User Guide

Context

This tool was built to understand the return period of heavy precipitation events across the UK (currently just England). So the unusualness of an event can be determined relative to that location's characteristics, which can differ markedly in areas of high / complex terrain present across the northwest half of the UK. The total size of the database to store all >950 gauges would exceed 90 GB (more memory than available on my laptop), so a subset of ~160 gauges has been selected for this test page.

Data

Currently data is Environment Agency 15 minute gauge data sourced from their API, only a limited subset number of stations have been selected via a 1 x 1 degree lat/long box logic, with some manual addition of stations to make sure extreme high ground stations are included, and larger gaps have been plugged. All suspect readings have been removed, but some erroneous data may remain (despite the best efforts to filter most of these datapoints out). The recent extreme precipitation accumulations table (see below) is a good way to sanity-check any single site's most extreme recent readings for yourself, and find recent analogue events.

The underlying data is not likely to be updated more than annually, unless some specific request is received.

Currently England only: the Environment Agency's 15-minute API is what this page is built on, and it only covers England. Wales/NRW gauges would need a separate registration and a still-unconfirmed historical-readings endpoint on their API — that's a distinct, not-yet-started piece of work, not a design choice to exclude Wales.

What is Extreme Value Theory?

Extreme Value Theory (EVT) is the branch of statistics concerned specifically with rare, extreme values — the tail of a distribution — rather than its overall average behaviour. An ordinary statistical model fitted to all your data (a normal distribution, say) is usually a poor guide to how often a once-in-20-year event happens, because that event sits far outside the bulk of the data the model was fitted to. EVT instead fits a model only to the extreme observations themselves, and provides a mathematically justified way to extrapolate a little beyond the range actually observed — e.g. estimating a 20-year return level from 15 years of data.

There are two classical approaches. Block maxima takes the single highest value in each block of time (e.g. the accumulation each block, per month or year in this case) and fits a Generalized Extreme Value (GEV) distribution to that series of maxima. Peaks-over-threshold (POT) instead takes every value that exceeds some high threshold, and fits a Generalized Pareto Distribution (GPD) to the amount by which each of those exceedances clears the threshold. This page uses POT, for reasons explained below.

A GPD fit has two parameters:

• Scale (σ, sigma): controls how spread out the exceedances are above the threshold. A larger scale means that when the threshold is cleared, it tends to be cleared by a wide and unpredictable margin.
• Shape (ξ, xi): controls the basic character of the tail. A positive shape means the tail is heavy/unbounded — extreme values can, in principle, keep growing without any hard ceiling. A negative shape implies a finite upper bound on possible precipitation accumulation (the model believes some maximum physically cannot be exceeded). A shape close to zero behaves like a simple exponential decay — no hard ceiling, but no runaway heaviness either.

Alongside these are the thresholds themselves — the precipitation accumulation for each period above which a reading counts as an exceedance and is used to fit the model. Everything below the threshold is ignored entirely; only the extremes and how far they exceed the threshold inform the fit.

Peaks Over Threshold: how it's applied here

POT was chosen over block-maxima annual-GEV for two reasons. First, it makes use of every exceedance, not just the single worst day of the block — which allows return periods to be estimated down to monthly, not just annual, resolution.

The threshold used for each site is that site's own 95th percentile of precipitation accumulations for each window — i.e. a 1-in-20-day event, calculated separately for every station. This adapts automatically to each site's own climate (a mountain summit and a sheltered valley get very different thresholds, both meaningfully "extreme" for that location). On average, the 95th percentile captures the wettest ~18 days per year at a site — close to the typical frequency of Heavy Rain National Severe Weather Warning Service (NSWWS) warnings, which was a deliberate consideration in choosing this percentile.

Declustering

With 15 minute data, there is a chance that one extreme 12 hour event could dominate many successive 12 hour extreme events across a series of 15 minute steps. So for this analysis, the maximum accumulation has been selected in a 12 hour window, and then all events that fall 12 hours before and after this window have been removed. The same logic has been done at all accumulation windows, and analysis suggests this has been effective at declustering events.

Tables: dataset length and exceedances

Below each site's plot, a small table lists — for each curve shown — the record length behind it, the threshold used, the number of independent exceedances the fit is based on, and the fitted scale and shape parameters. These numbers matter for judging how much to trust a given curve: a site with a short record or few exceedances has a much less stable estimate than one with decades of data and hundreds of exceedances, even if both curves look equally smooth on the page.

Illustrative example (invented numbers, not a real station) — note how much shorter the 6h record and how much smaller its exceedance count are next to the 24h curve: that curve's return-level estimates, especially at the longer return periods, deserve more caution than the 24h one.

Recent events table

This table is a quick way to find recent real-world analogues at a site — useful, for example, when trying to recall or communicate how a currently-forecast precipitation accumulation compares to what has actually happened in recent history.

These recent events have been split up into return period windows.

Maps

The map has two options, accumulation period and return period, and the sites will dynamically update with the combination of the two.

This allows context of what is extreme for that location, which in areas of high and complex terrain shows marked variations over short distances.

Plots

The detail plot shows return level against return period (log scale) for the clicked station. Use the checkboxes in the sidebar to add or remove different accumulation curves — each with its own shaded 95% confidence interval (only available for return periods of 1 year or more; the extRemes package in R doesn't support confidence intervals below that).

Click any of the ticks on the plot to place a line marking the precipitation accumulation and return period at that point — click again to remove it. With more than one curve shown, the line follows the longest-duration curve. A "Download plot (.png)" button above the plot saves the current view in a 16:10 aspect ratio, including any marked point, as an image file named after the station and accumulation period(s) selected.

Disclaimer

Feedback

Please feel free to pass on any feedback and suggestions to nick.silkstone@gmail.com.