Emergent constraints on climate sensitivities

Despite major advances in climate science over the last 30 years, persistent uncertainties in projections of future climate change remain. Climate projections are produced with increasingly complex models that attempt to represent key processes in the Earth system, including atmospheric and oceanic circulations, convection, clouds, snow, sea ice, vegetation, and interactions with the carbon cycle. Uncertainties in the representation of these processes feed through into a range of projections from the many state-of-the-art climate models now being developed and used worldwide. For example, despite major improvements in climate models, the range of equilibrium global warming due to doubling carbon dioxide still spans a range of more than 3. Here a promising way to make use of the ensemble of climate models to reduce the uncertainties in the sensitivities of the real climate system is reviewed. The emergent constraint approach uses the model ensemble to identify a relationship between an uncertain aspect of the future climate and an observable variation or trend in the contemporary climate. This review summarizes previous published work on emergent constraints and discusses the promise and potential dangers of the approach. Most importantly, it argues that emergent constraints should be based on well-founded physical principles such as the fluctuation-dissipation theorem. This review will stimulate physicists to contribute to the rapidly developing field of emergent constraints on climate projections, bringing to it much needed rigor and physical insights.

Figure 1

Schematic showing the most common procedure used to derive emergent constraints on Earth system sensitivities. An ensemble of ESMs (each red dot is an individual ESM) running the same experiment (the PDF on the right-hand $y$ axis represents the spread in the ensemble) is used to identify an emergent relationship (black dashed line with gray uncertainty range) between an uncertain Earth system sensitivity $Y$ ($y$ axis) and an observed trend or variation $X$ ($x$ axis). An observation of the trend or variation (blue PDF on the $x$ axis) can then be combined with the model-based emergent relationship to derive an emergent constraint on the Earth system sensitivity (green PDF on the left-hand $y$ axis).

Figure 2

Emergent relationship between springtime snow albedo feedback (SAF) across Northern Hemisphere land under climate change ($Y$) and an observable snow albedo feedback associated with the current climate’s seasonal cycle ($X$). An observational estimate derived from satellite data is shown as a vertical bar. Each point represents an individual climate model from the three most recent generations (CMIP3, CMIP5, and CMIP6). Methodology for calculating SAF is adapted from [132] [further details were provided by 172].

Figure 3

Emergent constraints on Earth system sensitivities based on some key examples published in the literature. (a) Snow albedo feedback derived from the snow seasonal cycle ([59]). (b) Sensitivity of tropical land carbon to global warming calculated from interannual variability in ${\mathrm{CO}}_2$ ([35]). (c) Atmospheric ${\mathrm{CO}}_2$ concentration at 2060 projected from atmospheric ${\mathrm{CO}}_2$ concentration at 2010 ([70]). (d) ${\mathrm{CO}}_2$ fertilization of plant photosynthesis calculated from changes in the seasonal cycle of ${\mathrm{CO}}_2$ ([189]). (e) Sensitivity of tropical ocean primary production to warming derived from interannual variability ([91]). (f) Global ocean carbon sink in the 2090s projected from the current day carbon sink in the Southern Ocean ([80]). (g) Equilibrium climate sensitivity calculated from interannual variability of temperature ([34]). (h) Transient climate response determined from the increase in global mean temperature ([121]). In each case the emergent constraint was reconstructed from data available in the literature or provided directly by the authors. The model ensemble used in each original study is shown in the brackets after the panel title.

Figure 4

High correlations between pairs of variables across small ESM ensembles are expected by chance. To illustrate this point, the fraction of all possible pairs of variables across a toy ESM ensemble of size $n$ plotted against correlation $r$. Each ESM is not a real ESM: it is represented by a random variable drawn from a normal distribution of unit standard deviation, and each of the $n$ ESMs produces $m=100$ output variables, giving 4950 different possible variable pairs to correlate with each other. This example is designed to be a worst case scenario yet still shows that a calculated correlation even between uncorrelated objects can be large in small enough ensembles. Left panel: histograms of fraction of datasets with correlation falling in a particular interval. Right panel: total fraction of datasets with magnitude of correlation greater than $|r|$. Ensemble size is varied for toy ESM ensemble sizes of $n=5$, 30, and 100.

Figure 5

Different types of emergent constraints proposed in the literature to date. Each number corresponds to a study listed in Table 1. ECs are sorted by the timescale of their current climate quantity and the type of future constrained quantity. ECs are also sorted by whether the future quantity relates to an impact or a physical or geochemical quantity.

Figure 6

Using a quadratic relationship decreases the uncertainty in $Y$ compared to a linear fit provided that the observations line up with the shallow section of the quadratic function. Illustration with synthetic data.

Figure 7

Standard, ordinary least squares linear regression $p(y|x)$ compared with the reverse regression $p(x|y)$. If the latter were to be used as the relationship on which the emergent constraint is founded, the final constraint has a bias.