Thermodynamics of Climate
– Part 1 –
Valerio Lucarini
University of Hamburg
University of Reading
Email: valerio.lucarini@uni-hamburg.de
Cambridge, 23/10/2013
1
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 are2
interested in T, P, precipitation”
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
3
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
4
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).
5
Map of Complexity
 Climate Science is mysteriously missing!
6
Map of Complexity
 Climate Science is perceived as being too technical, political
Climate Science
7
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
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properties of the CS.
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 fluctuationdissipation 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.
9
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” science10
Scales of Motions
(Stommel/Smagorinsky)
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
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Features/Particles
Focus is on specific (self)organised structures
Hurricane physics/track
13
Atmospheric (macro) turbulence
Energy, enstrophy cascades, 2D vs 3D
Note:
NOTHING
is really 2D
in the
atmosphere
14
Waves in the atmosphere
Large and small scale patterns
15
“Waves” in the atmosphere?
Hayashi-Fraedrich decomposition
16
“Waves” in
GCMs
GCMs differ in
representation of
large scale
atmospheric
processes
Just Kinematics?
What we see are
only unstable
waves and their
effects
17
Evolution of Climate Models
With improvement of CPU and of scientific
knowledge, CMs have gained new components
definition of “climate” has also changed
18
Full-blown
Climate
Model
Since the ‘40s, some of largest
computers are devoted to
climate modelling
G
O
A
L
S
O
F
M
O
D
E
L
L
I
N
G
Local evolution in
the phase space
NWP
vs.
Statistical
properties on the
attractor
Climate Modeling
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?
21
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
22
All models are “wrong”! (but we are not blind!)
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 1961-2000
(L. et al. 2008)
Purple is EM: what
does it tell us?
24
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
Webster et al. 2001
 This PDF contains a huge amount of info!
 We can assess risks, this is an instrument of decision-making
25
E
N
E
R
G
Y
T
R
A
N
S
P
O
R
T
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 27
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
28
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
29
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
•PreIndustrial
control runs
(100 years)
•SRESA1B
720 ppm
CO2
stabilizatio
n (100
years, as far
as possible
from 2100)
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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
31
L. and Ragone, 2011
PI – Atmosphere Energy Balance
32
PI – Ocean Energy Balance
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
33
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)
34
 Need for longer integrations (τ >300 y)
Estimated B(P-E) vs Total Runoff – (Annual)
Results - XX Century Climate – (1961-2000)
Energy Imbalance
From Energy Balance to Transports


From energy conservation:

 


 i    k      h    k v     H
t
Long term
averages
If we integrate vertically, zonally  Transports
d
Ttot ( y) = -RTOA ( y)
dy
d
Tatm ( y) = -RTOA ( y) + H surf ( y)
dy
d
Toce  y    H surf  y 
dy
• 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
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TOA and surface
PI -Transports
T
A
O
Stone ‘78 constraint
well obeyed
38
Max Transport - TOA
6 ° (2,3 gridpoints)
1.2 PW
20%
39
Max Transport - Atmosphere
0.8 PW
15%
4°
40
Max Transport - Ocean
0.8 PW
50%
5°
41
SRESA1B -Transports
T
A
O
42
Δ Atm Transport
43
Increase of Atm Transport: LH effect
Δ peak NH Atm Transport
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Poleward shift of Storm track: SH & NH
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
climate
Multiscale
(Kleidon, 2011)
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 EQ47
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
48
Proposing parameterisations
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
49
Next time! Entropy, Efficiency, Tipping Points
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)
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