9.6 Observational Constraints on Climate Sensitivity

This section assesses recent research that infers equilibrium climate sensitivity and transient climate response from observed changes in climate. ‘Equilibrium climate sensitivity’ (ECS) is the equilibrium annual global mean temperature response to a doubling of equivalent atmospheric CO₂ from pre-industrial levels and is thus a measure of the strength of the climate system’s eventual response to greenhouse gas forcing. ‘Transient climate response’ (TCR) is the annual global mean temperature change at the time of CO₂ doubling in a climate simulation with a 1% yr^–1 compounded increase in CO₂ concentration (see Glossary and Section 8.6.2.1 for detailed definitions). TCR is a measure of the strength and rapidity of the climate response to greenhouse gas forcing, and depends in part on the rate at which the ocean takes up heat. While the direct temperature change that results from greenhouse gas forcing can be calculated in a relatively straightforward manner, uncertain atmospheric feedbacks (Section 8.6) lead to uncertainties in estimates of future climate change. The objective here is to assess estimates of ECS and TCR that are based on observed climate changes, while Chapter 8 assesses feedbacks individually. Inferences about climate sensitivity from observed climate changes complement approaches in which uncertain parameters in climate models are varied and assessed by evaluating the resulting skill in reproducing observed mean climate (Section 10.5.4.4). While observed climate changes have the advantage of being most clearly related to future climate change, the constraints they provide on climate sensitivity are not yet very strong, in part because of uncertainties in both climate forcing and the estimated response (Section 9.2). An overall summary assessment of ECS and TCR, based on the ability of models to simulate climate change and mean climate and on other approaches, is given in Box 10.2. Note also that this section does not assess regional climate sensitivity or sensitivity to forcings other than CO₂.

9.6.1 Methods to Estimate Climate Sensitivity

The most straightforward approach to estimating climate sensitivity would be to relate an observed climate change to a known change in radiative forcing. Such an approach is strictly correct only for changes between equilibrium climate states. Climatic states that were reasonably close to equilibrium in the past are often associated with substantially different climates than the pre-industrial or present climate, which is probably not in equilibrium (Hansen et al., 2005). An example is the climate of the LGM (Chapter 6 and Section 9.3). However, the climate’s sensitivity to external forcing will depend on the mean climate state and the nature of the forcing, both of which affect feedback mechanisms (Chapter 8). Thus, an estimate of the sensitivity directly derived from the ratio of response to forcing cannot be readily compared to the sensitivity of climate to a doubling of CO₂ under idealised conditions. An alternative approach, which has been pursued in most work reported here, is based on varying parameters in climate models that influence the ECS in those models, and then attaching probabilities to the different ECS values based on the realism of the corresponding climate change simulations. This ameliorates the problem of feedbacks being dependent on the climatic state, but depends on the assumption that feedbacks are realistically represented in models and that uncertainties in all parameters relevant for feedbacks are varied. Despite uncertainties, results from simulations of climates of the past and recent climate change (Sections 9.3 to 9.5) increase confidence in this assumption.

The ECS and TCR estimates discussed here are generally based on large ensembles of simulations using climate models of varying complexity, where uncertain parameters influencing the model’s sensitivity to forcing are varied. Studies vary key climate and forcing parameters in those models, such as the ECS, the rate of ocean heat uptake, and in some instances, the strength of aerosol forcing, within plausible ranges. The ECS can be varied directly in simple climate models and in some EMICs (see Chapter 8), and indirectly in more complex EMICs and AOGCMs by varying model parameters that influence the strength of atmospheric feedbacks, for example, in cloud parametrizations. Since studies estimating ECS and TCR from observed climate changes require very large ensembles of simulations of past climate change (ranging from several hundreds to thousands of members), they are often, but not always, performed with EMICs or EBMs.

The idea underlying this approach is that the plausibility of a given combination of parameter settings can be determined from the agreement of the resulting simulation of historical climate with observations. This is typically evaluated by means of Bayesian methods (see Supplementary Material, Appendix 9.B for methods). Bayesian approaches constrain parameter values by combining prior distributions that account for uncertainty in the knowledge of parameter values with information about the parameters estimated from data (Kennedy and O’Hagan, 2001). The uniform distribution has been used widely as a prior distribution, which enables comparison of constraints obtained from the data in different approaches. ECS ranges encompassed by the uniform prior distribution must be limited due to computer time limiting the size of model ensembles, but generally cover the range considered possible by experts, such as from 0°C to 10°C. Note that uniform prior distributions for ECS, which only require an expert assessment of possible range, generally assign a higher prior belief to high sensitivity than, for example, non-uniform prior distributions that depend more heavily on expert assessments (e.g., Forest et al., 2006). In addition, Frame et al. (2005) point out that care must be taken when specifying the uniform prior distribution. For example, a uniform prior distribution for the climate feedback parameter (see Glossary) implies a non-uniform prior distribution for ECS due to the nonlinear relationship between the two parameters.

Since observational constraints on the upper bound of ECS are still weak (as shown below), these prior assumptions influence the resulting estimates. Frame et al. (2005) advocate sampling a flat prior distribution in ECS if this is the target of the estimate, or in TCR if future temperature trends are to be constrained. In contrast, statistical research on the design and interpretation of computer experiments suggests the use of prior distributions for model input parameters (e.g., see Kennedy and O’Hagan, 2001; Goldstein and Rougier, 2004). In such Bayesian studies, it is generally good practice to explore the sensitivity of results to different prior beliefs (see, for example, Tol and Vos, 1998; O’Hagan and Forster, 2004). Furthermore, as demonstrated by Annan and Hargreaves (2005) and Hegerl et al. (2006a), multiple and independent lines of evidence about climate sensitivity from, for example, analysis of climate change at different times, can be combined by using information from one line of evidence as prior information for the analysis of another line of evidence. The extent to which the different lines of evidence provide complete information on the underlying physical mechanisms and feedbacks that determine the climate sensitivity is still an area of active research. In the following, uniform prior distributions for the target of the estimate are used unless otherwise specified.

Methods that incorporate a more comprehensive treatment of uncertainty generally produce wider uncertainty ranges for the inferred climate parameters. Methods that do not vary uncertain parameters, such as ocean diffusivity, in the course of the uncertainty analysis will yield probability distributions for climate sensitivity that are conditional on these values, and therefore are likely to underestimate the uncertainty in climate sensitivity. On the other hand, approaches that do not use all available evidence will produce wider uncertainty ranges than estimates that are able to use observations more comprehensively.