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
Vf1
Ct
Cw
Rhcrit
Flow dependent Rhcrit
Large scale cloud
Large scale cloud
Large scale cloud
Large scale cloud
Large scale cloud
Cloud fraction at saturation
Vertical gradient of cloud water in
grid box
Entrainment rate coefficient
Time scale for destruction of
CAPE
Convective anvils: excluding
convective precipitation from
cloud water path
Convective anvils: updraught
factor
Convective anvils: shape factor
Sea ice albedo
Ocean-ice diffusion coefficient
Ice particle size
Non-spherical ice particles
Shortwave water vapour
continuum absorption
Sulphur cycle
Large scale cloud
Large scale cloud
Order of diffusion operator
Diffusion e-folding time
Starting level for gravity wave
drag
Surface gravity wave parameters
Dynamics
Dynamics
Dynamics
Surface-canopy energy exchange
Land surface
Forest roughness lengths
Land surface/
Boundary Layer
Land surface
Dependence of stomatal
conductance on CO2
Number of soil levels accessed
for evaoptranspiration
Charnock constant
Free convective roughness length
over sea
Boundary layer flux profile
parameter, G0
Asymptotic neutral mixing length
parameter, λ
Description/Process Affected
Convection
Convection
Ice fall speed
Cloud droplet to rain conversion rate
Cloud droplet to rain conversion threshold
Threshold of relative humidity for cloud formation
Parameterisation of Rhcrit in terms of local variance of grid box
average relative humidities.
Cloud cover calculation
Account for effect of vertical cloud water gradients on cloud cover
calculation
Scales rate of mixing between environmental air and convective plume
Intensity of convective mass flux
Convection
Radiative properties of convective cloud
Convection
Fraction of convective cloud in which updraught occurs
Convection
Sea ice
Sea ice
Radiation
Radiation
Radiation
Shape of convective cloud
The dependence of sea ice albedo on temperature
Ocean to ice heat transfer
Effective radius of cloud ice spheres
Option to account for non-spherical ice particles
Option to account for shortwave absorption due to the self-broadened
continuum of water vapour
Option to include interactive calculation of sulphate aerosol loadings
accounting for sources, transport, physical removal and chemistry.
Spatial scale of diffusive damping of heat, momentum and moisture
Diffusion coefficients for heat, momentum and moisture
The lowest model level at which drag is applied
Radiation
Dynamics
Magnitude of hydrostatic and non-hydrostatic (trapped lee wave)
surface gravity wave stress
Option to account for effect of vegetation canopy on surface energy
balance
Surface fluxes over areas containing forest
Land surface
Option to remove dependence of stomatal conductance on carbon
dioxide concentration
Root depths
Boundary Layer
Boundary Layer
Roughness lengths and surface fluxes over sea
Surface fluxes over tropical oceans
Boundary Layer
Functions used to determine stability dependence of turbulent mixing
coefficients
Neutral mixing length required for calculation of turbulent mixing
coefficients
Boundary Layer
2
Supplementary Table 2: Parameter values and their effects on climate change feedback strength
Parameter/Property
Low
Intermediate
High
Switch
Vf1 (ms-1)
0.5
1.0
2.0
Effect on Climate Change
Feedback Strength (Wm-2K-1), of
perturbing parameter relative to
its setting in STD
δλ(low) = -0.17; δλ(high) = 0.02
Ct (s-1)
0.5x10-4
1x10-4
4x10-4
δλ(low) = 0.21; δλ(high) = -0.14
Cw (kgm-3)
land
sea
Rhcrit
Flow dependent Rhcrit
1x10-4
2x10-5
0.6
2x10-4
5x10-5
0.7
2x10-3
5x10-4
0.9
δλ(low) = -0.04; δλ(high) = 0.09
Cloud fraction at saturation
boundary layer value
free troposphere value
Vertical gradient of cloud water in grid box
0.5
0.5
Entrainment rate coefficient
Time scale for destruction of CAPE (hours)
0.6
1
On/Off
δλ(int) = 0.36; δλ(high) = 0.79
Convective anvils: excluding convective
precipitation from cloud water path
Convective anvils: updraught factor
Convective anvils: shape factor
Sea Ice Albedo
Albedo at 0 OC
Albedo at Tcold
Tcold (OC)
0.1
1
0
0.5
0.8
-10
Ocean-ice diffusion coefficient (m2s-1)
Ice particle size (  m)
2.5x10-5
25
Non-spherical ice particles
Shortwave water vapour continuum
absorption
Sulphur cycle
Order of diffusion operator*
Diffusion e-folding time* (hours)
Starting level for gravity wave drag*
Surface gravity wave parameters
Typical wavelength (m)
Trapped lee wave constant (m-3/2)
Surface-canopy energy exchange
Forest roughness lengths* (m)
dense evergreen needleleaf forest
dense deciduous needleleaf forest
dense deciduous broadleaf forest
equatorial rainforest
Dependence of stomatal conductance on CO2
Number of soil levels accessed for
evaoptranspiration*
forest
grass
Charnock constant
Free convective roughness length over sea
(m)
Boundary layer flux profile parameter
Asymptotic neutral mixing length parameter
δλ(low) = 0.02; δλ(high) = -0.08
δλ(on) = -0.12
0.7
0.6
3
2
0.8
0.65
9
4
2
1.0
3
0.57
0.8
-5
0.65
0.8
-2
1x10-4
30
3.75x10-4
40
4
6
3
6
12
4
24
5
1x104
1.5x105
1.5x104
2.25x105
2x104
3x105
0.5
0.5
0.5
1.05
0.78
0.78
0.70
2.10
On/Off
δλ(on) = 0.33
On/Off
δλ(low) = -0.54; δλ(high) = 0.08
δλ(on,low) = 0.09
δλ(on,int) = 0.08
δλ(on,high) = 0.02
On/Off
λ(on) = -0.04
On/Off
On/Off
δλ(on,low)=0.00
δλ(on,int)=0.04; δλ(on,high)=0.02
δλ(int) = -0.04; λ(high-int) = -0.10
δλ(low) = -0.14; δλ(int) = -0.07
δλ(low) = 0.01; λ(high-int) = 0.05
On/Off
On/Off
δλ(on) = -0.03
δλ(on) = 0.03
On/Off
δλ(on) = 0.02
δλ(low) = -0.01
δλ(low) = -0.05; δλ(high) = 0.02
δλ(int) -0.03; δλ(high) = -0.07
δλ(low) = -0.04; δλ(int) = -0.04
On/Off
δλ(on) = -0.05
δλ(low) = 0.00
δλ(int) = 0.00
δλ(high) = 0.00
On/Off
δλ(on) = 0.19
δλ(low) = 0.00; δλ(int) = -0.04
2.0
2.0
2.0
2.9
2
1
0.012
2x10-4
3
2
0.016
1.3x10-3
4
3
0.020
5x10-3
δλ(int) = 0.00; δλ(high) = -0.05
δλ(low) = -0.02; δλ(high) = 0.02
5
0.05
10
0.15
20
0.5
δλ(low) = 0.00; δλ(high) = 0.00
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 CO 2
and ΔT is the equilibrium response of globally averaged surface temperature to ΔQ.
3
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 CO 2)
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
CPI jk 
1
2
 ANN
MSE , where MSE 
1 n
 wi (mi  oi )2
n i 1
.
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 latitudeheight 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. ERA 5 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 measurements 10.
4
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
1.5m temperature (oC)
Pressure at mean sea level (hPA)
Precipitation (mm/day)
Westerly wind (ms-1)
Temperature (oC)
Relative humidity (%)
Outgoing long-wave radiation at top of
atmosphere (Wm-2)
Outgoing short-wave radiation at top of
atmosphere (Wm-2)
Short-wave cloud forcing (Wm-2)
Long-wave cloud forcing (Wm-2)
High-top optically thick cloud (%)
High-top medium optical thickness cloud (%)
High-top optically thin cloud (%)
Medium-top optically thick cloud (%)
Medium-top medium optical thickness cloud
(%)
Medium-top optically thin cloud (%)
Low-top optically thick cloud (%)
Low-top medium optical thickness cloud (%)
Low-top optically thin cloud (%)
Net downward short-wave radiation flux at
surface (Wm-2)
Net downward longwave radiation flux at
surface (Wm-2)
Sensible heat flux (Wm-2)
Latent heat flux (Wm-2)
Diurnal temperature range (oC)
250hPa velocity potential (s-1)
500hPa streamfunction (s-1)
Meridional streamfunction (s-1)
500hPa transient eddy kinetic energy (m2s-2)
Total runoff efficiency rate (%)
Sea-ice extent (m2)
Specific humidity
Source
CRU
ERA
Xie-Arkin
ERA
ERA
ERA
ERBE
Region used
Land only
Globe
Ocean between 30oS and 30oN and all land
Globe
Globe
Globe
Between 60oS and 60oN
Type of data used
Grid-point
Grid-point
Grid-point
Lat-height zonal-mean
Lat-height zonal-mean
Lat-height zonal-mean
Zonal mean
Weight
1
1
1
1
1
1
1
ERBE
Between 60oS and 60oN
Zonal mean
1
ERBE
ERBE
ISCCP D2
ISCCP D2
ISCCP D2
ISCCP D2
ISCCP D2
Between 60oS and 60oN
Between 60oS and 60oN
Ocean between 50oS and 50oN and all land
Ocean between 50oS and 50oN and all land
Ocean between 50oS and 50oN and all land
Ocean between 50oS and 50oN and all land
Ocean between 50oS and 50oN and all land
Zonal mean
Zonal mean
Grid-point
Grid-point
Grid-point
Grid-point
Grid-point
1
1
1/3
1/3
1/3
1/3
1/3
ISCCP D2
ISCCP D2
ISCCP D2
ISCCP D2
SOC
Ocean between 50oS and 50oN and all land
Ocean between 50oS and 50oN and all land
Ocean between 50oS and 50oN and all land
Ocean north of 40oS
Ocean north of 40oS
Grid-point
Grid-point
Grid-point
Grid-point
Zonal mean
1/3
1/3
1/3
1/3
1
SOC
Ocean north of 40oS
Zonal mean
1
SOC
SOC
CRU
ERA
ERA
ERA
ERA
GRDC/CRU
HadISST1
ERA
Ocean north of 40oS
Ocean north of 40oS
Globe
Globe
Globe
Globe
Globe
29 river basin catchments
13 sea-ice regions
Globe
Zonal mean
Zonal mean
Grid-point
Grid-point
Grid-point
Lat-height zonal-mean
Grid-point
Regional averages
Regional averages
Lat-height zonal-mean
1
1
1
1
1
1
1
1
1
1
Accounting for errors in statistical predictions of climate sensitivity
Linear predictions of the feedback strength of model versions containing multiple parameter perturbations (mpp) are constructed
from the impacts of individual parameter perturbations (ipp) diagnosed from the N (=52) experiments listed in Supplementary Table
2. 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. We make predictions of the form
N
pred  std   i (i  std ),
Eq. (2)
i 1
where λstd is the feedback strength found in the STD experiment (based on the simulated 600 year average), λi is the value of
feedback strength found in the ith ipp experiment (based on simulated 20 year averages) and 0≤ αi ≤1. We obtain values of λpred for
4x106 random combinations of values of the 29 perturbed parameters, generated assuming uniform a priori probabilities for all
possible values of each parameter. For parameters consisting of continuous variables this involves specifying a constant probability
for values within the extremes specified by experts. For logical switches we specify a 50% probability of on or off. Several of the
5
parameters (Supplementary Table 2) possess three discrete possible values and one (forest roughness lengths) possesses four.
For these we specify a probability of 1/M for each of the M possible values. For a given parameter value a piecewise linear
interpolation of predicted feedback strength is achieved by appropriate choices of αi for the relevant ipp integrations in Eq (2).
Suppose we run a verifying mpp simulation for a prediction obtained from Eq (2) for some particular choice of parameter
perturbations. If λmpp is the feedback strength in this simulation, the expected error variance of the prediction is
N
N
i 1
i 1
 (pred  mpp) 2   (t pred  t mpp) 2   i 2 2 (i )  (1  i ) 2  2 (std )   2 (mpp) ,
Eq. (3)
where < > denotes an average over many independent realisations and σ2(λ i), σ2(λ std) and σ2(λ mpp) are the error variances arising
from noise (natural variability) in the simulations from which the predictions are constructed and verified. The term
(t pred  t mpp) 2 is the prediction error which would be obtained given noise free (i.e. infinitely long) model integrations with
which to construct and verify the predictions. This term arises from non-linearity in the effects of combining individual parameter
perturbations.
It is clear from Eq (2) that the predictions λpred will be sensitive to λ std, because we sum the effects of a large number of parameter
perturbations calculated relative to its value. We therefore calculate values of λpred for each of 21 values of λstd sampling at equal
intervals the ± two standard deviation uncertainty range of 600 year mean values of 1.069 Wm-2K-1 to 1.088 Wm-2K-1 (estimated from
sampling statistics obtained from STD). For each value of λ std we use the following procedure to obtain the appropriate errors to
associate with our 4x106 mpp predictions:
(a)
We assume that the error variance terms in Eq (3) are all independent of location in parameter space, and calculate the
average value of the non-linear term from
N
(t pred  t mpp) 2  (pred  mpp) 2  i 2 2 (i )   2 (mpp),
Eq. (4)
i 1
where the overbar represents an average over parameter space. Equation (4) is a rearrangement of Eq (3) without the
σ2(λ std) term, since we are calculating the prediction error expected assuming the relevant value of λ std is the true
(population mean) value. We approximate the first term on the right hand side using predictions for 13 mpp cases for
which we possess (20 year) verifying simulations. The noise terms on the right hand side are estimated from the variability
of 20 year mean climate sensitivities found in STD.
(b)
Using our estimates of
(t pred  t mpp) 2
and σ2(λ i) from (a), we loop through our 4x106 mpp choices and calculate the
expected error associated with each λpred as the sum of the first two terms on the right hand side of Eq (3). The non-linear
term is the larger of the two, typically amounting to ~(0.12 Wm-2K-1)2.
Repeating this procedure for 21 values of λstd gives us 21x4x106 values of λpred, each expressed as a Gaussian distribution with
standard deviation based on the accompanying error. These distributions are then combined to form the the blue pdf of Figure 3 in
the main text, weighting distributions derived from different values of λstd according to the probability of λstd obtained from its
sampling distribution. The red pdf is produced in the same manner, with an additional weighting of exp(-½CPI2) applied to the
different mpp combinations. Values of CPI were obtained using linear predictions of the properties of the present day (control)
simulations of the mpp combinations. These were found to be accurate for the 13 mpp cases for which verifying simulations were
available.
The widths of the pdfs are influenced most strongly by several parameters associated with cloud properties (see Supplementary
Table 2), notably convective entrainment rate (the low value substantially increases climate sensitivity relative to STD), cloud
fraction at saturation (increasing this reduces climate sensitivity relative to STD) and the switch to account for sub grid scale
variations in cloud water (reduces climate sensitivity when activated).
Our estimates of
(t pred  t mpp) 2 are uncertain, having been obtained from only 13 verifying mpp cases. We checked the
sensitivity of our results by doubling the estimates of the errors applied to the 21x4x10 6 predictions, finding that this increased the
upper confidence limit of our pdfs from 5.3°C to 5.7°C (non-CPI weighted version) and from 5.4°C to 5.9°C (CPI weighted version).
The results also depend on our assumed distributions of parameter values, in particular the expert-specified limits for the ranges of
continuously variable parameters. We performed a sensitivity test in which we assumed a 15% chance of values outside both the
lower and upper specified limits. This represents an extreme scenario in which all experts are assumed to have underestimated the
6
ranges of continuous parameters by 43%. This test significantly widened the 5-95% confidence interval of the unweighted pdf to 1.78.0°C, but changed that of the CPI-weighted pdf only modestly (to 2.4-5.9°C), demonstrating that the CPI provides a highly effective
observational constraint on both the low and high end of the predicted sensitivity range.
Finally we checked our sampling of parameter space by recalculating the pdfs based on a subset of 1x10 6 parameter combinations,
finding almost identical results to those based on all 4x106 combinations.
Impact of biases in sea surface temperature
Our experimental design ensures that time-averaged sea surface temperatures (SSTs) in the present day (control) simulations remain
close to the observed climatology. Ideally, however, our ensemble should sample biases in SST consistent with observational
uncertainties. We tested the impact of SST biases by repeating the simulations of four ensemble members with the heat convergence file
calibrated for the relevant experiment (see discussion in Methods) replaced by the heat convergence file from STD. Use of the wrong
heat convergences introduced systematic biases to SSTs by supplying heat fluxes to the mixed layer ocean different from those
calibrated to achieve reproduction of observed SSTs. We chose ensemble members which would develop relatively large SST biases
when run with the STD heat convergence file. One simulation (convective entrainment =0.6) gave a simulation so unrealistic that it
eventually became numerically unstable. The other three experiments produced biases dominated by a systematic shift in globally
averaged SST of 1.6°C, -2.2°C and -6.5°C respectively. These biases are much larger than is justified by observational uncertainties: for
example interannual variability of global SST about the long term moving average amounts to approximately 0.2°C11. In order to estimate
the impact of less extreme SST biases we repeated our test experiments using heat convergences following the pattern found in the
standard model version, but corrected to produce the same global mean value as in the original experiment. In this case the convective
entrainment experiment remained stable, so we obtained four further simulations showing a smaller (but still substantial) set of biases of
-2.8°C, -0.8°C, 0.7°C and 1.0°C. On doubling CO2 six of our seven simulations gave changes in climate feedback strength in the range 0.16 to 0.18 Wm-2K-1, equivalent to an uncertainty in climate sensitivity of ~0.5°C when applied to a model version with a typical value of
3.5°C. All cases with a negative SST bias led to a reduction in climate sensitivity while cases with a positive bias increased climate
sensitivity. The case with the largest warm bias of 1.6°C gave a reduction in feedback strength of 0.28 Wm-2K-1, due to an enhancement
of the potential for positive cloud feedback caused by unrealistically strong convection driven by the unrealistically warm SSTs. This
would imply a typical increase in climate sensitivity of 1.2°C, demonstrating that extreme positive values of SST bias can affect climate
sensitivity to a significant degree. However the effect in cases with smaller positive biases is much more modest, amounting to no more
than 0.5°C.
In summary, the results indicate that the impact on climate sensitivity of accounting for SST biases consistent with observed natural
variability, or even with the change of ~0.5°C observed since the industrial revolution11, is unlikely to exceed 0.5°C. We estimated the
impact that incorporating this additional uncertainty would have by repeating the calculation of our climate sensitivity pdf with uncertainty
arising from SST bias treated as an additional “GCM parameter” in Eq (2). We assumed an uncertainty in feedback strength sampled
uniformly from a range bounded by extrema of ±0.16 Wm-2K-1. This resulted in a marginal increase in the 5-95% confidence intervals
associated with our pdfs. For example the range for the blue pdf in Figure 3 (main text) changed from 1.9-5.3°C to 1.8-5.4°C. These
results suggest that accounting for the influence of SST biases consistent with observational uncertainties would increase only slightly
the spread of climate sensitivity found by perturbing parameters in the GCM.
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