The Weather and Climate: Emergent Laws and Multifractal Cascades

Εξώφυλλο
Cambridge University Press, 4 Απρ 2013 - 475 σελίδες
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.
 

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Περιεχόμενα

Introduction
1
Classical turbulence modern evidence
21
Spectral analysis in arbitrary dimensions
53
Cascade phenomenology and spectral analysis
55
Spectral transfers
58
Scalebyscale simplicity an introduction to multiplicative cascades
59
The convexity of Kq
82
Empirical analysis of cascades in the horizontal
83
Revisiting the revised EOLE experiment the effect of temporal averaging
225
Crossspectral analysis between wind altitude and pressure
227
Generalized scale invariance and cloud morphology
229
The normalization constant in anisotropic continuousinscale multifractal simulations
271
Spacetime cascades and the emergent laws of the weather
274
The effect of the vertical wind on the temporal statistics
313
Causal spacetime cascades the emergent laws of waves and predictability and forecasting
314
The emergent laws of macroweather and the transition to the climate
337

Trace moments of quasie_x2010Gaussian processes46 Summary of emergent laws in Chapter 4
111
Cascades dimensions and codimensions
113
Divergence of highorder statistical moments
165
Continuousinscale cascades the autocorrelation and finite size effects
167
A Mathematica code for causal and acausal multifractal simulations
172
Multifractal simulations on a sphere
174
Tendency poor mans and Haar structure functions and the MFDFA technique
175
Vertical stratification and anisotropic scaling
183
The dimensional transition asymptotic scaling of cascades in the macroweather regime
366
Stochastic linear forcing paradigm versus the fractionally integrated flux model
371
A comparison of monthly surface temperature series
374
Coupled oceanatmosphere modelling
378
The climate
383
References
427
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Σχετικά με τον συγγραφέα (2013)

Shaun Lovejoy is Professor of Physics at McGill University, Montréal, 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 École des Ponts ParisTech, Université de Paris-Est, 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 European Geophysical Union (EGU) and American Geophysical Union (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).

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