Estimation of climate sensitivity Magne Aldrin, Norwegian Computing - PowerPoint PPT Presentation

Estimation of climate sensitivity Magne Aldrin, Norwegian Computing Center and University of Oslo Sm¨ ogen workshop 2014

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. 1

Climate sensitivity S Definition: Climate sensitivity = S = The temperature increase due to a doubling of CO 2 concentrations compared to pre-industrial time (1750), when all else is constant Today: 40 % increase in CO 2 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) 2

Radiative forcing • CO 2 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 3

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 4

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 5

The“true” global state of the earth in year t • TNH t - Temperature at the northern hemisphere • TSH t - Temperature at the southern hemisphere • OHC t - Ocean heat content 6

Simple climate model • Deterministic computer model (Schlesinger et al., 1992) • based on ◦ energy balance X X S N ◦ upwelling diffusion ocean NH Atmosphere SH Atmosphere • where the earth is divided into θ ASHE θ ASHE ◦ atmosphere and ocean θ M θ M Mixed layer Mixed layer θ P ◦ northern and southern hemisphere S θ UV θ OIHE • with θ UV θ VHD θ VHD NH Polar Ocean SH Polar Ocean ◦ radiative forcing into the system θ VHD θ UV θ UV θ VHD θ OIHE ◦ energy mixing ∗ between the atmosphere and the ocean θ UV θ OIHE θ UV θ VHD θ VHD ∗ within the ocean 7

Simple climate model cont. m t ( x 1750: t , S, θ ) • Yearly time resolution • Output ◦ temperature northern hemisphere ◦ temperature southern hemisphere ◦ ocean heat content • Input ◦ x 1750: 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 8

Response data • y t - 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) 9

Observations 1.0 (a) Observed temperatures, northern hemisphere Temperature [ ° C ] NH1, HadCRUT3 0.5 NH2, GISS NH3, NCDC 0.0 −0.5 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 1.0 (b) Observed temperatures, southern hemisphere Temperature [ ° C ] SH1, HadCRUT3 0.5 SH2, GISS SH3, NCDC 0.0 −0.5 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 Ocean heat content [10^22 J] 15 (c) Observed global ocean heat content 10 5 0 Levitus −5 CSIRO Ishii and Kimoto 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 10

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 ◦ . . . 11

Priors of components of radiative forcing Radiative forcing [W/m2] Radiative forcing [W/m2] LLGHG NH LLGHG SH 3.0 3.0 Figure not updated 2.0 2.0 1.0 1.0 0.0 0.0 1750 1800 1850 1900 1950 2000 1750 1800 1850 1900 1950 2000 Radiative forcing [W/m2] Radiative forcing [W/m2] Sun NH Sun SH 0.5 0.5 0.3 0.3 0.1 0.1 −0.1 −0.1 1750 1800 1850 1900 1950 2000 1750 1800 1850 1900 1950 2000 Radiative forcing [W/m2] Radiative forcing [W/m2] Volcanos NH Volcanos SH 0 0 −4 −4 −8 −8 −12 −12 1750 1800 1850 1900 1950 2000 1750 1800 1850 1900 1950 2000 Radiative forcing [W/m2] Radiative forcing [W/m2] dirAero NH dirAero SH 0.0 0.0 −1.0 −1.0 1750 1800 1850 1900 1950 2000 1750 1800 1850 1900 1950 2000 12

Prior of total radiative forcing Mean 90% credible interval 2 Radiative forcing [ W m − 2 ] 0 −2 −4 1750 1770 1790 1810 1830 1850 1870 1890 1910 1930 1950 1970 1990 2010 13

Model for“true” global state of the earth g t = ( TNH t , TSH t , OHC t ) T Combined deterministic + stochastic model g t = m t ( x t :1750 , S, θ ) + n siv + n liv + n m t t t • n siv : short-term internal variation, related to El Nin˜ o episodes t • n liv t : long-term internal variation, estimated from an AOGCM • n m t : model error, VAR(1) • All terms have dimension 3 14

Model for observations y t = Ag t + n o t • A : 9x3 matrix copying each data series 3 times, to compare model values with observations • n o t : observational (measurement) error, dimension 9, VAR(1) 15

Estimation • Bayesian approach (Kennedy and O’Hagan 2001), using MCMC • Vague prior for S • Informative priors for x t :1750 and θ • Vague priors for other parameters 16

Posterior of the climate sensitivity S Probability density 0.8 a) Main analysis (CanESM 10) E(ECS) = 1.86 90% C.I. = (0.91,3.21) 0.4 P(ECS>4.5) = 0.016 0.0 ● 0 0 1 1 2 2 3 3 4 4 5 5 6 6 Probability density Degrees Celcius 17

From the 5th Assessment Report of IPCC b) Aldrin et al. (2012) Bender et al. (2010) 1.2 S Lewis (2013) S i i m m Lin et al. (2010) i i l a l a r Lindzen & Choi (2011) 0.8 b c l a i m Murphy et al. (2009) s e a Olson et al. (2012) s t a Otto et al. (2013) 0.4 Schwartz (2012) Tomassini et al. (2007) Instrumental 0.0 Probability / Relative Frequency (°C -1 ) 1.2 Chylek & Lohmann (2008) Hargreaves et al. (2012) 0.8 Holden et al. (2010) K¨ ohler et al. (2010) Palaeosens (2012) 0.4 Schmittner et al. (2012) Palaeoclimate 0.0 0.8 Aldrin et al. (2012) Libardoni & Forest (2013) 0.4 Olson et al. (2012) Combination 0.0 0 1 2 3 4 5 6 7 8 9 10 Equilibrium Climate Sensitivity (°C) 18

Effect of 10 more years of data Main analysis R90 = 1.23 ● Data up to 2008 R90 = 1.39 ● Data up to 2006 R90 = 1.59 ● Data up to 2004 R90 = 1.93 ● Data up to 2002 R90 = 1.78 ● Data up to 2000 R90 = 2.17 ● 0 1 2 3 4 5 6 Equilibrium climate sensitivity [ ° C ] 19

Validation Based on only one OHC series 20

Re-estimation 1850-1990 + prediction 1991-2007 1.0 Temperatures, northern hemisphere, NH1, HadCRUT3 Temperature [ ° C ] Predicted 95% credible interval 0.5 Observed Fitted 0.0 −0.5 1850 1900 1950 2000 1.0 Temperatures, southern hemisphere, SH1, HadCRUT3 Temperature [ ° C ] Predicted 95% credible interval 0.5 Observed Fitted 0.0 −0.5 1850 1900 1950 2000 Ocean heat content [10^22 J] 20 Global ocean heat content 15 Predicted 95% credible interval Observed 10 Fitted 5 0 −5 1850 1900 1950 2000 21

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 22

The CMIP3 experiment • Coupled Model Intercomparison Project phase 3 • CO 2 increased by 1 % per year until a doubling in 1920, then constant • Corresponding RF increased from 0 to 3.7 W/m 2 • (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 23

CMIP3 - Radiative forcing prior 5 4 Mean Radiative forcing [W/m2] 95% credible interval 3 2 1 0 −1 1750 1800 1850 1900 1950 2000 2050 24