1. Thermodynamics of Climate – Part 1 –
Valerio Lucarini
University of Hamburg
University of Reading
Cambridge, 23/10/2013

2. 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”

3. 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

4. Some Properties of Complex Systems
Spontaneous Pattern formation
Symmetry break and instabilities
Irreversibility
Entropy Production
Variability of many spatial and temporal scales
Non-trivial numerical models
Sensitive dependence on initial conditions
limited predictability time

5. Complicated vs Complex
Not Complicated and Not Complex
Harmonic oscillator in 1D
Complicated and Not Complex
Gas of non-interacting oscillators (phonons)
Integrable systems are always not complex
Not Complicated and Complex
Lorenz 63 model has only 3 degrees of freedom
Complicated and Complex
Turbulent 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).

6. Map of Complexity
Climate Science is mysteriously missing!

7. Map of Complexity
Climate Science is perceived as being too technical, political
Climate Science

8. Some definitions
The 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 freedom
This makes it complicated
The CS features variability on many time-space scales and sensitive dependence on IC
This makes it complex.
The climate is defined as the set of the statistical properties of the CS.

9. 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 system
impossibility 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 system
non-equivalence between the external and internal fluctuations  Climate Change is hard to parameterise
Numerics: Climate is a stiff problem (very different time scales) “optimal” resolution?
brute force approach is not necessarily the solution.

10. Three major experimental challenges in analysing the CS
Synchronic coherence of data
Data feature hugely varying degree of precision
Diachronic coherence of data
Technology and prescriptions for data collection have changed with time
Space-time coverage
Data density change with location (Antarctica vs Germany)
We have “direct” data only since Galileo time
Before, we have to rely on indirect (proxy) data
Unusual with respect to “typical” science

11. Scales of Motions (Stommel/Smagorinsky)

12. Atmospheric Motions Three contrasting approaches:
Those who like maps, look for features/particles
Those who like regularity, look for waves
Those who like irreversibility, look for turbulence
Let’s see schematically these 3 visions of the world

13. Features/Particles Focus is on specific (self)organised structures
Hurricane physics/track

14. Atmospheric (macro) turbulence
Energy, enstrophy cascades, 2D vs 3D
Note:
NOTHING
is really 2D
in the
atmosphere

15. Waves in the atmosphere
Large and small scale patterns

16. “Waves” in the atmosphere?
Hayashi-Fraedrich decomposition

17. “Waves” in GCMs
GCMs differ in representation of large scale atmospheric processes
Just Kinematics?
What we see are only unstable waves and their effects

18. Evolution of Climate Models
With improvement of CPU and of scientific knowledge, CMs have gained new components definition of “climate” has also changed

19. Full-blown Climate Model
Since the ‘40s, some of largest computers are devoted to climate modelling

20. G O A L S F M D E I N
Local evolution in the phase space NWP vs. Statistical properties on the attractor Climate Modeling

21. Climate Models uncertainties
Uncertainties of the 1st kind
Are our initial conditions correct? Not so relevant for CM, crucial for NWP
Uncertainties of the 2nd kind
Are 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?

22. Plurality of Models
In 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 CS
Less expensive , more flexible – parametric exploration
CMs uncertainties are addressed by comparing
CMs 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!)

24. Multimodel ensemble
Outputs 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 (L. et al. 2008)
Purple is EM: what does it tell us?

25. 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

26. E N R G Y
T R A N S P O R T

27. Energy & GW – Perfect GCM
Forcing τ
L. and Ragone, 2011
Total warming
NESS→Transient → NESS
Applies to the whole climate and to to all climatic subdomains
for atmosphere τ is small, always quasi-equilibrated

28. Energy and GW – Actual GCMs
L. and Ragone, 2011
Forcing τ
Not only bias: bias control ≠ bias final state
Bias depends on climate state!  Dissipation

29. 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) publications
Should we do the same?
Food for thought

30. PCMDI/CMIP3 GCMs - IPCC4AR
Model
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-Mk3.0
CSIRO-Mk3.5
CSIRO, Australia 7.
FGOALS-g1.0
LASG, China 8. 9.
GFDL-CM2.0
GFDL-CM2.1
GFDL, USA
10.
11.
12.
GISS-AOM
GISS-EH
GISS-ER
NASA-GISS, USA
13.
14.
HADCM3
HADGEM
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 CCSM
NCAR PCM
NCAR, USA
Pre-Industrial control runs (100 years)
SRESA1B 720 ppm CO2 stabilization (100 years, as far as possible from 2100)

31. PI – TOA Energy Balance
Is the viscous loss of kinetic energy re-injected in the system? (Becker 03, L & Fraedrich 2009)
IPCC4AR
Models
Control Run
L. and Ragone, 2011

32. PI – Atmosphere Energy Balance

33. PI – Ocean Energy Balance
Most models bias (typ. >0) is < 1 Wm-2
Larger interannual variability than atmosphere
PI – Land Energy Balance
Thin (à la Saltzman) climate subsystem
Most models bias (typ. >0) is < 2 Wm-2
Model 5 bias is 2 Wm-2; 10 Wm-2 excess for Model 19

34. Δ TOA Energy Balance
In 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)

35. Estimated B(P-E) vs Total Runoff – (Annual) Results - XX Century Climate – (1961-2000)

36. Energy Imbalance

37. From Energy Balance to Transports
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!

38. PI -Transports T A O
Stone ‘78 constraint
well obeyed

39. Max Transport - TOA
6 ° (2,3 gridpoints)
1.2 PW 20%

40. Max Transport - Atmosphere
0.8 PW
15%
4 °

41. Max Transport - Ocean
0.8 PW
50%
5 °

42. SRESA1B -Transports T A O

43. Δ Atm Transport
Increase of Atm Transport: LH effect

44. Δ peak NH Atm Transport
Poleward shift of Storm track: SH & NH

45. 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

46. Disequilibrium in the Earth system
climate
Multiscale
(Kleidon, 2011)

47. Looking for the big picture
Global 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 perspective
Planets are non-equilibrium thermodynamical systems
Thermodynamics: large scale properties of the climate system; definition of robust metrics for GCMs, data
Stat Mech for Climate response to perturbations
EQ NON EQ 47

48. Thermodynamics of the CS
The 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

49. Concluding…
The CS seems to cover many aspects of the science of complex systems
We 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

50. 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, (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 (2012)