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Mathematics
in the Geosciences, September 2001 - June 2002
Talk
Abstracts:
September
24, 2001
Audio
Recordings Material
from Talks
Michael
Ghil
(Professor of Atmospheric Sciences and Director, IGPP/UCLA)
http://www.atmos.ucla.edu/tcd/
ghil@atmos.ucla.edu
or mghil@igpp.ucla.edu
Spatio-temporal
pattern analysis in the atmosphere and oceans Slides
The study of large-scale atmospheric and oceanic motions depends
critically on a description of these motions that should be
as reliable and as precise as possible. There exists thus
a trade-off between the wealth of information that one wishes
to extract from limited data sets, on the one hand, and the
statistical confidence in that information, on the other.
This trade-off is optimized by applications of Karhunen- Loeve
theory in the space and time domain, separately, as well as
concurrently in the spatio-temporal domain. I shall illustrate
this approach by applications to climate variability on the
intraseasonal (10--100 days), interannual (1--10 years) and
interdecadal (10--1000 years) time scales. The applications
will involve phenomena that reside mainly in the atmosphere
(so-called low-frequency variability), mainly in the ocean
(its wind-driven and thermohaline circulation), and finally
in the coupled atmosphere-ocean (the El Nino-Southern Oscillation).
Connections
between this parsimonious, optimal description of climate
variability and its explanation via dynamical systems theory
will be outlined. I shall select one of the examples above
to illustrate this connection in greater depth.
References
- Ghil
M., R. M. Allen, M. D. Dettinger, K. Ide, D. Kondrashov, M.
E. Mann, A. Robertson, A. Saunders, Y. Tian, F. Varadi, and
P. Yiou (2001) "Advanced spectral methods for climatic time
series," Rev. Geophys., accepted. http://www.atmos.ucla.edu/tcd/MG/mg_ref_preprints.html
- Pascal
Yiou, Didier Sornette and Michael Ghil Data-adaptive wavelets
and multi-scale singular-spectrum analysis
Physica D: Nonlinear Phenomena, Volume 142, Issue 3-4 (2000),
pp. 254-290
[Abstract] [Full text] (PDF 1.1 Mb) (one of the 8 Hottest
Papers in Physica D) http://www.elsevier.com/inca/publications/store/5/0/5/7/1/4/
Software
(free)
Vladimir
Keilis-Borok (Institute of Geophysics and Planetary
Physics and Department of Earth and Space Science, University
of California, Los Angeles and International Institute for Earthquake
Prediction Theory and Mathematical Geophysics, Russian Academy
of Sciences, Moscow) vkb@ess.ucla.edu
Complexity
of Lithosphere and Earthquake Prediction
1.
Earthquakes occur in the lithosphere - an upper shell of the
solid Earth. Its thickness ranges from few km near oceanic ridges,
to few hundred km in some continental regions. The lithosphere
is set in motion by the large-scale currents in the underlying
Earth's mantle and some internal processes like gravitational
and chemical differentiation. In seismically active regions
large part of this motion is realized through the earthquakes
in a stick-slip fashion.
2.
Two major factors cause complexity of the lithosphere: (i) Hierarchical
structure, extending from about 10 tectonic plates to the about
10^25 grains of rocks. (ii) Instability, caused by a multitude
of non-linear mechanisms, controlling the {strength - stress}
field. In the time scale relevant to earthquake prediction,
these factors turn the lithosphere into a hierarchical dissipative
complex system. Strong earthquakes are regarded as the critical
phenomena; an earthquake may be a critical phenomenon in certain
volume of lithosphere, and a part of the background seismicity
in a larger volume.
3.
Development of the earthquake prediction algorithms brought
together three methodologies: (i) phenomenological analysis
of observations - I. Gelfand's type of pattern recognition and
J. Tukey's kind of exploratory data analysis; (ii) "universal"
lattice models of complex systems such as considered in statistical
mechanics and non-linear dynamics; and (iii) Earth-specific
models of tectonic faults' networks. In addition, (iv) theory
of optimal control is used to link earthquake prediction with
the earthquake preparedness.
4. Ongoing global test of the intermediate term prediction algorithms
is discussed.
Donald
L. Turcotte (Department of Geological Sciences Cornell
University) Turcotte@Geology.Cornell.edu
Spatio-temporal
patterns in solid-earth geophysics Slides
Examples
of spatio-temporal patterns considered: Earthquakes, landslides,
stratigraphy (sediment deposition), earth's magnetic field.
Examples of spatio patterns considered: Oil fields, mineral
deposits, faults, river networks. Examples of temporal patterns
considered: Time series of river flows (floods), climate.
Eli
Tziperman (Department of Environmental Sciences,
Weizmann Institute of Science) eli@beach.weizmann.ac.il
http://www.weizmann.ac.il/~eli
Glacial
cycles: extreme natural climate change events, and still an
unsolved puzzle...
The
major glaciations that have occurred over the earth every 100,000
years during the past 1 million years are the largest natural
climate variability signal in recent geological history. During
each glaciation, global sea level dropped by 120 meters and
this large amount of water has then accumulated as 2-3 km high
glaciers over land; global temperature varied by many degrees,
and the concentration of CO2 in the atmosphere changed by 30%.
Understanding these large amplitude natural climatic events
seems essential for us to be able to predict future climate
change with reasonable certainty. In spite of the large amplitude
and obvious significance of these events we still do not have
an accepted theory for them. Some extremely varied theories
were proposed for the mechanism of glacial cycles. Some of these
theories suggested that the glacial cycles are a result of random
noise processes, due to a stochastic resonance, external forcing
by variations in solar radiation due to earth orbital changes,
due to effects of the elasticity of the earth crust, self-sustained
internal variability of the climate system, nonlinear chaotic
dynamics, relaxation oscillations due to nonlinear sea ice-land
ice interaction, and more. The phenomenology of glacial cycles
will be briefly introduced and some of the main theoretical
ideas regarding the possible mechanism of these cycles will
be presented.
Audio
Recordings Material
from Talks
Tutorial:
Spatio-temporal Patterns in the Geosciences
Workshop:
Spatio-temporal Patterns in the Geosciences
2001-2002 IMA Thematic Year on Mathematics in the Geosciences
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