The Methodology

Slope shapes where humans can build, farm, and lay infrastructure. Steep terrain raises construction and transport costs, restricts mechanised agriculture, and limits population density. Although humans live across a wide range of topographies — from Andean valleys to Tibetan plateaus to Himalayan villages — there is a hard upper bound on slope above which sustained settlement and agriculture become prohibitive.

Slope is computed from the GMTED2010 1 km global mean elevation product (Danielson & Gesch 2011, USGS OFR 2011–1073) using Horn's algorithm (Horn 1981, Proc. IEEE 69:14) and aggregated as cell-mean to the 30 km analysis grid. 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, hard cliff — structurally infeasible for sustained settlement); linear interpolation in between. The earlier 3-class FAO/UNESCO scheme (Soils Bulletin 32) used 8°/16° breakpoints, which over-penalised mid-slopes where settlement remains common (Cohen & Small 1998, PNAS 95:14009 documents the cell-mean masking effect). The 30° cliff is the more defensible engineering limit. Topography is time-invariant across all epochs.

Soil determines whether a cell can support agriculture and the food security of its population. Modern food systems redistribute calories globally, but sustained habitation still depends on local soil productivity, especially during disruption to long supply chains. Permafrost soils additionally shift role under warming — frozen permafrost is structurally unbuildable and biologically inert, while thawing permafrost transitions to waterlogged, methane-emitting, foundation-unstable conditions that remain hostile to settlement and 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 (very severe constraints) → 0.15; linear interpolation in between. Cliffs: class 7 (FAO's own label "unsuitable, ineffective" — desertic or glacial soils with no agricultural potential) and class 0 (non-soil / inland water) both → 0. For 2100 and 2300 epochs, permafrost zones projected to thaw under CMIP6 SSP5-8.5 mean annual temperature are reclassified to a marginal-equivalent score of 0.5 (thermokarst / variable fertility / unstable foundation; Chadburn et al. 2017). HWSD SQ1 measures nutrient chemistry rather than aridity, so sand-desert cells (e.g. central Sahara) are often not class 7 — they're constrained by water rather than nutrient deficiency, and the composite captures that via the CDD and water factors.

Without renewable water supply, no human community sustains itself. Water stress — the ratio of withdrawals to renewable supply — captures whether a catchment's hydrology can support continued use. Catchments under severe stress face declining reliability, salinisation, ecosystem collapse, and forced migration; arid catchments with low absolute supply face the same outcome regardless of demand level. While irrigation, desalination, and inter-basin transfer can defer the constraint, they do not eliminate 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 is the cross-framework consensus for "stressed but managed" vs "severely stressed" used by UN SDG 6.4.2 and Wada et al. 2011 (Hydrol. Earth Syst. Sci. 15:3785). The baseline raster (Aqueduct Global Maps 2.1, 2010-vintage climatology) is held constant across all three epochs — this isolates climate-driven changes in other factors against a fixed hydrological baseline.

Human thermoregulation depends on evaporative cooling. Wet-bulb temperature (T_w) combines heat and humidity into a single physiological-load metric — unlike dry-bulb temperature, it captures the actual cooling capacity available to the body. Above ~35 °C T_w, healthy adults cannot dissipate metabolic heat even at rest in shade with abundant water; sustained outdoor activity is impossible. Where annual peak T_w crosses this ceiling, an area becomes biologically uninhabitable regardless of cooling adaptation, since the same survivability limit applies indoors during power outages.

Wet-bulb temperature is computed from CMIP6 monthly maximum temperature and ERA5 monthly relative humidity using the Stull (2011) approximation; the raster reports the annual maximum T_w at each cell — the worst single hour of an average year. Both future epochs draw from the CMIP6 SSP5-8.5 long-term-extension subset — the 8 models that ran SSP5-8.5 monthly tasmax past 2100 (ACCESS-ESM1-5, CESM2-WACCM, CanESM5, EC-Earth3-Veg, GISS-E2-1-G, GISS-E2-1-H, MIROC-ES2L, UKESM1-0-LL). The 2100 epoch uses the 2081–2100 mean of annual max from this subset; 2300 uses 2281–2300. The production central estimate uses an ECS-screened 6-model subset, dropping CanESM5 (ECS = 5.62 K) and UKESM1-0-LL (5.36 K) — both above AR6 WG1's "very likely" 5.0 K upper bound for equilibrium climate sensitivity (Sherwood et al. 2020). This follows the explicit recommendation of Hausfather et al. 2022 (Nature 605:26) for high-warming projections: the unscreened 8-model mean inherits the high-ECS tail and runs ~+1.4 °C high in 2300 T_w relative to the screened estimate. The unscreened 8-model raster is retained as a sensitivity output. This whole structure replaces an earlier uniform +8 °C scaling on the 2100 raster, which over-warmed the tropics relative to polar latitudes and was unphysical for a metric where the binding 35 °C ceiling lives in the tropics. Humidity is now per-epoch for 2100 and 2300, drawn from each model's own hurs (relative humidity) field in the same 8-model long-extension ensemble (CESM2-WACCM excluded from the humidity ensemble — its ESGF replicas are presently unreachable; 7-model RH ensemble for those epochs). The 2014 baseline still uses ERA5 reanalysis humidity. Holding ERA5 RH constant under several K of warming was the previous methodology and is the fallback when the per-epoch raster is missing; that approach overestimated tropical T_w and underestimated arid mid-latitude T_w by 1-2 K (Buzan et al. 2015). Scoring is a continuous ramp: T_w ≤ 24 °C → 1.0; ≥ 35 °C → 0 (cliff); linear in between. The 35 °C cliff is the Sherwood & Huber 2010 (PNAS 107:9552) thermodynamic survivability limit — beyond it, healthy adults cannot dissipate metabolic heat even at rest in shade. Currently-populated humid metros (Mumbai 28°C → score 0.64; Houston/Lagos 30-31°C → 0.36-0.45) sit well below the cliff today. The 2300 long-extension ensemble puts ~37 % of land past 35 °C annual peak T_w under the ECS-screened ensemble (vs ~49 % unscreened) — that's the dominant driver of the 2300 cliff geography.

Inter-model spread. The wet-bulb maps shown here are the equal-weighted ensemble mean of the ECS-screened set; the underlying model-to-model spread is held back as separate spread rasters and made visible below. Across the screened models the 17-83% inter-model "likely range" of annual-max T_w over land has a median width of 2.7 °C at 2100 and 4.7 °C at 2300 — widest over the high northern latitudes (10.5 °C median over the boreal Arctic at 2300, where Arctic-amplification disagreement compounds with sea-ice retreat) and narrowest over the tropics (2.2 °C median at 30°S-30°N, 2300) — the same tropical band where the 35 °C cliff actually binds. The decision-relevant question is which cells cross 35 °C: at 2300, 32.6 % of land has the 35 °C cliff sitting inside the 17-83% inter-model range (cool model says habitable, hot model says lethal); 21 % is past the cliff even in the cool model and 54 % in the hot model. Read the production map as the centre of a wide envelope, not a point forecast.

Inter-model 17-83% likely-range width, T_w at 2300 (°C). Brighter cells indicate larger model disagreement; the boreal Arctic and central Asia carry the widest spread, while the tropical cliff zone is narrowest.

ClimWIP sensitivity. A separate sensitivity ensemble was built using the Knutti et al. 2017 / Brunner et al. 2020 ClimWIP weighting (performance against the project's observational anchor + pairwise-independence factor) — full per-model weights stored at output/04-WetBulb/climwip_weights.json. Not adopted as production. ClimWIP on this 5-model subset moves the 2300 cliff fraction up by ~4 percentage points (37.2 % → 41.3 %) by up-weighting EC-Earth3-Veg and downweighting the cooler GISS pair on within-family independence, which works against the ECS-screen we just adopted to reduce the hot-tail bias. A defensible production ClimWIP would require true ERA5 t2m+d2m references over 1995-2014 (the current anchor is a CMIP-derived raster) and ideally the unscreened 8-model set so independence weighting can act on real lineage redundancy. Equal-weighted remains production; ClimWIP is documented as a flagged sensitivity.

Two distinct wet-bulb limits matter and are easily conflated. The 35 °C cliff used here is the thermodynamic survivability ceiling (Sherwood & Huber 2010): the temperature beyond which a healthy human at rest in shade cannot dissipate metabolic heat at all, even with abundant water. A second, lower limit from Vecellio et al. 2022 (J. Appl. Physiol. 132:340) — the PSU HEAT empirical compensability ceiling — sits at 26-31 °C T_w for young, healthy, acclimatised adults; it is the boundary above which sustained exertion (e.g. agricultural labour, walking) cannot be thermally compensated, and is lower still for older adults, children, and people with cardiovascular conditions. Refugia commits to the 35 °C thermodynamic cliff because it is the harder physical limit, with the explicit caveat that this is conservative against the empirical compensability literature: the real habitability boundary for vulnerable populations is several degrees lower than the ceiling we cliff at.

Drought duration determines whether rainfed agriculture, livestock, and natural ecosystems persist through dry seasons. Long unbroken dry spells exhaust soil moisture, kill perennial vegetation, and disrupt food production cycles. While irrigation can partially mitigate, climate-driven CDD lengthening is a leading driver of regional agricultural collapse and out-migration, especially 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 matches the FAO/UNESCO "Extremely Arid + Arid" boundary in CDD terms — six unbroken dry months at which rainfed agriculture becomes infeasible. Note that 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.

Methodology note (2026-05-08). SPEI was prototyped as a replacement for CDD but produced an unintended regression: as a relative-anomaly index standardised against a reference period, SPEI cannot represent absolute aridity — Phoenix/Tehran/ Riyadh-class permanently arid cells score near "no drought" because they are not anomalously dry compared to their own climatology. CDD captures the absolute signal (Riyadh hits the 180-day cliff today) and was kept. The trade-off is that the 2300 epoch reuses the 2100 CDD raster (no Atlas projection past 2100), so dryness is frozen between 2100 and 2300 even as heat advances. A future iteration may use Aridity Index (P/PET, UNESCO thresholds) computed from the CMIP6 long-extension pr and tas rasters already cached, which preserves both absolute aridity and forward projection.

Inundation directly displaces populations and destroys infrastructure. Coastal sea-level rise progressively claims low-elevation areas as permanently lost to the sea; riverine flooding adds episodic destruction to floodplains, even in catchments that are otherwise habitable. Together they bound the lowlands where cities, agriculture, and dense settlement can persist — and historically, mass population displacement in this century has come predominantly from these two hazards.

Two flood hazards are combined into a single 3-class suitability mask, taking the worst classification at each cell. Coastal sea-level rise is keyed to the GMTED2010 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. 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 multi-millennial total-melt commitment of ~65 m from Antarctica + Greenland; Clark et al. 2016, Nat. Clim. Change; Van Breedam et al. 2020, Geosci. Model Dev.), 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 100-year return-period inundation depth: depth ≥ 1 m is unsuitable, 0.1–1 m is marginal, and < 0.1 m is suitable. The current epoch has no SLR component and applies only the riverine layer. Riverine depth at the future horizon is the per-pixel ensemble maximum across four CMIP5 GCMs (NorESM1-M, GFDL-ESM2M, HadGEM2-ES, IPSL-CM5A-LR) for the RCP 8.5 / 2080 horizon; the historical (WATCH) baseline is used for the current epoch, and the 2080 horizon is reused as a proxy for 2300 since no published Aqueduct projections run past 2080.