Interpolation 2013


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Interpolation 2013

  2. 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. 3. The study area includes different states of USA :  Nevada  Idaho – Rocky Mountains (side of Montana)  Oregon  Wyoming  Utah  Washington DC Study Area
  4. 4. Google Earth View
  5. 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. 6. Map Layout
  7. 7. Map Layout
  8. 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 Methodology
  9. 9. Literature Review
  10. 10. Interpolating A Surface from Sample 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
  11. 11. Interpolation
  12. 12. Extrapolation
  13. 13. Linear Interpolation Elevation profile Sample elevatio n data A B If A = 8 feet and B = 4 feet then C = (8 + 4) / 2 = 6 feet C
  14. 14. Non-linear Interpolation Elevation profile Sample elevatio n data A B C • Often results in a more realistic interpolatio n but estimating missing data values is more complex
  15. 15. Sampling Strategy Random Regular Sampling Strategies
  16. 16. Guarantees a good spread of points. Regular Strategy
  17. 17.  It produces a pattern with clustering some areas. Random Strategy
  18. 18. Spatial Interpolation Methods SpatialInterpolation Methods Global Deterministic Exact Inexact Geo-Statistical Exact Inexact Local Deterministic Exact Inexact Geo-Statistical Exact Inexact
  19. 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. 20. Local Interpolation Sample data • Uses a local neighborhood to estimate value, i.e. closest n number of  Uses a neighborhood of sample points to estimate the a value at unsampled location.  Produce local estimation.  Useful for abrupt changes.
  21. 21. Grouping of Interpolation Grouping Deterministic Geo- Statistical
  22. 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. 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 Geo-statistical Technique
  24. 24. Exact Interpolation: predicts a value that is identical to the measured value at a sampled location.
  25. 25. Inexact interpolator: predicts a value that is different from the measured value
  26. 26. Examples
  27. 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. 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. 29. Result IDW with 8 IDW with power 2
  30. 30. IDW with power 4
  31. 31. IDW with power 8
  32. 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).
  33. 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.
  34. 34. Result Regular Spline
  35. 35. Tension Spline
  36. 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. 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. 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. 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. 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. 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.
  42. 42. Result Ordinary Kriging
  43. 43. Universal Kriging
  44. 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. 45. It can be:  Spherical  Circular  Exponential  Gaussian
  46. 46. Kriging Spherical
  47. 47. Result Kriging
  48. 48. Kriging
  49. 49. Kriging
  50. 50. Summary Serial No. Techniques Observatio ns 01. IDW 02. Regularize d Spline 03. Tension Spline 04. Krging Universe with 05. Krging
  51. 51. Serial No. Techniques Observatio ns 06. Krging Gussain 07. Kriging Exponentia l 08. Kriging Circular 09. Kriging Spherical
  52. 52.  The final outcome of our experimentation is : Conclusion