottom typing by current thematic classification methods.

Interestingly, the estimated spectral K values are very close to sea-truth derived values.

Some sea-truth data is needed though for fine-tuning the estimation of Z, while the "low tide view of the shallow bottom" remains unaffected.

This method was presented by Morel and Lindell (1998),
and is illustrated on the Internet at http://pws.prserv.net/RSP.4SM/

It is very close to – but much more comprehensive than- the method used
by Malthus and Karpouzli (2003) who relied heavily on field data
both for atmospheric correction and for optical calibration.

It is distinctly different from -and much better than-
NOAA's "Log ratio method" by Stumpf and Holdereid (2003).

An example of the results of the optical calibration is presented in table 1 below.

Ch ⁽¹⁾

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17

WL ⁽²⁾

442

464
490
510
520
530
540
555
566
575
586
595
605
625
654
685
850

K ⁽³⁾

0.332
0.265
0.229
0.219
0.223
0.226
0.227
0.236
0.253
0.277
0.321
0.434
0.580
0.651
0.801
1.065
3.950

Zmax ⁽⁴⁾

18.1
22.4
25.7
27.4
26.7
26.6
26.4
25.5
23.9
22.5
19.4
14.2
10.3
9.0
7.2
5.3
1.6

Table 1 : Optical calibration of the shallow water body at Mahone Bay, Nova Scotia, Canada, as estimated from CASI imagery (2001).

Water type was found to be approximately JERLOV type OIII+0.12
for an observed ratio K ₄₉₀/K ₆₅₄=0.286.

(1): the CASI image has 17 wavebands
(2): wavelengths are in units of nanometers
(3): two-ways operational attenuation coefficients are in units of m ^-1
(4): maximum depth of bottom detection Zmax
over bright bottom is in meters

HOW CAN 4SM POSSIBLY WORK?

A DETAILED AND ILLUSTRATED SUMMARY OF THE 4SM PROCESS

Operating the Radiative Transfer Equation (RTE)

SOME COMMON SIMPLIFYING ASSUMPTIONS

The water body is homogeneous: each waveband i is assumed to have a specific operational two-ways attenuation coefficient K _i for radiance
The water body and the atmosphere are homogeneous: each waveband i is assumed to exhibit a deep water radiance value Lsw _i over a deep water area in the image
Backscatter of the deep water column Lw(water volume reflectance)
- Atmospheric path radiance is noted La
- We assume that we may write Lsw=La+Lw and that the glint at sea-surface is negligible
Then in 4SM we introduce some more assumptions as follows.

On the beach:

THE SOIL LINE ASSUMPTION (SL)

A clean and fine-grained coral sand pixel on the beachis bright in both bands i and j in the image: LsB _iand LsB _j
A black body pixel on the beachis black in both bands in the image: La _iand La _j
From the brightest pixel to the darkest pixel on the beach,we may consider the linear radiometric model of the Soil Line (SL)
All intermediate pixels on the beachideally plot along the linear SL in a ~diagonal position in a bidimensional histogram natural SL
Of course, this is a sheer reduction of spectral diversity of natural substrates

Shallow bottoms:

THE BRIGHTEST PIXELS LINE ASSUMPTION (BPL)

Let the tide come : Ls _Z=Lsw + (LsB-Lsw)/exp(K*Z)

Ls _(Z)decreasesfrom Ls=LsB _(Z=0) all the way to Ls=Lsw _(Z=infinite) as Z increases
This model accounts for the backscatter of the shallow water column (i.e. color of the water) because Lsw=La+Lw
Let K _i<K _j, and examine the scatter plotLs _{i (Z)}= f( Ls _j(Z)) plot of natural RTE
==> the brightest pixels plot along an exponential-shaped bulge: the Brightest_Pixels_Line (BPL) : this is the "exponential decay"
==> The BPL may be thought of as the outer physical limit of the scatter plot natural_BPL

THE RATIO K _i/K _j

Linearize this model: X = ln(Ls-Lsw) = XB - K*Z

View the scatter plotof X _i= f( X _j) plot of Linearized RTE HowNice!
The brightest pixels now plots along a linear BPL :
- the exponential decay is linearized linearized BPL
The ratio K _i/K _jmay be measured as the slope of the linearized BPL

A RATIO METHOD:
a consistent system of ratios

for a 3-bands image i, j and k, one gets a consistent system of 3 ratios
- K _i/K _j
- K _i/K _k
- K _j/K _k
for a 4-bands image i, j, k and l, one gets a consistent system of 6 ratios
and so on

A SEED VALUE FOR K

A seed value may be introduced for K _iat any particular wavelength
- in order to specify spectral K , from K _ito K _n, for all wavebands available i to n
This seed value does not need to be realistic: it might as well be taken as K _i=any_value,
- as all other values are then specified through the series of ratios
This choice of a seed value only affects the depth computed in meters,
- while "water column correction" actually depends on the ratios among spectral K values to compute spectral bottom signature.

SHALLOW WATER COLUMN CORRECTION

Invert the RTE: LB = Lw + (Ls-Lsw)*exp(K*Z)

The water column correction of a shallow pixel may be achieved by bringing it back
- to where it belongs on the Beach, i.e. on the Soil Line: LB = Lw + (Ls-Lsw)*exp(K*Z)
This is done by increasing Z until the "averaged" spectral LB sits on the Soil Line
- see Computing Depth Z Computed Depth Z
Water Column Correction: a" low tide spectral view"of all shallow water pixels has been achieved
Spectral diversity of natural shallow substrates is restored to some extent in this process
More wavebands with bottom detection result in a more realistic spectral bottom signature

COMPUTED DEPTH IN METERS

Computed Depth Z still needs to be calibrated in meters. In 4SM, this last step is done :
- by interpolating a seed value from Jerlov's table of diffuse attenuation coefficients of Marine/Coastal Water Types (case 1 waters)
No fielddata is needed
Spectral K obtained through this process are very close to reality, by some trick of the upwelling radiance vs irradiance scenario: see discussion of the Q factor page 370 of Voss et al. , 2003: "The spectral upwelling radiance distribution in optically shallow waters"

SEA TRUTH

Some sea truth is still needed to fine-tune this calibration of Z:

A tide correction may be applied,

and a CoefZ must be estimated from sea truth depth data through linear regression:

Zfinal = CoefZ * Zcomputed - TideHeight

The END
The following attempts to answer most current objections.

WHY DOES 4SM POSSIBLY WORK?

The following attempts to answer most current objections, like

Field data shall always be needed for calibration
Atmospheric correction must be applied prior to shallow water processing
Depth over dark bottoms is well known to be badly underestimated
One should be aware that K_upis much higher than K_down
One should be wary of multiple reflectionof the in-water photon path
Radiances versus irradiances: the RTE was established for irradiances
NOAA make extensive use of a their own new " Log ratio method"

Preamble

Experience : since 1994, we have capitalized the experience of processing several tens of SPOT images, some Landsat TM images, over ten Landsat ETM images, over ten large CASI hyperspectral datasets, over ten scanned color aerial photographs, and even some multispectral video, in the tropical clear coral reef waters in the Pacific, the Caribbean Sea, the Red Sea, in the Gulf of Arabs, along the coasts of France, Canada, Borneo, and Australia, and also on Canadian riverine waters.
Shallow water refers to areas in the imagery where the bottom contrast Ls-Lsw is significant , whether negative or positive : this is to mean that the radiance measured at the remote sensor includes a significant contribution by the light that has been reflected on the sea-bottom when compared with the contribution by the light that has been backscattered by the water column (or even reflected by the water surface).
Optically deep water refers to areas in the imagery where such contribution caused by the existence of a shallow bottom may safely be assumed to be non-significant.
Operational K _wl : the wavebands of a multi/hyperspectral remote sensing image are rated in terms of the operational two-ways water attenuation coefficient, denoted K _wl, which is specific to each waveband's wavelength (a delicate concept!).
Optical water type : spectral values of K also depend on the optical properties (i. e. turbidity) of the particular water mass under study.
Visible spectrum : bathymetry modeling takes advantage of the very large variation of the attenuation properties of light in marine/coastal waters across the visible part of the solar spectrum.
Water Column Correction: the purpose of optical modeling is to "un-mix" depth from spectral reflectance for a shallow bottom: 4SM modeling allows for estimating and accounting for the variations of the spectral reflectance of the bottom in the process of estimating the depth in shallow areas.

The simplified optical model

for remote sensing shallow water radiance at Top Of Atmosphere (TOA)

is referred to by O'Neil and Miller (1989)

as the " most familiar form of shallow water reflectance model".

Ls = Lsw + (LsB-Lsw)/exp(K*Z)

where ,

Ls=L+La is the radiance measured at the sensor
Lsw=Lw+La is expected to be constant over the scene
LsB=LB+La is the radiance if the bottom were at null depth (Z=0), i. e. the bottom reflectance

K is an operational two-ways attenuation coefficient for remotely sensed radiance
Z is the depth of the shallow bottom

" In conclusion, the approximate formula can be safely adopted in operation when interpreting or predicting the reflectance of shallow waters, in particular if Lw and K have been estimated from remotely sensed data. " (equation 9a of Maritorena rt al. (1994), pp 1689-1703).

The above statement actually refers to irradiance reflectances (R, A and 2K _d) , whereas we are dealing with remote sensing radiances here (La, Lw, LB and K). It remains to be seen whether or not it may safely be re-written, as we do here, for remote sensing radiances for an operational purpose. This question in particular bears on what K value is adopted, and therefore on the error on computed depths.

We think that this most important and debated question is properly addressed by the following statement of Jerlov (1976): " It should be borne in mind that, in the surface region 0-10 m, the irradiance attenuation coefficient K _dfor high solar elevation is close to the absorption coefficient a ."

We have come to the conclusion that a similar statement applies to upwelling remote sensing shallow water radiances: most of the photon paths which reach to the remote sensor have experienced a direct path from the bottom upwards, thus accounting for an attenuation coefficient which is just a little higher than the absorption coefficient a. Indeed, any upwelling photon path that departs significantly from the vertical shall be refracted even further away from the vertical upon crossing the water-air interface, and therefore stands a very low probability of being captured by the remote sensor. According to our own experience, and in contrast with prevailing opinions which consider the fate of upwelling shallow water irradiance, it would appear that operational 2K for remote sensing radiance over shallow bottoms is very close to 2K _dof Jerlov, i. e. just a little higher than the absorption coefficient a.

See in the following paragraph a complete discussion of that most important point.

This might explain why the observed 4SM performance in computed depths exceeds by far the performance predicted by Maritorena et al. (1994).

BPL: spectral K values

are estimated from the image itself
through the concept of the Brightest Pixels Line

BPL concept : for a given pair of bands i and j with K _i<K _j, it is assumed that the outer exponential shape in a bidimensional scatter plot is most likely to be caused by the brightest end member bottom substrate that exists in the area of interest.
Sample the BPL in the imagery through an automatic process for all pairs of wavebands available: see natural BPL and SL in scatter plot of band i vs band j.
Measure all ratios K _i/K _j: through the linearization of the BPL pixels, the ratio K _i/K _jis measured for all possible pairs of available wavebands i and j: see linearized BPL and SL in scatter plot of linearized data band i vs band j.
A consistent system of ratios : it is important to verify the internal consistency of all these ratios. Spectral K values are estimated from the image itself in such a way that their ratios must achieve the values observed for all pairs of wavebands in the spectral image: see tarawa_polygonred.jpg and tarawa_m2.eps.png .
A seed value for operational K : at this stage, spectral operational K may be derived for all wavebands available by just providing a seed value of K at any of these wavebands. Any seed value may be used, so that spectral operational K can be fully specified and the "water column correction" may be conducted over shallow areas.In practice, two approachesare proposed:
- Alternative A: K~=2K _d this is done in line with the statement by J. Kirk that " a family of curves, of progressively changing shape, determined mainly by phytoplancton concentration, is observed. Thus, for any given oceanic water, specification of the ratio of radiances or radiance reflectances at any two wavelengths should, in effect, specify the whole radiance reflectance curve, and therefore the optical character of the water".
  - A first step consists in estimating one interpolated marine water type of Jerlov for which one of these ratios - conveniently for example the ratio K _blue/K _green- matches the observed value: this yields an estimate of K _blueand K _green.
  - A second step consists in deriving all other K values using the observed ratios and either K _blueor K _green: see mb4.sh.jpg for a 17-bands hyperspectral case study.
  - Wavelength vs waveband : in this approach, a precise wavelength must be specified for each waveband.This isa major source of uncertainty.
  - Radiance vs irradiance : then we need to figure out how/why properties observed for downwelling irradiances may possibly be applied to two-ways water-leaving near-nadir upwelling radiances.
    - K _d ~= a : as stated by Jerlov " the spirit of this classification is that the irradiance attenuation coefficient K _dfor any wavelength can be expressed as a linear function of a reference wavelength. It should be borne in mind that, in the surface region 0-10 m, the irradiance attenuation coefficient K _d for high solar elevation is close to the absorption coefficient a ".
    - K ~= 2 K _down : we have observed that 4SM yields operational spectral K values which are in satisfactory agreement with sea truth of computed depths. Therefore, we have to assume here that, due to refraction of water-leaving radiance, the photon paths which manage to enter the field of view of the remote sensor are mostly those which had a near-nadir in-water upwelling path.
    - In other words, and for upwelling remote sensing radiances, K _up would be quite close to a .
    - In other words also, and in spite of warnings by Kirk in respect of K _up , as oblique upwelling in-water photon paths stand a very poor chance of being captured by the remote sensor, scattering would appear to play a second or third order role in the formation of operational K for shallow water remote sensing radiances.
    - Hence the observation that we can use an operational K~=2K _dof Jerlov for shallow water modeling.

Alternative B: K _nir : we are experimenting on a seed value for K _nir quasi-absolute_calibration , provided of course that a NIR band is available and that the imagery contains a fair coverage of very shallow clean sandy bottoms away from any breaking waves.
- This second approach seems to be promising as K _nirwould appear to be very stable from Oceanic to Coastal water types, because a _nir is much higher than b _nir in all Case I waters.
- In other words, scattering would appear to play a second or third order role in the formation of operational K for shallow water remote sensing radiances in a NIR waveband.
- If/when this is confirmed, we should reach to a quasi-absolute calibration of spectral operational K for remote sensing radiances.

No field data? the final CoefZ : we lack the experience of numerous sea truth experiments for a variety of spectral images in diverse environments. Therefore, all computed depths still need to be multiplied by a final depth correcting factor CoefZ to be derived from some sea truth when it becomes available, and of course a tide correction must be applied :

Zfinal = CoefZ * Zcomputed - TideHeight

This final correction doesnot affect the computed bottom reflectances though.

SL: atmospheric path radiance La
is estimated from the image itself
through the concept of the average Soil Line

Null depth : in 4SM, the average spectral Soil Line is used as a reference of pixels at null depth (Z=0).
Brightest to darkest : the spectral radiometric model for the average Soil Line is observed using the dry land parts of the image, preferably non-vegetated, from brightest to darkest.
Natural/Linearized: the Soil Line runs as a straight line in a bidimensional histogram of natural data. It runs as a curved line in most bidimensional histograms of linearized data.
Lsw=La+Lw : this concept of the average Soil Line starts from the spectral radiance of a black body on land (i.e. the atmospheric path radiance La) and runs through an ideal average very bright non-vegetated dry land pixel like a bright sandy beach.
- The key relationship here is Lsw=La+Lw.
- Lsw, the deep water radiance, is observed from the image.
- Lw, the color of optically deep water, is assumed to be null in the Red to NearInfraRed region of the visible spectrum: this is referred to as the "black pixel assumption" in the litterature.
- Lwis assigned a value which allows an acceptable match of the Soil Line with the average Soil Line observed in the image itself.
- For clear blue waters, it is usually observed that Lw _blue>>Lw _green

==>> The spectral path radiance La is estimated accordingly, then removed from the image.
==>> By subtracting La from Ls - L=Ls-La at each pixel -, one obtains the "water-leaving" radiance measured at the Base Of Atmosphere.
==>> This is equivalent to conventional atmospheric correction, BUT
- the atmospheric adjacency effect is still very much present in the image,
- the effect of oblique vs nadir viewing is not corrected for,
- BOA radiances are still in digital numbers, i. e. not in units of reflectance.

CALIBRATION DIAGRAM and
SHALLOW WATER OPTICAL MODELING

Multiple reflection==> non-linearities? In spite of all the complexities of underwater optics for irradiance, it is demonstrated that the above simplified RTE for remote sensing radiances in its operational form Ls=Lsw+(LsB-Lsw)/exp(K*Z) does behave in a linear manner across the visible spectrum .
- See in particular for a SPOT XS image that multiple reflection at extremely shallow depths does not appear to be a problem : this is demonstrated by the very linear shape of the BPL at depths of just a very few decimeters in the X[1-2] vs X[3] scatter plot of a very bright BPL in tarawa-subset

Fully framed: once all aspects of the calibration diagram are satisfactory , the spectral model is fully " framed" and ready for inversion .
Depths over dark bottoms: accounting for the water volume reflectance:
- model inversion accounts for the volume reflectance of the shallow water column through the term Lw - Lw/ exp (KZ) .
- In their "simple ratio method", Polcyn et al.'s well known condition that " a pair of bands may be found..." amounts to assuming that the Soil Line is a straight linein a linearized scatter plot of band i vs band j.
- We know that this only holds true when Lw is null in both bands i and j, i.e. in the red-nir range of the solar spectrum.
- The result of that shortcoming is that depths computed through the "simple ratio" algorithm are badly underestimated over dark bottoms.
- For any pair of bands that involves a Blue or a Green band, the linearized Soil Line is a distinctly curved line.
- Water volume reflectance is properly accounted for in 4SM, unlike in NOAA's " Log ratio" method which overestimates depths over darker bottoms.

Computing Z in meters and LB in DNs : for the current pixel, modeling then consists in searching iteratively for a depth value Zwhich yields a spectral bottom signature LsB=Lsw+(Ls-Lsw)*exp(K*Z) that is consistent with the average spectral Soil Line observed in the image.
Final Z : we lack the experience of numerous sea truth experiments for a variety of spectral images in diverse environments.
Therefore, all computed depths still need to be multiplied by a final depth correcting factor CoefZto be derived from some sea truth when it becomes available.This doesnot affect the computed bottom reflectances though.

4SM References

Jerlov N., “ Marine Optics”, Elsevier Scientific Publishing Co, Amsterdam, 1976.

Kirk J. T., " Light and Photosynthesis in Aquatic Ecosystems", Cambridge U. Press, Cambridge, 1994.

Lyzenga D. R., “ Passive remote sensing techniques for mapping depth and bottom features”, Applied Optics, vol. 13, no 3, 379-383, 1978.

Malthus T. and Karpouzli E., “ Integrating field and high spatial resolution satellite-based methods for monitoring shallow submersed aquatic habitats in the Sound of Eriskay, Scotland, UK”, Int. J. Remote Sensing, 2003, vol. 24, 2585-2593.

Maritorena S., Morel A. and B. Gentilly B., " Diffuse reflectance of oceanic shallow waters: influence of water depth and bottom albedo", Limn. and Ocean., Vol. 39, No 7, pp. 1689-1703, 1994.

Maritorena S., " Remote sensing of water attenuation in coral reefs: a case study in French Polynesia", Int. J. Remote Sensing, Vol. 17, No 1, pp. 155-166, 1996.

Morel Y. and Lindell T., “ Passive multispectral bathymetry mapping of Negril Shores, Jamaica ", Fifth International Conference on Remote Sensing for Marine and Coastal Environments, San Diego, California, 5-7 October 1998.

Philpot W. D., " Bathymetry mapping with passive multispectral imagery", Applied Optics, Vol. 28, No. 8, pp. 1569-1578, April 1989.

Polcyn F. C. , Brown W. L. , and Sattinger I. J., " The measurement of water depth by remote sensing techniques", Report 897326-F, Willow Run Laboratories, U. of Michigan, Ann Arbor, 1970.

Stumpf R. P. and K. Holderied K.," Determination of water depth with high resolution satellite imagery over variable bottom types", Limnol. Oceanogr. Vol 48, 547-556, 2003.