Data-driven regionalization of forested and non-forested ecosystems in coastal British
Columbia with LiDAR and RapidEye imagery
Shanley D. Thompson a,1,*, Trisalyn A. Nelson a,2, Ian Giesbrecht b,3, Gordon Frazer b,4, Sari C.
a Spatial Pattern Analysis and Research Lab, Department of Geography, University of
Victoria, PO BOX 3060, Victoria, British Columbia, Canada, V8W 3R4
b Hakai Institute, Box 309, Heriot Bay, British Columbia, Canada, V0P 1H0
c BC Ministry of Forests, Lands and Natural Resources, 2100 Labieux Rd., Nanaimo
British Columbia, Canada, V9T 6E9
Email: firstname.lastname@example.org (* Corresponding author)
Pre-print of published version.
Reference: Thompson, S.D., Nelson, T.A., Giesbrecht, I., Frazer, G., & Saunders, S.C.
(2016). Data-driven regionalization of forested and non-forested ecosystems in coastal
British Columbia with LiDAR and RapidEye imagery. Applied Geography 69: 35-50.
The pdf document is a copy of the final version of this manuscript that was subsequently
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Data-driven regionalization of forested and non-forested ecosystems in coastal British
Columbia with LiDAR and RapidEye imagery
Traditionally, forest inventory and ecosystem mapping at local to regional scales rely on manual
interpretation of aerial photographs, based on standardized, expert-driven classification schemes.
These current approaches provide the information needed for forest ecosystem management but
constrain the thematic and spatial resolution of mapping and are infrequently repeated. The goal
of this research was to demonstrate the utility of an unsupervised, quantitative technique based
on Light Detection And Ranging (LiDAR) data and multi-spectral satellite imagery for mapping
local-scale ecosystems over a heterogeneous landscape of forested and non-forested ecosystems.
We derived a range of metrics characterizing local terrain and vegetation from LiDAR and
RapidEye imagery for Calvert and Hecate Islands, British Columbia. These metrics were used in
a cluster analysis to classify and quantitatively characterize ecological units across the island. A
total of 18 clusters were derived. The clusters were attributed with quantitative summary
statistics from the remotely sensed data inputs and contextualized through comparison to
ecological units delineated in a traditional expert-driven mapping method using aerial
photographs. The 18 clusters describe ecosystems ranging from open shrublands to dense,
productive forest and include a riparian zone and many wetter and wetland ecosystems. The
clusters provide detailed, spatially-explicit information for characterizing the landscape as a
mosaic of units defined by topography and vegetation structure. This study demonstrates that
using various types of remotely sensed data in a quantitative classification can provide scientists
and managers with multivariate information unique from that which results from traditional,
expert-based ecosystem mapping methods.
Statistical clustering of remotely sensed data produced a map of 18 ecosystems
Spatially-explicit topographic and vegetation structural data quantify each cluster
The approach complements traditional methods based on air photo interpretation
ecosystem, ecoregion, classification, cluster analysis, ecosystem structure, terrain
An ecosystem, as defined by the Convention on Biological Diversity (CBD) and the
Millennium Ecosystem Assessment (MA), is a dynamic complex of biotic components, and the
interaction between these components and their physical environment. Ecosystems can be
conceptualized at a variety of spatial scales, in a hierarchical manner (Bailey, 1987; Franklin,
2013). As reviewed by Whittaker (1967) and Kent et al. (1997), boundaries between ecosystems
are, in reality, most often gradual and fuzzy; attributes such as species composition overlap along
environmental gradients. The science of delineating regions (e.g., ecological or biogeographical)
in geographical space is referred to as regionalization (Loveland & Merchant, 2004; Olstad,
2012) and is important for the understanding and management of the natural world (Mackey,
Berry, & Brown, 2007; McMahon, Wiken, & Gauthier, 2004). Envisioned use of regions often
determines the appropriate scale for mapping and thus which and how many regions can or will
be delineated for a given project. National- or regional-scale conservation planning, resource
management, and ecosystem services assessments benefit from maps that delineate spatial units
on the basis of regional climate, large landforms, land cover class, and/or patterns of primary
productivity (e.g., Handcock and Csillag 2002; Leathwick et al. 2003; Sayre et al. 2009).
Differences in vegetation composition and structure, as influenced by micro-scale soil moisture
and nutrient conditions, define ecological communities at plot to landscape scales, supporting
more specific local and regional science and management activities (e.g., Banner et al. 1996).
Many jurisdictions rely on the manual interpretation of aerial photographs and field
observations to delineate ecological regions and forest attributes at local to national scales.
Interpreters use a set of methodological standards (e.g., Resources Inventory Committee 1998;
Canadian Forest Service 2001; Resource Information Management Branch 2005) that provide
the information desired for forest or ecosystem management, but inherently limit the spatial and
thematic resolutions of the resulting map. For instance, forest stand or ecosystem polygons are
delineated and attributed with information regarding composition and structure that is considered
representative of the entire polygon (Wulder et al., 2006). Alternative methods for mapping that
incorporate other types of remotely sensed imagery in a quantitative classification may be used
to delineate local regions with measurable attributes at improved spatial precisions. Further,
relative to the manual delineation of ecological regions, a quantitative approach may be
automated or semi-automated, offering increased consistency, repeatability, and cost-efficiency
for monitoring over time and across large areas (MacMillan, Moon, & Coupé, 2007; Morgan,
Gergel, & Coops, 2010).
Remote sensing can capture various structural, compositional, and functional aspects of
ecosystems. Multispectral imagery at high to moderate spatial resolutions is frequently used to
distinguish among vegetation life form and age class (e.g., Wulder et al. 2004; Johansen et al.
2007; Valeria et al. 2014). Multispectral data are also used generate indices such as the
Normalized Difference Vegetation Index (NDVI) (Rouse, Haas, Schell, & Deering, 1974), which
correlates well with patterns of net primary productivity (Goward, Tucker, & Dye, 1985) and has
been useful for wetland delineation (e.g., Dechka et al. 2002; Barron et al. 2014; White et al.
2015). Hyperspectral imagery is well suited to species composition mapping (e.g., Dalponte et al.
2013, Feret & Asner 2013). Light Detection And Ranging (LiDAR) technology captures highly
accurate, direct measurements of three-dimensional vegetation structure (Lim, Treitz, Wulder,
St-Onge, & Flood, 2003; van Leeuwen & Nieuwenhuis, 2010). In particular, LiDAR provides
excellent measurements of forest structural properties such as tree height and canopy closure
(Coops et al., 2007; Holmgren, 2004; Lefsky et al., 1999). The high spatial resolution of LiDAR-
derived elevation data may (Hogg & Holland, 2008; Maxa & Bolstad, 2009) or may not (Knight
et al. 2013) lead to improved wetland delineation compared to use of aerial photography,
especially in areas of low topographic variation.
As no single sensor can capture all of the structural, functional and compositional
characteristics of terrestrial ecosystems at the spatial resolution and extent typically desired by
environmental managers, researchers often combine multiple types of remotely sensed data
together to generate improved and more complex maps (e.g., Ke et al. 2010, Wulder et al. 2007,
Jones et al. 2010). Combining various types of remotely sensed data in a quantitative (statistical)
regionalization, researchers have effectively captured environmental domains over large regions
(e.g., Handcock and Csillag 2002; Coops et al. 2009; Fitterer et al. 2012; Powers et al. 2012).
Drawing on the high spatial resolution and information content of remotely sensed data,
regionalizations are also possible that highlight ecosystem patterns, gradients, and ecotones at
local scales (Hargrove & Hoffman, 2004; Kupfer, Gao, & Guo, 2012; Long, Nelson, & Wulder,
2010; Olstad, 2012). These smaller regions have higher internal homogeneity, a desirable
property for local-scale management (Bryan, 2006) and for serving as strata for field-based
sampling. As computing power increases and is more able to accommodate very large datasets,
quantitative methods that combine numerous remotely sourced datasets at high to moderate
spatial resolutions, including LiDAR, can produce information-rich (i.e., multivariate)
categorical maps for environmental research and management. investigated., Researchers
continue to evaluate new techniques and data for regionalization in ecological contexts (e.g., Xu
et al. 2013, Niesterwiscz et al. 2013), however, research incorporating vegetation structural data
from LiDAR with other remotely sensed data for local-scale regionalization has been limited.
The goal of this research was to demonstrate the utility of LiDAR and high spatial
resolution multispectral imagery for mapping and characterizing the variety of local-scale
ecosystems over a complex landscape of forested and non-forested ecosystems on the outer coast
of British Columbia. Given that different ecosystem maps of the same area are possible
depending on data and methodology, the objective was to use an unsupervised, quantitative
regionalization method to determine what types of ecosystem units would be captured when
using high resolution remotely sensed measures representing vegetation structure and
topography. Following attribution of the resulting regions with the remotely sensed data, we
contextualize our findings by comparing the results of the unsupervised classification to those of
an expert-driven classification. We conclude with a discussion of implications for ecosystem
management and recommendations for local-scale ecosystem mapping that will be useful in a
variety of remote regions characterized by heterogeneous landscapes where field data collection
is logistically challenging.
2.1 Study Area
Calvert and Hecate Islands (total 37,433 ha) are remote islands on the central coast of
British Columbia, Canada (Figure 1). The islands are dominated by fairly subdued topography
from low to moderate elevations in a biogeoclimatic unit classified as the Coastal Western
Hemlock zone, Very Wet, Hypermaritime subzone, Central variant (CWHvh2). Elevations in the
study area reach ~1000 m; these areas classified as the Mountain Hemlock zone, Wet
Hypermaritime Subzone (MHwh1). Gridded climate data for the region (ClimateBC v5 - Wang
et al. 2012) indicate that average (1990–2012) annual temperature is 7.6C°C for the CWHvh2
and 4.8°C for the MHwh. Average annual precipitation in these biogeoclimatic units is 3512.2
mm and 5140.7 mm, respectively. High precipitation, abundant fog, and low evapotranspiration
result in an abundance of wet soils, wetland ecosystems, and relatively unproductive forests
(Banner, LePage, Moran, & de Groot, 2005).
Figure 1 Study area in coastal British Columbia, Canada
2.2 Remotely Sensed Data
The quantitative regionalization used in this study relied on a combination of LiDAR data
and multispectral satellite imagery with differing native spatial resolutions. All data were
aggregated to a common spatial resolution of 20 m, a scale widely used in LiDAR-based forest
inventories, soil mapping, and terrain analysis (Brosofske et al., 2014; Gillin et al., 2015).
Airborne LiDAR data were acquired across Calvert and Hecate Islands in August 2012. Mounted
on a fixed-wing aircraft flying at 1150 m above ground level with a maximum scan angle of
±26°, the discrete-return (4 returns/pulse), small-footprint (0.3 mrad) V-Gen LiDAR system
acquired data with an average point density of 2.32 pt/m2 and a standard deviation of 1.07 pt/m2.
Relative and absolute vertical accuracies at one standard deviation were estimated by the data
provider to be ±15 cm and ± 30 cm, respectively. A small number of data voids in the LiDAR
coverage were present and were excluded from the analysis.
Several data processing steps were required to extract candidate topographic indices and
vegetation metrics from the LiDAR dataset. First, LiDAR returns were separated into ground and
non-ground feature classes using TerraScan’s (Terrasolid Ltd.) automated ground-filtering
routine. Manual refinement of the point classification was undertaken in areas of steep, complex
topography to correct any obvious classification errors created by the automated ground filter
(Merrick Advanced Remote Sensing–MARS–software suite). Second, we used the BLAST
extension pack (blast2dem) of LAStools (rapidlasso GmbH) to construct a gridded one-meter,
‘bare-earth’ Digital Terrain Model (DTM) from a Triangulated Irregular Network (TIN) of
ground-classified points. The gridded one-meter DTM was subsequently resampled to a spatial
resolution of 20 meters using the cell-area weighted mean elevation prior to computing several
topographic indices (System for Automated Geoscientific Analyses–SAGA). Third, we
converted (i.e., height normalized) each elevation in the LiDAR point cloud to an estimated
height in meters above the ground surface using the difference in elevation between a point and
its corresponding elevation on the TIN of ground-classified points (LAStools). We extracted the
following terrain indices from the 20 m DTM: slope (%), the Topographic Radiation ASPect
(TRASP) (Roberts & Cooper, 1989), the Topographic Position Index (TPI) normalized to the
local standard deviation in elevation as per De Reu et al. (2013), and the Topographic Wetness
Index (TWI) calculated using the D-infinity algorithm (Tarboton, 1997) (Table 1). Elevation,
slope, TRASP, TPI, and TWI are considered useful inputs in automated ecosystem classification
and predictive vegetation mapping because these variables directly and indirectly influence plant
growth and community composition via effects on temperature, precipitation, soil moisture, soil
nutrients, and wind exposure (Franklin, 1995). These types of topographic derivatives are
commonly used in predictive ecosystem mapping (e.g., MacMillan et al. 2007; Chastain and
Struckhoff 2008; Dobrowski et al. 2008; Fraser et al. 2012), and standard ecosystem
classification in British Columbia at the local scale relies heavily on topographic concepts
(Banner et al., 1996).
We used the height normalized LiDAR point cloud to compute several area-based
(gridded) canopy height and density metrics on the same 20 m grid shared by the DTM and
derivative topographic indices. Area-based height metrics included estimates of the mean,
maximum, standard deviation, coefficient of variation (CV), and percentiles of canopy height
computed using all laser points with heights greater than or equal to 2 m within a single grid cell
(Magnussen and Boudewyn, 1998; Næsset, 2002). A measure of canopy density or gap fraction
was estimated for each grid cell as the ratio of the number laser points found below 2 m to the
total number of laser points located within the cell (Hopkinson and Chasmer, 2009). All grid
cells devoid of laser returns greater than 2 m in height were considered to be non-forested in this
Multispectral reflectance data (5 m spatial resolution) were acquired from the RapidEye
satellite sensor (BlackBridge) in 2011. Using PCI Geomatica, the RapidEye imagery was first
converted to Top of Atmosphere units to adjust for sun angle and earth-sun distance and further
corrected for atmospheric noise using the Dark Object Subtraction method (Chavez, 1996). We
calculated the NDVI as an overall proxy for vegetation greenness or productivity. The NDVI
was resampled to 20 m spatial resolution to match the LiDAR data. Finally, as our focus was on
terrestrial systems, we used a provincial water body database
, as well as the NDVI layer (values
< 0.2) to remove water and un-vegetated pixels.
The Freshwater Atlas (FWA): http://geobc.gov.bc.ca/base-mapping/atlas/fwa/index.html
Table 1. Description of remotely sensed variables used in analyses
Elevation above sea level in metres, derived
Elevations in the study site range from
0 (sea level) to 1012 m.
The ratio of total number of laser points < 2 m
in height to the total number of laser points
within a grid cell.
A density-based statistic, higher values
represent lower canopy cover.
2nd central moment about the mean
A high coefficient of variation means
the vegetation has a strong vertical
LiDAR Canopy Height Model = value of
maximum laser point return per grid cell.
Height of the tallest tree or shrub in
the grid cell.
Height – mean
Arithmetic mean height (m) of laser points ≥
the minimum height threshold (2 m in this
Average height of tree canopy.
NDVI = (NIR reflectance –red reflectance) /
(NIR reflectance +red reflectance) (Rouse et
A measure of vegetation greenness,
widely used as a proxy for
productivity. Values near zero are
considered non-vegetated or sparsely
Slope in percent rise, derived from the DEM
Slopes in the study area range from
level (0%) to very steep (~120%)
TPI = zo - zavg where zo = elevation of focus
pixel and zavg = average elevation neighbouring
pixels (Weiss 2001). Calculated here for a 100
m neighbourhood and standardized to z-scores
as per De Reu et al. (2013).
Positive values (> 0.5 in this study)
represent ridges and upper slopes,
whereas negative values (< -0.5 in this
study) represent lower slopes and
valley bottoms; values near zero are
mid-slope or flat (Weiss 2001; Tagil
and Jenness 2008; De Reu et al. 2013).
TRASP = (1 - cos((3.1416/180)(aspect-30)))/2
where aspect is in degrees (Roberts and
Values near 0 (~ < 0.5) are N, E, NE
or NW facing (cooler slopes) while
those near 1 (or ~ > 0.5) are S, W,
SW, or SE facing (warm slopes).
TWI = ln(specific catchment area / tan(slope)).
Calculated using the D-infinity algorithm
Higher values are considered wetter,
lower values drier.
2.3 Existing Ecosystem Data
The study area was recently mapped using British Columbia’s provincial standard of
Terrestrial Ecosystem Mapping (TEM) (Green, 2014; Resources Inventory Committee, 1998).
TEM uses a well-defined hierarchical classification system referred to as Biogeoclimatic
Ecosystem Classification (BEC) (Banner et al., 1996; Pojar, Klinka, & Meidinger, 1987). At the
regional level, vegetation, soils, and topography are used to infer climatic zones. Within these
regional climate zones, subzones are defined by the climax plant association typical of a zonal
site (zonal sites are those on which vegetation is primarily influenced by climate, not edaphic
features). Variants may be used to distinguish finer-scaled variation in climate within the
Subzone. Within each subzone or variant, a set of ecosystems is defined, which are referred to as
site series. The site series (each given a unique two letter and two- or three-digit code) are
classified with reference to established rules that associate each with a particular combination of
terrain, soil and vegetation characteristics.
TEM relies on analysts to interpret aerial photographs, topographic maps, and other
available geospatial information to identify site series. Interpreted TEM polygons may contain
up to three site series each, where individual patches of these site series are smaller than the
minimum mapping unit (typically 0.5–2.0 ha). In these complex polygons, the relative proportion
of each site series is noted, although the exact location is not. The TEM for the study area
identified 38 site series, including six non-vegetated site series, seven non-forested site series,
and 25 forested site series (Green, 2014). Ground sampling is used to calibrate and assess the
TEM. Field surveys were conducted in 2013 and 2014 by provincial ecologists and Hakai
Institute and affiliated researchers, primarily in the northern part of Calvert Island and the
southern part of Hecate Island following provincial BEC standards (BC Ministry of Forests and
Range and BC Ministry of Environment, 2010). Field plots identified 10 ecosystem types,
including several sub-types not explicitly captured in the TEM (e.g., shallow minerotrophic
blanket bogs, and deep ombrotrophic blanket bogs).
2.4 Unsupervised regionalization
Multivariate clustering was used to determine the types of local-scale ecosystems that are
distinguishable on Calvert and Hecate Islands with key metrics derived from LiDAR and
RapidEye data. Clustering is an unsupervised, multivariate technique, which can be used to
group observations or sample units that are similar with respect to the variables used to define
them. These techniques generally seek to minimize within-group variability and maximize
A Spearman’s rank correlation analysis was conducted to assess collinearity among all
the aforementioned terrain (slope, TRASP, TWI, and TPI) and vegetation variables (NDVI,
mean height, maximum height, and gap fraction). Correlations were fairly low (< 0.5) between
the terrain variables and the vegetation variables, as well as among the terrain variables (Table
2). Correlations were moderate to high (> 0.7) among the vegetation variables. From these four
vegetation variables, we chose to retain one of the LiDAR vegetation variables (mean height)
and the multispectral vegetation variable (NDVI) as inputs for the clustering.
With each of the chosen variables having been clipped and resampled to a consistent
spatial extent and spatial resolution (20 m), and being projected to the same datum (NAD 83), a
“raster stack” was built (using the “raster” package in R) to combine the variables into a single
data frame for clustering. Clustering was conducted separately for the forested and non-forested
regions of the island, since the average height and coefficient of variation of height from LiDAR
were only available for the forested region (defined here as vegetation > 2 m in height). All data
were standardized to z-scores prior to clustering in order to ensure approximately equal weight
for all variables. A clustering methodology called TwoStep, employing a probability-based
distance measure, was implemented in SPSS (v22). The TwoStep approach was chosen because
it is well suited to very large datasets. It begins with an initial partition of the data, followed by a
hierarchical clustering of these partitions. The number of resulting clusters may be explicitly
specified by the analyst. To select an appropriate number, we first considered several statistical
criteria: the Bayesian Information Criterion (BIC), the Calinski–Harabasz (CH) criterion
(Calinski and Harabasz 1974) and the Average Silhouette Width (ASW) (Table 4.3). Whereas
the BIC is calculated internally during the TwoStep clustering procedure, we calculated the CH
and ASW statistics based on k-means partitioning using the pamk() function from the fpc library
in R (v3.1.2). In choosing the number of clusters, we also took into consideration the number of
site series identified in the existing ecosystem map and in field surveys conducted in 2013 and
Once the desired number of clusters was determined, the clusters were mapped in
geographic space and a majority filter of 4 x 4 pixels was applied to remove speckle in the final
product. Otherwise, no minimum mapping unit was imposed. Clusters were attributed with
summary statistics for each data layer input into the cluster analysis (e.g., NDVI, elevation, and
slope). Additionally, the LiDAR-derived variables of gap fraction and maximum height
(excluded from the cluster analysis because of high collinearity with each other as well as with
NDVI and average mean height) were also used to describe the clusters.
Table 2. Spearman’s rank correlation coefficients
Height – mean
NDVI = Normalized Difference Vegetation Index (NDVI), TPI = Topographic Position Index, TRASP = Topographic Radiation
ASPect, TWI = Topographic Wetness Index
2.5 Map Comparisons
We used several approaches to contextualize our unsupervised ecosystem map relative to
the expert-driven TEM. First, each cluster was attributed with field survey information by
overlaying the field survey points on the clusters in ArcGIS, extracting the cluster value at each
point, and summarizing by cluster type. Second, TEM information was attributed to each cluster
as follows: the majority (modal) cluster value occurring within each TEM polygon was extracted
and joined to the TEM database. Next, the total area of each TEM site series within each cluster
type was derived using information on the proportional area of each site series within each TEM
polygon. We used pie charts to summarize the detailed composition of our clusters in terms of
TEM units and the composition of TEM units in terms of our clusters.
Third, we calculated the diversity of different TEM site series comprising each cluster, as
well as the inverse (diversity of clusters within each TEM site series) to determine
correspondence between the two mapping methodologies. More diverse clusters or TEM site
series represent poor agreement between the two maps. We assessed this relationship both
graphically (via pie-charts) and numerically, via Simpson’s Diversity Index, which is commonly
used in ecological studies to indicate species diversity in a way that captures both richness (a
count of species) and evenness (relative abundance of each species). The Simpson’s Diversity
Index is calculated using the formula
D = 1 – [sum(n/N)2]
where n is the number of individuals of a particular species, and N is the total number of
all individuals for a given location. In our case, rather than species diversity, we calculated the
index to measure the diversity of site series in each cluster and again to measure the diversity of
clusters within each site series. The values ranged from 0 to 1, with higher values indicating a
poor association between the two mapping methodologies. We note, however, that the index of
diversity used to compare the maps at this level does not take into account ecological similarity
among site series and that a cluster containing many similar site series may not be as severely
mismatched to the TEM as a cluster containing the same number of ecologically dissimilar site
series. To avoid bias due to the variation in the size and number of each TEM polygon and each
TEM site series, TEM site series that are rare on the landscape were excluded (those below the
5th percentile in number of polygons as well as area). Individual TEM polygons below the 5th
percentile in area, regardless of site series, were also removed.
Finally, to allow direct comparison of the two maps with a single classification scheme,
we assigned each TEM site series and each cluster to one of six broad ecosystem classes. We
used broad ecosystem classes suggested by the local TEM authors as well as the regional
handbook for ecosystem classification (Green & Klinka, 1994). Clusters were assigned to broad
classes based on interpretation of the calculated terrain metrics, particularly topographic wetness,
slope and topographic position. The generalized classes maintain distinctions between forested
and non-forested ecosystems and emphasize differences along a moisture gradient. To compare
the unsupervised regionalization with the expert-driven TEM, we calculated the spatial extent of
each of these generalized ecosystem types for both systems.
3.1 Unsupervised regionalization
We identified 12 forested clusters (Clusters 1–12) and six non-forested clusters (Clusters
13–18) (Figure 2 and 3), drawing on several lines of information to judge an appropriate and
useful number of clusters in each group. The statistically optimal number of clusters varied from
two to three for non-forested regions and two to 25 for forested regions (Table 3), while the TEM
and field plot data suggested upwards of 32 vegetated site series may be present on the island.
Upon visual inspection of the resulting map, 18 clusters were chosen to provide the desired
spatially-detailed characterization of the landscape without sub-dividing beyond the limits of the
data or our ability to interpret, describe, and—potentially—sample the landscape mosaic in the
Table 3. The statistical optimum number of clusters according to three different criteria
ASW = [ ∑Si/n]
The similarity (e.g., distance) of each data point i
to other points in the same cluster a, relative to
distance to points in other clusters, b averaged for
all points. In an optimal solution, values are close
to 1.0, meaning clusters are very homogenous and
BSS(K-1)/ WSS(n-K), where BSS is between
group sum of squares, WSS is within group sum
of squares, K is number of clusters and n is
number of data points. Optimal number of
clusters maximizes this index.
BIC identifies the model (cluster solution) that
would most likely produce the observed data,
penalizing for complexity (number of clusters *
number of observations). Optimal number of
clusters maximizes this index (i.e., BIC will be
higher for smaller numbers of clusters).
a ASW and CH were calculated in R based on k-means clustering.
b BIC was calculated in SPSS based on Two-Step clustering.
Figure 2. Eighteen clusters representing a range of forested and non-forested terrestrial
ecosystems on Calvert and Hecate Islands. Clusters 1 through 12 are forested and Clusters
13 through 18 are non-forested. White areas within the land mass are data voids.
Figure 3. Zoomed in view of 18 clusters on Calvert and Hecate Islands. Clusters 1 through
12 are forested and Clusters 13 through 18 are non-forested.
Cluster 1 described a forest of intermediate wetness (mean TWI = 6.07) and moderate
productivity (mean NDVI = 0.75, mean height = 7.7 m), relative to the study area (Table 4, Fig.
4 and 5). It occurred in the middle of the range of elevations found in the study area (average of
292 m) on steep slopes (average of 44%), and cool aspects (mean TRASP = 0.16). Cluster 2 was
more productive, and had relatively tall trees (mean NDVI = 0.78, mean maximum height =
20.3, mean height = 13 m). It was found at low elevations (average of 86 m). Clusters 3 and 4
were the most abundant classes across the study area (3903 ha and 3696 ha, or 11.2% and 10.6%
of the study area, respectively). They were characterized as forests of intermediate to high
wetness (mean TWI = 6.52 and 6.93, respectively) with moderate productivity (mean NDVI =
0.74). Both occurred at low elevations (average < 82 m). Cluster 3 occurred on warm aspects
(mean TRASP = 0.83), while Cluster 4 occurred on cool aspects (mean TRASP = 0.16).
Cluster 5 occurred primarily on ridges (mean TPI = 1.52) at low elevations (average 119
m) and was predicted to be the driest cluster (mean TWI = 4.4). Productivity was moderate
(mean NDVI = 0.75) and tree heights averaged 9 m. Clusters 6 and 8 had a similar topographic
wetness to Clusters 3 and 4, but were considerably less productive (mean NDVI values were
0.64 and 0.65 for Clusters 6 and 8, respectively). Both had open canopies (gap fractions of 0.69)
and short trees (average mean and max heights < 6 m). Cluster 6 represented cool aspects, while
Cluster 8 was associated with warm aspects. Cluster 7 was found at low elevations (mean =
85m), at fairly level sites (mean slope = 8%), and at lower slope positions (mean TPI = -0.88). It
was predicted to have very high wetness (mean TWI = 12.89) with moderate productivity (mean
NDVI = 0.74). Cluster 9 was predicted to be relatively dry, similar to Cluster 5 (mean TWI =
4.59), with moderate productivity (mean NDVI = 0.71) and short vegetation (mean height 5.73
m). Cluster 9 was found at the highest slope positions among our clusters (mean TPI = 1.55), at
high elevations (506 m on average) on very steep slopes (51% on average).
Cluster 10 was found in moderately productive forest (mean NDVI = 0.73) with average
tree heights of 6.5 m. It occurred at middle elevations (average 311 m), on moderate slopes
(average 33%) of distinctly warm aspect (mean TRASP = 0.86), and was predicted to be found
on sites with moderate wetness (mean TWI = 5.96). Clusters 11 and 12 were the tallest, densest,
and most productive forests on the island: maximum tree heights averaged > 21 m, mean gap
fractions were ≤ 0.16, and NDVI averaged 0.79 and 0.82, respectively. Cluster 11 occurred at
low elevations (average of 120 m) and moderate slopes (average 33%), while Cluster 12 was
found at higher elevations (average of 461 m) on very steep slopes (average 65%).
The remaining six clusters were characterized as non-forested (mean and maximum
vegetation height less than 2 m). All non-forested clusters had low mean NDVI values (≤ 0.6)
and very high mean gap fractions (≥ 0.93), relative to the forested clusters. Despite this low
NDVI and high gap fraction, NDVI boxplots suggest that some non-forested pixels reach forest-
like levels of productivity (Fig. 5). Cluster 13 was relatively scarce (849 ha of the study area) and
was found across a wide range of elevations (mean 361 m) and at relatively steep slopes (38%).
It was predicted to be relatively dry, similar to Clusters 5 and 9 (mean TWI = 4.86). Cluster 14
was also relatively scarce (696 ha in total) and generally restricted to low elevations (79 m
average). It had the lowest productivity and lowest canopy cover of any cluster (average NDVI
of 0.42 and average gap fraction of 0.98). Cluster 15 was a wetter cluster (mean TWI = 7.03) that
occurred at high elevations (average 413 m) across a wide range of aspects. Cluster 16 was
predicted to have very high wetness (mean TWI = 11.95), and it was uncommon across the study
site (720 ha). Generally it occurred at low elevations (99 m average) and on level sites (mean
slope 4%). Cluster 17 and 18 were predicted to have moderately high wetness (mean TWI ranged
from 6.82 to 7.20) and were found on very gentle slopes (8% average). Cluster 17 occurred on
cool aspects (mean TRASP = 0.16), and was extensive across the island (covering 2449 ha),
while Cluster 18 was less abundant (1674 ha) and occurred on warm aspects (mean TRASP =
Figure 4. Distribution of clusters across each LiDAR-derived terrain index. Clusters 1
through 12 are forested, and Clusters 13 through 18 are non-forested.
Figure 5. Distribution of clusters across LiDAR and RapidEye vegetation data. Clusters 1
through 12 are forested, and Clusters 13 through 18 are non-forested.
Table 4. Mean values of remotely sensed inputs and descriptors of 18 clusters. Clusters 1 through 12 are forested and Clusters
13 through 18 are non-forested
NDVI = Normalized Difference Vegetation Index (NDVI), TPI = Topographic Position Index, TRASP = Topographic Radiation
ASPect, TWI = Topographic Wetness Index
3.2 Map Comparisons
The clusters contained information that was unique from that contained in the TEM. Most
clusters in our established set of 18 were comprised of a variety of TEM site series (Table 5,
Supplementary Figure A.1) and each TEM site series contained multiple clusters (Supplementary
Figure A.2). Measured in terms of relative area, Cluster 14 was the most homogenous, with two
site series (bedrock and blanket bogs) comprising 84% its total area, with few site series
comprising the remaining area. When measured in terms of the Simpson’s diversity index, which
was based on counts (i.e., number of TEM site series within each cluster, and number of cluster
types within each TEM site series), Cluster 16 was the least diverse (most homogenous), with a
Diversity Index value of 0.53 (Figure 6). Less extensive classes (defined by either method) were
often less diverse, presumably in part because the chance of including additional classes is
smaller when area is very limited. Cluster 9 was the most diverse, followed by Cluster 7, with
values of 0.89 and 0.87, respectively (Figure 6).
Areas mapped as rivers (RI) in the TEM were entirely captured by Cluster 7 (Fig. A.2,
Fig. 7), which we have identified as a riparian ecosystem; Cluster 7 thus incorporated the actual
river as well as the riparian vegetation. Aside from rivers, the most homogenous TEM site series
were high elevation ecosystem types occurring in the Mountain Hemlock (MHwh1)
biogeoclimatic subzone (e.g., MHwh1/01(MB), MHwh1/06(MD), MHwh1/02(MM), MHwh1
03(MR), MHwh1/00(MS), and MHwh1/09(YC). Across their full spatial extent, these site series
consistently overlapped the same one to three cluster types (particularly Cluster 9). When
measured in terms of counts, Simpson’s diversity indices for these montane classes were also
low, ranging from 0 to 0.44 (Fig. 6). Conversely, the lower elevation forested site series such as
CWHvh2/00(TS), CWHvh2/12(LS), and CWHvh2/02(LR), overlapped with many different
cluster types, likely due in part to their larger extents. Despite the heterogeneous composition of
the 18 clusters in terms of TEM classes and vice versa, a generalized (six-class) comparison
showed greater similarity (Table 6, Fig. 7). Specifically, the islands were dominated by wet and
wetland forests with low productivity (~35% of the total area). Drier forests, and especially drier
non-forested ecosystems, comprised considerably less area (~15% of the total area combined).
Both mapping approaches indicated that both fresh to very moist forests and shrub/herb wetland
ecosystems occupy ~22 % to 27% of the islands.
Table 5. Comparison of 18 clusters to existing Terrestrial Ecosystem Mapping data
Dominant TEM unita,b (% of cluster)
Zonal forest (36)
Zonal forest (49)
Bog forest (42)
Bog forest (41)
Cedar - salal forest (38)
Bog woodland (42)
Zonal forest (28)
Bog woodland (52)
Cedar - salal (31)
Bog forest (38)
Zonal forest (47)
Zonal forest (35)
Bedrock (42), Blanket bog (42)
Blanket bog (65)
Blanket bog (65)
Blanket bog (56)
a Zonal forest = CWHvh2/01(HS); Blanket bog = CWHvh2/00(TS); Bog forest = CWHvh2/11(YG); Cedar - salal
forest = CWHvh2/03(RS); Bog woodland = CWHvh2/12(LS), Fen = CWHvh2/00(FS), Bedrock = RO.
b See pie charts in Fig A.1 for further details.
Figure 6. Diversity of TEM site series (with respect to cluster composition) and diversity of
clusters (with respect to TEM site series). Lower values of the Simpson’s Diversity Index
represent greater similarity between TEM and cluster types
Table 6. Extent of generalized ecosystem classes on Calvert and Hecate Islands, British
Columbia, using an unsupervised classification of remotely sensed data (cluster analysis)
and an expert-driven classification (Terrestrial Ecosystem Mapping)
Corresponding BEC units present
in study area TEMa,
14, 15, 16, 17, 18
3, 4, 6, 7, 8
Fresh to very
1, 2, 10, 11, 12
analysis to extent
Bedrock (RO), rivers (RI), ponds
(PD), lakes (LA), shallow open
water (OW), exposed soil (ES)
a MHwh1 = Mountain Hemlock zone (Wet Hypermaritime Subzone); CWHvh2 = Coastal Western Hemlock zone
(Very Wet Hypermaritime Subzone, Central variant). The two-digit numbers (and associated two-letter acronyms)
following the forward slash refer to Site Series; those with numbers 00 are generally non-forested or not formalized
in the current version of the provincial classification for the area (Banner et al. 1993; Green and Klinka 1994;
MacKenzie and Moran 2004).
Figure 7. Generalized ecosystem classes as depicted by the expert-based classification
(Terrestrial Ecosystem Map) in the left panel, and the unsupervised regionalization on the
Our analysis generated a total of 18 clusters (ecological regions) including open, shrub-herb
dominated ecosystems (e.g., Clusters 13 to 18), a riparian zone (Cluster 7), wetter and wetland
ecosystems (e.g., Clusters 3, 4, 6 to 8, 14 through 18), and less wet, more productive forests (e.g.,
Clusters 2, 11, 12). We assessed what unique ecological information is contained in these
clusters derived from a variety of high spatial resolution remotely sensed data and what
information complements an expert-driven classification. For a generalized (six-class)
classification, both the quantitative classification and the expert-driven classification tell a
similar story. Namely, there is a high abundance of wetter and wetland ecosystems on the island,
and productive forests are limited in extent.
At a more detailed level, the 18 clusters complement or augment the expert-driven map.
First, whereas the TEM for our study area does not explicitly differentiate based on aspect,
several of the 18 clusters were differentiated primarily by aspect. For instance, Clusters 3 and 4
were found to have similar values of elevations, height, NDVI, slope, and TWI, but are different
in terms of TRASP (Table 4, Figure 4 and 5). Likewise, Cluster 6 and 8 had similar values of
elevation, slope, gap fractions, similar height, and NDVI profiles, and were predicted to be
similar in topographic wetness. However, Cluster 6 was associated with cooler aspects while
Cluster 8 was associated with warmer aspects. Another example is Clusters 17 and 18, which
were similar with respect to the majority of remotely sensed variables but were quite different
with respect to TRASP. We included TRASP as an input variable because it is known to
influence ecological patterns and processes. In particular, in temperate regions, localized aspect-
dependent differences in sun exposure, temperature, and moisture can lead to differences in plant
growth, plant composition and structure, growth and response to disturbance (Åström, Dynesius,
Hylander, & Nilsson, 2007; Diggins & Catterlin, 2014; Fekedulegn, Hicks, & Colbert, 2003;
Holland & Steyn, 1975), as well as to soil microbial communities (Carletti et al., 2008).
Another unique and promising aspect of the quantitative regionalization demonstrated in
this research relates to the delineation of wetland (defined here to include wet forest) ecosystems.
Wetlands provide a range of important ecological processes and ecosystem services, including
critical habitat, water quality and quantity regulation, and nutrient cycling and climate regulation,
which may vary according to wetland extent, type, and location within a watershed (Brinson,
1993; Emili, 2003; Fennessy, 2014; Zedler & Kercher, 2005). Consequently, a mapping
methodology that readily identifies wetland distributions at high spatial resolutions is desirable.
Yet these ecosystems are often poorly mapped remotely because of their small size relative to the
spatial resolution of commonly used satellite imagery such as Landsat (30 m) (Congalton, Birch,
Jones, & Schriever, 2002; Ozesmi & Bauer, 2002) or relative to a standard minimum mapping
unit, such as the 0.5 to 2 ha unit typical of TEM. Further, classification of wetlands with
multispectral imagery is driven by vegetation or land cover spectral response (Dechka et al.,
2002). Additional features used to classify wetlands to a particular class or site series in the field
such as acidity/alkalinity and magnitude of lateral and vertical water flow (MacKenzie & Moran,
2004) are not apparent in multispectral imagery, particularly under heavy vegetation cover
(Dechka et al., 2002; Rosenqvist, Finlayson, Lowry, & Taylor, 2007). Terrain indices such as the
Topographic Wetness Index may be useful for wetland delineation by estimating surface water
flow and accumulation but cannot capture all the hydrological properties typically used to
classify wetland type in the field. In this study, we predicted the location of wetlands using
terrain and vegetation structural indices generated from the LiDAR data, combined with multi-
spectral imagery from RapidEye. Our study demonstrates that in addition to multispectral
imagery and terrain indices provided by a 20 m LiDAR-derived DEM, 3D vegetation structural
information provided by the LiDAR data may also be of great value. For instance, in our study
the wetland vegetation was shown to be quite distinct from less wet vegetation with regards to
productivity and structure (e.g., canopy height and openness). The clusters we assigned to the
broad wetland classes (Clusters 3, 4, 6, 7, 8, and 15 through 18) overlapped considerably with
various types of BEC-TEM (expert-delineated) wetlands or water bodies (Figure 7, and A.1).
Thus, although a precise ecological interpretation of these clusters is challenging in the absence
on-the-ground verification, we can be reasonably confident that they do represent wetlands (e.g.,
Figures 2, 3, 7 and A.2). Future research could examine the potential of using even higher spatial
resolution (e.g., < 5m) LiDAR DEMs, the effect of neighbourhood sizes for metrics such as TPI,
and alternative terrain metrics for generating variables that are a stronger proxy for hydrological
processes, and thus for enabling more detailed wetland mapping and classification.
A final key and uniquely informative aspect of the quantitative regionalization approach
is the ability to quantify and map spatial variation in forest height and productivity at 20 m
spatial resolution. Forest inventories generally do measure stand height, basal area, canopy
cover, and so on, however these attributes are aggregated over larger polygons. A system in
British Columbia known as Site Index by BEC Site Series (SIBEC) estimates heights at age 50
for particular tree species within each site series. The SIBEC system adds to the utility of TEM
by allowing a comparison of productivity across sites, yet when mapped, is constrained by the
same spatial ambiguity as is TEM, and is based on a model rather than direct measurement. Our
study has shown that tree heights for the study area are quite low (most clusters have a mean
height <10 m). Low tree heights were also measured and predicted for the CWHvh2 in a nearby
SIBEC study within the CWHvh2, where mean tree heights in old-growth stands ranged from 5.2
m for Western redcedar (Thuja plicata) in the site series 04, to 2.0 m for Western hemlock
(Tsuga heterophylla) in site series 12 (Banner et al., 2005). Our research also indicated that
canopies are generally very open (forested clusters have, on average, a canopy closure of <60%),
and are variable in terms of vertical heterogeneity. Combined with NDVI, a measure of
vegetation greenness, our clusters contained rich and detailed structural and productivity
Understanding the unique information contained within an expert-driven compared to a
quantitative ecological classification using newer geographic technologies has been the subject
of several contemporary studies (e.g., Thomas et al. 2002). There are several reasons for
differences between an expert-driven and a quantitative remotely sensed classification, including
the fact that expert systems may be better at separating ecologically meaningful information
from within large amounts of (non-ecologically meaningful) variation (Schmidtlein, Tichý,
Feilhauer, & Faude, 2010). Experts manually interpreting aerial photos for ecosystem mapping
inherently incorporate multiple characteristics such as tone or colour, shape, size, pattern,
texture, shadow, and landscape context (Morgan et al., 2010). Various types of information can
be automatically extracted from remotely sensed imagery to approximate but not replicate some
of these same visual cues for ecosystem classification, including spectral reflectance, image
texture, shape information derived from object-based classifiers, as well as landscape pattern
indices. With high spatial resolution LiDAR data, an additional dimension of data is available for
interpretation that is not present in standard multispectral satellite imagery. The three-
dimensional forest structure provided by LiDAR and the high spatial resolution terrain models
providing a range of ecological mapping applications (Lefsky, Cohen, Parker, & David, 2002;
Vierling, Vierling, Gould, Martinuzzi, & Clawges, 2008). Through this study we aim to
demonstrate the utility of a quantitative, unsupervised remote-sensing based regionalization, and
to assess the unique and complementary information content of mapping, relative to
conventional expert-driven ecosystem mapping. Future work should focus on the use of high-
spatial resolution remotely sensed data (especially LiDAR) in a supervised classification
approach (e.g., Predictive Ecosystem Mapping, (MacMillan et al. 2007)) to assess the ability to
model and map ecosystem distributions, including BEC site series. Such an approach should also
focus on incorporating data and metrics chosen to capture compositional attributes of
ecosystems. In particular, it may be useful to incorporate hyperspectral remotely sensed data,
which is well suited to mapping vegetation composition (e.g., Jones et al. 2010).
This study has demonstrated that LiDAR and high spatial resolution multi-spectral
imagery can be combined using a quantitative regionalization to map a variety of ecosystem
types across a heterogeneous landscape. Given the quantitative nature of our approach, it is
transparent and easily repeatable, and likely to succeed in other regions where topography is
subdued and forest structure complex. The ecosystem classes highlight vegetation structure and
productivity, refined by topography, and may have a variety of applications beyond—yet
complementary to—those provided by expert-based ecosystem mapping from aerial
photography. For instance, we have identified clusters that are attributed with quantitative
vegetation height information (mean height and variation in mean height) and are spatially
explicit. Height information can be used for carbon accounting, because carbon storage in
vegetation can be estimated through allometric equations that use variables such as tree height to
estimate biomass. As well, estimates regarding relative primary productivity are readily available
in our dataset because of the NDVI incorporated into the clustering. Productivity is an essential
ecosystem function that supports a range of ecosystem services; while approximations of site
productivity (or potential) within traditional mapped polygons can be made based on species
composition, our methodology may facilitate monitoring because of the increased spatial
precision with which it is estimated. As LiDAR and high-spatial resolution multispectral imagery
become increasingly available in the future, they will be important complementary datasets in
local-scale ecosystem mapping.
We are grateful to the Tula Foundation for supporting this research. Additional funding was
provided by the Natural Sciences and Engineering Research Council of Canada (PGS-D and
Discovery grants). The LiDAR data were acquired by Terra Remote Sensing Inc. for the Hakai
Institute. Thank you to Keith Holmes and Luba Reshitnyk of the Hakai Institute, members of the
Coastal Ecosystem Dune Dynamics (CEDD) lab at the University of Victoria, and Richard
Fournier (Université de Sherbrooke) for additional data processing, preparation, and
management. Will MacKenzie (Provincial BEC Ecologist) summarized the ClimateBC data for
the BEC subzones. Finally, thank you to Ken Lertzman (Simon Fraser University), Trevor Lantz
(University of Victoria), Nicholas Coops (University of British Columbia), and Mike Wulder
(Natural Resources Canada) for valuable comments and discussions.
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Figure A.1. Composition of each cluster in terms of provincial map units (TEM site series). Rare
TEM site series and very small polygons were excluded
Figure A.2. Composition of each TEM site series in terms of the 18 clusters. Rare TEM site
series and very small polygons excluded.