Supplementary Information s89

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Supplementary Information

Parameters and their perturbations

Several parameters were selected from each major component of atmospheric and surface physics in the GCM, namely large scale cloud; convection; radiation; boundary layer; dynamics; land surface processes; sea ice. Supplementary Table 1 lists the parameters and the physical processes they affect or represent. This is followed by their uncertainty ranges specified by experts (Supplementary Table 2) and a brief description of how perturbations were implemented.

Supplementary Table 1: Parameters identified for perturbation.

Component of GCM physics

Description/Process Affected

Flow dependent Rhcrit

Supplementary Table 2: Parameter values and their effects on climate change feedback strength

Vf1 (ms-1)

Flow dependent Rhcrit

Cloud fraction at saturation

Vertical gradient of cloud water in grid box

Entrainment rate coefficient

Grey shading denotes settings in the standard model version STD. Discrete parameters capable of assuming only the values shown are denoted by *. For forest roughness lengths three perturbation experiments were run since the setting for equatorial forest in STD corresponded to the low end of its uncertainty range, whereas the settings for other forest types were set to an intermediate value. Feedback strength, λ, is inversely related to climate sensitivity (ΔT) through the relationship λ=ΔQ/ΔT, where ΔQ is the radiative forcing at the top of the atmosphere resulting from a doubling of CO2 and ΔT is the equilibrium response of globally averaged surface temperature to ΔQ.

The “low” and “high” values represent the extremes of plausible ranges estimated by experts. Each perturbation not involving a logical switch was implemented simply by altering the relevant parameter to one of the values shown in Supplementary Table 2. Some parameters were perturbed as a linked set, namely Cw, cloud fraction at saturation, sea ice albedo, surface gravity wave parameters, forest roughness lengths, number of soil levels accessed for evapotranspiration. Perturbations requiring a logical switch involved invoking an additional feature or process (non-spherical ice particles, shortwave water vapour continuum absorption, sulphur cycle, surface-canopy energy exchange), removing a process (dependence of stomatal conductance on CO2) or altering the method of representing a process (flow dependent Rhcrit, vertical gradient of cloud water in grid box).

Several perturbations involved combinations of logical switches and changes to the value of a variable:

·  The intensity of the convective mass flux was varied by switching from the buoyancy-dependent parameterisation used in STD to an alternative approach in which it depends on CAPE/τ, where CAPE is the convective available potential energy and τ is the timescale for destruction of CAPE as convection proceeds. We then varied the mass flux by running ensemble members with τ set to 1,2 and 4 hours.

·  The assumption in STD that convective cloud occurs in a uniform column can be relaxed by switching on a parameterisation of convective anvils1. The scheme contains elements to adjust the cloud water path and the shape of the cloud. Implementing the anvil scheme involves setting a flag to exclude convective precipitation from the cloud water path. We ran an experiment with anvils on and updraught and shape factors equal to unity (as in STD) to quantify the impact of setting this flag. We ran a second anvil experiment with an updraught factor of 0.1 which further reduces the cloud water path by reducing the fraction of the cloud in which the updraught is assumed to occur. The shape factor introduces an anvil shape to the cloud (cloud cover at top of cloud = cloud cover at bottom x square of shape factor). We ran additional anvil experiments with shape factors of 2 and 3, in both of which the updraught factor was unity.

·  In STD RHcrit is a prescribed constant which takes different values on different atmospheric levels. We varied the value used above the lowest three levels (Table 1) while keeping values at the lowest three levels fixed at the settings of STD. A further experiment was run using an alternative approach in which RHcrit is specified in terms of the local variance of grid box relative humidity2, thus allowing it to vary with horizontal location and time as well as with vertical level.

GCM integrations

The GCM uses a 50m mixed layer ocean in which heat transport is prescribed as a heat convergence which varies with position and season. The heat convergences ensure that time averaged SSTs remain close to observed climatological values in the control simulation, however SSTs are allowed to vary in response to natural and forced variations. For each ensemble member heat convergences are calibrated from a preliminary simulation in which sea surface temperatures (SSTs) are reset to observed climatological values at each time step. Control (i.e. present day) and doubled CO2 GCM integrations are then run to equilibrium followed by a further 20 years from which climate statistics are generated. During both integrations SSTs vary in response to changes in the simulated atmosphere-ocean heat flux and the pre-calculated heat convergences are also added.

The Climate Prediction Index (CPI) and its components

The components of the CPI were generated by verifying simulated 20 year mean spatial fields against observational multi-year averages of varying length taken from the period 1960-2000 The observational datasets are listed in Supplementary Table 3. Verification was performed only over the region where a given observational field is considered reliable according to the accompanying reference. Variables listed as “Grid-point” consisted of single-level latitude-longitude fields, those listed as “Zonal mean” of single-level zonal averages varying with latitude. Those listed as “Lat-height zonal mean” are latitude-height distributions of zonal averages on 12 atmospheric pressure levels between 1000 hPa and 10 hPa. Observations of sea ice extents consisted of areal coverage in 13 separate regions, consisting of eight northern hemisphere seas3 plus five longitudinal sectors covering the southern oceans. The sub-components of the CPI for each season (March-May, June-August, September-November and December-February, denoted by j=1, 4) and climate variable (k) are defined as

, where . Eq. 1

In Eq (1) mi and oi are the simulated and observed data, n is the number of grid points, latitude bands or regions (for sea-ice), wi is the appropriate area-weight and σ2ANN is the spatial average of the simulated interannual variance. For fields consisting of latitude-height cross sections we applied equation (1) separately at each pressure level and then calculated CPIjk as a mass-weighted average of the results. The square of the CPI is a weighted average of the squares of the CPIjk, where the weights for the various components are shown in Supplementary Table 3. All components receive equal weight in the CPI apart from the nine fields of cloud cover (measured in each of three height and optical thickness categories). These were each given a relative weight of 1/3 since the observations of high, medium and low cloud for a given optical thickness are interdependent. Figure 4 of the main text shows the range of values across the ensemble of the CPI, and of components CPIk obtained by averaging sub-components CPIjk over the four seasonal values.

The CRU dataset4 provides gridded averages of surface air temperature and diurnal temperature range over land. ERA5 provides time averaged reanalyses of observations for various atmospheric variables. From SOC6 we obtain surface energy balance components zonally averaged over all ocean basins. Observations of cloud cover stratified according to height and optical thickness are obtained from the ISCCP D2 satellite retrievals7,8 while ERBE9 provides observations of zonally averaged planetary radiation budget components. Long-term averages of precipitation are based on a dataset combining gauge and satellite measurements10. Sea-ice extents are provided by the HadISST1 climatology11. Observations of runoff efficiency are obtained for 29 of the world’s major river basins by dividing runoff (obtained from river discharge observations12) by precipitation.

Supplementary Table 3. Observational data used in the climate prediction index.

Accounting for errors in statistical predictions of climate sensitivity