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Advances in nonlinear dynamics, especially modern multifractal cascade models, allow us to investigate the weather and climate at unprecedented levels of accuracy. Using new stochastic modelling and data analysis techniques, this book provides an overview of the nonclassical, multifractal statistics. By generalizing the classical turbulence laws, emergent higher-level laws of atmospheric dynamics are obtained and are empirically validated over time-scales of seconds to decades and length-scales of millimetres to the size of the planet. In generalizing the notion of scale, atmospheric complexity is reduced to a manageable scale-invariant hierarchy of processes, thus providing a new perspective for modelling and understanding the atmosphere. This new synthesis of state-of-the-art data and nonlinear dynamics is systematically compared with other analyses and global circulation model outputs. This is an important resource for atmospheric science researchers new to multifractal theory and is also valuable for graduate students in atmospheric dynamics and physics, meteorology and oceanography.
Preface
1. Introduction
2. Classical turbulence - modern evidence
3. Scale by scale simplicity: an introduction to multiplicative cascades
4. Empirical analysis of cascades in the horizontal
5. Cascades, dimensions and codimensions
6. Vertical stratification and anisotropic scaling
7. Generalized scale invariance and cloud morphology
8. Space-time cascades and the emergent laws of the weather
9. Causal space-time cascades: the emergent laws of waves, predictability and forecasting
10. The emergent laws of low frequency weather and the climate
References
Index
Shaun Lovejoy is Professor of Physics at McGill University, Montreal, and has been a pioneer in developing and applying new ideas in nonlinear dynamics to the geosciences since the late 1970s. This has included multifractals, generalized (anisotropic) scale invariance, universal multifractals, space-time multifractal modeling of geofields (especially clouds, precipitation and topography). He has published over 200 papers applying these ideas to the Earth and environmental sciences. The unifying theme of this work is that when the notion of scaling is generalized to include anisotropy and multifractality, many key geofields display scaling behaviour over enormous ranges of scale; and that this nonclassical extreme variability is a new paradigm for the geosciences. In addition to these scientific contributions, Professor Lovejoy has actively promoted nonlinear processes in geophysics by co-founding the Nonlinear Process section at the European Geosciences Union (EGU) and the Nonlinear Processes in Geophysics journal. He has been Vice-chair and subsequently Chair of the Nonlinear Geophysics focus group at the American Geophysical Union (AGU) since 2004.
Daniel Schertzer is a professor at Ecole des Ponts ParisTech, Universite Paris-East, and Scientific Director of the Chair 'Hydrology for Resilient Cities', sponsored by VEOLIA Water. His research introduced multifractals and related techniques in hydrology, after having contributed to their theoretical developments in turbulence, in particular with the definition of a co-dimension formalism, the concepts of generalized scale invariance and universal multifractals. His work has covered many domains of geophysics and the environment, with a particular emphasis on atmospheric dynamics, precipitation extremes and remote sensing. His publications include two books and 115 ISI-indexed publications, which have received more than 4000 citations, and he is executive editor of the journal Nonlinear Processes in Geophysics, which he co-founded as well as the nonlinear geophysics divisions of EGU and AGU. Professor Schertzer has been a union officer of the EGU and an officer of AGU committees and the International Association for Hydrological Sciences bureau. He is also vice-president of the French National Committee of Geodesy and Geophysics and a member of the Higher Council of Meteorology (France).
