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 attribute of Elevation field. (others
can also be used).
Methodology
10. Interpolating A Surface fromSample 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 values.
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 points, or within a given
search radius
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 produce not only prediction surfaces but also
error or uncertainty surfaces, giving you an indication of
how good the predictions are
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).
They can be Local, Deterministic, and Exact.
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
