## 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)

#### Assignment part A

### 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:

- Lecture slides (splines, point selection)
- Lecture Interpolation Splines
- Lecture Interpolation Point selection

- 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