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. 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.

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…

Points Removed Along Steepness (Perpendicular to Contour) Point ID True DTM Value IDW2 Krigging IDW4 In Place Removed – - 732 235.29 235.84 239.50 -0.55 -4.21 234.579 236.864 0.71 -1.57 235.293 237.205 0.00 -1.92 725 260.40 258.92 256.46 1.48 3.94 256.764 257.518 3.64 2.88 260.399 252.989 7.41 724 256.72 258.05 262.07 -1.33 -5.35 257.475 262.888 -0.75 -6.17 257.46 262.179 -0.74 -5.46 755 357.87 357.89 337.95 -0.02 19.92 358.988 348.017 -1.12 9.85 357.876 350.841 -0.01 7.03 269 380.12 380.22 396.56 -0.10 -16.44 380.543 385.387 -0.42 -5.27 384.976 -4.86 698 405.47 405.73 451.24 -0.26 -45.77 406.67 429.463 -1.20 -23.99 405.506 442.161 -0.04 -36.69 225 508.92 508.18 506.54 0.74 2.38 503.086 503.275 5.83 5.65 508.917 508.827 0.09 227 523.54 522.50 514.26 1.04 9.28 522.558 523.941 0.98 -0.40 523.525 512.25 0.01 11.29 229 533.66 532.87 531.17 0.79 2.49 532.077 530.603 1.58 3.06 534.093 -0.43 495 523.16 523.59 531.26 -8.10 523.615 524.867 -0.46 -1.71 528.484 -5.32

Regularized Spline Tension Spline Points Removed Along Steepness (Perpendicular to Contour) Point I.D. True DTM Values Regularized Spline Tension Spline In Place Predicted – - Removed 732 235.29 237.576 232.055 -2.29 3.23 237.511 235.652 -2.22 -0.36 725 260.40 261.597 258.267 -1.20 2.13 260.552 258.173 -0.15 2.23 724 256.72 255.947 267.686 0.77 -10.97 257.013 266.66 -0.29 -9.94 755 357.87 357.426 350.938 0.44 6.93 357.343 350.188 0.53 7.68 269 380.12 378.887 380.065 1.23 0.06 378.733 382.208 1.39 -2.09 698 405.47 403.072 424.194 2.40 -18.72 403.058 429.871 2.41 -24.40 225 508.92 511.49 514.602 -2.57 -5.68 511.88 514.466 -2.96 -5.55 227 523.54 523.034 530.863 0.51 -7.32 523.527 529.646 0.01 -6.11 229 533.66 533.451 527.932 0.21 5.73 533.471 530.464 0.19 3.20 495 523.16 522.798 527.416 0.36 -4.26 522.855 525.974 0.30 -2.81

Points Removed Along Contour I.D. True DTM Values IDW2 Krigging IDW4 In Place Removed – - In Place 208 516.42 515.09 503.64 1.33 12.78 515.35 495.60 1.07 20.82 516.145 0.00 0.27 210 517.92 517.17 487.87 0.75 30.05 511.89 482.67 6.03 35.25 491.153 26.77 211 519.42 518.04 462.42 1.38 57.00 516.73 481.04 2.69 38.38 519.80 444.839 -0.38 74.58 212 521.29 520.92 472.27 0.37 49.02 520.73 481.64 0.56 39.65 445.582 75.71 214 525.04 523.92 492.01 1.12 33.03 523.53 482.64 1.51 42.40 525.03 475.951 0.01 49.09 215 526.91 527.00 485.14 -0.09 41.77 521.82 475.29 5.09 51.62 526.98 474.499 -0.07 52.41 216 525.79 527.91 489.50 -2.12 36.29 521.63 480.45 4.16 45.34 526.51 480.613 -0.72 45.18 217 550.15 540.53 507.68 9.62 42.48 541.43 492.46 8.72 57.69 545.83 507.247 4.32 42.90 218 526.16 525.78 508.04 0.38 18.12 522.20 489.70 3.96 36.46 483.588 42.57 219 523.54 522.18 498.53 1.36 25.01 516.43 491.91 7.11 31.63 523.51 472.306 0.03 51.23 220 515.69 508.02 1.49 9.15 517.35 497.22 -0.18 19.95 516.94 493.245 0.23 23.93 221 514.92 510.16 502.23 4.76 12.69 511.76 491.07 3.16 23.85 510.39 494.739 4.53 20.18 222 505.92 506.49 500.75 -0.57 5.17 507.46 487.65 -1.54 18.27 505.97 499.427 -0.05 6.49 223 506.15 495.56 -0.22 10.36 507.30 484.61 -1.38 21.31 502.672 3.25 224 508.17 508.10 489.12 0.07 19.05 507.65 474.24 0.52 33.93 498.562 9.61 225 508.92 508.18 485.38 0.74 23.54 503.09 473.94 5.83 34.98 496.603 12.32 226 510.79 510.17 0.62 21.30 504.46 479.41 6.33 31.38 510.78 494.241 16.55 430 514.54 514.41 498.88 0.13 15.66 514.59 490.31 24.23 477.569 36.97 429 514.45 510.47 0.09 4.07 511.74 491.01 2.80 23.53 500.82 13.72 433 513.44 508.62 1.10 5.92 504.39 495.52 10.15 19.02 514.29 497.256 0.25 17.28

Points Removed Along Contour I.D. True DTM Values Regularized Spline Tension Spline In Place Removed – In Place - 208 516.42 514.523 516.712 1.90 -0.29 514.175 513.178 2.25 3.24 210 517.92 517.2 498.754 0.72 19.17 517.323 497.768 0.60 20.15 211 519.42 519.948 481.002 -0.53 38.42 519.909 485.304 -0.49 34.12 212 521.29 514.573 471.078 6.72 50.21 514.736 475.618 6.55 45.67 214 525.04 524.732 487.068 0.31 37.97 524.659 484.995 0.38 40.05 215 526.91 524.41 480.475 2.50 46.43 524.436 477.231 2.47 49.68 216 525.79 524.987 488.417 0.80 37.37 525.017 482.148 0.77 43.64 217 550.15 549.355 503.349 0.79 46.80 548.983 495.831 1.17 54.32 218 526.16 526.343 488.02 -0.18 38.14 526.205 490.047 -0.05 36.11 219 523.54 520.361 497.241 3.18 26.30 527.856 498.405 -4.32 25.14 220 517.17 515.801 499.868 1.37 17.30 515.839 497.621 1.33 19.55 221 514.92 515.021 494.015 -0.10 20.91 513.278 491.264 1.64 23.66 222 505.92 502.98 489.005 2.94 16.92 502.838 485.876 3.08 20.04 223 504.683 486.858 1.24 19.06 503.725 483.415 2.19 22.51 224 508.17 504.962 478.77 3.21 29.40 503.994 473.554 4.18 34.62 225 508.92 511.49 496.136 -2.57 12.78 511.88 488.488 -2.96 20.43 226 510.79 508.621 499.715 2.17 11.08 513.758 487.018 -2.97 23.77 430 514.54 511.229 487.453 3.31 27.09 511.068 486.8 3.47 27.74 429 508.713 484.358 5.83 30.18 508.978 487.129 5.56 27.41 433 516.917 506.459 -2.38 8.08 516.485 505.407 -1.95 9.13

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…

Mean, Median and Standard Deviation for Different Interpolation Methods for Points Removed along Steepness IDW2 Krigging IDW4 Regularized Spline Tension Spline True DTM - In Place Values – Removed Mean 0.10 -5.12 0.71 -2.56 -0.07 -3.87 0.02 -3.63 -0.05 -4.47 Median -0.10 -4.21 -0.42 -1.57 0.00 -1.92 0.36 -4.26 0.19 -2.81 Std. Dev 0.82 17.05 2.24 9.11 0.22 12.99 1.48 8.05 8.66

Mean, Median and Standard Deviation for Different Interpolation Methods for Points Removed along Contour IDW2 Krigging IDW4 Regularized Spline Tension Spline True DTM - In Place Values – Removed Mean 1.05 22.4 3.37 31.77 0.39 29.42 1.61 26.25 1.2 28.43 Median 0.622 19.049 3.163 31.633 0.002 23.925 1.369 26.299 1.331 25.135 Std. Dev 2.34 16.03 3.25 11.45 1.36 23.16 2.28 13.77 2.75 13.14

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.

Comparison of Standard Deviations Among Interpolation Methods

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!

All Points in Place Regularized Spline Tension Spline

Points Removed Along Contour Regularized Spline Tension Spline

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

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.

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.

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.

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

The Sleeping Giant