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Surface Interpolation

Surface Interpolation. Applied GIS 4215 Project 4 By Stephanie Wilkie. Project Description. Five different kinds of surface interpolation were conducted on three DTM point datasets. IDW 2 , IDW 4 , Krigging, Regularized Spline, and Tension Spline were the interpolation methods used.

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Surface Interpolation

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  1. Surface Interpolation Applied GIS 4215 Project 4 By Stephanie Wilkie

  2. Project Description Five different kinds of surface interpolation were conducted on three DTM point datasets. IDW2, IDW4, Krigging, Regularized Spline, and Tension Spline were the interpolation methods used. The DTM datasets consisted of one set with all points present, one with points removed along steepness (perpendicular to contour) and another set with points along contour. The differences between each interpolation method were analysed to determine how well each method predicted unknown values with the different datasets.

  3. Project Description The true DTM values were obtained from the DTM dataset with all points present. The predicted values for points in place and points removed were determined from the interpolated surfaces. The differences in these values were determined by subtracting the ‘In Place’ values from the true DTM values which gives a measure of accuracy. The ‘Removed values’ were also subtracted from the true DTM values to determine how well each method predicts the DTM value. These values are shown in table form on the following slides…

  4. Points Removed Along Steepness (Perpendicular to Contour)

  5. Points Removed Along Steepness (Perpendicular to Contour)

  6. Points Removed Along Contour

  7. Points Removed Along Contour

  8. Project Description The median, Mean and Standard Deviation were then calculated for each method and each dataset. These values are shown in table form on the following slides…

  9. Mean, Median and Standard Deviation for Different Interpolation Methods for Points Removed along Steepness

  10. Mean, Median and Standard Deviation for Different Interpolation Methods for Points Removed along Contour

  11. Results On Comparing the standard deviations for steepness and contour among each of the interpolation methods, it becomes obvious that almost all of the interpolation methods prove to be more accurate for points removed across steepness with the exception of IDW to the power of 2. Regularized Spline, Tension Spline and Krigging were the most accurate methods for both contour and steepness. IDW to the power of 4 produced the least accurate results in both cases.

  12. Comparison of Standard Deviations Among Interpolation Methods

  13. Results The following three slides show a visual comparison of the Regularized Spline and Tension Spline methods of interpolation for each of the three DTM datasets. Look closely, and you’ll see the differences!

  14. All Points in Place Regularized Spline Tension Spline

  15. Points Removed Along Contour Regularized Spline Tension Spline

  16. Points Removed Along Steepness (Perpendicular to Contours) Regularized Spline Tension Spline

  17. Conclusion Based on the previous analyses, • All interpolation methods with the exception of IDW2 produce more accurate results for steepness than for contour points. • Krigging is the most accurate method for predicting points along contours. • Regularized Spline is the most accurate method for predicting points along a steepness gradient.

  18. Conclusion The results for points removed across steepness are somewhat unexpected, however there was very little difference between regularized spline, tension spline and krigging. Further testing may be required. IDW places more emphasis on local values, which may be a better method for a terrain with more gentle changes in elevation, and not the terrain we used in this experiment. Spline has the effect of ‘smoothing’ the surface and places less emphasis on local values. Regularized Spline is less conforming to control points values than Tension Spline, matter the latter less smooth in appearance. The spline method is best applied to surfaces with gentle variation.

  19. Conclusion Krigging is the most complex method of interpolation, however it is said to produce the best results. In this case, it produced the best results for the surface with points removed along the contour. It did not produce the best results for the surface with points removed across a steepness gradient.

  20. Bonus You may be wondering what this is a digital terrain model of…

  21. The Sleeping Giant

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