Thermodynamics of Climate – Part 1 – Valerio Lucarini University of Hamburg University of Reading Email: [email protected] Cambridge, 23/10/2013
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Transcript Thermodynamics of Climate – Part 1 – Valerio Lucarini University of Hamburg University of Reading Email: [email protected] Cambridge, 23/10/2013
Thermodynamics of Climate
– Part 1 –
Valerio Lucarini
University of Hamburg
University of Reading
Email: [email protected]
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
8
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
12
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
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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
37
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
44
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
45
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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