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