Theoretical foundations of emergent constraints: relationships between climate sensitivity and global temperature variability in conceptual models

This is the final version. Available on open access from OUP via the DOI in this recordBackground: The emergent constraint approach has received interest recently as a way of utilizing multimodel General Circulation Model (GCM) ensembles to identify relationships between observable variations of climate and future projections of climate change. These relationships, in combination with observations of the real climate system, can be used to infer an emergent constraint on the strength of that future projection in the real system. However, there is as yet no theoretical framework to guide the search for emergent constraints. As a result, there are significant risks that indiscriminate data-mining of the multidimensional outputs from GCMs could lead to spurious correlations and less than robust constraints on future changes. To mitigate against this risk, Cox et al (hereafter CHW18) proposed a theory-motivated emergent constraint, using the one-box Hasselmann model to identify a linear relationship between equilibrium climate sensitivity (ECS) and a metric of global temperature variability involving both temperature standard deviation and autocorrelation (Ψ). A number of doubts have been raised about this approach, some concerning the application of the one-box model to understand relationships in complex GCMs which are known to have more than the single characteristic timescale. Objectives: To study whether the linear Ψ-ECS proportionality in CHW18 is an artefact of the one-box model. More precisely we ask ‘Does the linear Ψ-ECS relationship feature in the more complex and realistic two-box and diffusion models?’. Methods: We solve the two-box and diffusion models to find relationships between ECS and Ψ. These models are forced continually with white noise parameterizing internal variability. The resulting analytical relations are essentially fluctuation-dissipation theorems. Results: We show that the linear Ψ-ECS proportionality in the one-box model is not generally true in the two-box and diffusion models. However, the linear proportionality is a very good approximation for parameter ranges applicable to the current state-of-the-art CMIP5 climate models. This is not obvious - due to structural differences between the conceptual models, their predictions also differ. For example, the two-box and diffusion, unlike the one-box model, can reproduce the long term transient behaviour of the CMIP5 abrupt4xCO2 and 1pcCO2 simulations. Each of the conceptual models also predict different power spectra with only the diffusion model’s pink 1/f spectrum being compatible with observations and GCMs. We also show that the theoretically predicted Ψ-ECS relationship exists in the piControl as well as historical CMIP5 experiments and that the differing gradients of the proportionality are inversely related to the effective forcing in that experiment. Conclusions: We argue that emergent constraints should ideally be derived by such theory-driven hypothesis testing, in part to protect against spurious correlations from blind data-mining but mainly to aid understanding. In this approach, an underlying model is proposed, the model is used to predict a potential emergent relationship between an observable and an unknown future projection, and the hypothesised emergent relationship is tested against an ensemble of GCMs.European Union Horizon 2020Engineering and Physical Sciences Research Council (EPSRC)European Research Counci

Risk-opportunity analysis for transformative policy design and appraisal

The climate crisis demands a strong response from policy-makers worldwide. The current global climate policy agenda requires technological change, innovation, labour markets and the financial system to be led towards an orderly and rapid low-carbon transition. Yet progress has been slow and incremental. Inadequacies of policy appraisal frameworks used worldwide may be significant contributors to the problem, as they frequently fail to adequately account for the dynamics of societal and technological change. Risks are underestimated, and the economic opportunities from innovation are generally not assessed in practice. Here, we identify root causes of those inadequacies and identify them to structural features of standard analysis frameworks. We use a review of theoretical principles of complexity science and the science of dynamical systems and formulate a generalisation of existing frameworks for policy analysis and the appraisal of outcomes of proposed policy strategies, to help better identify and frame situations of transformational change. We use the term “risk-opportunity analysis” to capture the generalised approach, in which conventional economic cost-benefit analysis is a special case. New guiding principles for policy-making during dynamic and transformational change are offered

Risk-opportunity analysis for transformative policy design and appraisal

This is the final version. Available from Elsevier via the DOI in this record. The climate crisis demands a strong response from policy-makers worldwide. The current global climate policy agenda requires technological change, innovation, labour markets and the financial system to be led towards an orderly and rapid low-carbon transition. Yet progress has been slow and incremental. Inadequacies of policy appraisal frameworks used worldwide may be significant contributors to the problem, as they frequently fail to adequately account for the dynamics of societal and technological change. Risks are underestimated, and the economic opportunities from innovation are generally not assessed in practice. Here, we identify root causes of those inadequacies and identify them to structural features of standard analysis frameworks. We use a review of theoretical principles of complexity science and the science of dynamical systems and formulate a generalisation of existing frameworks for policy analysis and the appraisal of outcomes of proposed policy strategies, to help better identify and frame situations of transformational change. We use the term “risk-opportunity analysis” to capture the generalised approach, in which conventional economic cost-benefit analysis is a special case. New guiding principles for policy-making during dynamic and transformational change are offered.Children's Investment FundDepartment for BEI

Beyond forcing scenarios: predicting climate change through response operators in a coupled general circulation model

Global Climate Models are key tools for predicting the future response of the climate system to a variety of natural and anthropogenic forcings. Here we show how to use statistical mechanics to construct operators able to flexibly predict climate change for a variety of climatic variables of interest. We perform our study on a fully coupled model - MPI-ESM v.1.2 - and for the first time we prove the effectiveness of response theory in predicting future climate response to CO2 increase on a vast range of temporal scales, from inter-annual to centennial, and for very diverse climatic quantities. We investigate within a unified perspective the transient climate response and the equilibrium climate sensitivity and assess the role of fast and slow processes. The prediction of the ocean heat uptake highlights the very slow relaxation to a newly established steady state. The change in the Atlantic Meridional Overturning Circulation (AMOC) and of the Antarctic Circumpolar Current (ACC) is accurately predicted. The AMOC strength is initially reduced and then undergoes a slow and only partial recovery. The ACC strength initially increases as a result of changes in the wind stress, then undergoes a slowdown, followed by a recovery leading to a overshoot with respect to the initial value. Finally, we are able to predict accurately the temperature change in the Northern Atlantic

Introduction to the special issue on the statistical mechanics of climate

We introduce the special issue on the Statistical Mechanics of Climate by presenting an informal discussion of some theoretical aspects of climate dynamics that make it a topic of great interest for mathematicians and theoretical physicists. In particular, we briefly discuss its nonequilibrium and multiscale properties, the relationship between natural climate variability and climate change, the different regimes of climate response to perturbations, and critical transitions

Risk-opportunity analysis for transformative policy design and appraisal

The climate crisis demands a strong response from policy-makers worldwide. The current global climate policy agenda requires technological change, innovation, labour markets and the financial system to be led towards an orderly and rapid low-carbon transition. Yet progress has been slow and incremental. Inadequacies of policy appraisal frameworks used worldwide may be significant contributors to the problem, as they frequently fail to adequately account for the dynamics of societal and technological change. Risks are underestimated, and the economic opportunities from innovation are generally not assessed in practice. Here, we identify root causes of those inadequacies and identify them to structural features of standard analysis frameworks. We use a review of theoretical principles of complexity science and the science of dynamical systems and formulate a generalisation of existing frameworks for policy analysis and the appraisal of outcomes of proposed policy strategies, to help better identify and frame situations of transformational change. We use the term “risk-opportunity analysis” to capture the generalised approach, in which conventional economic cost-benefit analysis is a special case. New guiding principles for policy-making during dynamic and transformational change are offered