=Paper=
{{Paper
|id=Vol-2323/SKI-Canada-2019-7-2-4
|storemode=property
|title=A Functional Data Analysis Approach for Characterizing Spatial-temporal Patterns of Landscape Disturbance and Recovery from Remotely Sensed Data
|pdfUrl=https://ceur-ws.org/Vol-2323/SKI-Canada-2019-7-2-4.pdf
|volume=Vol-2323
|authors=Mathieu L. Bourbonnais,Trisalyn A. Nelson,Gordon B. Stenhouse,Michael A. Wulder,Joanne C. White,Geordie W. Hobart,Txomin Hermosilla,Nicholas C. Coops,Farouk Nathoo,Chris T. Darimont
}}
==A Functional Data Analysis Approach for Characterizing Spatial-temporal Patterns of Landscape Disturbance and Recovery from Remotely Sensed Data==
https://ceur-ws.org/Vol-2323/SKI-Canada-2019-7-2-4.pdf
Spatial Knowledge and Information Canada, 2019, 7(2), 4
A functional data analysis approach for
characterizing spatial-temporal patterns of
landscape disturbance and recovery from
remotely sensed data
MATHIEU L. BOURBONNAIS MICHAEL A. WULDER NICHOLAS C. COOPS
Earth, Environmental and Canadian Forest Service Integrated Remote Sensing
Geographic Sciences Natural Resources Canada Studio
University of British University of British
Columbia Okanagan JOANNE C. WHITE Columbia
Canadian Forest Service
TRISALYN A. NELSON Natural Resources Canada FAROUK NATHOO
School of Geographical Mathematics & Statistics
Sciences and Urban Planning GEORDIE W. HOBART University of Victoria
Arizona State University Canadian Forest Service
Natural Resources Canada CHRIS T. DARIMONT
GORDON B. STENHOUSE Applied Conservation
Grizzly Bear Program TXOMIN HERMOSILLA Science Lab, Department of
Foothills Research Institute Integrated Remote Sensing Geography
Studio University of Victoria
University of British
Columbia
ABSTRACT mixture model. The resulting eight
watershed clusters were mapped with mean
Contemporary landscape regionalization functions representing unique temporal
approaches, frequently used to summarize trajectories of disturbance and recovery.
and visualize complex spatial patterns and There was considerable variability in
disturbance regimes, often do not account disturbance amplitude among the clusters
for the temporal component which may which increased markedly in the mid-1990’s
provide important insight on disturbance, while remaining low in parks and protected
recovery, and change in ecological areas. The regionalization highlights unique
processes. The objective of this research was temporal trajectories of disturbance and
to employ novel statistical approaches in recovery driven by anthropogenic and
functional data analysis to quantify and natural disturbances and enables insight
cluster spatial-temporal patterns of regarding how cumulative spatial
landscape disturbance and recovery in 223 disturbance patterns evolve through time.
watersheds using a Landsat disturbance
time series from 1985 – 2011 in western 1. Introduction
Alberta, Canada. Cumulative spatial
patterns of disturbance, representing the Terrestrial ecosystems are subject to a range
proportion, arrangement, size, and number of natural and anthropogenic disturbances
of disturbances per watershed, were that influence landscape dynamics and
modelled as functions and scores from a heterogeneity. In North America, the
functional principal component analysis frequency, extent, and severity of natural
were clustered using a Gaussian finite disturbances, including forest fires and
2 Functional data analysis regionalization
insect infestations, has been increasing due Alberta, Canada from 1985 to 2011 using
to anthropogenic influences and climate Landsat disturbance time series data
change (Turner, 2010). Similarly, (Hermosilla et al., 2015). Methods in
anthropogenic activities and anthropogenic functional data analysis (FDA) are
pressures on many terrestrial ecosystems specifically designed to characterize
are growing as resource extraction activities, multivariate high-dimensional time series
including forest harvest, road network data (Ramsay & Silverman, 2005). Using
development, and energy development and the FDA framework, our regionalization
mining contribute to land use change and identifies unique temporal trajectories of
landscape fragmentation (Pickell et al., cumulative disturbance patterns
2016). Cumulatively, landscape disturbance representing underlying distributions and
is temporally dynamic given post- spatial-temporal dynamics of specific
disturbance recovery, regeneration, and natural and anthropogenic disturbance
succession. As such, monitoring and types, including forest fires, harvest, and
quantifying how spatial patterns of natural roads (Bourbonnais et al., 2017).
and anthropogenic landscape disturbance
change over time is critical for 2. Methods and Data
understanding how ecological processes are
influenced by disturbance and recovery.
2.1 Landsat data and disturbance
Change detection and attribution of pattern metrics
disturbance from remotely sensed time
series data provide opportunities to develop The study used a novel Canada-wide
new hypotheses on disturbance recovery landscape disturbance time series derived
and land cover change. The spatial from a best-available pixel Landsat data
resolution and longevity of the Landsat product where disturbances, including
mission, in particular, allows detection of forest harvest, oil and gas well-sites, roads,
landscape alterations that are the result of a forest fires, and non-stand replacing
given management or land use decision over disturbances (e.g., insects and drought)
large areas in a systematic fashion (Wulder were detected and attributed annually from
et al., 2012). While regionalization 1985 – 2011 (Hermosilla et al., 2015). Using
approaches, where geographic entities are the Landsat disturbance time series, spatial
grouped based on common factors to patterns of landscape disturbance were
summarize complex landscape and quantified annually using the proportion
environmental factors (Hargrove and area disturbed, the probability of
Hoffman 2004), have been developed to disturbance adjacency, the mean
characterize spatial patterns of landscape disturbance patch area, and the number of
disturbance (e.g., Long et al., 2010), the disturbance patches in 223 watersheds in
temporal dynamics of disturbance and western Alberta. Watersheds were selected
recovery are often left unaccounted which as the landscape unit of analysis for the
can influence interpretation of resulting regionalization as they are commonly used
patterns (Pickell et al., 2016). as an environmentally relevant scale for
monitoring forest and land cover changes
The goal of this study is to characterize (Wulder et al., 2009). The disturbance
disturbance as a temporally dynamic, pattern metrics were adjusted annually to
allowing us to quantify and map cumulative account for recovery by comparing the
patterns of landscape disturbance while normalized burn ratio (NBR = (B4-
simultaneously accounting for recovery. To B7)/(B4+B7) where B4 and B7 correspond
this end, we develop a novel functional data to Landsat bands 4 – near-infrared – and 7
analysis regionalization of landscape – short-wave infrared, respectively) from
disturbance in 223 watersheds in western the pre- and post-disturbance periods (Key
& Benson, 2006). A disturbance pixel was
Functional data analysis regionalization 3
considered recovered, and subsequently our regionalization. We regionalized
masked from the annual disturbance watersheds with common disturbance
pattern metrics, when the post-disturbance patterns by clustering the FPC scores using
NBR values reached 80% of the mean pixel Gaussian finite mixture models with the
NBR values from the two years preceding optimal number of groups selected using the
disturbance (Pickell et al., 2016). negative of the Bayesian Information
Criterion (Fraley & Raftery, 2002). The
2.2 Functional data analysis clustered watersheds were then mapped and
regionalization compared using the mean disturbance
pattern metric curves by region. We further
In the FDA framework, discrete time series explored variability in pattern metrics of
observations (i.e., disturbance pattern attributed disturbances (fire, harvest, roads,
metrics) are considered to arise through the well-sites, and non-stand replacing) for each
regular sampling of a smooth function (i.e., watershed cluster using a functional
curve) rather than thought of as a analysis of variance (FANOVA) by
realization from a multivariate distribution comparing the mean curves based on shape
(Ramsay & Silverman, 2005). Following the and temporal variability (Ramsay &
FDA approach, the time series of discrete Silverman, 2005).
disturbance pattern metrics in each
watershed were converted to curves using B- 3. Results
splines as the basis function. We used a
functional principal component analysis Three FPCA scores were required to explain
(FPCA), which estimates a set of eigenvalue- 90% of the variance in the proportion
eigenfunction pairs, to quantify the primary disturbance, probability of disturbance
modes of temporal variation among the adjacency, and mean disturbance patch
curves for each of four disturbance pattern area, and two scores for the number of
metrics (Ramsay & Silverman, 2005). For disturbance patches (Figure 1). Amplitude
each of the four disturbance pattern metrics, in the first FPCA score, representing the
we computed the minimum number of greatest deviation of the curve from the
FPCA scores, representing the difference mean, generally increased markedly
from the mean disturbance pattern curve, beginning in the mid-1990’s characterizing
required to explain 90% of the functional differing disturbance pattern trajectories
variance in the curves. The FPCA scores (n = resulting from a rapid increase in resource
11), which represent the primary modes of extraction and industrial activity in the
temporal variation in the disturbance region.
pattern metric curves, formed the basis for
4 Functional data analysis regionalization
Figure 1. Functional principal components analysis (FPCA) for disturbance pattern
metric curves of proportion disturbance (A), probability of disturbance adjacency
(B), mean disturbance patch size (C) and number of disturbance patches (D). The
upper plot maps the score with the highest absolute value for each watershed. The
lower panel shows the mean of the fitted disturbance pattern metric curve (solid
black line) and how the amplitude of the mean curve varies if the FPCA curve is
added (+) or subtracted (-).
The Gaussian finite mixture model throughout the study period with notable
incorporating the eleven FPCA scores with recovery beginning circa 2005. Conversely,
the greatest support (BIC = -2095.35) regions occurring primarily in parks and
resulted in eight disturbance pattern regions protected areas (clusters 4, 7, and 8) had the
(Figure 2). Watersheds in clusters 1 lowest overall disturbance amplitude.
(35.92%), 5 (16.33%), and 4 (13.46%) Interestingly, while the mean proportion
represented the greatest proportion of the disturbance, probability of disturbance
study area. The amplitude (i.e., vertical) and adjacency, and mean disturbance patch size
phase (i.e., horizonal) variability of the four- curves demonstrated periods of recovery
disturbance pattern metric mean curves (i.e., periods of decreasing amplitude in the
characterized periods of increasing curve), the number of disturbance patches
disturbance (i.e., increasing curve generally increased over time suggesting
amplitude) and spectral recovery (i.e., spatial variability in recovery may result in a
decreasing curve amplitude) among the complex spatial mosaic of patches in
watershed regions. Watersheds in clusters 1, different successional states (Gómez et al.,
2, 3, 5, and 6 had increasing amplitude 2011).
Functional data analysis regionalization 5
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, FDA-
While piece-wise properties of curves have
based approaches can be useful for
been employed to detect and quantify
quantifying and summarizing complex
disturbance patterns (Gómez et al., 2011),
spatial-temporal landscape patterns.
modelling patterns of landscape disturbance
6 Functional data analysis regionalization
Figure 3. Results of the functional analysis of variance showing mean curves of the
proportion area disturbed (Pd), probability of disturbance adjacency (Pdd), mean
disturbance patch area (Mdpa), and number of disturbance patches (Ndp), for the
attributed disturbances (fire, harvest, non-stand replacing, roads, and well-sites)
by cluster.
Fraley, C., & Raftery, A. E. (2002). Model-
based clustering, discriminant analysis,
Acknowledgements and density estimation. Journal of the
American Statistical Association, 97(458),
This work was supported by the Natural
611–631.
Sciences and Engineering Research Council
of Canada through a Collaborative Research Gómez, C., White, J. C., & Wulder, M. A.
and Development Grant (CRDPJ 486174- (2011). Characterizing the state and
15), a Canadian Graduate Scholarship, and processes of change in a dynamic forest
by the Foothills Research Institute Grizzly environment using hierarchical spatio-
Bear Project and its many funding partners. temporal segmentation. Remote Sensing
of Environment, 115(7), 1665–1679.
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