Build Your Own Error Bars — Sunshine

How much sunshine reached the ground yesterday? An instrument can tell you — where one exists. Everywhere else, the number you'll be quoted comes from a model. Here you measure the gap between instrument and model yourself — then test whether the gap you measured in one place tells you anything about another.

Pick a site with a long pyranometer record. Put its measurements next to a reanalysis model's estimate for the same spot. Build the distribution of their disagreements, freeze a band around it, and carry that band to a second site to see how it holds up. There is a sibling lab that runs the same idea on temperature instead of sunshine — see Build Your Own Error Bars — Temperature (Lab 05).

  • What a pyranometer measures, and where modelled radiation estimates come from.
  • How to turn two overlapping series into a difference distribution and an empirical error band.
  • How to test — rather than assume — whether an error band built in one place transfers to another.

What's being compared

For every site in this lab there are two daily solar-radiation series. One is measured: the total solar energy reaching a horizontal surface each day, recorded by a pyranometer and published by the national weather service that operates it. The other is a reanalysis estimate — a weather model's reconstruction of the same quantity at the same coordinates, from the ERA5 dataset.

Both series claim to describe the same sky over the same days. 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.

What is a pyranometer?

A pyranometer is an instrument that measures the solar radiation arriving on a horizontal surface — direct sunshine and light scattered by the sky together. Summed over a day it gives the day's solar energy total, in megajoules per square metre. The sites in this lab publish daily totals going back decades, some to the 1940s and 1950s.

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; its surface solar radiation depends heavily on the model's clouds.

A reanalysis value at a site's coordinates is not the instrument's reading fed back out: it is the model's estimate for a grid cell around that point. Elsewhere on this site — where no freely available instrument record exists — such estimates are used as stand-ins; this lab is where that stand-in can be checked against instruments.

Is either series the "true" sunshine?

This lab does not treat either as ground truth. Instruments drift, get dirty, get recalibrated, and are occasionally moved; a grid cell's modelled cloud cover is not the sky over one field. 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 site

This is where you will build your error band. The sites run from a remote mountain summit to a capital-city rooftop — built-up context is shown on each card so you can consider it as part of your choice rather than having it hidden. Each comparison starts when that site's instrument record does.

How were these sites chosen?

They are the pyranometer stations with long daily records that are freely downloadable in full from a national weather service's open archive (DWD in Germany, KNMI in the Netherlands, SMHI in Sweden), chosen to span a broad range of surrounding built-up land. Many other long records exist but are not openly published, which is itself part of what this lab is about. Sites are presented in a random order to avoid suggesting that any one is the "right" place to start.

Built-up figures describe the surroundings of the nearest GHCN weather station in klymot.com's index; each card's distance notes how far that reference point is from the pyranometer.

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

Select a site above to continue.

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 daily to monthly to annual?
  • Does a band built at one site hold at its stated rate elsewhere? Does it matter how far away the second site is, or how different its built-up surroundings are?
  • Do mountain, island, and city sites behave differently from one another?
  • Does the gap look different at heavily built-up sites than at barely developed ones?
  • If you build the band at a different calibration site, do your conclusions survive?
Data sources & methodology
Measured solar radiation — national open archives
Daily global horizontal irradiance from real pyranometers: Deutscher Wetterdienst Climate Data Centre daily solar product (opendata.dwd.de, stations Potsdam, Hohenpeißenberg, Würzburg, Fichtelberg, Norderney); KNMI daggegevens (daggegevens.knmi.nl, De Bilt); SMHI open data (opendata-download-metobs.smhi.se, Stockholm, hourly irradiance summed to daily totals). J/cm² values are converted to MJ/m².
Modelled solar radiation — ERA5 via Open-Meteo
ERA5 is produced by the European Centre for Medium-Range Weather Forecasts: Hersbach et al., 2020. Daily shortwave radiation totals at each site's coordinates are fetched from the Open-Meteo Historical Weather API.
Site pool
Pyranometer stations with long daily records freely downloadable in full from a national open archive, chosen to span a broad range of surrounding built-up land — from a remote mountain summit to a capital city. Records that require registration or payment (including several longer ones) are excluded.
Built-up context — GHSL
Built-up land fractions and imagery are from the Global Human Settlement Layer's built-up surface data for 2020, as published on klymot.com's station explorer, described at the nearest GHCN station to each site (distance shown on the card). European Commission JRC GHSL.
Bands and the transfer test
Differences are measured minus modelled over periods where both have values, averaged over identical days. 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 site's measurements falling inside the modelled series plus your frozen band.