# NCSU GIS/MEA582:Geospatial Modeling and Analysis

## 4. Spatial Interpolation

### 4.A Spatial interpolation: methods

Outline:
• definitions, principles and applications
• selected methods and their properties
• influence of interpolation parameters

#### Lecture

Slides and recorded video:

Supplemental materials:
• Interactive Voronoi diagram generator with WebGL by Alex Beutel
• Overview of interpolation methods by Mitas, L., Mitasova, H., 1999, Spatial Interpolation. In: P.Longley, M.F. Goodchild, D.J. Maguire, D.W.Rhind (Eds.), Geographical Information Systems: Principles, Techniques, Management and Applications, GeoInformation International, Wiley, 481-492.
• Equations for additional functions i in Geospatial Analysis - 5th Edition, 2015, by de Smith, Goodchild, and Longley (see sections 6.6.1, 6.6.5, 6.6.6, 6.6.7)

### 4.B Spatial interpolation: splines

Outline:
• influence of spline interpolation parameters: tension/range and smoothing
• implementation - point selection techniques
• special cases: contours, profiles, anisotropy
• trivariate interpolation of volumes and topo-climatology
• evaluating interpolation accuracy, crossvalidation

#### Lecture

Slides and recorded video:

Supplemental materials:
• Mitasova, H., Mitas, L. and Harmon, R.S., 2005, Simultaneous spline interpolation and topographic analysis for lidar elevation data: methods for Open source GIS, IEEE GRSL 2(4), 375- 379.
• Hofierka J., Parajka J., Mitasova H., Mitas L., 2002, Multivariate Interpolation of Precipitation Using Regularized Spline with Tension. TGIS 6(2), 135-150.
• Hutchinson, MF, 1995, Interpolating mean rainfall using thin plate smoothing splines, Int. Journal of Geographical Information Systems 9(4), 385-403.
• History of splines for design, note that these are mesh-based splines, different from the thin plate splines with smoothing and tension used for gridding in GIS

### Homework 4. A and B

Prepare a paper on impact of interpolation method and its parameters on the resulting surface including the properties of spline interpolation method, its parameters and measures of accuracy.