Geoscience Reference
In-Depth Information
(a)
(b)
1357
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1289
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1400
1455
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1462
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1243
1455
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1297
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982
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1362
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914
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1167
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1300
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977
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1342
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1487
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1089
1089
1400
1125
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1276
1547
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943
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1400
Figure 6.12 (a) Scatter of weighted dots. (b) Partition of dot scatter into mutually
exclusive sets (done by hand for illustrative purposes). (Arlinghaus, S. L., unpub-
lished lecture notes.)
Consider a scatter of dots with weights attached (often elevation); Figure
6.12a. Use a line to partition the scatter into three mutually exclusive and
exhaustive sets (Figure 6.12b):
• All values on the line are identical.
• All values on one side of the line are less than the value along the line.
• All values on the other side of the line are greater than the value along
the line.
There are an infinite number of ways that the contours can be placed between
nearest neighbors—via a simple linear split or perhaps via some sort of split
representing concavity of the surface, or distance decay. There is also the
“spline” or “rubber sheeting” method that seeks to minimize total curvature.
Also, contours can be run off the edge of the page instead of wrapping across,
as does the 1300 contour in Figure 6.12b. The process of approximating
contours in the plane is not difficult, using this sort of simple partitioning
scheme, but it is complex.
Figure 6.13
shows a professionally drawn topo-
graphic map with a complicated pattern of contours; the juxtaposition of the
hand-drawn with the professionally crafted map illustrates how a simple par-
titioning procedure in the plane becomes complex.
Try some of the accompanying exercises at the end of the chapter! Learn about
the importance of slope, not only in skiing but also in mapping. Study a vari-
ety of the linked exercises to examine important real-world concepts related
to contours and slope such as steepness, hill shading, aspect, and orientation.
6.5.2 Mapplets
Maps portrayed as “applets”—hence, “Mapplets” may offer a visual display
for identifying breakpoints in data, although one must exercise thoughtful
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