Climate sensitivity increases under higher CO₂ levels due to feedback temperature dependence

Equilibrium climate sensitivity‐the equilibrium warming per CO2 doubling‐increases with CO2 concentration for 13 of 14 coupled general circulation models for 0.5–8 times the preindustrial concentration. In particular, the abrupt 4 × CO2 equilibrium warming is more than twice the 2 × CO2 warming. We identify three potential causes: nonlogarithmic forcing, feedback CO2 dependence, and feedback temperature dependence. Feedback temperature dependence explains at least half of the sensitivity increase, while feedback CO2 dependence explains a smaller share, and nonlogarithmic forcing decreases sensitivity in as many models as it increases it. Feedback temperature dependence is positive for 10 out of 14 models, primarily due to the longwave clear‐sky feedback, while cloud feedbacks drive particularly large sensitivity increases. Feedback temperature dependence increases the risk of extreme or runaway warming, and is estimated to cause six models to warm at least an additional 3K under 8 × CO2

A state-dependent quantification of climate sensitivity based in paleo data of the last 2.1 million years

The evidence from both data and models indicates that specific equilibrium climate sensitivity S[X] — the global annual mean surface temperature change (DTg) as a response to a change in radiative forcing X (DR[X]) — is state-dependent. Such a state dependency implies that the best fit in the scatter plot of (DTg versus DR[X] is not a linear regression, but can be some non-linear or even non-smooth function. While for the conventional linear case the slope (gradient) of the regression is correctly interpreted as the specific equilibrium climate sensitivity S[X], the interpretation is not straightforward in the non-linear case. We here explain how such a state-dependent scatter plot needs to be interpreted, and provide a theoretical understanding — or generalization — how to quantify S[X] in the non-linear case. Finally, from data covering the last 2.1 Myr we show that — due to state dependency — the specific equilibrium climate sensitivity which considers radiative forcing of CO2 and land ice sheet (LI) albedo, S[CO2;LI], is larger during interglacial states than during glacial conditions by more than a factor two

Equilibrium climate sensitivity estimated by equilibrating climate models

The methods to quantify equilibrium climate sensitivity are still debated. We collect millennial‐length simulations of coupled climate models and show that the global mean equilibrium warming is higher than those obtained using extrapolation methods from shorter simulations. Specifically, 27 simulations with 15 climate models forced with a range of CO2 concentrations show a median 17% larger equilibrium warming than estimated from the first 150 years of the simulations. The spatial patterns of radiative feedbacks change continuously, in most regions reducing their tendency to stabilizing the climate. In the equatorial Pacific, however, feedbacks become more stabilizing with time. The global feedback evolution is initially dominated by the tropics, with eventual substantial contributions from the mid‐latitudes. Time‐dependent feedbacks underscore the need of a measure of climate sensitivity that accounts for the degree of equilibration, so that models, observations, and paleo proxies can be adequately compared and aggregated to estimate future warming. Key points 27 simulations of 15 general circulation models are integrated to near equilibrium All models simulate a higher equilibrium warming than predicted by using extrapolation methods Tropics and mid‐latitudes dominate the change of the feedback parameter on different timescales on millennial timescale

The Green's function model intercomparison project (GFMIP) protocol

The atmospheric Green's function method is a technique for modeling the response of the atmosphere to changes in the spatial field of surface temperature. While early studies applied this method to changes in atmospheric circulation, it has also become an important tool to understand changes in radiative feedbacks due to evolving patterns of warming, a phenomenon called the “pattern effect.” To better study this method, this paper presents a protocol for creating atmospheric Green's functions to serve as the basis for a model intercomparison project, GFMIP. The protocol has been developed using a series of sensitivity tests performed with the HadAM3 atmosphere‐only general circulation model, along with existing and new simulations from other models. Our preliminary results have uncovered nonlinearities in the response of the atmosphere to surface temperature changes, including an asymmetrical response to warming versus cooling patch perturbations, and a change in the dependence of the response on the magnitude and size of the patches. These nonlinearities suggest that the pattern effect may depend on the heterogeneity of warming as well as its location. These experiments have also revealed tradeoffs in experimental design between patch size, perturbation strength, and the length of control and patch simulations. The protocol chosen on the basis of these experiments balances scientific utility with the simulation time and setup required by the Green's function approach. Running these simulations will further our understanding of many aspects of atmospheric response, from the pattern effect and radiative feedbacks to changes in circulation, cloudiness, and precipitation

Causes and Implications of Time-Varying Climate Sensitivity

Climate studies often assume that a key metric of global warming, the equilibrium climate sensitivity (∆T2x,eq, the long-term warming from doubling atmospheric CO2), is constant, and that it has the same value as the instantaneous climate sensitivity (∆T2x,inst, an estimate of ∆T2x,eq made using time series of surface temperature and net top-of-atmosphere radiative flux). Recent studies have shown that both assumptions should be reconsidered: in computer simulations, ∆T2x,eq can depend on the background state under anthropogenic levels of forcing, and ∆T2x,inst often differs from ∆T2x,eq. These discrepancies suggest that past estimates of climate sensitivity and of future warming may be incorrect. In this thesis, we explore the causes of these two discrepancies and develop new models that account for them, allowing for more accurate forecasting of future warming. We explore the first issue by extending a simple energy balance model to account for the fact that the feedback processes that determine the climate sensitivity can change strength in a warmer world, causing ∆T2x,eq to vary. We use a measure of this feedback temperature dependence, a, to show that positive values of a predict the large increases in ∆T2x,eq under successive doublings of CO2 seen in some general circulation models (GCMs). Using this simple model, we show that the range of values of a seen in GCMs implies that observational probabilistic forecasts of climate sensitivity underestimate the risk of high warming. The degree of this underestimate depends on how sensitive the planet is initially. We perform offline calculations on the ECHAM6.1 model to demonstrate that changes in equilibrium climate sensitivity are partly driven by feedback temperature dependence through increases in the water vapor feedback. Perturbing the convective parameters in ECHAM6.1 demonstrates that a small uncertainty in present day climate sensitivity can translate into large uncertainties in sensitivity at higher forcings when a is positive. We explore the second discrepancy by developing an energy balance model that accounts for the spatially nonuniform nature of the Earth's radiative feedbacks (the primary cause in the difference between ∆T2x,eq and ∆T2x,inst). We demonstrate a method for estimating these spatial radiative feedbacks from interannual variability by using multiple regression of top-of-atmosphere fluxes against local and non-local surface temperature. Our method can separate the global feedback into local and nonlocal components, and we show that most models have strong negative nonlocal feedbacks associated with warming in regions of tropical convection. Since warming is initially more weighted towards the tropics, these negative feedbacks make initial values of ∆T2x,inst lower than ∆T2x,eq. These two issues are compounding, in that if we are underestimating the ∆T2x,eq associated with the present climate due to spatially varying feedbacks, this makes it much more likely that we are underestimating the value ∆T2x,eq will have in the warmer future due to feedback temperature dependence. While the chapters of this thesis use results from computer simulations of climate to assess the power of these effects, they also point towards ways that observations and physical reasoning can be used to measure their strength. Regardless of the method, the present work makes clear that we must account for these two causes of time-varying climate sensitivity to properly forecast future warming

Software for "The Green's Function Model Intercomparison Project (GFMIP) Protocol"

<p>A Jupyter notebook, running Julia 1.7.1, used for performing the analysis in the GFMIP Protocol paper.</p&gt

Circus Tents, Convective Thresholds, and the Non‐Linear Climate Response to Tropical SSTs

Abstract Using model simulations, we demonstrate that the climate response to localized tropical sea surface temperature (SST) perturbations exhibits numerous non‐linearities. Most pronounced is an asymmetry in the response to positive and negative SST perturbations. Additionally, we identify a “magnitude‐dependence” of the response on the size of the SST perturbation. We then explain how these non‐linearities arise as a robust consequence of convective quasi‐equilibrium and weak (but non‐zero) temperature gradients in the tropical free‐troposphere, which we encapsulate in a “circus tent” model of the tropical atmosphere. These results demonstrate that the climate response to SST perturbations is fundamentally non‐linear, and highlight potential deficiencies in work which has assumed linearity in the response

Feedback temperature dependence determines the risk of high warming

The long-term warming from an anthropogenic increase in atmospheric CO2 is often assumed to be proportional to the forcing associated with that increase. This paper examines this linear approximation using a zero-dimensional energy balance model with a temperature-dependent feedback, with parameter values drawn from physical arguments and general circulation models. For a positive feedback temperature dependence, warming increases Earth's sensitivity, while greater sensitivity makes Earth warm more. These effects can feed on each other, greatly amplifying warming. As a result, for reasonable values of feedback temperature dependence and preindustrial feedback, Earth can jump to a warmer state under only one or two CO2 doublings. The linear approximation breaks down in the long tail of high climate sensitivity commonly seen in observational studies. Understanding feedback temperature dependence is therefore essential for inferring the risk of high warming from modern observations. Studies that assume linearity likely underestimate the risk of high warming

Evolving CO 2 rather than SST leads to a factor of ten decrease in GCM convergence time

The high computational cost of Global Climate Models (GCMs) is a problem that limits their use in many areas. Recently an inverse climate modeling (InvCM) method, which fixes the global mean sea surface temperature (SST) and evolves the urn:x-wiley:19422466:media:jame21464:jame21464-math-0001 mixing ratio to equilibrate climate, has been implemented in a cloud-resolving model. In this article, we apply InvCM to ExoCAM GCM aquaplanet simulations, allowing the SST pattern to evolve while maintaining a fixed global-mean SST. We find that InvCM produces the same climate as normal slab-ocean simulations but converges an order of magnitude faster. We then use InvCM to calculate the equilibrium urn:x-wiley:19422466:media:jame21464:jame21464-math-0002 for SSTs ranging from 290 to 340 K at 1 K intervals and reproduce the large increase in climate sensitivity at an SST of about 315 K at much higher temperature resolution. The speedup provided by InvCM could be used to equilibrate GCMs at higher spatial resolution or to perform broader parameter space exploration in order to gain new insight into the climate system. Additionally, InvCM could be used to find unstable and hidden climate states, and to find climate states close to bifurcations such as the runaway greenhouse transition

Evolving CO2 Rather Than SST Leads to a Factor of Ten Decrease in GCM Convergence Time.

The high computational cost of Global Climate Models (GCMs) is a problem that limits their use in many areas. Recently an inverse climate modeling (InvCM) method, which fixes the global mean sea surface temperature (SST) and evolves the CO2 mixing ratio to equilibrate climate, has been implemented in a cloud-resolving model. In this article, we apply InvCM to ExoCAM GCM aquaplanet simulations, allowing the SST pattern to evolve while maintaining a fixed global-mean SST. We find that InvCM produces the same climate as normal slab-ocean simulations but converges an order of magnitude faster. We then use InvCM to calculate the equilibrium CO2 for SSTs ranging from 290 to 340 K at 1 K intervals and reproduce the large increase in climate sensitivity at an SST of about 315 K at much higher temperature resolution. The speedup provided by InvCM could be used to equilibrate GCMs at higher spatial resolution or to perform broader parameter space exploration in order to gain new insight into the climate system. Additionally, InvCM could be used to find unstable and hidden climate states, and to find climate states close to bifurcations such as the runaway greenhouse transition