6
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.
Parameter /Component of GCM physics
/Description/Process Affected
Vf1 / Large scale cloud / Ice fall speedCt / Large scale cloud / Cloud droplet to rain conversion rate
Cw / Large scale cloud / Cloud droplet to rain conversion threshold
Rhcrit / Large scale cloud / Threshold of relative humidity for cloud formation
Flow dependent Rhcrit
/ Large scale cloud / Parameterisation of Rhcrit in terms of local variance of grid box average relative humidities.Cloud fraction at saturation / Large scale cloud / Cloud cover calculation
Vertical gradient of cloud water in grid box / Large scale cloud / Account for effect of vertical cloud water gradients on cloud cover calculation
Entrainment rate coefficient / Convection / Scales rate of mixing between environmental air and convective plume
Time scale for destruction of CAPE / Convection / Intensity of convective mass flux
Convective anvils: excluding convective precipitation from cloud water path / Convection / Radiative properties of convective cloud
Convective anvils: updraught factor / Convection / Fraction of convective cloud in which updraught occurs
Convective anvils: shape factor / Convection / Shape of convective cloud
Sea ice albedo / Sea ice / The dependence of sea ice albedo on temperature
Ocean-ice diffusion coefficient / Sea ice / Ocean to ice heat transfer
Ice particle size / Radiation / Effective radius of cloud ice spheres
Non-spherical ice particles / Radiation / Option to account for non-spherical ice particles
Shortwave water vapour continuum absorption / Radiation / Option to account for shortwave absorption due to the self-broadened continuum of water vapour
Sulphur cycle / Radiation / Option to include interactive calculation of sulphate aerosol loadings accounting for sources, transport, physical removal and chemistry.
Order of diffusion operator / Dynamics / Spatial scale of diffusive damping of heat, momentum and moisture
Diffusion e-folding time / Dynamics / Diffusion coefficients for heat, momentum and moisture
Starting level for gravity wave drag / Dynamics / The lowest model level at which drag is applied
Surface gravity wave parameters / Dynamics / Magnitude of hydrostatic and non-hydrostatic (trapped lee wave) surface gravity wave stress
Surface-canopy energy exchange / Land surface / Option to account for effect of vegetation canopy on surface energy balance
Forest roughness lengths / Land surface/ Boundary Layer / Surface fluxes over areas containing forest
Dependence of stomatal conductance on CO2 / Land surface / Option to remove dependence of stomatal conductance on carbon dioxide concentration
Number of soil levels accessed for evaoptranspiration / Land surface / Root depths
Charnock constant / Boundary Layer / Roughness lengths and surface fluxes over sea
Free convective roughness length over sea / Boundary Layer / Surface fluxes over tropical oceans
Boundary layer flux profile parameter, G0 / Boundary Layer / Functions used to determine stability dependence of turbulent mixing coefficients
Asymptotic neutral mixing length parameter, λ / Boundary Layer / Neutral mixing length required for calculation of turbulent mixing coefficients
Supplementary Table 2: Parameter values and their effects on climate change feedback strength
Parameter/Property / Low / Intermediate / High / Switch / Effect on Climate Change Feedback Strength (Wm-2K-1), of perturbing parameter relative to its setting in STDVf1 (ms-1)
/ 0.5 / 1.0 / 2.0 / δλ(low) = -0.17; δλ(high) = 0.02Ct (s-1) / 0.5x10-4 / 1x10-4 / 4x10-4 / δλ(low) = 0.21; δλ(high) = -0.14
Cw (kgm-3)
land
sea / 1x10-4
2x10-5 / 2x10-4
5x10-5 / 2x10-3
5x10-4 / δλ(low) = -0.04; δλ(high) = 0.09
Rhcrit / 0.6 / 0.7 / 0.9 / δλ(low) = 0.02; δλ(high) = -0.08
Flow dependent Rhcrit
/ On/Off / δλ(on) = -0.12Cloud fraction at saturation
boundary layer valuefree troposphere value / 0.5
0.5 / 0.7
0.6 / 0.8
0.65 / δλ(int) = 0.36; δλ(high) = 0.79
Vertical gradient of cloud water in grid box
/ On/Off / δλ(on) = 0.33Entrainment rate coefficient
/ 0.6 / 3 / 9 / δλ(low) = -0.54; δλ(high) = 0.08Time scale for destruction of CAPE (hours) / 1 / 2 / 4 / On/Off / δλ(on,low) = 0.09
δλ(on,int) = 0.08
δλ(on,high) = 0.02
Convective anvils: excluding convective precipitation from cloud water path / On/Off / λ(on) = -0.04
Convective anvils: updraught factor / 0.1 / 1.0 / On/Off / δλ(on,low)=0.00
Convective anvils: shape factor / 1 / 2 / 3 / On/Off / δλ(on,int)=0.04; δλ(on,high)=0.02
Sea Ice Albedo
Albedo at 0 OC
Albedo at Tcold
Tcold (OC) / 0
0.5
0.8
-10 / 0.57
0.8
-5 / 0.65
0.8
-2 / δλ(int) = -0.04; λ(high-int) = -0.10
Ocean-ice diffusion coefficient (m2s-1) / 2.5x10-5 / 1x10-4 / 3.75x10-4 / δλ(low) = -0.14; δλ(int) = -0.07
Ice particle size (m) / 25 / 30 / 40 / δλ(low) = 0.01; λ(high-int) = 0.05
Non-spherical ice particles / On/Off / δλ(on) = -0.03
Shortwave water vapour continuum absorption / On/Off / δλ(on) = 0.03
Sulphur cycle / On/Off / δλ(on) = 0.02
Order of diffusion operator* / 4 / 6 / δλ(low) = -0.01
Diffusion e-folding time* (hours) / 6 / 12 / 24 / δλ(low) = -0.05; δλ(high) = 0.02
Starting level for gravity wave drag* / 3 / 4 / 5 / δλ(int) -0.03; δλ(high) = -0.07
Surface gravity wave parameters
Typical wavelength (m)
Trapped lee wave constant (m-3/2) / 1x104
1.5x105 / 1.5x104
2.25x105 / 2x104
3x105 / δλ(low) = -0.04; δλ(int) = -0.04
Surface-canopy energy exchange / On/Off / δλ(on) = -0.05
Forest roughness lengths* (m)
dense evergreen needleleaf forest
dense deciduous needleleaf forest
dense deciduous broadleaf forest
equatorial rainforest / 0.5
0.5
0.5
1.05 / 0.78
0.78
0.70
2.10 / 2.0
2.0
2.0
2.9 / δλ(low) = 0.00
δλ(int) = 0.00
δλ(high) = 0.00
Dependence of stomatal conductance on CO2 / On/Off / δλ(on) = 0.19
Number of soil levels accessed for evaoptranspiration*
forest
grass / 2
1 / 3
2 / 4
3 / δλ(low) = 0.00; δλ(int) = -0.04
Charnock constant / 0.012 / 0.016 / 0.020 / δλ(int) = 0.00; δλ(high) = -0.05
Free convective roughness length over sea (m) / 2x10-4 / 1.3x10-3 / 5x10-3 / δλ(low) = -0.02; δλ(high) = 0.02
Boundary layer flux profile parameter / 5 / 10 / 20 / δλ(low) = 0.00; δλ(high) = 0.00
Asymptotic neutral mixing length parameter / 0.05 / 0.15 / 0.5 / δλ(low) = 0.01; δλ(high) = 0.00
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.
Climate variable / Source / Region used / Type of data used / Weight1.5m temperature (oC) / CRU / Land only / Grid-point / 1
Pressure at mean sea level (hPA) / ERA / Globe / Grid-point / 1
Precipitation (mm/day) / Xie-Arkin / Ocean between 30oS and 30oN and all land / Grid-point / 1
Westerly wind (ms-1) / ERA / Globe / Lat-height zonal-mean / 1
Temperature (oC) / ERA / Globe / Lat-height zonal-mean / 1
Relative humidity (%) / ERA / Globe / Lat-height zonal-mean / 1
Outgoing long-wave radiation at top of atmosphere (Wm-2) / ERBE / Between 60oS and 60oN / Zonal mean / 1
Outgoing short-wave radiation at top of atmosphere (Wm-2) / ERBE / Between 60oS and 60oN / Zonal mean / 1
Short-wave cloud forcing (Wm-2) / ERBE / Between 60oS and 60oN / Zonal mean / 1
Long-wave cloud forcing (Wm-2) / ERBE / Between 60oS and 60oN / Zonal mean / 1
High-top optically thick cloud (%) / ISCCP D2 / Ocean between 50oS and 50oN and all land / Grid-point / 1/3
High-top medium optical thickness cloud (%) / ISCCP D2 / Ocean between 50oS and 50oN and all land / Grid-point / 1/3
High-top optically thin cloud (%) / ISCCP D2 / Ocean between 50oS and 50oN and all land / Grid-point / 1/3
Medium-top optically thick cloud (%) / ISCCP D2 / Ocean between 50oS and 50oN and all land / Grid-point / 1/3
Medium-top medium optical thickness cloud (%) / ISCCP D2 / Ocean between 50oS and 50oN and all land / Grid-point / 1/3
Medium-top optically thin cloud (%) / ISCCP D2 / Ocean between 50oS and 50oN and all land / Grid-point / 1/3
Low-top optically thick cloud (%) / ISCCP D2 / Ocean between 50oS and 50oN and all land / Grid-point / 1/3
Low-top medium optical thickness cloud (%) / ISCCP D2 / Ocean between 50oS and 50oN and all land / Grid-point / 1/3
Low-top optically thin cloud (%) / ISCCP D2 / Ocean north of 40oS / Grid-point / 1/3
Net downward short-wave radiation flux at surface (Wm-2) / SOC / Ocean north of 40oS / Zonal mean / 1
Net downward longwave radiation flux at surface (Wm-2) / SOC / Ocean north of 40oS / Zonal mean / 1
Sensible heat flux (Wm-2) / SOC / Ocean north of 40oS / Zonal mean / 1
Latent heat flux (Wm-2) / SOC / Ocean north of 40oS / Zonal mean / 1
Diurnal temperature range (oC) / CRU / Globe / Grid-point / 1
250hPa velocity potential (s-1) / ERA / Globe / Grid-point / 1
500hPa streamfunction (s-1) / ERA / Globe / Grid-point / 1
Meridional streamfunction (s-1) / ERA / Globe / Lat-height zonal-mean / 1
500hPa transient eddy kinetic energy (m2s-2) / ERA / Globe / Grid-point / 1
Total runoff efficiency rate (%) / GRDC/CRU / 29 river basin catchments / Regional averages / 1
Sea-ice extent (m2) / HadISST1 / 13 sea-ice regions / Regional averages / 1
Specific humidity / ERA / Globe / Lat-height zonal-mean / 1
Accounting for errors in statistical predictions of climate sensitivity