The Bamber Bridge projectAn interval tree over a year of rain near Bamber Bridge
Four gauges, 2,201 rain episodes, 365 morning questions, and a shortcut that silently gives wrong answers.
The Environment Agency publishes 15-minute rainfall readings for its gauges. Four lie within 11 kilometres of Bamber Bridge: Moor Park at 5.5 km, Common Bank at 8.6 km, Haighton at 8.9 km and Clifton Marsh at 11.0 km. For each we downloaded all 35,040 readings of 2025. Readings the Agency flags as suspect were left out, 570 at Moor Park, 2,509 at Haighton and 2,940 at Clifton Marsh, and the learner reports those numbers, because data cleaning is part of the result. Then each gauge's year is turned into rain episodes: runs of wet quarter-hours, with dry gaps of up to 30 minutes joined in.
That gives 506 episodes at Moor Park, 656 at Common Bank, 541 at Haighton and 498 at Clifton Marsh, 2,201 intervals of time in all. They overlap, because rain often falls at several gauges at once. The longest lasted 32.75 hours; the median lasted 45 minutes. The question is asked once for every day of the year: which episodes include the 08:30 reading?
The slow answer checks all 2,201 intervals each morning, 803,365 checks for the year. The interval tree picks the middle time point, stores the intervals that cross it at that node in two sorted lists, and sends the rest left or right. To answer a query the program walks down one path and, at each node, reads only the sorted list until the intervals stop matching. Our tree was 12 levels deep and needed 2,968 checks for the whole year, about 8 a morning, with exactly the same answers as the full scan.
Gauges inside a rain episode at 08:30, each day of 2025, our Python run| Gauges with rain | Days |
|---|
| None of the four | 281 |
| One | 40 |
| Two | 18 |
| Three | 13 |
| All four | 13 |
The tempting shortcut is to sort the episodes by start time, use binary search to find the last one that began before 08:30, and check only that. It is fast and it looks right. Over the year it found only 69 of the 167 true matches and missed 98, because a long episode that began earlier at a different gauge is hidden behind a short one that began later. With intervals from a single gauge, which never overlap, the shortcut would have been correct; with four gauges it is not. The learner writes a test that compares every answer with the full scan, which is the only reason the bug shows up.
Ages 8 to 11
Strips of paper on a timeline: which strips cross the pencil line? Then sort them and find a faster way to look.
Ages 11 to 15
Turn a week of 15-minute readings into rain episodes in Python and answer questions by scanning.
Ages 15 and up
Build the interval tree, count checks per query, and test it against the scan and the binary search shortcut.
Sources and limits
Rainfall is from the Environment Agency Hydrology service, under the Open Government Licence. The 30-minute joining rule and the 08:30 question are our choices; another rule would give different episode counts. The interval tree follows de Berg and colleagues, Computational Geometry (2008). Gauge distances are straight lines from the gazetteer point for Bamber Bridge.
