Estimating suspended sediment concentrations in surface waters of the Amazon River wetlands from Landsat images

REMOTE SENS. ENVIRON. 43:281-301 (1993)

Estimating Suspended Sediment Concentrations in Surface Waters of the Amazon River Wetlands from Landsat Images Leal A. K. Mertes, Milton O. Smith, and John B. Adams Department of Geological Sciences, University of Washington, Seattle

method has been developed, based on spectral A mixture analysis, to estimate the concentration of suspended sediment in surface waters of the Amazon River wetlands from Landsat MSS and TM images. Endmembers were derived from laboratory reflectance measurements of water-sediment mixtures with a range of sediment concentrations. Using these reference spectra, we applied a linear mixture analysis to multispectral images after accounting for instrunwnt and atmosphere gains and offsets. Sediment concentrations were estimated for individual pixels from the mixture analysis results based on a nonlinear calibration curve relating laboratory sediment concentrations and reflectance to endmember fractions. The uncertainty in the sediment concentrations derived from this analysis for three Amazon images is predicted to be within ± 20 mg/L, and the concentrations fall within a range of concentrations of suspended sediment that were measured at several times and places in the field over the past 15 years. The emphasis of our work is to use the patterns of sediment concentrations to compute the approximate volumes of sediment that are transferred between the main channel and floodplain of the Amazon River. However, the methodology can be applied universally if the

Address correspondence to Dr. L. Mertes, Department of Geography, University of California, Santa Barbara, CA 93106-4060. Receit~l 31 July 1991; revised 27June 1992. 0034-4257 / 93 / $6.00 ©Elsevier Science Publishing Co. Inc., 1993 655 Avenue of the Americas, New York, NY 10010

optical properties of water and sediment at the site are known, and it is, therefore, useful for the study of suspended sediment concentrations in surface waters of wetlands elsewhere.

INTRODUCTION Wetlands and floodplains provide a substrate for biological and chemical processes in riverine systems. In large rivers, seasonally wet areas can be extensive, can influence global biogeochemistry (Matthews and Fung, 1987), and can encompass environments ranging from swamps to levees. The transport of water and sediment through these different environments influences not only the rates and types of biological and chemical processing, but also the geomorphic processes constructing the landforms. In our effort to test hypotheses related to biological, chemical, and geomorphic processes active on the Amazon River and its wetlands and floodplains (Richey, 1983), we require information regarding water and sediment transport at both large and small spatial and temporal scales (Mertes, 1990). Remotely sensed images provide regional coverage with the potential for monthly to daily coverage. In this article, we test a new application of spectral mixture analysis (Smith et al., 1990) for estimating concentrations of suspended sediment in the surface

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waters of the Amazon River wetlands from Landsat images. The interaction of light with a water-sediment mixture is complex because both materials scatter and absorb radiation. The apparent upwelling radiance measured remotely is not only a function of water and sediment properties, but also is a function of initial solar input, atmospheric transmission of the radiation, the upwelling radiance at the water surface, and specular reflection off the water surface due to both sunlight and skylight. These variables in turn are dependent on the illumination geometry, atmospheric conditions, and water surface parameters such as water surface roughness. If all of these variables can be accounted for, it may be possible to determine accurately the relationship between remotely sensed reflectance and sediment concentration (Curran and Novo, 1988; Vertucci and Likens, 1989; Kirk, 1986; 1989; Holyer, 1978). However, this relationship depends on a direct proportionality between reflectance and suspended solids, which may not be the case for very high sediment concentrations (Kirk, 1986). After the light is reflected and refracted through the air-water boundary, it is absorbed and scattered by the water and sediment particles. The water-leaving radiance produced by the upwelling light stream is the property measured by remote sensing detectors and is a function in part of the sediment concentration (Kirk, 1986; Holyer, 1978). The upwelling light stream in the water is primarily due to backscattering off of particles, but some portion is due to forward scattering of photons initially traveling at an angle to vertical (Kirk, 1989). As the number of particles increases, the amount of scattering increases, and, hence, the effective backscattering increases proportionally, depending on the specific optical characteristics of the sediment particles. The increase in the magnitude of the upwelling light due to scattering as the sediment concentration increases is not linear, because light is also being absorbed. As scattering increases, the path length of the light also increases. An increase in path length results in a decrease in light intensity as the light passes through more water and more particles and radiation is absorbed. The increased absorption with increased path length counteracts the increased scattering in a nonlinear manner, and the effect varies with wavelength. These two

interacting effects combined with the increased scattering with increased particle number result in a nonlinear increase in reflectance of water as sediment concentration increases (Kirk, 1986; 1989). The rate of absorption of light in water-sediment mixtures is primarily affected by the water itself and the dissolved materials in the water. Absorption by pure water is nearly undetectable at shorter wavelengths, but increases dramatically above 600 nm where absorption vibration harmonics of the O - H bonds are encountered (Kirk, 1986). In contrast to pure water, natural waters often have high absorption coefficients at the shorter wavelengths due to strong absorption by organic acids dissolved in the water (Kirk 1986). Several studies point to the significant influence of varying concentrations of dissolved organic carbon (DOC) (Witte et al., 1982a; Bukata et al., 1983; 1988; Kirk, 1986; Vertucci and Likens, 1989) and the relative proportions of humic and fulvic acids (Carder et al., 1989) on light absorption in water and, therefore, remote sensing reflectance. The rate of scattering and backscattering by suspended particles is a function of the mineralogical and textural characteristics of the particles. Laboratory studies confirm theoretical studies that state that variations in sediment color, type, and size (Kirk, 1986; Curran and Novo, 1988; Novo et al., 1989a; Albanakis, 1990; Bhargava and Mariam, 1990; 1991; Nanu and Robertson, 1990; Chen et al., 1991; Choubey and Subramanian, 1991) and the illumination geometry of the laboratory setting (Novo et al., 1989b) significantly affect the range of reflectance values observed. Accounting for variations in water and sediment optical characteristics is critical for estimating sediment concentrations from the nonlinear relationship between remotely sensed reflectance and suspended sediment concentration. The wavelengths between 400 nm and 1000 nm are the most effective for estimating the concentration of sediment in water from reflectance because of the low rate of absorption by the water and high rate of scattering. Laboratoryreflectance data described by Witte et al. (1981; 1982b) and Bhargava and Mariam (1991) and field data reported by Ritchie et al. (1976), Holyer (1978), and Vertucci and Likens (1989) showed a maximum range in reflectance at 650-750 nm from less than 1% to

Quantifying Sediment Concentration in Surface Waters 283

slightly over 30% with suspended sediment concentrations ranging from 0 m g / L to 1200 mg/L. Hence, because of the sensitivity of reflectance to sediment concentration at the visible and near-infrared wavelengths and in spite of the nonlinearity of the relationship between sediment concentration and reflectance, many methods have been developed to use remotely sensed data, especially Landsat, Coastal Zone Color Scanner (CZCS), and AVHRR data, of water-particle mixtures to estimate sediment and chlorophyll concentrations. Reviews of this subject were provided by Colwell (1983) and Curran and Novo (1988) and various methods were compared by Munday and Alf6ldi (1979). The earliest studies involved qualitative interpretations of patterns of grey levels on Landsat images that represented patterns of sediment concentration to determine flow dynamics in water bodies (Kritikos et al., 1974; Rouse and Coleman, 1976). Quantitative interpretations typically have been based on simultaneous collection of remotely sensed data, ground radiance data, and field sediment concentration data. Polynomial or logarithmic calibration curves were calculated from the relationship between the spectral and concentration data (Bennett and Sydor, 1974; McCauley and Yarger, 1975; Johnson, 1975; Holyer, 1978; Aranuvachapun and LeBlond, 1981; Carpenter and Carpenter, 1983; Viollier and Sturm, 1984; Amos and Topliss, 1985; Ritchie et al., 1976; 1987; Ritchie and Cooper, 1988; Topliss et al., 1990; Choubey and Subramanian, 1990, with the Indian remote sensing satellite, 1A-LISSI; Froidefond et al., 1991; Harrington et al., 1992). The problem with these regression analyses is that they are only able to predict the variation of sediment concentration for the original field site. Variations in atmosphere or water and sediment properties preclude their use at other locations. Many of the more recent studies have relied on chromaticity models developed by Alf61di and Munday (1978), Amos and Alf6ldi (1979), and Alf61di (1982), who partially worked around the problem of a variable atmosphere by basing their relationship on ratios of Landsat Multi-Spectral Scanner (MSS) Band 4 and MSS Band 5 to the sum of MSS Bands 4, 5, and 6. These chromaticity parameters were correlated to simultaneously collected field data of sediment concentration in the Bay of Fundy using a logarithmic transform.

Alf61di (1982) reported the successful prediction of sediment concentrations in Swedish, U.S., and Australian lakes from Landsat images using the logarithmic curves derived from the Bay of Fundy data set and by accounting for change in illumination with solar angle. Linking remotely sensed radiance measurements of the water-leaving radiance to ground or laboratory measurements of reflectance from water-sediment mixtures based on theoretical calculations of reflectance from simple radiative transfer models has been successfully attempted in a few studies including Stumpf and Pennock (1989), Vertucci and Likens (1989), Sydor (1980), and Munday and Alf61di (1979). Maul and Gordon (1975) developed a diffuse reflectance model, and Kirk (1986; 1989) discussed a variety of Monte Carlo and empirical techniques to predict reflectance for changing sediment concentration and wavelength. Two studies discussed the use of Landsat data to determine water quality in the Amazon Basin. Bayley and Moreira (1980) used qualitative classifications of Landsat reflectance to distinguish sediment-rich from sediment-poor water in the Amazon wetlands. Bradley et al. (1979) used data from Alf61di and Munday (1978) and from Yarger and McCauley (1975) to compute a logarithmic curve based on band ratios that predicted sediment concentrations from Landsat images of several scenes from the Amazon Basin. Although the accuracy of their results is difficult to determine, because they did not have any field data, it is clear that a wide range of sediment concentrations can be detected with Landsat images in Amazon wetland environments. The goal of the work described here is to quantify sediment concentrations in surface waters of the wetlands of the Amazon Basin for use in large-scale analyses of the hydrology, biogeochemistry, sediment transport, and geomorphology of these wetlands. Therefore, a remote sensing technique was needed that could be applied throughout the basin taking into account variable atmospheric conditions and with basic information on the optical properties of the water and sediment. As described, the most common techniques for analysis of remotely sensed data to determine brightness gradients associated with changes in sediment concentration have relied on data from

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individual bands, band ratios, or chromaticity ratios. In the past few years, eigenvector and principal component analysis have been applied to these same types of problems in an attempt to extract a clearer pattern of the brightness variations in the image data (Topliss, 1984; Lodwick and Harrington, 1985; Jensen et al., 1989; Hinton, 1991). In these studies the principal component images displayed similar qualitative patterns as shown by chromaticity transforms (Jensen et al., 1989) or ground data of sediment concentrations (Hinton, 1991; Topliss, 1984; Lodwick and Harrington, 1985). However, in all cases the specific interpretation of the individual principal components remained qualitative and primarily involved a discussion of the respective band contributions to each component. Spectral mixture analysis as a data analysis tool is similar in many ways to principal components analysis. A key difference is that spectral mixture analysis defines a fixed reference (endmember) that is spatially and temporally invariant, whereas the principal components vary depending on the scene. An endmember, in this case, is represented by spectral data from either the purest pixel of a specific material on an image or the purest material in the laboratory (Smith et al., 1990; Adams et al., 1989). In addition, principal components analysis separates orthogonal factors, whereas spectral mixture analysis is only dependent on the specified endmembers. Spectral mixture analysis has been used previously to analyze images for vegetation, soil, shade, and other land-surface components at the subpixel scale (Smith and Adams, 1985; Adams et al., 1986; Ustin et al., 1986; Smith et al., 1990). The estimates of sediment concentrations from Landsat data described here are based on a linear spectral mixture analysis of each image with endmembers derived from laboratory data of reflectance from water-sediment mixtures reported by Witte et al. (1981). In order to estimate sediment concentrations from the results of the linear mixture analysis, we account for the nonlinear nature of the relationship between sediment concentration and reflectance using a calibration curve, computed from a linear mixture analysis, that relates laboratory sediment concentrations and reflectance to endmember fractions. The analytical framework we describe here provides a new technique for estimating sediment concentrations from remotely sensed data that relies less

heavily on field calibration than previous methods and, like principal components analysis, also allows the simultaneous use of the radiance data from all of the spectral bands available for a given remote sensing instrument.

STUDY AREA The section of the Amazon River system described in this paper lies approximately 50 km upstream of the city of Manaus in the Central Amazon Basin (Fig. 1). The river at the Manacapurtl gage drains approximately 2.2 million km2; the average high-water discharge is 130,000 m 3/s, and the average low-water discharge is 70,000 m 3/s (Richey et al., 1989). The water stage rises on average 10-12 m, which nearly doubles the average low-water depth of 13.5 m, from low water in late September to high water in June and July (Meade, 1985; Richey et al., 1989). In this reach of the river the flood lasts an average of 150 days and inundates nearly 5000 km ~ of floodplain and wetlands [according to criteria by Mitsch and Gosseling (1986)] with maximum water depths averaging 4 m (Mertes, 1990). Depth-averaged suspended sediment concentrations averaged across the Manacapurd and Marchantaria cross sections (see Fig. 1) range from about 100 mg/L at low water to over 300 m g / L during rapidly rising water in January and February (Meade, 1985). Based on nearly 6 years of data (Meade, 1985; Dunne et al., forthcoming) the seasonal increase and decrease in suspended sediment concentration is consistent from year to year. Most importantly, concentrations can be estimated as a function of water discharge and time of sampling relative to the time of the peak flow for the annual flood. Amazon suspended sediments are predominantly silt size or finer (Meade, 1985) and comprised predominantly of quartz and kaolin (Martinelli, 1989). Other materials transported by the river that affect the reflectance from the water include the particulate and dissolved organic compounds. The particulate organic carbon will have an affect on both scattering and absorption, while the dissolved component will mostly affect light absorption. Based on 3-5 years of data, the following conclusions have been drawn concerning the dynamics of suspended and dissolved organic corn-

Quantifying Sediment Concentration in Surface Waters 285

Manaus Manacapuru Cross-Section

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pounds in this section of the river. As a weight percentage of suspended sediment, neither fine particulate organic carbon (FPOC< 63 /~m) at about 1% nor coarse particulate organic carbon (CPOC > 63/,tm) also at about 1% significantly varied seasonally (Richey et al., 1990; Hedges et al., 1986a). Dissolved organic carbon (DOC) had an overall mean value in the mainstem of the river of 3.6 m g / L also with no significant seasonal differences, except downstream of the Rio Negro confluence (i.e., downstream of the study area), where the DOC increased during falling water due to the large input of DOC from the highly concentrated (>10 mg/L) Rio Negro (Richey et al., 1990). Based on data from one rising water cruise (February-March 1984), the fulvic to humic acid ratio for the mainstem upstream of the Rio Negro confluence averaged 5.4 + 0.5 and both acid types were transported conservatively through the Manacapurd reach (Ertel et al., 1986). The data sets for characterizing the composition of the dissolved organic materials are limited, but organic ~4C ages suggest that the residence times for the fulvic and humic acids are similar to residence times based on the potential rates of

transfer of these materials through the soils in the basin. These isotope results therefore indicate that, due to the damping effect caused by the tremendous size of the river basin, the concentration of the DOC and relative concentrations of fulvic and humic acids are controlled by the chromatographic transfer rates through soils and are less affected by the seasonal patterns of water discharge in the river itself. Hence, the concentrations of dissolved organic acids are not expected to vary significantly over the water year (Hedges et al., 1986b). DATA SOURCES Landsat Data

The wavelengths covered by the Multi-Spectral Scanner (MSS) bands include: Band 4 (500-600 nm), Band 5 (600-700 nm), Band 6 (700-800 nm), and Bank 7 (800-1100 nm). The wavelengths covered by the Thematic Mapper (TM) and used in this study include: Band 1 (450-520 nm), Band 2 (520-600 nm), Band 3 (630-690 nm), and Band 4 (760-900 nm).

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Landsat images from two geographical locations were used. An MSS image of the Bay of Fundy was supplied by T. Alf61di. The image was taken 18 October 1978 at 45.58 N and 64.13 W with sun elevation at time of acquisition of 28 ° . Three images of the central Amazon Basin were used (Fig. 1). An MSS image was supplied by J. Melack for 31 July 1977. Two TM images were obtained from R. Almeida Filho of the Instituto Nacional Pesquisas Especiais (INPE) for 2 August 1988 and for 15 August 1989. Geometrically registered subsamples from each image measure 41 km x 32 km with the upper left boundary at 3.22°S and 60.77°W (Fig. 1). Sun elevation at times of acquisition were 50 ° , 50.5 ° , and 53 ° , respectively. Figure 2 shows the time of acquisition of these images with respect to the hydrograph of the corresponding year. The 1988 image was taken when the river stage was 16.19 m, 46 days after the peak stage of 18.33 m. The 1977 image was taken when the river stage was 18.27 m, 36 days after the peak stage of 19.09 m. The 1989 image was recorded when the river stage was 19.45 m, 26 days after the flood crested at 19.94 m.

Lake Chicot, Arkansas, which is an oxbow lake adjacent to the west bank of the Mississippi River. The sediments were a reddish brown color and were likely to be predominantly silt- and claysized, although grain-size characteristics were not reported by Witte et al. (1981). In the laboratory experiments the lake sediments were resuspended in an l l,600-L tank filled with filtered, deionized water. The sediments were homogeneously mixed by continuous pumping through jets lining the tank, and concentrations ranged from near 0 m g / L to over 600 m g / L . The lighting source simulated solar input at an elevation angle (measured from horizontal) of 30 °. Reflectances of the water-sediment mixtures relative to a 99% white reflecting surface were measured every 16 nm between 400 nm and 980 nm. Accuracy of these results was reported as _+20% in the 400-600-nm range and ( + 12% in the 600-900-nm range. Sediment Concentration Data

Methods for measurement of surface sediment concentrations in Amazon waters were described in detail in Mertes (1990) following the method described by Meade (1985). Briefly, samples were collected within 1 m of the water surface with a bucket or Niskin bottle sampler attached vertically to a winch cable on a large boat or held by hand over the side of a small boat. After collection,

Laboratory Spectral D a t a

The set of laboratory data used extensively in this study (Fig. 3) was reported by Witte et al. (1981). The sediments were taken from the bottom of

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Quantifying Sediment Concentration in Surface Waters 287

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the sample was poured into a splitter, two to three samples were collected, and subsequently filtered on tared Millipore filters with a nominal pore size of 0.00045 mm. Locations of sampling sites were determined either by triangulating from bank markers for mainstem cross section locations (Richey et al., 1986) or by approximating distances from local landmarks on aerial images and maps for floodplain sites. Amazon data reported here (see Fig. 2 for timing relative to corresponding hydrograph) were collected on 27 May 1977, when the stage was 18.54 m 28 days before the peak discharge (Meade et al., 1979), 25-26 July 1986, when the stage was 18.38 m 9 days after the peak discharge, 1 December 1988, when the stage was 10.54 m and the water was rising 49 days after the lowest discharge, and 30 August 1991, when the stage was 15.78 m 54 days after the peak discharge. Surface sediment concentrations reported here for the Bay of Fundy were obtained according to the method described by Amos and Alf61di (1979) on the same day that the image was recorded. Determination of the sediment concentrations in the tank experiments was described by Witte et al. (1981). In the latter two studies, sediment concentrations were also determined

A remotely sensed, multispectral image encodes information on atmosphere, lighting, and instrument conditions as well as information on the properties of the surface materials. In addition to these potential inputs, every pixel may include information on a mixture of surface materials. In order to extract information regarding the surface materials, one must account for all of these effects (e.g., Smith et al., 1990). Spectral mixture analysis was used in this study in two ways. First, it was used to estimate for each image the effects of the atmosphere and instrument drift. Second, the analysis was used to estimate concentrations of suspended sediment from Landsat encoded radiance from water bodies. A discussion of these two applications of spectral mixture analysis follows a description of the technique. Figure 4 shows the essential features of a

Figure 4. Illustration of a two-endmember mixing model. The lower and upper reflectance spectra plotted in this figure are based on the laboratory reflectance data reported by Witte et al. (1981) for suspended sediment concentrations of 5.6 m g / L and 207 m g / L ; the laboratory data were convolved with TM filter specifications and are graphed at the center wavelength for TM Bands 1,2,3, and 4. The middle spectrum is an arbitrary spectrum representing Pixel a, with an unknown concentration.

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simple two-endmember mixing model. In this case three reflectance curves are plotted for TM Bands 1-4. The upper and lower laboratory spectra represent high and low concentrations of sediment, respectively. The middle curve is a hypothetical curve for Pixel a. Given the relative magnitudes of each of the spectra, Pixel a has a sediment concentration that is intermediate between the two endmenbers. For multispectral images the spectral endmembers represent the purest sample of each component. Using these "image" endmembers, it is possible to calculate a least-squares, best fit for Pixel a along the mixing line extending between the endmembers for each band. The set of equations for each band is DNb = ~" F , DN~,b+ Eb

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High rms errors, that is, larger than instrument noise, in any group of pixels indicate a poor fit of the modeled image endmembers. Atmosphere and instrument calibration. Smith et al. (1990) described a calibration method, to account for instrument and atmosphere effects, that is based on spectral mixture analysis. The first step of this method is to choose pixels from the image that best represent endmembers of surface materials such as vegetation and soil, and of shade (to account for variable illumination). These image endmembers are aligned to reference endmembers from either laboratory or field measurements according to:

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where Gb is the calibration gain, Ob is the calibration offset, Rr,b is the laboratory or field reflectance in band b for reference endmember r, and DN,~ is the encoded radiance in band b for image endmember i (Smith et al., 1990). By calculating a least-squares solution to Eqs. (4) and (5), the appropriate calibration gains and offsets can be computed. These calibration coefficients are then applied to the image in order to compute the nominal surface reflectance values from the image radiance data. If the atmosphere varies significantly across the image, then the image must be subsampled and appropriate Gb's and Ob's must be calculated for each subimage. Ideally, the endmembers selected from an image would contain only one material. In practice, the pixels that represent image endmembers are mixtures of surface materials (Smith et al., 1990). For example, most vegetation has some component of shade due to self-shading by leaves and branches (Roberts et al., 1990). On the other hand, the reference spectra measured in the laboratory usually represent a pure substance. For example, a reflectance spectrum for a single leaf does not include information on the bark or on the lighting geometry of the plant. Because of this mixed-pixel problem, the gains and offsets cannot be simply calculated from the differences between image and reference endmember pairs. Instead the gains and offsets are calculated by a least-squares fit to Eqs. (4) and (5). By using these equations, it is possible to account for impurity of the image endmembers. Suspended sediment concentrations. Once the surface reflectance values were computed for an image by applying the gains and offsets computed from Eqs. (4) and (5), a linear spectral mixture analysis [Eqs. (1) and (2)] was used to quantify sediment concentrations in surface waters based on reference endmembers derived from laboratory measurements. From the results of the mixing model with laboratory sediment reference endmembers, the amount that each endmember contributed to the composition of each pixel was computed. These fraction values, F~, were then

Quantifying Sediment Concentration in Surface Waters 289

transformed to sediment concentrations based on a mixture analysis of the laboratory data. The same laboratory endmembers as in the image analysis were used to calculate the endmember fractions for each laboratory reflectance, producing a nonlinear curve. From these results it was possible to relate endmember fractions to the laboratory sediment concentrations, and, therefore, also to estimate sediment concentrations for individual pixels on images.

DATA ANALYSIS

Atmosphere and Instrument Calibration Encoded radiance values for each band for the image (/) and reflectance for the reference (R) endmember pairs of vegetation, clear water, and soil were used to compute the combined atmosphere and instrument gains and offsets for the Bay of Fundy and Amazon images. The differences between the spectra of the image endmembers and the reference endmembers varied from image to image, indicating that the gains and offsets were different for each image. Image and reference endmembers were used to compute surface reflectances from the Landsat encoded radiance values for the corresponding images by taking a least squares fit to Eqs. (4) and (5). The gains (G) and offsets (O) are listed in Table 1. Sites that are predicted to have constant spectral properties over the years can be used to check the radiometric and atmospheric calibration. Finding these absolute reference sites is difficult, be-

Endmembers for Suspended Sediment Concentrations

Table 1. G a i n s (G) a n d Offsets (O) for C o m b i n e d A t m o s p h e r e a n d I n s t r u m e n t Calibration a

Image

4

Bay of Fundy 18 October 1978 Amazon 31 July 1977

167.2 16.6 521.9 7.2

MSS Band 5 6 393.1 3.3 463.8 3.3

220.4 5.4 311.1 -5.2

7

Coefficient Type

259 -1.2 199.9 -4.6

G O G O

TM Band Amazon 15 August 1988 Amazon 2 August 1989

1

2

3

4

344.2 54.4 186.9 53.5

243.7 16.8 148.3 18.0

361.5 10.0 231.3 13.4

242.4 2.5 204.8 2.6

cause the spectral properties of surface materials are influenced by many factors that may also change seasonally. For example, wet vegetation is spectrally different from dry vegetation, and a shaded material will look spectrally different than the same material in direct sunlight. Therefore, the effects of lighting need to be normalized and removed from an image in order to get a temporally comparable surface reflectance. In our analysis, shade, represented by deep, clear water, is one of the endmembers, and we have therefore accounted for variable illumination across the images. For the three Amazon images, which span 12 years, several areas were located that appeared to have constant spectral properties across all of the years and among the eight spectral bands represented by MSS and TM. These sites included the sediment-poor water for the lakes and tributaries whose water drains from local drainages, terra firme (nonriparian) forest, and a few areas in the town of Manacapurtl. After normalizing and removing shade, the combined atmosphere and instrument calibration to surface reflectance was checked by comparing the reflectance spectra for the reference sites among the three images. The spectra of these few sites were within 1% on all three images. These results support the hypothesis that observed differences in the surface reflectances for the three images were due to changes in the properties of the surface materials, and not due to errors in the calibration.

G O G O

a The data are displayed as DN values and convert encoded radiance to surface reflectance according to (DN(raw) - O) / G = reflectance.

Once the image data were converted to surface reflectance the mixing model was used [Eqs. (1) and (2)] with laboratory data reported by Witte et al. (1981) to estimate sediment concentrations. In choosing to use the laboratory data described by Witte et al. (1981) for the reference endmembers for analysis of Amazon River suspended sediment concentrations, we are risking errors associated with differences between the optical properties of the laboratory materials and the predominantly silt- and clay-sized (Meade, 1985; Mertes, 1990), quartz- and kaolin-rich (Martinelli 1989) Amazon sediments, and organic-acid-rich river water (Richey et al., 1990). The two areas

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of concern are the potentially different scattering properties of the particulates and absorption properties of the dissolved constituents. Although Witte et al. (1981) did not describe in detail the textural or mineralogical characteristics of the Chicot sediments, given that they were reddish-brown lake sediments originally transported by the Mississippi River, it is likely that they were fine-grained clays and perhaps quartz particles, which would be generally similar to Amazon sediments. Figure 5 shows the variation in the percent POC fraction of the laboratory samples as a function of sediment concentration. The percentages range from 0% to 4%, but most are less than 2% and are therefore close to the 1% reported for Amazon sediments (Richey et al., 1990; Hedges et al., 1986a). Although not conclusive, these comparisons indicate that it was not unreasonable to consider the sediments from Lake Chicot as a surrogate for Amazon sediments. In contrast to the likely similarity between the two sediments, the filtered, deionized laboratory water initially would have had significantly different optical characteristics than Amazon waters containing about 4 mg / L DOC. This difference could be important because other experimental data show that, with increasing DOC concentrations, the reflectance at wavelengths between 400 nm and 720 nm decreases, especially for DOC concentrations less than 3 mg/L (Witte et al., 1982b). However, from Figure 5 it can be seen that the DOC concentration in the laboratory water measured during the Chicot experiments ranged from 0 mg/L to 6 mg/L and was generally a function Figure 5. DOC concentration (mg/L) and percent POC in water samples from Lake Chicot reflectance experiments reported by Witte et al. (1981).

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of sediment concentration. The moderate DOC concentrations in the laboratory water for the Chicot experiments could therefore explain the relatively low reflectance measurements in the shorter wavelengths (Fig. 3) which would also be expected for Amazon water. An additional complication is that Carder et al. (1989) noted that the proportion of humic versus fulvic acid has a marked effect on the absorption of light, because humic acids tend to absorb light more strongly than fulvic acids. The data reported by Ertel et al. (1986) and Hedges et al. (1986b) suggest that the relative proportions of fulvic to humic acids in the Amazon River near Manacapurti remain fairly constant at about 4.7. Thurman (1985) reported that the DOC concentration for the Mississippi River was 4.0 mg/L from data described by (Malcolm and Durum, 1976) and that, on average, fulvic to humic acid ratios for rivers are 85% to 15% or 5.7. Hence, the organic material associated with the sediments and water in Lake Chicot, which is probably from the Mississippi River, has very similar characteristics to the Amazon River. We used the reflectance data from the Lake Chicot experimental data, as surrogates for Amazon water-sediment mixtures, for the 5.6 mg/L sample as the low concentration reference endmember and the 207 mg/L samples as the high concentration endmember (Fig. 4). These concentrations bracket the range of concentrations expected for the surface waters in the study area and also have POC and DOC concentrations closest to Amazon values. To obtain the corresponding MSS and TM reference endmembers, the Lake Chicot laboratory data were convolved with the filter specifications for MSS and TM. The linear mixture analysis with the 5.6 mg/L and 207 mg/L endmembers produced fraction images which were then transformed to relative DN values with a fraction of 0% equal to a DN of 100 and a fraction of 100% equal to a DN of 200 with respect to the 207 mg/L endmember. These DN values only indicate the relative contribution of the endmembers to the composition of each pixel. In order to estimate suspended sediment concentrations from the fraction DN's for individual pixels, the 5.6 mg/L and 207 mg/L reference endmembers were used to determine the proportional contribution of each endmember to all of

Quantifying Sediment Concentration in Surface Waters 291

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the laboratory spectra reported by Witte et al. (1981). The fraction data were computed for the laboratory data according to Eqs. (1) and (2), they were transformed to DN values, and are plotted in Figure 6.

Residuals Analysis Figure 7 is a flow diagram that outlines the procedure for estimating sediment concentrations from

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Landsat data. Assumptions were made at each step of the procedure, and, therefore, errors were incorporated at each step. The errors associated with the atmosphere and instrument calibration for obtaining surface reflectance are difficult to estimate, although sites predicted to have constant spectral properties had surface reflectance spectra within 1% on all three images. Even a 1% error in surface reflectance yields a high error in sediment concentration, because the variation in the reflectance of a water-sediment mixture is very narrow. The minimum range in reflectance for the images used in this study was in MSS Band 7 from 0% to 5%, yielding an average error of 40 m g / L per 1% reflectance error for the concentration range 5.6 mg/L to 207 mg/L. However, due to the nonlinearity of the relationship, higher concentrations would have higher errors and lower concentrations would have lower errors per unit reflectance error. The maximum sensitivity to concentration was in MSS Band 5 and TM Band 3, where reflectance ranged from 0% to 11%. These values yield an average error of 18 mg/L over 201 mg/L, again with higher errors predicted for higher concentrations. The errors described for individual bands give a reasonably conservative estimate of the predicted errors associated with the atmosphere and instrument calibration. On the other hand, the mean root-mean-squared residuals (rms error), that is, the residuals calculated from Equation (3), provide a way for estimating both in magnitude and spatially the errors specifically associated with the fit of the endmembers to the image data. Assuming that the endmembers perfectly represent the mix of materials on the image, the rms errors should equal the noise levels of the image data (Sabol, 1992). A higher rms error implies a lack of fit of the endmember data, and, in this study, uncertainty regarding the predicted sediment concentration. The mean rms errors associated only with water pixels that had no vegetation fraction were 5 DN with maximum 7 DN for the 1977 image, 2 DN with maximum 5 DN for the 1988 image, and 2 DN with maximum 4 DN for the 1989 image. These residuals translate to average and maximum uncertainty of 9 m g / L and 14 m g / L for the 1977 image, 4 mg/L and 10 mg/L for the 1988 image, and 3 m g / L and 8 mg/L for the 1989 image. The mixing model was also run with

292

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e n d m e m b e r s of 5.6 m g / L and 155 m g / L with insignificantly different sediment concentrations and slight differences in the rms errors. Any errors associated with the potential inadequacy of the Chicot data as a surrogate for Amazon reflectance would be partially represented in the rms errors as a lack of fit of the model. These errors are on average less than 10 mg / L, although higher for MSS, suggesting a close correspondence between Chicot reflectances and Amazon reflectances. This conclusion is in part confirmed by a comparison of the spectral curves of the laboratory data to the calibrated surface reflectance curves from the image data. A comparison of Figures 8a, b, and c shows that the general shapes and magnitudes for the MSS data are fairly different from the laboratory curves for the closest corresponding sediment concentration. This dissimilarity shows up as a relatively higher rms error in the MSS image. In contrast, the laboratory data convolved for the TM bands compares well to the mean spectral curves extracted from the TM images from 1988 and 1989 (Fig. 9). In the future, e n d m e m b e r s based on reflectance data from controlled laboratory experiments with Amazon water and sediments or radiative transfer predictions of reflectance for e n d m e m b e r s based on Amazon water and sediment optical characteristics will provide more accurate predicted sediment concentrations. Meanwhile, these comparisons of the spectral curves indicate that it is reasonable to use the Chicot data to determine the feasibility of using spectral mixture analysis for estimating Amazon suspended sediment concentrations. Combining the two different types of errors yields a predicted minimum mean uncertainty of + 9 m g / L , + 4 m g / L , and + 3 m g / L for the 1977, 1988, and 1989 images, respectively, if the atmosphere and instrument calibration were perfect and the Chicot reflectances represent Amazon reflectances accurately. Assuming a small error in the calibrated surface reflectance values and incorporating the rms errors, we predict that the error associated with the estimated sediment concentrations for the images is on the order of + 2 0 m g / L for the 1977 MSS image and + 1 5 m g / L for the 1988 and 1989 TM images. The best way to check these predicted errors is to compare the predicted sediment concentrations from Landsat data to field measurements of sediment concentration that were collected at the same time as the image was taken. Even after

Quantifying Sediment Concentration in Surface Waters 293

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several attempts over 6 years, these data are not yet available for the Amazon River. However, these data were available for the Bay of Fundy for 18 October 1978 (supplied by T. Alf61di). Using the Chicot data set again for reference endmembers, suspended sediment concentrations were predicted for the Bay of Fundy region to see if the methodology could provide concentration estimates close to the measured values. Observed and predicted sediment concentrations for the Bay of Fundy are compared in Figure 10. All of the suspended sediment concentrations were overestimated from the Landsat data. The closest prediction was 210 mg/L for a measured value of 196 mg/L. These results are not completely surprising, because, according to Amos and Alf61di (1979), the lower the concentration of sediment in the Bay of Fundy waters, the higher the organic content of the suspended materials. In the seaward part of the bay, where the sediment concentrations were low, organic particles comprised over 80 % of the suspended material. Therefore, in these waters a high proportion of the scattering would be contributed by plankton and other suspended organic particles, which would be very different from the Chicot samples. The effect of phytoplankton on reflectance is to de-

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crease the reflectance in the short wavelengths, from 400 nm to 515 nm, and to increase the reflectance in the wavelengths from 515 nm to 600 nm (Kirk, 1986, p. 154; Quibell, 1991). The spectral mixture analysis used to analyze the Bay of Fundy image did not include an endmember to account for the effect of the phytoplankton on the reflectance. According to Amos and Alf61di (1979), the concentration of the organic material decreased to less than 20% and less than 0.5% chlorophyll close to the estuary of the Avon River. The only field data point from this area of the bay is the 196 m g / L data point. This sample is the only sample that had characteristics that were similar to the reference endmembers from Lake Chicot used in the spectral mixture analysis. This riverine concentration was predicted within 14 m g / L or 7% of the field value, a similar error to the predicted errors of the Amazon images.

AMAZON SUSPENDED SEDIMENT RESULTS Three Amazon images were analyzed, including: an MSS image for 31 July 1977 when the river stage at Manacapurti was 18.27 m; a TM image for 15 August 1988 when the stage was 16.19 m; and a TM image for 2 August 1989 when the stage was 19.45 m (Fig. 11). Sediment concentrations ranged from 0 m g / L to 180 mg/L. All of the pixels that had any component of vegetation are blacked out on the images.

Spatial Variability Figure 11 shows the color-coded images for the three years in order of increasing stage height. The highest sediment concentrations of 180 m g / L were observed in both the 1988 and 1989 images. The maximum concentration in the 1977 image was only 140 mg/L. All three images show the same general pattern of sediment concentration in the main channel. At the upstream end of the reach, the lowest concentrations hugged the right bank and probably represent the more dilute Rio Purtls waters which had not yet mixed with the mainstem water. As the river rounded the bend, the highest sediment concentrations appear to

have followed the high velocity core toward the left bank. Downstream of the bend the input of the sediment-poor Lake Manacapurti water is seen as low concentrations along the left bank. Generally, the blue colors on all three images delineate the sediment-poor waters of the tributaries and lakes supplied with water from local drainage basins. Based on field measurements of sediment concentrations in this reach, any water with sediment concentrations greater than 40 m g / L was probably originally from the main channel (Mertes, 1990). We have not yet succeeded in acquiring simultaneous field and remotely sensed measurements of suspended sediment concentrations during several field excursions over the past 6 years. However, the relative consistency of sediment transport both seasonally and year to year (Meade, 1985; Dunne et al., forthcoming) and of the background POC and DOC concentrations and composition (Richey et al., 1990; Hedges et al., 1986a,b; Ertel et al., 1986) makes comparisons of sediment concentrations estimated from Landsat data to field data collected in other years a reasonable test of the feasibility of using spectral mixture analysis and the accuracy of the results. Sediment concentration data from field measurements from four different times (Fig. 2) and from the three Landsat images are plotted in Figure 12 for the Manacapurti cross section. All three of the Landsat data sets show the low sediment concentrations, 20-60 mg/L, of the Lake Manacapurti water on the left bank. The concentrations all increased toward the center of the channel to values as high as 160 m g / L for 1989. In 1977 the concentration remained fairly constant across the center of the channel at 100 m g / L and then decreased to about 80 m g / L at the right bank. In contrast, both the 1988 and 1989 concentrations remained near 140 m g / L across the center of the channel and then decreased to about 100 m g / L along the right bank. In the 1989 image, the abrupt increase in concentration to over 120 m g / L in the pixels nearest the right bank may be due to erosion of sediment off the top of the bank into shallow water increasing sediment concentrations at the bank-river boundary. Field measurements for flows of this magnitude over the bank surfaces are not yet available to confirm this pattern. From the comparison of the field and Landsat data for the Manacapurti cross section, it is clear

Quantifying Sediment Concentration in Surface Waters 295

Figure 11a. Color-coded TM image for 15 August 1988, 16.19-m stage, showing distribution of suspended sediment. Water flows from left to right.

Figure 11b. Color-coded MSS image for 31 July 1977, 18.27-m stage, showing distribution of suspended sediment. Water flows from left to right.

Figure 11c. Color-coded TM image for 2 August 1989, 19.45-m stage, showing distribution of suspended sediment. Water flows from left to right.

296

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that the Landsat data show less of a range of sediment concentrations than the range for the field measurements. This difference may in part reflect the fact that the images were all recorded during the falling water period when sediment concentrations are dropping slowly as the river stage decreases. The field data, on the other hand, were collected during late rising water in 1977, peak flow in 1986, falling water in 1991, and early rising water in 1988 (Fig. 2), covering nearly all of the different times of the water year. Based on the data for the Manaeapurd cross section, the Landsat data appear to be within the appropriate range of values expected for the Amazon River in this reach. Another way to check the accuracy of the concentrations is to look at the gradients in concentration at the main chanel-

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Figure 12. a) Cross-channel suspended sediment concentrations from field data at Manacapurtl. Results for 27 May 1977 are plotted for concentrations at the surface (5/77-sur) and at 1-m depth (5/77-1m) according to data reported by Meade et al. (1979). The data are plotted for concentrations measured 25-26 July 1986 at the surface (1986-sur) and at 1-m depth (1986-1m), for 1 December 1988 at the surface (12/88-sur) (Mertes, 1990), and for 30 August 1991 (Mertes, unpublished data). The stage in 1977 was 18.5 m, in 1986 it was 18.54 m, in 1988 it was 10.54 m, and in 1991 it was 15.78 m. b) Cross-channel surface suspended sediment concentrations predicted from Landsat data at Manacapurtl. The envelope of the field data shown in Figure 12a is plotted for comparison.

floodplain boundary. Figure 13 shows a magnified view of the right bank of the river just downstream of the Manacapurfi cross section. In each of the TM images an individual pixel measures 30 m x 30 m. The MSS image was registered to the TM images by resampling the 90 m x 90 m pixels with a nearest neighbor algorithm to yield 30 m x 30 m pixels. On each image the concentration of sediment decreased dramatically over as few as three or four pixels (a few hundred meters) from the main channel into the floodplain. For example, on the 1977 image the water supplied at the main channel-floodplain boundary had a maximum concentration of 100 m g / L (yellow). Within less than 100 m the concentration had decreased to as low as 80 m g / L (light green). The concentration gra-

Quantifying Sediment Concentration in Surface Waters 297

dient is even more dramatic in the 1989 image. dilution by sediment-poor water draining from The maximum sediment concentration supplied local drainages represent the general pattern for along the channel-floodplain boundary was 120these times along the mainstem of the river, then 140 m g / L (pink), and it decreased to 20-40 lower concentrations of sediment would be exm g / L (dark blue) within a few hundred meters. pected for these high flows. In contrast, in 1988 In general, this rate of decrease and the dis~ e suspended sediment concentrations were tance over which it occurred are similar to conslightly higher because less water was probably centration gradients measured in the field in 1986 contributed from these more dilute sources. and as predicted from a simple sediment-routing analysis (Mertes, 1990). During high flow in 1986 measured total suspended sediment concentra- . CONCLUSION tions from five sites at the main channel-fl0odplain boundary in the study area averaged 78 This study of central Amazon surface sediment m g / L at the surface. Measured concentrations concentrations was the beginning of a long-term dropped to less than 25 m g / L a few hundred project to develop this new application of spectral meters into the floodplain along transects perpenmixture analysis such that we can efficiently quantify sediment concentrations at other Amazon dicular to the channel-floodplain boundary. Theoretical calculations of advective transport of setsites as well as in other rivers and wetlands where tling sediment in typical floodplain flows also field data are sparse. Generally the procedure show the same transport and settling pattern. includes an initial radiometric and atmospheric With a typical measured depth of 2 m, depthcalibration based on reference endmembers and averaged velocity of 0.3 m / s, and boundary shear linear mixing, calculation of subpixel fractions stresses reduced to near 0 dyn / cm z, it would take based on laboratory endmembers and linear mix200 m for all sand-sized particles and 700 m for. ing, and estimates of sediment concentrations 0.03 mm silt to settle entirely from suspension. from endmember fractions based on a nonlinear Over 50% of the sediment in suspension is siltcurve relating laboratory sediment concentrations sized or coarser. Therefore, concentrations of susand reflectance to endmember fractions. The estipended sediment could be expected to decrease mated uncertainty, based on an analysis of the rapidly as flows move onto the floodplain (Mertes, residuals of the model results, for the predicted 1990). These results, therefore, also indicate that sediment concentrations calculated from the mixing model for three Amazon images ranged from the suspended sediment concentrations predicted from the Landsat data are consistent with the as low as + 15 m g / L to over +50 mg/L. It was measured and predicted concentrations. difficult to determine the absolute accuracy of the sediment concentrations predicted for the three Amazon Landsat images, because no sediment Temporal Variability concentrations were measured at the same times that the images were recorded. However, the The most noticeable temporal pattern among the predicted concentrations fall within a range of three images is that, although the 1988 image bad concentrations of suspended sediment that were the lowest water discharge through the reach, overall the Landsat suspended sediment concenmeasured in the surface waters of this reach of trations were higher than in the 1977 or 1989 the Amazon River at several times over the past 15 years. images (Fig. 11). This apparent anomaly probably exists because the water in the main channel at On all the Amazon images there are patterns these times in 1977 and 1989 was diluted by of decreasing concentration from the main chansediment-poor runoff from local drainages. For nel onto floodplain surfaces and through floodexample, the unmixed plume of more dilute Rio plain drainage channels. The rate of decrease Pur6s water extended farther downstream along of sediment concentration and the distance over which this decrease occurred are similar to meathe right bank in both 1977 and 1989. At the same time, the initial flow of sediment-poor water sured gradients of sediment concentration in the out of Lake Manacapurd was wider in 1977 and field, and to predicted gradients of sediment con1989 than in 1988. If these two examples of centration based on the theory of sediment set-

298

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2/31/7?

Figure 13. Detailed view of distribution of suspended sediment concentrationsalongthe right bank near the Manacapurticross section showingthe rapid decrease in sediment concentration across the main channel-floodplain boundary.

tling. This match of image-derived concentration patterns with both field measurements and theoretical predictions suggests that the sediment concentration values derived from the Landsat images are accurate enough for use in predicting general patterns of sediment exchange between the main channel and floodplain. These Landsat sediment concentrations have been combined with hydrodynamic data from numerical simulations to calculate rates of sediment exchange between the main river and floodplain and to predict order of magnitude rates of deposition and erosion on the floodplain surface (Mertes 1990; forthcoming). Spectral mixture analysis is a powerful tool for estimating suspended sediment concentrations in the surface waters of wetlands for several reasons. First, if the appropriate laboratory endmembers are available or can be calculated based on the optical characteristics of the water and sediment from radiative transfer scattering theory (Mertes, 1990), then it will be possible in the future to estimate sediment concentrations with spectral mixture analysis from images for which little or no field data are available. Second, like principal components analysis, the technique incorporates spectral information from an unlimited number of bands simultaneously, thus accessing the high sensitivity to low concentrations in the blue to green wavelengths and the high sensitivity to high concentrations in the red to near-infrared wavelengths. Finally, at the spatial resolution of a Landsat pixel wetlands are complex mosaics of water, soil or sediment, and vegetation. With spectral

mixture analysis, the presence of vegetation in a pixel can be readily determined from a fraction image of vegetation if a vegetation endmember is included in the analysis, or the root-mean-square error will be high for pixels that are composed of significant vegetation cover if the analysis does not initially include a vegetation endmember. Discrimination of pixels with vegetation from vegetation-free pixels increases the overall accuracy and reliability of sediment concentration estimates, as well as helping to delimit boundaries of open water. Most importantly, none of the assumptions incorporated in this procedure preclude its use to estimate suspended sediment concentrations for any wetland scene recorded on a multispectral image if the optical properties of the water and sediment are known. Dr. J. Richey, Dr. B. Forsberg, and the crew of the Amanai in Brazil collected field data. Dr. T. Alf61di provided images and field data for the Bay of Fundy. Dr. J. Melack loaned the 1977 Landsat MSS image. Other images were obtained from R. Almeida Filho of the Instituto Nacional Pesquisas Especiais (INPE) of Brazil. S. Willis assisted with image processing and software development. This work was supported by the National Science Foundation Grant BSR-8107522, the Geological Society of America, a J. Hoover Mackin Grant, and the Society of Photogrammetry and Remote Sensing, a William A. Fischer Memorial Scholarship. CAMREX contribution number 63.

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