CESD
Scottish Alliance for Geoscience, Environment & Society
Constraining Climate Sensitivity using Top Of
Atmosphere Radiation Measurements
Simon Tett 1 , Mike Mineter 1 , Coralia Cartis 2 , Dan Rowlands 3 & Ping
Liu 2
1: School of Geosciences, University of Edinburgh
2: School of Mathematics, University of Edinburgh
3: AOPP, Department of Physics, University of Oxford

Aims
CESD
• Report on attempts to optimise atmospheric model parameters to observed global-mean radiation measurements.
• Use results from these simulations to give probabilistic estimate of climate sensitivity.

Key results
CESD
• Successfully optimised HadAM3 to outgoing longwave (OLR) and Reflected Shortwave
(RSR) observations.
• Many large scale simulated variables correlate strongly with OLR and RSR
• There is a relationship between equilibrium climate sensitivity and simulated outgoing radiation
• Uncertainty analysis on “plausible” HadAM3 models rules out ECS > 5.6K (and < 2.7K)

CESD
Estimates of Climate Sensitivity using models and observations
From IPCC
CH9 (fig 9.2), after Hegerl et al., Nature
2006. Bars are
5-95% range

Philosophy
CESD
• Model is a tool which encapsulates our (best) knowledge of relevant physics of the system.
• Future predictions are based on models
• A model is useful for specific purpose if it is consistent with relevant observations
• Uncertainty in future predictions arises because many models are consistent with observations but make different predictions.

Observational Data
CESD
• Use the CERES (Clouds and the Earth's Radiant
Energy System) record of Leob et al, 2009.
• CERES flying on TERA & AQUA satellites
• Two instruments:
– 0.3 to 5 μm (SW)
– 0.3 to 200 μm (Total)
– Estimate LW from difference between Total & SW
– Adjusted to be in net imbalance as estimated from ocean data.
– For M arch 2000-Feb 2005
• Also explore sensitivity to use of ERBE data

Experimental Design
CESD
• HadAM3 (Atmospheric model – Pope et al,
2000) simulations forced by observed Sea
Surface Temperatures & Sea Ice.
• Modify four parameters in model which are known to affect climate sensitivity
– ENTCOEF -- rate at which convective plumes and environment mix
– VF1 -- speed of falling precipitation
– CT -- rate at which water vapour converted to precipitation
– RHCRIT -- critical humidity at which clouds form.
• Simulations started Dec 1998 and ran though to
April 2005 starting from same initial condition.

Experimental Design (Cont.)
CESD
• Modified package of forcings as Tett et al, 2007
– Well mixed GHG, Ozone, Land-Surface, Aerosols,
Volcanoes and Total Solar Irradiance
• Modifications:
– Fix to long-standing bug in SW Rayleigh scattering
– Use recent values of TSI (1361 W/m 2 from Kopp &
Lean, 2011)
– Slight changes to GHG – using observed values rather than A2.
• Compare simulated global-avg RSR and OLR with CERES observations for the average March
2000 to Feb 2005. First 14 months ignored allowing land-sfc to adjust to parameter change.

Optimisation Algorithm applied to
HadAM3 simulations
CESD
• Error= Root Mean Square difference of 5-year global average RSR and OLR from simulation vs target
• “Line search”
– Compute finite derivatives d Error/d param for each one of four parameters. Need to perturb parameters enough to make reasonable estimate of the derivative. We perturbed by 5-
10% of the parameter range.
– Use these to compute direction in which Error is most reduced.

Optimisation Algorithm (Cont.)
CESD
• Parameters are scaled so they have similar magnitudes.
• Jacobian is under-determined so regularise by adding scaled identity matrix till it is invertible.
This makes us prefer solutions where all parameters have similar magnitudes.
• Do trials at 30%, 90 % and the full vector.
• If these values are outside the range of permissible parameter values we move along the boundary.

Optimisation Algorithm (Cont.)
CESD
• Use the smallest of the three “line search” values to update the parameters and start again.
• Terminate when error less than specified value
(normally 1 W m -2 ) or no improvement in line search.
Deriv
Initial
Line
Search

CESD
CERES
High Sens
Optimisation Trials
ERBE
• Convergence
Low Sens to “zero” error for all but
CERES high sens case
• CERES case took 3 iterations
• ERBE cases took 8 & 9 iterations

Optimisation
CESD
• Carried out 16 optimisation cases with initial values the extreme parameter choices with
CERES target. Extreme parameter choice is set each one of 4 parameters to maximum or minimum value.
• Many simulations failed… (“blew up”)
• Redo at 75% of distance between reference case and max/min.
• Then carry out set of trials with various target values

Optimisation Trials (Summary)
Target Suc.
M. Fail Fail Con.
Iter.
(99.5, 239.6) 4 12 0 3-6 (4) CERES
(100%)
CERES(75%) (99.5, 239.6) 15 0 1 1-8 (4)
ERBE
Nr ERBE
TGT#1
TGT#2
TGT#3
(106.5, 234.4) 12
(105.5, 234.4) 13
(97, 245) 4
(98, 237)
(101, 243)
13 2
12 2
4
2
1
1
1
0
1
11
3-7 (3)
2-8 (4)
2-9 (5)
1-6 (3)
2-8 (4)

Optimisation Summary
CESD
• Failure to converge as (un)common as model failure.
• Can adjust model parameters to produce models that are within 1 Wm 2 of observations.
• Takes about 3-4 iterations. Each iteration requires 7 simulations each of 6 years of atmospheric model. This is very efficient…

CESD
What is responsible for changes in
RSR/OLR?
Little change in clear sky
OLR due to compensation between RH and temperature.
Changes in radn arise from cloud changes.

Other variables
CESD
• Why did you not include more variables in
RMS error and minimise the total?
• Answers:
1. Model needs to have good simulation of
Energy balance as energy key to climate.
2.
Interested in radiative processes as those key to climate sensitivity
3. Other variables are strongly related to radiation so including them would add no new information.

Predicted from RSR & OLR vs
Simulated
CESD
67%
70 %
Simulated
90%
93%
Simulated
89 %
38%
Simulated Simulated
Tech issue. Need to weight to cope with uneven sampling.
“Voronoi” – see latter.

Estimating Climate Sensitivity
CESD
• Our experimental design doesn’t give us an estimate of climate sensitivity
• But climate prediction .net done 14,000 doubled CO2 slab model experiments (HadSM3) each 20 years long.
• Can estimate equilibrium climate sensitivity (ECS) for many parameters from these simulations.
• We constructed an emulator of ECS for HadSM3. Give the emulator model parameters and the emulator provides an estimate of climate sensitivity.
• Essentially sophisticated regression/interpolation and so generates some additional uncertainty.

CESD
Climate Sensitivity vs radn
(optimisation simulations)
Reflected SW

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Sampling equally in CS and from the 14000 CPDN configurations

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Feedback vs total outgoing radn
Summary
There is a relationship between climate feedback/ sensitivity and outgoing radiation

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Probabilistic ECS estimate:
Schematic
Simulated
Observed
Parameters
Prior
S
Likelihood Posterior
Uncertainty Estimate
23

Uncertainty estimate for OLR and
RSR
CESD
• Need estimate of uncertainty to decide what is a
“plausible” simulation of OLR and RSR?
• Make estimates for sources of uncertainty and sum them assuming everything Gaussian.
• For Audience..
– Anything major missing?
– Anything too small?
• From “plausible” configurations can generate
“plausible” range.
• Using (simple) Bayesian reasoning make probabilistic estimate of ECS.

Sources of Uncertainty
CESD
• Consider uncertainties that don’t affect climate sensitivity but could affect the outgoing radiation.
Assume all uncertainties are independent multivariate Gaussian and combine them.
• Observational uncertainty
• Forcing uncertainty
• Modelling uncertainty
• SST uncertainty
• NOT including uncertainty in model structure
– results are conditional on HadAM3 structure.

Observational uncertainty
CESD
– Reflected SW Radn (RSR): 1 Wm -2
– Outgoing LW Radiation (OLR): 1.4 Wm -2
– Then combined with uncertainty on total energy leaving the Earth (0.5 Wm -2 ) mainly arising from uncertainty in incoming solar radiation.

Forcing and Aerosol Uncertainty
CESD
• Forcing Uncertainty (from IPCC AR4)
– RSR: 1 Wm -2 (mainly aerosol uncertainty)
– OLR: 0.25 Wm -2 (O
3
& GHG)
• Convert to TOA radiation using simulations with aerosols, human forcings, and GHG removed. Then scaling results based on comparison between forcing and TOA fluxes.
• Natural aerosol – RSR 1 Wm -2 (Carslaw et al, 2010 is about 0.5) while Penner et al, 2006 models are about
1 Wm -2

Modelling Error
CESD
• Internal climate variability: 0.1 Wm -2 in both RSR and OLR and is negligible.
• Parameter uncertainty – what about parameters that don’t affect climate sensitivity but do affect radiation?
– From climate prediction .net database find those model configurations that have a climate sensitivity from 3.2-3.4K (standard configuration is 3.3K). Gives 13 cases. Run the cases and compute covariance of RSR and OLR. Then treat as another source of uncertainty.

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SST Uncertainty

SST Uncertainty
CESD
• Computed:
– Difference between two successive Hadley climatologies is less than 0.2K over most of globe.
– Being conservative estimate SST 1 sigma error as 0.2K.
– Increase HadISST by 0.5K over non sea-ice points, run standard configuration and compute difference in RSR and OLR from reference case
(-0.4 & 1.2 W/m 2 ). Then scale for 0.2K case.
• Replacement of HadISST dataset with Reynolds dataset (AVHRR + buoys) has negligible impact on OLR and RSR

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Sources of Uncertainty

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Which Simulations are consistent with Observations?

CESD
Which HadAM3 climate sensitivities are consistent with observations?
• Find all configurations that have OLR and
RSR consistent (95%) level with observations.
• What is the range of climate sensitivies?
• CERES: 3.0-4.1 K
• ERBE: 3.0-5.1 K

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Generating A PDF for Climate
Sensitivity

Generating a PDF for climate
Sensitivity
CESD
• Want to use uncertainty estimate and model configurations to generate PDF
• Issue: Model configurations not generated randomly and density varies enormously
• Assume properties vary smoothly and explore impact of different prior assumptions
• Use Bayes theorem to compute:
𝑃 𝑀 𝑖
𝑂 ∝ 𝐿 𝑀 𝑖
P 𝑀 𝑖
Which is the same as P(Si|O)

CESD
Calculating Likelihoods for each configuration f(r)
Areas are the areas of the
Voronoi polygons capped at
π (gray polygons)
36

Computing a probability distribution
CESD
• Individual model realisations not randomly generated though have 16 different initial conditions and 5 different targets
• Explore several different prior assumptions on the individual realisations.
Uniform all configurations equally likely
Radiation OLR and RSR equally likely
Parameter Parameter values equally likely
S ECS values equally likely in range
1/S All feedbacks equally likely in range

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Cumulative Distribution Functions
38

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Taking Account of Emulator
Uncertainty
Error varies with climate sensitivity.
coherent over all samples and montecarlo sampling. (modify the estimated sensitivity of each configuration)

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Taking account of Emulator Error
2.7-4.2

Sensitivity Studies
CESD
• Use ERBE observations
• Amplify Observational co-variance by a factor of 20 – makes CERES and ERBE consistent…
• Amplify total covariance by two.
• And some more including using a single year rather than 5.
• Only the first three make any difference.

CESD
Cumulative Distribution Functions
2 x Cov: 2.7-4.9
20xSat: 2.7-5.2
ERBE:2.9-5.5
ERBE
42

Summary
CESD
• Found could automatically tune HadAM3 to fit TOA radiation observations.
• Variation largely due to changes in clouds with clear sky cancelling
• Get to within 1 W/m 2 RMS with median of 3-4 iterations.
• Other climatologies strongly related to RSR/OLR
• Made an estimate of uncertainty in model-data difference which is dominated by modelling uncertainty rather than observational uncertainty.
• Used this to make probabilistic estimate of climate sensitivity for
HadAM3.
• This is 2.7-4.2 K for CERES with little sensitivity to prior assumptions
• Amplifying observational error to make CERES and ERBE consistent gives range of 2.6-5.4K with considerable sensitivity to prior.

Thoughts
CESD
• Straight forward to tune models to global SW
& LW radiation
• Could probably do it with a series of short (18 months) simulations
• It matters for three reasons
1. Coupled models with poor radiation balance will drift (or need flux correction)
2. Related to feedbacks in HadAM3 (and probably other models)
3. Modifies the climate in SST forced – energy balance is probably physical reason.

Next stages
CESD
• Couple tuned atmosphere models to ocean.
– Do they behave as well as we expect?
• Explore methods to allow more parameters and observations
– Would allow better constraints and explore which parameters and observations really matter.
– Bringing observations and modelling together in coherent way.
– Which observations are sufficiently independent?
– Parameter importance from d error/d param

Next Stages (cont.)
CESD
• Use optimisation to efficiently generate atmospheric model configurations that are appropriately sampled from model/obs uncertainty estimate
– Allows generation of uncertainty in future model properties. Not just ECS. Would be helped by reasonable first guesses.
• Use optimisation to efficiently generate models of differing resolution consistent (on large scales) with observations and each other
– Allows exploration of impact of resolution change without error in energy balance/basic climatology

Thanks and Questions

CESD
Failures

Equi-finality
CESD
• Can different parameter choice results in models with similar climatologies?
• Do this by looking at final configurations of
CERES and ERBE optimisation cases + cases within 1 W/m 2 of target.

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Precip vs Temp

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Parameter Values
Compensation

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Land Zonal Means

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Difference from Standard Config for CERES warm cluster

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Difference from Standard Config for ERBE warm cluster
ERBE Cluster #2 (Warm)