Preface ..................................................... ix
Acknowledgements ............................................ xi
1 Climate Variability .......................................... 1
1.1 The observational database .............................. 2
1.2 Phenomena: temporal and spatial scales .................. 4
1.3 The climate system ...................................... 6
1.4 The stochastic dynamical systems framework .............. 7
1.5 Overview of the book .................................... 9
2 Deterministic Dynamical Systems ............................. 11
2.1 Finite dimensional dynamical systems ................... 11
2.2 Stability theory and transient behaviour ............... 13
2.3 Bifurcation theory: fixed points ....................... 19
2.4 Bifurcation theory: periodic orbits .................... 25
2.5 Beyond simple behaviour: attractors .................... 28
3 Introduction to Stochastic Calculus ......................... 35
3.1 Random variables ....................................... 35
3.2 Stochastic processes ................................... 38
3.3 Stochastic calculus .................................... 40
3.4 Stochastic differential equations ...................... 45
3.5 The Fokker-Planck equations ............................ 51
3.6 Numerical solutions of SDEs ............................ 58
4 Stochastic Dynamical Systems ................................ 64
4.1 Nonautonomous dynamical systems ........................ 64
4.2 Random dynamical systems ............................... 67
4.3 Stochastic bifurcations ................................ 77
5 Analysing Data from Stochastic Dynamical Systems ............ 83
5.1 Classical univariate methods ........................... 83
5.2 Hypothesis testing and significance .................... 89
5.3 Bivariate and multivariate analysis .................... 93
5.4 Nonstationary methods: wavelets ....................... 102
5.5 Nonlinear methods ..................................... 103
6 The Climate Modelling Hierarchy ............................ 116
6.1 Model traits: scales and processes .................... 117
6.2 Scientific questions and model choice ................. 123
6.3 Deterministic versus stochastic models ................ 124
6.4 Model error ........................................... 128
7 The North Atlantic Oscillation ............................. 131
7.1 Midlatitude atmospheric variability ................... 131
7.2 Minimal model ......................................... 137
7.3 Variability in conceptual models ...................... 139
7.4 Beyond conceptual models .............................. 149
7.5 Regime transitions and metastable states .............. 160
7.6 Synthesis ............................................. 163
8 El Nino Variability ........................................ 167
8.1 Phenomena ............................................. 167
8.2 A minimal model ....................................... 170
8.3 The ENSO mode ......................................... 177
8.4 Excitation of the ENSO mode ........................... 185
8.5 ENSO's phase locking to the seasonal cycle ............ 190
8.6 The irregularity of El Nino ........................... 192
8.7 Synthesis ............................................. 200
9 Multidecadal Variability ................................... 202
9.1 Introduction .......................................... 202
9.2 Stability of the thermally driven ocean flows ......... 206
9.3 Excitation of the AMO mode ............................ 213
9.4 Dynamical mechanisms of excitation .................... 217
9.5 Context of the AMO: two time scales? .................. 225
9.6 Synthesis ............................................. 227
10 Dansgaard-Oeschger Events .................................. 231
10.1 Phenomena ............................................. 231
10.2 The meridional overturning circulation ................ 233
10.3 Sensitivity of the MOC: hysteresis .................... 236
10.4 Variability of the MOC: oscillations .................. 240
10.5 Effects of noise: stochastic resonance ................ 248
10.6 Climate models ........................................ 263
10.7 Synthesis ............................................. 265
11 The Pleistocene Ice Ages ................................... 270
11.1 Phenomena ............................................. 270
11.2 The'null hypothesis': Milankovitch theory ............. 272
11.3 Potentially important feedbacks ....................... 274
11.4 Basic theories of interglacial-glacial cycles ......... 282
11.5 The role of the carbon cycle .......................... 293
11.6 Synthesis ............................................. 299
12 Predictability ............................................. 301
12.1 The prediction problem ................................ 302
12.2 Concepts of predictability ............................ 307
12.3 Behaviour of nearby trajectories ...................... 314
12.4 Data assimilation ..................................... 324
12.5 Outlook ............................................... 334
References ................................................. 337
Copyright Acknowledgements ................................. 353
Index ...................................................... 355
Colour plates follow page .................................. 180
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