Interpolation 2013
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The document discusses various interpolation techniques used in GIS, including inverse distance weighted (IDW), spline, and kriging. IDW, spline, and kriging were analyzed in more depth. The study area includes states in the western US and weather station data was used, including station names, coordinates, elevation, and rain percentage. Different interpolation techniques were tested in ArcGIS and ArcScene to compare the results.
Interpolation 2013
- 1. In context of Arc GIS INTERPOLATION TECHNIQUES
- 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
- 6. Map Layout
- 7. Map Layout
- 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.
- 11. Interpolation
- 12. Extrapolation
- 13. 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
- 14. 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
- 16. Guarantees a good spread of points. Regular Strategy
- 17. It produces a pattern with clustering some areas. RandomStrategy
- 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
- 24. Exact Interpolation: predicts a value that is identical to the measured value at a sampled location.
- 25. Inexact interpolator: predicts a value that is different from the measured value
- 26. Examples
- 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
- 29. Result IDW with 8 IDW with power 2
- 30. IDW with power 4
- 31. IDW with power 8
- 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.
- 35. Tension Spline
- 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
- 45. It can be: Spherical Circular Exponential Gaussian
- 49. Kriging Gaussian
- 50. Summary Serial No. Techniques Observations 01. IDW 02. Regularized Spline 03. Tension Spline 04. Krging Universe with 05. Krging Universe with
- 51. Serial No. Techniques Observations 06. Krging Gussain 07. Kriging Exponential 08. Kriging Circular 09. Kriging Spherical
- 52. The final outcome of our experimentation is : Conclusion