Spatial interpolation

Lubos Mitas and Helena Mitasova

Abstract

This chapter formulates the problem of spatial interpolation from scattered data as a method for prediction and representation of multi-variate fields. The role and specific issues of interpolation for GIS applications are discussed and methods based on locality, geostatistical and variational concepts are described. Properties of interpolation methods are illustrated by examples of 2D, 3D and 4D interpolations of elevation, precipitation, and chemical concentrations data. Future directions focus on a robust data analysis with automatic choice of spatially variable interpolation parameters, and model or process-based interpolation.

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Illustrations

Interpolation of elevation surface using different methods available in GIS:
Fig.1a Voronoi diagram
Fig.1b TIN
Fig.1c IDW
Fig.1d Kriging
Fig.1e Topogrid
Fig.1f s.surf.tps/s.surf.rst , see(RST method)

Impact of interpolation on results of erosion/deposition modeling:
Fig.2a
Fig.2b
Fig.2c

Interpolation of a large DEM using segmented processing:
Fig.3
Fig.3inset
Fig.3leg

Interpolation of rainfall data without and with incorporation of terrain influence:
Fig.4a
Fig.4b
the imapct of terrain can tuned using tension anisotropy in vertical direction
animated gif
mpeg movie

Regularized spline with tension: impact of tension parameter in 2D and 3D:
Fig.5a gif
Fig.5b
Fig.5c
Fig.5d
Fig.5e
Fig.5f

Snapshot from quad-variate interpolation of chemical concentrations data:
Fig.6

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