The Refugia habitability index is a composite raster across seven environmental factors. Each factor is scored on a continuous gradient between a "fully habitable" anchor (score 1.0) and an established uninhabitability threshold (a hard cliff at score 0). Within the habitable band, scoring is graduated rather than binned — a boreal forest does not score the same as a Mediterranean climate the way a 3-class scheme would force. The composite at each cell is the geometric mean of the seven factor scores, but if any factor hits its cliff the cell is marked uninhabitable (composite = 0).
Each factor scores cells on a 0 – 1 scale. The ramps below show the colour of a cell's score from cliff (red, score 0) to fully habitable (green, score 1). Tick marks call out the values at which a cliff or anchor sits, and any intermediate breakpoint that's methodologically meaningful.
The climate-driven factors (wet-bulb temperature, drought, sea-level rise) are computed from a multi-model ensemble rather than any single climate model's projection. Above: each line is one CMIP6 SSP5-8.5 long-extension model's annual global cos(lat)-weighted mean tasmax anomaly relative to the 2015–2034 reference period, drawn from the cached monthly NetCDF on this machine. Hover a line to identify the model. The fan grows from a tight cluster near 2020 (all models still close to the historical baseline) to a 9–15 °C spread by 2300 — that spread is irreducible structural uncertainty about how sensitive the climate system is to forcing, and it is the central reason the habitability surfaces should be read as ranges, not point estimates.
The production central estimate for wet-bulb & humidity is the ECS-screened 6-model mean: CanESM5 (ECS 5.62 K) and UKESM1-0-LL (ECS 5.36 K) sit above AR6 WG1's "very likely" 5.0 K upper bound and inflate the multi-model mean by ≈ 0.9 °C at 2300 (Hausfather et al. 2022, Nature 605:26). Both hot models are still shown here (dashed red) for spread visibility but excluded from the central estimate. CESM2-WACCM is in the per-epoch ensemble means but drops from this trajectory plot because its run begins 2101, below the 2015–2034 baseline window. The broader CMIP6 SSP5-8.5 ensemble contains roughly 30 additional models that all reach 2100 but lack the long extension.
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 (BWSs, 0–5), the ratio of total annual withdrawals to available renewable supply per catchment. Scoring is continuous and has no cliff: BWSs ≤ 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 four epochs — this isolates climate-driven changes in other factors against a fixed hydrological baseline.
Human thermoregulation depends on evaporative cooling. Wet-bulb temperature (Tw) 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 Tw, healthy adults cannot dissipate metabolic heat even at rest in shade with abundant water; sustained outdoor activity is impossible. Where annual peak Tw crosses this ceiling, an area becomes biologically uninhabitable regardless of cooling adaptation, since the same survivability limit applies indoors during power outages.
Tw is computed from CMIP6 monthly maximum temperature and ERA5
monthly relative humidity via the Stull (2011) approximation; the raster reports
the annual maximum Tw at each cell — the worst single
hour of an average year. Future epochs draw from the SSP5-8.5 long-term-extension
subset (8 models reaching 2300). Production central estimate uses an
ECS-screened 6-model subset, dropping CanESM5 (5.62 K) and UKESM1-0-LL
(5.36 K) — 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 (5-model ECS-screened RH ensemble at 2100 / 2200 / 2300; the
2014 baseline still uses ERA5). Scoring is a continuous ramp: Tw ≤
24 °C → 1.0; ≥ 35 °C → 0 (cliff); linear between. The
2300 ensemble puts ~37 % of land 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) — the empirical compensability ceiling — sits at 26-31 °C Tw for healthy young adults; sustained exertion is thermally uncompensable above it, and the floor 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 (4.7 °C
median 17-83% inter-model width over land at 2300; 32 % of land has the
35 °C cliff sitting inside the 17-83% range), 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.
Cold is the only factor in the composite that gets better under warming. Today, far-northern Russia / interior Greenland / the Canadian Arctic Archipelago / interior Antarctica are uninhabitable due to short growing season, frozen soil, and the energy cost of heating — not because of any single climate variable they cross, but because their mean annual temperature falls below the lower edge of the human climate niche (Xu et al. 2020). As SSP5-8.5 warms the planet, MAT in these regions rises and the cold cliff lifts. Without a cold-side factor, the composite was one-sided: it tracked the contraction of currently-habitable mid-latitudes but missed the conditional unlocking of currently-cold-cliffed land.
tas (Amon) from ESGF for the 8 long-extension models; 6-model ECS-screened production ensemble (ACCESS-ESM1-5, CESM2-WACCM, EC-Earth3-Veg, GISS-E2-1-G, GISS-E2-1-H, MIROC-ES2L).
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
(same ensemble as wet-bulb). MAT per cell per epoch = annual mean of monthly tas,
20-year window centred on each epoch. Anchor (score 1.0) at
MAT ≥ 5 °C (lower edge of Xu et al. 2020 niche shoulder);
linear ramp to a cliff at -5 °C (boreal/tundra ecotone;
Beck et al. 2018 Köppen Dfc/Dfd → ET boundary); soft floor of
0.05 between -5 and -15 °C (Yakutia, Nunavut, northern
Fennoscandia all have demonstrably small but non-zero population — a hard
zero here would be empirically wrong); hard zero 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". The cold factor only removes a cliff — it does not add positive habitability. A formerly-frozen cell that warms past -5 °C still has to pass soil (HWSD permafrost-thaw cliff persists for decades after MAT crosses zero; IPCC AR6 WG1 Ch.9), water stress, flooding, and wet-bulb. 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.
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. 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: 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; 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 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.
Biodiversity is not a constraint on human habitability — humans live readily in biodiverse landscapes — but intact ecosystems are themselves an asset that climate-driven displacement threatens. As habitable land contracts under warming, remaining intact biomes face encroachment pressure from migrating populations, development, and agricultural expansion. The places that emerge as 21st-century climate refugia (boreal forests, montane regions, high-latitude wetlands) overlap heavily with the planet's last intact ecosystems. Modeling the spatial co-occurrence makes that conflict visible.
Until 2026-05 the biodiversity asset was held at the static 2020 PREDICTS BII baseline across all four epochs because no public gridded future-scenario BII raster exists (Newbold/De Palma & Purvis 2018 publish only country aggregates, not rasters). The asset has now been swapped to a per-epoch BII proxy derived from LUH2 v2.1 land-state grids (Hurtt et al. 2020). Per cell: natural-land fraction = primf + primn + secdf + secdn (primary forested, primary non-forested, secondary forested, secondary non-forested), 20-year mean centred on each epoch from the SSP5-8.5 v2.1f file (2015–2100) and the v2.1e extension (2100–2300). LUH2 is the only public gridded land-state product that natively reaches 2300, matching the wet-bulb long-extension ensemble. The proxy is narrower in concept than species-abundance intactness but moves in the same direction — Newbold et al. 2015 (Nature 520:45) attribute the dominant BII signal to land-use change, the variable LUH2 carries. Cross-validation: GLOBIO 4 MSA SSP5-RCP8.5 2050 (Schipper et al. 2020) is conceptually closer to BII (true species abundance) but is published only for one future epoch; a future iteration may bias-correct the LUH2 proxy against GLOBIO at 2050. BII is not multiplied into the habitability composite — under the redesigned biodiversity-risk methodology (see Biodiversity Risk — methodology below), the LUH2 natural-land fraction at 2020 is used as the frozen Ncurrent input to the encroachment-pressure term, while per-epoch LUH2 panels remain visible here as transparency on the SSP5-8.5 land-use trajectory itself.
The seven factors are scored continuously on [0, 1]. Each factor has two anchors: a "fully habitable" lower bound (below which → 1.0) and a hard cliff (above which → 0, where the factor crosses an established uninhabitability threshold). Linear ramp in between gives the gradient within habitability. Cliffs: slope ≥ 30° (alpine, structurally unbuildable), soil HWSD SQ1 class 7 (FAO "unsuitable, ineffective" — desertic/glacial soils with no agricultural potential) or class 0 (no soil), annual-max wet-bulb Tw ≥ 35 °C (Sherwood & Huber survivability ceiling), mean annual T ≤ -15 °C (continuous tundra / ice cap), consecutive dry days ≥ 180 (six unbroken dry months — rainfed agriculture infeasible, desert-margin classification), flood depth ≥ 1 m (RP100 riverine, or 5 m / 65 m SLR commitment for 2100 / 2300). Water stress is gradient-only — no cliff, since BWSs=5 conflates engineered settlements (Phoenix, Cairo) with arid no-use cells, and we don't want to falsely flag the former as uninhabitable. The composite is the geometric mean of factor scores unless any factor hits its cliff, in which case the cell is marked uninhabitable (0). Ocean and inland water bodies are masked out using slope-derived water detection.
Until 2026-05-11 the biodiversity-risk raster was computed as
habit_suit × BII_proxy. That formulation collapsed two
physically distinct pressures into one term — the human-encroachment
pressure that "places becoming habitable for humans" exert on intact
ecosystems, and the direct climate damage that biodiversity
itself takes (heat anomalies, drought, climate velocity, polar warming).
The redesign splits them, then combines via probabilistic OR:
bio_risk = 1 − (1 − encroachment) × (1 − climate_threat).
Each term is in [0, 1]; either pressure alone can saturate a cell, and
stacking pressures is monotonically worse than either alone without
double-counting (Tonmoy et al. 2014, WIREs Clim Change 5:775).
encroachment(epoch) = nuf(epoch) × Ncurrent, where nuf(epoch) is the cell-aggregated fraction of 1 km cells flipping from non-urban to urban between Chen et al. (2020)'s 2015 baseline and the target year, under SSP5 (matched to our SSP5-8.5 climate trajectory). Ncurrent is the LUH2 v2.1f natural-land fraction at 2020 (primf + primn + secdf + secdn) — frozen at 2020, not per-epoch. Using per-epoch N would let SSP5-8.5's own land-use trajectory convert those cells by 2300 and self-cancel the signal; we want the encroachment term to measure pressure on what is intact today and is becoming attractive to humans.
Chen 2020 publishes 1 km decadal urban-land projections through 2100. For 2200 and 2300 epochs we linearly extrapolate the cumulative cell-level newly-urbanized fraction (multiply by (year − 2015) / 85, where 2015 is the Chen-published baseline year), clipped to [0, 1]. Our pipeline's "current" epoch nominally anchors at 2014, a 1-year offset that is negligible (~1.2% of the 85-year extrapolation interval).
climate_threat = 1 − cliff-aware geometric mean of six biodiversity-specific factor scores, each in [0, 1]. Any factor at exactly 0 collapses the composite to 0 (climate_threat = 1). The factor set differs from the human-habitability composite — not all human-habitability factors apply to ecosystems, and the ones that do apply at different thresholds:
Adversarial pushback (pre-empted). (1) Aren't you double-counting drought? No — the human-hab CDD cliff (180 d) and the bio CDD cliff (120 d) live in two independent composites and are combined via probabilistic OR, which by construction does not double-count. (2) The BII proxy isn't BII. True — LUH2 natural-land fraction is land-cover intactness, not species-abundance intactness; this is disclosed in the asset section above. The Ncurrent 2020 baseline used here is the same proxy. (3) Climate velocity is scale-dependent. True (Burrows 2014, Methods); we publish at the native 30 km analysis resolution. (4) Encroachment assumes humans actually move there. True — this is a pressure surface, not a realised land-use trajectory. Chen 2020 SSP5 is itself a socioeconomic-driven projection, not observed migration. The companion realised-LUC layer is LUH2 v2.1f/v2.1e shown above. (5) Cold-loss as a threat is counter-intuitive. Boreal/Arctic biomes depend on cold; warming above +6 °C in a MAT ≤ 0 °C cell breaks the regime ecosystems are adapted to (Post 2009, Stirling 2012, Bjorkman 2018). (6) Why drop topography? Slope is a human-build constraint; biomes have already colonised steep terrain.
What the redesign does NOT capture (yet).
A Fire Weather Index factor (Van Wagner 1987; Abatzoglou 2019) is defined in
composite_utils.py but not yet wired in — it requires a
precipitation-on-grid preparation step deferred to a follow-on iteration. A
permafrost frost-index factor (Nelson & Outcalt 1987) is similarly framed
but deferred. Both are pure derivations from cached CMIP6 inputs — no external
downloads — and can be added to the climate_threat composite later without
changing the combination formula. ISIMIP3b burnt-area products would supply a
validation cross-check on the derived FWI but are not required.
The composite habitability raster describes where the planet remains liveable,
but not what stands to lose by its decline. The two paired surfaces here cross
habitability with the human population on one side, and combine projected urban
expansion with direct climate threat to intact ecosystems on the other.
Human Exposure = (1 − habitability) × population: a static-population
cartogram surfacing where today's population is concentrated in cells projected to lose
habitability.
Biodiversity Risk is the two-term redesign documented in the
methodology section above:
bio_risk = 1 − (1 − encroachment) × (1 − climate_threat). Encroachment
uses Chen et al. 2020 SSP5 urban-land projections multiplied by today's natural-land
fraction (frozen at LUH2 2020) — pressure on what is intact now and is
about to become attractive to humans. Climate-threat is a cliff-aware composite of
six biodiversity-specific factors (Tair anomaly, cold-loss, climate
velocity, water stress, drought, flood) at thresholds tighter than the human-hab
equivalents.
Exposure is not a migration projection. The climate-mobility literature (Black et al. 2013; Cattaneo & Peri 2016; Cundill et al. 2021) is unambiguous that the most climate-vulnerable populations are often least able to relocate — migration is expensive, and the same conditions that erode habitability also erode the resources needed to leave. A high-population × low-habitability cell may therefore contain trapped populations facing maximum exposure precisely because they cannot move, not displacement-prone populations on the verge of moving; this surface cannot distinguish the two. Population is also held at the 2020 WorldPop baseline, so the 2100 and 2300 panels read present-day settlement against future climate fields and should be interpreted as exposure cartograms, not forecasts of where people will actually live. No peer-reviewed migration projection exists at the 2300 horizon.