The Trowbridge projectStrahler stream order for the River Biss network
Load the mapped streams, turn them into a network, and let a recursive function rank every stream from the headwaters down.
The learner downloads every river and stream that OpenStreetMap volunteers have mapped in a box around Trowbridge, 350 lines in all, and joins them into a network in which each point knows the point downstream of it. Walking upstream from the spot just before the River Biss meets the River Avon collects the whole Biss network: 34.3 km of mapped channel. Strahler's rule is then three lines of recursion. A stream with nothing flowing into it has order 1. Where two streams of the same order meet, the order goes up by one. Where a smaller stream joins a larger one, the larger order simply carries on.
Streams of each Strahler order in the mapped River Biss network, after the split channel is handled (our Python run)| Strahler order | Number of streams | Mapped channel length |
|---|
| 1 | 16 | 12.0 km |
| 2 | 5 | 10.9 km |
| 3 | 1 | 11.3 km |
The first run said the Biss reaches order 4 where it meets the Avon. That was wrong, and finding out why is the real lesson. Less than a kilometre, in a straight line, before it reaches the Avon, the mapped river splits into two channels for about 62 m and then rejoins. The recursive function saw two order-3 streams meeting and duly raised the order. But they were one river, not two tributaries: the network was not a tree. Once the short side channel is treated as part of the main one, the Biss is order 3 at the Avon. Sixteen headwater streams feed it; five order-2 streams form where they meet, including Biss Brook and Lambrok Stream as named on the map, and order 3 begins south of the town where Bitham Brook meets another order-2 stream. The longest path from a headwater to the Avon runs 16.0 km.
The same rule counts registers. A compiler turns a line such as (a+b)*(c+d) into a tree, and the Strahler number of that tree, known in computing as the Ershov number, is the fewest processor registers needed to work it out without saving anything to memory. Our Python version gives 2 for a*b + c, 3 for (a+b)*(c+d), and 4 for (a+b)*(c+d) + (e+f)*(g+h). The streams of the Biss and the arithmetic of a compiler are, to a recursive function, the same shape.
Ages 8 to 11
Draw a tree of streams on paper, label the sources 1, and apply the joining rule until you reach the sea.
Ages 11 to 15
Write the rule as a recursive Python function, test it on small drawn trees, then on the Biss network.
Ages 15 and up
Load the map data, find the split channel, fix the network, and compare stream order with register counting.
Where the data comes from, and the limits
Map data is from OpenStreetMap contributors, available under the Open Database Licence. Only lines tagged as rivers or streams were used; ditches, drains and canals were left out, and anything unmapped is missing, so the counts describe the map rather than the ground. Direction comes from the mapping convention that waterways are drawn downstream. The network building, the fix for the split and all counts are our own work.
