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In context of Arc GIS
INTERPOLATION
TECHNIQUES
• Rabia Munsaf Khan01
• Atiqa Ijaz Khan03
• Zertasha Ramzan10
• Anwar Akhtar16
• Kalsoom Anjum22
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
The study area includes different states of USA :
Nevada
Idaho – Rocky Mountains (side of Montana)
Oregon
Wyoming
Utah
Washington DC
Study Area
Google Earth View
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
Map Layout
Map Layout
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
Literature Review
Interpolating A Surface from Sample Point Data
InterpolationEstimating the attribute values of locations that are within the range of available data using known data values.ExtrapolationEstimating the attribute values of locations outside the range of available data using known data values.
Interpolation
Extrapolation
Linear Interpolation
Elevation profile
Sample elevation data A
B
If
A = 8 feet and
B = 4 feet
then
C = (8 + 4) / 2 = 6 feet
C
Non-linear Interpolation
Elevation profile
Sample elevation data A
B
C
• Often results in a more realistic interpolation but estimating missing data values is more complex
Sampling Strategy
Random
Regular
Sampling Strategies
Guarantees a good spread of points.
Regular Strategy
It produces a pattern with clustering some areas.
Random Strategy
Spatial Interpolation Methods
Spatial Interpolation Methods
Global
Deterministic
Exact
Inexact
Geo-Statistical
Exact
Inexact
Local
Deterministic
Exact
Inexact
Geo-Statistical
Exact
Inexact
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.
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.
Grouping of Interpolation
Grouping
Deterministic
Geo-Statistical
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
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
Exact Interpolation: predicts a value that is identical to the measured value at a sampled location.
Inexact interpolator: predicts a value that is different from the measured value
Examples
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.
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
Result
IDW with 8
IDW with power 2
IDW with power 4
IDW with power 8
SplineThose points that are extended to the
height of their magnitudeAct 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.
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.
Result
Regular Spline
Tension Spline
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.
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
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
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
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
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.
Result
Ordinary Kriging
Universal Kriging
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
It can be: Spherical
Circular
Exponential
Gaussian
Kriging Spherical
Result
Kriging Circular
Kriging Exponential
Kriging Gaussian
Summary
Serial No. Techniques
Observations
01. IDW
02. Regularized Spline
03. Tension Spline
04. Krging Universe with
05. Krging Universe with
Serial No. Techniques
Observations
06. Krging Gussain
07. Kriging Exponential
08. Kriging Circular
09. Kriging Spherical
The final outcome of our experimentation is :
Conclusion