The Bedford projectA double mass curve for the Great Ouse
Plot running totals against running totals, and look for a bend.
The learner downloads daily flows for both gauges and keeps only water years where each has at least 360 days of data. That leaves 27 years between 1984 and 2023; many years drop out because one gauge or the other has gaps, which is the first lesson in itself. For each year the program works out the mean flow at each gauge, then keeps a running total of those yearly means. By 2023 the running totals reach 290.0 at Roxton and 142.7 at Newport Pagnell.
Our Python double mass results, Roxton against Newport Pagnell, 27 water years 1984 to 2023| Measure | Value | What it tells us |
|---|
| Slope of running totals | 2.036 | Roxton carries about twice the flow |
| Ratio of final totals | 2.032 | Agrees with the slope |
| Ratio of catchment areas | 2.075 | A sensible physical check |
| Single-year ratio, lowest | 1.718 (2020) | One year alone can mislead |
| Single-year ratio, highest | 3.068 (2002) | Noise, not necessarily an error |
| Slopes either side of 2002 | 2.055 then 1.986 | A change of about 3 per cent |
Plotted against each other, the two running totals make an almost straight line with a slope of 2.036, very close to the ratio of the catchment areas, 1,660 to 800. That straightness is the point. Individual years swing wildly, from 1.72 times the upstream flow in 2020 to 3.07 in 2002, because rain falls unevenly and groundwater responds slowly. A learner who compared single years would see alarms everywhere. The running totals smooth the noise, so only a lasting change bends the line.
Next the learner hunts for the single most likely bend by fitting two straight lines, trying every possible break year. The strongest split is at 2002, with slopes of 2.055 before and 1.986 after, a change of about 3 per cent. The archive notes that the Roxton record was reprocessed in 2018, and that the station has some artificial influences, so small shifts are expected. The learner reports it carefully: a small bend, worth a question, not proof of a fault. Tests use a made-up pair of gauges where a 10 per cent change is planted in a known year, to check the program finds it.
Ages 8 to 11
Keep running totals of two dice for twenty throws and plot one against the other.
Ages 11 to 15
Write the running totals in Python and draw the double mass line.
Ages 15 and up
Fit two lines, search for the likeliest break, and test with a planted change.
Agency flows, our curve
The daily flows come from the Environment Agency hydrology service and the station details from the National River Flow Archive. The running totals, slopes and break search are ours.
