Emergent constraints on carbon budgets as a function of global warming.

Earth System Models (ESMs) continue to diagnose a wide range of carbon budgets for each level of global warming. Here, we present emergent constraints on the carbon budget as a function of global warming, which combine the available ESM historical simulations and future projections for a range of scenarios, with observational estimates of global warming and anthropogenic CO2 emissions to the present day. We estimate mean and likely ranges for cumulative carbon budgets for the Paris targets of 1.5 °C and 2 °C of global warming of 812 [691, 933] PgC and 1048 [881, 1216] PgC, which are more than 10% larger than the ensemble mean values from the CMIP6 models. The linearity between cumulative emissions and global warming is found to be maintained at least until 4 °C, and is consistent with an effective Transient Climate Response to Emissions (eTCRE) of 2.1 [1.8, 2.6] °C/1000PgC, from a global warming of 1.2 °C onwards.

Emergent constraint on equilibrium climate sensitivity from global temperature variability.

Equilibrium climate sensitivity (ECS) remains one of the most important unknowns in climate change science. ECS is defined as the global mean warming that would occur if the atmospheric carbon dioxide (CO2) concentration were instantly doubled and the climate were then brought to equilibrium with that new level of CO2. Despite its rather idealized definition, ECS has continuing relevance for international climate change agreements, which are often framed in terms of stabilization of global warming relative to the pre-industrial climate. However, the 'likely' range of ECS as stated by the Intergovernmental Panel on Climate Change (IPCC) has remained at 1.5-4.5 degrees Celsius for more than 25 years. The possibility of a value of ECS towards the upper end of this range reduces the feasibility of avoiding 2 degrees Celsius of global warming, as required by the Paris Agreement. Here we present a new emergent constraint on ECS that yields a central estimate of 2.8 degrees Celsius with 66 per cent confidence limits (equivalent to the IPCC 'likely' range) of 2.2-3.4 degrees Celsius. Our approach is to focus on the variability of temperature about long-term historical warming, rather than on the warming trend itself. We use an ensemble of climate models to define an emergent relationship between ECS and a theoretically informed metric of global temperature variability. This metric of variability can also be calculated from observational records of global warming, which enables tighter constraints to be placed on ECS, reducing the probability of ECS being less than 1.5 degrees Celsius to less than 3 per cent, and the probability of ECS exceeding 4.5 degrees Celsius to less than 1 per cent.

Detection of bifurcations in noisy coupled systems from multiple time series.

We generalize a method of detecting an approaching bifurcation in a time series of a noisy system from the special case of one dynamical variable to multiple dynamical variables. For a system described by a stochastic differential equation consisting of an autonomous deterministic part with one dynamical variable and an additive white noise term, small perturbations away from the system's fixed point will decay slower the closer the system is to a bifurcation. This phenomenon is known as critical slowing down and all such systems exhibit this decay-type behaviour. However, when the deterministic part has multiple coupled dynamical variables, the possible dynamics can be much richer, exhibiting oscillatory and chaotic behaviour. In our generalization to the multi-variable case, we find additional indicators to decay rate, such as frequency of oscillation. In the case of approaching a homoclinic bifurcation, there is no change in decay rate but there is a decrease in frequency of oscillations. The expanded method therefore adds extra tools to help detect and classify approaching bifurcations given multiple time series, where the underlying dynamics are not fully known. Our generalisation also allows bifurcation detection to be applied spatially if one treats each spatial location as a new dynamical variable. One may then determine the unstable spatial mode(s). This is also something that has not been possible with the single variable method. The method is applicable to any set of time series regardless of its origin, but may be particularly useful when anticipating abrupt changes in the multi-dimensional climate system.