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

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8Experimental design

nonlinMIP is composed of a set of abruptCO2 experiments (the primary tools), plus a CO2-forced transient experiment. These build on the CMIP5 and CMIP6 DECK protocols (the required runs from these are detailed in Table 1). The additional nonlinMIP runs (Table 2) are assigned three priority levels. Three options for participation are: 1) only the ‘essential’ simulation; 2) all ‘high priority’ plus the ‘essential’ simulations; or, preferably, 3) all simulations. The experiments in Table 1 are required in all cases. All experiments must be initialized from the same year of a pre-industrial control experiment, except for abrupt4xto1x (see Table 2). A typical analysis procedure is outlined in section 5.
The nonlinMIP design is presently limited to CO2 forcing, although the same principles could be applied to other forcings.

9Basic analysis principles

This section outlines the general principles behind analysis of nonlinMIP results. The primary idea is to find where the step-response model (section 2) breaks: since the step-response model is based on a linear assumption, this amounts to detecting non-linear responses.
The aim is to focus subsequent analysis. If non-linearities in a quantity of interest are found to be small, then analysis may focus on understanding different timescales of response from a single abruptCO2 experiment: linearity means that the physical response (over a useful range of CO2 concentrations) is captured by a single abruptCO2 experiment. This represents a considerable simplification. If, on the other hand, non-linearities are found to be important, the focus shifts to understanding the different responses in different abruptCO2 experiments. The choice of which abruptCO2 experiments to focus on, and over which timescales, is discussed below.

9.1First step: check basic traceability of abrupt4xCO2 to the transient-forced response near 4xCO2

This is to confirm that the abruptCO2 experiments contain realistic physical responses in the variables of interest (as previously done for global-mean temperature and heat uptake for a range of CMIP5 models (Good et al., 2013), and for other global-mean quantities for HadCM3 (Good et al., 2011). This also, rules out the most pathological non-linearities (e.g. if the response to an abrupt CO2 change in a given GCM was unrealistic).
The linear step-response model should first be used with the abrupt4xCO2 response, to predict the response near year 140 of the 1pctCO2 experiment (i.e. near 4xCO2). This prediction is then compared with the actual GCM 1pctCO2 result. This should first be done for global mean temperature: this assessment has been performed for a range of CMIP5 models (Good et al., 2013; see Figure 8), giving an idea of the level of accuracy expected. If the abruptCO2 response is fundamentally unrealistic, it is likely to show up in the global temperature change. This approach may then be repeated for spatial patterns of warming, and then for the quantities of interest. Abrupt4xCO2 is used here as it has larger signal/noise than abrupt2xCO2, yet is representative of forcing levels in a business-as-usual scenario by 2100. However, the tests may also be repeated using abrupt2xCO2 – but compared with year 70 of the 1pctCO2 experiment (i.e. at 2xCO2).
The step-response model emulation under these conditions should perform well for most cases: the state at year 140 of the 1pctCO2 experiment is very similar to that of abrupt4xCO2 (same forcing, similar global-mean temperature), so errors from non-linear mechanisms should be minimal. If large errors are found, this may imply caution about the use of abruptCO2 experiments for these variables, or perhaps point to novel non-linear mechanisms that may be understood by further analysis.

9.2Second step: detecting nonlinear responses

Having established some level of confidence in the abruptCO2 physical response, the second step is to look for nonlinear responses. This first involves repeating the tests from step 1 above, but for different parts of the 1pctCO2 and 1pctCO2 ramp-down experiments, and using different abruptCO2 experiments for the step-response model.
An example is given in Figure 9 (but for different transient-forcing experiments). This shows results for global-mean precipitation in the HadCM3 GCM (Good et al., 2012). Here, the step-response model prediction using abrupt4xCO2 (red curves) only works where a transient-forced experiment is near to 4xCO2. Similarly, the prediction using abrupt2xCO2 (blue curves) works only near 2xCO2. Otherwise, quite large errors are seen, and the predictions with abrupt2xCO2 and abrupt4xCO2 are quite different from each other. This implies that there are large non-linearities in the precipitation response in this GCM, and that they may be studied by comparing the responses in the abrupt2xCO2 and abrupt4xCO2 experiments.
Having identified some non-linear response, and highlighted two or more abruptCO2 experiments to compare (in the previous example, abrupt2xCO2 and abrupt4xCO2), the non-linear mechanisms may be studied in detail by comparing the responses in the different abruptCO2 experiments over the same timescale (e.g. via the doubling difference, as in Figures 6,7). This allows (Good et al., 2012;Chadwick and Good, 2013) non-linear mechanisms to be separated from linear mechanisms (not possible in a transient-forcing experiment).


This paper outlines the basic physical principles behind the nonlinMIP design, and the method of establishing traceability from abruptCO2 to gradual forcing experiments, before detailing the experimental design and finally some general analysis principles that should apply to most studies based on this dataset.

This work was supported by the Joint UK DECC/Defra Met Office Hadley Centre Climate Programme (GA01101). Nathaelle Bouttes received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013), ERC Grant Agreement 247220, project “Seachange.”

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Table 1. List of CMIP5/CMIP6 DECK experiments required by nonlinMIP.





Pre-industrial control experiment


CO2 abruptly quadrupled, then held constant for 150 years.

Separate different timescales of response.


CO2 increased at 1% per year for 140 years (i.e. as CMIP5 1pctCO2 experiment), then decreased by 1% per year for 140 years (i.e. returning to pre-industrial conditions).

To test traceability of the abruptCO2 experiments to more realistic transient-forcing conditions. Adding the ramp-down phase explores physics relevant to mitigation and geo-engineering scenarios.

Table 2. NonlinMIP experimental design. Three options are: only the ‘essential’ simulation; all ‘high priority’ plus the ‘essential’ simulations; or, preferably, all simulations. The experiments in Table 1 are required in all cases.

Experiment (priority)



Abrupt2xCO2 (essential)

As abrupt4xCO2 (see Table 1), but at double pre-industrial CO2 concentration.

To diagnose non-linear responses (in combination with abrupt4xCO2).
Assess climate response and (if appropriate) make climate projections with the step-response model at forcing levels more relevant to mid- or low-forcing scenarios.

1pctCO2 ramp-down (high priority)

Initialised from the end of 1pctCO2. CO2 is decreased by 1% per year for 140 years (i.e. returning to pre-industrial conditions).

To test traceability of the abruptCO2 experiments to more realistic transient-forcing conditions. Adding the ramp-down phase explores a much wider range of physical responses, providing a sterner test of traceability. Relevant also to mitigation and geo-engineering scenarios, and offers a sterner test of.

Extend both abrupt2xCO2 and abrupt4xCO2 by 100 years (high priority)

Allow traceability tests (via the step-response model) against most of the 1pctCO2 ramp-up-ramp-down experiment.
Explore longer timescale responses than in CMIP5 experiment.
Permit improved signal/noise in diagnosing some regional-scale non-linear responses
Provide a baseline control for the abrupt4xto1x experiment.

Abrupt4xto1x (medium priority)

Initialised from year 100 of abrupt4xCO2, CO2 is abruptly returned to pre-industrial levels, then held constant for 150 years.

Quantify non-linearities over a larger range of CO2 (quantifies responses at 1xCO2).
Assess non-linearities that may be associated with the direction of forcing change.

Abrupt8xCO2 (medium priority)

As abrupt4xCO2, but at 8x pre-industrial CO2 concentration. Only 150 years required here.

Quantify non-linearities over a larger range of CO2.

Figure 1. Schematic illustrating a situation where linear mechanisms can cause climate patterns to evolve. This represents a scenario where forcing (black line) is ramped up, then stabilised.

Figure 2. Adapted (red ovals overlaid) from the IPCC Fifth Assessment Report (IPCC, 2013), Figures SPM.7 and SPM.9. Global mean warming (top) and global mean sea level rise (bottom), relative to 1986-2005, for rcp8.5 (red) and rcp2.6 (blue).

Figure 3. Illustrating a method (Gregory et al., 2004) for separating ‘fast’ and ‘slow’ responses to radiative forcing change. Figure adapted (labels in rectangles overlaid) from Zelinka et al. (2013). Global-mean cloud-induced SW flux anomalies against global warming, for the CanESM2 model (black & grey represent two methods of calculating cloud-induced fluxes). This also illustrates one test of traceability of abrupt4xCO2 to 1pctCO2 responses: the linear fit to the abrupt4xCO2 response (straight lines) passes through the 1pctCO2 response near 4xCO2 (i.e. near year 140 of that experiment).

Figure 4. Schematic illustrating the point that nonlinear mechanisms can cause climate patterns to differ at different forcing (and hence global temperature) levels.

Global mean temperature, K

Figure 5. Albedo feedback (dotted line) strength (y-axis) decreasing with global mean temperature (x-axis, K) in a climate model (figure from Colman and McAvaney, 2009).

Figure 6. Defining the ‘doubling difference’. Doubling difference = Δ42 – Δ21 (the difference in response between the first and second CO2 doublings. This is defined for a specific timescale after the abrupt CO2 change – in this example, it is the mean over years 50-149.

Doubling difference

Figure 7. Non-linear regional precipitation responses over the ocean in HadGEM2-ES (figure from Chadwick and Good, 2013). Precipitation change (mm/day) averaged over years 50-149 for (top) abrupt2xCO2 and (middle) abrupt4xCO2, and the doubling difference (bottom). Note that the top and bottom panels have the same scale.

Figure 8. Checking basic traceability of abrupt4xCO2 to a transient forcing experiment (1pctCO2) (figure from Good et al., 2013). Global-mean warming (K) averaged over years 120-139 of 1pctCO2 for (y-axis) the GCM simulation and (x-axis) the reconstruction from abrupt4xCO2 using the step-response method.

Figure 9. Finding nonlinear responses in transient forcing experiments. (figure from Good et al., 2012). Left: where CO2 is increased by 1% per year, then stabilised at 2x pre-industrial levels. Right: where CO2 is increased by 2% per year for 70 years, then decreased by 2% per year for 70 years. Black: GCM. Red: step-response model using the abrupt4xCO2 response. Blue: the abrupt2xCO2 response.
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