Contemporary landscape regionalization approaches, frequently used to summarize and visualize complex spatial patterns and disturbance regimes, often do not account for the temporal component which may provide important insight on disturbance, recovery, and change in ecological processes. The objective of this research was to employ novel statistical approaches in functional data analysis to quantify and cluster spatial-temporal patterns of landscape disturbance and recovery in 223 watersheds using a Landsat disturbance time series from 1985 – 2011 in western Alberta, Canada. Cumulative spatial patterns of disturbance, representing the proportion, arrangement, size, and number of disturbances per watershed, were modelled as functions and scores from a functional principal component analysis were clustered using a Gaussian finite mixture model. The resulting eight watershed clusters were mapped with mean functions representing unique temporal trajectories of disturbance and recovery. There was considerable variability in disturbance amplitude among the clusters which increased markedly in the mid-1990’s while remaining low in parks and protected areas. The regionalization highlights unique temporal trajectories of disturbance and recovery driven by anthropogenic and natural disturbances and enables insight regarding how cumulative spatial disturbance patterns evolve through time.
Terrestrial ecosystems are subject to a range
of natural and anthropogenic disturbances
that influence landscape dynamics and
heterogeneity. In North America, the
frequency, extent, and severity of natural
disturbances, including forest fires and
insect infestations, has been increasing due
to anthropogenic influences and climate
change (Turner, 2010). Similarly,
anthropogenic activities and anthropogenic
pressures on many terrestrial ecosystems
are growing as resource extraction activities,
including forest harvest, road network
development, and energy development and
mining contribute to land use change and
landscape fragmentation (Pickell et al.,
2016). Cumulatively, landscape disturbance
is temporally dynamic given
postdisturbance recovery, regeneration, and
succession. As such, monitoring and
quantifying how spatial patterns of natural
and anthropogenic landscape disturbance
change over time is critical for
understanding how ecological processes are
influenced by disturbance and recovery.
Change detection and attribution of
disturbance from remotely sensed time
series data provide opportunities to develop
new hypotheses on disturbance recovery
and land cover change. The spatial
resolution and longevity of the Landsat
mission, in particular, allows detection of
landscape alterations that are the result of a
given management or land use decision over
large areas in a systematic fashion
The goal of this study is to characterize disturbance as a temporally dynamic, allowing us to quantify and map cumulative patterns of landscape disturbance while simultaneously accounting for recovery. To this end, we develop a novel functional data analysis regionalization of landscape disturbance in 223 watersheds in western Alberta, Canada from 1985 to 2011 using Landsat disturbance time series data (Hermosilla et al., 2015). Methods in functional data analysis (FDA) are specifically designed to characterize multivariate high-dimensional time series data (Ramsay & Silverman, 2005). Using the FDA framework, our regionalization identifies unique temporal trajectories of cumulative disturbance patterns representing underlying distributions and spatial-temporal dynamics of specific natural and anthropogenic disturbance types, including forest fires, harvest, and roads (Bourbonnais et al., 2017).
The study used a novel Canada-wide
landscape disturbance time series derived
from a best-available pixel Landsat data
product where disturbances, including
forest harvest, oil and gas well-sites, roads,
forest fires, and non-stand replacing
disturbances (e.g., insects and drought)
were detected and attributed annually from
1985 – 2011 (Hermosilla et al., 2015). Using
the Landsat disturbance time series, spatial
patterns of landscape disturbance were
quantified annually using the proportion
area disturbed, the probability of
disturbance adjacency, the mean
disturbance patch area, and the number of
disturbance patches in 223 watersheds in
western Alberta. Watersheds were selected
as the landscape unit of analysis for the
regionalization as they are commonly used
as an environmentally relevant scale for
monitoring forest and land cover changes
In the FDA framework, discrete time series observations (i.e., disturbance pattern metrics) are considered to arise through the regular sampling of a smooth function (i.e., curve) rather than thought of as a realization from a multivariate distribution (Ramsay & Silverman, 2005). Following the FDA approach, the time series of discrete disturbance pattern metrics in each watershed were converted to curves using Bsplines as the basis function. We used a functional principal component analysis (FPCA), which estimates a set of eigenvalueeigenfunction pairs, to quantify the primary modes of temporal variation among the curves for each of four disturbance pattern metrics (Ramsay & Silverman, 2005). For each of the four disturbance pattern metrics, we computed the minimum number of FPCA scores, representing the difference from the mean disturbance pattern curve, required to explain 90% of the functional variance in the curves. The FPCA scores (n = 11), which represent the primary modes of temporal variation in the disturbance pattern metric curves, formed the basis for our regionalization. We regionalized watersheds with common disturbance patterns by clustering the FPC scores using Gaussian finite mixture models with the optimal number of groups selected using the negative of the Bayesian Information Criterion (Fraley & Raftery, 2002). The clustered watersheds were then mapped and compared using the mean disturbance pattern metric curves by region. We further explored variability in pattern metrics of attributed disturbances (fire, harvest, roads, well-sites, and non-stand replacing) for each watershed cluster using a functional analysis of variance (FANOVA) by comparing the mean curves based on shape and temporal variability (Ramsay & Silverman, 2005).
Three FPCA scores were required to explain 90% of the variance in the proportion disturbance, probability of disturbance adjacency, and mean disturbance patch area, and two scores for the number of disturbance patches (Figure 1). Amplitude in the first FPCA score, representing the greatest deviation of the curve from the mean, generally increased markedly beginning in the mid-1990’s characterizing differing disturbance pattern trajectories resulting from a rapid increase in resource extraction and industrial activity in the region.
The Gaussian finite mixture model incorporating the eleven FPCA scores with the greatest support (BIC = -2095.35) resulted in eight disturbance pattern regions (Figure 2). Watersheds in clusters 1 (35.92%), 5 (16.33%), and 4 (13.46%) represented the greatest proportion of the study area. The amplitude (i.e., vertical) and phase (i.e., horizonal) variability of the fourdisturbance pattern metric mean curves characterized periods of increasing disturbance (i.e., increasing curve amplitude) and spectral recovery (i.e., decreasing curve amplitude) among the watershed regions. Watersheds in clusters 1, 2, 3, 5, and 6 had increasing amplitude throughout the study period with notable recovery beginning circa 2005. Conversely, regions occurring primarily in parks and protected areas (clusters 4, 7, and 8) had the lowest overall disturbance amplitude.
Interestingly, while the mean proportion disturbance, probability of disturbance adjacency, and mean disturbance patch size curves demonstrated periods of recovery (i.e., periods of decreasing amplitude in the curve), the number of disturbance patches generally increased over time suggesting spatial variability in recovery may result in a complex spatial mosaic of patches in different successional states (Gómez et al., 2011). Figure 2. Mean curves by cluster for the proportion disturbance (A), the probability of disturbance adjacency (B), the mean disturbance patch area (C), and the number of disturbance patch (D) pattern metrics. Each mean curve is associated with the watersheds mapped by cluster membership (E). Parks and protected areas are shown in green. and recovery as a single continuous function The watershed clusters also revealed can reveal properties of the underlying variability in the amplitude and phase of the ecological processes and how patterns of mean disturbance pattern metrics for the landscape disturbance evolve over a attributed disturbance types compared continuum (Pickell et al., 2016). However, it using FANOVA (Figure 3). Mean forest fire is difficult to quantify landscape disturbance curves were significantly different (p < 0.05) cumulatively and to account for the among the watershed clusters, with large temporal dynamics of disturbance and forest fires prevalent in clusters 2 and 5. recovery, as well as the interaction of Trajectories representing the mean multiple sources of natural and proportion area disturbed and number of anthropogenic disturbance. Using the novel disturbed patches for forest harvest, roads, FDA approach described here, regional and well-sites were also significantly spatial-temporal disturbance patterns can different among the clusters, and had the be interpreted through representative greatest amplitude in clusters 6, 1, 5, and 2 disturbance trajectories which illuminate representing watersheds primarily outside the different disturbance processes and of parks and protected areas. indicate where and when anthropogenic disturbance is the dominant driver of 4. Conclusion observed patterns in the study area. As new time series of disturbance and land cover data become increasingly available, FDAbased approaches can be useful for quantifying and summarizing complex spatial-temporal landscape patterns.
While piece-wise properties of curves have been employed to detect and quantify disturbance patterns (Gómez et al., 2011), modelling patterns of landscape disturbance This work was supported by the Natural Sciences and Engineering Research Council of Canada through a Collaborative Research and Development Grant (CRDPJ 48617415), a Canadian Graduate Scholarship, and by the Foothills Research Institute Grizzly Bear Project and its many funding partners.
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