Making topogrid look bad: problems inherent in grid-based topographic analysis, chapter 0

What is topogrid?

Topogrid is a command in the grid module of ESRI's ARC/INFO software. It converts spot data and contour lines to a lattice of elevations. Topogrid is based on a software package called ANUDEM from the Australian National University. It is a very powerful and complex package, using an iterative finite difference interpolation. See the ESRI documentation for details.

Making it look bad

Rather than giving topogrid a difficult task, let's give it an absolutely simple problem to solve. I define 12 blocks of regularly-spaced contour lines, representing 6 uniform slopes. These blocks are 600m square, contour intervals are 30 meters, and contours are densified to 5 meters. I will be working exclusively with a lattice spacing of 30 meters. I chose contour spacing of 13m, 19m, 25m, 35m, 50m, and 70m to be out of phase with the 30-meter lattice. The slopes are 19°, 26°, 35°, 45°, 52°, and 62°. These are steeper than most users encounter, but they are in the range that are routinely logged in the Northwest. The important thing is the relationship of lattice spacing to contour spacing, and these same spatial relationships can be seen in flatter landscapes if the contour interval is decreased or the lattice spacing increased.

Then I ask [version 7.1.1] topogrid to create a lattice of elevations.

Of course, the spaces between blocks are garbage. The areas near the edges of the blocks show a surprising degree of action-at-a-distance from neighboring blocks, but that is not my concern today. Let's define subregions of the blocks for further analysis.

The first image is the elevations clipped to small windows. The second image is calculated slope minus the true slope.

All this was done with default values of tolerance = 2.5m, 30 iterations, and drainage enforcement turned on. Let's try to be thorough by trying 42 different combinations of these parameters:

I compiled statistics on maximum - minimum slope, mean slope - true slope, and standard deviation of slope. I was tempted to study variation in aspect, but refrained. For each of the 6 slopes, here are the rankings by standard deviation: Combining all the slopes, the rankings are:
The best 8 of 42 parameter values for each contour set
toleranceiterationsdrainage
enforcement
Max -
mean
mean -
true
standard
deviation
19
70m
12.520off7.71.592.45
2520off7.71.592.45
2.520off7.71.592.45
12.540off7.81.592.48
12.550off7.81.592.48
12.560off7.81.592.48
2540off7.81.592.48
2550off7.81.592.48
26
50m
12.520off5.79-.152.02
2520off5.79-.152.02
2.520off5.79-.152.02
12.540off6.21-.142.14
12.550off6.20-.142.14
2540off6.21-.142.14
2550off6.20-.142.14
2.540off6.21-.142.14
35
35m
12.550off12.62.523.25
2550off12.62.523.25
2.550off12.62.523.25
12.540off12.64.523.26
12.560off12.63.523.26
2540off12.64.523.26
2560off12.63.523.26
2.540off12.64.523.26
45
25m
12.520off4.38-.041.42
2520off4.38-.041.42
2.520off4.38-.041.42
12.550off4.54.011.44
2550off4.54.011.44
2.550off4.54.011.44
12.540off4.5501.45
12.560off4.550.21.45
52
19m
12.540off4.08.02.99
12.550off4.11.04.99
2540off4.08.02.99
2550off4.11.04.99
2.540off4.08.02.99
2.550off4.11.04.99
12.560off4.14.051.00
2560off4.14.051.00
62
13m
12.530on1.13.23.29
2530on1.12.22.29
2.530on1.13.24.29
12.540on1.29.21.30
2540on1.25.20.30
2.540on1.30.22.30
12.530off1.24.28.31
2530off1.24.28.31
Gridding with the three parameters on the left yields the three measures of accuracy shown on the right. Lower absolute value are better. The recommended tolerance and the default iterations and drainage enforcement off, the results rank 13th, 13th, 13th, 13th, 10th and 7th. Using the default of drainage enforcement on, the results rank 17th 27th 28th 25th 19th and first. Generally, the topogrid parameters have less effect on data quality than the spacing between contour lines. Where contour spacing is close to cell size, we see a variation of 12 with a standard deviation of 3.25.

Summarizing all the contours together, the results are:
Ranking by lower standard deviation of parameters for lattice generation
toleranceiterationsdrainage
enforcement
Max -
mean
standard
deviation
12.540off6.121.77
2.540off6.121.77
2.540off6.121.77
12.550off6.141.77
2.550off6.141.77
2.550off6.141.77
12.520off6.081.78
2.520off6.081.78
2.520off6.081.78
12.560off6.171.79
2.560off6.171.79
2.560off6.171.79
12.530off6.161.79
2.530off6.161.79
2.530off6.161.79
2.530on6.321.85
2.540on6.351.85
2.550on6.391.86
2.540on6.391.87
12.540on6.411.87
2.550on6.431.87
2.560on6.431.87
12.530on6.401.87
2.560on6.451.88
12.560on6.451.88
2.520on6.441.88
2.520on6.461.88
2.530on6.451.89
12.550on6.491.89
12.520on6.481.89
12.510off7.842.28
12.510on7.842.28
2.510off7.842.28
2.510off7.842.28
2.510on7.842.28
2.510on7.852.28
12.55off9.852.90
12.55on9.852.90
2.55off9.852.90
2.55on9.852.90
2.55off9.852.90
2.55on9.852.90

Conclusions

Do it yourself

My contour lines
Those little squares
stuff.aml (approximately how I did everything.)

ESRI acknowledges this as a feature.


Direct questions to Harvey Greenberg

Main Mountain Drainage Research Group Page