Build Your Own Error Bars — Temperature

What's being compared

For every station in this lab there are two monthly temperature series. One is the station's own record: monthly means built from thermometer readings, published in the NOAA GHCN monthly dataset. The other is a reanalysis estimate — a weather model's reconstruction of past conditions at the station's coordinates, from the ERA5 dataset.

Both series claim to describe the same place and the same months, from 1940 to the present. This lab never treats one as the answer key for the other; it only measures how much, and when, they disagree — and puts that measurement in your hands.

Rather than compare raw temperatures, the lab compares each series as an anomaly — its departure from its own 1991–2020 average, measured separately for each calendar month. That strips out a fixed gap between the two: a station sitting above or below the average height of ERA5's grid cell reads a degree or two apart from it for reasons that have nothing to do with climate. Set that offset aside and what remains is the thing this lab is about — the shape of the disagreement over time.

Why anomalies, and not raw temperatures?

An anomaly is a value measured against a fixed reference average instead of against zero degrees. Here every series — station and reanalysis alike — is expressed as its departure from its own 1991–2020 monthly average (the current WMO climate normal), using the same thirty-year window for every station.

The reason is that a reanalysis value is a grid cell's average, tied to the average elevation of the terrain across that cell. A station that sits higher or lower than that average reads a roughly constant amount cooler or warmer than the reanalysis — a fixed offset set by geometry, not by any disagreement about the climate. Left in, that offset dominates the chart and hides what is worth looking at. Subtracting each series' own baseline removes it, so the two start from a common zero and any gap that remains is a real difference in how they vary over time. The offset itself is neither error nor signal; it is expected, and the anomaly view simply sets it aside.

What is a reanalysis?

A reanalysis runs a modern weather-forecast model over the past, continuously nudged toward millions of historical observations — weather balloons, ships, aircraft, satellites, and surface stations. The output is a physically consistent estimate of the atmosphere everywhere on a grid, including places and times nothing was measured. ERA5, produced by the European Centre for Medium-Range Weather Forecasts, covers 1940 to the present.

A reanalysis value at a station's coordinates is not the station's reading fed back out: it is the model's estimate for a grid cell around that point, shaped by everything the model assimilated and by the model's own physics.

How is the model's series made comparable to the station's?

GHCN monthly means are built from daily maximum and minimum readings: each day contributes (Tmax+Tmin)/2, and the month averages those. The reanalysis series here is aggregated the same way — ERA5's daily maximum and minimum at the station's coordinates, combined as (Tmax+Tmin)/2 and averaged over each month (months missing more than 10% of days are dropped). Comparing like-for-like on definition matters: whether (Tmax+Tmin)/2 is itself a good stand-in for a day's true mean temperature is a separate question, deliberately outside this lab.

Is either series the "true" temperature?

This lab does not treat either as ground truth. Station records carry their own histories — siting, instrument changes, moves, time-of-observation changes. Reanalysis estimates carry model assumptions, a grid cell's worth of terrain standing in for a point, and an observing system that changed over the decades. The one thing that can be measured directly is how much the two disagree; what to make of that is yours to decide.

Choose a calibration station

This is where you will build your error band. The stations span a wide range of surrounding built-up land, from very little local development to dense urban areas — built-up context is shown on each card so you can consider it as part of your choice rather than having it hidden. The comparison window starts in 1940, when the reanalysis begins.

How were these stations chosen?

Every station here is a reference-grade long record. Most are stations in recognised reference networks — the GCOS Surface Network and the US Historical Climatology Network — chosen for long, well-documented records. A few are co-located "gold" sites, where a long record carries through a documented same-place instrument handover with no break in continuity (Stillwater, kept on university land through its move, is one). They are chosen to be trustworthy first, then to span surrounding built-up land from open country to city, so you can weigh the built-up context yourself — in either direction. Reference grade is a quality criterion fixed before any comparison, not chosen to favour a result, and the non-gold stations are drawn at random within each built-up band, in a random order, so no station reads as the "right" place to start.

Stations are shown in a random order to avoid nudging your choice.

Select a station above to continue.

Choose which version of the station record to use

Every GHCN station has two published versions of its monthly record. Both are real, maintained datasets; they differ in whether adjustments for station changes have been applied. Pick the one you want to compare against the model — you can switch later, though switching clears the difference, band, and scorecard you've built, because they belong to one version of one record.

What kinds of adjustments are these?

Station histories contain changes that have nothing to do with climate: the station moves, the instrument is replaced, the time of day the thermometer is read changes. NOAA's pairwise homogenization algorithm compares each station with its neighbours to detect such changes and estimates an offset for each one; the adjusted series is the reported series with those offsets applied. The unadjusted series is the reported series without them.

You can inspect what the adjustments look like for any individual station on klymot.com (Adjustments tab in the station view).

The two versions are shown in a random order to avoid nudging your choice.

Choose a version above to continue.

Look at the two series together

Both series are drawn as anomalies — each one's departure from its own 1991–2020 average — with equal weight; which one gets which colour, and which is listed first, is randomized on each visit, so neither is presented as the baseline the other is checked against. With the constant offset removed, the two lines share a common zero and you can watch where they part company. Change the averaging to see how much the comparison depends on it: a single calendar month, a single season, or whole years. When you compare by month or season, a second control picks which one — so like is always compared with like, rather than mixing times of year that can disagree with the model by very different amounts.

Averaging

Time of year

The starting averaging level and time-of-year filter are randomized on each visit; both are yours to change at any time.

How are seasons and years averaged?

Both series are averaged over exactly the same months, and only over months where both have a value. Seasons are the standard meteorological quarters (DJF, MAM, JJA, SON, with December counted into the following year's winter); a season needs all three months and a year needs all twelve, so a missing winter can't skew a year's comparison.

Station and reanalysis anomaliesAnomaly (°C, vs 1991–2020)

Overlap—

Periods compared—

Averaging—

View the paired values as a table

Period	Station anomaly (°C)	Reanalysis anomaly (°C)

Construct the difference

So far you've seen the two series side by side. The next step subtracts one from the other, period by period — station minus reanalysis — and collects every one of those differences into a distribution you can put a band around.

Subtracts the reanalysis from the station record at your chosen averaging.

The difference, period by period

Each point is the station's anomaly minus the reanalysis anomaly for the same period. Because the fixed offset between them has already been removed, zero marks their typical 1991–2020 relationship: points above zero are periods where the station ran warmer relative to the model than it did on average across the baseline; points below, cooler. The averaging control above still applies.

Station minus ERA5 reanalysis, anomaliesAnomaly (°C, vs 1991–2020)

Your difference distribution

The same differences, tallied — for the month, season, or year the controls above select. The shaded band marks the central share of them — you pick how central. A 50% band that misses half the points is behaving exactly as labelled; the label is the claim being tested later, so it stays on screen.

Band coverage

The starting coverage level is randomized on each visit; it's yours to change at any time.

Distribution of the differencesAnomaly (°C, vs 1991–2020)

Differences—

Mean—

Median—

Band—

What does the band mean?

It spans the central share of the differences you built — at 90%, the range that contains the middle 90% of them, computed directly from the values (no distribution shape is assumed). By construction it holds at this station over this period; that is not a finding, it's arithmetic. Whether the same band holds anywhere else is the open question the next step tests.

Freezing locks the band so you can test it at another station.

Test your band somewhere else

Every time a model output stands in for a missing measurement, an assumption is being made: that the model's error where it can be checked resembles its error where it can't. Here you get to check it. Pick another station; your frozen band is drawn around the reanalysis series there, with the station's own measurements hidden until you choose to reveal them.

Stations are shown in a random order to avoid nudging your choice.

Select a station above to draw your band there.

Reanalysis anomalies with your frozen bandAnomaly (°C, vs 1991–2020)

Pick a station above first.

Your scorecard

Each station you reveal adds a row: how many of its measurements your band caught, against the share the band held at your calibration station. Built-up land around each station is listed so you can look for any relation to built-up context yourself — in either direction.

Station	BU in 1 km	Inside band	Share inside	Band claimed

Questions you might like to ask

Written before we computed any of the answers ourselves — they are prompts, not hints, and the lab takes no position on any of them.

Does the size of the disagreement depend on the season? On the decade?
Does the picture change when you switch the averaging from monthly to annual?
Does the adjusted (QCF) version of a record sit differently against the reanalysis than the unadjusted (QCU) version?
Does a band built at one station hold at its stated rate elsewhere? Does it matter how far away the second station is, or how different its built-up surroundings are?
Does the gap look different at heavily built-up stations than at barely developed ones?
If you build the band at a different calibration station, do your conclusions survive?

Data sources & methodology

Station temperature records — NOAA GHCNm v4: Monthly mean temperatures from the NOAA Global Historical Climatology Network Monthly v4, in both its unadjusted (QCU) and adjusted (QCF) versions. Menne et al., 2018. Series are fetched per station from klymot.com's published data mirror (www.klymot.com/data/{qcu,qcf}/<station-id>.csv), the same files behind the main site's station explorer.
Reanalysis temperature — ERA5 via Open-Meteo: ERA5 is produced by the European Centre for Medium-Range Weather Forecasts: Hersbach et al., 2020. Daily 2 m maximum and minimum temperature at each station's coordinates are fetched from the Open-Meteo Historical Weather API and aggregated to monthly means of (Tmax+Tmin)/2 — the GHCNm definition — keeping months with at least 90% of days present. Open-Meteo downscales ERA5's coarse grid to the station's own recorded elevation, so the model and the thermometer are compared at the same height rather than at whatever elevation a terrain model happens to assign the grid cell.
Anomalies — 1991–2020 baseline: Every series, station and reanalysis alike, is shown as an anomaly: its departure from its own average for each calendar month over 1991–2020 — the current WMO climate normal — the same thirty-year window applied to every station. Working per calendar month subtracts out the seasonal cycle, so the monthly and seasonal views show departures rather than the seasons themselves. This also removes the near-constant offset between a station and ERA5 that comes from the station's height relative to the grid cell's mean elevation (geometry, not climate), leaving a comparison of how the two vary rather than of a fixed gap. Any month with no data inside the baseline window is omitted.
Station pool: Reference-grade GHCN long records only: stations in the GCOS Surface Network (GSN) or the US Historical Climatology Network (HCN) — external NOAA/WMO quality flags, not our own selection — each with a near-continuous annual record from 1940 to today. Added to these are co-located "gold" reference sites, where a long COOP record is spliced onto its co-located successor: the newer reference station anchors the recent era unchanged, and the older record is shifted onto its level by the offset measured over their overlap (estimated per calendar month and documented in the data file). For these the record-version choice is not QCU vs QCF but Spliced (offset-corrected) vs Raw (the same records joined with no offset applied), so you can see what the correction does rather than take it on trust. From the eligible stations, one is drawn per built-up band so the pool spans open country to city. ("Gold" here means unbroken record continuity through the handover, not low development — Stillwater, for instance, is a gold reference that still sits in a town.)
Built-up context — GHSL: Built-up land fractions and imagery around each station are from the Global Human Settlement Layer's built-up surface data for 2020, as published on klymot.com's station explorer. European Commission JRC GHSL.
Bands and the transfer test: Differences are station minus reanalysis over periods where both have values, averaged over identical months. The band spans the central quantiles of those differences at your chosen coverage (empirical, no distribution assumed; at least 30 differences required). The transfer test counts the share of another station's values falling inside the reanalysis series plus your frozen band.