Estimation of climate sensitivity - Chalmersaila/presentation.slides.pdf · 2014. 9. 4. · (b) Estimates of ECS are compared to overall assessed likely range (solid grey), with solid

Estimation of climate sensitivity

Magne Aldrin, Norwegian Computing Center and

University of Oslo

Smogen workshop 2014

1

References

• Aldrin, M., Holden, M., Guttorp, P., Skeie, R.B., Myhre, G. and

Berntsen, T.K. (2012).

Bayesian estimation of climate sensitivity based on a simple climate

model fitted to observations of hemispheric temperatures an global

ocean heat content.

Environmetrics, vol. 23, p. 253-271.

• Skeie, R.B., Berntsen, T., Aldrin, M., Holden, M., Myhre, M.

(2014).

A lower and more constrained estimate of climate sensitivity using

updated observations and detailed radiative forcing time series.

Earth System Dynamics, vol. 5, p. 139-175.

2

Climate sensitivity S

Definition:

Climate sensitivity = S

= The temperature increase due to a doubling

of CO2 concentrations compared to pre-industrial time (1750),

when all else is constant

Today: 40 % increase in CO2 concentrations

Estimate from IPCC AR4 (2007): 3◦C, 90 % C.I. =(2.0-4.5)

Estimate from IPCC AR5 (2013): 2.5◦C, 90 % C.I. =(1.5-4.5)

3

Radiative forcing

• CO2 is only one of several factors

that affect the global temperature

• Radiative forcing = The change in net irradiance into the earth

relative to 1750

• Measured in Watts per square meter

• The global temperature depends on the radiative forcing

• The climate sensitivity measures the strength of this dependency

4

Aim of study

To estimate the climate sensitivity

• by modelling the relationship between

◦ estimates of radiative forcing since 1750 and

◦ estimates of hemispheric temperature

based on measurements since 1850

◦ estimates of global ocean heat content

based on measurements since about 1950

• using a climate model based on physical laws

5

Climate model

Could use

• an Atmospheric Ocean General Circulation Model,

but complex and very computer intensive

• an approximation to an AOGCM, an emulator

• a simple climate model, our approach

6

The“true” global state of the earth in year t

• TNHt - Temperature at the northern hemisphere

• TSHt - Temperature at the southern hemisphere

• OHCt - Ocean heat content

7

Simple climate model

• Deterministic computer model (Schlesinger et al., 1992)

• based on

◦ energy balance

◦ upwelling diffusion ocean

• where the earth is divided into

◦ atmosphere and ocean

◦ northern and southern hemisphere

• with

◦ radiative forcing into the system

◦ energy mixing

∗ between the atmosphere and the ocean

∗ within the ocean

SH Atmosphere NH Atmosphere

SH P

olar

Oce

an

Mixed layer Mixed layer

X XS N

NH

Polar Ocean

θ P

S

θM

θOIHE

θOIHE

θOIHE

θASHE θASHE

θM

θUV

θUV θUV

θUV

θUV θUV

θVHD

θVHD

θVHD

θVHD

θVHDθVHD

8

Simple climate model cont.

mt(x1750:t, S,θ)

• Yearly time resolution

• Output

◦ temperature northern hemisphere

◦ temperature southern hemisphere

◦ ocean heat content

• Input

◦ x1750:t - yearly radiative forcing from 1750 until year t,

separate for northern and southern hemisphere

◦ S - the climate sensitivity, the parameter of interest

◦ θ - 6 other physical parameters

9

Response data

• yt - 9-dimensional vector with yearly observed temperatures and

ocean heat content

• Three pairs of series with temperature measurements for northern

and southern hemisphere

◦ 1850-2010 (HadCRUT3, Brohan et al.,2006)

◦ 1880-2010 (GISS, Hansen et al. 2006)

◦ 1880-2010 (NCDC, Smith and Reynolds 2005)

• Three series with ocean heat content measurements 0-700m

◦ 1955-2010 (Levitus et al. 2009)

◦ 1950-2010 (Domingues et al. 2008; Church et a. 2011)

◦ 1945-2010 (Ishii and Kimoto 2009)

10

Observations−

0.5

0.0

0.5

1.0

Tem

pera

ture

[°C

]

1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

(a) Observed temperatures, northern hemisphere

NH1, HadCRUT3NH2, GISSNH3, NCDC

−0.

50.

00.

51.

0

Tem

pera

ture

[°C

]

1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

(b) Observed temperatures, southern hemisphere

SH1, HadCRUT3SH2, GISSSH3, NCDC

−5

05

1015

Oce

an h

eat c

onte

nt [1

0^22

J]

1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010

(c) Observed global ocean heat content

LevitusCSIROIshii and Kimoto

11

Radiative forcing

• We will specify our best knowledge about historical radiative forcing

as prior distributions of 11 independent components,

based on temperature-independent estimates of each component,

including uncertainties

◦ long-lived greenhouse gases

◦ direct aerosols

◦ indirect aerosols

◦ solar radiation

◦ volcanoes

◦ land use

◦ . . .

12

Priors of components of radiative forcing

Figure not updated

1750 1800 1850 1900 1950 20000.

01.

02.

03.

0 LLGHG NH

Rad

iativ

e fo

rcin

g [W

/m2]

1750 1800 1850 1900 1950 2000

0.0

1.0

2.0

3.0 LLGHG SH

Rad

iativ

e fo

rcin

g [W

/m2]

1750 1800 1850 1900 1950 2000−0.

10.

10.

30.

5

Sun NH

Rad

iativ

e fo

rcin

g [W

/m2]

1750 1800 1850 1900 1950 2000−0.

10.

10.

30.

5

Sun SH

Rad

iativ

e fo

rcin

g [W

/m2]

1750 1800 1850 1900 1950 2000

−12

−8

−4

0

Volcanos NH

Rad

iativ

e fo

rcin

g [W

/m2]

1750 1800 1850 1900 1950 2000−

12−

8−

40

Volcanos SH

Rad

iativ

e fo

rcin

g [W

/m2]

1750 1800 1850 1900 1950 2000

−1.

00.

0

dirAero NH

Rad

iativ

e fo

rcin

g [W

/m2]

1750 1800 1850 1900 1950 2000

−1.

00.

0

dirAero SH

Rad

iativ

e fo

rcin

g [W

/m2]

13

Prior of total radiative forcing−

4−

20

2

Rad

iativ

e fo

rcin

g [W

m−2

]

1750 1770 1790 1810 1830 1850 1870 1890 1910 1930 1950 1970 1990 2010

Mean

90% credible interval

−4 −2 0 2 4

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Radiative forcing [W m−2]

Den

sity

Prior density 2010

E(RF) = 1.5090% C.I. =[0.3,2.5]

14

Model for“true” global state of the earth

gt = (TNHt, TSHt, OHCt)T

Combined deterministic + stochastic model

gt = mt(xt:1750, S,θ) + nsivt + nliv

t + nmt

• nsivt : short-term internal variation, related to El Nino episodes

• nlivt : long-term internal variation, estimated from an AOGCM

• nmt : model error, VAR(1)

• All terms have dimension 3

15

Model for observations

yt = Agt + not

• A: 9x3 matrix copying each data series 3 times, to compare model

values with observations

• not : observational (measurement) error, dimension 9, VAR(1)

16

Estimation

• Bayesian approach (Kennedy and O’Hagan 2001), using MCMC

• Vague prior for S

• Informative priors for xt:1750 and θ

• Vague priors for other parameters

17

Posterior of the climate sensitivity S

0 1 2 3 4 5 6

0.0

0.4

0.8

0 1 2 3 4 5 6

●

E(ECS) = 1.8690% C.I. = (0.91,3.21)P(ECS>4.5) = 0.016

a) Main analysis (CanESM 10) ● posterior median

posterior mean


0 1 2 3 4 5 6

0.0

0.4

0.8

0 1 2 3 4 5 6

●

E(ECS) = 1.9290% C.I. = (0.76,3.61)P(ECS>4.5) = 0.027

b) NorESM 10

0 1 2 3 4 5 6

0.0

0.4

0.8

0 1 2 3 4 5 6

●

E(ECS) = 1.9290% C.I. = (0.96,3.3)P(ECS>4.5) = 0.015

c) HadCRUT4 instead of HadCRUT3 data

0 1 2 3 4 5 6

0.0

0.4

0.8

0 1 2 3 4 5 6

●

E(ECS) = 1.8890% C.I. = (0.89,3.41)P(ECS>4.5) = 0.017

d) OHC deep water included

0 1 2 3 4 5 6

0.0

0.4

0.8

0 1 2 3 4 5 6

●

E(ECS) = 1.8790% C.I. = (0.9,3.36)P(ECS>4.5) = 0.018

e) Two ECSs

0 1 2 3 4 5 6

0.0

0.4

0.8

0 1 2 3 4 5 6

●

E(ECS) = 2.2390% C.I. = (0.62,5.45)P(ECS>4.5) = 0.071

f) Data up to 2000

0 1 2 3 4 5 6

0.0

0.4

0.8

0 1 2 3 4 5 6

●

E(ECS) = 4.4790% C.I. = (1.11,14.64)P(ECS>4.5) = 0.296

g) Data up to 2000 − 1 OHC

0 1 2 3 4 5 6

0.0

0.4

0.8

0 1 2 3 4 5 6

●

E(ECS) = 1.7590% C.I. = (1.15,2.58)P(ECS>4.5) = 0.003

h) Without internal variability

Pro

babi

lity

dens

ityP

roba

bilit

y de

nsity

Pro

babi

lity

dens

ityP

roba

bilit

y de

nsity

Pro

babi

lity

dens

ity

Equilibrium climate sensitivity [ °C ] Equilibrium climate sensitivity [ °C ]

Degrees Celcius

18

From the 5th Assessment Report of IPCC

925

10

Detection and Attribution of Climate Change: from Global to Regional Chapter 10

0 1 2 3 4 5 60

0.5

1

1.5

Dashed lines AR4 studies

Transient Climate Response (°C)

Prob

abilit

y / R

elat

ive

Freq

uenc

y (°

C-1)

Prob

abilit

y / R

elat

ive

Freq

uenc

y (°

C-1)

Knutti & Tomassini (2008) uniform ECS prior

Knutti & Tomassini (2008) expert ECS prior

Meinshausen et al (2009)

Harris et al (2013)

Rogelj et al (2012)

Otto et al (2013) −− 1970−2009 budget

Otto et al (2013) −− 2000−2009 budget

Tung et al (2008)

Gillett et al (2013)

Stott & Forest (2007)

Gregory & Forster (2008)

Padilla et al (2011)

Libardoni & Forest (2011)

Schwartz (2012)

a)

b)

0 1 2 3 4 5 6 7 8 9 10Equilibrium Climate Sensitivity (°C)

0.0

0.4

0.8

1.2Aldrin et al. (2012)Bender et al. (2010)Lewis (2013)Lin et al. (2010)Lindzen & Choi (2011)Murphy et al. (2009)Olson et al. (2012)Otto et al. (2013)Schwartz (2012)Tomassini et al. (2007)

0.0

0.4

0.8

1.2Chylek & Lohmann (2008)Hargreaves et al. (2012)Holden et al. (2010)Kohler et al. (2010)Palaeosens (2012)Schmittner et al. (2012)

0.0

0.4

0.8Aldrin et al. (2012)Libardoni & Forest (2013)Olson et al. (2012)

Instrumental

Similar climate

base state

Similar feedbacks

Close to equilibrium

Uncertainties accountedfor/known

Overall level of

scientific understanding

Palaeoclimate

Combination

Figure 10.20 | (a) Examples of distributions of the transient climate response (TCR, top) and the equilibrium climate sensitivity (ECS, bottom) estimated from observational con-straints. Probability density functions (PDFs), and ranges (5 to 95%) for the TCR estimated by different studies (see text). The grey shaded range marks the very likely range of 1°C to 2.5°C for TCR and the grey solid line represents the extremely unlikely <3°C upper bound as assessed in this section. Representative distributions from AR4 shown as dashed lines and open bar. (b) Estimates of ECS are compared to overall assessed likely range (solid grey), with solid line at 1°C and a dashed line at 6°C. The figure compares some selected old estimates used in AR4 (no labels, thin lines; for references see Supplementary Material) with new estimates available since AR4 (labelled, thicker lines). Distributions are shown where available, together with 5 to 95% ranges and median values (circles). Ranges that are assessed as being incomplete are marked by arrows; note that in contrast to the other estimates Schwartz (2012), shows a sampling range and Chylek and Lohmann a 95% range. Estimates are based on changes over the instrumental period (top row); and changes from palaeoclimatic data (2nd row). Studies that combine multiple lines of evidence are shown in the bottom panel. The boxes on the right-hand side indicate limitations and strengths of each line of evidence, for example, if a period has a similar climatic base state, if feedbacks are similar to those operating under CO2 doubling, if the observed change is close to equilibrium, if, between all lines of evidence plotted, uncertainty is accounted for relatively completely, and summarizes the level of scientific understanding of this line of evidence overall. A blue box indicates an overall line of evidence that is well understood, has small uncertainty, or many studies and overall high confidence. Pale yellow indicates medium, and dark red low, confidence (i.e., poorly understood,very few studies, poor agreement, unknown limitations, after Knutti and Hegerl, 2008). Where available, results are shown using several different prior distributions; for example for Aldrin et al. (2012) solid shows the result using a uniform prior in ECS, which is shown as updated to 2010 in dash-dots; dashed: uniform prior in 1/ECS; and in bottom panel, result combining with Hegerl et al. (2006) prior, For Lewis (2013), dashed shows results using the Forest et al. (2006) diagnostic and an objective Bayesian prior, solid a revised diagnostic. For Otto et al. (2013), solid is an estimate using change to 1979–2009, dashed using the change to 2000–2009. Palaeoclimate: Hargreaves et al. (2012) is shown in solid, with dashed showing an update based on PMIP3 simulations (see Chapter 5); For Schmittner et al. (2011), solid is land-and-ocean, dashed land-only, and dash-dotted is ocean-only diagnostic.

19

Effect of 10 more years of data

Equilibrium climate sensitivity [ °C ]

0 1 2 3 4 5 6

●

Main analysisR90 = 1.23

●

Data up to 2008R90 = 1.39

●

Data up to 2006R90 = 1.59

●

Data up to 2004R90 = 1.93

●

Data up to 2002R90 = 1.78

●

Data up to 2000R90 = 2.17

20

Validation

Based on only one OHC series

21

Re-estimation 1850-1990 + prediction 1991-2007

1850 1900 1950 2000

−0.

50.

00.

51.

0

Tem

pera

ture

[°C

] Temperatures, northern hemisphere, NH1, HadCRUT3

PredictedObservedFitted


1850 1900 1950 2000

−0.

50.

00.

51.

0

Tem

pera

ture

[°C

] Temperatures, southern hemisphere, SH1, HadCRUT3



1850 1900 1950 2000

−5

05

1015

20

Oce

an h

eat c

onte

nt [1

0^22

J]

Global ocean heat content



22

Validation on data from an AOGCM

• The reality is complex, but our model are simple

• Can we trust the posterior for the climate sensitivity?

• True S is unknown, can not validate on real data

• Validate on artificial data generated from an AOGCM

23

The CMIP3 experiment

• Coupled Model Intercomparison Project phase 3

• CO2 increased by 1 % per year until a doubling in 1920, then

constant

• Corresponding RF increased from 0 to 3.7 W/m2

• (Deterministic) simulation 1859-2079 of temperature and OHC

• Our validation experiment, based on the Canadian CGCM3.1 model

◦ “True” climate sensitivity = 3.4◦C

◦ Training data: Temperatures 1860-2007, OHC 1955-2007

24

CMIP3 - Radiative forcing prior

1750 1800 1850 1900 1950 2000 2050

−1

01

23

45

Rad

iativ

e fo

rcin

g [W

/m2]

Mean


25

CMIP3 - Data and predictions

1900 1950 2000 2050

01

23

4

Tem

pera

ture

[°C

] Temperatures, northern hemisphere, NH1, HadCRUT3

PredictedTrueObservedFitted


1900 1950 2000 2050

01

23

4

Tem

pera

ture

[°C

] Temperatures, southern hemisphere, SH1, HadCRUT3



1900 1950 2000 2050

020

040

060

0

Oce

an h

eat c

onte

nt [1

0^22

J]

Global ocean heat content



26

CMIP3 - Posterior for climate sensitivity

• “True” climate sensitivity = 3.4◦C

• Posterior mean 3.5◦, CI=(2.4-5.3)

27

Further work

• Work in progress

◦ Update model using data including 2013

◦ Using updated RF prioirs from IPCC AR5

◦ Including one more temperature series

◦ Including one more OHC (above 700 m) series

◦ Including data for OHC below 700 meters!

• Planned work

◦ Improve the simple climate model

◦ Using different simple climate models

◦ Including other data types (ice melting, sea level, ...)

28

Thank you for your attention!

Documents

Estimation of climate sensitivity - Chalmersaila/presentation.slides.pdf · 2014. 9. 4. · (b) Estimates of ECS are compared to overall assessed likely range (solid grey), with solid