The six bars in metres, and the three things a metre meant
Showing the misleading chart
A sensor-selection slide we drew ranks six earth-observation platforms by spatial resolution in metres, every figure lifted from the operator’s own specification page, on one linear axis from zero with every value printed — and across the six rows “metres” names three different things. Landsat’s 15 m is one band of eleven, and that band carries no colour. Sentinel-1’s 10 m is a grid step, not a resolution: what it resolves is 20.4 m by 22.5 m, covering 4.59 times the ground of the Sentinel-2 pixel its bar ties with. And MODIS, a third finer than VIIRS on the slide, is a third coarser band for band. Nothing is drawn wrong; the unit is the problem.
01The claim
Six platforms, one unit, one axis: metres on the ground. Every figure is the operator’s own published spatial resolution — USGS and NASA for Landsat, ESA for Sentinel-1 and Sentinel-2, NASA for MODIS, NOAA for VIIRS, Planet for PlanetScope. The axis is linear and starts at zero, every bar’s value is printed beside it, and nothing is indexed, rebased, logged or truncated. Lower is better, and the six span 3 m to 375 m — a range of 125 to 1. Read-out for the desk: pair Sentinel-2 with Sentinel-1, because both are 10 m, so the radar fills the cloudy days at no loss of detail. Treat Landsat as the same tier — 15 m is within 50% of both, so mosaic the three freely. And take MODIS over VIIRS for the daily continental product: 250 m against 375 m is a third finer for the same revisit.
02The trick
Every number on the slide is the operator’s own, the axis starts at zero, the values are all printed, and no bar is drawn a pixel wrong. Nothing is exaggerated and no axis is bent. The unit is the problem. Every length on a bar chart is an assertion that the rows are counting the same thing in the same way, and across these six rows “metres” is doing three different jobs. One: the ground sampling distance of an instrument’s finest bands, which is what Sentinel-2’s 10 m, Landsat’s 15 m, MODIS’s 250 m and VIIRS’s 375 m are. Two: the pixel spacing of an output grid, which is a sampling interval and not a resolving distance at all, which is what Sentinel-1’s 10 m is. Three: the pixel size a product was resampled to after orthorectification, which is what PlanetScope’s 3 m is. Three answers to three different questions, laid end to end on one axis under one word. Take the rows in turn. Landsat 8/9 carries eleven bands, and 15 m describes exactly one of them: band 8, panchromatic, 0.50–0.68 µm, a single grey channel. The seven reflective OLI bands a land-cover classifier works from — bands 1 to 7 — are 30 m. Band 9 is 30 m too, and is the cirrus channel, sited in a water-vapour absorption feature precisely so that the ground reads dark; USGS does not even carry it into the Collection 2 Level-2 surface reflectance product. The two TIRS thermal bands are acquired at 100 m and delivered resampled to 30 m. So the bar the desk laid alongside Sentinel-2 is drawn from the one band of eleven that carries no colour. Band 8 earns its place — pan-sharpening the 30 m stack with it is routine, and 15 m is genuinely better for boundaries — but it is the one band of eleven you cannot classify from on its own, and it is the one the chart chose to represent the instrument. Sentinel-1 is the quietest of the three, because its number is not a resolution in any sense. An IW GRDH product is sampled onto a 10 × 10 m grid, and ESA publishes the resolution separately: 20.4 × 22.5 m for IW1, 20.3 × 22.6 for IW2, 20.5 × 22.6 for IW3. Multi-looking is half of why, and ESA prints the other half in the same table: the looks are five in range and one in azimuth, so the 20.4 m across the range dimension is five samples averaged to suppress speckle, while the 22.5 m across the other is simply what a TOPSAR burst resolves, looks or no looks. Both are perfectly ordinary and perfectly documented things for a SAR product to do, and neither is 10 m. Its bar and Sentinel-2’s are the same length; the ground under them is not. That IW1 cell covers 459 m²; the Sentinel-2 pixel its bar ties with covers 100. Same length, four and a half times the ground. Sentinel-2’s own 10 m is honest as far as it goes, and it goes four bands of thirteen: six more are 20 m and three are 60 m, and the red-edge and SWIR bands are in the 20 m six — which is where the burn indices live, NBR and dNBR both needing the 2.19 µm SWIR, along with NDMI and the whole red-edge family. NDVI and EVI, by contrast, are 10 m throughout, which is the honest half of Sentinel-2’s headline figure. The pattern holds at the coarse end. MODIS’s 250 m describes 2 bands of 36 — five are 500 m and twenty-nine are 1,000 m. VIIRS’s 375 m describes 5 of 22, the rest being the sixteen M-bands and the Day/Night Band at 750 m. Which produces the finding that survives every version of the picture: the two wide-swath instruments change places. MODIS leads by a third on the slide, 250 m against 375 m. Median band against median band it trails by a third, 1,000 m against 750 m — and in ground covered that median MODIS pixel is 1.78 times the VIIRS one, 1,000,000 m² against 562,500 m². Same two instruments, same published figures, opposite ranking, and what decided which way round they went was whether the chart took each instrument’s best band or its typical one. The median is our statistic, over the instrument’s band list, and a band list is a design decision as much as a capability — MODIS carries twenty-nine bands at 1 km largely because it carries a lot of atmosphere and ocean channels. Pick instead the band you would actually use for land and you get a third answer again, which is rather the point. There is also a fourth job the word is doing that the slide does not mention: every figure on it is a nadir figure, and the two wide-swath instruments leave nadir at very different rates. MODIS’s 1 km pixel grows to roughly 4.8 by 2 km at the edge of its scan, about ten times the ground. VIIRS aggregates detector samples on board — three to one near nadir, two to one further out, one to one at the edge — specifically to stop that, and its 750 m pixel reaches only about 1.6 km. The instrument that looks worse on the slide is the one built so that its metre travels. Then there is the arithmetic sitting underneath all of it, which is not the area illusion and is worth keeping distinct from it: nothing here is drawn wrong, and every bar is exactly proportional to its own number. The unit itself is the side of a square. So a ratio read off the axis is the square root of the ratio in ground covered — 10 m against 30 m reads as three and is nine, 100 m² against 900 m² — and one MODIS 1 km pixel holds ten thousand Sentinel-2 10 m pixels. A chart that answers “how much sharper” in metres is answering in the square root of what an analyst actually buys. (The operators publish the figures; both drawings are ours, and the desk, the read-out and the recommendation on the first are invented.)
03The fix
One panel per definition. Measured, spaced, resampled — three axes, because three questions. The redraw does it by dropping the headline figure altogether and drawing every band of every instrument as a dot on one logarithmic axis, ticked at every √10 step, with the figure the slide used ringed in red and the median band ticked in black. The ring then sits to the left of the tick on every one of the six rows, and that distance — between the band a specification leads with and the band in the middle of the instrument — is the whole of the story. On two of the rows there is no dot under the ring at all: Sentinel-1, because 10 m is not a resolution the instrument has, and PlanetScope, because 3 m is a delivery grid rather than a measurement, its eight bands sitting out at the published 3.7 m. Dots rather than bars, because a log axis can encode a position and never a length. Underneath it, two panels answer the two questions the slide got wrong. The first puts ground area on a linear axis from zero, which is what an analyst is really buying — the pale bar what the slide’s metre implies, the solid bar the ground each measurement is actually drawn from: Sentinel-2’s headline pixel covers 100 m² and its median band 400; Sentinel-1’s bar implies 100 m² and its resolution cell covers 459, overlapping its neighbours by design rather than tiling; Landsat’s panchromatic 15 m implies 225 m² and its multispectral bands cover 900. MODIS and VIIRS run clean off that axis at 1,000,000 m² and 562,500 m², which is said on the panel rather than quietly cropped. The second draws MODIS and VIIRS twice, once on the slide’s figure and once on the median band, and the pair changes places between the two. In general: before putting a spec-sheet number on an axis, ask what a single unit of this actually is, and ask it once per row. Where the answer differs — a best band against a typical one, a grid step against a resolving distance, a delivered pixel against a measured one — the lengths have stopped being comparable, and one panel per definition beats one axis with a footnote. Then plot the band you will actually use rather than the one the specification leads with; for land cover that is Sentinel-2’s 20 m against Landsat’s 30 m, which is a real comparison, and a much closer one than the slide’s 10 against 15. Print beside each row how many bands are at the figure quoted and what the rest are, the way you print a unit — “4 of 13”, “1 of 11”, “2 of 36” is one line, and it is the line no specification page will write for you. The same trap waits wherever an industry publishes one number per product and different vendors compute it differently: camera megapixels against sensor size, model context windows counted in tokens of different vocabularies, storage throughput quoted at different queue depths, battery life measured on different test loops. The unit is the same word every time. That is what makes it a chart you can draw at all, and what makes it a chart nobody checks.