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| Titel |
EGS Richardson AGU Chapman NVAG3 Conference: Nonlinear Variability in Geophysics: scaling and multifractal processes |
| VerfasserIn |
D. Schertzer, S. Lovejoy |
| Medientyp |
Artikel
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| Sprache |
Englisch
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| ISSN |
1023-5809
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| Digitales Dokument |
URL |
| Erschienen |
In: Nonlinear Processes in Geophysics ; 1, no. 2/3 ; Nr. 1, no. 2/3, S.77-79 |
| Datensatznummer |
250000000
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| Publikation (Nr.) |
 copernicus.org/npg-1-77-1994.pdf |
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| Zusammenfassung |
1. The conference
The third conference on "Nonlinear VAriability in Geophysics: scaling and
multifractal processes" (NVAG 3) was held in Cargese, Corsica, Sept. 10-17, 1993.
NVAG3 was joint American Geophysical Union Chapman and European Geophysical Society
Richardson Memorial conference, the first specialist conference jointly sponsored by the
two organizations. It followed NVAG1 (Montreal, Aug. 1986), NVAG2 (Paris, June 1988;
Schertzer and Lovejoy, 1991), five consecutive annual sessions at EGS general assemblies
and two consecutive spring AGU meeting sessions.
As with the other conferences and workshops mentioned above, the aim was to develop
confrontation between theories and experiments on scaling/multifractal behaviour of
geophysical fields. Subjects covered included climate, clouds, earthquakes, atmospheric
and ocean dynamics, tectonics, precipitation, hydrology, the solar cycle and volcanoes.
Areas of focus included new methods of data analysis (especially those used for the
reliable estimation of multifractal and scaling exponents), as well as their application
to rapidly growing data bases from in situ networks and remote sensing. The corresponding
modelling, prediction and estimation techniques were also emphasized as were the current
debates about stochastic and deterministic dynamics, fractal geometry and multifractals,
self-organized criticality and multifractal fields, each of which was the subject of a
specific general discussion.
The conference started with a one day short course of multifractals featuring four
lectures on a) Fundamentals of multifractals: dimension, codimensions, codimension
formalism, b) Multifractal estimation techniques: (PDMS, DTM), c) Numerical simulations,
Generalized Scale Invariance analysis, d) Advanced multifractals, singular statistics,
phase transitions, self-organized criticality and Lie cascades (given by D. Schertzer and
S. Lovejoy, detailed course notes were sent to participants shortly after the conference).
This was followed by five days with 8 oral sessions and one poster session. Overall, there
were 65 papers involving 74 authors. In general, the main topics covered are reflected in
this special issue: geophysical turbulence, clouds and climate, hydrology and solid earth
geophysics.
In addition to AGU and EGS, the conference was supported by the International Science
Foundation, the Centre Nationale de Recherche Scientifique, Meteo-France, the Department
of Energy (US), the Commission of European Communities (DG XII), the Comite National
Francais pour le Programme Hydrologique International, the Ministere de l'Enseignement
Superieur et de la Recherche (France). We thank P. Hubert, Y. Kagan, Ph. Ladoy, A.
Lazarev, S.S. Moiseev, R. Pierrehumbert, F. Schmitt and Y. Tessier, for help with the
organization of the conference. However special thanks goes to A. Richter and the EGS
office, B. Weaver and the AGU without whom this would have been impossible. We also thank
the Institut d' Etudes Scientifiques de Cargese whose beautiful site was much appreciated,
as well as the Bar des Amis whose ambiance stimulated so many discussions.
2. Tribute to L.F. Richardson
With NVAG3, the European geophysical community paid tribute to Lewis Fry Richardson
(1881-1953) on the 40th anniversary of his death. Richardson was one of the founding
fathers of the idea of scaling and fractality, and his life reflects the European
geophysical community and its history in many ways. Although many of Richardson's
numerous, outstanding scientific contributions to geophysics have been recognized, perhaps
his main contribution concerning the importance of scaling and cascades has still not
received the attention it deserves.
Richardson was the first not only to suggest numerical integration of the equations of
motion of the atmosphere, but also to attempt to do so by hand, during the First World
War. This work, as well as a presentation of a broad vision of future developments in the
field, appeared in his famous, pioneering book "Weather prediction by numerical
processes" (1922). As a consequence of his atmospheric studies, the nondimensional
number associated with fluid convective stability has been called the "Richardson
number". In addition, his book presents a study of the limitations of numerical
integration of these equations, it was in this book that - through a celebrated poem -
that the suggestion that turbulent cascades were the fundamental driving mechanism of the
atmosphere was first made. In these cascades, large eddies break up into smaller eddies in
a manner which involves no characteristic scales, all the way from the planetary scale
down to the viscous scale. This led to the Richardson law of turbulent diffusion (1926)
and tot he suggestion that particles trajectories might not be describable by smooth
curves, but that such trajectories might instead require highly convoluted curves such as
the Peano or Weierstrass (fractal) curves for their description. As a founder of the
cascade and scaling theories of atmospheric dynamics, he more or less anticipated the
Kolmogorov law (1941). He also used scaling ideas to invent the "Richardson dividers
method" of successively increasing the resolution of fractal curves and tested out
the method on geographical boundaries (as part of his wartime studies). In the latter work
he anticipated recent efforts to study scale invariance in rivers and topography.
His complex life typifies some of the hardships that the European scientific community has
had to face. His educational career is unusual: he received a B.A. degree in physics,
mathematics, chemistry, biology and zoology at Cambridge University, and he finally
obtained his Ph.D. in mathematical psychology at the age of 47 from the University of
London. As a conscientious objector he was compelled to quit the United Kingdom
Meteorological Office in 1920 when the latter was militarized by integration into the Air
Ministry. He subsequently became the head of a physics department and the principal of a
college. In 1940, he retired to do research on war, which was published posthumously in
book form (Richardson, 1963). This latter work is testimony to the trauma caused by the
two World Wars and which led some scientists including Richardson to use their skills in
rational attempts to eradicate the source of conflict. Unfortunately, this remains an open
field of research.
3. The contributions in this special issue
Perhaps the area of geophysics where scaling ideas have the longest history, and where
they have made the largest impact in the last few years, is turbulence. The paper by
Tsinober is an example where geometric fractal ideas are used to deduce corrections to
standard dimensional analysis results for turbulence. Based on local spontaneous breaking
of isotropy of turbulent flows, the fractal notion is used in order to deduce diffusion
laws (anomalous with respect to the Richardson law). It is argued that his law is
ubiquitous from the atmospheric boundary layer to the stratosphere. The asymptotic
intermittency exponent i hypothesized to be not only finite but to be determined by the
angular momentum flux.
Schmitt et al., Chigirinskaya et al. and Lazarev et al. apply statistical multifractal
notions to atmospheric turbulence. In the former, the formal analogy between multifractals
and thermodynamics is exploited, in particular to confirm theoretical predictions that
sample-size dependent multifractal phase transitions occur. While this quantitatively
explains the behavior of the most extreme turbulent events, it suggests that - contrary to
the type of multifractals most commonly discussed in the literature which are bounded -
more violent (unbounded) multifractals are indeed present in the atmospheric wind field.
Chigirinskaya et al. use a tropical rather than mid-latitude set to study the extreme
fluctuations form yet another angle: That of coherent structures, which, in the
multifractal framework, are identified with singularities of various orders. The existence
of a critical order of singularity which distinguishes violent "self-organized
critical structures" was theoretically predicted ten years ago; here it is directly
estimated. The second of this two part series (Lazarev et al.) investigates yet another
aspect of tropical atmospheric dynamics: the strong multiscaling anisotropy. Beyond the
determination of universal multifractal indices and critical singularities in the
vertical, this enables a comparison to be made with Chigirinskaya et al.'s horizontal
results, requiring an extension of the unified scaling model of atmospheric dynamics.
Other approaches to the problem of geophysical turbulence are followed in the papers by
Pavlos et al., Vassiliadis et al., Voros et al. All of them share a common assumption that
a very small number of degrees of freedom (deterministic chaos) might be sufficient for
characterizing/modelling the systems under consideration. Pavlos et al. consider the
magnetospheric response to solar wind, showing that scaling occurs both in real space
(using spectra), and also in phase space; the latter being characterized by a correlation
dimension. The paper by Vassiliadis et al. follows on directly by investigating the phase
space properties of power-law filtered and rectified gaussian noise; the results further
quantify how low phase space correlation dimensions can occur even with very large number
of degrees of freedom (stochastic) processes. Voros et al. analyze time series of
geomagnetic storms and magnetosphere pulsations, also estimating their correlation
dimensions and Lyapounov exponents taking special care of the stability of the estimates.
They discriminate low dimensional events from others, which are for instance attributed to
incoherent waves.
While clouds and climate were the subject of several talks at the conference (including
several contributions on multifractal clouds), Cahalan's contribution is the only one in
this special issue. Addressing the fundamental problem of the relationship of horizontal
cloud heterogeneity and the related radiation fields, he first summarizes some recent
numerical results showing that even for comparatively thin clouds that fractal
heterogeneity will significantly reduce the albedo. The model used for the distribution of
cloud liquid water is the monofractal "bounded cascade" model, whose properties
are also outlined. The paper by Falkovich addresses another problem concerning the general
circulation: the nonlinear interaction of waves. By assuming the existence of a peak (i.e.
scale break) at the inertial oscillation frequency, it is argued that due to remarkable
cancellations, the interactions between long inertio-gravity waves and Rossby waves are
anomalously weak, producing a "wave condensate" of large amplitude so that wave
breaking with front creation can occur.
Kagan et al., Eneva and Hooge et al. consider fractal and multifractal behaviour in
seismic events. Eneva estimates multifractal exponents of the density of micro-earthquakes
induced by mining activity. The effects of sample limitations are discussed, especially in
order to distinguish between genuine from spurious multifractal behaviour. With the help
of an analysis of the CALNET catalogue, Hooge et al. points out, that the origin of the
celebrated Gutenberg-Richter law could be related to a non-classical Self-Organized
Criticality generated by a first order phase transition in a multifractal earthquake
process. They also analyze multifractal seismic fields which are obtained by raising
earthquake amplitudes to various powers and summing them on a grid. In contrast, Kagan,
analyzing several earthquake catalogues discussed the various laws associated with
earthquakes. Giving theoretical and empirical arguments, he proposes an additive
(monofractal) model of earthquake stress, emphasizing the relevance of (asymmetric) stable
Cauchy probability distributions to describe earthquake stress distributions. This would
yield a linear model for self-organized critical earthquakes.
References:
Kolmogorov, A.N.: Local structure of turbulence in an incompressible liquid for very large
Reynolds number, Proc. Acad. Sci. URSS Geochem. Sect., 30, 299-303, 1941.
Perrin, J.: Les Atomes, NRF-Gallimard, Paris, 1913.
Richardson, L.F.: Weather prediction by numerical process. Cambridge Univ. Press 1922
(republished by Dover, 1965).
Richardson, L.F.: Atmospheric diffusion on a distance neighbour graph. Proc. Roy. of
London A110, 709-737, 1923.
Richardson, L.F.: The problem of contiguity: an appendix of deadly quarrels. General
Systems Yearbook, 6, 139-187, 1963.
Schertzer, D., Lovejoy, S.: Nonlinear Variability in Geophysics, Kluwer, 252 pp, 1991. |
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