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We acknowledge that the model and analysis are relatively simple, but we believe there is value in this endeavour; looking back can help us build models which better reflect reality, allow us to frame decisions which lie in the future, and to detangle how we consider responsibilities for past actions.

The model has been used extensively since its introduction in the early s, and recently in assessments of emissions pathways necessary to achieve the Paris temperature goals The model solves iteratively for a pathway that maximizes inter-temporal social welfare itself a function of consumption , given assumptions about population and labor productivity which drives economic growth, discounting, costs of emissions reductions and a function relating global mean temperature to climate damages on the economy.

Optimal solutions are calculated by identifying pathways of savings rates and emissions reduction rates that maximize the discounted sum of social welfare over time. This solution produces an emissions pathway that effectively minimizes combined damages and mitigation costs.

DICE has perfect foresight, so decisions about savings and emissions reductions are made in the full knowledge of how the price of mitigation will evolve in the future, and how costly different levels of climate change will be. This is clearly a simplification although not an uncommon one of much more complicated types of knowledge and uncertainty about the future, and we discuss its implications in the main text.

Baseline emissions are those that result from the optimal solution to the model when it is assumed that there are no climate damages and no emissions mitigation.

The baseline scenario for our default model parameters follows 40 , and is illustrated in Supplemental Fig. Emissions abatement is calculated as a fraction of the baseline emissions, and is controlled by an emissions control rate MIU 22 , which we fix at zero until the time at which mitigation begins.

After the mitigation start date, MIU is allowed to increase such that emissions can be reduced compared with the baseline allowing for negative emissions if MIU is greater than 1. DICE has an exogenous representation of carbon emissions per unit economic output, and the economy can pay for additional emissions reductions by means of a mitigation module in which the cost of emissions reduction is a function of the control rate. Land use emissions are exogenously defined in the model, non-CO 2 forcing agents are represented in a bulk form, and their emissions are scaled by the same abatement factor as CO 2.

The climate response is simulated by a global energy balance model with a two-layer diffusive ocean as per the default configuration in 22 with the exception of the climate sensitivity parameter, which is explicitly perturbed.

All model simulations begin in and are run through In each section of the study, we perform a member perturbed ensemble using a Latin hypercube sampling strategy over the parameter space defined in Table 1. A flat prior is used for social rate of time preference, backstop cost and damage coefficients, whereas an empirical PDF from 51 is used for Equilibrium Climate Sensitivity. We use this ensemble to produce a diverse range of baseline and counterfactual simulations, conditional on the parametric PDFs used.

Each parameter configuration is used for a set of simulations, all initialized on the same date - but differing in the date at which abatement is allowed to have a non-zero value, and in the cost function described below. A wide range of social time preference from 0 to 0.

We explore the plausible range of mitigation cost by modulating the initial backstop cost of carbon such that, for a initialization, the ensemble range of mitigation cost for a given level of abatement in evaluated as a fraction of Gross World Product, or GWP is consistent with the range of mitigation costs observed in the IPCC AR5 emissions database 52 see Fig. The baseline simulations are largely implemented as in 20 - with all exogenous inputs identical to the baseline simulation in that paper.

Additional data are used to initialize the model to conditions. Exogenous global population from Initial GDP data is taken from the World Bank 54 , global mean surface temperature from 55 and global fossil fuel and land use emissions from Key variables from the resulting baseline simulation with default parameters are plotted in Supplemental Fig.

Each parameter configuration exhibits a different global mean temperature evolution, but the baseline simulations have no climate damages nor abatement costs. Temperature constraints for the 1. The damage functions are illustrated in the Supplementary Material, Fig.

The default DICE damage function is not active for these simulations. The damage estimate is therefore not useful in itself, but forces the model to produce an optimal pathway if possible that does not exceed the desired temperature target and does not account for climate damages.

Using a ramp function rather than a step function was found empirically to create stability for the solver by allowing the model to solve with short overshoots of the temperature target, however, with the chosen damage function the damage costs associated with the least cost solution are in practise negligible with respect to the abatement costs.

In the second set of experiments, the semi-linear climate damage function is replaced with the quadratic damage function used in the default model configuration. The quadratic coefficient is allowed to vary in the ensemble sufficiently to span the range of global damage estimates from a number of sources 5 , 10 , 11 , 12 , 13 , 14 , 15 - allowing for damages to be significantly greater than the current range used in the IAMs which contributed to the 5th Assessment Report of the IPCC.

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