Credit: Allen, M., Ingram, W. (2002). Precipitation change at the time of CO2 doubling averaged over all the members of the CMIP-2 ensemble for which the data were available (14 models), for the 20 years centred on the time of CO2 doubling.

Reducing Uncertainties in Climate Projections With Emergent Constraints. Part 2: Examples

In a previous post, I described the concept of emergent constraints, which allow us to narrow uncertainties in climate change projections through empirical relationships that relate a model’s climate response to observable metrics. The credibility of an emergent constraint relies upon the strength of the statistical relationship, a clear understanding of the mechanisms underlying the relationship, and the accuracy of observations. A number of emergent constraints have already been identified, with different weaknesses and strengths. This post aims to summarize some of them.

The pioneers

In the late 1990s, signs of climate feedback started to be constrained by using climate models along with observations (e.g., Hall and Manabe, 1999). But even today, inter-model differences in climate projections remain large, and need to be constrained. To my knowledge, the first attempt at establishing an emergent constraint was made by Allen and Ingram in 2002. It is also the first paper introducing the concept of an “emergent constraint” in the climate sciences. The authors tried to constrain the global-mean future precipitation change simulated by the set of climate models participating in the CMIP2 model intercomparison project through observable temperature variability and a simple energetic framework. Despite the inability to robustly quantify future precipitation changes from the inter-model differences, they introduced the concepts that established emergent constraints in the climate sciences: emphasizing the need for physical understanding of emerging constraints and discussing how observations can be used to constrain climate projections.

An early application of emergent constraints concerned the snow-albedo feedback. Hall and Qu (2006) showed that differences among models in seasonal northern hemisphere surface albedo changes are well correlated with global-warming albedo changes in CMIP3 models. The three main criteria for a robust emergent constraint are satisfied: the physical mechanisms are well understood, the statistical relationship between the quantities of interest is strong, and uncertainties in the observed variations are weak, allowing Hall and Qu to constrain the snow-albedo feedback under global warming. Despite this successful application of an emergent constraint, the generation of models that followed (CMIP5) continued to exhibit a large spread in seasonal variability of snow-albedo changes (Qu and Hall 2014). 

Model biases and climate sensitivity

The success of the Hall and Qu study paved the way for a number of studies seeking emergent constraints for equilibrium climate sensitivity (ECS). A way to do so is to find highly correlated relationship between characteristics of the current climate and the spread in ECS. Then, ECS values suggested by the models that are least biased relative to observations can be assumed to be more likely.

The first study using this framework is Volodin (2008), who showed that models with higher ECS in the current climate exhibit larger differences in cloud cover between the tropics and the extra-tropics (see also the study by Siler et. al 2017) and lower tropical relative humidity (also seen in Fasullo and Trenberth 2012). The observational constraint in Volodin (2008) suggests that climate sensitivity more likely lies in the upper range of model estimates (ECS most likely around 3.5 K), in agreement with more recent studies by Siler et. al (2017) (ECS around 3.7 K), Fasullo and Trenberth (2012) (ECS around 4 K), and Brown and Caldeira (2017) (ECS around 3.7 K).

A number of additional metrics to potentially constrain ECS have been found. Sherwood et. al (2014) related the spread in ECS to the strength of convective mixing in the atmosphere, defined as the sum between an index of small-scale mixing and an index of large-scale mixing. Observations suggest that most models underestimate the large-scale mixing. Comparison with observations indicates that ECS is most likely larger than 3 K. The level of confidence in this estimate is related to the trust one gives to the link between the lower-tropospheric characteristics these indices aim to quantify and the low-cloud feedback, which primarily controls the intermodel spread in ECS. The observational constraint should also be viewed with caution since it is based on re-analysis data and hence is influenced by weather forecasting models.

Nevertheless, Sherwood et. al (2014) highlight that misrepresentation of tropical dynamics by models may explain differences in ECS. This is related to the study by Tian (2015), which links the intensity of the double ITCZ bias to the spread of ECS. They show that the more realistic models are those with the highest climate sensitivities (~4 K). Recently, cloud processes have been highlighted as potential drivers of the double ITCZ bias in climate models (Hwang and Frierson 2013, Adam et. al 2016, 2017). Together these studies suggest hidden relationships between low clouds, circulation, and climate sensitivity, which remain to be unraveled.

Cloud feedback

Knowing that the spread in ECS is mostly related to uncertainties in low-cloud feedback, it seems obvious that constraining how low clouds respond to global warming can reduce the spread of climate sensitivity among models. Conversely, many emergent constraints on ECS can be understood as encoding properties of shortwave low-cloud feedbacks (Qu et. al 2018).

A number of studies have highlighted relationships between low-cloud amount changes under global warming and modeled variations of low clouds with changes in specific meteorological conditions (such as surface temperature, inversion strength, subsidence) (Qu et. al 2013, 2015, Myers and Norris 2015, 2016, Brient and Schneider 2016). These studies show that the decrease in low-cloud amount with surface warming overcompensates the low-cloud increase by inversion strengthening seen in a warmer climate, and more realistic models tend to exhibit larger low-cloud feedback and higher ECS (see this blog post for a more thorough discussion). Criticisms may arise (1) about inconsistencies between the dynamics of model clouds and those in the real world; (2) about the short time period (a decade or so) of observed cloud variability, which may not reflect long-term feedback (Zhou et. al 2015); or (3) about the fact that climate models might all be biased. Yet the convergence of studies using different methodologies and different observations increases our confidence that low-cloud feedback and ECS more likely lie in the upper range of the state-of-the-art climate model estimates. It is worth noting that inferences of climate sensitivity from energy budget estimates suggest low ECS values, i.e., ~2 K, but their uncertainty is so large that they cannot exclude much higher ECS (Forster 2016). 

Two important cloud responses need to be constrained as well. The changes in liquid water content (related to the cloud optical depth) and the high-cloud feedback. The former response has been investigated in Gordon and Klein (2014). They suggest that models are usually biased high, suggesting that the negative mid-latitude low-cloud feedback should be weaker than the models’ average. This bias may be explained by a misrepresentation of mixed-phase extratropical clouds, often pinpointed as playing a key role in driving global-cloud feedback and uncertainties in climate sensitivity estimates (e.g., Tan et. al 2016). The latter feedback remains largely unconstrained despite the well-known physical mechanisms explaining the high-cloud elevation with warming (Hartmann and Larson, 2002). Yet it remains unknown to what extent high-cloud amount and high-cloud optical depth change with warming. These changes are related to upper-tropospheric divergence and microphysics, which need to be constrained individually. Some recent studies suggest a decreasing high-cloud amount due to more efficient large-scale organization with warming (Bony et. al 2016), results that may point the way toward mechanistic emergent constraints on high-cloud feedback.

Merging realistic estimates of low-cloud amount, high-cloud amount, and extratropical optical depth feedbacks would likely increase our confidence in constraints on climate sensitivity from climate models.

Climate change

Other branches of climate science use the concept of emergent constraints. Following Allen and Ingram (2002), the response of precipitation continues to be studied with a specific focus on the most extreme events. Links between interannual variability of extreme precipitation and temperatures offer possible observational constraints, especially since the underlying physical mechanisms are relatively well understood (e.g., O’Gorman and Schneider, 2009). These constraints usually suggest a stronger intensification of heavy rainfall with warming (O’Gorman 2012, Borodina et. al 2017).

A second highlighted topic is the sensitivity of the carbon cycle change. Cox et. al (2013) found a robust relationship between the efficiency of carbon release into the atmosphere with interannual variations of tropical temperature and the weakening in carbon storage under global warming. Observations highlight that most climate models overestimate the present-day sensitivity of land CO2 changes, suggesting a too strong weakening of CO2 tropical land storage with climate change. This has been followed by a number of studies that constrain other aspects of the climate-carbon cycle feedbacks (e.g., Wenzel et. al 2016).

Paleoclimate simulations

Changes in global-mean temperature induced by Earth’s orbital variations may be used to quantify the climate sensitivity. When imposing such orbital variations, climate models suggest different global-mean temperature responses. These differences may be related to the spread in ECS. For instance, Hargreaves et. al (2012) showed that the simulated global-mean cooling during the Last Glacial Maximum (LGM, 19-23 ka before present) is inversely correlated to ECS in CMIP3 models. Constraining the LGM cooling from proxy data yields a most likely climate sensitivity around 2.5 K, which is lower than ECS estimates based on present-day variability and/or the mean state. A number of criticisms may arise from this inference, such as the realism of the LGM CMIP simulations, uncertainty in the temperatures inferred from proxies, and the use of paleoclimates as a surrogate for global warming (differences in temperature patterns, albedo feedback etc.). These uncertainties may partly explain the typically weak correlations found between paleoclimate indices and climate projections, and the difficulty in narrowing the spread in models’ climate sensitivity estimates from paleoclimate-based emergent constraints (Schmidt et. al 2014, Harrison et. al 2015).


This diversity of emergent constraints highlights the commitment of the climate community to narrowing uncertainties in climate projections. This interest will likely continue to grow since a large number of changes in climate phenomena remain uncertain, even when fundamental mechanisms are relatively well understood (e.g., changes in monsoons, heat waves, cyclones). The upcoming CMIP6 project will likely boost the enthusiasm for emergent constraints. This calls for robust statistical inference for giving credible constraint estimates that should be shared across studies. And beyond the post-facto model evaluation, it will be interesting to see whether new climate models will take advantage of emergent constraints to improve their simulation of present-day climate and to reduce uncertainties in future projections.