Spatial interpolation techniques are used to estimate values at unsampled locations based on known sample points. There are two main types of interpolation methods: global methods which apply a single mathematical function to all points, and local methods which apply functions to subsets of points. Specific interpolation methods covered include Thiessen polygons, triangulated irregular networks, spatial moving average, trend surfaces, inverse distance weighting, and Kriging. Kriging is similar to inverse distance weighting but uses minimum variance to calculate weights.

1. Spatial interpolation
techniques
By:-Manisha

2. Definition:
“Spatial interpolation is the procedure of
estimating the values of properties at
unsampled sites within an area covered by
existing observations.”
What is Spatial Interpolation??

3. classification
• Global methods:
– single mathematical function applied to all points
– tends to produces smooth surfaces
• Local methods:
– single mathematical function applied repeatedly to subsets of the
total observed points
– link regional surfaces into composite surface

4. • Exact methods:
– honour all data points such that the resulting surface passes
exactly through all data points
– appropriate for use with accurate data
• Approximate methods:
– do not honour all data points
– more appropriate when there is high degree of uncertainty about
data points

5. Interpolation methods
–Thiessen polygons
–Triangulated Irregular Networks (TINs)
–Spatial moving average
–Trend Surfaces
–Kriging
–Inverse distance weighting (IDW)

6. • Thiessen (Voronoi) polygons:
– assume values of unsampled locations are equal to
the value of the nearest sampled point
• Vector-based method
– regularly spaced points produces a regular mesh
– irregularly spaced points produces an network of
irregular polygons
Thiessen Polygons

7. Thiessen polygon construction

8. Example Thiessen polygon
Source surface with sample points Thiessen polygons with sample points

9. • Another vector-based method often used to create
digital terrain models (DTMs)
– adjacent data points connected by lines (vertices) to create a
network of irregular triangles
calculate real 3D distance between data points along vertices using
trigonometry
calculate interpolated value along facets between three vertices
TINs

10. EXAMPLE- TIN

11. • Vector and raster method:
– most common GIS method
– calculates new value of each location based on range of values
associated with neighbouring points
– Neighbourhood determined by a filter
Spatial moving average

12. Example SMA (circular filter)
Source surface with sample points 21x21 circular filter SMA 41x41 circular filter SMA

13. Trend surfaces
• Uses a polynomial regression to fit a least-squares surface
to the data points
– normally allows user control over the order of the polynomial
used to fit the surface
– as the order of the polynomial is increased, the surface being
fitted becomes progressively more complex
higher order polynomial will not always generate the most accurate
surface, it dependent upon the data
the lower the RMS error, the more closely the interpolated surface
represents the input points

14. Week 17 GEOG2750 – Earth Observation and GIS of the Physical Environment 14
data point
interpolated point
Fitting a single polynomial trend surface

15. Spatial Analysis Lecture #8 (Exploring Continuous Data)
Example trend surfaces
Goodness of fit
(R2) = 45.42 %
Goodness of fit
(R2) = 92.72 %
Goodness of fit
(R2) = 82.11 %
Linear Quadratic Cubic
Source surface with
sample points

16. Inverse Distance Weighting (IDW)
Estimates the values at unknown points using the distance and values
to nearby know points (IDW reduces the contribution of a known point to
the interpolated value)
Weight of each sample point is an inverse proportion to the distance.
The further away the point, the less the weight in helping define the
unsampled location

17. Example: IDW

18. Kriging
Similar to Inverse Distance Weighting (IDW)
Kriging uses the minimum variance method to calculate the
weights rather than applying an arbitrary or less precise
weighting scheme

20. Example: Kriging