Jonathan D. Phillips
Department of Geography, College of Geosciences, Texas A&M University, College Station, TX

Position Statement
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Position Statement

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. 


Curriculum Vitae

 

 


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Jonathan D. Phillips
Department of Geography
College of Geosciences
Texas A&M University
College Station, TX 77845-7141
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