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We review how the international modelling community, encompassing integrated assessment models, global and regional Earth system and climate models, and impact models, has worked together over the past few decades to advance understanding of Earth system change and its impacts on society and the environment and thereby support international climate policy. We go on to recommend a number of priority research areas for the coming decade, a timescale that encompasses a number of newly starting international modelling activities, as well as the IPCC Seventh Assessment Report (AR7) and the second UNFCCC Global Stocktake. Progress in these priority areas will significantly advance our understanding of Earth system change and its impacts, increasing the quality and utility of science support to climate policy. We emphasize the need for continued improvement in our understanding of, and ability to simulate, the coupled Earth system and the impacts of Earth system change. There is an urgent need to investigate plausible pathways and emission scenarios that realize the Paris climate targets – for example, pathways that overshoot 1.5 or 2 °C global warming, before returning to these levels at some later date. Earth system models need to be capable of thoroughly assessing such warming overshoots – in particular, the efficacy of mitigation measures, such as negative CO<sub>2</sub> emissions, in reducing atmospheric CO<sub>2</sub> and driving global cooling. An improved assessment of the long-term consequences of stabilizing climate at 1.5 or 2 °C above pre-industrial temperatures is also required. We recommend Earth system models run overshoot scenarios in CO<sub>2</sub>-emission mode to more fully represent coupled climate–carbon-cycle feedbacks and, wherever possible, interactively simulate other key Earth system phenomena at risk of rapid change during overshoot. Regional downscaling and impact models should use forcing data from these simulations, so impact and regional climate projections cover a more complete range of potential responses to a warming overshoot. An accurate simulation of the observed, historical record remains a fundamental requirement of models, as does accurate simulation of key metrics, such as the effective climate sensitivity and the transient climate response to cumulative carbon emissions. For adaptation, a key demand is improved guidance on potential changes in climate extremes and the modes of variability these extremes develop within. Such improvements will most likely be realized through a combination of increased model resolution, improvement of key model parameterizations, and enhanced representation of important Earth system processes, combined with targeted use of new artificial intelligence (AI) and machine learning (ML) techniques. We propose a deeper collaboration across such efforts over the coming decade. With respect to sampling future uncertainty, increased collaboration between approaches that emphasize large model ensembles and those focussed on statistical emulation is required. We recommend an increased focus on high-impact–low-likelihood (HILL) outcomes – in particular, the risk and consequences of exceeding critical tipping points during a warming overshoot and the potential impacts arising from this. For a comprehensive assessment of the impacts of Earth system change, including impacts arising directly as a result of climate mitigation actions, it is important that spatially detailed, disaggregated information used to generate future scenarios in integrated assessment models be available for use in impact models. Conversely, there is a need to develop methods that enable potential societal responses to projected Earth system change to be incorporated into scenario development. The new models, simulations, data, and scientific advances proposed in this article will not be possible without long-term development and maintenance of a robust, globally connected infrastructure ecosystem. This system must be easily accessible and useable by modelling communities across the world, allowing the global research community to be fully engaged in developing and delivering new scientific knowledge to support international climate policy.
