A minimal state-dependent impulse-response model for exploring the surface temperature response multi-gas emission scenarios and the properties of complex ESMs.

While AOGCMs and ESMs are crucial tools for understanding the countless ways in which the Earth will change with artificial climate forcing, they require massive amounts of both energy and time to run -- such as in the CMIP experiments. This has led to the development of far simpler (often one-dimensional) models that can be used to explore possible future scenarios for the purposes of integrated assessment or policy-making far more easily and quickly. However, these models often remain relatively complicated and difficult for the non-specialist to understand fully.

Here we present a set of six equations, based on an extension of the AR5 Impulse Response Model utilising a linear state-dependence on the 100-year integrated impulse-response. We show that these six equations can well represent changes in atmopsheric composition of three of the most important greenhouse gases with different atmospheric chemistries - CO2, CH4 and N2O; and the changes in surface temperature to anthropogenic emissions. The model is tuned to reproduce best-estimate observed emissions, concentrations, forcing and temperature response, but can be tuned to reproduce the behaviour of CMIP6 ESMs, allowing these equations to act as an emulator for these more complex models and enabling the results of experiments that have not been carried out with such models to be estimated.

These equations are simple enough to be written in any iterative programming language, such as python, but can also be implemented in more widely used and less specialist programs like Excel. The transparency and simplicity of using only six equations provide a strong argument in favour of getting a much wider group of modellers to employ the same equation set as a 'lowest common denominator' in large assessments. For example, if this single set of equations could be used throughout IPCC's AR6, they would significantly improve the transparency and consistency of the entire assessment.