ShallowH2O

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.

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 photographs.

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 depth.

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 recorded signal.

The radiance emerging from the water in shallow areas (L_E) 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.

where z is the water depth, L_E is the radiance emerging from the water mass, L_b is the radiance of (wet) substrate material for no water cover (i.e. for z = 0), L_w 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, L_w, 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:

In clear shallow waters, we assume that the water column reflectance, R_w, is small relative to substrate reflectance. If R_w is constant over the scene, it may also be subtracted during correction procedures described later. The last term in equation 2 is ignored giving:

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, R_E (as described later), equation 3 is a convenient base from which to describe our method for unmixing the effects of substrate reflectance, R_bi, from those of depth, z.

In this set of equations where the depth is unknown and constant, the substrate reflectances (R_bi) are also unknown and vary. Given that water mass reflectances, R_Ei, and water attenuation coefficients, k_i, 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:

The aim is to unmix or solve for the substrate reflectances or a factor representing R_bi 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. R_bi=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 (z):

Substituting this value into equation 3 gives a solution for substrate reflectance:

where R_Bi is the derived estimate of true substrate reflectance (R_bi). The values for Z and R_Bi 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:

and the estimated substrate reflectance (R_Bi) can be represented in terms of the true reflectance (R_bi) by:

There is a problem here since variations in z will alter the intra-band (spectral) relationship or hue, because of differing values of k_i . 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 R_bi(1/2ki) so that:

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.

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, R_W. 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):

Here G is the instrument gain and L_min 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 R_Bi. 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.

The method for deriving water attenuation coefficients (K_i) 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 (R_Ei) is graphically plotted against the bathymetry (z) (see Bierwirth et al, 1992), the data should fall on a line with slope equal to -2k_i. 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 k_i's were determined for Landsat TM bands 1,2 and 3 and were: k₁ = 0.10, k₂ = 0.13 and k₃ = 0.19

Values of k are specific to the unit of depth (metres in this case) and are independent of atmospheric absorption or scaling effects on R_Ei (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.

After correcting the Landsat data (bands 1,2 and 3) to reflectance estimates as described above, these data together with the attenuation coefficients (k_i) 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, 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.

Since chlorophyll absorbs strongly in band 1 (Gordon et al,1980), the ratios of substrate reflectance R_b2/R_b1 and R_b3/R_b1 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 R_b3/R_b1 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 (Figure 7).

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.

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 multispectral data.

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 k_i from the data. The coefficents given here might at least be used as a starting point for processing other scenes.

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 truth information.

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Figure 1: Factors influencing the amount of radiance reaching a sensor over a water-mass.

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 (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.