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Spatiotemporal interpolation methods in GIS

Lixin Li, University of Nebraska - Lincoln

Abstract

In this dissertation, spatiotemporal interpolation of geographic data is considered. Two methods are discussed which are the reduction and the extension methods. The reduction method treats time as an independent dimension, whereas the extension method treats time equivalent to a spatial dimension. Both 2-D and 3-D shape functions are adopted, usually used in finite element methods, for the spatiotemporal interpolation of 2-D spatial & 1-D temporal and 3-D spatial & 1-D temporal data sets. Domains are divided into a finite number of sub-domains (such as triangles and tetrahedra) in which local shape functions are assumed. New 4-D shape functions that can be applied for each 4-D Delaunay Tessellation element are developed using the extension method for 3-D spatial & 1-D temporal problems. The visualization of shape function interpolation results is also explained and illustrated. ^ Using an actual real estate data set with house prices, we compare these methods with other spatiotemporal interpolation methods based on inverse distance weighting and kriging. We compare these methods with respect to interpolation accuracy, error-proneness to time aggregation, invariance to scaling on the coordinate axes, and the type of constraints used in the representation of the interpolated data. Our experimental results show that the extension method based on shape functions is the most accurate and the overall best spatiotemporal interpolation method. ^ Constraint databases provide a general approach to express and solve constraint problems. We show that spatiotemporal interpolation data can be represented in constraint databases efficiently and accurately. The advantage of constraint databases is that many queries that could not be done in traditional GIS systems can now be easily expressed and evaluated in constraint database systems. ^ Finally, the constraint database system MLPQ (Management of Linear Programming Queries) is used to animate and query some spatiotemporal data examples. A translation algorithm between ArcGIS shape files and MLPQ input data files is also discussed. ^

Subject Area

Remote Sensing|Computer Science

Recommended Citation

Li, Lixin, "Spatiotemporal interpolation methods in GIS" (2003). ETD collection for University of Nebraska - Lincoln. AAI3092570.
http://digitalcommons.unl.edu/dissertations/AAI3092570

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