Environmental Engineering Reference
In-Depth Information
wavelet analysis [
74
,
81
], and wombling (lattice, triangulation, categorical). The
two former families of methods require the data to be in a contiguous fashion (grid)
without any missing values while the latter one can either be used with contiguous
or irregularly sampled data. All methods compute the magnitude of rate of change
between adjacent locations over the entire extent of the study area. To determine
which rates of changes are significantly higher than the others, different statistics
and significance tests having been developed. Wombling typically uses arbitrary
percentile thresholds of boundary elements to identify significant boundaries [
7
].
James et al. [
74
] proposed a series of restricted randomization procedures to test the
significance of wavelet boundaries using variogram-based spatial null models.
Oden et al. [
103
] developed boundary statistics to test the cohesiveness properties
of the boundaries. Once cohesive boundaries have been detected and tested,
subsequent hypothesis testing can be performed by comparing the spatial overlap
and movement of boundaries using spatial overlap statistics [
7
,
104
,
105
]or
polygon change analysis [
106
].
Future Directions
The detection and characterization of spatial structure is necessary for developing the
understanding of ecosystem function and for ensuring sustainable management and
use of landscape resources. Indeed, the current scale and pace of anthropogenic
influence on the natural environment is without precedent and the ways in which
novel human-created spatial patterns interact with and influence natural processes are
uncertain. Even more uncertain are the relationships among different scales of spatial
and temporal pattern and what such cross-scale interactions may mean to ecosystem
dynamics [
107
]. Future directions in the analysis of spatial pattern will require
approaches and methods that can begin to tease apart the separate scales, both spatial
and temporal, of processes that contribute to spatial patterns both within and among
ecosystems. These methods should include multi-scale approaches such as the wave-
let-based methods described above, tools to assess statistically significant changes
over time, and methods that can identify local spatially significant subregions within
larger spatial contexts [
74
].Meaningful inference in these regards will only be possible
if the spatial pattern analysis is applied within a hypothesis testing framework, where
competing notions of how individual processes percolate through the landscape to
produce pattern can be tested statistically [
8
]. Finally, increasing availability of
remotely sensed data (e.g., NDVI, LiDAR, Quickbird, LANDSAT, MODIS) will
allow people to detect spatial patterns at finer spatial and temporal scales over much
larger spatial extents than has been previously possible. These huge amounts of data
will also require focused, hypothesis-driven questions, the use of data-mining tools
[
108
], and the further development of spatiotemporal statistics.
Acknowledgments This work was funded by a Killam Postdoctoral fellowship at the University
of Alberta to PMAJ and an NSERC Discovery grant to MJF.
