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
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
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
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
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.
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
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
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.
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.
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
