Accuracy of remotely sensed estimates of landscape

1School of Natural Resources & Environment

University of Michigan

Ann Arbor, MI 48109-1115 USA

Ph: 734-763-5803

Fax: 734-936-2195

danbrown@umich.edu

2BioMedware, Inc.

516 N. State Street

Ann Arbor, MI 48104

Ph: 734-913-1098

Jacquez@BioMedware.com

Keywords: remote sensing, spatial variability, change detection, forestry

Abstract

In this paper, we compare the relative amount of error in estimates of change in each of two different classes of spatial pattern statistics calculated from remotely sensed imagery. The more commonly used patch-based statistics require image classification and identification of individual patches. The advantage is that this process isolates particular information classes (e.g., forest) and focuses the analysis on a ecologically meaningful unit of analysis (i.e., the patch). However, classification and patch-delineation are processes that are sensitive to image variability and uncertainty (Brown et al., 2000). Boundary-based statistics, on the other hand, operate directly on continuous-variable surfaces (e.g., NDVI) to identify areas of rapid spatial change (Barbujani et al., 19), referred to here as boundaries. Our analysis, based on multi-temporal remotely sensed data, shows that a selected set of boundary-based statistics was substantially less sensitive to image variability than are several patch-based statistics. We attribute this decreased sensitivity to differences in approach, i.e., identifying classes and patches versus boundaries. Further, because edge effects are important causes of the ecological impact from forest fragmentation, boundary-based statistics may be as ecologically meaningful as patch-based statistics.

1. Introduction

Dozens of statistics have been developed to describe landscape pattern and used to manage spatial patterns on the landscape (McGarigal and Marks, 1995; Gustafson, 1998). Within this quantitative approach to landscape ecology, a landscape is commonly defined as a mosaic of distinct patches. These patches often represent habitat types that have different compositions and structures and affect ecosystem functioning through their spatial arrangement. Although there are several different processes of landscape change that concern landscape ecologists (Forman, 1997), forest fragmentation is of particular interest because of its importance to forest species composition and diversity, primary production, and suitability of the forest for habitat (Iida and Nadashizuka, 1995; Flather and Sauer, 1997; Laurance et al., 1997).Although remotely sensed imagery provides most of the data used for analyses of landscape pattern, little is known about the effects of image variability and uncertainty on the calculation of landscape pattern statistics. The problem of error in spatial pattern statistics becomes particularly acute when comparing statistic values across multiple images to ascertain change, which is needed to analyze processes of landscape pattern evolution. Sources of image variability and uncertainty that can negatively affect a remote sensing based analysis of changes in landscape pattern include: positional uncertainty; inherent fluctuations in the radiometric characteristics of the sensors; differences in atmospheric conditions, including clouds and haze; variations in solar angles; and variations in phenological stage (Yuan and Elvidge, 1998). Those influences that are spatially heterogeneous (particularly atmospheric conditions) introduce the most uncertainty into spatial pattern statistics.

Image classification and patch-delineation are required in order to make use of the patch-based spatial pattern statistics described above. The process of defining information classes from raw imagery can introduce additional uncertainty in the analysis of spatial pattern. Regardless of the approach taken to classification (i.e., supervised and unsupervised), it is impossible to achieve a perfect assignment of each pixel to one and only one class. This is partially due to the sources of uncertainty named in the previous paragraph, but also to the mixed nature of many pixels and to the assumptions inherent in the classification process (e.g., multi-variate normal distribution of class memberships on the spectral variables).

In this paper we evaluate the potential for an alternative approach to characterizing forest fragmentation to yield estimates of forest pattern change that are less sensitive to image variability and uncertainty. Specifically, we compare patch-based statistics with a class of statistics that is based on the identification of boundaries within the images. This approach involves calculation of local estimates of spatial rate-of-change in a variable and assumes that the number and pattern of boundaries in the landscape is a direct indication of fragmentation. This is consistent with many conceptions of forest fragmentation, which include an understanding of its effect on the density of edges between forested and non-forested patches. We describe (1) the two contrasting approaches to characterizing pattern, focusing on the application of boundary-based statistics; (2) our approach to calculating error in the statistics and their sensitivity to image characteristics, and (3) the results of the comparison of error levels between patch-based and edge-based metrics.

2. Contrasting Approaches to Describing Forest Pattern

2.1 Patch-Based Statistics

Landscape patterns have been studied by identifying patches of habitable (forested or undisturbed) vs. uninhabitable (deforested or disturbed) land, through a process that converts continuous data in the form of imagery or species abundance maps to discrete binary data through classification. One advantage of classification is the simplification of more complex information through reduction, a common theme with most multivariate statistical techniques. The corollary disadvantage is loss of information that is perhaps ecologically meaningful. For example, ecologists have established that the presence and properties of edges can greatly influence plant colonization rates, animal movement rates, effective patch size, and species composition within and around a patch (Kupfer et al. 1997), and yet maps of patches generated by the classification process yield locations of patch edges and edge density but not necessarily edge strength or width (fuzziness). In addition to a loss of information, both the classification and patch-delineation processes introduce uncertainties associated with the reduction of information. The implications of these uncertainties are often unknown and unquantified.2.2 Boundary Statistics

Boundary analysis methods study landscape pattern by focusing on boundaries demarcating transition zones where the value(s) associated with pixels change rapidly through geogrpahic space. Boundaries are of fundamental scientific interest because their locations reflect underlying physical, biomedical and/or social processes that determine landscape form and function. In forest ecology boundaries are associated with ecotones indicating zones of rapid change in species composition (Fortin 1992), and in general landscape boundaries potentially represent contact zones between distinct ecosystems (Hansen and di Castri 1992; Fortin 1994; Holland et al. 1991).

In addition to identifying locations where determinants of landscape form and function are manifested as landscape boundaries, Jacquez and Maruca (In Press) offer four motivations for boundary analysis. In sampling design boundaries are transitional areas boundaries that may be intensively sampled in order to quantify sample variance. Second, in spatial pattern quantification boundaries circumscribe areas that are relatively homogeneous, and indicative of spatial autocorrelation and spatial scale. Third, in exploratory spatial data analysis sufficient knowledge to parameterize a formal model may be lacking, and statistics such as boundary overlap are an alternative measure of spatial association that do not rely on correlation models that presuppose specific linear or nonlinear relationships among variables. Finally, in GIS boundary analyisis provides one mechanism for identifying objects (boundaries) on spatial fields.

Thus while there are good reasons for using boundary analysis to study landscape pattern, these techniques have not been compared and contrasted with patch-based metrics. In particular, the sensitivity of boundary-based techniques to image variability hasn’t been quantified, nor has it been compared to the sensitivity of patch-based metrics.

Boundary detection methods may be classified for convenience into seven groups (refer to Jacquez and Maruca, In Press for a review): moving split windows, lattice delineation, triangulation delineation, categorical delineation, spatially agglomerative clustering, image analysis, fuzzy set modeling. All of these techniques result in boundaries that may be closed to circumscribe relatively homogeneous areas, or open, so that they do not necessarily return to their point of beginning. Lattice delineation has seen increasing use in landscape ecology (e.g. Fortin et al.1996). In this study we compare we assess its to image error and uncertainty in the context of patch-based statistics.

3. Methods

3.1 Data

Our work makes use of the North American Landscape Characterization (NALC) data set, which contains Landsat MSS data for three epochs (1972-1975, 1983-1985, and 1990-1992). We chose two study areas in the Upper Midwest, USA (Figure 1), corresponding to two areas of overlap between adjacent NALC scene areas (i.e., same row, neighboring paths). The study areas were selected in northern Lower Michigan (hereafter referred to as Study Area A) and northern Wisconsin on the border with Michigan (hereafter referred to as Study Area B) because of extensive forest cover in each but differences in relative amount. As of the early 1990s, Study Area A had about 56 percent forest cover and Study Area B was about 83 percent forest covered.We obtained all NALC images covering these two study areas, twelve in all (three epochs, four path-row locations). The NALC data set in general is described in more detail elsewhere by Lunetta et al. (1998) and the specific data set used by Brown et al. (2000). All twelve images were classified into four different classes: forest, non-forest, water, and cloud/shadow. Forest was defined as any place with greater than 40 percent tree cover. Classification and accuracy assessment was supported by a database of scanned and rectified aerial photography. Classification accuracies (i.e., percent correctly classified) averaged 80.5 percent and ranged from 72.5 to 91.2 percent.

Figure 1, Locations of Study Areas A and B in Michigan and Wisconsin, USA (Brown 2000). In addition to classification, we calculated the normalized difference vegetation index (NDVI) for each image. NDVI is used here as the surface on which the boundary analysis was performed. Although boundary analysis can operate on multi-variate surfaces (e.g., multi-spectral channels), NDVI provides an index of vegetation greenness that relates directly to the object of interest, vegetation cover. However, it should be noted that NDVI is not a measure of forest cover. For this reason, the information content of boundary statistics, based on NDVI, and patch-based statistics, calculated on classified images, may not directly comparable. A better approach to generating a surface for boundary analysis of forest fragmentation might be to identify tree cover within each pixel. Such a quantity could be derived using linear mixture modeling (e.g., Brown, In Press).

3.2.1 Patch-Based Statistics

Our goal is to characterize changes in the degree of fragmentation in the forests of the Upper Midwest. Table 1 lists four patch-based statistics that we selected as representative of a range available statistics for characterizing forest fragmentation. The four statistics characterize the amount of forest (PF), the size and number of patches (MPS and NP), and the amount of non-forest--forest edge (ED).

All patch-based statistics were calculated using the Fragstats software package (McGarigal and Marks 1995). The calculations involve aggregating neighboring forest cells in the imagesMetric Abbr.Definition

PATCH-BASED

edge density ED length of forest/non-forest edge ÷ landscape area mean patch size MPS average size of forest patches

number of patches NP number of forest patches

percent forest PF percentage of the landscape covered by forest BOUNDARY-BASED

number of boundary elements BE number of high-gradient cells

maximum sub-graph length ML Maximum number of boundary elements in a sub-

graph

number of sub-graphs SG number of connected groups of boundary elements number of singletons SI number of single-cell sub-graphs

Table 1, List of patch-based and boundary-based pattern statistics used in this comparison.

Into patches. The patches were summarized by counting the number of patches and calculating their average area. Further, the total length of edge between forest and non-forest patches was calculated and divided by the partition area to give the edge density (ED). Clouds or cloud shadows that occurred within a partition were treated as holes, decreasing the total area of the partition and not counting towards the amount of edge.

3.2.2 Boundary-Based Statistics

The lattice boundary method is originally attributed to Womble (1951), who described a method for evaluating the gradient of several spatial variables by averaging the absolute values of their first derivatives. Assume X and Y to be Cartesian coordinates in the geographic plane, and Z to be the variable of interest. Values of Z at the four pixel locations {A, B, C, D} are written {z A, z B, z C, z D}. These pixels are adjacent and form a unit square with coordinates (0,0), (1,0), (1,1) and (0,1), respectively. Functions describing the interpolated value and slope and aspect (direction of gradient) at any location (x,y) n the unit square are easily derived (Maruca and Jacquez In Press).

Boundaries are considered to be composed of boundary elements (BE’s) where the magnitude of the slope of the underlying data surface is large. This means the value of NDVI changes rapidly between adjacent pixels. These boundaries are connected into subgraphs based on adjacency criteria that constrain only adjacent pixels to be members of the subgraph. A BE that is the only element in a subgraph is called a singleton. The boundary statistics quantified in this study (Table 1) are the number of boundary elements on a partition; the maximum subgraph length, given in BE’s; the number of subgraphs in a partition; and the number of singletons. Clouds and cloud shadows were treated as holes that did not contribute to either the boundaries or to the area of the partition in the calculation of boundary-based statistics. The slope and aspect were calculated for each location in partitions and boundary elements are those locations with `large' slope. The definition of `large' is somewhat arbitrary, and past researchers have declare locations with magnitudes in the upper 10% of all slope magnitudes to be boundary elements (e.g. Barbujani, Oden et al. 19; Jacquez 1995), a definition we employ here. This definition was further constrained by additional criteria to assure boundary continguity Barbujani et al. (1990) retain only those candidate boundary elements that (1) are adjacent to other boundary elements and (2) have aspects that differ by less than 30 degrees from adjacent boundary elements.3.3 Calculating and Comparing Error

Our methodology for evaluating error in landscape change statistics makes use of repeated sampling of areas in overlapping satellite paths (Brown et al., 2000). The change in pattern in each partition was characterized by differencing landscape statistics calculated at two different times. When two values of a pattern statistic are calculated within the same epoch (i.e., at roughly the same time) any difference between the values can be attributed to short-term landscape change or image variability that is unrelated to landscape change (i.e., error or noise). For this analysis we assume that the former effect is negligible and that any differences were due to the latter.

To estimate error, we calculated the differences in values of forest fragmentation statistics for overlapping scene pairs from the same time frame (or epoch). We calculated the difference for each of the eight pattern statistics from images that are taken within the same time period, so that the accuracy of differences between statistic values can be estimated. In previous work (Brown et al., 2000), we developed a model to predict the amount of error in landscape change statistics as a function of amount of forest cover, landscape phenology due to seasonality, and atmospheric variability (e.g., haze and clouds). Real inter-annual landscape change within an epoch is unaccounted for and tends to be fairly small relative to changes between epochs.

Here we summarize the differences between same-time statistic values by calculating the root-mean-squared-error (RMSE). This is an estimate of the magnitude, but not direction, of difference across all landscape partitions for a given metric. To compare the levels of error of the different statistics we calculated the RMSE as a proportion of the mean statistic value. This is a ratio that can be used to interpret the relative sensitivity of the different statistics to image variability. Statistics with higher relative errors are more sensitive to image variability and must be used more carefully in any multi-temporal analysis of changes in landscape pattern. Statistics with lower relative errors were less likely to be affected by image variability and more likely to provide meaningful information about landscape change.

4. Results

The principal results are displayed in Figure 2. For each statistic and each image pair, the magnitude of statistic difference between two scenes of the same location at approximately the same time is expressed as a proportion of the mean statistic value.

Figure 2, Relative level of error in (A) four patch-based statistics and (B) four boundary-based statistics. Error levels are reported separately for each image pair--defined by study

area (a or b) and date (1970s, 1980s, and 1990s).

The relative error in the patch-based statistics is quite variable, from less than 5 percent (for percent forest in study area b) to nearly 250 percent of the mean statistic value (for mean patch size in study area a). Whereas PF and ED exhibit a relatively high degree of consistency between images taken at the same time (RMSE was usually less than 50 percent of the mean statistic value), NP and, especially, MPS are relatively inconsistent and, therefore, strongly affected by image variability.

By contrast, all four boundary-based statistics were consistently less sensitive to image variability (RMSE was always less than 50 percent of the statistic value). The number of boundary elements (BE) and number of sub-graphs (SG) were the statistics exhibiting the least variability. The number of singletons (SI) and max sub-graph length (ML) were more sensitive to image variability than BE and SG, but were relatively insensitive in comparison to the patch-based statistics (especially NP and MPS).

5. Discussion

These results demonstrate that, for the statistics considered, patch-based metrics had substantially higher error than boundary-based metrics. Is this result unique to the data and system studied, or is it explained by fundamental differences in how the metrics are calculated and in what they are measuring? The boundary- and patch-based metrics analyzed in this study differ in at least one property: The quantities underlying the patch-based metrics arise from an exhaustive classification of the scene; the quantities underlying the boundary-based metrics arise from the scene’s first derivative (slope). This difference provides insights into the pattern of results, and more importantly, suggests two reasons why the boundary-based metrics are less sensitive to image variability and uncertainty.

Sensitivity to spatially autocorrelated errors: The slope is calculated from spatially adjacent pixels and thus is not sensitive to error terms that are spatially autocorrelated such that nearby locations have similar errors. In contrast, a classification is biased by any error that relocates pixels within the variable space on which the classification operates. When the error term is large enough the pixel is misclassified. When errors of the same magnitude are applied to adjacent pixels, the slope estimate is relatively unchanged. Hence we expect patch-based metrics based on classification to be less accurate than boundary-based metrics when spatially autocorrelated error is present.

Local versus global tests for spatial pattern: Boundary-based metrics are local tests for spatial pattern, while patch-based metrics are global in that they require

classification of the entire scene. In general local tests are sensitive to local departures from statistical null hypotheses; global tests search for pattern in an entire data set as a whole at the cost of losing power to detect pattern in local areas.

The lattice delineation technique used in this study is a local test for spatial pattern that asks “is there significantly large boundary element?” in each grid cell on the map. Hence it is not particularly sensitive to spatially autocorrelated errors introduced by clouds and atmospheric effects on remotely sensed scenes. In adjacent pixels of a scene such errors cause NDVI to be increased (or decreased) by about the same amount, and the slope magnitude estimate is relatively unchanged. Obviously, errors that are introduced as sharp, local changes would bias this technique to falsely detect significant boundaries, resulting in an increased error. In contrast, patch-based metrics are global, being based on classification of the entire scene. Hence errors in observations on NDVI can cause locations to be wrongly interpreted as another cover type – a misclassification.Acknowledgements

This work was supported, in part, by grants from the National Aeronautics and Space Administration (#NAG5-6042), the National Cancer Institute (#CA698), and the National Institute for Environmental Health Sciences (#ES10220).

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