1. Spatial interpolation
GEOG 4103 spring 06
April 3rd

2. Real world phenomena represented as:
DISCRETE:
homogeneous or spatially averaged units, e.g. subwatersheds, counties, polygons
VECTOR
FIELDS:
grid cells or meshes
RASTER

3. What are statistical surfaces?
Features that contain Z values distributed throughout area defined by (x,y) coordinate pairs
Examples?
any measurable phenomena that varies across
space (temperature, elevation, precipitation, etc)
called “field” like (continuous) data

4. What is a field? a conceptual model of geographic variation
at every point in the frame (x,y) there exists a single value of a variable Z
e.g. a field of temperature
e.g. a field of land surface elevation
Field data are continuous

5. Representation of field phenomena
A) CELLS
B) REGULARLY
SPACED POINTS
C) IRREGULARLY
D) CONTOURS
E) POLYGONS
F) TINs- Triangulated
Irregular Network

7. Spatial sampling e.g. elevation Regular lattice restricted to
X,Y locations
Irregular lattice
not restricted
based on knowledge about how
smooth/rugged the surface is

8. Interpolation
procedure of estimating the value at unsampled locations from existing observations

9. Two types of interpolation based on the mathematical function used
Linear interpolation
Non-linear interpolation

10. Linear interpolation ? 100’ 150’ 110 120 130 140
Surface changes in a linear fashion
can use simple mathematical functions

11. Non-linear interpolation
Tobler's Law of Geography:
points close together in space are more likely to have similar values than points farther apart
Distance-weighted interpolation

12. E.g. Inverse Distance Weighted interpolation method
Software measures distance
from each neighboring point
you can select the number of
points to include in the search
then distance is calculated
according to a formula B • C •
100 40 ? • A 20
200 • D

13. Global vs. local interpolation
global interpolators determine a single function which is mapped across the whole region
e.g. trend surfaces
local interpolators apply an algorithm repeatedly to a small portion of the total set of points
e.g IDW

14. Point-based interpolation
used for data which can be collected at point locations
e.g. weather station readings, spot heights, soil measurements etc.

21. Green Lakes Valley Snow Survey
Figure 5. Location of snow depth measurements in the Green Lakes Valley from 1997 to We also added zero depths on about a 50 meter grid for non snow covered area
that was too steep to sample.

22. Estimated snow depth for 1999
using various interpolation
techniques

23. Estimating error

24. A special case of statistical surfaces: DEM / DTM
Digital elevation models = a way of representing surfaces.
Quantitative model of a topographic surface in digital form.
continuous surfaces.

25. Two methods of representing a topography inside a computer
Raster surfaces:
e.g. DEM (Digital Elevation Model)
Vector surfaces:
TIN’s (Triangulated Irregular Network)

32. Problems with interpolation
Accuracy
Visual representation
Edge effects (lack of data at the margins)