State-dependence of climate sensitivity: attractor constraints and palaeoclimate regimes

Equilibrium climate sensitivity (ECS) is a key predictor of climate change. However, it is not very well constrained, either by climate models or by observational data. The reasons for this include strong internal variability and forcing on many time scales. In practise this means that the 'equilibrium' will only be relative to fixing the slow feedback processes before comparing palaeoclimate sensitivity estimates with estimates from model simulations. In addition, information from the late Pleistocene ice age cycles indicates that the climate cycles between cold and warm regimes, and the climate sensitivity varies considerably between regime because of fast feedback processes changing relative strength and time scales over one cycle. In this paper we consider climate sensitivity for quite general climate dynamics. Using a conceptual Earth system model of Gildor and Tziperman (2001) (with Milankovich forcing and dynamical ocean biogeochemistry) we explore various ways of quantifying the state-dependence of climate sensitivity from unperturbed and perturbed model time series. Even without considering any perturbations, we suggest that climate sensitivity can be usefully thought of as a distribution that quantifies variability within the 'climate attractor' and where there is a strong dependence on climate state and more specificially on the 'climate regime' where fast processes are approximately in equilibrium. We also consider perturbations by instantaneous doubling of CO$_2$ and similarly find a strong dependence on the climate state using our approach.Comment: 32 pages, 10 figure

Extreme sensitivity and climate tipping points

A climate state close to a tipping point will have a degenerate linear response to perturbations, which can be associated with extreme values of the equilibrium climate sensitivity (ECS). In this paper we contrast linearized (`instantaneous') with fully nonlinear geometric (`two-point') notions of ECS, in both presence and absence of tipping points. For a stochastic energy balance model of the global mean surface temperature with two stable regimes, we confirm that tipping events cause the appearance of extremes in both notions of ECS. Moreover, multiple regimes with different mean sensitivities are visible in the two-point ECS. We confirm some of our findings in a physics-based multi-box model of the climate system.Comment: 11 figure

The Mid-Pleistocene Transition induced by delayed feedback and bistability

The Mid-Pleistocene Transition, the shift from 41 kyr to 100 kyr glacial-interglacial cycles that occurred roughly 1 Myr ago, is often considered as a change in internal climate dynamics. Here we revisit the model of Quaternary climate dynamics that was proposed by Saltzman and Maasch (1988). We show that it is quantitatively similar to a scalar equation for the ice dynamics only when combining the remaining components into a single delayed feedback term. The delay is the sum of the internal times scales of ocean transport and ice sheet dynamics, which is on the order of 10 kyr. We find that, in the absence of astronomical forcing, the delayed feedback leads to bistable behaviour, where stable large-amplitude oscillations of ice volume and an equilibrium coexist over a large range of values for the delay. We then apply astronomical forcing. We perform a systematic study to show how the system response depends on the forcing amplitude. We find that over a wide range of forcing amplitudes the forcing leads to a switch from small-scale oscillations of 41 kyr to large-amplitude oscillations of roughly 100 kyr without any change of other parameters. The transition in the forced model consistently occurs near the time of the Mid-Pleistocene Transition as observed in data records. This provides evidence that the MPT could have been primarily a forcing-induced switch between attractors of the internal dynamics. Small additional random disturbances make the forcing-induced transition near 800 kyr BP even more robust. We also find that the forced system forgets its initial history during the small-scale oscillations, in particular, nearby initial conditions converge prior to transitioning. In contrast to this, in the regime of large-amplitude oscillations, the oscillation phase is very sensitive to random perturbations, which has a strong effect on the timing of the deglaciation events

Projections of the Transient State-Dependency of Climate Feedbacks

When the climate system is forced, e.g. by emission of greenhouse gases, it responds on multiple time scales. As temperatures rise, feedback processes might intensify or weaken. Current methods to analyze feedback strength, however, do not take such state dependency into account; they only consider changes in (global mean) temperature and assume all feedbacks are linearly related to that. This makes (transient) changes in feedback strengths almost intangible and generally leads to underestimation of future warming. Here, we present a multivariate (and spatially explicit) framework that facilitates dissection of climate feedbacks over time scales. Using this framework, information on the composition of projected (transient) future climates and feedback strengths can be obtained. Moreover, it can be used to make projections for many emission scenarios through linear response theory. The new framework is illustrated using the Community Earth System Model version 2 (CESM2).Comment: main text: 11 pages, 4 figures, 1 table Supporting Information: 14 pages, 17 figures, 1 table, 8 movie

Multivariate Estimations of Equilibrium Climate Sensitivity from Short Transient Warming Simulations

One of the most used metrics to gauge the effects of climate change is the equilibrium climate sensitivity, defined as the long-term (equilibrium) temperature increase resulting from instantaneous doubling of atmospheric CO$_2$. Since global climate models cannot be fully equilibrated in practice, extrapolation techniques are used to estimate the equilibrium state from transient warming simulations. Because of the abundance of climate feedbacks - spanning a wide range of temporal scales - it is hard to extract long-term behaviour from short-time series; predominantly used techniques are only capable of detecting the single most dominant eigenmode, thus hampering their ability to give accurate long-term estimates. Here, we present an extension to those methods by incorporating data from multiple observables in a multi-component linear regression model. This way, not only the dominant but also the next-dominant eigenmodes of the climate system are captured, leading to better long-term estimates from short, non-equilibrated time series.Comment: Main Text (10 pages, 4 figures) plus Supporting Information (36 pages, 18 figures, 1 table

The relationship between the global mean deep-sea and surface temperature during the Early Eocene

EGU General Assembly, Vienna, Austria 23-27 May 2022, https://doi.org/10.5194/egushere-egu22-9897 Under continued high anthropogenic CO2 emissions, the atmospheric CO2 concentration around 2100 will be like that of the Early Eocene Climate Optimum (EECO, 56–48 Ma) hothouse period. Hence, reconstructions of the EECO climate give insight into the workings of the climate system under the possible future CO2 conditions. Our current understanding of global mean surface temperature (GMST) during the Cenozoic era relies on paleo-proxy estimates of deep-sea temperature (DST) combined with assumed relationships between global mean DST (GMDST), global mean sea-surface temperature (GMSST), and GMST. The validity of these assumptions is essential in our understanding of past and future climate states under hothouse conditions. We analyse the relationship between these global temperature indicators for the end-of-simulation global mean temperature values in 25 different millennia-long model simulations of the EECO climate under varying CO2 levels, performed as part of the Deep-Time Model Intercomparison Project (DeepMIP). The model simulations show limited spatial variability in DST, indicating that local DST estimates can be regarded representative of GMDST. Linear regression analysis indicates that GMDST and GMST respond stronger to changes in atmospheric CO2 than GMSST by factors 1.18 and 1.17, respectively. Consequently, the responses of GMDST and GMST to atmospheric CO2 changes are similar in magnitude. This model-based analysis indicates that changes in GMDST can be used to estimate changes in GMST during the EECO, validating the assumed relationships. To test the robustness of these results, other Cenozoic climate states besides EECO should be analysed similarly

Climate response and sensitivity: time scales and late tipping points

Climate response metrics are used to quantify the Earth’s climate response to anthropogenic changes of atmospheric CO2. Equilibrium climate sensitivity (ECS) is one such metric that measures the equilibrium response to CO2 doubling. However, both in their estimation and their usage, such metrics make assumptions on the linearity of climate response, although it is known that, especially for larger forcing levels, response can be nonlinear. Such nonlinear responses may become visible immediately in response to a larger perturbation, or may only become apparent after a long transient period. In this paper, we illustrate some potential problems and caveats when estimating ECS from transient simulations. We highlight ways that very slow time scales may lead to poor estimation of ECS even if there is seemingly good fit to linear response over moderate time scales. Moreover, such slow processes might lead to late abrupt responses (late tipping points) associated with a system’s nonlinearities. We illustrate these ideas using simulations on a global energy balance model with dynamic albedo. We also discuss the implications for estimating ECS for global climate models, highlighting that it is likely to remain difficult to make definitive statements about the simulation times needed to reach an equilibrium

Fragmented tipping in a spatially heterogeneous world

Many climate subsystems are thought to be susceptible to tipping—and some might be close to a tipping point. The general belief and intuition, based on simple conceptual models of tipping elements, is that tipping leads to reorganization of the full (sub)system. Here, we explore tipping in conceptual, but spatially extended and spatially heterogenous models. These are extensions of conceptual models taken from all sorts of climate system components on multiple spatial scales. By analysis of the bifurcation structure of such systems, special stable equilibrium states are revealed: coexistence states with part of the spatial domain in one state, and part in another, with a spatial interface between these regions. These coexistence states critically depend on the size and the spatial heterogeneity of the (sub)system. In particular, in these systems the crossing of a tipping point not necessarily leads to a full reorganization of the system. Instead, it might lead to a reorganization of only part of the spatial domain, limiting the impact of these events on the system's functioning