ClimateBench also includes a selection of more idealised simulations which are intended to provide training data at the ‘corners’ of the four-dimensional input space, again helping reduce the chances of extrapolation in the resulting emulators (as demonstrated in Figure A1). Two simulations that are commonly used to diagnose the equilibrium and transient climate sensitivity are abrupt-4xCO2 and1pctCO2, respectively. As the name suggests, theabrupt-4xCO2 includes an abrupt quadrupling of CO2 over the pre-industrial concentrations while all other forcing agents remain unchanged. This level of concentration represents the high end of future scenarios, broadly in line with ssp585 but with no contribution from the other forcers, simplifying its interpretation. The abrupt nature of the forcing also allows the timescale of the responses to be determined which can be useful for emulators which account for this. The1pctCO2 simulation gradually increases the atmospheric concentration of CO2 by 1% per year, again with other forcing agents unchanged. Two simulations performed as part of the Detection-Attribution Model Intercomparison Project (DAMIP; Gillett et al., 2016) represent the historical period forced by only CO2 and other long-lived greenhouse gases (hist-GHG ), or only anthropogenic aerosol (hist-aer ). Again, these provide opportunities to train emulators in regions of the input (emissions) space that are at the limits of plausible future scenarios.

Finally, the piControl simulation provides a baseline simulation with all forcings remaining unchanged from their pre-industrial values. All target variables are calculated as a change against this climatology to simplify the training and interpretation of the results. This long (500 year) simulation also enables a robust estimation of internal variability of the climate system for those emulators which are able to represent it, as discussed further in Section 5.1.

The input data for these simulations is prescribed by the experimental protocol and provided by the input4MIPS project (https://esgf-node.llnl.gov/search/input4mips/), which we collate and pre-process for ease of use. Specifically, we extract the provided global mean emissions of CO2 and CH4 for each of the realistic (historical, ScenarioMIP and DAMIP) experiments from the checksum files provided by the Community Emissions Data System (CEDS) dataset (Hoesly et al., 2018). We sum over each sector and each month in order to derive annual total emissions and convert from Kg to Gt of CO2. Some historical and future periods are only provided in 5-yearly increments, so we linearly interpolate to yearly values for consistency. The CO2 emissions are summed cumulatively since, for realistic scenarios, a compensation between forcing efficiency and ocean uptake means the temperature response to CO2 is approximately linear in the cumulative emissions (Matthews and Caldeira 2008; Allen et al. 2009). Figure 1 shows the global mean emissions of each of the forcing agents under different future emissions scenarios, showing a wide range of possible pathways.