The Methodology

Slope limits where people can build and farm. Steep ground drives up construction and transport costs and rules out most mechanised agriculture, so population density falls off as terrain steepens. People settle a wide range of slopes, but above a certain grade sustained settlement and farming stop being practical.

Slope is computed on the native NOAA ETOPO 2022 30 arc-second grid (ice-surface topography + bathymetry, EGM2008 heights, NOAA NCEI, DOI 10.25921/fd45-gt74) using Horn's algorithm (Horn 1981, Proc. IEEE 69:14) with a per-row east-west pixel width scaled by cos(latitude). An earlier pass gave gdaldem one metres-per-degree constant for both axes, which understated the east-west gradient by 1/cos(latitude) (2× at 60°N) because a degree of longitude shortens toward the poles while a degree of latitude does not; the fix applies a separate, latitude-dependent pixel width to each row. Land membership comes from Natural Earth 10m land minus lakes, because the DEM's own sign is a poor coastline: ETOPO carries sea-floor and lake bathymetry, and genuine dry land such as the Dead Sea shore sits below 0 m. Ocean and lake pixels are excluded from every cell's slope mean and the output is NaN there (the earlier pass let sea-floor slope into ocean cells and wrote cells without data as 0°, i.e. flat). The Natural Earth coastline and the DEM disagree in places, so two documented rules reconcile them. First, land the polygon calls dry but the DEM puts more than 500 m below sea level, or more than 50 m below sea level within 3 pixels of the sea, is treated as ocean. No dry land on Earth lies below about −430 m (the Dead Sea shore) and none beside the sea lies below −50 m, so these pixels are islet or fjord polygons drawn over sea floor, which would otherwise put an invented cliff against the sea surface. Second, an ocean pixel enters the slope stencil at its DEM height where that height is above sea level (at 0 m otherwise), capped at the highest adjacent land pixel. Ocean on high ground (ice-shelf fronts, fjord walls) then forms no invented drop beside land, and an ETOPO spike offshore cannot tower over a low coast. Per-pixel slope is then averaged over the land pixels in each 30 km analysis cell. The resulting continuous slope-in-degrees raster is scored as a piecewise-linear suitability ramp: ≤ 4° → 1.0 (flat to gently undulating, fully habitable for any settlement or agriculture); ≥ 30° → 0 (steeply mountainous, structurally infeasible for sustained settlement); linear interpolation in between. An earlier 3-class split used roughly 8%/16% slope-class boundaries (≈ 8° / 16°), which over-penalised mid-slopes where settlement remains common; the single 30° threshold is the more defensible engineering limit for sustained settlement. The threshold is resolution-dependent: it describes per-pixel terrain, and averaging over a 30 km cell smooths out the steepest pixels, so a cell mean stays well below the steepest ground inside it. At 30 km the measured maximum cell-mean slope on soil-class land is 26.6°, so no land cell reaches the threshold at this resolution and the factor acts only through its 4–30° gradient; the zero-score limit becomes active at finer grids. At 30 km, 43 High Arctic land cells (soil class 6) contain no Natural Earth land pixel centre and so have no slope value; the composite scores them on the remaining factors. Topography is time-invariant across all epochs.

Soil sets how much food a place can grow locally. Global trade moves calories around, but local productivity still matters for sustained habitation, and it matters most when long supply chains are disrupted. Permafrost is a special case, and warming cuts both ways on it: frozen, it is unbuildable and biologically inert; thawing, it becomes waterlogged and unstable and starts venting methane. Neither state supports settlement or agriculture.

Soil-quality classes from the FAO/IIASA Harmonized World Soil Database (HWSD v1.2, 1 km native, "soil quality 1 — nutrient availability" derivative) are scored on a continuous gradient: class 1 (no/slight constraints, best) → 1.0; class 6 (permafrost) → 0.15; linear interpolation in between. Cliffs: class 7 (inland water bodies) and class 0 (ocean / no soil) both → 0 in the scoring function, and the soil-class land mask removes both from the composite, so in practice the soil cliff never applies to a cell inside the land mask (those class-0 and class-7 cells receive no habitability score). For the 2100, 2200 and 2300 epochs, class-6 (permafrost) cells where the end-of-century (2081–2100) CMIP6 SSP5-8.5 ensemble mean of monthly daily-maximum temperature exceeds 0 °C are reclassified to a marginal-equivalent score of 0.5 (one static thaw map; no thaw at the current epoch) — thawed permafrost is thermokarst-prone, of variable fertility, and foundation-unstable. Chadburn et al. (2017) constrains where permafrost thaw occurs; the 0.5 score is our judgement, not their result. HWSD SQ1 measures nutrient chemistry rather than aridity, so sand-desert cells (e.g. central Sahara) are not cliffed by the soil factor. They're constrained by water rather than nutrient deficiency, and the composite captures that via the CDD and water factors.

No community lasts without renewable water. Water stress — withdrawals as a fraction of renewable supply — indicates whether a catchment can keep meeting demand. Severely stressed catchments lose supply reliability and degrade their groundwater and ecosystems; very dry catchments reach the same point on low supply alone, whatever their demand. Irrigation, desalination, and inter-basin transfer can postpone the limit but not remove it.

Water availability is encoded as the WRI Aqueduct Baseline Water Stress score (BWS_s, 0–5), the ratio of total annual withdrawals to available renewable supply per catchment. Scoring is continuous and has no cliff: BWS_s ≤ 1 (Low) → 1.0; ≥ 5 (Extremely High) → 0.05 (steep penalty but not zero); linear ramp in between. We deliberately omit the cliff because Aqueduct's "Extremely High" tier conflates two physical cases — engineered settlements drawing on long-distance transfers or aquifer mining (Phoenix, Cairo, Riyadh) and arid no-water-use cells — and we don't want to falsely flag the engineered-habitable cases as uninhabitable. The 40% withdrawal-to-availability boundary between "stressed but managed" and "severely stressed" is the long-standing Falkenmark / UN SDG 6.4.2 convention that Aqueduct's own tiering adopts; Wada et al. 2011 (Hydrol. Earth Syst. Sci. 15:3785) maps global water stress consistent with it. The baseline raster (Aqueduct Global Maps 2.1, 2010-vintage climatology) is held constant across all four epochs — this isolates climate-driven changes in other factors against a fixed hydrological baseline.

The body sheds heat by sweating, and sweat only cools if the air can absorb the moisture. Wet-bulb temperature (T_w) folds heat and humidity into one number for how much cooling capacity is left, which dry-bulb temperature alone misses. Near 35 °C T_w a healthy adult can no longer shed metabolic heat even resting in shade with water at hand, so it is a hard physiological ceiling rather than a comfort threshold. An area whose annual peak T_w crosses it is unsurvivable outdoors, and indoors too whenever the power fails.

T_w is computed from CMIP6 monthly maximum temperature (tasmax, Amon) and monthly relative humidity via the Stull (2011) approximation; the raster reports the annual maximum of the monthly-mean T_w at each cell — the hottest month's value, not a true daily/sub-daily peak. This monthly construction understates the real annual-max T_w: we measured the gap against daily tasmax (MIROC-ES2L, 2081–2085) at a tropical-cliff-zone median of ~0.9 °C (larger, 2–6 °C, in dry mid-latitude interiors where T_w sits far below the cliff and the gap doesn't matter). The reported cliff-exceedance fractions are therefore conservative lower bounds. The 2014 baseline and the future epochs both use monthly tasmax, so this smoothing applies consistently across epochs. A daily-resolved ensemble is not cleanly possible here (daily humidity is unpublished for two of the six production models), so the monthly construction is retained and disclosed rather than half-corrected. Future epochs draw from the SSP5-8.5 long-term-extension subset (8 models reaching 2300). Production central estimate uses an ECS-screened subset (6 models at 2200 and 2300, 5 at current and 2100), dropping CanESM5 (ECS ~5.6 K) and UKESM1-0-LL (~5.3 K; Meehl et al. 2020) — both above AR6 WG1's "very likely" 5.0 K upper bound (Hausfather et al. 2022). Humidity is per-epoch from each model's own hurs (same-month hurs from each screened model at every epoch, the current baseline included; ERA5 is a validation and fallback input only). Scoring is a continuous ramp: T_w ≤ 24 °C → 1.0; ≥ 35 °C → 0 (cliff); linear between. The 2300 ensemble puts 23.3 % of land area past the cliff under ECS-screened.

Two-limit framing. Two distinct wet-bulb limits matter and are easily conflated. The 35 °C cliff is the thermodynamic survivability ceiling (Sherwood & Huber 2010). A second, lower limit from Vecellio et al. 2022 (PSU HEAT; J. Appl. Physiol. 133:340) — the empirical compensability ceiling — sits near 31 °C T_w in humid conditions for healthy young adults (and lower, ~25–28 °C, in hot-dry conditions); sustained exertion is thermally uncompensable above it, and the limit is lower for vulnerable populations. Refugia cliffs at 35 °C because it is the harder physical limit; the real habitability boundary for vulnerable populations is several degrees lower.

Uncertainty framing. Per-model spread is real (4.0 °C median p17-p83 inter-model width over land at 2300 across the six ECS-screened models; the 35 °C cliff sits inside the member range on 24 % of land area, 18.5 % of land cells), widest at high latitudes and narrowest in the tropical cliff zone. Full quantification is documented in research/white-paper/wetbulb-uncertainty-quantification.md; read the production map as the centre of a wide envelope, not a point forecast.

The published composite scores the ensemble-mean wet-bulb temperature. Each screened model (five through 2100, six from 2200) is also scored separately, with every other factor unchanged. At 30 km the composite falls inside the range of those model composites on all land at every epoch. That result follows from the construction and confirms the inputs match. It does not measure how well the models sample climate uncertainty, and the range reflects wet-bulb disagreement only. Inside it the composite usually sits on the more habitable side (median position 0.60 today, 0.70 by 2200). The heat cliff is the exception: in 2300, 13.7 % of land scores zero because the ensemble-mean wet-bulb reaches 35 °C while at least one model stays below it.

Cold is the one factor that eases under warming. Far-northern Russia, interior Greenland, the Canadian Arctic Archipelago, and interior Antarctica are uninhabitable today because their mean annual temperature sits below the cold end of the human climate niche (Xu et al. 2020): the growing season is short, the ground stays frozen, and heating is costly. Warming under SSP5-8.5 raises mean annual temperature in those regions and lifts the cold limit. A composite with no cold-side term would see only the habitable mid-latitudes shrinking and would miss the high-latitude land that conditionally opens up.

The factor is computed from the CMIP6 SSP5-8.5 long-extension monthly tas (mean surface T) for the 6-model ECS-screened production ensemble (the same six screened models as wet-bulb; for tas CESM2-WACCM is available at every epoch, so MAT is 6-model throughout while wet-bulb is 5-model at current and 2100). MAT per cell per epoch = annual mean of monthly tas over the 20-year window ending at each epoch (current: 2015–2034). Anchor (score 1.0) at MAT ≥ 5 °C — a calibration set on the cold side of the ~11–15 °C peak of the Xu et al. 2020 human climate niche. Below the anchor the score falls on a linear ramp, (MAT + 5) / 10, floored at 0.05. The ramp meets the floor at -4.5 °C, so it bottoms out near -5 °C, a proxy for the boreal/tundra ecotone informed by the Beck et al. 2018 Köppen mapping (Köppen ET is a warmest-month rule, so -5 °C MAT is our proxy, not a Köppen-defined threshold). The score then holds at the soft floor of 0.05 down to and including -15 °C (Yakutia, Nunavut, northern Fennoscandia all have demonstrably small but non-zero population, and a hard zero here would be empirically wrong). The hard cliff (score 0) applies only below -15 °C (continuous tundra, ice cap).

Anticipated pushback. A critic might claim this "makes the polar regions look too habitable under SSP5-8.5". Warming can only raise the cold score (it is monotonic in MAT). A formerly-frozen cell that warms from below -15 °C into the floor band moves from 0 to 0.05, and it reaches the 1.0 anchor only at 5 °C. The composite is a geometric mean, so that cell still has to pass soil, water stress, flooding and wet-bulb. On soil, permafrost (HWSD class 6) scores 0.15 until the end-of-century (2081–2100) CMIP6 SSP5-8.5 ensemble mean of monthly daily-maximum temperature exceeds 0 °C, when it is reclassified as thawed and scores 0.5. One static thaw map is applied at 2100, 2200 and 2300; there is no thaw at the current epoch and no thaw lag. The boreal wildfire pressure that follows warming is a known gap.

Current-epoch baseline note. Local cache lacks CMIP6 historical 1995–2014 tas; we use the SSP5-8.5 2015–2034 mean as the "current" baseline. ~+0.3 °C warm bias vs the historical baseline; doesn't change which cells fall in the cliff or soft-floor bands.

How long the dry season runs unbroken decides whether rainfed farming, livestock, and native vegetation survive it. A long enough dry spell drains soil moisture and kills perennials before the rains return. Irrigation offsets this where it exists, but the lengthening of dry spells under warming is a recognised driver of agricultural failure and out-migration, most acutely in continental interiors and the subtropics.

The maximum number of consecutive dry days (CDD, days with precipitation < 1 mm) per year is sourced from the IPCC AR6 Interactive Atlas (Santander Meteorology Group) ensemble export of CMIP6 projections under SSP5-8.5: 1995–2014 historical mean for the current epoch, 2081–2100 mean for the 2100 epoch, with 2300 reusing the 2100 raster since no published Atlas projection extends past 2100. Scoring is a continuous ramp: ≤ 30 days → 1.0 (no meaningful dry-season constraint); ≥ 180 days → 0 (cliff); linear between. The 180-day cliff is an internal calibration — roughly six unbroken dry months, the point at which rainfed agriculture becomes infeasible, and broadly the dry-spell length of arid/hyper-arid zones (FAO/UNESCO aridity is itself defined on the Aridity Index and growing-period length, not on consecutive dry days, so this is an approximate correspondence, not an FAO-defined CDD threshold). The published ETCCDI annual-max-CDD climatology smooths extreme single-year stretches and caps around 260 days even for Atacama-class deserts, so the 180-day cliff (rather than 200+) is calibrated to the actual data envelope while remaining physically defensible.

Flooding displaces people and destroys infrastructure outright. Sea-level rise takes low-lying coast permanently; riverine flooding hits floodplains episodically, including otherwise-habitable ones. Together they set the lower-elevation limit on where dense settlement and farming can hold, and they account for much of this century's flood-driven displacement to date.

The two flood hazards enter the composite differently, and since this revision their scores are multiplied in the single flood slot (the worse of the two classes used to be taken). Coastal sea-level rise stays a hard cliff, because permanent inundation drowns low coast outright. Riverine flooding is graded, since river floods are episodic and recede (see below). The two masks are still unioned, worst class first, into the 3-class display shown above, which the biodiversity-risk layer reads as its drowning input. Coastal sea-level rise is keyed to the NOAA ETOPO 2022 DEM. For the 2100 epoch: cells with elevation ≤ 1 m are unsuitable (deep inundation under the IPCC AR6 likely range of ~0.6–1.0 m by 2100 under SSP5-8.5), 1–5 m are marginal (high-tide and storm-surge exposure), and > 5 m are suitable. The 2200 epoch sits between the two (≤ 3 m unsuitable, 3–30 m marginal). For the 2300 epoch we use a wider 65 m commitment marginal band: ≤ 5 m are unsuitable (within IPCC AR6 likely 1.7–6.8 m at 2300 under SSP5-8.5; Fox-Kemper et al. 2021), 5–65 m are marginal (encompassing the ~65 m total ice-volume sea-level equivalent of Antarctica + Greenland; the multi-millennial total-melt-commitment framing follows Clark et al. 2016 and Van Breedam et al. 2020), and > 65 m are suitable. The 65 m number is a commitment ceiling, not a 2300 prediction — it bounds where coasts are guaranteed safe over the long run, not where the 2300 shoreline actually sits.

Riverine flooding uses the WRI Aqueduct Floods v2 100-year return-period inundation depth at its native 1 km resolution, converted to a graded severity: depth ≤ 0.15 m scores severity 0, depth ≥ 1.5 m scores severity 1, linear in between. 0.15 m is the Rentschler, Salhab & Jafino (2022) exposure threshold, the World Bank boundary for "no significant risk to life"; 1.5 m is the World Bank "very high risk" boundary, where the JRC depth-damage functions (Huizinga et al. 2017) put residential damage at half or more of full loss on every continent. Severity is averaged over the Aqueduct pixels inside each analysis cell that carry data, so a cell keeps its true flooded share; the earlier method took one bilinear point sample per cell. Where Aqueduct has no coverage at all, severity is NaN (no data) and the riverine reading drops out: the flood slot then takes the SLR score where one exists, and otherwise the composite is scored on the remaining factors. Read as zero severity, an uncovered cell would score a false 1.0. The future horizon takes the median across four CMIP5 GCMs (NorESM1-M, GFDL-ESM2M, HadGEM2-ES, IPSL-CM5A-LR), replacing the per-pixel maximum used before this revision. IPCC AR6 WGII Ch. 4 reports river-flood change as a multi-model median, and with four models the median is the mean of the middle two, so one outlier GCM no longer decides the score. The historical (WATCH) baseline serves the current epoch; the RCP8.5/2080 horizon is reused for 2100, 2200 and 2300, since no published Aqueduct projection runs past 2080.

Severity converts to a score of 1 − severity × 0.5, so it never drops below a floor of 0.5 even at full severity, and that score multiplies with the SLR class score for the flood slot: inland, where the SLR score is 1, the flood slot equals the riverine score outright, and in the SLR marginal band the two hazards compound. The same severity drives the 3-class display mask above (≥ 0.10 marginal, ≥ 0.50 unsuitable, the 0.285 m and 0.825 m depths under the ramp), which still feeds the biodiversity-risk stage further down this page. Why not a cliff. Deep floodplains are among the most densely settled land on Earth: 23 % of humanity lives in RP100 zones flooded past 0.15 m (World Bank 2020), and settlement in the highest-hazard flood zones grew 122 % from 1985 to 2015, against 85 % for settled land overall (Rentschler et al. 2023). A single depth threshold that zeroed the whole composite treated that settled land as uninhabitable, which the evidence does not support, so riverine flooding now only lowers the score. Known limits. The Aqueduct hazard layer carries no flood defences, so the depth is undefended everywhere, protected floodplain and unprotected alike. Coastal land cells whose bilinear-resampled DEM value is at or below 0 m never receive the SLR cliff, since the DEM threshold treats DEM ≤ 0 m as void; under this revision those cells take the riverine reading on its own. This is registered as a follow-on: a land-masked DEM mean, the same fix already applied to slope, would close the gap.