Application the Cloud Feedback Model Intercomparison Project (cfmip) to become a cmip6-Endorsed mip

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Thanks to D. Konsta for providing text for Section 2.9.

The nonlinMIP intercomparison project: physical basis, experimental design and analysis principles
P. Good1, T. Andrews1, N. Bouttes2, R. Chadwick1, J. M. Gregory2,1, J. A. Lowe1

[1]{ Met Office Hadley Centre, Exeter, United Kingdom}

[2]{ NCAS-Climate, University of Reading, Reading, United Kingdom}

Correspondence to: P. Good (


nonlinMIP aims to quantify and understand, at regional scales, climate responses that are non-linear under CO2 forcing (mechanisms for which doubling the CO2 forcing does not double the response). Non-linear responses can be large at regional scales, with important implications for understanding mechanisms and for GCM emulation techniques (e.g. energy balance models and pattern-scaling methods). However, these processes are hard to explore using traditional experiments, explaining why they have had little attention in previous studies. Some single model studies have established novel analysis principles and some physical mechanisms. There is now a need to explore robustness and uncertainty in such mechanisms across a range of models.

nonlinMIP addresses this using a simple, small set of CO2-forced experiments that are able to separate linear and non-linear mechanisms cleanly, with good signal/noise – while being demonstrably traceable to realistic transient scenarios. The design builds on the CMIP5 and CMIP6 DECK protocols, and is centred around a suite of abruptCO2 experiments, with a ramp-up-ramp-down experiment to test traceability to gradual forcing scenarios. The understanding gained will help interpret the spread in policy-relevant scenario projections.
Here we outline the basic physical principles behind nonlinMIP, and the method of establishing traceability from abruptCO2 to gradual forcing experiments, before detailing the experimental design and finally some analysis principles. The discussion on traceability of abruptCO2 to transient experiments is also relevant to the abrupt4xCO2 experiment in the CMIP5 and CMIP6 DECK protocols.


Climate impacts assessments require, at regional scales, understanding of physical mechanisms of climate change in GCM projections. Also required is the ability to emulate (using fast simplified climate models) GCM behaviour for a much larger range of policy-relevant scenarios than may be evaluated using GCMs directly. These two requirements may be combined into a single question: what is the simplest conceptual framework that has quantitative predictive power and captures the key mechanisms behind GCM scenario projections?
Often, a pragmatic choice has been to assume some form of linearity. In studies of the global energy balance, linearity is often assumed in the form of a constant climate feedback parameter. This parameter may be used to quantify feedbacks in different models (e.g. Zelinka et al., 2013) or, in emulation methods, to parameterise global energy balance models (e.g. Huntingford and Cox, 2000). In understanding or emulating regional patterns of climate change, it is often assumed that regional climate change is roughly proportional to global mean warming. In emulation work, this is termed 'pattern scaling' (Mitchell, 2003;Santer et al., 1990;Tebaldi and Arblaster, 2014), but this assumption may also be applied either explicitly or implicitly in understanding mechanisms. Sometimes, patterns of change per K of global warming are quantified; often, physical mechanisms are studied for a single period of a single forcing scenario (implicitly assuming that the understanding is relevant for other periods or scenarios).
While these approximations appear to work well under some circumstances, significant limitations are increasingly being revealed in such assumptions. These are of two types: different timescales of response, and non-linear responses. In discussing this, a complication arises in that different linearity assumptions exist. Henceforth we define 'linear' as meaning 'consistent with linear systems theory' - i.e. responses that are linear in model forcing (i.e. where doubling the forcing doubles the response; this is different from assuming that pairs of responses are linearly related to each other – as in pattern scaling).
Even in a linear system (where responses are linear in forcing), the relationship between two system outputs (e.g. between global-mean temperature and regional sea surface temperature - SST) will in general be non-linear. This is due to different timescales of response in different locations and/or variables. Examples include lagged surface ocean warming due to a connection with the deeper ocean (Chadwick et al., 2013;Held et al., 2010;Williams et al., 2008;Manabe et al., 1990;Andrews and Ringer, 2014) or the direct response of precipitation to forcings (Andrews et al., 2010;Allen and Ingram, 2002;Mitchell et al., 1987). One (generally false) assumption of pattern scaling, then, is that regional climate responds over the same timescale as global-mean temperature. Different timescales of response are especially important in understanding and predicting behaviour under mitigation and geoengineering scenarios (or over very long timescales).
Non-linear system responses (e.g. Schaller et al., 2013) are more complex to quantify, understand and predict than those of linear systems. Some examples have been known for some time, such as changing feedbacks through retreating snow/sea-ice (Colman and McAvaney, 2009;Jonko et al., 2013), or the Atlantic Meridional Overturning Circulation. More recently, substantial non-linear precipitation responses have been demonstrated in spatial patterns of regional precipitation change in two Hadley Centre climate models with different atmospheric formulations (Good et al., 2012;Chadwick and Good, 2013). This is largely due to simultaneous changes in pairs of known robust pseudo-linear mechanisms (Chadwick and Good, 2013). Non-linearity has also been demonstrated in the response under idealised geoengineering scenarios, of ocean heat uptake, sea-level rise, and regional climate pattterns, with different behaviour found when forcings are decreasing than when they are increasing (Bouttes et al., 2013;Schaller et al., 2014).
Investigation of these mechanisms at regional scales has been constrained by the type of GCM experiment typically analysed. Most previous analyses (e.g. Solomon et al., 2007) have used results from transient forcing experiments, where forcing changes steadily through the experiment. There are three main problems with this approach. First, information about different timescales of response is masked. This is because the GCM response at any given time in a transient forcing experiment is a mixture of different timescales of response (Good et al., 2013;Held et al., 2010;Li and Jarvis, 2009), including short-timescale responses (e.g. ocean mixed layer response from forcing change over the previous few years) through long-timescale behaviour (including deeper ocean responses from forcing changes multiple decades to centuries earlier). Secondly, in transient forcing experiments, non-linear behaviour is hard to separate from linear mechanisms. For example, in an experiment where CO2 is increased by 1% per year for 140 years ('1pctCO2'), we might find different spatial patterns at year 70 (at 2xCO2) than at year 140 (at 4xCO2). This could be due to nonlinear mechanisms (due to the different forcing level and associated different climate state). However, it could also be due to linear mechanisms: year 140 follows 140 years of forcing increase, so includes responses over longer response timescales than at year 70 (only 70 years of forcing increase). Thirdly, signal/noise ratios of regional climate change can be relatively poor in such experiments.
These three issues may be addressed by the use of idealised abruptCO2 GCM experiments (Forster et al., 2012;Zelinka et al., 2013;Jonko et al., 2013;Good et al., 2013;Good et al., 2012;Chadwick and Good, 2013;Chadwick et al., 2013;Bouttes et al., 2013;Gregory et al., 2004): an experiment where CO2 forcing is abruptly changed, then held constant. In abrupt CO2 experiments, responses over different timescales are separated from each other. Further, responses at different forcing levels may be directly compared, e.g. by comparing the response in abrupt2xCO2 and abrupt4xCO2 experiments over the same timescale - both have identical forcing time histories, apart from the larger forcing magnitude in abrupt4xCO2. Thirdly, high signal/noise is possible: averages may be taken over periods of 100 years or more (after the initial ocean mixed layer adjustment, change is gradual in such experiments). Recent work (Good et al., 2011;Good et al., 2012;Good et al., 2013;Zelinka et al., 2013) has established that these experiments contain global and regional-scale information quantitatively traceable to more policy-relevant transient experiments - and equivalently, that they form the basis for fast simple climate model projections traceable to the GCMs.
The CMIP5 abrupt4xCO2 experiments have thus been used widely: including quantifying GCM forcing and feedback behaviour (Gregory et al., 2004;Zelinka et al., 2013), and for traceable emulation of GCM projections of global-mean temperature and heat uptake (Good et al., 2013;Stott et al., 2013). Abrupt4xCO2 is also part of the CMIP6 DECK protocol (Meehl et al., 2014).
NonlinMIP extends the CMIP5 and CMIP6 DECK designs to explore non-linear responses (via additional abruptCO2 experiments at different forcing levels. It also explores responses over slightly longer timescales (extending the CMIP5 abrupt4xCO2 experiment by 100 years).

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