Past and Present Variability of the Solar-Terrestrial System: Measurement, Data Analysis and Theoretical Models

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1 ITALIAN PHYSICAL SOCIETY PROCEEDINGS OF THE INTERNATIONAL SCHOOL OF PHYSICS «ENRICO FERMI» COURSE CXXXIII edited by G. ClNI CASTAGNOLI and A. PROVENZALE Directors of the Course VARENNA ON LAKE COMO VILLA MONASTERO 25 June - 5 July 1996 Past and Present Variability of the Solar-Terrestrial System: Measurement, Data Analysis and Theoretical Models 1997 IOS Press = = = Ohmsha AMSTERDAM, OXFORD, TOKYO, WASHINGTON DC

2 G. CINI CASTAGNOLI and A. PROVENZALE - Preface pag. xv Gruppo fotografico dei partecipanti al Corso fuori testo J. M. PAP - Total solar irradiance variability: A review 1. Introduction pag Variations observed in total solar irradiance» 2 3. Modeling total solar irradiance variations» Modeling variations on active-regions time scale» 9 3"1.1. Results of multivariate spectral analysis» Results of singular spectrum analysis» 12 3'2. Modeling variations over the solar cycle» Uncertainties of irradiance measurements» 19 3'2.2. Limitation of the irradiance models» Conclusions '. ':..» 21 J. BEER - Cosmogenic isotopes as a tool to study solar and terrestrial variability 1. Introduction.» Cosmogenic isotopes» 26 2'1. Production of cosmogenic isotopes» 26 2'2. Transport of cosmogenic isotopes...» 27 2'3. Detection of cosmogenic isotopes» Cosmogenic isotopes and solar variability» Cosmogenic isotopes and terrestrial variability» Precipitation rates» 32 4'2. 36 C1 bomb pulse» 32 4"3. The "35 ky peak"» 33 4'4. Solar variability and climate» Summary» 35

3 VI INDICE G. CINI CASTAGNOLI and A. PROVENZALE - Records of the solar cycle in terrestrial archives 1. Introduction pag The 11 y solar cycle» '- 38,. 3. Records of the solar hydromagnetic variability» Records of the solar bolometric variability» Conclusions '...'» 44 G. CINI CASTAGNOLI - The 200 y variability in terrestrial archives: solar forcing? 1. Cosmogenic isotope records» Climatic records» Records in the shallow-water cores of the Gallipoli terrace» The cores and their dating» 49 3'2. The total carbonate time series» 50 3'3. Comparison of the carbonate record with the tree ring radiocarbon record» 53 3'4. The thermoluminescence (TL) time series» Conclusions» 56 G. CINI CASTAGNOLI, G. BONINO, P. DELLA MONICA and C. TARICCO - The solar-irradiance variability recorded by thermoluminescence in shallow Ionian Sea sediments 1. Introduction» Experimental procedure» Spectral properties of the TL profiles» Conclusion» 68 G. BONINO and G. CINI CASTAGNOLI - Solar cylces recorded in meteorites 1. Introduction,» Solar modulation of GCR in the inner heliosphere» Modelling of cosmogenic nuclide production in meteorites» The 11 y and the century scale solar cycle in meteorites» The 11 y solar cycle» 76 4'2. The century scale solar cycle» Conclusions» 79 I. HAJDAS, J. BEER, G. BONANI, G. BONINO, G. CINI CASTAGNOLI and C. TARICCO - Radiocarbon time scale of the Mediterranean core CT85-5: the last years 1. Radiocarbon dating» Dating method and radiocarbon time scale» Radiocarbon dating of the deep-sea core CT85-5» 85

4 VII G. CINI CASTAGNOLI, G. BONINO and GUANG-MEI ZHU - Long-term global change from Mediterranean Sea sediments 1. Introduction pag Core dating...'» Comparison of carbonate profiles in Tyrrhenian and North Atlantic cores..» Conclusions» 92 N. BHANDARI - Records of solar activity in planetary objects» Charge particle environment in the interplanetary space» Interaction of charged particles with matter» Rates of production of tracks and their depth profiles» Tracks due to WH CZ>30) nuclei» Rates of production of stable and radio nuclides» Isotope production by solar particles» 104 4'2. Production of nuclides by GCR protons» 107 4'3. Neutron capture effects» Application of cosmogenic effects for paleosolar activity» 109 N. BHANDARI - Paleoactivity of the Sun: Meteoritic perspective» Meteorite records over decades to century» Meteorite records over years..a» Meteorite records relating to the earliest stages of the solar system» Meteorite records of the early activity of the Sun» 120 N. BHANDARI - The Sun through time: The lunar and planetary perspective» Lunar samples as monitors of solar processes» The diagnostic signatures of the Sun and possible interferences» Lunar rocks as monitors of solar-flare fluxes and their variation over the past few million years» Lunar breccias and soils as monitors of solar processes and long-term secular variations in solar-wind characteristics :..» The exposure history of grains and rocks» 131 3'2. The characteristic signatures of the contemporary Sun» 131 3'3. Measurements and possible interferences» 132 3'4. Observed long-term changes in isotopic ratios» 132 3'5. The solar-wind velocity» Evidence of solar variability from other planetary records» 134 M. GHIL and C. TARICCO - Advanced spectral-analysis methods 1. Introduction» Classical spectral estimation» Periodogram» Variance reduction» Leakage reduction» 140 2'2. Correlogram» Maximum-entropy method (MEM)» Parametric spectral estimation» 141

5 VIII INDICE 3'2. Some problems with MEM spectra pag *3. Multi-channel MEM» Multi-taper method (MTM)» Singular-spectrum analysis (SSA).» Basic algorithms.» 147 5*2. Reconstruction and power spectrum» 150 5*3. Monte Carlo SSA (MC-SSA)1.^» 150 5*4. Multi-channel SSA (MSSA)»> Wavelet analysis» Windowed Fourier transform (WFT)» 152 6*2. The wavelet transform (WT)» Concluding remarks» 154 J. VON HARDENBERG and A. PROVENZALE - Dynamics of forced and coupled systems 1. Introduction» Time series analysis: A matter of motivations» Phase space reconstruction» Correlation dimension» Self-similar random processes and surrogate data» Systems with on/off intermittency» Weakly coupled systems t» Conclusions and perspectives» 174 L. A. SMITH - The maintenance of uncertainty 1. Introduction» Preliminaries» State-space dynamics» Linearized dynamics of infinitesimal uncertainties» Instantaneous infinitesimal dynamics» Finite-time evolution of infinitesimal uncertainties» 186 2'2. Lyapunov exponents and predictability» 189 2*2.1. The Baker's apprentice map» 189 2*2.2. Infinitesimals and predictability» 191 2*3. Dimensions» 192 2*3.1. The Grassberger-Procaccia algorithm» 193 2'3.2. Towards a better estimate from Takens' estimators» 194 2*3.3. Space-time-separation diagrams» 197 2'3.4. Intrinsic limits to the analysis of geometry» 198 2*4. Takens' theorem» 200 2*5. The method of delays» 201 2*6. Noise» Prediction, prophecy, and pontification» Introduction» 204 3*2. Simulations, models and physics» 205 3*3. Ground rules» 205 3*4. Data-based models: dynamic reconstructions» 206 3*4.1. Analogue prediction» 206 3*4.2. Local prediction» 207 3*4.3. Global prediction» 207

6 IX 3*5. Accountable forecasts of chaotic systems pag *6. Evaluating ensemble forecasts» 211 3*7. The annulus» 211 3*7.1. Prophecies» Aids for more reliable nonlinear analysis» 215 4*1. Significant results: surrogate data, synthetic data and self-deception..» 215 4*1.1. Surrogate data and the bootstrap» 219 4*1.2. Surrogate predictors: Is my model any good?» 219 4*2. Hints for the evaluation of new techniques» 220 4*2.1. Avoiding simple straw men» 220 4*3. Feasibility tests for the identification of chaos» 221 4*3.1. On detecting "tiny" data sets» Building models consistent with the observations» Cost functions» 222 5*2. t-shadowing: Is my model any good? (reprise)» 223 5*2.1. Casting infinitely long shadows (out-of-sample)» 224 5*3. Distinguishing model error and system sensitivity» 225 5*3.1. Forecast error and model sensitivity» 225 5*3.2. Accountability >» 225 5*3.3. Residual predictability» Deterministic or stochastic dynamics?» Using ensembles to distinguish the expectation from the expected» Numerical Weather Prediction {» Probabilistic prediction with a deterministic model» 232 7*2. The analysis» 233 7*3. Constructing and interpreting ensembles» 234 7*4. The outlook(s) for today» 236 7*5. Conclusion..'.» Summary» 238 J. KURTHS, U. FEUDEL, W. JANSEN, U. SCHWARZ and H. Voss - Solar variability: Simple models and proxy data 1. A nonlinear dynamo model :» Subject and methods of qualitative analysis» 248 1*2. Bifurcation phenomena in the nonlinear dynamo model» Reconstruction of grand minima of solar activity from A 14 C data» Historical sunspot observations and grand minima» 253 2*2. Determination of a record of grand minima from proxy data» 253 2*2.1. Preprocessing.» 254 2*2.2. Estimation procedure '» 255 2*3. Result» 256 2*4. Test of models..» 256 2*5. Comments >» 258 Appendix A - Testing the AR model» 258 M. G. ROSENBLUM, A. S. PIKOVSKY and J. KURTHS - Phase synchronization of chaotic oscillators and analysis of bivariate data 1. Introduction» Instantaneous phase of signals and systems» 264

7 3. Phase synchronization of chaotic self-sustained oscillators pag Looking for synchronization phenomena in real data» Conclusions» 273 J. R. BUCHLER - Search for low-dimensional chaos in observational data 1. Introduction» The underlying dynamics» A test case: the Rossler oscillator» The test data sets '...d» 279 3*2. The flow reconstruction» 282 3*3. Noise» A real system: the light curve of R Scuti» Conclusion >» 288 T. SERRE and E. NESME-RIBES - The evolution of the solar cycle 1. Introduction» The reconstruction of the solar cycle back to 1609» Original measurement devices» 292 2*2. Wolf sunspot number» 293 2*3. Group sunspot number» Solar-diameter measurements» Original techniques and data» 295 3*2. Comparison of historical radius with modern values» 295 3*3. Period analysis of the solar-diameter data» Maunder Minimum» Butterfly diagram and rotation distributions» 300 4*2. Wavelet analysis» 302 4*3. Further evidences from solar-type stars» Alpha-omega dynamo and solar cycle» Nonlinear prospects» Conclusion» 309 E. A. SPIEGEL - Catastrophes, chaos and cycles 1. Astromathematics» Sensitive systems» Gradient systems» 312 2*2. Excitability» 314 2*3. Chaotic systems» 315 2*4. Intermittency» The macculate Sun» Variable solar maccularity» 319 3*2. The solar tachocline» 321 3*3. Solar solitoids» Cycles» A model solar oscillation» 322 4*2. Solar activity waves» 323

8 XI N. 0. WEISS - Physics of the solar dynamo 1. Introduction.'. pag Stellar magnetic cycles» Solar magnetic activity» *2. Stellar activity» 327 2*3. Origins of the Sun's magnetic field» Dynamo theory» The kinematic dynamo problem» 328 3*2. Nonlinear equilibration» 329 3*3. Mean-field dynamo theory» Modulation of activity cycles» Toy models» 331 4*2. Global models» Solar activity and climatic change» Observational correlations» 338 5*2. Mechanisms and speculations» 339 J. TOOMRE - Dynamics of the solar convection zone 1. Introduction».» Multiple discrete scales of convection» 344 1*2. Probing of structure and flows with helioseismology» 344 1*3. Multitude of magnetic structures and dynamo action» 345 1*4. Structures and inverse cascades in turbulence» 346 1*5. Dynamical range of solar turbulence» Local models of rotating compressible convection» Formulation of local /-plane models» 348 2*2. Nature of rotating turbulent convection» 348 2*3. Driving of mean flows and implications for differential rotation» 350 2*4. Penetrative convection and intermittency in transport of heat» Global models of spherical convection» Formulation of anelastic convection in rotating shells» 352 3*2. Nature of global convection and the mean flows» Reflections» 354 A. BRANDENBURG - Recent developments in the theory of large-scale dynamos 1. Large-scale magnetic fields in the Sun» Traditional aq dynamos» The effective a in accretion disc simulations» Strengths of fluctuations» Quenching of a and rj t» Convection with shear» Forced turbulence with shear» Variety of solar dynamo models» 384

9 XII INDICE M. E. SCHLESINGER, N. G. ANDRONOVA, B. ENTWISTLE, A. GHANEM, N. RAMANKUTTY, W. WANG and F. YANG - Modeling and simulation of climate and climate change 1. Introduction pag Energy balance models» 389 2*1. Formulation» 390 2*2. Governing equations» 390 2*3. Calibration: simulation of the present-day seasonal cycle >> 397 2*4. Simulation of 2 x CO 2 -induced temperature and sea-level changes» Radiative-convective models» Formulation.'.» 399 3*2. Governing equations» 400 3*2.1. Surface convection» 402 3*2.2. Convective adjustment» 402 3*2.3. Model specification and initialization» 405 3*3. Simulation of the present-day temperature» 405 3*4. Simulation of the temperature change induced by doubling the CO 2 concentration» General circulation models» 408 4*1. Formulation of atmospheric GCMs» 410 4*2. Formulation of ocean/sea-ice models» 412 4*3. Model validation: simulation of the present climate» 420 4*4. Simulation of 2 x CO 2 -induced climate change» 421 Appendix A - Description of the UIUC 11-layer atmospheric general circulation/ mixed-layer-ocean model» 421 Al. Background» 421 A*2. Atmospheric general circulation model» 422 A*2.1. Predicted quantities and numerical solution methods» 422 A*2.2. Parameterizations-Treatment of unresolved-scale physical processes» 422 A* Surface and planetary boundary flayer» 422 A* Subgrid-scale transports, convection" large-scale condensation, precipitation and clouds» 423 A* Radiative transfer» 425 A*2.3. Calibration and tuning» 426 A"3. Mixed-layer ocean» 426 K. FRAEDRICH - Atmospheric variability: modelling, diagnostics, and forecasting 1. The atmosphere: a component of the climate system» Modelling: conceptual and comprehensive» Modelling strategy.» 433 2*2. A toy climate model» 434 2*2.1. Dynamic analysis» 435 2*2.2. Stochastic analysis (and the two-time-scale approach)» 438 2*3. A new general circulation model» 438 2*3.1. Numerics, physics, and climatology» 439 2*3.2. GCM-experiments» Diagnostics: stormtracks and Grosswetter» A toy weather model: linear quasi-geostrophic flow» 446

10 XIII 3*1.1. Eulerian analysis pag *1.2. The textbook linear 2-layer model» 448 3*1.3. Energetics!.» 448 3*1.4. Spectral model» 449 3*1.5. Rossby waves» 450 ' 3*1.6. Baroclinic instability» 451 3*1.7. Stochastic forcing» 452 3*2. Midlatitude cyclone tracks: a Lagrangian view» 453 3*2.1. Lagrangian analysis» 454 3*2.2. Storm track scaling» 456 3*3. Time series analysis: degrees of freedom and dimension» 456 3*3.1. Linear analysis: degrees of freedom» 457 3*3.2. Non-linear analysis: dimension» Forecasting: persistence, hurricanes, and rain» A toy predictability model: persistence in red noise» 467 4*1.1. Red noise»> 467 4*1.2. Chance, climate, and persistence» 468 4*1.3. Forecast verification» 469 4*2. Tropical-cyclone tracks: linear and non-linear forecasts» 473 4*2.1. Linear combination of forecasts» 473 4*2.2. Non-linear forecasts» 474 4*3. Probability of precipitation (PoP)» 476 4*3.1. Rainfall Markov chain,» Conclusion» 480

Contents. Parti Fundamentals. 1. Introduction. 2. The Coriolis Force. Preface Preface of the First Edition

Contents. Parti Fundamentals. 1. Introduction. 2. The Coriolis Force. Preface Preface of the First Edition Foreword Preface Preface of the First Edition xiii xv xvii Parti Fundamentals 1. Introduction 1.1 Objective 3 1.2 Importance of Geophysical Fluid Dynamics 4 1.3 Distinguishing Attributes of Geophysical