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21 May 2015 Geostatistical modeling of uncertainty, simulation, and proposed applications in GIScience
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Geostatistical modeling of spatial uncertainty has its roots in the mining, water and oil reservoir exploration communities, and has great potential for broader applications as proposed in this paper. This paper describes the underlying statistical models and their use in both the estimation of quantities of interest and the Monte-Carlo simulation of their uncertainty or errors, including their variance or expected magnitude and their spatial correlations or inter-relationships. These quantities can include 2D or 3D terrain locations, feature vertex locations, or any specified attributes whose statistical properties vary spatially. The simulation of spatial uncertainty or errors is a practical and powerful tool for understanding the effects of error propagation in complex systems. This paper describes various simulation techniques and trades-off their generality with complexity and speed. One technique recently proposed by the authors, Fast Sequential Simulation, has the ability to simulate tens of millions of errors with specifiable variance and spatial correlations in a few seconds on a lap-top computer. This ability allows for the timely evaluation of resultant output errors or the performance of a “down-stream” module or application. It also allows for near-real time evaluation when such a simulation capability is built into the application itself.
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Peter Doucette, John Dolloff, and Michael Lenihan "Geostatistical modeling of uncertainty, simulation, and proposed applications in GIScience", Proc. SPIE 9473, Geospatial Informatics, Fusion, and Motion Video Analytics V, 94730E (21 May 2015);

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