This document discusses and compares various spatial interpolation techniques used in GIS, including inverse distance weighting (IDW), spline interpolation, kriging, and radial basis functions. It analyzes the results of applying IDW, spline, and kriging methods to weather station data from several US states. Ordinary and universal kriging techniques produced the smoothest surfaces that best modeled trends in the elevation data.

1. In context of Arc
GIS
INTERPOLATION
TECHNIQUES

2. Our aim is to apply interpolation
techniques, mostly in the context of GIS.
We have discussed few of the methods
such as: Nearest
neighbor, IDW, Spline, Radial Basis
Function, and Kriging.
But we have done analysis on:
IDW, Spline (tension and registration)
and Kriging (ordinary and universal).
Introduction

3. The study area includes different
states of USA :
 Nevada
 Idaho – Rocky Mountains (side of Montana)
 Oregon
 Wyoming
 Utah
 Washington DC
Study Area

4. Google Earth
View

5. The data we use to achieve our goal is
of the different weather stations in
different states of the USA.
The information it includes is:
 Station Names (in text format)
 Lat/long (in degress)
 Elevation Values (in meters)
 Rain Percentage (in %)
Given Data

6. Map Layout

7. Map Layout

8.  The method which we adopt here is the
technique of Interpolation data from
sample points.
 As defined earlier, the software that
aid us is the Arc GIS and Arc Scene
(version 9.3) .
 Different types of interpolation
techniques gives us separate results.
 As we display the sample points on Arc
GIS, and also label them.
 We interpolate data using the
Methodology

9. Literature
Review

10. Interpolating A Surface from
Sample Point Data
Interpolation
Estimating the attribute values of
locations that are within the range
of available data using known data
values.
Extrapolation
Estimating the attribute values of
locations outside the range of
available data using known data

11. Interpolation

12. Extrapolation

13. Linear Interpolation
Elevation
profile
Sample
elevatio
n data
A
B
If
A = 8 feet
and
B = 4 feet
then
C = (8 + 4) / 2 =
6 feet
C

14. Non-linear Interpolation
Elevation
profile
Sample
elevatio
n data A
B
C
• Often
results in a
more
realistic
interpolatio
n but
estimating
missing data
values is
more complex

15. Sampling
Strategy
Random
Regular
Sampling
Strategies

16. Guarantees a good spread of
points.
Regular
Strategy

17.  It produces a pattern with
clustering some areas.
Random
Strategy

18. Spatial Interpolation
Methods
SpatialInterpolation
Methods
Global
Deterministic
Exact
Inexact
Geo-Statistical
Exact
Inexact
Local
Deterministic
Exact
Inexact
Geo-Statistical
Exact
Inexact

19. Global
Interpolation
Sample
data
 Uses all Known Points to estimate
a value at unsampled locations.
 More generalize estimation.
 Useful for the terrains that do
not show abrupt change.

20. Local Interpolation
Sample
data
• Uses a local
neighborhood to
estimate value, i.e.
closest n number of
 Uses a neighborhood of sample
points to estimate the a value at
unsampled location.
 Produce local estimation.
 Useful for abrupt changes.

21. Grouping of
Interpolation
Grouping
Deterministic
Geo-
Statistical

22.  Deterministic interpolation
techniques create surfaces from
measured points.
 A deterministic interpolation can
either force the resulting
surface to pass through the data
values or not.
Deterministic
Technique

23.  Geo-statistical techniques
quantify the spatial
autocorrelation among measured
points and account for the
spatial configuration of the
sample points around the
prediction location.
 Because geo-statistics is based on
statistics, these techniques
Geo-statistical
Technique

24. Exact Interpolation: predicts a
value that is identical to the
measured value at a sampled
location.

25. Inexact interpolator: predicts a
value that is different from the
measured value

26. Examples

27. Nearest
Neighbor(NN)
Predicts the value on the basis of the
perpendicular bisector between
sampled points forming Thiession
Polygons.
Produces 1 polygon per sample point,
With sample point at the center.
It weights as per the area or the
volume.
They are further divided into two more
categories.
 It is Local, Deterministic, and Exact.

28. Inverse Distance
Weighted (IDW)
It is advanced of Nearest Neighbor.
Here the driving force is Distance.
It includes ore observation other
than the nearest points.
It is Local, Deterministic, and Exact.
With the high power, the surface get
soother and smoother

29. Result
IDW with
8
IDW with power 2

30. IDW with power 4

31. IDW with power 8

32. Spline
Those points that are extended to the
height of their magnitude
Act as bending of a rubber sheet while
minimizing the curvature.
Can be used for the smoothing of the
surface.
Surface passes from all points.
They can be 1st , 2nd , and 3rd order:
 Regular (1st, 2nd , & 3rd )
 Tension (1st , & 2nd )
They can 2D (smoothing a contour) or 3D
(modeling a surface).

33.  Regularized Spline: the higher the
weight, the smoother the surface.
 Typical values are: 0.1, 0.01, 0.001, 0.5
etc
 Suitable values are: 0-5.
 Tension Spline: the higher the weight,
the coarser the surface.
 Must be greater than equal to zero
 Typical values are: 0, 1, 5, 10.

34. Result
Regular
Spline

35. Tension Spline

36.  The number of point are set by default
in most of the software.
 The number of points one define, all
the number are used in the calculation
 Maximum the number, smoother the
surface.
 Lesser the stiffness.

37. Radial Basis
Function (RBS)
Is a function that changes its
location with distance.
It can predicts a value above the
maximum and below the minimum
Basically, it is the series of exact
interpolation techniques:
 Thin-plate Spline
 Spline with Tension
 Regularized Spline
 Multi-Quadratic Function
 Inverse Multi-quadratic Spline

38. Trend Surface
 Produces surface that represents
gradual trend over area of interest.
 It is Local, Estimated, and Geo-
statistical.
 Examining or removing the long range
trends.
 1st Order
 2nd Order

39. Kirging
 It says that the distance and
direction between sample points
shows the spatial correlation that
can be used to predict the surface
 Merits: it is fast and flexible method.
 Demerit: requires a lot of decision
making

40.  In Kriging, the weight not only depends
upon the distance of the measured and
prediction points, but also on the
spatial arrangement of them.
 It uses data twice:
 To estimate the spatial correlation, and
 To make the predictions

41.  Ordinary Kriging: Suitable for the
data having trend. (e.g. mountains
along with valleys)
 Computed with constant mean “µ”
 Universal Kriging: The results are
similar to the one get from regression.
 Sample points arrange themselves
above and below the mean.
 More like a 2nd order polynomial.

42. Result
Ordinary
Kriging

43. Universal Kriging

44.  It quantifies the assumption that
nearby things tend to be more similar
than that are further apart.
 It measures the statistical
correlation.
 It shows that greater the distance
between two points, lesser the
similarity between them.
Semi-variogram

45. It can be:
 Spherical
 Circular
 Exponential
 Gaussian

46. Kriging Spherical

47. Result
Kriging

48. Kriging

49. Kriging

50. Summary
Serial No. Techniques Observatio
ns
01. IDW
02. Regularize
d Spline
03. Tension
Spline
04. Krging
Universe
with
05. Krging

51. Serial No. Techniques Observatio
ns
06. Krging
Gussain
07. Kriging
Exponentia
l
08. Kriging
Circular
09. Kriging
Spherical

52.  The final outcome of our
experimentation is :
Conclusion