Thermodynamics of Climate – Part 1 – Valerio Lucarini University of Hamburg University of Reading Email: valerio.lucarini@uni-hamburg.de Cambridge, 23/10/2013

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”

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

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

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).

Map of Complexity Climate Science is mysteriously missing!

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

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.

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.

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

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

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

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

Waves in the atmosphere Large and small scale patterns

“Waves” in the atmosphere? Hayashi-Fraedrich decomposition

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

Evolution of Climate Models With 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

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

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?

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!)

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?

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

E N 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

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

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

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)

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

PI – Atmosphere 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

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

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!

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

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

Max Transport - Atmosphere 0.8 PW 15% 4 °

Max Transport - Ocean 0.8 PW 50% 5 °

SRESA1B -Transports T A O

Δ Atm Transport Increase of Atm Transport: LH effect

Δ peak NH Atm Transport 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

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 EQ 47

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

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

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