The 43 million square kilometres that were really 6.7 million

Dark navy board slide, masthead “Northlight Earth Observation · Monitoring programme review · Board pack, FY27”, headlined “The Arctic is four fifths of the programme”. A subhead reads: every square kilometre of the FY27 monitoring commitment, measured the only way the platform can measure it — the four theatres’ national boundaries, taken whole, each one’s area computed by the same function, from the same boundary file, in the same coordinate system the operations map is drawn in; nothing sampled, nothing estimated, nothing set aside. Filling the left of the slide, under the label “FY27 monitoring theatres · Natural Earth 1:50m boundaries · platform basemap (EPSG:3857)”, is a Web Mercator world map on a dark ocean, with a faint graticule at 15° parallels and 30° meridians. Greenland and Norway, including Svalbard, are filled gold and are enormous — Greenland alone dominates the northern half of the map. The Democratic Republic of the Congo and the Indonesian archipelago are filled blue and look modest by comparison. A legend reads “Ice & snow theatres” in gold and “Forest & peatland theatres” in blue. In the centre column, under the label “Ground under watch · square kilometres”, four horizontal bars stand on a zero-based axis running 0 to 40 millions: Greenland 35,395,741, a gold bar running nearly the full width; Norway 3,452,856, a short gold bar; DR Congo 2,359,632 and Indonesia 1,885,417, two shorter blue bars. Down the right-hand side, a gold-bordered card carries 43.1 M km² over the line “Total ground under watch in FY27, across all four theatres”. A card headed “Ground by theatre · FY27” lists Greenland 35,395,741, Norway 3,452,856, DR Congo 2,359,632, Indonesia 1,885,417 and a total of 43,093,646. A gold card headed “Read-out for the board” argues that Greenland is not one theatre among four but is the programme, carrying 82% of the ground under watch, 15 times the Congo Basin and 4.6 times the other three theatres put together, and recommends that FY27 headcount follow the ground — both new analysts to the ice desk, the equatorial theatres held at current staffing. A card headed “How the areas were measured” says one boundary file, one function, one coordinate system: ST_Area over the Natural Earth 1:50m admin polygons, in the platform’s own CRS, the same projection the operations map is drawn in, so the map and the table cannot disagree with each other. A final card, “Basis of measurement”, gives four theatres, 1:50m generalisation, coordinate system EPSG:3857, and four of four territories measured whole. Three ticked boxes run along the bottom: “Zero-based axis. Every bar starts at 0. No truncation, no break, no log scale and no second axis anywhere on this slide”, “Nothing cherry-picked. All four FY27 theatres, whole national territories, complete boundaries — not a sample, not a window, nothing set aside”, and “One unit throughout. Every bar is square kilometres, from one boundary file, one function and one coordinate system, computed once”. A footnote credits Natural Earth 1:50m Admin 0 – Countries, notes that the Norway polygon includes Svalbard and Jan Mayen, records that the areas were computed by us on 22 August 2026 as planar polygon areas in EPSG:3857 (WGS 84 / Pseudo-Mercator, sphere R = 6,378,137 m), the coordinate system of the basemap above, and states that the slide is a demonstration drawn by us in the manner of a board pack and has never been published anywhere. — Showing the misleading chart

The same four territories on a cream background, kicked “The same four territories · measured on the globe · Natural Earth 1:50m” and headlined “The basemap multiplied the programme by 6.4.” A subhead explains that Web Mercator is conformal, not equal-area: it stretches both directions by sec(latitude) and therefore stretches area by sec² of it — 1.3× at 30°, 2× at 45°, 4× at 60°, 33× at 80° — so although every boundary on the slide was right and every bar started at zero, the areas were measured in the projection the map was drawn in; measured on the globe instead, 43.1 million km² becomes 6.7 million and Greenland’s 82% of the programme becomes 32%. Across the top, a panel headed “Ground under watch · planar area in EPSG:3857 against geodesic area on the sphere · km²” draws two bars per theatre on one zero-based axis running to 36 million, gold for the projected figure and navy for the ground, with the factor between them printed at the right: Greenland 35,395,741 against 2,154,808, ×16.43; Norway 3,452,856 against 384,251, ×8.99; DR Congo 2,359,632 against 2,334,626, ×1.01; Indonesia 1,885,417 against 1,872,160, ×1.01. Beneath it, a panel headed “The same four theatres, the same boundary file, two projections” sets two small world maps side by side. The first, captioned “Web Mercator · EPSG:3857 — Greenland takes more of this page than the whole of Africa; Africa is 13.9 times its size”, shows a vast gold Greenland and a small blue Congo and Indonesia. The second, captioned “Equal Earth · equal-area — every square kilometre gets the same ink, wherever on the globe it sits; shapes bend a little, areas hold exactly”, shows the same four territories at their true relative sizes, Greenland now a modest gold patch. Beside them, a panel headed “Web Mercator’s area scale factor · sec²(φ)” plots the multiplier against latitude from 0° to 84°, flat and near 1 across the tropics — a shaded band marked “Congo Basin · Indonesia” — and then climbing steeply through marked points at 1.3× at 30°, 2.0× at 45°, 4.0× at 60°, 14.9× at 75° and 33.2× at 80°, through a second shaded band marked “Greenland & Norway”. Five cards run down the right. “Where the number came from” explains that the area was measured in the coordinate system the map is drawn in: in PostGIS, ST_Area(geom) on a column stored as 3857 returns square metres of the projection plane, and the projection plane is not the ground, while ST_Area(geom::geography) returns the ground — one cast, a six-fold difference. “sec² of the latitude” tabulates 1.00× at the equator, 1.33× at 30°, 2.00× at 45°, 4.00× at 60°, 8.55× at 70°, 14.93× at 75° and 33.16× at 80°, the latitude of Svalbard and northern Greenland. “The ranking reversed” records that the slide drew Greenland 15.0 times the Democratic Republic of the Congo, with the bar chart agreeing with the map, when on the ground the Congo is the larger of the two by 8%. “Norway is the sharper case” notes 384,000 km², a sixth of the Congo’s ground, reported as 1.46 times it, because the Norway polygon includes Svalbard at 78° north where a square kilometre is drawn 23 times its size. “What the slide got right” lists a zero-based axis, whole territories, one boundary file, one function, one unit and every number printed — six things right, and the coordinate system enough on its own. “The check, in five seconds” says to ask which CRS the area was measured in, and that if the answer is the one the map is drawn in and the map is a web basemap, the figure is too big by sec² of wherever the thing sits. A gold-ruled callout at the foot reads “Mercator is not a bad map. It is a map of angles,” and explains that it holds shape and bearing locally, which is why every tile server uses it and why a navigator wants nothing else, that area is the one thing it never promised, and that nothing went wrong when somebody chose Mercator to draw the map — it went wrong when the map’s coordinate system was asked a question about amount. A footnote gives the Natural Earth source, notes that Norway includes Svalbard and Jan Mayen, records that both sets of areas were computed by us on 22 August 2026 from the identical polygons — the planar shoelace area in EPSG:3857 and the geodesic area on a sphere of radius 6,371.0088 km — lists the agreement with published national totals to within 1.7%, credits the Equal Earth projection to Šavrič, Patterson and Jenny (2018), and says both drawings are our own. — Showing the misleading chart

Be the first to star this exhibit

Four national territories, taken whole, measured by one function from one boundary file — in the coordinate system the map was drawn in. Web Mercator stretches area by sec² of the latitude, so the programme came back 6.4 times too big: Greenland billed as 82% of ground it is 32% of, drawn 15 times a country that is larger than it.

Natural Earth 1:50m Admin 0 – Countries (public domain); areas computed by us in EPSG:3857 and geodesically on 22 August 2026, 2026Added August 22, 2026

01The claim

Here is where the FY27 monitoring programme actually is, and how much ground it comes to. Four theatres, four national territories, every one of them taken whole — no sampling, no windowing, no set-aside — with the area of each computed by the same function, from the same boundary file, in the same coordinate system the operations map above it is drawn in. That last point is the one the slide is proudest of: the map and the table cannot disagree with each other, because they are the same arithmetic drawn twice. The bars start at zero, as bars must. Every number is printed. The unit never changes: a square kilometre, four times over. And the finding is not subtle. Greenland is not one theatre among four; it is the programme. It carries 82% of the ground under watch — 15 times the Congo Basin, and 4.6 times the other three theatres put together — for a total commitment of 43.1 million square kilometres. The recommendation follows from the picture and from the table alike: let FY27 headcount follow the ground. Both new analysts to the ice desk. The equatorial theatres, small ground and dense revisit, hold where they are.

02The trick

Everything on that slide is right except the projection, and the projection is not a decoration — it is the ruler. Web Mercator, the coordinate system under nearly every map on the internet and the one this platform draws in, is conformal: it preserves angles and local shape, which is exactly what a tile server and a navigator want. It buys that by stretching. Each direction is multiplied by the secant of the latitude, so area is multiplied by the square of it — sec² φ, which is 1.00 at the equator, 1.33 at 30°, 2.00 at 45°, 4.00 at 60°, 14.9 at 75° and 33.2 at 80°. Nothing about that is hidden or disputed; it is the defining property of the projection, and you can work out the damage before you look at the data. Here the damage is arithmetic. The Congo Basin sits between 13.5° south and 5.3° north, so it is inflated by 1.01 — near enough to nothing. Indonesia, straddling the equator, by 1.01. Greenland runs from 59.8° to 83.6° north, and comes back inflated 16.43 times: 2,154,808 real square kilometres reported as 35,395,741. Norway, whose polygon includes Svalbard at 78° north, comes back 8.99 times too big. Add the four together and a programme covering 6,745,844 km² of ground is billed at 43,093,646 — a factor of 6.4, arrived at without a single wrong boundary or a single bent axis. What that does to the ranking is the part worth keeping. The slide draws Greenland at 15.0 times the Democratic Republic of the Congo, and the bar chart, being honest about the numbers it was handed, agrees with the map exactly. On the ground the Congo is the larger of the two, by 8%. Norway is the sharper case: 384,251 km², a sixth of the Congo’s ground, reported as 1.46 times it. And Greenland’s 82% share of the programme is really 32% — less than the Congo Basin’s. The board was asked to move headcount toward the theatre with the least ground of the four. The mechanism has a name in the trade, and it is a coding error rather than a design one. Ask a GIS for an area in the coordinate system it happens to be drawing in and it will answer in square metres of the projection plane, correct to the metre, with no note that the plane is not the ground. In PostGIS that is `ST_Area(geom)` on a column stored as 3857, against `ST_Area(geom::geography)` on the identical geometry. One cast, six-fold difference. (The slide is our own demonstration, drawn in the manner of a board pack. The boundaries and both sets of areas are real.)

03The fix

Measure on the globe and draw on an equal-area map, and the picture stops arguing with the ground. The four theatres come to 6.7 million square kilometres, of which Greenland is 2.15 million, the Congo Basin 2.33 million, Indonesia 1.87 million and Norway 0.38 million — four theatres of broadly comparable size, three of them within a quarter of each other, which is a completely different programme from the one on the slide and a completely different staffing conversation. On Equal Earth the same four polygons come out at their true relative sizes: continents look a little squashed toward the poles, Africa looks enormous, Greenland looks modest, and that unfamiliar impression is what correct looks like. Where the numbers came from matters more than where they were drawn. Areas belong in a coordinate system chosen for area — an equal-area projection, or better, measured geodesically on the ellipsoid so no projection is involved at all. Every serious toolchain offers it and it is usually a one-word change: `ST_Area` on geography rather than geometry in PostGIS, the ellipsoidal measurement setting in QGIS, `pyproj.Geod.geometry_area_perimeter`, `sf::st_area` on unprojected data. Reserve Web Mercator for what it is superb at, which is tiles, bearings and local shape, and never let a figure that came out of it wear the word “area” without a note saying so. Then say which projection the map is in, in the caption, the way an axis carries its units — a map without that line is a chart whose scale is a secret. The check takes five seconds and works on anything: ask which CRS the area was measured in, and if the answer is the one the map is drawn in and the map is a web basemap, the number is too big by sec² of wherever the thing sits. It is worth knowing how far this reaches beyond a table of square kilometres. Dots, bins and choropleth shading all inherit the same stretch, so a heat map on Mercator hands high-latitude ground several times the ink per unit of whatever is being counted, before anyone has chosen a colour scale. And where the question is really a comparison — is this bigger than that — the honest move is to take it off the map entirely. Two shapes at different latitudes will never be comparable by eye. A sorted bar chart of the areas settles in a glance what a world map cannot settle at all.