The Model for Economic Tipping point Analysis

META is an advanced, social-cost integrated assessment model. It was originally designed to carry out a model-based meta-analysis of the effects of tipping points on the economic costs of climate change, although it can be run without tipping points. It is particularly suited to estimating the social cost of carbon (SCCO2) and the social cost of other greenhouse gases like methane (SCCH4). The model simulates greenhouse gas emissions, temperature and sea-level rise, and market and non-market damages at the country level, as well as the effects of eight climate tipping points that have been studied in the climate economics literature.

META was introduced in Dietz, S., Rising, J., Stoerk, T. and Wagner, G., 2021. Economic impacts of tipping points in the climate system. Proceedings of the National Academy of Sciences, 118(34), p.e2103081118. [https://doi.org/10.1073/pnas.2103081118]. This paper used the 2021 version of the model, which is available at https://github.com/openmodels/META-2021/.

META has been updated gradually to produce the analysis for new papers. A new Antarctic Ice Sheet module was added in Dietz, S. and Koninx, F., 2022. Economic impacts of melting of the Antarctic Ice Sheet. Nature Communications, 13(1), p.5819.

The current version of META was used in Stoerk, T., Rising, J., Shindell, D. and Dietz, S., 2025. Global methane action pays for itself at least six times over. Science, 390(6772), p.eadu7392. The model is fully described in the Supplementary Information of this paper.

This version of the model is implemented in Mimi [https://www.mimiframework.org/], an integrated assessment modeling framework developed in Julia [https://julialang.org/]. The model code consistent with the Dietz et al. (2021) paper is available in both Excel and Mimi formats.

Please cite the paper corresponding to the META version you are using.

The following directories are used for the Mimi model:

• data: Input parameters and validation outputs (under data/benchmark).
• src: The model code. The scripts directly contained in this directory support various types of analyses, with internal model code in subdirectories. Specifically, the model components are under src/components and additional functions are in src/lib.
• test: Unit tests, for each component, for the system-wide results, and for the Monte Carlo system.

Please note that all code is designed to be run with the working directory set to a subdirectory of the repository (e.g., src or you can create a subdirectory analysis). Installation time for META on a standard desktop computer should be in the hours, while the speed of results production depends on the number of Monte Carlo draws. Monte Carlo sample sizes of 1,000 likely take around 15 minutes per run for a single calculation (such as the global SC-CO2 in any one given pulse year). Computing time can be expected to increase to hours and possibly days on a standard laptop once all computations and larger Monte Carlo sample sizes of 10,000 and beyond required for a full research project are run.

The full model is constructed using full_model(...), defined in src/MimiMETA.jl. The full_model function can be called with no arguments to use the default construction, otherwise override the defaults with the following arguments:

• rcp: Emissions scenario; one of RCP3-PD/2.6, RCP4.5 (default), RCP6, or RCP8.5.
• ssp: Socioeconomic scenario; one of SSP1, SSP2 (default), SSP3, SSP4, SSP5.
• tdamage: Temperature damages; one of none, distribution, pointestimate (default), low, or high.
• slrdamage: Sea-level rise damages; one of none, distribution, mode (default), low, or high.
• nonmarketdamage: Non-market damages; may be false (to not use, default) or true.
• saf: Surface albedo feedback calibration; may be false (to not use) or Distribution mean (default)
• pcf: Permafrost carbon feedback calibration; may be false (to not use) or one of Fit of Hope and Schaefer (2016), Kessler central value, Kessler 2.5%, Kessler 97.5%, Fit of Hope and Schaefer (2016) (default), or Fit of Yumashev et al. (2019).
• omh: Ocean methane hydrates calibration; may be false (to not use) or one of Whiteman et al. beta 20 years (default), Whiteman et al. uniform 10 years, "Whiteman et al. triangular, mode 10%, 10 years", Whiteman et al. beta 10 years, "Ceronsky et al. (2011), 1.784GtCH4 per year, beta", "Ceronsky et al. (2011), 7.8GtCH4 per year, beta", "Ceronsky et al. (2011), 0.2GtCH4 per year, beta", Whiteman et al. beta 20 years, Whiteman et al. beta 30 years, Whiteman et al. uniform 20 years, or "Whiteman et al. triangular, mode 10%, 20 years".
• amaz: Amazon dieback calibration; may be false (to not use) or one of Cai et al. central value (default), Cai et al. long, or Cai et al. short.
• gis: Greenland icesheet calibration; May be false (to not use) or one of Nordhaus central value (default), Robinson, Non-linear equilibrium function, Ice/SLR low, or Ice/SLR high.
• ais: (West) Antarctic icesheet calibration; May be "AIS" (default), "WAIS" (as implemented in Dietz et al., 2022) or "none" (not used).
• ism: Indian summer monsoon calibration; may be false (to not use) or Value (default).
• amoc: Atlantic meridional overturning circulation; May be false (to not use) or one of Hadley, BCM, IPSL (default), or HADCM.
• interaction: Tipping point interactions; may be false (to not use) or true (default).

There is also a base_model function which includes only the non-tipping-point calibration options.

A basic usage is as follows:

include("../src/MimiMETA.jl")
model = full_model(rcp="RCP4.5", ssp="SSP2")
run(model)
explore(model)

Other examples are shown in test/test_system_tp.jl (for the full model) and test/test_system_notp.jl (for the no-tipping-point model).

To run the model in Monte Carlo mode, run sim_full(...), which is defined in src/montecarlo.jl, using a model with all the relevant components.

The sim_full function takes the following parameters, all of which must be provided:

• model: A full Mimi model.
• trials: The number of Monte Carlo simulations.
• pcf_calib: May be "Kessler probabilistic" to draw stochastic parameters for the PCF model, or one of the options described in the deterministic use case.
• amazon_calib: May be "Distribution" to draw stochastic parameters for the Amazon dieback model, or one of the options described in the deterministic use case.
• gis_calib: May be "Distribution" to draw stochastic parameters for the GIS model, or one of the options described in the deterministic use case.
• wais_calib: May be "Distribution" to draw stochastic parameters for the WAIS model, or one of the options described in the deterministic use case.
• saf_calib: May be "Distribution" to draw stochastic parameters for the SAF model, or one of the options described in the deterministic use case.
• ais_used: Set to true if the AIS component is included; otherwise false.
• ism_used: Set to true if the ISM component is included; otherwise false.
• omh_used: Set to true if the OMH component is included; otherwise false.
• amoc_used: Set to true if the AMOC component is included; otherwise false.
• persist_dist: May be true to draw the level of temperature damages persistance stochastically, or false.
• emuc_dist: May be true to draw the level of elasticity of marginal utility stochastically, or false.
• prtp_dist: May be true to draw the level of pure rate of time preference stochastically, or false.

There is also a sim_base, which includes just the non-tipping-point parameters.

A basic usage is as follows:

include("../src/MimiMETA.jl")
include("../src/montecarlo.jl")
model = full_model(rcp="RCP4.5", ssp="SSP2")
results = sim_full(100, "Fit of Hope and Schaefer (2016)", # PCF
               "Cai et al. central value", # AMAZ
               "Nordhaus central value", # GIS
               "none", # WAIS
               "Distribution", # SAF
			   true, # AIS
			   true, # ISM
			   true, # OMH
			   true, # AMOC
               false, # persit
               false, # emuc
               false) # prtp

Other examples are included in test/test_montecarlo_tp.jl.

The src/scc.jl script includes functions that help with the calculation of the SCC, using the infrastructure within Mimi.

The current standard method is calculate_scc_mc which takes the following parameters (all given, in order):

• model: A version of the META model.
• preset_fill: A function to fill in parameters from a pre-computed Monte Carlo collection.
• maxrr: The number of Monte Carlos to perform.
• pulse_year: The year to add an additional pulse of CO2.
• pulse_size: The number of Gt to add.
• emuc: The elasticity of marginal utility to use.

A basic usage is:

include("../src/MimiMETA.jl")
include("../src/lib/presets.jl")
include("../src/scc.jl")
benchmark = CSV.read("../data/benchmark/ExcelMETA-alltp.csv", DataFrame)
model = full_model()
preset_fill(rr) = preset_fill_tp(model, benchmark, rr)
calculate_scc_mc(model, preset_fill, nrow(benchmark), 2020, 10., 1.05) # Runs 500 MC reps; ensure the value of `emuc` corresponds with the value of the same parameter in the component/module `utility.jl`.