Presentation on theme: "Thermodynamics of Climate – Part 1 –"— Presentation transcript:
1 Thermodynamics of Climate – Part 1 – Valerio LucariniUniversity of HamburgUniversity of ReadingCambridge, 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 partsReductionism, 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 formationSymmetry break and instabilitiesIrreversibilityEntropy ProductionVariability of many spatial and temporal scalesNon-trivial numerical modelsSensitive dependence on initial conditionslimited predictability time
5 Complicated vs Complex Not Complicated and Not ComplexHarmonic oscillator in 1DComplicated and Not ComplexGas of non-interacting oscillators (phonons)Integrable systems are always not complexNot Complicated and ComplexLorenz 63 model has only 3 degrees of freedomComplicated 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).
6 Map of ComplexityClimate Science is mysteriously missing!
7 Map of ComplexityClimate Science is perceived as being too technical, politicalClimate Science
8 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 complicatedThe 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.
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 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.
10 Three major experimental challenges in analysing the CS Synchronic coherence of dataData feature hugely varying degree of precisionDiachronic coherence of dataTechnology and prescriptions for data collection have changed with timeSpace-time coverageData density change with location (Antarctica vs Germany)We have “direct” data only since Galileo timeBefore, we have to rely on indirect (proxy) dataUnusual with respect to “typical” science
12 Atmospheric Motions Three contrasting approaches: Those who like maps, look for features/particlesThose who like regularity, look for wavesThose who like irreversibility, look for turbulenceLet’s see schematically these 3 visions of the world
13 Features/Particles Focus is on specific (self)organised structures Hurricane physics/track
15 Waves in the atmosphere Large and small scale patterns
16 “Waves” in the atmosphere? Hayashi-Fraedrich decomposition
17 “Waves” in GCMsGCMs differ in representation of large scale atmospheric processesJust 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 GOALSFMDEINLocal evolution in the phase space NWP vs. Statistical properties on the attractor Climate Modeling
21 Climate Models uncertainties Uncertainties of the 1st kindAre our initial conditions correct? Not so relevant for CM, crucial for NWPUncertainties 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?
22 Plurality of ModelsIn Climate Science, not only full-blown models (most accurate representation of the largest number of processes) are usedSimpler models are used to try to capture the structural properties of the CSLess expensive , more flexible – parametric explorationCMs 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 instrumentsAll models are “wrong”! (but we are not blind!)
24 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 realityIntensity 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 ProbabilityThe 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 exploredThis PDF contains a huge amount of info!We can assess risks, this is an instrument of decision-makingWebster et al. 2001
27 Energy & GW – Perfect GCM ForcingτL. and Ragone, 2011Total warmingNESS→Transient → NESSApplies to the whole climate and to to all climatic subdomainsfor atmosphere τ is small, always quasi-equilibrated
28 Energy and GW – Actual GCMs L. and Ragone, 2011ForcingτNot only bias: bias control ≠ bias final stateBias depends on climate state! Dissipation
29 Comments “Well, we care about T and P, not Energy” Troublesome, practically and conceptuallyA 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
30 PCMDI/CMIP3 GCMs - IPCC4AR ModelInstitution1.BCCR-BCM2.0Bjerknes Center, Norway2.3.CGCM3.1(T47)CGCM3.1(T63)CCCma, Canada4.CNRM-CM3Mètèo France, France5.6.CSIRO-Mk3.0CSIRO-Mk3.5CSIRO, Australia7.FGOALS-g1.0LASG, China8.9.GFDL-CM2.0GFDL-CM2.1GFDL, USA10.11.12.GISS-AOMGISS-EHGISS-ERNASA-GISS, USA13.14.HADCM3HADGEMHadley Center, UK15.INM-CM3.0Inst. Of Num. Math., Russia16.IPSL-CM4IPSL, France17.18.MIROC3.2(hires)MIROC3.2(medres)CCSR/NIES/FRCGC, Japan19.ECHO-GMIUB, METRI, and M&D, Germany/Korea20.ECHAM5/MPI-OMMax Planck Inst., Germany21.MRI-CGCM2Meteorological Research Institute, Japan22.23.NCAR CCSMNCAR PCMNCAR, USAPre-Industrial control runs (100 years)SRESA1B 720 ppm CO2 stabilization (100 years, as far as possible from 2100)
31 PI – TOA Energy BalanceIs the viscous loss of kinetic energy re-injected in the system? (Becker 03, L & Fraedrich 2009)IPCC4ARModelsControl RunL. and Ragone, 2011
33 PI – Ocean Energy Balance Most models bias (typ. >0) is < 1 Wm-2Larger interannual variability than atmospherePI – Land Energy BalanceThin (à la Saltzman) climate subsystemMost models bias (typ. >0) is < 2 Wm-2Model 5 bias is 2 Wm-2; 10 Wm-2 excess for Model 19
34 Δ TOA Energy BalanceIn 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)
37 From Energy Balance to Transports From energy conservation:If we integrate vertically, zonally TransportsLong termaveragesIf fluxes integrate globally to 0 – as they should – the T functions are zero at BOTH polesOtherwise (relatively small!) biasesWe compute annual meridional transports starting from annual TOA and surface zonally averaged fluxesCan be done for TOA with satellites!
38 PI -TransportsTAOStone ‘78 constraintwell obeyed
39 Max Transport - TOA6 ° (2,3 gridpoints)1.2 PW 20%
43 Δ Atm TransportIncrease of Atm Transport: LH effect
44 Δ peak NH Atm TransportPoleward 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 transportCompensating mechanism tends to become stronger with GWAbout the same in the SHBjerknes compensation mechanism
46 Disequilibrium in the Earth system climateMultiscale(Kleidon, 2011)
47 Looking for the big picture Global structural properties (Saltzman 2002).Deterministic & stochastic dynamical systemsExample: stability of the thermohaline circulationStochastic forcing: ad hoc “closure theory” for noiseStat 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 perturbationsEQ NON EQ47
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 sensitivitiesProposing parameterisations
49 Concluding…The CS seems to cover many aspects of the science of complex systemsWe know a lot more, a lot less than usually perceivedSurely, 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 ideasI believe that non-equilibrium thermodynamics & statistical mechanics may help devising new efficient strategies to address the problemsNext time! Entropy, Efficiency, Tipping Points
50 BibliographyHeld, I.M., Bull. Amer. Meteor. Soc., 86, 1609–1614 (2005)Hasson S.,, V. Lucarini, and S. Pascale, Earth Syst. Dynam. Discuss., 4, 109–177, 2013Lucarini, 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)