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)
Point ID
True
DTM
Value
IDW2
Krigging
IDW4 In
Place
Removed – -
732
235.29
235.84
239.50
-0.55
-4.21
0.71
-1.57
0.00
-1.92
725
260.40
258.92
256.46
1.48
3.94
3.64
2.88
7.41
724
256.72
258.05
262.07
-1.33
-5.35
-0.75
-6.17
257.46
-0.74
-5.46
755
357.87
357.89
337.95
-0.02
19.92
-1.12
9.85
-0.01
7.03
269
380.12
380.22
396.56
-0.10
-16.44
-0.42
-5.27
-4.86
698
405.47
405.73
451.24
-0.26
-45.77
406.67
-1.20
-23.99
-0.04
-36.69
225
508.92
508.18
506.54
0.74
2.38
5.83
5.65
0.09
227
523.54
522.50
514.26
1.04
9.28
0.98
-0.40
512.25
0.01
11.29
229
533.66
532.87
531.17
0.79
2.49
1.58
3.06
-0.43
495
523.16
523.59
531.26
-8.10
-0.46
-1.71
-5.32

5. 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
-2.29
3.23
-2.22
-0.36
725
260.40
-1.20
2.13
-0.15
2.23
724
256.72
0.77
-10.97
266.66
-0.29
-9.94
755
357.87
0.44
6.93
0.53
7.68
269
380.12
1.23
0.06
1.39
-2.09
698
405.47
2.40
-18.72
2.41
-24.40
225
508.92
511.49
-2.57
-5.68
511.88
-2.96
-5.55
227
523.54
0.51
-7.32
0.01
-6.11
229
533.66
0.21
5.73
0.19
3.20
495
523.16
0.36
-4.26
0.30
-2.81

6. 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
0.00
0.27
210
517.92
517.17
487.87
0.75
30.05
511.89
482.67
6.03
35.25
26.77
211
519.42
518.04
462.42
1.38
57.00
516.73
481.04
2.69
38.38
519.80
-0.38
74.58
212
521.29
520.92
472.27
0.37
49.02
520.73
481.64
0.56
39.65
75.71
214
525.04
523.92
492.01
1.12
33.03
523.53
482.64
1.51
42.40
525.03
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
-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
-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
4.32
42.90
218
526.16
525.78
508.04
0.38
18.12
522.20
489.70
3.96
36.46
42.57
219
523.54
522.18
498.53
1.36
25.01
516.43
491.91
7.11
31.63
523.51
0.03
51.23
220
515.69
508.02
1.49
9.15
517.35
497.22
-0.18
19.95
516.94
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
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
-0.05
6.49
223
506.15
495.56
-0.22
10.36
507.30
484.61
-1.38
21.31
3.25
224
508.17
508.10
489.12
0.07
19.05
507.65
474.24
0.52
33.93
9.61
225
508.92
508.18
485.38
0.74
23.54
503.09
473.94
5.83
34.98
12.32
226
510.79
510.17
0.62
21.30
504.46
479.41
6.33
31.38
510.78
16.55
430
514.54
514.41
498.88
0.13
15.66
514.59
490.31
24.23
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
0.25
17.28

7. Points Removed Along Contour
I.D.
True
DTM
Values
Regularized Spline
Tension Spline
In Place
Removed –
In Place -
208
516.42
1.90
-0.29
2.25
3.24
210
517.92
517.2
0.72
19.17
0.60
20.15
211
519.42
-0.53
38.42
-0.49
34.12
212
521.29
6.72
50.21
6.55
45.67
214
525.04
0.31
37.97
0.38
40.05
215
526.91
524.41
2.50
46.43
2.47
49.68
216
525.79
0.80
37.37
0.77
43.64
217
550.15
0.79
46.80
1.17
54.32
218
526.16
488.02
-0.18
38.14
-0.05
36.11
219
523.54
3.18
26.30
-4.32
25.14
220
517.17
1.37
17.30
1.33
19.55
221
514.92
-0.10
20.91
1.64
23.66
222
505.92
502.98
2.94
16.92
3.08
20.04
223
1.24
19.06
2.19
22.51
224
508.17
478.77
3.21
29.40
4.18
34.62
225
508.92
511.49
-2.57
12.78
511.88
-2.96
20.43
226
510.79
2.17
11.08
-2.97
23.77
430
514.54
3.31
27.09
486.8
3.47
27.74
429
5.83
30.18
5.56
27.41
433
-2.38
8.08
-1.95
9.13

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
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

10. 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

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