Jonathan D. Phillips
Department of Geography, College of Geosciences, Texas A&M
University, College Station, TX
Deterministic Uncertainty and Spatial Analysis
At least some (and perhaps many) earth surface systems exhibit complex
nonlinear dynamics, including dynamical instability, deterministic chaos,
and self-organization due to the unstable growth of small perturbations.
The spatial complexity and predictive problems associated with such behavior
has been called deterministic uncertainty. The deterministic uncertainty
concept differs from traditional views of spatial complexity in that spatial
variability is seen as arising from the deterministic growth of perturbations
or variations in initial conditions rather than (or, more likely, in addition
to) stochastic forcings or apparently random environmental heterogeneity.
Deterministic uncertainty differs from mainstream chaos and complexity
theory (in which the term deterministic complexity is common) in that it
recognizes the possibility of eventually measuring and accounting for the
underlying deterministic source(s) of spatial variation. For example, a
deterministic uncertainty-based view of soil variability might attribute
some portion of the surface variation to variations in parent material
which are unmeasurable, or which cannot be measured in sufficient detail.
However, this view recognizes that improved measurement technologies might
reduce uncertainty and increase predictability--i.e., the uncertainty is
not necessarily irreducible.
Spatial analysis has not yet accepted the challenge posed by deterministic
uncertainty, or by mainstream nonlinear dynamical systems (NDS) theory.
Efforts to detect, model or assess complex behaviors in the spatial domain
have largely been limited to simulation models, and have not addressed
real landscapes or geographical data sets. This is largely attributable
to two factors. First, many of the seminal concepts and methods of NDS
theory arise from mathematical models and simple laboratory systems, and
are simply not well-suited for the noisy, dirty, real world of geography
and geoscience. Second, the majority of NDS work has focussed on the temporal
domain. As a result, the standard methods of NDS are ill-suited to spatial
data, and the standard methods of spatial analysis cannot readily distinguish
deterministic complexity or uncertainty from noise.
The challenge, then, is to develop spatial analytic concepts and methods
suitable for detecting and assessing deterministic uncertainty. At least
three approaches are possible--the adaptation of standard NDS methods to
spatial data, the adaptation of existing spatial analytic methods to complex
nonlinear dynamics, or the production of new methods explicitly designed
to deal with deterministic uncertainty in dirty, noisy geographical data.
GIS research is only now moving beyond the limitations of hardware and
software to incorporate problem-specific spatial analysis. If GIS is to
keep pace with geography and the geosciences as a whole, GIS-based spatial
analysis must build upon that recent progress and confront the issues of
deterministic complexity and uncertainty.
Jonathan D. Phillips
Department of Geography
College of Geosciences
Texas A&M University
College Station, TX 77845-7141
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