CESDSAGES Scottish Alliance for Geoscience, Environment & Society

Constraining Climate Sensitivity using Top Of Atmosphere Radiation MeasurementsSimon Tett1, Mike Mineter1, Coralia Cartis2, Dan Rowlands3

& Ping Liu2

1: School of Geosciences, University of Edinburgh2: School of Mathematics, University of Edinburgh

3: AOPP, Department of Physics, University of Oxford

CESDAims

• 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.

CESDKey results

• 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

CESDPhilosophy

• 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.

CESDObservational Data

• 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 March 2000-Feb 2005

• Also explore sensitivity to use of ERBE data

CESDExperimental Design

• 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.

CESDExperimental Design (Cont.)

• 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/m2 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.

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Optimisation Algorithm applied to HadAM3

simulations• 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.

CESDOptimisation Algorithm (Cont.)

• 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.

CESDOptimisation Algorithm (Cont.)

• 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.

InitialDeriv

Line Search

CESDOptimisation Trials

ERBE

CERES Low Sens

High Sens

• Convergence to “zero” error for all but CERES high sens case

• CERES case took 3 iterations

• ERBE cases took 8 & 9 iterations

CESDOptimisation

• 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

CESDOptimisation Trials (Summary)

Name Target Suc. M. Fail Fail Con. Iter.

CERES (100%)

(99.5, 239.6) 4 12 0 3-6 (4)

CERES(75%) (99.5, 239.6) 15 0 1 1-8 (4)

ERBE (106.5, 234.4) 12 4 0 3-7 (3)

Nr ERBE (105.5, 234.4) 13 2 1 2-8 (4)

TGT#1 (97, 245) 4 1 11 2-9 (5)

TGT#2 (98, 237) 13 2 1 1-6 (3)

TGT#3 (101, 243) 12 2 1 2-8 (4)

CESDOptimisation Summary

• Failure to converge as (un)common as model failure.

• Can adjust model parameters to produce models that are within 1 Wm2 of observations.

• Takes about 3-4 iterations. Each iteration requires 7 simulations each of 6 years of atmospheric model. This is very efficient…

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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.

CESDOther variables

• 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.

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Predicted from RSR & OLR vs Simulated

67%

70 %

90%

93%

38%

89 %

Simulated

Predicted

Simulated

SimulatedSimulated

Tech issue. Need to weight to cope with uneven sampling. “Voronoi” – see latter.

CESDEstimating Climate Sensitivity

• Our experimental design doesn’t give us an estimate of climate sensitivity

• But climateprediction.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.

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Climate Sensitivity vs radn (optimisation simulations)

Reflected SW

Out

goin

g LW

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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

Parameters

Simulated

Observed

Likelihood

PriorS

Posterior

Uncertainty Estimate23

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Uncertainty estimate for OLR and RSR

• 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.

CESDSources of Uncertainty

• Consider uncertainties that don’t affect climate sensitivity but could affect the outgoing radiation. Assume all uncertainties are independent multi-variate Gaussian and combine them.

• Observational uncertainty• Forcing uncertainty• Modelling uncertainty• SST uncertainty• NOT including uncertainty in model structure

– results are conditional on HadAM3 structure.

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Observational uncertainty

– 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.

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Forcing and Aerosol Uncertainty

• Forcing Uncertainty (from IPCC AR4) – RSR: 1 Wm-2 (mainly aerosol uncertainty)– OLR: 0.25 Wm-2 (O3 & 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

CESDModelling Error

• 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 climateprediction.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.

CESDSST Uncertainty

CESDSST Uncertainty

• 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/m2). Then scale for 0.2K case.

• Replacement of HadISST dataset with Reynolds dataset (AVHRR + buoys) has negligible impact on OLR and RSR

CESDSources of Uncertainty

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Which Simulations are consistent with Observations?

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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

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Generating a PDF for climate Sensitivity

• 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:

Which is the same as P(Si|O)

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Calculating Likelihoods for each configuration

f(r)

 

Areas are the areas of the Voronoi polygons capped at π (gray polygons) 36

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Computing a probability distribution

• 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 likelyRadiation OLR and RSR equally likelyParameter Parameter values equally likelyS ECS values equally likely in range1/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

Error varies with climate sensitivity.

Compute its impact by assuming error is coherent over all samples and monte-carlo sampling. (modify the estimated sensitivity of each configuration)

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Taking account of Emulator Error

2.7-4.2

CESDSensitivity Studies

• 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.

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Cumulative Distribution Functions

ERBE:2.9-5.5

42

20xSat: 2.7-5.22 x Cov: 2.7-4.9

ERBE

CESDSummary

• 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/m2 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.

CESDThoughts

• 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 reasons1. 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.

CESDNext stages

• 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

CESDNext Stages (cont.)

• 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

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Thanks and Questions

CESDFailures

CESDEqui-finality

• 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/m2 of target.

CESDPrecip vs Temp

CESDParameter Values

Compensation

CESDLand 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)