|P N Bierwirth, T Lee and R V Burne
|Australian Geological Survey Organisation,
|Environmental Geoscience and Groundwater
|P0 Box 378, Canberra
|ACT 2601, Australia
|Ph: (06) 2499231 Fax: (06) 2499970
Presented at the 6th Australasian Remote Sensing
Conference. Wellington, New ZeaIand.
In remote sensing images over shallow water, contrast effects due to water
depth variations tend to dominate and obscure sea-floor reflectance variations. This paper
describes a new method that unmixes and removes the exponential influence of depth in each
pixel by employing a mathematical constraint. This leaves a multispectral residual that
represents relative substrate reflectance. Input to the process are the raw multispectral
data and water attenuation coefficients. Outputs are substrate-reflectance images
corresponding to the input bands and a greyscale depth image. The method has been applied
in the analysis of Landsat TM at Useless Inlet in Shark Bay, Western Australia. Algorithm
derived substrate reflectance images for Landsat TM bands 1, 2, and 3 combined in colour
represent the optimum enhancement for mapping or classifying substrate types. By deriving
substrate colours and a depth image, three dimensional colour perspective views can be
created from the multispectral data alone.
Remote Sensing imagery provides a valuable tool for mapping the shallow-marine
environment. Multispectral scanners, mounted on aircraft and satellites, can detect
underwater features by measuring the light in different wavelengths reflecting from the
substrate. The main problem is that the substrate reflectance is mixed with effects due to
water depth, materials in the water column and light absorption properties (Jerlov, 1976),
(see Figure 1). As a consequence there is a lack of effective techniques for enhancing the
shallow marine substrate. This paper describes a newly developed technique for enhancing
the substrate and mapping water depth in shallow water scenes.
Spectral studies for mapping the concentration of water column materials, including
suspended sediments (Curran and Novo, 1988; Stumpf, 1992), algae, chlorophyll (Gordon et
al, 1980; Stumpf and Tyler, 1988) and salinity (Khorram, 1982), are well described in the
literature. These studies generally asume that light radiation fails to penetrate to the
bottom, so that substrate reflectance is not considered.
A number of studies derive water depth estimates from remote sensing data (Jupp,1988;
Nordman et al, 1990; Van Hengel and Spitzer, 1991) although these assume unchanging
reflectance from the substrate. A useful substrate enhancement technique is that of
Lyzenga (1981), although this only produces a single image from two bands with no depth
index. Both water depth and substrate mapping techniques assume that the water column is
clear or at least spatially homogeneous. Thus there is a polarisation between these
studies and water column studies which ignore substrate effects.
In this study, Landsat TM data is processed to derive multispectral substrate
reflectance parameters and water depth. Although we again assume no variations in water
column materials, this approach combines substrate and depth mapping in the one algorithm
and represents a starting point for a global model.
To determine substrate effects, near-visible wavelengths (300-700 nm) are optimum for
light penetration to the sea floor allowing for the detection of variations in substrate
reflectance (Smith and Baker, 1981). Therefore LandsatTM bands 1,2 and 3 are suitable
bands to analyse for substrate reflectance and water depth.
|Figure 1: Factors influencing the amount of
radiance reaching a sensor over a water-mass.
||Figure 2: Location map.
2.0 STUDY AREA
An area near the opening of Useless Inlet in the World Heritage area of Shark Bay in
Western Australia (see Figure 2) was selected for the study. In this area, distinctive
patterns of seagrass distribution have been mapped by LeProvost, Semeniuk and Chalmer
(1990), (see Figure 3), based on detailed ground truthing of 1:10,000 colour aerial
The water penetrating bands of Landsat TM, bands 1,2 and 3, are shown in Colour Plate A
as a colour composite of red, green and blue respectively. This image is contrast enhanced
to show detail in deeper areas (dark red). Some seagrass can be observed as dark areas,
but generally the dominating influence is brightness contrast due to variations in water
Clearly, a method is required to isolate the effect of water depth in the data so as to
effect an enhancement of substrate materials.
||Figure 3: Distribution of benthic communities in Useless Inlet After
leProvost, Semeniuk and Chalmer (1990).
The method follows the procedure presented in Bierwirth et al (1992). Initially, one
needs to understand the influence of the sea-floor reflectance on the radiance recorded at
the sensor. Figure 1 is a two dimensional representation of factors contributing to the
The radiance emerging from the water in shallow areas (LE) is a mixture of
(1) the reflectance properties of substrate materials, (2) the effects of water depth and
(3) the absorption and scattering properties of water molecules, dissolved solids and
suspended particulate matter (both organic and inorganic) (Jerlov, 1976). Jupp (1988)
provides a simple model of these effects based on the exponential reduction of radiant
flux (Jerlov, 1976) in a homogeneous medium.
LE = (e-2kz)Lb + (1- e-2kz)Lw
where z is the water depth, LE is the radiance emerging from the water mass,
Lb is the radiance of (wet) substrate material for no water cover (i.e. for z =
0), Lw is the radiance of deep water and k is the effective attenuation
coefficient for the water-body. All factors except the water depth may vary with the
wavelength of radiation measured. As the depth increases the emergent radiance is reduced
at a rate depending on the attenuation properties of the water column. Both the
attenuation coefficient, k, and the water radiance, Lw, are influenced by
absorption and scattering in the water column.
It is preferable to look at reflectance properties rather than radiance since
reflectance, of substrate and water column materials, is a measurable quantity independent
of illumination conditions. Reflectance is proportional to radiance since reflectance is
the ratio of emergent radiance relative to the total irradiance. From equation 1 we get:
RE = (e-2kz)Rb + (1- e-2kz)Rw
ALGORITHM FOR THE SEPARATION OF WATER DEPTH AND SUBSTRATE REFLECTANCE PARAMETERS
In clear shallow waters, we assume that the water column reflectance, Rw, is
small relative to substrate reflectance. If Rw is constant over the scene, it
may also be subtracted during correction procedures described later. The last term in
equation 2 is ignored giving:
REi = Rbie-2kiz i = 1,N.
The subscript i specifies the wavelength (band) for each equation and N is the number
of bands. Given that we have a means of converting sensor DN's to water mass reflectance,
RE (as described later), equation 3 is a convenient base from which to describe
our method for unmixing the effects of substrate reflectance, Rbi, from those
of depth, z.
Taking the logarithm of both sides of equation 3 gives:
ln (REi) = ln (Rbi) - 2kiz i = 1,N. (Equation 4)
In this set of equations where the depth is unknown and constant, the substrate
reflectances (Rbi) are also unknown and vary. Given that water mass
reflectances, REi, and water attenuation coefficients, ki, can be
derived, there are still N equations with N+l unknowns. Therefore it is not possible to
obtain a unique solution, yet a strategy is needed to map the multispectral features of
the substrate independent of depth effects. Summing equation 4 over N bands gives an
equation for the water depth:
(Equations 5 & 6)
The aim is to unmix or solve for the substrate reflectances or a factor representing Rbi
which is invariant with changes in water depth. This can be achieved by placing a
constraint on the quantity M so that M is constant for every pixel. Since reflectance is
between 0 and 1, the value of M will, in a true sense, he positive and tend toward zero at
100% reflectance (i.e. Rbi=1). We choose to set M=0 for reasons of convenience
as explained later. Combining equations 5 and 6 provides an estimate (Z) of the true depth
Substituting this value into equation 3 gives a solution for substrate reflectance:
RBi = REi e (2kiZ) I = 1,N.
where RBi is the derived estimate of true substrate reflectance (Rbi).
The values for Z and RBi are algorithm outputs which can be displayed as images
by scaling the numbers into the byte (0-255) range.
By setting M=0, the substrate reflectance is effectively brightened over all bands. The
effect of the constraint may be viewed as introducing an error, z, in the depth (i.e. z =
Z - z) which, conveniently if M=0, will always be positive. This may occur in areas of
dark substrate such as seagrass, which will appear deeper than surrounding sandy areas.
From equation 8 it can be seen that:
REi = Rbie-2kiZ = (Rbie2kiZ)e-2ki(z+z)
and the estimated substrate reflectance (RBi) can be represented in terms of
the true reflectance (Rbi) by:
RBi = (Rbie2kiZ) (Equation 10)
There is a problem here since variations in z will alter the intra-band (spectral)
relationship or hue, because of differing values of ki . This means that the
colours of the imaged substrate reflectance may change with variations in depth or
substrate albedo. However, this may be overcome by using the quantity Rbi (1/2ki)
Rbi (1/2ki) = Rbi (1/2ki)ez
The true reflectance properties will then be scaled by the same constant for each band
which varies between pixels. This means that the spectral hue of the substrate will be
preserved regardless of depth variations or errors in depth estimates. This then
represents the substrate enhancement that we set out to achieve.
The following inputs are needed:
- Landsat TM data (water penetrating bands) effectively converted to water mass
- Band values for the coefficients of radiation attenuation (Ki).
SENSOR DN'S TO PIXEL REFLECTANCE ESTIMATES
To use the above algorithm, the sensor DN's need to be converted to a value
representing reflectance of the water mass just below the surface, RW. The
sensor DN for a particular wavelength band can be related to surface radiances,
atmospheric influences and sensor effects by equation 2 (Richards, 1986; Bierwirth, 1992)
(see Figure 1):
(DN) = ARE + B (Equation 12)
where A=(IT/G), B = Lws (T/G) + (LP - Lmin)/G and I =
E0Tcos + ED
Here G is the instrument gain and Lmin is the instrument offset, both being
constant for a given wavelength. Other symbols are defined in the caption of Figure 1.
The correction procedure involves finding values for A and B which can be used to
correct the image DN's. This assumes that atmospheric effects, water surface radiance and
illumination conditions are relatively constant for each band.
To find B, the lowest pixel values are found within the image where the radiation in
the measured wavelengths fails to penetrate to the substrate. In this case, the emergent
water radiance will be negligible and (DN)min will equate to B (see equation
12). This value is then subtracted from equation 12 leaving only multiplicative effects.
Correction for A is not absolutely necessary since multiplying coefficients will end up
as a constant additive component in the estimated depth Z and a band constant scaling
effect on the estimated substrate reflectance RBi. However, it is useful to
examine reflectance values prior to analysis and an effective conversion would allow
multitemporal comparisons. To find A, we used published values for Landsat 5 TM sensor
gains and average solar irradiances (Markham and Barker, 1986). This does not account for
atmospheric absorption and illumination angle but provides a reasonable estimate of
spectral curve shape.
3.3 DERIVING ATTENUATION
The method for deriving water attenuation coefficients (Ki) involves the
co-analysis of multispectral data and digital bathymetry measured by shipboard soundings.
Since no detailed bathymetry was available for Useless Inlet, the coefficients used in
this study were derived in a previous study (Bierwith et al,1992) of the Hamelin Pool area
(see Figure 2).
Sub-areas were chosen so that substrate type remained constant but depth varied.
Referring to equation 4 and if pixel reflectance (REi) is graphically plotted
against the bathymetry (z) (see Bierwirth et al, 1992), the data should fall on a line
with slope equal to -2ki. The linearity of the plot indicates the degree of
homogeneity of substrate type and hence the acceptability of the chosen sub-area. By
performing regression analysis, the slope and ki's were determined for Landsat
TM bands 1,2 and 3 and were: k1 = 0.10, k2 = 0.13 and k3
Values of k are specific to the unit of depth (metres in this case) and are independent
of atmospheric absorption or scaling effects on REi (see equation 4). The
increase in k with wavelength shows the decreasing light penetration due to water
absorption. The values are higher than for optically clear water (Smith and Baker, 1981)
although low enough to indicate relatively clear water. Although K values will change
regionally, we assume that they will be similar for Useless Inlet and Hamelin Pool
particularly since they were both subscenes of the same Landsat TM scene.
4.0 APPLYING THE METHOD
After correcting the Landsat data (bands 1,2 and 3) to reflectance estimates as
described above, these data together with the attenuation coefficients (ki)
were input to the algorithm. During the processing, a TM band 7 threshold was applied to
black out all land areas. The outputs were substrate reflectance images for the same input
bands (shown as a colour composite in Colour Plate B) and water depth (Figure 4). Both
substrate reflectance and depth were output as floating point numbers and subsequently
scaled into the byte (0-255) range.
In the substrate image (Colour Plate B), colours show substrate types independent of
water depth (compare with Figure 3). Chlorophyll dominated materials like seagrasses show
as blue to cyan due to strong absorption of blue light (TM band 1) by chlorophyll. Yellow
to red areas are mainly sand bottom caused by high reflectance in Band 1. Purple areas in
the sub-littoral zone and green areas appear to be a mixture of less abundant aquatic
vegetation, either seagrass or algae, and bare sand, although more 'ground-truthing' needs
to be done to identify subtle changes in colours. On land is a greytone terrestrial
chlorophyll index derived by end-member analysis of the six non-thermal bands (Bierwirth,
|Figure 4: Water depth derived from Landsat TM bands 1, 2
and 3. Shallow sand bars are dark and deeper water is bright.
||Figure 5: Ratio of substrate reflectance bands 3 / band
1. This is an index of chlorophyll concentration.
||Figure 6: Maximum likelihood classification raw TM bands
1, 2 and 3. Six different classes are shown as grey tones.
||Figure 7: Classification of TM substrate enhancement
(see Colour Plate B). Six classes.
Since chlorophyll absorbs strongly in band 1 (Gordon et al,1980), the
ratios of substrate reflectance Rb2/Rb1 and Rb3/Rb1
are effective enhancements for the presence of chlorophyll. We present the latter ratio
(see Figure 5) which appears to give slightly better definition. Although TM band 3
contains the chlorophyll absorption band, it appears that increased backscatter and the
proximity to a reflectance peak at 7OOnm for organic particulate matter may be the reason
for the high reflectance of seagrass in this band (Dekker et al, 1992). Also Rb3/Rb1
may give greater contrast with sandy areas. In this image, seagrass areas show brightly
and are generally associated with the edge of sand bars.
The Landsat TM derived depth image (Figure 4) shows marginal sub-littoral platforms
with sand bars in the middle of the inlet. Slightly brighter tones occur for the areas of
seagrass and this is related to the depth error z, discussed earlier, which is induced by
the employed constraint (see equations 7 and 9). According to bathymetric maps, maximum
water depth is about 10 metres and generally depths derived by the satellite method
compare well statistically with depth sounding data (Bierwirth, 1992). In the previous
study of Hamelin Pool (Bierwirth, 1992), a scatterplot of hydrographic depth versus
satellite depth indicated that the water attenuation coefficients, ki, may decrease
slightly in deeper water due to varying concentrations of organic matter.
|Plate (A): Landsat TM bans 1, 2 and 3 shown in red,
green and blue (RGB) respectively.
||Plate (B): Derived substrate reflectance bands 1, 2 and
3 in RGB. This is a residual image after the removal of depth.
||Plate (C): Substrate enhancement and hill shaded water
depth combined using the HSI procedure.
||Plate (D): Perspective view looking north using depth as
height and the substrate image (B) as colour.
A common method for depicting substrate types in multispectral data is
unsupervised classification (Jupp et al,1985). The main problem with such an approach is
that water depth variation may interfere with the classification. Figure 6 shows the
results of a six class cluster analysis of TM raw bands 1,2 and 3. When comparing this
image to the water depth image (Figure 4), it is apparent that depth, not substrate type,
is the strongest influence on the derived classes. This problem is overcome if the
substrate reflectance image (Colour Plate B) is used as the base for classification
A useful way of combining the substrate-reflectance and depth images is to transform
the substrate-reflectance data to Hue, H, saturation, S, and intensity, I (Gillespie et
al, 1986). The intensity is then replaced by hillshaded depth (with an illumination source
at 100 azimuth, and 30 elevation) and the data transformed from HSI back to RGB colour
space (Colour Plate C).Colours of the substrate-reflectance are preserved, but the
intensity shows the structure of the depth image.
The water depth image is effectively an underwater digital elevation model. This means
that the substrate colours can be draped over a three dimensional perspective of the
bottom topography. Colour Plate D is a perspective view, looking northward along the
inlet, which has been created from Landsat data alone. Seagrass areas are seen to
correspond with the edges of sand bars.
5.0 DISCUSSION AND
The method derives substrate-reflectance parameters, for each band, which define
standard properties of bottom materials over the scene, free from the confusing effects of
depth variation. Substrate reflectance images represent the optimum enhancement which can
be used as a basis for substrate classification. Importantly, substrate reflectance and
water depth values are estimated in the one algorithm from a single data set. This allows
for the creation of colour 3D impressions of the shallow submarine landscape from the
Derived substrate reflectances and water depths are only estimates. There is simply not
enough information in the data to find the true values. The substrate parameters are found
by the constraint that the mean of the logarithm of substrate reflectance weighted by
attenuation properties is constant for each pixel. This is unlikely to be true in nature
where the substrate varies in overall brightness. However, we demonstrate that the
spectral hue rather than intensity is preserved. The constraint also introduces errors in
water depth determinations which are greatest for dark substrates. This is a similar
situation as for existing water depth algorithms, although the advantage of this method is
that an average depth is found from all water penetrating bands allowing for some
substrate type variation.
As mentioned previously, the correction for illumination, sensor and atmospheric gains
are not essential when only relative substrate reflectances are required. If, however,
standard values of substrate reflectance or depth are required for multi-date scene
comparisons, gain corrections may be necessary. This is because estimated depths will
contain a constant additive factor and substrate reflectances will be multiplied by a
factor, both related to the gains.
Water attenuation coefficients used as input were derived in a previous study of an
adjacent area by regressing known bathymetric data against Landsat TM radiances. However,
since the waters of Shark Bay are free of suspended sediment, low in nutrients and
phytoplankton, these coefficients may not be valid for other regions. More work needs to
be done, therefore, both in measuring water attenuation coefficients for various waters
and in developing alternative methods for deriving ki from the data. The
coefficents given here might at least be used as a starting point for processing other
In this work, water column conditions were assumed to be constant over the scene.
Although this may be a reasonable assumption in the relatively clear waters of Shark Bay,
it is unlikely to be true in many other coastal regions where variations in suspended
sediment concentration (SSC) and organic materials, for example, are important factors. In
future work, the effects of water column parameters need to be incorporated within the
context of a global model.
Although not presented here, aerial photographs and SPOT satellite data were also
processed with the described method. Sensing roughly similar wavelengths to Landsat TM
bands 1,2 and 3, aerial photographs can be digitally scanned and processed to provide
substrate analysis in much finer detail. SPOT data can also be processed to derive depth
data although the penetration capability is not as great as Landsat TM. SPOT depth data
with greater spatial resolution can then be combined with co-registered TM data as shaded
depth behind the colours of the substrate derived from the TM (see Colour Plate C).
In conclusion, the method presented here represents a significant development for
digital substrate mapping using multispectral data. The important aspect is that the
confusing effect of water depth variation is removed leaving, as a residual, the spectral
nature of the substrate. This facilitates improved accuracy in the remote mapping and
monitoring of tile shallow aquatic environment.
Within AGSO (formerly BMR) we wish to thank both Phil McFadden and Colin Simpson for
their comments on the original manuscript and also Peter Miller for the use of his
perspective view software. We also thank Shark Bay Salt Joint Venture and LeProvost
Environmental Consultants (formerly LeProvost, Semeniuk & Chalmer) for the ground
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8.0 FIGURE CAPTIONS
Figure 1: Factors influencing the amount of radiance reaching a sensor
over a water-mass.
Figure 2: Location map.
Figure 3: Distribution of benthic communities in Useless Inlet After
leProvost, Semeniuk and Chalmer (1990).
Figure 4: Water depth derived from Landsat TM bands 1, 2 and 3.
Shallow sand bars are dark and deeper water is bright.
Figure 5: Ratio of substrate reflectance bands 3 / band 1. This is an
index of chlorophyll concentration.
Figure 6: Maximum likelihood classification raw TM bands 1, 2 and 3.
Six different classes are shown as grey tones.
Figure 7: Classification of TM substrate enhancement (see Colour Plate
B). Six classes.
Plate (A): Landsat TM bans 1, 2 and 3 shown in red, green and blue
Plate (B): Derived substrate reflectance bands 1, 2 and 3 in RGB. This
is a residual image after the removal of depth.
Plate (C): Substrate enhancement and hill shaded water depth combined
using the HSI procedure.
Plate (D): Perspective view looking north using depth as height and
the substrate image (B) as colour.