The world's water hardness, from 611,858 samples of rivers, lakes and groundwater, and the rocks behind it.
Fill a kettle in Cambridge and in Aberdeen and, after a few months, only one of them will be furred with white scale. That scale is calcium and magnesium carbonate, and it got into the water from the ground. Rain is a very weak acid: it picks up carbon dioxide on the way down and through the soil, and that carbonic acid dissolves limestone, chalk and dolomite readily, while granite, gneiss and most sandstones barely give anything up. So the hardness of water is, more than anything, a map of the rocks it has passed through.
The familiar hardness maps of England and Wales show water supply zones, from soft in the west and north to very hard in the south and east. I wanted the world version. There is no open world map of tap water, so I used the next best thing: the UN's GEMS/Water archive of river, lake and groundwater measurements, 16,682 stations with a hardness figure in 34 countries. Then I asked how well the rocks alone could guess the answer where nobody has measured.
Each dot is a monitoring station, coloured by its median hardness over all its samples, in the same six classes as the England and Wales maps. Circles are rivers, squares lakes and reservoirs, triangles groundwater. Behind them, the modelled layer shows the hardness a river would typically have given the rocks within about 10 km and the rainfall; zoom into Britain and Ireland for a sharper 1 km version. Faded, hatched areas (71% of the modelled land) rest mainly on coarse geology: two world compilations and some plate-scale legend units, where single map units cover areas the size of countries, straight edges mark where they meet the detailed regional maps, and the rock is often named only as "sedimentary". Treat them with extra caution, or switch the fading off under Map layers. Click a station for its record over time, or search for a place.
Measured: UNEP GEMS/Water GFQA v3 (CC BY 4.0). Modelled: my estimate from Macrostrat, BGS and GSI geology and CRU CL 2.0 rainfall. Hill shading from AWS Terrain Tiles. Base map tiles © Esri when they load. Blank land on the modelled layer is too dry (under 200 mm of rain a year) or unmapped; faded and hatched land is low confidence.
Across all 16,682 stations the median is 202 mg/l. A quarter are very hard (26% over 300 mg/l) and 12% are soft. Groundwater is the hardest (median 276 mg/l at 3,861 stations), because it sits in the rock for months or years; rivers come next (199 mg/l), and lakes and reservoirs, fed partly by rain straight onto their surface and often in hard, old rock, are the softest (139 and 111 mg/l).
By country, the softest network is Norway's (median 8.2 mg/l over 133 stations) and the hardest Belgium's (330 mg/l over 83), among the 28 countries with at least 20 stations. A country's figure says as much about where its stations are as about the country: Mexico alone has 5,242 of them, 2,173 in wells, while India's are almost all rivers. Switch to the modelled view to rank 132 countries by the estimate instead, including the many with no stations in the open archive.
To link each station to its rocks I gave every unit on the world geological map shares of seven rock groups from its description (so "limestone and shale" is half carbonate, half mudstone), and measured the share of each group within 10 km of the station. The clearest signal in the measurements is not limestone but its opposite: where crystalline rocks such as granite, gneiss and schist cover more than four fifths of the ground, the median station has just 34 mg/l, against 220 mg/l where they cover less than a fifth.
The model then asks what hardness each rock group gives on its own. It mixes the groups by their shares (as waters from different rocks mix), lets wetter places be softer and lets groundwater and lakes differ from rivers. Fitted to all the stations, it says a river draining only granite and gneiss under a metre of rain a year would carry about 22 mg/l; only carbonate rock about 211 mg/l; and loose young sediments such as loess and glacial clays about 257 mg/l. Each doubling of rainfall makes water about 21% softer, groundwater comes out about 2.0 times as hard as river water nearby, and lake water about half as hard (0.48 times).
A model can look good simply by remembering its own data, so I tested it the hard way: the world was cut into 5 by 5 degree squares, whole squares were hidden, and each hidden station was predicted only from the others (spatial cross-validation). On that test the rock model explains 24% of the variation in log hardness, puts 29% of stations in exactly the right class and 64% within one class, and is typically out by a factor of 1.8. Guessing the global median for everyone gets only 38% within one class. Hiding whole countries is harsher still (61% within one class).
Within one class: predicted class is the measured class or next to it. Typical error: the median factor between measured and predicted.
The map's own detail matters as much as the model. Where at least half of the land around a station comes from a detailed regional map unit that names its rock, the model gets 68% of 10,363 stations within one class (R² 0.36); where it rests mainly on the coarse compilations it gets 56% of 4,430 (R² -0.12, no better than a flat guess). That is why the map fades those areas.
The misses are informative. The model over-predicts in Norway (measured water there is typically 24% of what it expects), Canada and Denmark, and under-predicts in Spain, the Netherlands, Serbia and Cyprus (by factors of about 2.0 to 4.6). The reasons will differ from place to place, from thin soils over ice-scoured rock to gypsum and salty groundwater, and this simple model cannot tell them apart. The biggest weakness is the map itself: over about half of the mapped land the world geology I used says only "sedimentary", without saying whether it is limestone or sandstone (50% of mapped land outside Antarctica).
The open archive has 388 stations in Ireland but none at all in Great Britain. For both islands I used the far more detailed BGS and GSI bedrock maps at about 1 km, merged into four groups (carbonate and evaporite; sandstone, mudstone and other sediments; volcanic; crystalline), and calibrated the model on the Irish stations, keeping the rainfall effect from the world model so it would not stretch too far across Britain's much wider range of rainfall. Under the same kind of test (hiding half-degree squares) it explains 60% of the variation in Ireland and gets 82% of stations within one class, far better than the world model does at the same Irish stations (71%).
The rocks alone reproduce the broad pattern: south and east of a line from the Tees to the Exe the modelled median is 92 mg/l and 21% of the land is hard or very hard; north and west of it the median is 35 mg/l and 71% is soft. The hardest counties are those on the chalk: East Riding of Yorkshire (330 mg/l), Hertfordshire (280) and Norfolk (251). The softest are in the Highlands and Islands, at about 20 to 23 mg/l.
The chalk that makes the Chilterns, the Downs and the Yorkshire Wolds is almost pure calcium carbonate, laid down in a warm sea. There are no British stations in the archive, but the same chalk runs under the Channel into northern France, where 141 stations between Rouen, Amiens and Paris have a median of 301 mg/l and 96% are hard or very hard.
The peninsula is a slab of limestone with almost no rivers on its surface: water runs underground and surfaces in cenotes. 92% of its stations are very hard. The world model misses this badly, at about 117 mg/l, because the map I used calls the rock simply "Eocene sedimentary". A good example of a model that is only as good as its map.
Guangxi and Guizhou hold some of the world's most famous limestone landscapes, the tower karst of Guilin among them. Here I have neither measurements nor a useful map: the world geology describes 81% of the area only as sedimentary rock of a given age, such as "Palaeozoic sedimentary rocks", so the estimate (about 108 mg/l) is probably too soft. I leave it on the map as a reminder of what this method cannot see.
Norway, Sweden and Finland sit on some of the oldest crystalline rock in Europe, scraped bare by ice. 90% of their stations are soft. The Canadian Shield is the same story: 54 Canadian stations surrounded mostly by crystalline rock have a median of 5 mg/l, against 42 for the rest of Canada's.
Ireland is a saucer: a lowland middle floored with Carboniferous limestone and a rim of older, harder mountains. Its 117 stations where at least half of the nearby rock is limestone have a median of 192 mg/l; its 103 stations on almost no limestone, 17 mg/l.
Hardness is usually given as the calcium carbonate that would carry the same calcium and magnesium: milligrams per litre, the same as parts per million. Europe also uses degrees. One German degree (°dH) is 17.85 mg/l; one English or Clark degree is 14.25 mg/l; one French degree (°f) is 10 mg/l. The map's unit buttons convert everything. Where a station measured calcium and magnesium but not hardness, I computed it as 2.497 times calcium plus 4.118 times magnesium, both in mg/l.
Derived data, text and figures: CC BY 4.0. Code: MIT. Data and code on GitHub. Paper and archived release: https://doi.org/10.5281/zenodo.23735824.