META 2021

The Model for Economic Tipping point Analysis

META 2021 is an advanced integrated assessment model (SC-IAM), designed as a model-based meta-analysis of the effects of tipping points on the social cost of carbon (SCC). The model simulates greenhouse gas emissions, temperature and sea-level rise, and market and non-market damages at the country level, and the effects of eight climate tipping points that have been studied in the climate economics literature.

META 2021 is introduced in; Dietz, Rising, Stoerk, and Wagner (2021): "Economic impacts of tipping points in the climate system", PNAS, 118(34), e2103081118. [https://doi.org/10.1073/pnas.2103081118]

See that paper and its supplementary information for further details. Please cite the paper when using META in your research.

Model versions

The repository contains two versions of the model, which produce identical results to high precision. The initial version of the model is implemented in Excel using the @RISK extension to perform Monte Carlo simulations. We have now produced a version implemented in Mimi [https://www.mimiframework.org/], an integrated assessment modeling framework developed in Julia [https://julialang.org/].

The Excel version is more user-friendly, but additional analyses may require the Mimi version. The Mimi version will be used for future developments.

Excel @RISK model

Installation and Use

It is recommended that you download this entire repository to use META, since the model relies on a number of linked files. You can do this at the Code link above or download a zip archive.

The main model is implemented as an Excel spreadsheet, which uses @RISK for Monte Carlo analysis. You should have @RISK installed to use META 2021.

To open the model, first load @RISK, and within @RISK load excel/META model July 2021.xlsx.

The model links to a number of supporting files. You should therefore also open the following files:

BHM betas v3pd.xlsx: Country-level damage function coefficients, derived from Burke et al. (2015).
National gdp per capita ppp.xlsx: Projected GDP per capita from the Shared Socioeconomic Pathways (SSPs).
National population.xlsx: Projected population totals from the Shared Socioeconomic Pathways (SSPs).

The first tab, Settings, allows you to activate tipping points, choose emissions and socioeconomic scenarios, and choose other settings. It also contains a dashboard, which provides an overview of your settings, including key parameters and sets of parameters (see below).

Input parameters and their uncertainty are defined in the Parameters tab. Cells that are intended to be changed, in order to switch from one parameter scheme to another, are shaded yellow.

All other tabs compute intermediate and final results, including global temperature rise (Temperatures column G), sea-level rise (SLR column D), country-level downscaled temperature (Pattern scaling), income levels after impacts (National cons per cap), and global social welfare (Welfare & SCCO2 calculator cell C2).

Contents of the Excel model

All model files are in the excel folder, and consist of:

META model July 2021.xlsx: The main model file (see Installation and Use).
API_NY.GDP.PCAP.PP.CD_DS2_en_excel_v2_126211.xls: World Bank historical GDP per capita.
API_NY.GNS.ICTR.ZS_DS2_en_excel_v2_41442.xls: World Bank historical savings rates.
API_SP.POP.TOTL_DS2_en_excel_v2_126122.xls: World Bank historical population totals.
BHM betas v3pd.xlsx: Country-level damage function coefficients, derived from Burke et al. (2015).
National gdp per capita ppp.xlsx: Projected GDP per capita from the Shared Socioeconomic Pathways (SSPs).
National population.xlsx: Projected population totals from the Shared Socioeconomic Pathways (SSPs).

The main model includes links to the other files in the excel folder.

Computing the social cost of carbon

To calculate the SCC, run the model without the additional pulse of CO2 (set Settings cell C14 to No) and record welfare (Welfare & SCCO2 calculator cell C2). Then run the model again with the additional pulse of CO2 (set Settings cell C14 to Yes) and record welfare (Welfare & SCCO2 calculator cell C2 again). Calculate the difference in welfare. Then divide by ∂W/∂C(2020), using world mean consumption/capita in Welfare & SCCO2 calculator cell C3. You may wish to inflate the resulting number to current dollars!

Running the model without @RISK

We very strongly recommend installing @RISK before loading META 2021. However, there is a setting that enables the models' many random parameters to be treated as deterministic (set Settings cell C16 to No). The model should then work in standard Excel but will not perform Monte Carlo simulations.

Model details

Settings

The top of the Settings tab provides a dashboard of high-level choices:

Each tipping point (under B2) can be independently turned Off or On. Each tipping point is discussed in more detail below. The Interactions option specifies if the triggering of one tipping point changes the probability of other tipping points.
The SCC section (under B13) has options for including an extra pulse of emissions (Extra tonne), including uncertainty (Stochastic), and calculating damages from climate change (Climate impacts).
The RCP scenario (at F3) sets the emissions scenario from amongst the CMIP5 representative concentration pathways.
The SSP scenario (at F9) sets the socioeconomic scenario from amongst the Shared Socioeconomic Pathways.
Non-market damages can be calculated, in addition to the standard Burke et al. market damages, if F3 is set to MERGE.
Four different representations of the AMOC tipping point are included, as selected in cell L3.

The bottom of the sheet draws from the Parameters sheet, based on the selections above.

Parameters

Column B contains inputs to the model, columns C onwards to the right provide various alternatives that you can choose. So, you set the yellow cells in column B equal to whichever input alternative (i.e. column) you want to use. Where available, 'distribution' gives you the stochastic option. Also change the title cell (e.g. cell B4 for the carbon cycle module) so that the dashboard is updated.

Mimi model

See the description of the Excel model for details on the component-based structure and parameterization, which are maintained in the Mimi model.

Directories in the repository

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.

Basic use cases

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).

1. Running the full deterministic model

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, or 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.
co2: CO2 model calibration; one of AR5-IR, AR5-PI, MESMO (lowest decay), ACC2 (highest decay), Expectation (default), or Distribution.
ch4: CH4 model calibration; one of default (default), low, or high.
warming: Forcing model calibration: one of Best fit multi-model mean (default), HadGEM2-ES (hottest model), or GISS-E2-R (coldest model).
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.
wais: West Antarctic icesheet calibration; May be false (to not use) or true (default).
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).

2. Running the full Monte Carlo model

To run the model in Monte Carlo mode, you need to first generate the simulation parameter values, using the getsim(...) function, and then run the Monte Carlos, using the runsim(...) function, both of which are defined in src/montecarlo.jl.

getsim takes the following arguments (all are required, and given in order):

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.
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.

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

model: A full Mimi model.
draws: The result of the getsim function.
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.
saf_used: Set to true if the SAF component is included; otherwise false.
amazon_calib: May be one of the options described in the deterministic use case or "none" if the Amazon dieback component is excluded.
wais_calib: Set to "Distribution" if the WAIS component is included, or one of the options described in the deterministic use case.
save_rvs: Set to true to save all random variables in the final result; otherwise false.

There are also getmodel_base and runsim_base functions, which include just the non-tipping-point parameters.