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To separate these uncertainties, it is necessary to adopt some kind of scaling methodology to aggregate the field data, collected at a smaller grain, to the grain of the remotely sensed pixel, and estimate the aggregation error. Separate comparison of the rescaled ground data to the interpreted value of the pixel allows verification of the remote sensing interpretation. If a satisfactory relationship is found, another rescaling operation may be required, extrapolating the relationship from the extent of the original field site (typically smaller than the image) to the extent of the landscape observed by the image. Further verification (sensu Mankin et al, 1975) is usually required.
Many landscape ecologists face the dilemma of how to compare datasets collected at different scales, which has led to many investigations of the effect of scale on sampling (Fuhlendorf and Smeins, 1996; Qi and Wu, 1996; McNaughton and Jarvis, 1991; Musick and Grover, 1991; Turner et al, 1991; Woodcock and Strahler, 1987) and of ecological scaling methodologies (Moody and Woodcock, 1995; Allen et al, 1993; Rastetter et al, 1992; Vitousek, 1991; Waring, 1991; Weins, 1989; O'Neill et al, 1986; Gardner et al, 1982). Most of these studies have found that the spatial scale of sampling has an important influence on the observed pattern, but have yet to find any general scaling rules for ecological phenomena (Jelinski and Wu, 1996; Levin, 1992).
Geostatistics has been used frequently in ecology and remote sensing, both for interpolation (Rossi et al, 1994; Atkinson et al, 1994; Van Der Meer, 1994; Atkinson et al, 1992; Rossi et al, 1992) and scale detection (Schlesinger et al, 1996; Hyppanen, 1996; Jackson and Caldwell, 1993; Legendre and Fortin, 1989; Curran, 1988). This paper advances the idea that geostatistics is also a useful scaling methodology. Based on the statistical properties of point scale measurements, geostatistics allows the investigator to estimate the value of a phenomenon at arbitrarily determined locations within the study site, with the goal of substantially increasing the number of observations at the point scale which can be compared to each area measurement. These point estimates can be aggregated at whatever grain and extent the investigator chooses, subject to the limits of the original grain and extent of the point measurements. Thus the investigator determines the scale to which the point estimates will be aggregated from a continuous range of possible scales and can precisely match them to the larger scale. Geostatistics works by estimating the spatial structure of a phenomenon (variogram analysis), then making an unbiased linear estimate (Issaks and Srivastava, 1989) of the value of the phenomenon at any point within the original study extent (kriging). The variogram guides the estimation process by assigning weights based on the modeled spatial autocorrelation. Further geostatistical algorithms allow for quantification of expected error in the estimates.
This paper shows how ecological field measurements were rescaled to
match remotely sensed observations by applying geostatistics to data from
a tidal salt marsh. Point measurements of canopy water content made over
one sampling site were rescaled to the grain of image data (pixels from
the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)) using variogram
analysis and kriging. Once a relationship was established over the extent
of the study site, the relationship was rescaled a second time, by extrapolating
from the extent of the site to the extent of the landscape. This second
rescaling was verified at a second, independent reference site.
The vegetation of Petaluma Marsh is dominated by Salicornia virginica, a succulent halophyte with high canopy water content. Two other species grow in zones parallel to the Petaluma River: Spartina foliosa, a halophytic cordgrass (Mahall and Park, 1976), and Scirpus robustus, a meso-halophytic bulrush (Ustin et al, 1981). Both of these are less succulent than Salicornia virginica and have lower water content (Zhang et al, 1997). A suite of other species grow along the banks of natural channels in the marsh. These species include Frankenia salina, Jaumea carnosa, Grindelia cunefolia, and Lepidium latifolium. Through the remainder of the paper, each species will be referred to by its generic name. All plant names follow the nomenclature of Hickman (1993).
Two sites were studied in the Petaluma Marsh. The first site (hereafter
the River Site) was intensively sampled with the intention of developing
a scaling relationship between field and remotely sensed measurements.
The River Site covered a rectangular area (385 m by 175 m) parallel to
the Petaluma River, including stands of Spartina and Scirpus,
as well as large areas of Salicornia, and a small channel network
(Figure 2). A second site, the Pond Site,
was located in the interior of the marsh, approximately 1.2 km from the
Petaluma River, beside several salt ponds or pans. The vegetation at the
Pond Site was dominated by Salicornia. This site was used to verify
extrapolated predictions of canopy water content based on the River Site
results.
At the River Site sample points were placed on an quasi-regular grid at approximately 15 m intervals (average nearest point-to-point distance was 12.3 m). The sample spacing was chosen to underestimate the grain of AVIRIS data which nominally has 20 m square pixels. Canopy reflectance measurements and cover estimates by species were made at 169 sampling points on the grid. Canopy water determinations by destructive harvest were made at a subset of 38 points, stratified approximately equally in different species zones, following the other measurements. See Zhang et al (1997) for methods. At the Pond Site fifteen sampling points were destructively harvested to determine canopy water content. All sampling at both sites was completed between May 15, 1994 and June 7, 1994 to coincide approximately with an AVIRIS overflight on May 21, 1994.
The location of each sampling point was determined as an average of
ten measurements using a Pathfinder Plus Global Positioning System (GPS)
(Trimble Navigation, Sunnyvale, CA). In our study, GPS location measurements
had a precision of 1-2 m (based on standard deviation of ten simultaneous
measurements) and an accuracy of 3-10 m (based on repeated sampling at
a later time.) Because of difficulties in processing the GPS measurements
and satellite availability, twenty-two data locations were not measured
directly, but had their position estimated relative to the other points.
The accuracy for these points is somewhat less, but no worse than 15 m.
The location of the natural channels and mosquito ditches were determined
by mapping relative to the known sampling points.
Canopy reflectance spectra were truncated to 400 to 1050 nm, averaged to 10 nm bands to correspond approximately to AVIRIS bands and normalized by dividing by the square root of the sum of squared reflectance values for each spectra. While normalization minimized albedo variations in the reflectance spectra, it produced more consistency in the shape of the spectra, which is the focus of the remote sensing method used. Normalization over the entire spectrum has been suggested recently (Price, 1994; Pinzon, 1995) and is analogous to using NDVI (Normalized Difference Vegetation Index) instead of a simple ratio (Tucker, 1979).
Canopy water content was approximated from the reflectance spectra using
a technique described as continuum removal (Clark and Roushe, 1984). This
semi-empirical technique assumes a linear relationship between the area
of an absorption feature and the chemical content that causes that absorption.
A linear continuum is calculated over the wavelength interval of the feature
to approximate a hypothetical reflectance in the absence of the feature.
The area between the hypothetical reflectance and the measured reflectance
is determined and compared to chemical content (in this case, canopy water
content) to derive an empirical (linear regression) relationship (Zhang
et al, 1997). This regression relationship was used to predict canopy water
content at the 169 sampling points at the River Site.
We also calculated cross-variograms between canopy water content and CORA, but because of sparse water content sampling (38 points), those variograms had poorly defined structure. As a result, co-kriging approaches, which estimate water content directly, as suggested by Atkinson et al (1992), gave poor estimations for our data set.
The CORA observational variogram was modeled using an exponential model and no nugget (Figure 3). The range of the omnidirectional variogram model was 100 m with a sill equivalent to a canopy water content of 0.71 kg/ m2. The nugget is defined as the semivariance at a lag distance of zero. Strictly the semivariance at lag zero should be zero; a nonzero nugget causes a discontinuity in the variogram which restricts the range of weighting values used in the estimation (Isaaks and Srivastava, 1989). Nonzero nuggets are often found in observed variograms and may indicate measurement error or short scale variability. In this study we attribute the nugget effect in the observed variogram to noise in the CORA estimates of canopy water content, so we did not include a nugget in the variogram model. See Atkinson et al, 1996, for further discussion on handling nugget effects in variograms calculated from remotely sensed data.
Ordinary kriging algorithms were used with the variogram model to estimate the canopy water content at a density of nine points per pixel, which was a marked increase over the original field data (an average 0.76 points per pixel, for the combined CORA and destructive harvests, or 0.14 points per pixel, for the destructive harvests only.) Point estimates from the geostatistics were averaged (or "blocked") to correspond to areas of the same size and location as the AVIRIS pixels.
Variogram modeling and kriging estimations were calculated using GEOPACK
(Yates and Yates, 1989) and GEO-EAS (Englund and Sparks, 1988) software
packages.
The image was calibrated to apparent surface reflectance using the Atmosphere Removal Program (ATREM, version 1.0) calibration algorithm (Gao et al, 1993). The calibration was optimized by adjusting the atmospheric calibration parameters and repetitively comparing calibrated pixel output to known ground spectra.
The calibrated image was viewed using the Spectral Image Processing System (SIPS) (Kruse et al, 1993) for analysis and interpretation. Using SIPS, we identified 16 bands in the near-infrared, from 918-1062 nm, which contained the 970 nm water absorption feature. These band reflectances were extracted from the image data cube to calculate the continuum removed area, using the same technique (Clark and Roushe, 1984) as described above for the canopy spectra. These steps were implemented using the Image Processing Workbench (Frew, 1990). The resulting one band image was imported in ARC/INFO and georeferenced using GPS acquired ground points at six road intersections on the image. The rectification error was less than 17.5 meters (i.e. one pixel) in both north-south and east-west directions.
The region of salt marsh vegetation was delineated by creating a mask
from the AVIRIS band centered at 1222 nm, which gave the maximum contrast
between the salt marsh vegetation and surrounding upland vegetation. This
band was extracted from the data cube using SIPS, reformatted to a pixel
grayscale map and contrast sharpened in XV, version 3.0 (John Bradley,
Bryn Mawr, PA), then used as a mask in ARC/INFO. A second mask of the open
water and channel network was prepared using the band centered at 1591
nm.
This site-based regression relationship was applied across the entire
image to estimate canopy water content values. Regression predictions of
water content less than zero kg/m2 were set to zero kg/m2.
In general the pixels with less than zero kg/m2 (8.6% of total)
corresponded to pixels lining the Petaluma River and tributaries, where
pixels were not masked out because they included both vegetation and water
elements.
The statistical distributions of canopy water content measured by destructive harvest and continuum removal (CORA) were similar but not identical. The univariate statistics of these distributions (Table 1) showed similar means, but a higher maximum value and higher standard deviation associated with the destructive harvest data. The distribution of the destructive harvest data was negatively skewed because of disproportionate sampling of Spartina, which had a lower canopy water content, relative to Spartina's areal coverage at the site. Although Spartina covers only approximately 1% of the sampled area (Figure 2), Spartina samples account for 26% of the destructive harvest water content observations.
The results of the kriging interpolation steps compared favorably with the ground measurements. The point kriged estimates were normally distributed with a mean identical to the mean CORA estimate of canopy water content, 2.08 kg/ m2 (Table 1), and with similar standard deviations (0.61 and 0.82 kg/ m2), respectively; however, the overall range of the kriged distribution was contracted. Like most estimation algorithms, kriging tends to smooth the data.
The distribution of block kriged estimates was also normal with a slight increase in the mean compared to the point estimates, to 2.10 kg/ m2 (Table 1), with a standard deviation of 0.57 kg/ m2. The extreme values were also truncated. In this case however the smoothing was not only a function of the kriging procedure, but also of the block averaging. Block averaging may be comparable to the smoothing due to pixel averaging by the sensor, and therefore not necessarily undesirable.
The block kriging estimates were very similar to the image-derived estimates (image CORA) of canopy water content. The block kriged estimate distribution (Table 1) was not statistically distinguishable from the image-derived distribution (Wilcoxon Rank Sum test (Z = -0.2872; p = 0.7740)), though the image-derived distribution had a greater range and was less regular. Given that the distributions were approximately normal, we applied a Student's t test (t = 0.033; p = 0.8552) to show that means were also statistically indistinguishable (Table 1).
The spatial patterns of canopy water content through the various interpolation and averaging steps are shown in Figure 6. The original field measurements (Figure 6a), the estimation steps for points (Figure 6b) and blocks (Figure 6c), and the image data (Figure 6d), all show similar patterns. Lower canopy water content was observed in the Spartina and Scirpus zones, and higher water content in the Salicornia zone, particularly along the channel networks.
The relationship between block kriged canopy water estimates and image derived CORA data showed some scatter, but had a strong, linearly increasing trend (see Figure 4). The Pearson correlation coefficient (r) between block and image derived water content estimates was 0.66. The regression equation had an R2 of 0.44 (p<0.001, n=157).
This site-based regression relationship was applied across the image to estimate the canopy water content distribution for the entire marsh landscape. The overall distribution was similar to the site level distribution, having similar mean and standard deviation (Table 1). The number of observations, however, was much larger (>39,000), and the range was wider, from 0-10.39 kg/m2. Zero values corresponded to areas of open or nearly open water which were not masked out by the channel mask. The shape of the distribution (not shown) was normal, but with a long, positively skewed tail of high values.
We verified the landscape level results by comparing image derived estimates
to point measurements made at the Pond Site. If the highest canopy water
content values were omitted (points > 4.5 kg/m2), then the regression
showed an approximately linear relationship between pixel and point values
at the Pond Site (R2 = 0.60; p<0.003, n=12) with a slope near one (m
= 1.27) (Figure 5).
Based on the spatial pattern of canopy water content, we hypothesized that the pattern was governed primarily by species distributions, and governed secondarily by the locations of tidal creeks, which may provide benefits to the neighboring vegetation (Zhang et al, 1997; Sanderson, in manuscript). Species distributions at the site were largely monotypic except immediately beside the channel networks and in the Scirpus zone, which was partially undergrown by Salicornia along its margins. Salicornia was clearly the dominant by area, covering 83% of the River Site (Figure 2). Areal percent coverage by other species declined sharply, Scirpus 11%, Frankenia 1.5%, Spartina 1.3% and all other species less than 1% coverage.
These species differed in their canopy water contents (Table 2). The destructive harvests showed Salicornia had the highest canopy water content, consistent with its succulent leaves, followed by Scirpus, then Spartina; however the differences between Scirpus and Spartina were largely a function of phenology at sampling time. Neither were at peak biomass: Scirpus typically has more new biomass than Spartina by late May (Cameron, 1972). Frankenia had an intermediate canopy water content.
The second aspect of the pattern, higher water content associated with
the channel network, can also be explained by the distribution and relative
water content of plant species (Figure 2;
Table 2). Several species (Frankenia
is representative) are associated with the levees along the channel network,
most which had healthy, green biomass at the time of sampling. These levee
species are hypothesized to be associated with tidal channels because of
tidal subsidies and reduced anoxia in the elevated sediments along the
channel (Hinde, 1954). Salicornia near the channels may also benefit
from tidal subsidies, causing them to grow more robustly than plants farther
away, although we had too few points near the channels to confirm this
pattern in our data.
For some localities, however, further explanations were needed to explain the pattern. For example, much higher water content was observed where San Antonio Creek, a fresh water stream, empties into the marsh in the northwest corner. Field reconnaissance after image analysis revealed large areas of upland, glycophytic species including Lolium multiflorum and Poa annua, and tall, lush broadleaf species lining the slough/creek in this area, including Raphanus sativus and one or more Conium spp. The biomass of these communities was probably higher on an area basis than the Salicornia dominated community characteristic of the main salt marsh, resulting in an apparently higher canopy water content, though we did not measure biomass or water content in this vegetation type. A series of abandoned fence posts demarcated the area, suggesting that at one time this portion of the marsh might have been reclaimed for pasture. The influx of freshwater from San Antonio Creek may be maintaining non-halophytic species in this area.
In contrast low canopy water content was observed in a well-defined area neighboring the sewage treatment plant northeast of the river (Figure 7). Field reconnaissance of this area showed that levees define an area which receives fresh-water (treated) effluent from the treatment plant. As a result of the lower salinities and periodic flooding, several species typical of brackish marshes grow in this area including Scirpus acutus and Typha spp., in addition to large areas of the meso-halophytic Scirpus robustus. These plants grow in stands alternating with flooded areas, resulting in a patchwork of low to zero canopy water contents in this area.
Finally, an overall gradient in canopy water content is observable at
the landscape level. It appears that canopy water content rises from the
margins of the marsh from the Petaluma River to the interior, with the
highest canopy water contents observed in the region where Zhang et al
(1997) reported a low growing, very dense form of Salicornia. This
pattern is not observed in strip marshes along the Petaluma River or its
tributaries, suggesting that some additional dynamic may be at work in
the large, interior marsh which is not expressed in the smaller strip marshes.
However evaluating the interpretation at the pixel scale is more difficult, because often we can not separate error in the interpretative methods from errors due to scale differences between the remotely sensed and field data (Verstraete et al, 1996). In fact, were we to compare the point measurements directly to image measurements, the observed error would subsume both interpretative and scaling errors. Combining these errors obscures both evaluation of the remote sensing method and the scaling procedure.
Our approach was to explicitly address and evaluate the scaling methodology separate from errors in remote sensing interpretation (Table 3). For the scaling methodology, kriging is advantageous because it allows estimation of the kriging variance at every point. In this example the kriging variances varied between 9-63%, with a mean variance of 14%. These variances measure the errors associated with the modeling of the autocorrelation structure (the variogram), the extent to which the distribution of canopy water content matched the assumptions of the kriging algorithms (stationarity and a normal distribution of the data), and the averaging of point estimates to pixel size areas. The criteria for evaluating the seriousness of these errors depends on the goals of the application, their magnitude and spatial distribution: here, the variances appeared to be randomly distributed spatially (not shown) and their magnitudes seemed reasonable, given known variances in the field measurements (37% unexplained variance) and errors in their locations.
The relative success of the scaling methodology provides additional information. Since kriging provided a satisfactory scaling method, we can infer that scaling of canopy water content met the assumptions of kriging as well, that is, canopy water content scales linearly over scales with grain from less than a square meter to over 300 m2 and within an extent of approximately 67,000 m2 (the River Site), despite spatial discontinuities due to species zonation. Moreover the canopy water content appears to be normally distributed over this range of scales. Canopy water content is autocorrelated at distances less than 100 meters, and the autocorrelation can be described using a exponential variogram model (Figure 3).
Although not perfect, these rescaled field measurements are at least known quantities, with known errors, which we can compare to the image. Like Zhang et al (1997), we used linear regression to compare the remote sensing data to the field data, but here we compare them at the pixel scale (Figure 4). Scatter in this relationship (R2 = 0.44) derives from problems in georeferencing and registering, atmospherically correcting and then interpreting the image, as well as variance in the kriged field data. Despite all these potential errors, the statistical distributions of the rescaled field data and the image data are remarkably similar (Table 1). Thus the scatter probably results mostly from slight pixel to pixel discrepancies in the spatial distributions of the blocked data (Figure 6 c,d), related to georeferencing and registering of the image, and pixel sampling by the sensor. Recall that AVIRIS pixels overlap approximately 2.5 m on each edge.
The final step is to evaluate the remote sensing procedure when it is
extrapolated beyond the primary site where it was developed, typically
by making measurements at a second site. Here the regression at the Pond
Site showed that the interpretation is satisfactory for canopy water content
values within the same range as was observed at the River Site, but may
be inadequate for predicting values outside that range (> 4 kg/m2),
which is consistent with deficiencies in both the scaling method (contraction
of the distributions due to smoothing) and in the spectral interpretation
(saturation of the water absorption feature) (Figure
5). Verifying the extrapolation informs us of the bounds of our interpretation
at the landscape level. For example, predictions of canopy water content
greater than 4 kg/m2 are known to be unreliable, based on the
verification process, so they are uniformly color coded on Figure
7. Despite this kind of limitation on our analysis, a synthesis of
field and remotely sensed data is the only tool we currently have to non-intrusively
estimate canopy water content, and many other ecological properties, over
landscape sized areas.
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