The heat map that paints its hottest hour darkest

Dark navy facilities-dashboard slide, masthead “Peak Load Desk · Campus Energy Services · Thermal & battery dispatch review · Phoenix, Arizona · Calendar year 2025”, headlined “Every hour of the year on one map — and the stress band runs through the mild hours”. A standfirst says there are 8,760 hourly air-temperature values averaged into one cell for each hour of the day in each month, 288 cells with every value in exactly one of them; that the colour scale below the map is linear and unbroken and runs from the coldest cell to the hottest, 3.60 °C to 41.83 °C, with nothing binned, capped, smoothed or set aside; and that the bright band is wide, sits either side of the mild hours, and that 281 of the 288 cells read lighter than the darkest cell of the afternoon block. The main panel is a heat map labelled “Mean 2 m air temperature, °C · hour of day (columns) × month (rows) · ERA5-Land reanalysis · 2025”: twenty-four columns of clock hours 00 to 23 across, twelve rows of months January to December down, drawn on the jet rainbow colour map. January and December run deep blue; the spring and autumn afternoons and the summer nights are cyan, green and vivid yellow; and the middle of the summer — June, July and August from about noon to seven in the evening — is a block of orange deepening to dark red at its centre. A horizontal colour bar beneath the map is ticked 5, 10, 15, 20, 25, 30, 35 and 40 and captioned “°C · minimum cell 3.60, maximum cell 41.83”, with a note that the scale is linear, has no bins and no cap, and that every one of the 8,760 hourly values is inside exactly one cell, 28 to 31 values per cell. A table headed “The year, month by month · °C” gives each month’s coolest hour, the hour it falls at, the monthly mean, the warmest hour and the hour it falls at: January 3.6 at 08:00, mean 11.3, 18.6 at 16:00; February 8.7 at 07:00, 17.6, 24.9 at 16:00; March 10.1 at 07:00, 17.9, 24.3 at 16:00; April 13.7 at 06:00, 22.7, 29.4 at 16:00; May 19.3 at 06:00, 27.8, 34.0 at 16:00; June 25.0 at 06:00, 33.6, 40.3 at 16:00; July 28.1 at 06:00, 35.4, 41.1 at 16:00; August 28.9 at 06:00, 36.0, 41.8 at 16:00; September 24.4 at 07:00, 30.6, 35.9 at 16:00; October 16.1 at 07:00, 24.1, 30.7 at 16:00; November 11.6 at 07:00, 18.6, 25.1 at 15:00; December 7.8 at 08:00, 14.6, 22.3 at 15:00. A second table, “Five of the brightest cells on the map”, lists July 06:00 at 28.07 °C, April 13:00 at 27.91, May 22:00 at 27.93, September 02:00 at 27.69 and June 04:00 at 27.37, each with a swatch of the vivid yellow they are drawn in, captioned that the brightest cells are the ones the eye finds first and these are five of them. Down the right-hand side, a gold-bordered card carries “281 / 288” over “hour-cells inside the elevated band — brighter than the map’s darkest afternoon”. A card headed “Read-out for the facilities board” says the load does not peak where the calendar says it should, that the bright band runs along the shoulder hours and the shoulder months while the August afternoons sit at the dark end of the scale alongside the January nights, and that two hard edges frame the band with a broad flat map between them. A “Dispatch note” card says to hold the battery for the bright band, let it ride through the dark blocks, and book the plant-room maintenance window for August, 15:00 to 18:00, because on this map it is the calmest cell of the year. A card headed “Why a rainbow scale” argues that a full spectrum uses the whole visible range so the eye has more to work with than a single-hue fade — more distinguishable steps and a colour name for every level — that it is the standard engineering map, and that readers are accurate at looking a value up against its key. A card headed “What we did not do” says no axis is truncated because there is no axis to truncate, nothing is binned so no bin edge was chosen, no cell is dropped, no series is indexed, no value is smoothed, and the scale is printed under the map with its two ends marked. A card headed “Definition — the elevated band” defines it as cells whose colour reads lighter than the darkest cell of the afternoon block, notes that 281 of 288 qualify, and says the band is therefore reported by its edges rather than its extent. A card headed “What a cell is” explains that one cell is the mean of that clock hour across that month, 28 to 31 hourly values, with columns as local clock hours 00 to 23 and rows as the twelve months, January at the top. A final card, “Basis of measurement”, names ERA5-Land hourly 2 m air temperature at 33.4 °N 112.1 °W, elevation 333 m, local time, 1 January to 31 December 2025, via the Open-Meteo historical weather API. Three ticked boxes run along the foot: “Linear, unbroken scale”, “Every value plotted” and “One source, one place, one year”. A footnote gives the reanalysis, the retrieval date, the coordinates and the grid point, records that Open-Meteo statistically downscales to a 90 m elevation model and that these are reanalysis values — model output for the grid cell, not instrument readings from a weather station — names the colour map as matplotlib 3.11.1 jet applied linearly between the minimum and maximum cell, and says the slide is a demonstration drawn by us in the manner of a facilities dashboard, that the desk and the dispatch note are invented, and that every temperature on it is real. — Showing the misleading chart

The same data on a cream background, kicked “The same 288 numbers · measured off the drawing · ERA5-Land 2 m air temperature · Phoenix, 2025” and headlined “The map’s brightest cells are 28 °C. The hottest hour is 41.8 °C.” A standfirst grants that every number on the dashboard is right, the scale linear and unbroken and no cell missing, and says what is wrong is the order the colours arrive in: lightness is the one channel with an order everybody already agrees on — hue has none until a convention supplies one — and jet’s lightness is not monotone, climbing from dark blue through cyan to a peak in the yellow at 28.0 °C and then falling away into dark red, so the hottest hour of the year is painted darker than a January night, 281 of the other 287 cells are lighter than it, and 19,222 of the 41,326 pairs of cells are painted in the wrong lightness order; redraw the same array on a ramp whose lightness only ever climbs and the picture rights itself without a number moving. The main panel repeats the twenty-four by twelve grid on the viridis ramp, dark purple through blue and green to yellow, with the hottest cell — August 16:00 at 41.83 °C — ringed in black; its colour bar is ticked 5 to 40 and captioned that the scale is linear from the coldest cell to the hottest, with a note that lightness rises with temperature from end to end so the hottest block is the brightest thing on the page. Below it, under “Print either map in black and white · the same cells, lightness only”, the two maps appear again converted to their lightness alone: the jet version shows a bright band running through the middle with both ends dark, captioned that two hours of the year 34.8 °C apart come out the same grey, and the viridis version keeps the summer block as the brightest thing on the page. Under “And as a reader with deuteranopia sees them · Viénot, Brettel & Mollon (1999) simulation”, the same two maps are simulated: the jet version becomes a blue-and-yellow map rather than a grey one, captioned that one degree buys ΔE00 0.37 in one place and 14.97 in another, while the viridis version keeps lightness climbing end to end at a per-degree spread of ×4.1 rather than ×40.4. The middle column carries two line charts drawn from the ramps themselves. “The ruler the eye actually reads · lightness against value” plots CIE lightness L* against cell temperature for both maps: viridis rises in a near-straight line from L* 14.9 to L* 90.9, while jet arches, marked “coldest cell: L* 12.9” where it starts, “jet is brightest at 28.0 °C (L* 96)” at its peak and “hottest cell: L* 25.4” where it ends. “How much colour one degree buys, across the scale” plots the CIEDE2000 distance between the colour at a temperature and the colour one degree warmer: jet spikes to 17.08 at 16.6 °C and drops to 0.46 at 7.8 °C, while viridis stays between 1.94 and 4.05 end to end. A note records that both panels are measured in CIE L* and CIEDE2000, sampled every 0.02 °C, that ΔE00 is built for small differences so the large values are indicative, and that the finding is the ratio across the scale — 37:1 on jet against 2:1 on viridis. A table headed “Two pairs of cells, about a degree apart each” gives January 13:00 at 16.72 °C against April 08:00 at 17.79 °C, 1.07 degrees apart, drawn at 18.08 ΔE00 per degree in jet and 4.33 in viridis; and February 07:00 at 8.74 °C against December 08:00 at 7.83 °C, 0.91 degrees apart, drawn at 0.51 in jet and 2.49 in viridis — per degree of air, jet drawing the first pair 36 times louder than the second, against a factor of 1.7 on viridis. A table headed “Five of the cells the jet map paints brightest” lists July 06:00 at 28.07 °C, April 13:00 at 27.91, May 22:00 at 27.93, September 02:00 at 27.69 and June 04:00 at 27.37 with their jet lightness values of 95.9, 95.6, 95.6, 95.4 and 95.0, their jet and viridis swatches, and how far short of the year’s hottest hour each falls: 13.8, 13.9, 13.9, 14.1 and 14.5 degrees. A short code panel headed “The one-line version” strikes through imshow(a, cmap="jet"), scale_fill_gradientn(colours = rainbow(20)) and d3.interpolateRainbow and replaces them with imshow(a, cmap="viridis"), scale_fill_viridis_c() and d3.interpolateViridis. Eight cards run down the right. “Two cells, 34.8 °C apart, the same shade” notes that January 03:00 at 6.74 °C and August 17:00 at 41.51 °C sit at L* 27.6 and 27.5 on the jet map so a photocopy cannot tell them apart, while on viridis they are L* 22.1 and 90.3. “But everyone knows red means hot” grants the convention, says it is why jet survives on temperature maps, and says it rescues the two ends and nothing in between, since nothing tells a reader whether cyan outranks green or green outranks yellow, and that on latency, error, pressure or dollars there is no convention left to lean on. “Not strategic binning” separates the two: no bin edge was chosen here, the scale being continuous, linear and unbroken — binning is a decision about where to cut, this is about which colours the ramp hands out along the way. “Rainbows are not all bad” says Ware, Stone and Szafir make the case in IEEE CG&A (2023) and that part of it is awkward for this page: readers are accurate at looking a single value up against a rainbow key, and the fast stretches separate values a single-hue ramp would flatten — what a rainbow is poor at is the job this map is doing, ranking a whole field at a glance. “Swapping in a nicer rainbow is not the fix” reports that turbo is far smoother than jet, a speed ratio of ×4.7 against ×37.0, but its lightness still turns over in the middle and on this grid it puts 24,766 of the 41,326 pairs in the wrong lightness order, more than jet does. “Two checks, ten seconds each” says to desaturate the picture or print it, and if the map stops making sense the colours were carrying work the lightness was not — then to run a colour-vision simulation, which is a different test, because dichromats keep a blue–yellow axis and greyscale is not what they see. “Not a default any more — but still everywhere” notes that matplotlib has defaulted to viridis since 2.0 and MATLAB to parula since R2014b, so jet had to be typed on that slide, and that rainbows still arrive unasked in GIS packages, older ParaView, thermal-camera firmware, Excel’s three-colour scale and a few JavaScript libraries. “Where you meet this” lists correlation and confusion matrices, spectrograms, GIS rasters, FEA and CFD plots, thermal cameras, dashboard heat grids, and every sparkline-sized tile too small to carry a legend. A summary table, “The three ramps, measured over this range”, gives for jet, viridis and turbo the lightness at the coldest cell (12.9, 14.9, 12.0), at the hottest cell (25.4, 90.9, 24.5), the highest lightness anywhere (95.9, 90.9, 90.9), whether lightness only ever climbs (no, yes, no), the slowest and fastest ΔE00 per °C (0.46–17.08, 1.94–4.05, 2.54–11.94), the ratio (×37.0, ×2.1, ×4.7) and the pairs painted in the wrong lightness order out of 41,326 (19,222, 0, 24,766). A gold-ruled callout at the foot reads “Colour is an axis, and this one has no tick marks,” and says a ramp is an exchange rate between a quantity and an appearance which, unlike an axis, prints neither its units nor its rate; so choose it for the job — one hue, light to dark, for magnitude, or a multi-hue ramp built to keep lightness monotone, which is what viridis, cividis, magma and Crameri’s Scientific colour maps are for — keep a diverging pair with a neutral middle for data with a real zero to diverge about, check it rather than trusting it by converting the ramp to greyscale, print the scale with numbers on it, and say which map you used the way you would name a unit. A footnote gives the reanalysis, the API, the retrieval date, the coordinates and grid point, the downscaling caveat and the fact that these are model output rather than instrument readings, the 8,760 values with no gaps averaged into 288 cells of 28 to 31 values each in local time with no daylight saving, the note that the 288 cells make 41,328 pairs of which two are exact ties leaving 41,326 with an order to get wrong, the three colour maps as taken from matplotlib 3.11.1 and applied linearly between 3.60 °C and 41.83 °C, the colour arithmetic (CIE L* and CIEDE2000 in sRGB under a D65 white point, with the per-degree figures comparing the colour at t with the colour at t plus one degree, sampled every 0.02 °C), the Viénot, Brettel and Mollon dichromacy simulation, and a line saying that both drawings are ours, that the facilities desk on the first is invented, and that every temperature on both is real. — Showing the misleading chart

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A year of hourly air temperature, 288 cells, one linear unbroken scale — drawn on the jet colour map. Its brightest cells are the 28 °C ones; the hottest hour of the year, at 41.83 °C, comes out darker than a January night. 281 of the other 287 cells are painted lighter than it, and 19,222 of the 41,326 pairs of cells are in the wrong lightness order. Nothing is binned, capped or smoothed: the ramp simply spends its lightness out of order.

ERA5-Land hourly 2 m air temperature (Copernicus Climate Change Service / ECMWF), retrieved for 33.4484 °N, 112.0740 °W via the Open-Meteo Historical Weather API; colour maps from matplotlib 3.11.1, 2025Added August 30, 2026

01The claim

Every hour of the year on one map. 8,760 hourly air-temperature values for one place, averaged into one cell for each hour of the day in each month — 288 cells, with every value in exactly one of them and 28 to 31 values behind each. The colour scale sits under the map, linear and unbroken, running from the coldest cell to the hottest, 3.60 °C to 41.83 °C. Nothing is binned, so no bin edge was chosen. Nothing is capped, smoothed, indexed or set aside, and there is no axis here to truncate. Read the map for where the building works hardest, and the answer is not the one the calendar would give: the bright band runs along the shoulder hours and the shoulder months, and the August afternoons sit at the dark end of the scale, alongside the January nights. 281 of the 288 cells read lighter than the darkest cell of the afternoon block. Two hard edges frame the band and the map is broad and flat between them. The five brightest cells on the page are July at 06:00, April at 13:00, May at 22:00, September at 02:00 and June at 04:00. Dispatch note: hold the battery for the bright band, let it ride through the dark blocks, and book the plant-room maintenance window for August, 15:00 to 18:00 — on this map it is the calmest cell of the year. And why a rainbow? Because a full spectrum uses the whole visible range, so the eye has more to work with than a single-hue fade: more distinguishable steps, and a colour name for every level. It is the standard engineering map, and readers are accurate at looking a value up against its key.

02The trick

Every number on that slide is right and the audit comes back clean, because the usual crimes are not available here: there is no axis to truncate, no bin edge to gerrymander, no series to index and no cell to leave out. The scale is linear, unbroken, printed, and stretched exactly once across the data. What is wrong is the order the colours arrive in. A colour ramp is an axis — it converts a quantity into an appearance and asks the reader to convert it back — and lightness is the one channel with an order everybody already agrees on. Hue has none until a convention supplies one, and jet does not spend its lightness in order. Measured as CIE L*, it climbs from 12.9 at the coldest cell, through the cyans, to a peak of 95.9 at 28.0 °C, and then falls away into the dark reds, reaching 25.4 at the hottest cell of the year. So the brightest cells on that map are the 28 °C ones — July at 06:00, April at 13:00 — every one of them 13.8 to 14.5 degrees short of the year’s peak; 281 of the other 287 cells are painted lighter than the 41.83 °C August afternoon; and of the 41,326 pairs of cells with an order to get wrong, 19,222 are painted in the wrong lightness order. Print it in black and white and January 03:00 at 6.74 °C and August 17:00 at 41.51 °C — 34.8 degrees apart — come out at L* 27.6 and 27.5, the same shade. The rate is wrong as well as the direction. Equal steps of data buy wildly unequal steps of colour: one degree of air is worth ΔE00 17.08 across the cyan edge at 16.6 °C and 0.46 in the blues at 7.8 °C, a 37:1 spread across one scale. On the real cells that comes out as January 13:00 and April 08:00, 1.07 degrees apart and drawn at 18.08 units of colour per degree, against February 07:00 and December 08:00, 0.91 degrees apart and drawn at 0.51 — the same air, thirty-six times louder in one place than the other. That is what makes the two “hard edges” the dashboard is scheduling around: they are places where the ramp accelerates, not places where the air does anything. And the broad flat middle is the same mechanism running the other way. Yes, everyone knows red means hot — but the convention rescues the two ends and nothing in between, since nothing tells a reader whether cyan outranks green or green outranks yellow, and that is where most of this map lives. Put the same ramp on latency, error, pressure or dollars and there is no convention left at all. One more reader to keep in mind: simulated for deuteranopia, jet’s per-degree spread widens from 37:1 to 40:1, and the distance between its green middle and its red end collapses from ΔE00 88 to 50. (Both drawings are ours, the facilities desk on the first is invented, and every temperature on both is real — ERA5-Land reanalysis values for the grid cell, which is to say model output rather than instrument readings from a weather station.)

03The fix

Let lightness carry the order, and the picture rights itself without a number moving. The same 288 cells on viridis run from L* 14.9 at the coldest to L* 90.9 at the hottest with lightness climbing the whole way, so not one of the 41,326 pairs is out of order, the summer block is the brightest thing on the page, and the ratio between the loudest degree and the quietest falls from 37:1 to 2:1 — the two cell pairs above land at 4.33 and 2.49 units of colour per degree instead of 18.08 and 0.51. For magnitude the general rule is one hue, light to dark, or a multi-hue ramp built so that lightness only ever climbs: viridis, cividis, magma, or the Scientific colour maps Crameri publishes and which he, Shephard and Heron argue for in their 2020 Nature Communications paper on the misuse of colour. Keep a diverging pair with a neutral middle for data with a real zero to diverge about, and never put a hue at the midpoint. In practice it is one argument: cmap="viridis" for cmap="jet", scale_fill_viridis_c() for scale_fill_gradientn(colours = rainbow(20)), d3.interpolateViridis for d3.interpolateRainbow. Then run two checks, ten seconds each, because they catch different things. Desaturate the finished picture, or print it: if the map stops making sense, the colours were carrying work the lightness was not. Then simulate colour-vision deficiency and look again — that is a separate test, not the same one, because a dichromat is not a monochromat: they keep a full blue–yellow axis, which is exactly why the deuteranope panel above renders jet in blues and yellows rather than in greys. Give the ramp the courtesies an axis gets: a legend with numbers on it, both ends labelled, and the name of the map in the caption the way you would print a unit, because a chart whose colour scale is a secret is a chart whose units are a secret. Where a specific level genuinely matters — a threshold, a setpoint, a limit — draw a labelled contour on it rather than hoping a colour boundary happens to land there, since a boundary the ramp invented will be read as one you meant. Three things this is not. It is not strategic binning: no bin edge was chosen here, the scale being continuous and linear throughout — binning is a decision about where to cut, this is about which colours the ramp hands out along the way. It is not a complaint about defaults, either: matplotlib has shipped viridis as its default since 2.0 and MATLAB parula since R2014b, so on that slide jet had to be typed. Where rainbows still arrive unasked is GIS packages, older ParaView, thermal-camera firmware, Excel’s three-colour scale and a few JavaScript libraries — and in every chart inherited from a colleague who typed it years ago. And it is not a case for banning rainbows. Where a rainbow accelerates it separates values a single-hue ramp would flatten, and readers are accurate at looking a single value up against a rainbow key — Ware, Stone and Szafir set that case out in IEEE Computer Graphics and Applications in 2023, sixteen years after Borland and Taylor’s “Rainbow Color Map (Still) Considered Harmful”. What a rainbow is poor at is the job this particular map is doing, which is ranking a whole field at a glance. Know which task you have. And do not assume a smoother rainbow settles it: measured over this same range, turbo is far smoother than jet, at a speed ratio of ×4.7 against ×37.0, but its lightness still turns over in the middle, and on this grid it puts 24,766 pairs in the wrong lightness order — more than jet does.