Spatial and Compositional Pattern of Alpine Treeline, Glacier National Park, Montana

Thomas R. Allen and Stephen J. Walsh

Abstract This study sought to quantify the complex patterns of alpine treeline across an extensive area of Glacier National Park, Montana. Satellite image classification, digital terrain model- ing, and geographic information system (GIS) measurements of landscape structure provided important tools for the anal- ysis. The study area was topographically partitioned into wa- tersheds and hillslope units in which to measure treeline patterns. Cluster analysis of selected spatial and composi- tional pattern metrics was used to infer major alpine treeline forms. Six significant treeline types were differentiated using patch richness, contagion, contrast, number of patches, frac- tal dimension, relative edge density, and forest-tundra juxta- position. Clusters were validated using split-sample replica- tion and discriminant analysis. Patterns were found to differ among types of terrain, affirming hypothesized sensitivities to topoclimatic gradients, natural disturbances, and geologic substrate.

Introduction The dynamics of ecotones, or boundaries between ecosys- tems and landscapes, are of particular interest to studies of landscape ecology (e.g., Johnston and Bonde, 1989; Hansen and dicastri, 1992; Swanson et al., 1992). Alpine treeline, the ecotone separating subalpine forest and alpine tundra ecosystems, has emerged as a highly studied landscape boundary because of its potential sensitivity to climate change (Hansen-Bristow and Ives, 1984; Hansen-Bristow et al., 1988; Armand, 1992; Walsh et al., 1994). Spatial metrics commonly applied in landscape ecology provide important tools to quantify the structure of the treeline ecotone and possibly separate climatic and other influences on its form (e.g., Baker et al., 1995). Treeline pattern must be examined in the context of potentially complex spatial variation in mi- croclimate, disturbances, resource availability, and biotic processes (Stevens and Fox, 1991; Slatyer and Noble, 1992; Malanson and Butler, 1994), factors whose relative influences on treeline patterns have not been fully synthesized. There is also an emerging need to critically evaluate measures of landscape structure (Hess, 1994), particularly in light of ef- forts to understand the dynamics of landscapes and their boundaries. This study applies digital image processing and geographic information system (GIS) techniques to examine the landscape structure of the alpine treeline ecotone in Gla- cier National Park (GNP), Montana.

The alpine treeline ecotone provides a suitable land- scape boundary for analysis of vegetation response to direct

effects of climate change and indirect effects of changing dis- turbance regimes (Beaudoin, 1989; Kullman, 1990). Land- scape disturbances and their regime changes have been shown to be evident and quantifiable in broader landscapes (Rex and Malanson, 1990; Spies et al., 1994). Baker et al. (1995) applied aerial photography and GIs techniques to map alpine treeline in the Colorado Front Range. Brown's (1992; 1994) predictive modeling of covertypes in Glacier National Park found that climatic gradients alone could not accurately predict cover type distributions. Using techniques similar to those reported here, Baker and Weisberg (1995) found and classified spatial patterns of landscape structure in Rocky Mountain National Park, Colorado. Their approach used aer- ial photography and transect measures of treeline structure (Baker et al., 1995; Baker and Weisberg, 1995.) This study presents a similar approach based on digital image process- ing of Landsat Thematic Mapper (TM), terrain modeling, and landscape analysis in hillslopes. Comparative analysis of treelines in regional contexts should improve our under- standing of ecotone responses to global climatic change. Con- troversy over patterns that may be diagnostic of climatic control (Wardle, 1993) may be addressed with the use of quantitative measures of spatial pattern. Quantification of al- pine treeline structure may generate data on the form and lo- cation of monitoring sites of treeline response to climatic changes. Further, understanding the structure of alpine tree- line will provide more information on the study of mountain habitats, biodiversity, and aesthetics.

The basic intent of this research was to examine the spa- tial structure of the alpine treeline ecotone relative to possi- ble biophysical controls. Specific research objectives were to

Map the alpine treeline ecotone utilizing satellite image clas- sification of multidate Landsat Thematic Mapper data, Identify common forms of alpine treeline ecotone patterns through GIS measured ecotone patterns and statistical analy- sis, and Integrate digital elevation models (DEMS) for landscape strati- fication and develop environmental variables to explain tree- line patterns.

The central hypothesis holds that alpine treeline exhibits a small number of distinguishable forms reflecting the influ- ence of topographic gradients, disturbances, and geologic fac- tors in the alpine environment, as has been observed in broader landscapes (Wickham and Norton, 1994). The alpine treeline ecotone (ATE) refers to the boundary between sub- alpine and alpine ecosystems. This boundary may be ex- pressed by patterns along a continuum from broad transition zone to a narrow, compressed boundary. "Patches" in this

T.R. Allen was with the Department of Geography, Univer- sity of Vermont, Box 54170, Burlington, VT 05405-4170. He is presently with the Department of Political Science and Ge- ography, Old Dominion University, Norfolk, VA 23529-0088,

S.J. Walsh is with the Department of Geography, University of North Carolina, Chapel Hill, NC 27599-3220.

Photogrammetric Engineering & Remote Sensing, Vol. 62, No. 11, November 1996, pp. 1261-1268.

0099-1112/96/6211-1261$3.00/0 O 1996 American Society for Photogrammetry

and Remote Sensing

Figure 1. Study area location in eastern Glacier National Park, Montana, including areas above 1,700 metres. Greys- cale display of Landsat TM band 4, 3 September 1990.

study refer to adjacent pixels of similar land-cover types, as opposed to individual patches of trees. Spatial patterns of the ATE include varying degrees of complexity of patch shapes and sizes, the altitudinal breadth of the ecotone, and the presence of interdigitating patches such as in ribbon for- ests and snow glades. The ATE also exhibits compositional variation through the number of different cover types present (diversity) and the distribution of area among cover types (evenness). Northern Rocky Mountain treeline patterns are likely influenced by topographic complexity (Arno and Ham- merly, 1984), climatic gradients (Wardle, 1993), snowmelt patterns (Allen and Walsh, 1993), disturbances such as snow avalanches and debris flows (Walsh et al., 1994), fire (John- son and Larsen, 1991; Barrett, 1993), and geologic substrate influences (Butler et al., 1991). This study provides a re- gional comparison to work by Baker et al. (1995) on alpine treeline in Rocky Mountain National Park, Colorado Front Range, and Timoney et al. (1993) who examined the spatial structure of arctic treeline along its latitudinal gradient. Rocky Mountain National Park, Colorado is geologically more resistant and less likely to exhibit geomorphic distur- bances at treeline (Hansen-Bristow and Ives, 1984) than Gla- cier National Park, Montana.

Continental Divide in the northern Rocky Mountains of northwest Montana at approximately 49"N latitude and 113"W longitude. The rugged, glaciated topography; situation between maritime and continental climates; relatively pris- tine environment; and floristic affinities to the middle and northern Rocky Mountains make GNP a highly suitable loca- tion for study of the ATE. The study area encompasses water- sheds along the eastern flank of the northern Rocky Moun- tains in eastern GNP (Figure 1). GNP exhibits steep topography associated with Pleistocene and limited Holocene valley glaciation. The climate is dominated by cold, snowy winters and brief, mild summers (Finklin, 1986). Elevations within the study area range from approximately 1,400 m to 3,000 m. The elevation zone between 1700 m and 2400 m, which captures climatic and elevationally depressed portions of alpine treeline, is the focus of the analysis. The entire study area is located east of the Continental Divide where the climate is harsher, having more severe lower tempera- tures, stronger winds, and drier conditions as compared to locations west of the Divide (Finklin, 1986). The ATE is dom- inated by subalpine fir (Abies lasiocarpa), whitebark pine (Pinus albicaulis) and/or limber pine (Pinus flexilis), and patches of Engelmann spruce (Picea engelmannil] (Arno and Hammerly, 1984).

Treeline within GNP has not shown straightforward re- sponses to climate change since the Little Ice Age (Butler et al., 1994). Repeat terrestrial photography has found little re- cent change in treeline patterns, including snow avalanche- impacted ecotones (Butler et al., 1994). Debris flows (Gard- ner, 1980; Butler and Walsh, 1994), snow avalanches (Butler, 1979; Walsh et al., 1994), fire (Kessell, 1979; Johnson and Larsen, 1991), and animals (Butler, 1995) are documented disturbance agents impacting the ATE. GNP is representative of much of the northern Rocky Mountains and provides a suitable study area for modeling ATE sensitivities to climate, disturbance, and stresses. Heretofore, no straightforward pat- tern or location for treeline advance in GNP has been dis- cerned, a likely result of extreme topographic complexity and recurrent disturbances (Arno and Hammerly, 1984). Identification of ATE patterns could, thus, guide activities to monitor changes in response to climate.

Methods Image and Land-Cover Data Multidate Landsat TM digital data were used to map alpine land cover in the GNP study area. Images sensed on 28 Au- gust 1988 and 3 September 1990 were atmospherically and geometrically corrected for integration into the GIS. Both im- ages showed clear conditions and apparently high radiomet- ric quality. Atmospheric corrections were applied using the histogram offset method. The 1988 TM image was georefer- enced to uSGS 1:24,000-scale quadrangles using ground con- trol points with <0.5 pixels root-mean-square (RMS) error. The 1990 TM image was coregistered using onscreen selec- tion of GCPs from the image and the 1988 reference TM im- age. The RMS error achieved for the 1990 image was <0.5 pixels. Both images were resampled using nearest neighbor interpolation and projected into the UTM Earth coordinate system for GIs integration. Topographic normalization was performed independently on both images to reduce the effect of topographic slope and aspect on the spectral reflectance characteristics of vegetation. A statistical-empirical regression model was developed for each band in both images based on the relationshiv between reflectances of forest cover in ground controi sites and a model of solar illumination for

Study Area the conditions of scene acquisition. This application is fur- Established in 1910 by the U.S. Congress, Glacier National ther documented elsewhere (Allen, 1995) and follows the Park (GNP) covers approximately 462,500 hectares astride the procedure evaluated by Meyer et al. (1993) for improvement

TABLE 1. STUDY AREA VARIABLES INTEGRATED WITHIN THE GIs.

Variable Source Format Scale Date

Vegetation type Lithology Surficial geology Faults Sillsldikes Historic fires and stand ages Snow cover Avalanche paths Debris flows Exposurelshelterdness Solar radiation potential Topographic wetness potential Elevation Slope angle Slope aspect Curvature/profile curvature Slopes

EOSAT USGSIWhipple USGSICarrara USGSlWhipple USGSIWhipple NPSIBarret EOSATIUSGS Butler and Walsh (1990) Butler and Walsh (1994) USGSIderived USGSIderived USGSIderived USGS USGSIderived USGSIderived USGSIderived USGSIderived

TM data Map Map Map Map Maps MSS data Maps, TM data Maps, TM data DEM DEM DEM DEM DEM DEM DEM Maps, DEM

of forest classification using topographic normalization. This substantial preprocessing step provided images with reduced topographic effects, visually flattening the images, which would improve image classification of the rugged study area.

Classification of the multidate images utilized a hierar- chical, or layered, approach. Spectral enhancements, feature selection from the multidate bands, and initial clustering were used to i d e n w the possible classificatory detail that could likely be achieved for class accuracies approaching 90 percent. Field work conducted in July and August 1994 used differential global positioning system (GPS) locating, transect sampling, and photography to identify training sites and ground verification areas for accuracy assessment. Classifica- tion was done hierarchically, initially segmenting the image data using unsupervised classification into strata defined by major covertypes (i.e., forest, meadow, and non-vegetated surfaces). Strata were then separately classified by supervi- sion using training sites, optimally selected feature sets from the multidate stack, and a maximum-likelihood decision rule. Feature inputs were carefully analyzed so that maxi- mum phenological information could be used in the decision process. The result was a classification with high sensitivity and accuracy for alpine vegetation types (Allen, 1995). Clas- sification accuracy was assessed using 492 photointerpreted or ground verified sites ranging from 19 to 56 sites per class in a stratified random sampling design. Overall accuracy was 90.2 percent, ranging individually from 59.4 percent (for- ested scree class) to nearly 100 percent (water). Hampered by residual shading on steep, north-facing slopes, barren cliffs were frequently misclassified as forested scree or water and required manual correction using field photographs and aer- ial photointerpretation. Derived forest classes included closed-, medium-, and open-canopy spruce-fir, forested scree, dense krummholz, and krummholz-scree. Non-forest vegeta- tion classes included krummholz-meadow mix, lush or wet meadow, sparse or dry meadow, grasslshrub, and dense tun- dra. Nonvegetated classes were bare rock, water, and snow- ice. Kappa statistics were calculated, including overall 0.89 for the study area and values from 0.58 (forested scree) to near 1.0 (water). The resulting map was judged to be a highly accurate portrayal of the major alpine covertypes.

Ancillary Data Integration The methodological integration of remote sensing, GIS, and landscape pattern metrics allowed the examination of ATE patterns relative to modeled terrain variables for the rugged environment. Previous work had accumulated a substantial digital spatial database (Table 1) for the study area (Walsh et

al., 1989; Brown, 1992; Allen and Walsh, 1993). All cover- ages were reprojected, resampled, and statistically and visu- ally verified during the development of the co-registered spatial database. A set of continuous environmental gradients were developed as explanatory variables within the GIS using 1:24,000-scale-derived digital elevation models (DEMS). These gradients included elevation, slope, aspect, relief/exposure, solar insolation, topographic wetness, and slope curvature. Directional relief, a measure for exposure/shelteredness, was derived to express the elevation of a DEM cell relative to its surroundings (Lapen and Martz, 1993). The algorithm calcu- lated the mean elevation of all cells in the southwest direc- tion and subtracted the core cell elevation from this average. For application to alpine treeline research, a 3-km limit on the search distance was used in the calculation of directional relief. The southwest direction was chosen to correspond to prevailing winter wind directions based on available meteo- rological data (Finklin, 1986). Snow cover patterns observed in multitemporal Landsat MSS imagery (Allen and Walsh, 1993) corroborated the use of the southwest direction for a single surface portrayal of winter exposure/shelteredness.

Direct solar insolation strongly influences the location of perennial snowfields in the region (Allen et al., 1995), and potential growing season may limit plant growth (Cairns, 1994; Scuderi et al., 1993). A program was written to simu- late potential direct solar radiation using DEMs. This program was adapted from equations published by Montieth and Uns- worth (1990). The algorithm also identified shadows for each simulated solar elevation and azimuth time step (specified hourly) and calculated direct radiance (assuming no cloud cover) from dawn to dusk (15 degrees above the horizon) for a specified Julian calendar day. A simulation for the summer solstice was selected to portray the general distribution of growing season solar insolation in the study area.

Topographically modified soil wetness is a potentially important factor in coniferous forests because waterlogged soils may exhibit grass, sedge, or forb-dominated growth that inhibits tree establishment. In most alpine treeline locations, topographic soil moisture is likely subordinate to other topo- graphic gradients and disturbances (Arno and Hammerly, 1984). Moisture sinks affecting ATE composition and pattern are locally important, especially in snow accumulation zones where meltwater is funneled and may continually bathe meadows for extended periods of the summer. A common approach to simulating soil moisture is to apply an index based on the log of the accumulation of flow from upslope cells in a DEM divided by the surface slope angle (e.g., TOPMODEL dynamic watershed model; Beven et a]., 1984). A

PE&RS November 1996

similar model was implemented using flow direction and ac- cumulation maps based on pixel-to-pixel flow routing (as- suming constant moisture transmissivity throughout the landscape; Moore et al., 1991). Topographic wetness potential provided an effective model needed to characterize channels, gullies, and moisture sinks in the ATE.

Topographic curvature was derived by measures of cur- vature/convexity from DEMs. Curvature integrates planform and profile curvature to portray localized topographic situa- tion (Moore et al., 1991). This distinguishes ATE slopes hav- ing a convex versus concave slope. Profile curvature, the vertical or downslope concavity/convexity, portrays slope steepness within treeline slopes. Because this characteristic of curvature affects the acceleration and deceleration of grav- ity flows (Zevenbergen and Thorne, 1987), it was judged im- portant for portraying the impact of mass wasting related disturbances.

Spatial Sampling To analyze the various ATE forms, it was necessary to devise methods to stratify and sample the extensive study area. A slope stratification algorithm was applied to segment the study area into basins and corresponding sub-basin slopes using DEMS and a watershed modeling algorithm (r.watershed; GRASS, 1993). A minimum watershed size of 625 pixels (each pixel 30 m by 30 m) was judged suitable after iterative tests. Slopes straddling the ecotone were generated by limi- ting the upper and lower elevations of acceptable hillslopes, ensuring that the hillslopes did not contain purely alpine or subalpine communities. A topographic partitioning method was adopted to map homogeneous areas of low topographic variance (reducing slope angle and aspect variation within slope units) (Band, 1989). Approximately 1,100 slopes were derived for the entire study area. The resulting basin and slope grids were masked to only include those within the 1700t m ATE study zone. After the algorithm identified the slopes and produced a map, the process was repeated to as- sess the size and shape of basins in different areas.

Representative basins and slopes within the alpine tree- line ecotone were selected using morphometric analysis and sampling. Baker and Weisberg (1995) used transects through the treeline ecotone to ensure representative measurement of ecotone patterns. In this study quantitative differences in morphometry of slope terrain were controlled through meas- urement of spherical variance of topography as per Band (1989). This procedure helped ensure that subsequent land- scape metrics would represent the local pattern and not sim- ply the chance placement of hillslopes in different topo- graphic positions. A morphometric operation to measure the width of a slope unit (second major axis) was applied in the ArcIInfo GRID module (ESRI, 1993). Slopes between 300 and 600 metres wide were selected for analysis following itera- tive querying. To avoid bias of omitting small slopes, a sam- ple of 40 basins removed by the minimum area threshold were aggregated into larger slopes and maintained in the sampling pool. These slopes typified very steep or high ele- vation areas such as cirques and couloirs. Rather than an ex- haustive census of slope patterns, sampling allowed more detailed analysis of fewer ecotone slopes. A random subsam- ple of 111 slopes was used in subsequent analyses of ATE patterns.

Spatial Metrics The suite of available landscape pattern metrics includes nu- merous, often correlated, measures of spatial structure (Hess, 1994; Riitters et a]., 1995). FRAGSTATS (McGarigal and Marks, 1993) and the "r.le" landscape metrics programs for GRASS (Baker and Cai, 1992) were available to calculate several met-

rics with little change in data structure in the GI~. Metrics describing patch shapes and density, density and complexity of edges, interspersion of patch types, and diversity of patch types were selected to analyze patterns in the ATE. A suite of indices was available to measure compositional structure of treeline, such as the diversity of patch types and their rela- tive areal distribution within ATE slopes. All metrics re- ported were calculated using the r.le landscape algorithms for GRASS (Baker and Cai, 1992). Landscape pattern metrics can be standardized for areal units such as slopes or water- sheds. These algorithms provided an efficient and diverse set of metrics, as well as the capability of subsequent multiscale analysis.

Landscape metrics to describe the distribution of edges and local texture (e.g., fine versus coarse grain) were com- pared for use as ATE pattern descriptors. Texture metrics quantify the adjacency of neighboring patch types and local diversity. Contrast, an index of local variation present in the landscape, was also calculated. Fractal dimension, a general index of complexity of slope texture, was selected to charac- terize overall edge and shape complexity across all types of patches on a slope. Fractal dimensions were derived from the perimeter-area relationship of patches and averaged across all classes and patches present. These texture metrics were expected to differentiate ecotones with simple or "zo- nal" patterns from ATE slopes having numerous inter-patch class adjacencies. An additional index, juxtaposition, specifi- cally highlighted the adjacencies of similar and dissimilar cover types. This index was developed to distinguish abrupt versus gradual ecotones. Stature, cover, canopy structure - (number and dominance of canopy layers), and species were used to rank the relative difference or similarity of patch ad- jacencies. Weight factors were selected to emphasize life form differences in vegetation for three recoded classes (for- est, krummholz, and treeless vegetation). Juxtaposition was calculated for each cell in a slope using its eight adjacent neighbors.

Edge metrics quantified the amount of total edge, edge of individual classes, and relative edge controlling for slope area. Total edge was calculated by summing the shared edges for all patch types. The total edge divided by the area of a slope provided a relative edge density metric for slope com- parisons. Perimeter of patches was also tabulated for each slope by counting pixel adjacencies. Metrics for quantifying the size distribution and density of patches in slopes in- cluded measures of relative patch area, relative number of patches, mean patch size, and total number of patches. Somewhat related to compositional and textural indices, these indices were selected to distinguish ecotones on the basis of potential fragmentation.

Statistical Analysis Cluster analysis was selected to determine the primary forms of spatial organization within the alpine treeline ecotone. Cluster analysis allows identification of fundamental rela- tionships between spatial pattern and composition metrics for the 111 sampled slopes and climatic, disturbance, and ge- ologic influences or controls. This application of cluster anal- ysis sought to identify the groups of slopes within the alpine treeline ecotone on the basis of spatial and compositional patterns measured by a remotely sensed vegetation classifica- tion. Three phases of cluster analysis (clustering, interpreta- tion, and profiling) were applied to classify ATE structure. Correlation analyses of pattern variables were used to deter- mine groups of theoretically versus statistically associated variables. Structural interpretations of three cluster proce- dures (four, five, and six clusters, respectively) were per- formed using visual interpretation, descriptive statistics of

November 1996 PE&RS

clusters, and boxplots of input variables for resulting clus- ters. Next, the cluster solutions were validated using internal and external techniques in order to select the most appropri- ate number of clusters to describe ecotone structure. Follow- ing selection of the "best" cluster set, clusters were profiled and validated using multiple analysis of variance (MANOVA) and descriptive statistics of exogenous pattern and environ- mental variables (variables not used in clustering).

Because many of the pattern metrics are based on simi- lar measures, it was necessary to quantify expected similari- ties. Prior to statistical analysis, all variables were examined using boxplots to determine potential non-normal distribu- tions and outlier observations. While all variables appeared near-normal, the entire set of variables was standardized to reduce possible bias in subsequent multivariate statistical techniques. Correlation matrices and scatter-plots of pattern and composition metrics were used to infer relative informa- tional value of metrics and combinations. Five general groups of variables were developed based on theoretical sim- ilarities and observed correlations of metrics: (1) Diversity, (2) Texture, (3) Patch Density, (4) Edge Complexity, and (5) Abruptness. These groups were identified by exploratory analysis of correlation matrices for the hillslope observations. Each set tended to contain variables having low correlations with variables in the other groups. Using these five structural categories, seven variables were selected for clustering tree- line slopes based on minimizing the correlation coefficients between structure groups. The selected diversity metric, Richness, was chosen to summarize the diversity of cover types. Contagion and Contrast measured slope texture and local heterogeneity. The Number of Patches quantified eco- tone patch density. Mean Fractal Dimension and Relative Edge Density characterized edge complexity. Finally, Mean Juxtaposition measured the abruptness of treelines.

Field observations and the results of Baker et al. (1995) suggested that five to seven different treeline clusters would emerge. Exploratory use of Ward's clustering method (Hair et al., 1987) indicated that four to six clusters would be most descriptive of the data collected, for significant separation of four to six clusters was evident in the diversity of cover types present, relative area of classes, and the local heteroge- neity and mixture of classes. Thus, a range of four to six clusters was deemed appropriate for subsequent detailed analysis. To enhance replicability and to limit computation requirements, a "K-means" non-hierarchical clustering proce- dure was implemented. K-means clustering iteratively parti- tions observations in multidimensional space to maximize between-cluster variance, while minimizing within-cluster variance (Hair et al., 1987; SYSTAT, 1992). Using the seven pattern metrics and specifying ten iterations, three clustering procedures were completed, generating four-, five-, and six- cluster solutions, respectively.

Treeline Cluster Profiling Profiling involves quantitative tests of variable influence and validation to evaluate and interpret the clustering algorithm. Two general types of validation, internal and external, were used to select the cluster procedure (four, five, or six clus- ters) producing the most appropriate number of ATE clusters. Internal validation of clustering used split-sample replication and discriminant analysis of the input metrics to discern the replicability and predictability of the different sets of clus- ters. Split-sample replication, where the original observations are sampled and reclustered, allows the investigator to assess the stability of emergent clusters (Hair et al., 1987). By com- paring the original and replicated cluster assignments of the sample, changes and stability of the clusters were noted. Dis- criminant analysis also assisted the interpretation of cluster

MATRIX FOR DISCRIMINANT ANALYSIS VERSUS CLUSTER OF SIX ATE STRUCTURE CLASSES (OVERALL AGREEMENT =

95.5%).

Cluster Discriminant Class Class 1 2 3 4 5 6 Total

1 36 0 0 0 0 0 36 2 1 37 0 0 0 0 38 3 0 0 8 0 0 0 8 4 0 3 0 6 0 0 9 5 1 0 0 0 14 0 15 6 0 0 0 0 0 5 5

Total 3 8 40 8 6 14 5 111

validity. If, as assumed, clusters represent different popula- tions of treeline patterns, then the majority of ecotone slopes should be classified into clusters that are remarkable in spe- cific aspects of pattern and unremarkable in others.

Approximately one-half of the 111 sample was deemed an adequate replication pool. A total of 61 slopes were ran- domly sampled for replication procedures. Membership in the original and replicated sample was assessed by compar- ing the cluster labels for each slope unit in the original and replication results. The replication procedure affirmed the overall stability of original clusters. Despite the overlap of the four-cluster solution, this grouping retained the largest percentage of unchanged samples (98 percent), a likely result because fewer clusters were involved. The five- and six-clus- ter solutions were approximately equivalent at 92 percent and 93 percent unchanged, respectively. This suggested that all procedures captured significant groups of slope patterns. However, the sample size limit (partially controlled by the size of the whole sample of slopes) likely biases against the effect of small but potentially significant clusters. Thus, rep- lication suggests that any of the three size cluster solutions would provide an adequate description. Further analysis was required to select between the five- and six-cluster solutions.

Discriminant analysis of the seven clustering variables was used to assess the potential predictability of cluster membership. The best clustering procedure would allow pre- diction of the highest number of slopes in the same pattern groups as the original clustering algorithm. For each of the three cluster solutions (four, five, and six), discriminant anal- yses predicted cluster memberships using linear combina- tions (factors) of the same seven pattern metrics used in original clustering. Cluster memberships were used as the dependent categorical variable (Dillon and Gddstein, 1984). Overall agreement between the original clusters and discrim- inant predictions was calculated as the percentage of obser- vations unchanged. Robust predictions were generated by discriminant analyses of the five-cluster (96.4 percent) and six-cluster (95.5 percent) solutions. Table 2 shows the error matrix for cluster class versus discriminant analysis pre- dicted class. Few slopes are found in off-diagonal cells, in- dicative of strong agreement between the methods, and high predictability of the cluster results. Based on these results, the five- and six-cluster solutions exhibited the most stable, predictable clusters.

Original and predicted cluster labels were used as sym- bols to plot slope observations on discriminant axes (i.e., dis- criminant space). Six ATE cluster results plotted in discrimi- nant space were most visually separable. Further, the higher discriminants were more useful to the six-cluster prediction (assessed by eigenvectors) and showed that clusters were well spaced on the first two discriminant axes and the third axis. In coniunction with the split-sample validation indicat- ing cluster stability, discriminant analysis indicated that the six-cluster solution contained predictable clusters that also

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Landscape Metric 1

Relative Edge Density 1.06 Fractal Dimension 0.68 Contagion -0.95 Richness 0.42 Number of Patches 0.5 Juxtaposition 0.54 Contrast 0.2

Standardized Cluster Means 3 4

-1.82 -0.68 -2.43 0.27

1.57 -0.55 -1.8 -1.67 -1.47 -0.93 -0.3 -1.83 -1.3 -0.99

Significance

0.000 0.000 0.000 0.000 0.000 0.000 0.000

were differentiated by the full set of pattern metrics (Table 2). This convergence of results is sufficient to accept the six- cluster solution as the most appropriate characterization of ATE patterns in the study area.

External variables, those with similar descriptive or the- oretical qualities to cluster variables, may be used to validate a cluster analysis (Hair et a]., 1987). One-way analysis of var- iance (ANOVA) was selected to test whether theoretically sim- ilar landscape metrics would also distinguish the identified clusters of slope patterns. The null hypothesis was held that k means (k = 6 clusters) of selected pattern variables were equal. Separate univariate F-tests were used to profile clus- ters with a set of theoretically similar but independent varia- bles not used in the original clustering. These included variables in the four pattern groups: (1) dominance, to char- acterize diversity; (2) mean patch size, for relative patchi- ness; (3) total patch perimeter lengths, for edge description; and (4) angular second moment (ASM), a texture index. Sig- nificance tests and F-values indicated in ANOVA tables were used to affirmldisaffirm the robustness of the six-cluster solu- tion and the information content of variable groups.

Results and Discussion Cluster interpretation consisted of plotting clusters on all seven input variables, statistically describing cluster variable values, and viewing cluster memberships against thematic and topographic maps. Visual overlap, separation, and the presence of outliers were recorded. Mean score profiles of variables generated within the clustering algorithm were in- terpreted along with boxplots and parallel coordinate plots. Cluster membership for each slope and each of the three pro- cedures were encoded in the GIS and used for mapping clus- ters. The four-cluster procedure distinguished groups of slopes primarily on the basis of relative edge density, fractal dimension, contagion, and richness. Table 3 shows the mean group scores (standardized), variable F-ratios, and p-values for the analysis of variance (ANOVA) for the six-cluster ATE results.

The six-cluster solution proved inferentially similar to the five-cluster procedure. The heterogeneous cluster 1 and barren-dominated alpine slope (cluster 3) were found in both results. Table 3 indicates that all variables were significant in clustering and that the relative density of edges, number of patches, and richness were important to separating these ATE patterns. The addition of a sixth cluster allowed differentia- tion of slopes with moderate (cluster 2) to strongly (cluster 4) zonal patterns (divided into distinct alpine and subalpine zones.) A simple example of this is found at two neighboring slopes on the south slope of Singleshot Mountain at the range front, near Saint Mary, Montana. Both treeline slopes are constricted by steep slopes, resulting in a wide forested scree zone upslope of closed-canopy subalpine forest. The slope with a longer transition from forest to scree contained interstitial patches of meadows and was designated as cluster 2 (moderately zonal). The more abrupt treeline transition slope (cluster 4) exhibits a narrow zone of forested scree sep-

arating a large barren area and subalpine forest downslope (strongly zonal). Further, cluster 5 contains ATE patterns with island-like patches of krummholz, scree, and tundra at high elevation interior passes (generating high contrast as in the five-cluster procedure). Cluster 6 contains a small number of slopes and similar patterns of high heterogeneity as exhibited by cluster 1. However, cluster 6 was differentiated from clus- ter 1 by an extremely high average number of patches. Inter- pretation of the six-cluster results showed a meaningful grouping of slopes and indicated an improved level of pat- tern differentiation over the general four- and five-cluster re- sults.

Cluster 1 represented a major portion of the treeline eco- tone, having an irregular spatial pattern with high density of patch edges and very high juxtaposition of alpine and subal- pine vegetation types (36 of 111 sampled slopes). This heter- ogeneous treeline type differed greatly from the other major type, a zonal pattern (cluster 2) with moderately sorted patches, interstitial meadows, and common late-lying snow- fields (38 slopes). Cluster 3 characterized highly uniform zones of treeline, typically dominated by a single class such as krummholz or meadow. This cluster had characteristic high dominance and low diversity metrics (eight slopes). The fourth emergent cluster exhibited an abrupt treeline transi- tion, often with a narrow zone of forested scree, likely re- lated to geological structures and mass wasting processes impinging on treeline (nine slopes). Cluster 5 was interpreted as a complex treeline zone with a signature of high contrast and numerous krummholz and tundra islands (15 slopes). Fi- nally, cluster 6 contained five treeline slopes that had ex- tremely high patch density. These patchy, fine-grained treelines included small patches of potential treeline ad- vances near the elevational limit of tree growth at interior passes and along the range front. These interpretations, based on cluster variables and emergent groups, could be further informed by profiling using topographic gradient variables.

Profiling results using additional landscape metrics cor- roborate and assist the interpretation of six ATE patterns (Table 4). Highest mean-square totals were observed for dom- inance, angular second moment, and mean patch size. All variables were significant (alpha = 0.001) in these tests. Wilk's A multivariate statistic (0.065) was approximated by an F-distribution (F = 16.447, degrees of freedom = 25 and 376) and found significant (alpha = 0.001). Thus, the six- cluster classification of treeline slopes was further validated by significant univariate and multivariate tests. Profiling the clusters using modeled terrain variables helped develop hy- potheses for explaining ATE patterns (Table 5). Major envi- ronmental gradients (i.e., elevation, slope angle, summer solar radiation potential, topographic wetness, and relieflex- posure) were selected for analysis. Terrain variables that were not significant included mean slope, curvature, profile curvature, and exposure. Mean elevation was the most signif- icant variable, followed by the coefficients of variation for slope angle and solar radiation potential. Elevation exerts the major control over ATE patterns, thus distinguishing the re-

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TABLE 4. UNIVARIATE ANALYSIS OF VARIANCE F-TESTS FOR CLUSTER PATTERN VALIDATIONS USING SELECTED VARIABLES THEORETICALLY SIMILAR TO I N I T I A L

CLUSTER VARIABLES.

Variable SS DF MS F Significance

Dominance Enor

Angular Second Moment

Error Patch Size

Error Patch Perimeter

Error Forest-Tundra Distance

Error

gional "climatic" control from more local disturbance, litho- logic, or antecedent biotic controls. Variability of steepness within ecotone slopes was the next important terrain varia- ble, suggestive that landforms within and along the ecotone could be of major importance. This suggests the importance of slope incision by snow avalanches and debris flows that have been previously known to locally affect treelines (Ha- beck, 1969; Walsh et ul., 1994). It further supports the impor- tance of geomorphic slope processes impacting ecotonal attributes such as density of edges (Swanson e t ul., 1992) and the local pattern of the ATE (Butler and Walsh, 1994). These results show that there is a linkage between ecotone patterns and environmental variation characterized by the selected terrain variables. Further statistical analyses using multiple dimensions of spatial pattern and terrain factors are neces- sary to quantify these relationships. It can be hypothesized that the ATE is influenced regionally by climatic control and locally primarily by landform conditions and slope stability. Analysis of specific geologic substrate influences remains to be conducted. Further, the relationships between specific landscape metrics and environmental gradients, disturbances, and landforms is the next step in identifying areas and pat- terns responsive to "climatic" control.

Conclusion Several empirical approaches to spatial pattern and terrain relationships have been applied in this research. GIs pro- vided the methodological framework for image classification (including topographic normalization), digital terrain models, and calculation of landscape pattern metrics. Cluster analysis was the primary method used to distinguish patterns within the ATE. This research found that correlation and cluster analysis of landscape metrics, guided by knowledge of the treeline ecology, could distinguish distinct spatial patterns of the ecotone. This affirms the central hypothesis, that treeline may exhibit distinctive patterns. Alpine treeline forms were differentiated by metrics of compositional and spatial pattern along a continuum from the simple to extremely heterogene- ous. Subtle differences were found in the last of six clusters. Validation procedures strongly supported interpretations of the six general treeline patterns. Results suggest that even in a complex alpine environment such as Glacier National Park, Montana, treeline forms may be recognized. The study cor- roborates the general findings of Baker and Weisberg (1995), who analyzed treeline patterns within transects as opposed to hillslopes. The primary control on pattern is the climatic gradient of elevation, yet important variability of ecotone structure is evident in relatively minor topographic gradients as well. The relative paucity of some treeline patterns sug- gests that there are important site-specific factors worthy of consideration in studies of habitat usage, biodiversity, or aes-

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Variable SS DF MS F Significance

Elevation 35.87 5 7.17 10.16 0.000 Error 74.12 105 0.71

Solar radiation potential 21.35 5 4.27 5.06

Error 88.63 105 0.84 Topographic wetness 12.0 potential 5 2.40 2.57

Error 97.97 105 0.93 Slope angle coeff. variation 27.85 5 5.57 7.12

Error 82.14 105 0.78 Solar radiation potential coeff. variation 28.45 5 5.6 7.33 0.000

Error 81.54 105 0.77

thetic and trail use concerns in the park. In distinct contrast to Rocky Mountain National Park, assessment of widespread treeline responses to climate change in Glacier National Park fundamentally depends on the inclusion of indirect re- sponses, especially to changes in disturbances, as well as general shifts in climatic gradients (Beaudoin, 1989). Synthe- sis of the complex influences of environmental gradients, disturbances, and geology upon alpine treeline and other landscapes may encourage increasing use of GIs.

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