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. The 2100 epoch uses the 2081–2100 mean of annual max from a 7-model CMIP6 SSP5-8.5 ensemble. The 2300 epoch uses the 2281–2300 mean of annual max from the 8-model CMIP6 SSP5-8.5 long-term-extension subset (ACCESS-ESM1-5, CESM2-WACCM, CanESM5, EC-Earth3-Veg, GISS-E2-1-G, GISS-E2-1-H, MIROC-ES2L, UKESM1-0-LL) — the only CMIP6 models that ran SSP5-8.5 monthly tasmax past 2100. This replaces an earlier uniform +8 °C scaling on the 2100 raster, which over-warmed the tropics relative to polar latitudes and is unphysical for a metric where the binding 35 °C ceiling lives in the tropics. ERA5 humidity is held constant across epochs; this is defensible at the global mean (Held & Soden 2006) and conservative for tropical projections where near-surface RH stays roughly stable. 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 ~half the planet's land past 35°C annual peak T_w — that's the dominant driver of the 2300 cliff geography. Lower thresholds in the physiological literature (e.g., Vecellio et al. 2022's 30 °C empirical compensability ceiling) describe sustained exposure and are not applied to annual-peak framing, where real-world heat is intermittent and people actively avoid worst-hour exposure.

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.

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 (5 m SLR scenario): cells with elevation ≤ 1 m are unsuitable (deep inundation), 1–5 m are marginal (high-tide and storm-surge exposure), and > 5 m are suitable. For the 2300 epoch (65 m multi-millennial commitment ceiling: Antarctica ~58 m + Greenland ~7 m + other glaciers): ≤ 5 m are unsuitable, 5–65 m are marginal, and > 65 m are suitable. 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.