How our data is built

FaIR is a climate model emulator, replicating the warming behaviour of more complex climate models without the computational complexity. It simplifies the Earth system to consist of four locations that each store carbon, which may be interpreted as the Earth's crust, the atmosphere and surface, the ocean mixing layer and the deep ocean. The levels of carbon in each layer are influenced by emissions, both human and natural. FaIR then calculates how these emissions translate into concentrations of greenhouse gas and aerosols using simple relationships, and combines them with estimates of other climate change drivers (such as cloud formation from aviation, solar variability and land use reflectiveness changes) to give a model of the total strength of the forcing imposed on the climate system. This is then used to calculate the change in the average Earth's temperature. The outputs are constrained to match both historic warming and the expected levels of future warming as set out by the Intergovernmental Panel on Climate Change (cross-chapter box 7 of the WG1 contribution to the Sixth Assessment Report, in chapter 5). We used FaIR version 1.6.4. For more details see Smith et al. 2018.

The Modular Earth System Model Emulator with spatially Resolved output (MESMER) is a statistical model that emulates the possible evolution of key climate variables over land areas for a given Global Mean Temperature (GMT) trajectory, by mimicking the behaviour from more computationally expensive Earth System Models (ESMs). Calibrated on existing scenario projections produced by ESMs, it combines two modules representing either the local forced response of the climate to increasing GMT or a statistical representation of the natural climate variability. These two aspects constitute a set of traits specific to each ESM, that can be captured by MESMER by calibrating on data from each ESM (i.e., ESM configuration) individually.

Its simplicity and flexibility allows it to produce robust estimates of future possible climate outcomes within minutes, even for scenarios that haven't been represented by ESMs. The current MESMER analyses are based on Beusch et al. (2020) and Beusch et al. (2022); for a full description of the data see Schwaab et al. (in preparation). For further information see here.

MESMER-M is the monthly downscaling module of MESMER, i.e. it produces results at monthly resolution based on MESMER results. It starts off by disaggregating the annual-level outputs of MESMER into their seasonal cycle, and further represents the effects of any remaining monthly natural climate variability. Similar to MESMER, MESMER-M is trained to produce scenario projections mimicking ESM-specific responses (i.e., ESM configurations) by calibrating on projection data from each ESM individually, The current MESMER-M analyses are based on Nath et al. (2022).

MESMER-X is a statistical model based on MESMER used to emulate key extreme climate variables over land areas for given GMT trajectories. Similarly as MESMER and MESMER-M, MESMER-X can be run in different configurations that each reproduce the response of a different ESM. Currently MESMER-X is able to represent local annual maximum temperatures (TXx, Quilcaille et al, 2022), annual average soil moisture, annual minimum of the monthly average soil moisture, and various indices related to the fire weather (see Quilcaille et al. 2023 and Quilcaille et al. 2023 for more information). MESMER-X relies on Generalised Extreme Value theory to represent the local response of these variables to rising GMT, and is also able to explore how they are further affected by natural climate variability. MESMER-X is calibrated on existing scenario projections from ESMs, to then reproduce the behaviour of key extreme climate variables under scenarios not generated by ESMs yet. Similar to MESMER and MESMER-M, it is calibrated on projection data from each ESM individually. The current MESMER-X analyses are based on Quilcaille et al. (2022) and Quilcaille et al. (2023).

The simulations of urban climate are performed with the urban boundary layer climate model UrbClim, designed to cover individual cities and their nearby surroundings at a very high spatial resolution. UrbClim consists of a land surface scheme containing simplified urban physics, coupled to a 3-D atmospheric boundary layer module. The latter is tied to synoptic-scale meteorological fields through the lateral and top boundary conditions, to ensure that the synoptic forcing is properly considered. The land surface scheme is based on the soil--vegetation--atmosphere transfer scheme of De Ridder and Schayes (1997) but is extended to account for urban surface physics. The main advantage of the UrbClim model is its high execution speed, while maintaining accurate results (about two orders of magnitude faster than full scale mesoscale models; García-Díez et al., 2016). A complete description of the UrbClim model can be found in De Ridder et al. (2015).

The heat impact metrics (i.e. ‘Population exposed to heatwaves’ and ‘Population exposed to moderate/high/very high/extreme heatstress’) are computed using the open-sourced and open-access natural hazard risk model CLIMADA (CLImate ADAptation). According to the IPCC methodology, risk is defined as the probability of an event occurring multiplied by its impact (or severity). The impact is calculated based on three components: hazard, exposure, and vulnerability. CLIMADA captures vulnerability with an impact function taking the hazard as an input and returning a quantification to which extent an exposure will be affected by the hazard due to vulnerability (Aznar-Siguan and Bresch, 2019). Then the final impact is calculated by multiplying the exposure to the output of the impact function. The detailed documentation of CLIMADA can be found in (Kropf et al., 2024).

GFDL-ESM2M is the latest version of the Geophysical Fluid Dynamics Laboratory (GFDL)'s Earth System Model (Dunne et al. 2012). Processes within the atmosphere, land, ocean and sea ice are each represented by a different component, while interactions between these components are also explicitly represented. The atmospheric component simulates the dynamics and composition of the Earth's atmosphere at a temporal resolution of 30 minutes to 3 hours depending on the considered variables and at a spatial resolution of 2° (latitude) × 2.5° (longitude). The land component is constituted of the LM3.0 model that represents water, energy and carbon fluxes in vegetation, soil or snow. The ocean model consists of the Modular Ocean Model version 4p1, which simulates physical ocean processes at a horizontal resolution of 1° (mid-to-high latitudes) to 0.3° (tropics), with 50 vertical layers.

We used the open-source Open Global Glacier Model (OGGM v1.6.1; Maussion et al., 2019, Maussion et al., 2024) to simulate individual glacier volume, area and runoff changes for the more than 200,000 glaciers worldwide (Randolph Glacier Inventory, v6). The term glaciers describes here all glaciers and ice caps outside the Greenland and Antarctic ice sheets (World Glaciers Explorer).

OGGM computes ice flow along a one dimensional glacier flowline, obtained from global digital elevation models and glacier outlines. Annual glacier mass balance (or glacier thinning rate, expressed in m water equivalent per year) is estimated with a temperature index melt model (Maussion et al., 2019). We calibrate the model to match glacier mass change observations averaged over 2000-2020 (Hugonnet et al., 2021) obtained with remote sensing, and use additional in-situ observations from the World Glacier Monitoring Service (WGMS) where available. The gridded monthly climate data used as reference for the 1979 to 2020 period is W5E5v2.0 (Lange and others, 2021). For the initialisation of the model to the 2020 glacier state, OGGM v1.6.1 relies on a dynamic spinup which iteratively searches for a 1979 glacier state and recalibrates the temperature index model to find a dynamically consistent model initialisation run which simultaneously matches (1) glacier area at the inventory date and (2) mass change observations.

For more information, please visit the model documentation website of the used OGGM version or the documentation of the OGGM standard projections.

The biodiversity information presented here is from the Wallace Initiative. The base Wallace Initiative individually modelled ~135,000 terrestrial fungi, plants, invertebrates, and vertebrates, at warming levels ranging from 1.5°C to 6°C, across 21 CMIP5 climate model patterns at a spatial resolution of ~20km x 20km based on occurrence data obtained from GBIF. More information on the overall project, results, modelling methodology, caveats, and uses can be found in a series of publications (Warren et al. 2013; Warren et al. 2018 a, b; Smith et al. 2018; Jenkins et al. 2021, Saunders et al. 2023, Price et al. 2024a). The data were also used for several figures and tables in Working Group II of the IPCC Sixth Assessment Report (AR6).
The individual species data were then aggregated into a metric called species richness remaining. This was calculated by dividing the number of species modelled as being present in a cell, based on future climate suitability, by the number of species in a cell according to current climate suitability. The number of species modelled makes it a reasonable proxy for the population as a whole. To standardize against specific warming levels, curves were generated for each cell allowing interpolation between modelled temperatures to calculate the percent species remaining at intervals of 0.1°C between 1.5° and 4°C.

The data were then elevationally downscaled to ~1km x 1km (Saunders et al. 2023, Price 2024b) to better understand which areas of each modelled 20km cell or pixel might be lost sooner or persist longer. In short, a given 50 km or 20 km cell is an average of the temperatures for all elevations within that cell (i.e., the average elevation). In areas with varied terrain, some areas will be warmer than the average and some will be cooler. Species in areas that are warmer than the average would be expected to potentially be more susceptible (exposed) to warming, while those in cooler areas would be expected to potentially be less susceptible (or be able to shift into these areas if they are currently too cool). Therefore, species within cooler areas within a climate ‘cell’ or ‘pixel’ would be expected to potentially be able to persist in that area longer.

The Wallace Initiative Species Richness Remaining Emulator (WISRRE) is a computational efficient tool that replicates the information on species richness remaining generated by the Wallace Initiative without the need to re-run ~135,000 species distribution models. Estimates of species richness remaining are generated by WISRRE relative to 1950-2000 for given temperature changes based on relationships derived from the Wallace Initiative.

OSCAR is a model of reduced-complexity that describes the interactions between large-scale components of the Earth system that relate to anthropogenic climate change. Its modules are calibrated to emulate the behavior of complex process-based models. OSCAR describes the temporal dynamic of key physical quantities through mass and energy balance. Among the models of its category, OSCAR is one of the most complex yet highly flexible, as sub-models can easily be isolated, or new equations plugged in.

As input, OSCAR takes an annual time series of emission of anthropogenic greenhouse gasses and other climatically active species (e.g. aerosol precursors), as well as time series of land use and land cover change drivers. As output, the model produces an annual time series of global temperature change (without stochasticity) and of any intermediate variable of the system (e.g. greenhouse gas concentrations). The outputs are constrained to match the historical observations. While OSCAR is firstly designed to provide a global perspective, a number of processes are differentiated at the regional scale (most notably, the land carbon cycle). The current OSCAR analyses are based on OSCAR v3.1. The projection for future peatland carbon emissions is achieved by coupling OSCAR to a newly developed peatland carbon emulator OSCAR-peat.

A northern peatland (>30°N) carbon module (OSCAR-peat) was developed to emulate peatland processes from five state-of-the-art process-based land surface models: LPJ-MPI, ORCHIDEE-PEAT, LPX-Bern, LPJ-GUESS and LPJ-GUESS_dynP (‘dynP’ for dynamic multi-peat layers). Each of these simulates the complex peat ecosystem differently, incorporating distinct approaches to representing peat hydrology, biogeochemistry, vegetation and soil thermal dynamics, which are critical drivers of feedback uncertainty. OSCAR-peat is forced by global temperature and CO2 emission anomaly, and simulates northern peatlands’ carbon cycle change, including peatland CO2 emissions, CH4 emissions, Carbon stock change and other carbon cycle related processes.

The macroeconomic damage function from Burke et al. (2015) is an empirical relationship between changes in country-level temperatures and economic growth. Burke et al. (2015) establish a quadratic dependency of temperature on long-term GDP growth across different countries. Productivity is maximized at an annual average temperature of 13°C.

MAGICC is a reduced complexity model that captures the key components of the Earth and climate system such as the atmosphere and ocean, the carbon and methane cycles, anthropogenic aerosol chemistry and sea level rise (SLR). It is emissions-driven, calibrated to emulate the behavior of more complex process-based models, and comes with a probabilistic model setup, providing information not only about our best estimate of future climate change, but also the uncertainties that arise along the causal chain from emissions to climate response from interactions between the Earth system’s many key climate components. The model is used in its AR6-consistent set-up MAGICCv7.5.3 (Forster et al. 2021), with MAGICC-SLR providing component-wise GMSLR estimates, sitting within the AR6 assessed GMSLR ranges (Nauels et al. 2025).

MAGICC-SLR is calibrated to reproduce process-based sea level rise (SLR) projections for all key climate-driven components: thermal expansion, global glacier mass changes, surface mass balance and solid ice discharge from the Greenland and Antarctic ice sheets, in addition to the non-climate-driven land-water storage contribution. MAGICC-SLR has been updated to reflect more recent process understanding (Nauels et al 2017a, Nauels et al 2017b). The Greenland ice sheet’s components have been updated to capture projections in line with the IPCC AR6 assessment (Nauels et al. 2025.). The Antarctic ice sheet's solid ice discharge component captures projections that simulate a very rapid Antarctic ice mass loss (Edwards et al. 2019), in line with the IPCC-AR6 low likelihood, high-impact storyline under high emission scenarios. The land water storage component has been revised to reproduce the IPCC AR6 assessment GMSLR and account for different population dynamics, assuming a statistical relationship between the main subcomponents of land water storage (dam impoundment and groundwater extraction) and population growth (Turner et al 2023). For more details on the underlying assumptions and reference datasets, see Nauels et al. 2025.