Model Structure🔗

C-ROADS is a system dynamics model. It consists of a set of ordinary differential equations in time. Variables calculated by integration are called “stocks” (also called “levels”); components of the rate of change of a stock are called “flows”; variables used for intermediate steps or calculating other values include auxiliary, constant, data, and initial variables.

Equations represent both physical processes and human decisions. There is no assumption of equilibrium or optimal decision making. The model represents the climate at the global level of aggregation, with emissions and land use for seven regions. The regions are organized into six or three regions, or to the global total, depending on the simulation setting.

C-ROADS is constructed using Vensim modeling software from Ventana Systems, and transformed into an online simulation via the SDEverywhere tools built by Climate Interactive and Todd Fincannon.

C-ROADS is calibrated to an extensive set of historical data, and its endogenous behavior is grounded in and made consistent with other models, in particular the Integrated Assessment Models used by the Intergovernmental Panel on Climate Change (IPCC).

Simulation Method🔗

The differential equations making up C-ROADS are non-linear and have no general closed form solution. Instead they are estimated numerically using the Euler method. At each time step (∆t), auxiliary and flow variables are calculated from previous values of stocks, along with constants and data as needed. Each stock is then computed by adding its previous value to the product of ∆t times the sum of all its flows. A sufficiently small time step is required for good approximation - a value of one quarter (0.25) year is appropriate in C-ROADS given the characteristic times and delays in the system as modeled.

C-ROADS starts from initial values in the year 1850 and runs using a combination of data and endogenous behavior through 2100. The model stores and can plot and print the output each year.

Sources of Historical Data🔗

Emissions

• Global Carbon Budget (2023): CO₂ Emissions from fossil fuels
• PRIMAP 2.5.1 (2024): Non-CO₂ GHG Emissions only
• Houghton and Nassikas (2017) (CO₂ Land Use only)

Land Areas

• Land Use Harmonization (LUH2) data (Hurtt et al., 2018)

Population and GDP

• UN World Population Prospects 2024
• World Development Indicators 2024

C-ROADS exogenously uses the historic population, GDP, CO₂ FF emissions, and other GHG emissions. We aggregate these data to import into our data model of 180 countries, which then aggregates those data into the 7 blocs.

Organization🔗

C-ROADS simulator is a synthesis of several sub-models.

• Energy and Industry Emissions;
• Land Use, Land Use Change, and Forestry;
• Terrestrial Biosphere Carbon Cycle;
• Well-Mixed Greenhouse Gas Cycles;
• Climate;
• Sea level rise; and
• Other Impacts.

In the model structure diagrams in the following chapters, there are four types of elements:

1. Variables with a box represent stocks, determined by integration.
2. Variables without a box are auxiliary variables.
3. Simple arrows indicate a causal relationship, one variable is a function of the other.
4. Pipes represent flows - the elements of the rate of change of stocks - shown flowing into, out of, and between stocks.