Our aim is to apply interpolation techniques, mostly in the contextof 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 andregistration) 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 DCStudy Area
The data we use to achieve our goal is of the different weatherstations 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
The method which we adopt here is the technique of Interpolationdata from sample points. As defined earlier, the software that aid us is the Arc GIS and ArcScene (version 9.3) . Different types of interpolation techniques gives us separateresults. As we display the sample points on Arc GIS, and also label them. We interpolate data using the attribute of Elevation field. (otherscan also be used).Methodology
Interpolating A Surface fromSample Point DataInterpolationEstimating the attribute values of locations that are within therange of available data using known data values.ExtrapolationEstimating the attribute values of locations outside the range ofavailable data using known data values.
Global InterpolationSampledata Uses all Known Points to estimate a value at unsampledlocations. More generalize estimation. Useful for the terrains that do not show abrupt change.
Local InterpolationSample data• Uses a local neighborhood toestimate value, i.e. closest nnumber of points, or within a givensearch radius Uses a neighborhood of sample points to estimate the a valueat unsampled location. Produce local estimation. Useful for abrupt changes.
Grouping of InterpolationGroupingDeterministicGeo-Statistical
Deterministic interpolation techniques create surfacesfrom measured points. A deterministic interpolation can either force the resultingsurface to pass through the data values or not.Deterministic Technique
Geo-statistical techniques quantify the spatialautocorrelation among measured points and account forthe spatial configuration of the sample points around theprediction location. Because geo-statistics is based on statistics, thesetechniques produce not only prediction surfaces but alsoerror or uncertainty surfaces, giving you an indication ofhow good the predictions areGeo-statistical Technique
Exact Interpolation: predicts a value that is identical to themeasured value at a sampled location.
Inexact interpolator: predicts a value that is different from themeasured value
Nearest Neighbor(NN)Predicts the value on the basis of the perpendicular bisector betweensampled 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 morecategories. 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
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.
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 thecalculation 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 theminimumBasically, 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 ofinterest. 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 pointsshows the spatial correlation that can be used to predict thesurface 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 themeasured and prediction points, but also on the spatialarrangement 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 fromregression. Sample points arrange themselves above and below the mean. More like a 2nd order polynomial.
It quantifies the assumption that nearby things tend to be moresimilar than that are further apart. It measures the statistical correlation. It shows that greater the distance between two points, lesser thesimilarity between them.Semi-variogram
It can be: Spherical Circular Exponential Gaussian