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![Page 1: 1 Thermodynamics of Climate – Part 1 – Valerio Lucarini University of Hamburg University of Reading Email: valerio.lucarini@uni-hamburg.devalerio.lucarini@uni-hamburg.de.](https://reader035.fdocuments.in/reader035/viewer/2022062417/5519d3075503468b0c8b48a6/html5/thumbnails/1.jpg)
1
Thermodynamics of Climate – Part 1 –
Valerio Lucarini
University of Hamburg
University of Reading
Email: [email protected]
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
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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
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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
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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
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Full-blown Climate Model
Since the ‘40s, some of largest computers are devoted to
climate modelling
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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
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TRANSPORT
ENERGY
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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
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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
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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)
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Estimated B(P-E) vs Total Runoff – (Annual)
Results - XX Century Climate – (1961-2000)
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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
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Δ Atm Transport
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Increase of Atm Transport: LH effect
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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
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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)