The Lambourn projectSmoothing a river without flattening it
35,040 readings from one gauge, four window lengths and three ways to smooth.
The learner downloads a year of readings from the Environment Agency's open hydrology service: the water level at the gauge called Shaw, on the River Lambourn, every 15 minutes through 2025. That is 35,040 quality-checked values with none missing; 98 extra readings taken at odd times on 11 to 13 November were marked unchecked, so they are left out. The level moves between 1.363 m and 1.832 m on the gauge's own scale. Most of the time it barely changes, with a typical 15-minute step of 0.62 mm, but the eight largest rises of the year, each at least three days apart, were all 76 mm or more within a day, the largest 143 mm to a peak at 23:15 on 5 January.
Three smoothers are tried on the whole year. A centred moving average replaces each reading with the mean of a window around it. A trailing average uses only the past, the way a live dashboard must. The Savitzky-Golay filter, published by Abraham Savitzky and Marcel Golay in 1964, fits a small polynomial through each window by least squares and keeps its middle value, so a curved peak can survive. In Python it is one call, scipy.signal.savgol_filter. For each of the eight big rises the learner measures how much of the rise is left after smoothing, and how far the peak moves.
Share of each big rise kept after smoothing (average, worst of eight) and median shift of the peak, our run on the 2025 Shaw readings| Window | Moving average | Savitzky-Golay, order 2 | Savitzky-Golay, order 4 |
|---|
| 3 hours | 98.4%, 95.0%, 30 min | 99.7%, 99.0%, 30 min | 100.0%, 99.6%, 15 min |
| 6 hours | 96.4%, 88.3%, 52 min | 99.1%, 96.5%, 30 min | 99.5%, 98.4%, 30 min |
| 12 hours | 90.9%, 79.7%, 82 min | 99.1%, 90.8%, 45 min | 99.4%, 94.4%, 30 min |
| 24 hours | 77.8%, 63.6%, 262 min | 94.5%, 83.5%, 82 min | 99.1%, 89.4%, 60 min |
With a day-long window the moving average keeps only 77.8% of a typical rise, as little as 63.6% of one, and moves the peak by more than four hours. Savitzky-Golay of order 4 over the same window keeps 99.1%. The trailing average keeps the same share as the centred one but reports peaks late: by a median of 982 minutes, more than 16 hours, at the 24-hour window. There is a price, and the learner measures it too. After the 24-hour moving average the typical step is 0.183 mm; after order-4 Savitzky-Golay it is 0.305 mm, so less of the wobble is removed. One more surprise: orders 2 and 3 gave identical results, a known property of the centred filter that the numbers confirm.
Ages 8 to 11
Plot a week of readings on squared paper and try averaging each point with its neighbours.
Ages 11 to 15
Read the file with Python's csv module and write a moving average with a loop.
Ages 15 and up
Use numpy and scipy to compare filters, then measure what each one costs on real peaks.
Where the data comes from
River levels are Environment Agency data from the Hydrology API, used under the Open Government Licence, read on 1 October 2026. The filter is from Savitzky and Golay, Analytical Chemistry, 1964. The choice of peaks, the windows and every percentage above are from our own Python; we say nothing about flooding or what caused any rise.
