Discrimination of Inundated and Non-Inundated Community Types with Multi-Spectral Multi-Angle POLDER Data

Submitted by: Martha Cecilia Díaz Barrios¹, Susan L. Ustin¹, Jorge E. Pinzón², Guillaume L. Perry³, Vern C. Vanderbilt³, Gerald P. Livingstone⁴, Leslie A. Morrissey⁴, Francois-Marie Bréon⁵ and Marc M. Leroy⁶ ¹Department of Land, Air and Water Resources, University of California, Davis, CA 95616, USA ²Department of Applied Mathematics, University of California, Davis, CA 95616, USA ³NASA Ames Research Center, Moffett Field, CA 93401, USA ⁴Department of Biology, University of Vermont, Burlington, VT 05405-0088, USA ⁵CEA/DSM/LMCE, Gif sur Yvette, France ⁶UMR CNES-CNRS-UPS, Tolouse, France

| Slide Presentation | Related Paper: Accuracy of Multiple View Angle and Nadir Spectral Based POLDER Images for Discrimination of Inundated and Non-Inundated Community Types

Author for Correspondence:
Susan L. Ustin
Department of Land, Air, and Water Resources
University of California
Davis, CA 95616
Phone: (530) 752-0621
FAX: (530) 752-5262
email: slustin@ucdavis.edu

Abstract

Better estimates of the areal extent of inundated vegetation types and open water would greatly reduce the uncertainties in atmospheric methane budget. We identify a method to estimate the areal extent and distribution of open water, inundated communities (bogs and fens), and upland boreal vegetation types using multi-view angle POLDER data. The study site is located in the vicinity of the southern study area of NASA’s BOREAS project in central Saskatchewan, Canada. Community identifications were based on multi-band multi-view angle signatures. We extended the application of spectral mixture analysis techniques to bi-directional remotely sensed data to take advantage of the multiple sun/view angle images available from POLDER. The development of multiple view angle spectral endmembers for vegetation mapping is a unique approach to image analysis. Bi-directional spectral mixture analysis (B-DSMA) techniques were evaluated for their ability to interpret POLDER mixed pixel data and provide areal estimates of land cover classes using BRDF endmembers. The glitter of specular sunlight off water bodies provides a strong and unique signature. Further, community structure, canopy architecture, and phenology are markedly different between these systems producing significant spectral view angle differences. The normalized view angle spectra were separated into open water, two dry upland vegetation types, soil, and wetlands. Those spectra and their correlation with physical differences among land cover types suggest that is possible to obtain a good classification for boreal wetlands using POLDER satellite data.

I. INTRODUCTION

Understanding the role of northern wetland ecosystems in global atmosphere-biosphere interactions is a key factor in predicting atmospheric concentrations of greenhouse gases, especially methane. The role of methane in climate forcing and the sources/sinks of circumpolar methane are of great uncertainty in such predictions. Boreal wetlands, north of 45° latitude, represent more than half of the Earth’s total wetland area and are a globally significant source of methane [1], [2]. Since climatic warming is predicted to be first observed and most dramatic in the northern high-latitudes, microbial decomposition processes acting on carbon stores will almost certainly lead to increased atmospheric loading of CO₂ and CH₄, potentially leading to a forward feedback to the climate system and enhanced greenhouse emissions [3], [4]. The organic carbon stored in peat and soil in these ecosystems exceeds that of any other terrestrial biome [5]. Because different land cover types can exhibit three orders of magnitude variation in methane fluxes, better mapping of wetland ecosystems in the boreal region is necessary to reduce uncertainties in global methane estimates [6], [7], [8], [9],[10], [11].

Accurate assessment of the areal extent of sinks and sources of methane is critical to determine the net global CH₄ balance. Exchange rates from various individual land cover types for methane vary from inundated herbaceous wetlands which are strong methane sources, to bogs which are weak sources, and non-inundated or non-wetland communities which may function as either sinks or have neutral exchange [12]. Boreal herbaceous wetlands are methane hot spots and represent the dominant global CH₄ source from northern ecosystems. An underestimate in the areal extent of these systems by oversampling bog wetlands greatly underestimates the contribution of boreal systems to the global methane budget. Further complicating methane estimates is the sporadic uptake of methane that has been observed in bogs and fens and upland tundra when the substrate becomes aerobic, e.g., after drying [12], [9], [13]. This is because the presence or absence of inundation largely determines oxygen availability in the underlying soils and thus whether microbial decomposition of organic materials will proceed via reductive (anaerobic) or oxidative (aerobic) pathways to yield, among other products, CO₂ or CH₄ [6], [13], [10]. In contrast to methane sources which vary greatly, the rates of methane exchange from sink areas are more consistent across ecosystems and latitude [8], particularly for boreal upland forests [12], [14].

Remote Sensing of Wetlands

The areal extent of wetlands is poorly known on regional to global scales, particularly the areal extent of inundated wetlands (bogs and fens), open water lakes and [7], [8], [15], [13], [9], [10], [16] dry land vegetation (herbaceous, and evergreen or deciduous woody trees and shrubs). Various estimates of wetland areal extent differ nearly seven-fold [1]. Remote sensing of ecosystems is the only practical means to monitor wetland condition and areal extent and could significantly aid in reducing uncertainties of these areal estimates. The identification of wetland types and their distributions typically has been performed using aerial photography. Recently, radar and satellite images have been incorporated into wetland studies although the successes of these methods have been mixed when applied over large areas. Radar imagery has been used to detect and map wetland regions. Pope et al. [17] developed a radar classified wetland distribution for a region in the central American tropics using a hierarchical classification algorithm based on different biophysical parameters derived from the SAR imagery.

The use of satellite images to map wetlands extends from the use of simple three-color visible or false color images to the use hyperspectral images. While it might seem straightforward to differentiate vegetation from water bodies using vegetation indices, it has not proved easy to do in wetlands. An areal estimate of Pantanal wetlands in the Amazon basin uses NDVI AVHRR composites and 37 GHz SMRR data [18]. They found significant interactions between spatial scales derived from SMMR data and AVHRR Channel 2, but radiance change in Channel 2 at both larger and smaller scales had little correspondence with the temporal appearance and disappearance of wetlands. They concluded that wetlands at four km and smaller were not accurately mapped using AVHRR.. Jennings et al. [19] developed a wetland discrimination using aerial videography over a sub-region of the Mississippi River. They identified some habitat types, especially open water and upland areas but could not classify floating and emergent aquatic macrophytes. [20] used a single near-infrared Landsat band to monitor a wetland region of East Africa and found that they could separate wetland types but could not further classify the system without multi-temporal data to determine changes in wetland coverage. Zhang et al. [21] found correlations between different wetland types and several vegetation indices in a San Francisco Bay salt marsh and applied a new type of directed spectral mixture analysis to separate plant species in the marsh using airborne visible infrared imaging spectrometry [22]. A freshwater wetland change detection method was presented by Jensen et al. [23] using a normalized radiance signature derived from historical Landsat data. Then, they used a posterior classifier for the region, and separated vegetation into different types of wetlands and followed changes in their distribution using multi-temporal imagery. The work of Steven et al. [24] also developed a wetland classification using Landsat data. In their study they compared several classification procedures to determine which produced an improved classification for wetlands. They concluded that the results of the unsupervised classification were not improved for any of the other methodologies used (GIS rule, hybrid classification, and Tasseled-Cap transformation).

Remote Sensing of Boreal Wetlands

Morrisey et al. [6] showed that estimated methane exchange in boreal systems could be improved using land cover classification developed from optical airborne sensors. Observation of green leaf area index (LAI) in fens would allow improved estimates of the magnitude of methane emissions [25], [26], [27] due to the correlation between emergent foliage and aerobic transport of methane within the plants vascular system [6].

Morrisey et al. [6] found that characteristically cloudy conditions in boreal regions, combined with the infrequent revisit schedules of Landsat and SPOT optical sensors, made acquisition of cloud-free optical data difficult to obtain. Further, previous studies using optical data also have had difficulty identifying wetland distributions in boreal systems because spectral patterns between communities are generally not distinctive. The distinction of boreal wetlands from non-wetland types has been difficult using conventional spectral band analysis. Although some cover type discrimination can be done misclassification between wetland types and conifer or upland forests remain. Similarly spectral detection of shallow water bodies, often only a few cm in depth, has not been possible using conventional optical remote sensing. Nonetheless, the potential of radar data for boreal classifications using ERS, JERS, or Radarsat sensors, while penetrating cloud cover and able to detect surface water, have been limited by the availability only single band data [6].

The spectral signature of a feature or object depends on many factors, including atmospheric conditions, topographic position, view angle, and solar zenith angle at the time of data acquisition. The directional radiance properties have been shown to exhibit important land cover differences [28] and could be used to classify vegetation types in the same manner as classification using spectral signatures at a constant view angle. The new polar orbiting satellite sensor, POLDER (POLarization and Directionality of Earth Reflectance), that was launched in November 1996, acquired multi-spectral multiple view angle data that may permit better separation of vegetation types in boreal systems than has been possible using conventional optical methods. The POLDER data measure polarized and directional solar radiation in the visible and the near-infrared spectral bands.

POLDER has several features that make it a candidate sensor to provide spatial estimates of boreal wetland distributions. It has a high revisit frequency, multiple passes daily over boreal regions, thus increasing the probability of cloud-free data. It has relatively coarse pixel resolution, varying between 6 Km and 10 Km, making direct identification of wetland types unlikely due to their smaller spatial extent. Its polarization, wide-angle, bi-directional, multi-spectral, multi-temporal capabilities and low spatial resolution suggest that spectral mixture analysis is an appropriate methodology for mapping wetland types and estimating areal extent. The approach we used is a new form of spectral mixture analysis applied to bi-directional POLDER data to map land cover classes and distributions in boreal ecosystems. This method should be appropriate for the relatively structurally simple communities found in these ecosystems. We extended the application of the B-DSMA techniques to bi-directional remotely sensed data to take advantage of the multiple sun/view angle images available from POLDER. The development of multiple view angle spectral endmembers is a unique approach to image analysis.

To test this hypothesis we examined the primary boreal plant communities of central Saskatchewan (bogs, fens, wetlands, forested (black spruce, jack pine, aspen), non-forested non-flooded lowlands, and open water) which exhibit large differences in their bi-directional radiance properties. Such differences were hypothesized to permit discrimination using multi-view angle sensor like POLDER [29]. Airborne POLDER simulator data was flown over the NASA BOREAS experiment site in central Canada, shown in Figure 1.

II. OBJECTIVES

Our objective was to identify the distribution of open water, inundated communities (bogs and fens), and other non-inundated vegetation types located around the southern NASA BOREAS study area (centered at 54^o N, 105^o W) South West, of Hudson Bay, in central Saskatchewan, Canada, using multi-spectral, multi-angle polarized POLDER Data. Community identifications were based on multi-view angle spectral signatures. The method used is a derived form of spectral mixture analysis [30], [31], [32], [33], based on multi-view angle endmembers to estimate the areal extent of constituent land covers within each mixed pixel [29]. The paper focuses on improved methodology for an areal inventory of CH₄ source and sink areas in northern circumpolar ecosystems. The methodology describes a sampling procedure to estimate areal extent of land cover types and is not a global mapping procedure.

III. METHODS

A. Image Datasets

POLDER measures the polarized and directional solar radiation in five bands that cover the visible and the near-infrared spectral ranges from 0.44 to 0.89 micrometers, two of these bands are polarized (Table 1). The data used here were obtained from a prototype aircraft version of the POLDER [34] that was acquired from the NASA C-130 airplane flying at approximately five km above the terrain on July 21, 1994. The images were flown over the southern study site area (SSA) of the NASA BOREAS Intensive Field Campaign 2 (IFC-2) (Figure 1). The data used in this study included nine parallel flight segments that were flown in the solar principle plane, either toward or away from the solar azimuth direction, between 9:00 a.m. and 1:00 p.m. (Local solar time) on July 21, 1994. Images have an apparent ground resolution of 50m x 50m.

B. Image Processing Techniques.

Multi-angle imagery from the POLDER sensor was measured only along the principal plane to control illumination variation that would be independent of the surface conditions. POLDER is a CCD camera with a wide field-of-view lens [34]. During the BOREAS experiment the atmospheric conditions were extremely clear. Aerosol optical thickness at 500 nm were generally in the range of 0.04 [35]. Data used here were calibrated using the May 1995 sensor calibration. POLDER data were collected in five spectral bands in the visible and near-infrared region centered at 443, 550, 665, 865, and 910 nm. Measurements are recorded as a filter wheel rotates through a sequence of 10 bands requiring 3 seconds to acquire data and 10 seconds between datasets. Approximately 95% of each image overlapped adjacent images. To improve spectral band registration in the images, a 3 x 3 moving pixel average was generated for the image yielding a pixel size of about 150 m. A Lambert conformal projection was used and effects of changing sensor altitude and aircraft yaw, pitch, and roll were removed.

The POLDER images were registered and organized to create synthetic images in which each band of data corresponds to a different view angle (Figure 2). Therefore, each pixel in our image is composed of a set of 16 different view angles, ranging between -50^o and +50^o where nadir is at 0^o with 5^o view angle intervals. The field-of -view in the across-track direction, perpendicular to the principal plane was approximately + 43^o. Because the image data were obtained in the solar principal plane, the radiance varies from the back scattering direction to the forward scattering direction. Pixels observed in the solar principal plane represent the maximum range of scattering directions in the POLDER imagery and for this reason just the principal plane of the flight line was studied. Flight line 5 was selected to illustrate illumination patterns because all land cover types are present within the flight line.

The image is described as an array I where the pixels I (x, y, 1) of the image correspond to the first view angle of the point x, y; the position I (x, y, 2) corresponds to the second view angle of the point x, y; the position I (x, y, b) corresponds to the b view angle of the point x, y, where:

In order to correctly register the view angle bands and ensure that view-angle segments were not shifted over the image, we normalized the data to the sun angle:

Normalized View Angle (NVA) = (f_s + f_v) / 2 f_s

(1)

Where

In this way, the first band corresponded to a normalized angle equal to zero in the hot spot direction (backward direction) and the last band corresponded to the normalized angle equal to one in the specular direction (forward direction). Nadir corresponds to a normalized view angle equal to 0.5.

IV. DATA ANALYSIS AND RESULTS

A. Construction of a Normalized view angle spectrum

Figure 3 shows the mean and standard deviation of radiance for all pixels (x, y) for two wavelengths, 0.665 nm (Figure 3a) and 0.865 nm. (Figure 3b). Mean radiance and standard deviation of radiance varies with view-angle as shown for flight line 5. This simple statistical analysis along the principal plane of the image shows that there are two important characteristics of the multiple view-angle signals. First, for normalized view-angles near to 0 (back scattering direction) the radiance approaches a local maximum value; at normalized view-angles equal to 0.5 (nadir direction) radiances are near minimum values and for normalized view-angles near +1 (forward scattering direction) the radiance approaches maximum values. These simple patterns, shown by the histogram of image pixels for bands 665 and 865 nm illustrate the basis for our method of classification. These data show that the directional radiance varies across different view angles. These variations in specific view angles can be used as a base for pattern recognition and discrimination of different land cover types over the image.

The multi-angle information takes advantage of two very important differences between the optical properties of water and vegetation. Reflectance from water bodies depends upon surface characteristics, that is, if the water surface is smooth and flat (e.g., when no wind is present) it behaves as a perfect mirror and will produce specular reflection and the radiance angle will be equal to the incidence angle [36]. If, on the other hand, the water surface is rough, (e.g., when waves are present), the incident light will produce diffuse radiance without a preferential scattering direction. The difference between these extremes modifies the radiance measured by the airborne sensor. When looking at a water surface from different view angles, the recorded radiance depends on the current (instantaneous) surface condition of the water which might change rapidly given local air turbulence conditions [36]. In contrast, the directional component of vegetation radiance presents unique optical properties that are stable for somewhat longer periods of time. Vegetation presents a maximum or peak radiance in the back scattering direction due to the low shadows in this view direction. This characteristic is commonly referred to as the canopy “hot spot” and has been the subject of extensive theoretical and experimental studies [37].

B. Extraction of Normalized view angle spectra

To gain more insight into which land cover patterns can be separated and correlated using multi-angle images, a pure pixel analysis was performed using the pixel purity index (PPI) in ENVI (Environmental Resources Inc., Boulder, CO) over the principal plane of each of the flight segment. The pixel purity index performs a series of projections on the spectral signatures for each pixel, extracting only the most extreme. Composed by repeatedly projecting n-dimensional scatterplots onto a random unit vector, the extreme pixels in each projection are recorded [38]. Clusters of pixels are identified and show correspondence to different land cover types, as seen in Figure 4. This Figure is a 3-D representation of the spectral radiance of three of the POLDER normalized view angle bands. As shown, each axis corresponds to one band of the multi-angle image. The three selected bands show large differences with land cover type. Band 1 corresponds to the back scattering direction, band 16 to the forward scattering direction, and band 11 is a normalized view angle of 0.67. In the Figure, one cluster corresponds to pixels with very high values in the specular direction but low values over the hot spot direction. The second group corresponds to pixels with high radiance values in the specular direction and intermediates in the hot spot direction. The third group has the high values in the backscattering direction (band 1) and low in the forward scattering directions.

C. Interpretation of Normalized view angle spectra

In general the normalized view angle spectra can be described in three ranges: back scattering directions, nadir direction and forward scattering directions. The peak radiance observed in the back scattering direction results from the hot spot and in general indicates a rough surface, as if covered by vegetation or soil. This type of normalized view angle spectrum shows decreasing radiance at angles away from this direction, with a minimum occurring near the nadir direction, a pattern that is also typical of vegetation signatures [37]. The largest peak observed for some pixels in the forward directions is due to the presence of standing water in the pixel. As described before, standing water produces specular reflection in this direction. If the water surface is rough because of surface waves, there is greater probability that the incident light will be specularly reflected at more view-angle directions than if it is a smooth surface where just one view-angle direction will show specular radiance. As more waves occur, the surface of the water is exposed over more angles, which creates more directions where specular reflection can be detected by the sensor. Therefore, the pixels that illustrate the mean normalized view angle spectrum of this group are consistent with open water surfaces.

The presence of emergent vegetation in the water modifies the signal described for the first group. Emergent vegetation creates a barrier to the formation of waves on the water surface and produces a flat smooth water surface. The effect of vegetation above the water is to produce a specular reflection of light within a comparably small range of view angle, near the extreme forward scattering direction. In addition, the presence of emergent vegetation in water increases the back scattering direction radiance of the water signature, enhancing the hot spot effect.

Therefore, the type of view-angle radiance signal for inundated vegetation can be conceptualized as the results from the combined action of vegetation radiance above standing water, and is correlated with several types of emergent communities. Figure 5 illustrates the hypothetical situation. Using this description, we use a spectral superposition to determine the spectral characteristics of inundated vegetation. These areas will be discriminated by peak radiance at both backward (hot spot) and forward (specular direction) directions.

V. CONVENTIONAL ANALYSIS

Based on the normalized view angle spectral patterns described above, two conventional analyses are present with the view-angle composite POLDER image. The first analysis corresponds to an unsupervised classification of the image. The second analysis used spectral unmixing of the signal based on the spectral patterns described above as endmembers.

A. Classification of the Image

The unsupervised classification used the ISODATA algorithm in which class means are calculated and the remaining pixels were clustered interactively using a minimum distance criterion. For each iteration the means were recalculated and this process continued until the number of specified iterations is reached (300) or the threshold for each class is satisfied. This procedure was initially performed for 20 classes with a threshold of 3. After studying the statistics, several classes were combined and a new classifier with four classes was developed. These four classes are correlated with physical interpretations of the normalized view angle spectra. The statistics for each of these classes are shown in Table 2.

We used infrared photography concurrently obtained on NASA’s C-130 over the same area to photointerpret vegetation distributions. The sampling process was repeated five times during different sessions. In each of these sessions the photointerpreter identified the principal plane of the photography and analyzed it by sampling the non-overlapping regions of the photos. For the sampling procedure a fixed scale was used and just the points that present sunglint were classified as inundated. The results of the photointerpretation are presented in Table 3. As can be seen, the unsupervised classification process and the manual photointerpretation procedure produced comparable areal estimates for inundated and non-inundated areas.

Until this point we have shown discrimination between inundated and non-inundated areas based on differences in spectral view-angle signatures. We will explore other methods for improving this classification by increasing the number of land cover classes.

B. Using B-DSMA for classification and Unmixing

As shown in Figure 4, the spectra of the image pixels could be confined inside of a spectral volume delimited by the extreme pure pixels. Pure pixels in this sense, is meant to indicate the pixels having the closest approximation to pure conditions that were found in the image. From the three clusters of pixels presented in Figure 4, five spectral endmembers were chosen that maximize the difference between surface cover types. The five Bi-Directional Spectral Mixture Analysis (B-DSMA) endmembers classify open water, inundated areas and non-inundated upland vegetation areas (two land cover types), and a soil endmember. The mean normalized view angle spectra for each of the B-DSMA endmembers we identified are presented in Figure 6. Based on success in identifying B-DSMA endmembers, a Spectral Mixture Analysis was performed over the image to obtain the fractional composition of the pixels in the image.

Spectral mixture analysis is a methodology for analysis of mixed pixels in which the radiance produced for a pixel is assumed to be a linear combination of the radiance of the individual elements that compose the pixel weighted by the areal coverage of each element [32]. The spectral mixture analysis is based on the assumption that there is a linear (additive) relationship between the areal extent of an element and its contribution to the mixed pixel radiance. The procedures have been widely applied and have produced good estimates of cover for semi-arid deserts [31], [33], grasslands [39], [40], forests [41], and others land cover sites that exhibit little multiple scattering by dense canopies [40]. Given the spectral contrast among the five multi-angle patterns described, a robust spectral mixture decomposition was expected for the image.

The radiance of a determined pixel at a normalized view angle can be expressed as the sum of the radiance of each endmember in this direction, weighted by an unknown areal fraction as follows:

F(fs,fv, j)= f₁ B_soil + f₂ B_{open water} + f₃ B_Inundated + f₄ B_vegetation1 + f₅ B_vegetation2
(2)

Where

_{endmember i}

The system of equations can be solved to determine the fractions that represent the areal percentage of the pixel cover for each endmember. Three different algorithms were tested to obtain the best results for unmixing the images. These algorithms each use different constraints for the unmixing procedure: linear unconstrained unmixing, linear constrained unmixing and a special algorithm with two constraints was used. The first of these algorithms (linear unconstrained mixing) solves the system of equations without any restriction on value of the fractions. Often fractions are produced that exceed physically interpretable fraction limits, i.e., between 0-100%, and subsequently, cannot be directly interpreted. Many pixels may remain unclassified using this method. The outlier fractions could imply that the endmembers did not occupy the outside hull of the spectral mixture data volume. The second algorithm (linear constrained method), solves the system of equations under the restriction that the sum of the fractions should be equal to one. In this methodology, unrealistic fractions exceeding 100% are eliminated but negative fractions are still permitted. Although this algorithm satisfies the numerical system it does not give meaningful areal fractions. Also this type of spectral mixture analysis requires a shadow endmember to account for albedo variation among pixel spectra. This endmember is difficult to experimentally measure and the theoretical radiance (of near zero at all wavelengths) is most commonly used. This transfers most of the analysis uncertainties into the shade fraction.

We used a third algorithm to avoid the problems found in the other spectral mixture procedures and to gain a more robust method. In this method, an optimization procedure is performed to obtain the fractions of endmembers subject to two constraints, one that the sum of the fractions has to be less than or equal one and second that all the fractions have to be positive [42]. Three datasets were used, two synthetic images and one composite airborne POLDER image. The synthetic image was generated to test the B-DSMA algorithm.

1) Synthetic Data:

These data define a mixed data set of the selected endmembers. Multiplying a fraction matrix (fi) by the matrix of endmembers (B) created the data set. The fraction matrix was set using a random uniformly distributed number generator. The random generator produces values between 0 and 1, which were assigned as a fraction of the pixel area cover by the endmember. The sum of the fractions was restricted to be less than or equal to 1.

f_ij = R_i B_ij	(3)
	(4)

Where
R_iFraction of the pixel area covered by the endmember i
B_ijRadiance of the endmember i on the normalized view angle j
f_ijContribution by the endmember i to the radiance of the pixel in the normalized view angle j
F_j Pixel Radiance for normalized view angle j

This means that the selected endmembers will represent part or the totality of the pixel area. Using this method an image of 340 samples by 3 lines was composed and used as the first data set for the B-DSMA.

The second data set used for the B-DSMA followed the procedure described above, but in this case Gaussian noise was incorporated into the data. For this case the radiance for the normalized view angle j can be expressed as:

(5)

Where,

2) Results of B-DSMA:

B-DSMA was applied to both synthetic datasets. The first synthetic data set was used to test the method. The results for the first data set (Figure 7) show that the method used is capable of reproducing the known fractions for each endmember. The system of equations used to solve B-DSMA, does not have a unique solution but demonstrates that the B-DSMA algorithm optimizates the procedure yielding a percent of each endmenber within a pixel that corresponds very closely to known values. The histogram of the mean square error has an order of magnitude of 1x10^-4. It is important to note in Figure 7, that the method identified both the large and small fractions of the endmembers.

The second data set introduces Gaussian noise, which helps to evaluate the performance of the B-DSMA over noisy images. Figure 8 shows the result of B-DSMA. Here again the algorithm yields high r² values but less than those showed in Figure 7. In this case the method is primarily confusing the two non-inundated vegetation endmembers. The open water and inundated vegetation endmembers are still easily identified where their percentage of the pixel is greater than 0.05. When the inundated regions exceed 50% of the pixel area we believe that the classification will improve. Because of the distinctive endmembers used it is expected that the B-DSMA method will provide better results as seen in the case for open water (fractions between 0 and 0.8) shown in Figure 8.

The confusion of the two types of non-inundated vegetation can be explained by the similarity between endmembers. In order to discriminate more precisely between these two types of vegetation we suggest the use of an NDVI ratio over the composite POLDER data. The NDVI ratio for the compose POLDER image will also help to discriminate between pixels with small fractions of inundated regions and non-inundated pixels [36].

Based on the algorithm results using the two synthetic datasets and because the regions of study are easily characterized using five endmembers, we expected similar results when applying this discrimination process to the composite POLDER image data. The resulting classifications for the POLDER data are shown in Figure 9.

The images presented correspond to the fraction of each component in each pixel. The fractions are displayed so that a pixel having 100% of the endmember is white and 0% is black while intermediate fractions are shades of gray. The results of this analysis can be compared with the results of the standard unsupervised classification method. For the unsupervised classification a pixel is considered to be pure and covered just by one land cover feature. When this assumption is incorrect, the classification produces an overestimate for the areal extent of that endmember in the image. With Spectral Mixture Analysis, however the area can be calculated as the fraction fi for each endmember represented in the pixel. In this study, the airborne composite POLDER data have relatively small pixels hence the spectral mixture issues are of less importance than they would be if this image were taken by a spaceborne sensor, nonetheless it illustrates the value of this approach.

The B-DSMA for the inundated endmember identified 501 pixels having some fraction of inundated area within the pixel. However, for some pixels where the inundated endmembers occupied less than 20% of a pixel area it could easily be confused with a dry land vegetation signature. Therefore, to avoid this situation, just endmembers whose fractions were greater than 20% were considered. In this example, inundated endmembers that occupy more than 20% of the pixel totaled 164. If all 164 pixels were considered as pure, as assumed in the unsupervised classification, this class would represent 18.7% of the image. By eliminating those pixels where the inundated endmember was less than 20% we found that the inundated endmember class composed 11.6% of the image.

Table 4, shows the fractional coverage of these endmembers. These percentages come from the accumulation of the B-DSMA fractions over the pixels studied.

C. Extending B-DSMA to satellite image resolution and large pixel size.

The satellite version of POLDER will have a lower spatial resolution than the airborne sensor. Spaceborne image pixel sizes are approximately 7 Km. The present methodology for detecting B-DSMA was tested on aggregated synthetic datasets and on aggregated airborne pixels (150m by 150m) to simulate pixels of the space platform resolution.

Using spatial averaging of 4 x 4 pixels of both synthetic and real datasets, a new image with larger pixels was created. The two synthetic data set were aggregated and analyzed with the B-DSMA algorithm and the results are shown in Figures 10 and 11. Again the B-DSMA gave positive results very close to the total area of the known fractions. Notice that for this aggregation very small fractions of inundated regions are well predicted by the method. When Gaussian noise was introduced the synthetic data also gave positive results and an improvement in the determination of the two non-inundated vegetation endmembers is reflected in Figure 11. After aggregating to space platform resolution we also find that fractions smaller than 0.05 can be correctly determined for the inundated endmember. Thus, the method appears to be suitable for subpixel estimation of inundated boreal wetlands.

The original airborne POLDER image was also aggregated at different levels. First, a new image with 300m pixels was synthesized and the B-DSMA applied to that aggregate. At the same time the results of the B-DSMA from the original 150m image were aggregated into these new pixels sizes for comparison. A comparison of these results (100% correct matches) also suggests that this type of B-DSMA methodology can be used to predict sub-pixel areal cover of endmembers at larger scales. A second aggregation was performed when pixels were four times bigger thanthe original (600m). B-DSMA was again found in agreement with the proportional cover of different land cover types and the original areal aggregation.

These results show that for bigger pixel sizes it is still possible to spectrally unmix an image using normalized view angle spectra derived from a composite POLDER image. In spite of the fact that this aggregation does not consider some external scaling factors such as atmospheric conditions and altitude of the satellite, and the fact that we assume the aggregation of the radiance for the larger pixel be linear, we believe that the special characteristics of the endmembers used in this unmixing will remain in the spaceborne data and this will provide a method to discriminate between inundated and non-inundated regions using satellite POLDER imagery.

VI. EVALUATION OF CONVENTIONAL TOOLS RESULTS

Inundated regions present distinctive scattering patterns that extend the application of conventional clustering analysis and traditional image analysis in new ways. Because most conventional methods of image analysis require clear spectral differences between land cover types, studies that employ multi-angle imagery are ideal where surface structures and architecture are at a scale relevant for scattering phenomena. Even a relatively simple unsupervised classification succeeded in separating the basic patterns between open water and emergent vegetation. The multi-angle imagery provides a way to discriminate between wetland, open water and dry land vegetation over an area where nadir-looking or vertical images fail. Because the normalized view angle spectral patterns utilizing spectral radiance differences are so clear, we believe that the simple procedures tested here can be used in other boreal areas without special tuning of the classification and unmixing procedures.

These results confirm that the use of normalized view angle spectra as endmembers give a robust discrimination between different community types in the BOREAS region and that B-DSMA is both an accurate and scalable way of determining the areal extend of each vegetation types and other end members in spatial imagery with low resolution.

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1998, Center for Spatial Technologies and Remote Sensing (CSTARS)
University of California, Davis