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Thermodynamics of Climate – Part 1 –

Valerio Lucarini

University of Hamburg

University of Reading

Email: valerio.lucarini@uni-hamburg.de

Cambridge, 23/10/2013

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Climate and Physics“A solved problem, just some well-known

equations and a lot of integrations”“who cares about the mathematical/physical

consistency of models: better computers, better simulations, that’s it!

… where is the science?“I regret to inform the author that geophysical

problems related to climate are of little interest for the physical community…”

“Who cares of energy and entropy? We are interested in T, P, precipitation”

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What’s a Complex system?A complex system is a system composed of

interconnected parts that, as a whole, exhibit one or more properties not obvious from the properties of the individual parts

Reductionism, which has played a fundamental role in develpoing scientific knowledge, is not applicable.

The Galilean scientific framework given by recurrent interplay of experimental results (performed in a cenceptual/real laboratory provided with a clock, a measuring and a recording device), and theoretical predictions is challenged

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Some Properties of Complex Systems

Spontaneous Pattern formationSymmetry break and instabilitiesIrreversibilityEntropy ProductionVariability of many spatial and temporal scalesNon-trivial numerical modelsSensitive dependence on initial conditions

limited predictability time

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Complicated vs ComplexNot Complicated and Not Complex

Harmonic oscillator in 1DComplicated and Not Complex

Gas of non-interacting oscillators (phonons)Integrable systems are always not complex

Not Complicated and ComplexLorenz 63 model has only 3 degrees of freedom

Complicated and ComplexTurbulent fluid, Society

‘Complex’ comes from the past participle of the Latin verb complector, -ari (to entwine).

‘Complicated’ comes from the past participle of the Latin verb complico, -are (to put together).

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Map of Complexity Climate Science is mysteriously missing!

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Map of Complexity

Climate Science

Climate Science is perceived as being too technical, political

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Some definitionsThe climate system (CS) is constituted by four

interconnected sub-systems: atmosphere, hydrosphere, cryosphere, and biosphere,

The sub-systems evolve under the action of macroscopic driving and modulating agents, such as solar heating, Earth’s rotation and gravitation.

The CS features many degrees of freedomThis makes it complicated

The CS features variability on many time-space scales and sensitive dependence on ICThis makes it complex.

The climate is defined as the set of the statistical properties of the CS.

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Three major theoretical challenges in analysing the CS

Mathematics: In dynamical systems, the stability properties of the time mean state say nothing about the properties of the full nonlinear systemimpossibility of defining a theory of the time-mean

properties relying only on the time-mean fields. Physics: It is impossible to apply the fluctuation-

dissipation theorem for a chaotic dissipative system such as the climate systemnon-equivalence between the external and internal

fluctuations Climate Change is hard to parameteriseNumerics: Climate is a stiff problem (very different

time scales) “optimal” resolution? brute force approach is not necessarily the solution.

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Three major experimental challenges in analysing the CS

Synchronic coherence of dataData feature hugely varying degree of precision

Diachronic coherence of dataTechnology and prescriptions for data collection

have changed with timeSpace-time coverage

Data density change with location (Antarctica vs Germany)

We have “direct” data only since Galileo timeBefore, we have to rely on indirect (proxy) data

Unusual with respect to “typical” science

Scales of Motions (Stommel/Smagorinsky)

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Atmospheric MotionsThree contrasting approaches:

Those who like maps, look for features/particlesThose who like regularity, look for wavesThose who like irreversibility, look for

turbulence

Let’s see schematically these 3 visions of the world

Features/ParticlesFocus is on specific (self)organised structures Hurricane physics/track

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Atmospheric (macro) turbulenceEnergy, enstrophy cascades, 2D vs 3D

Note:NOTHING is really 2D in the atmosphere

Waves in the atmosphere

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Large and small scale patterns

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“Waves” in the atmosphere?Hayashi-Fraedrich decomposition

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“Waves” in GCMs

GCMs differ in representation of large scale atmospheric processes

Just Kinematics?What we see are

only unstable waves and their effects

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Evolution of Climate ModelsWith improvement of CPU and of scientific

knowledge, CMs have gained new components definition of “climate” has also changed

Full-blown Climate Model

Since the ‘40s, some of largest computers are devoted to

climate modelling

Local evolution in the phase space

NWP

vs.

Statistical properties on the

attractor Climate Modeling

GOALS OF

MODELLING

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Climate Models uncertaintiesUncertainties of the 1st kind

Are our initial conditions correct? Not so relevant for CM, crucial for NWP

Uncertainties of the 2nd kindAre we representing all the most relevant processes for

the scales of our interest? Are we representing them well? (structural uncertainty)

Are our heuristic parameters appropriate? (parametric uncertainty)

Uncertainty on the metrics: Are we comparing propertly and in a meaningful way

our outputs with the observational data?

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Plurality of ModelsIn Climate Science, not only full-blown models

(most accurate representation of the largest number of processes) are used

Simpler models are used to try to capture the structural properties of the CSLess expensive , more flexible – parametric exploration

CMs uncertainties are addressed by comparingCMs of similar complexity (horizontal)CMs along a hierarchical ladder (vertical)

The most powerful tool is not the most appropriate for all problems, addressing the big picture requires a variety of instruments

All models are “wrong”! (but we are not blind!)

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Multimodel ensembleOutputs of different models should not be merged: not

different realisations of the same process in the world of metamodels (“large numbers law”) Each model has a different attractor with different

properties, they are different objects! There is no good reason to assume that the model

average is the best approximation of reality

Intensity of the hydrological cycle over the Danube basin for IPCC4AR models for 1961-2000 (L. et al. 2008)

Purple is EM: what does it tell us?

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Probability The epistemology pertaining to climate science implies that

its answers must be plural and stated in probabilistic terms. Here, parametric uncertainty for a given model is explored

This PDF contains a huge amount of info! We can assess risks, this is an instrument of decision-making

Webster et al. 2001

TRANSPORT

ENERGY

Energy & GW – Perfect GCM

NESS→Transient → NESS Applies to the whole climate and to to all climatic subdomains

for atmosphere τ is small, always quasi-equilibrated

Forcing

τ

Total warming

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L. and Ragone, 2011

Energy and GW – Actual GCMs

Not only bias: bias control ≠ bias final state Bias depends on climate state! Dissipation

Forcing τ

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L. and Ragone, 2011

Comments“Well, we care about T and P, not Energy”Troublesome, practically and conceptually

A steady state with an energy bias?How relevant are projections related to forcings of

the same order of magnitude of the bias? In most physical sciences, one would dismiss

entirely a model like this, instead of using it for O(1000) publicationsShould we do the same?

Food for thought

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PCMDI/CMIP3 GCMs - IPCC4ARModel Institution

1. BCCR-BCM2.0 Bjerknes Center, Norway

2.3.

CGCM3.1(T47)CGCM3.1(T63)

CCCma, Canada

4. CNRM-CM3 Mètèo France, France

5.6.

CSIRO-Mk3.0CSIRO-Mk3.5

CSIRO, Australia

7. FGOALS-g1.0 LASG, China

8.9.

GFDL-CM2.0GFDL-CM2.1

GFDL, USA

10.11.12.

GISS-AOMGISS-EHGISS-ER

NASA-GISS, USA

13.14.

HADCM3HADGEM

Hadley Center, UK

15. INM-CM3.0 Inst. Of Num. Math., Russia

16. IPSL-CM4 IPSL, France

17.18.

MIROC3.2(hires)MIROC3.2(medres)

CCSR/NIES/FRCGC, Japan

19. ECHO-G MIUB, METRI, and M&D, Germany/Korea

20. ECHAM5/MPI-OM Max Planck Inst., Germany

21. MRI-CGCM2 Meteorological Research Institute, Japan

22.23.

NCAR CCSMNCAR PCM

NCAR, USA

• Pre-Industrial control runs (100 years)

• SRESA1B 720 ppm CO2 stabilization (100 years, as far as possible from 2100)

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PI – TOA Energy BalanceIs the viscous loss of kinetic energy re-injected in the

system? (Becker 03, L & Fraedrich 2009)

L. and Ragone, 2011

IPCC4ARModels

Control Run

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PI – Atmosphere Energy Balance

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PI – Ocean Energy Balance

PI – Ocean Energy BalanceMost models bias (typ. >0) is < 1 Wm-2 Larger interannual variability than

atmospherePI – Land Energy Balance

Thin (à la Saltzman) climate subsystemMost models bias (typ. >0) is < 2 Wm-2

Model 5 bias is 2 Wm-2; 10 Wm-2 excess for Model 19

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Δ TOA Energy Balance

In 2200-2300 system is out of equilibrium by additional O(1 Wm-2)

Most excess heat goes into the ocean (atmosphere, land unchanged)

Need for longer integrations (τ >300 y)

Estimated B(P-E) vs Total Runoff – (Annual)

Results - XX Century Climate – (1961-2000)

Energy Imbalance

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From Energy Balance to Transports

Hvkhkit

yHyTdy

dsurfoce

From energy conservation:

If we integrate vertically, zonally Transports

Long term averages

• If fluxes integrate globally to 0 – as they should – the T functions are zero at BOTH poles

• Otherwise (relatively small!) biases

• We compute annual meridional transports starting from annual TOA and surface zonally averaged fluxes

• Can be done for TOA with satellites!

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PI -TransportsTAO

Stone ‘78 constraint well obeyed

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Max Transport - TOA

1.2 PW

20%

6 ° (2,3 gridpoints)

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Max Transport - Atmosphere

0.8 PW

15%

4 °

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Max Transport - Ocean

5 °

0.8 PW

50%

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SRESA1B -Transports

TAO

Δ Atm Transport

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Increase of Atm Transport: LH effect

Δ peak NH Atm Transport

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Poleward shift of Storm track: SH & NH

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NH - Correlation btw A & O Transports A negative correlation

exists between the yearly maxima of atmospheric and oceanic transport

Compensating mechanism tends to become stronger with GW

About the same in the SH

Bjerknes compensation mechanism

Disequilibrium in the Earth system

(Kleidon, 2011)

climate

Multiscale

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Looking for the big pictureGlobal structural properties (Saltzman 2002).Deterministic & stochastic dynamical systems

Example: stability of the thermohaline circulation Stochastic forcing: ad hoc “closure theory” for noise

Stat Mech & Thermodynamic perspectivePlanets are non-equilibrium thermodynamical systemsThermodynamics: large scale properties of the climate

system; definition of robust metrics for GCMs, dataStat Mech for Climate response to perturbations

47EQ NON EQ

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Thermodynamics of the CSThe CS generates entropy (irreversibility),

produces kinetic energy with efficiency η (engine), and keeps a steady state by balancing fluxes with surroundings (Ozawa et al., 2003)

Fluid motions result from mechanical work, and re-equilibrate the energy balance.

We have a unifying picture connecting the Energy cycle to the MEPP (L. 2009);

This approach helps for understanding many processes (L et al., 2010; Boschi et al. 2012):Understanding mechanisms for climate transitions;Defining generalised sensitivities Proposing parameterisations

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Concluding…The CS seems to cover many aspects of the science

of complex systemsWe know a lot more, a lot less than usually perceived

Surely, in order to perform a leap in understanding, we need to acknowledge the different episthemology relevant for the CS and develop smart science tackling fundamental issues

“Shock and Awe” numerical simulations may provide only incremental improvements: heavy simulations are needed, but climate science is NOT just a technological challenge, we need new ideas

I believe that non-equilibrium thermodynamics & statistical mechanics may help devising new efficient strategies to address the problems

Next time! Entropy, Efficiency, Tipping Points

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Bibliography Held, I.M., Bull. Amer. Meteor. Soc., 86, 1609–1614 (2005) Hasson S.,, V. Lucarini, and S. Pascale, Earth Syst. Dynam.

Discuss., 4, 109–177, 2013 Lucarini, V., R. Danihlik, I. Kriegerova and A. Speranza. J.

Geophys. Res., 113, D09107 (2008) Peixoto J. and A. Oort, Physics of Climate (AIP, 1992) Saltzman B., Dynamic Paleoclimatology (Academic Press,

2002) Lucarini V., Validation of Climate Models, in Encyclopaedia

of Global Warming and Climate Change, Ed. G. Philander, 1053-1057(2008)

V. Lucarini, F. Ragone, Rev. Geophys. 49, RG1001 (2011) B. Liepert and M. Previdi, Inter-model variability and

biases of the global water cycle in CMIP3 coupled climate models, ERL 7 014006 (2012)