Mathematical Geophysics and Complex Systems
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Mathematical Geophysics and Complex Systems
EuroConference
INTRODUCTION
1) Evènements Extrêmes dans la Terre (Extreme Earth Events)
Lieu et date de la conférence: Juin 18-23, 2000, Villefranche sur mer, FRANCE
Responsable scientifique : Anne et Didier Sornette
Contact : Laboratoire de Physique de la Matière Condensée, CNRS UMR6622
and Université des Sciences, B.P. 70, Parc Valrose
06108 Nice Cedex 2, France
tel: (33) (0) 4 92 07 67 99
fax: (33) (0) 4 92 07 67 54
E-mail: anne@unice.fr et sornette@unice.fr
2) Weather risk: predictability, uncertainty and modelling
Date: 10-13 September 2001
Venue: Pembroke College, Oxford, England
Contact : Leonard Smith (44) 1865 270 518 (direct)
Mathematical Institute (44) 1865 270 515 (fax)
26-29 St Giles
Oxford OX1 3LB, England
E-mail : lenny@maths.ox.ac.uk
http://www.maths.ox.ac.uk/~lenny/
This cycle of two conferences have focused on the characterization of large and extreme risks and on their prediction
with applications in a variety of scientific domains with strong links with economic and societal impacts. These two
conferences are part of the TMR European program. We describe in turn these two conferences, the first one in french
since the venue was in France and the second one in English, since the venue was in England. At the end, we present a
brief synthetic conclusion of the value derived from these two conferences.
1. Report on first event
Evènements Extrêmes dans la Terre (Extreme Earth Events)
Les derniers développements de la recherche scientifique dans le domaine des systèmes complexes révèlent des liens
profonds entre des phénomènes aussi divers que les tremblements de terre comme d’étoiles à neutrons, les crashes
financiers, les phénomènes de blocage sociaux, les récessions économiques nationales et mondiales, les éruptions
volcaniques, les ouragans, la turbulence hydro- et aéro-dynamique, etc. En généralisant, les systèmes dynamiques
possédant de fortes nonlinéarites sont caractérisés par des crises, certes rares, mais souvent catastrophiques avec des
impacts majeurs aux courtes échelles aussi bien qu’aux longues échelles de temps. Les sciences géologiques et
géophysiques sont un terrain d’étude fertile pour ce type d’analyse car les phénomènes épisodiques sont très courants et
sont interprétés comme autant de discontinuités. Avec notre compréhension croissante que les systèmes physiques
complexes soumis à des sollicitations incohérentes donnent souvent des réponses non-linéaires catastrophiques, les
scientifiques sont au seuil de découvertes fondamentales concernant la manière dont notre planète terre fonctionne.
La conférence intitulée « Evénements Extrêmes en Géosciences » a eu pour objectif de réunir un certain nombre parmi
les meilleurs experts mondiaux sur ce sujet pendant une semaine de travail et deux week-ends, de manière à faire le
point sur l’état de l’art et à établir une concertation accrue interdisciplinaire entre les différentes disciplines concernées,
allant de la géologie aux mathématiques. Elle suit la conférence « Géophysique Mathématique: Structures
Géophysiques Spatio-Temporelles Complexes » que nous avions également organisé à Villefranche-sur-Mer en 1994 et
qui avait connu un grand succès. Ce cycle de conférences est soutenue également par l’Union Internationale de
Géodésie et de Géophysique. La conférence qui vient d’avoir lieu est la première d’un cycle de deux conférences sur la
prédiction des crises dans les sciences géophysiques organisées dans le cadre des conférences européennes du
programme TMR de l’Union Européenne.
D’un point de vue scientifique, l’impact de cette conférence a été très important car le sujet d’étude a des conséquences
directes sur la prévision et la prévention de grandes catastrophes naturelles comme les tremblements de terre, auxquels
le département des Alpes-Maritimes est potentiellement exposé. De plus, la grande majorité des conférenciers et
1participants étaient de nationalités étrangères avec une proportion équilibrée provenant des pays développés et des pays
en voie de développement. La conférence a aussi soutenu un grand nombre de jeunes chercheurs et d’étudiants.
Le programme de la conférence a été organisé de la manière progressive suivante. La première session sur les
CONCEPTS ET OUTILS a fait le point sur les méthodes théoriques de pointes pour traiter les grandes fluctuations.
Des relations intéressantes ont été établies entre les approches mathématiques des grandes déviations, les approches de
traitement de signaux multi-échelles et des applications en économie et en finance pour la définition et la couverture de
produits dérivés financiers basés sur les catastrophes.
La deuxième session s’est focalisée sur les évènements extrêmes apparaissant dans la dynamique couplée entre les
océans, l’atmosphère et le climat. Les problèmes associés à la grande gamme d’échelles de temps et d’espace ont été
particulièrement soulignés. Les exposés ont montré la diversité des approches combinant la théorie des systèmes
dynamiques, les approches en terme de structures cohérentes et celles plus classiques mais interdisciplinaires couplant
la thermodynamique des ouragans et la dynamique atmosphérique.
La troisième session a regroupé les exposés concernant les phénomènes extrêmes en hydrologie ainsi que ceux inscrits
dans les données paléontologiques. Des exposés ont montré l’existence de déviations très significatives à l’universalité
souvent professée un peu hâtivement concernant les lois d’organisation des réseaux fluviaux et leur fluctuation de débit.
Un débat stimulant a eu lieu concernant les couplages pertinents entre biologie et les autres facteurs géologiques vis-à-
vis du cycle du carbone et son rôle dans le forçage du climat.
La quatrième session a porté sur les grandes crises de la partie terre « solide » et plus particulièrement les tremblements
de terre. Cette session très active et controversée a souligné la grande complexité de l’organisation spatiale et
temporelle des tremblements de terre ainsi que l’importance de la compréhension du rôle des échelles de temps très
courtes de la rupture dynamique vis-à-vis de l’organisation aux temps longs. Le concept selon lequel les très grands
tremblements de terre pourraient être des phénomènes critiques analogues aux transitions critiques étudiées en physique
statistique s’est vu renforcé par des simulations numériques intensives et fines qui ont montré la croissance des
corrélations et de l’activité sismique à l’approche d’un grand tremblement de terre. Les aspects de modélisation ont été
reliés à des tentatives de prédiction basées sur l’identification de précurseurs par méthodes de reconnaissance de
structures et utilisation du concept de criticalité multi-échelle.
La cinquième et dernière session a concerné les évènements extrêmes associés à l’environnement et l’organisation de la
planète à plus grande échelle. Ici, les phénomènes sont moins bien compris et demandent encore un grand effort
d’intégration des échelles plus petites qui cascadent vers les grandes. Des exposés ont également souligné la relation
entre l’aspect scientifique de la modélisation des catastrophes et leur prise en compte par des approches de contrôle de
risques dans les sciences de l’ingénieur. Les impacts des grandes catastrophes pour les problèmes d’assurance et de ré-
assurance ont été quantifiés et montrent l’importance d’une collaboration entre scientifiques des sciences naturelles
d’une part et économistes et assureurs d’autre part, de manière à mieux appréhender les différentes dimensions du
risque à couvrir pour la société.
En conclusion, la conférence a été une occasion unique d’échanges très stimulants qui, de l’avis de la grande majorité
des participants, ont été très fructueux. La conférence associée qui suivra l’année prochaine se focalisera sur l’aspect de
la prédictabilité et du contrôle des erreurs associées aux évènements notables dans les sciences géologiques et
géophysiques.
ORGANISMES DE COFINANCEMENT : E.U (Europeen Union); I.U.G.G (International Union of Geodesy and
Geophysics); N.S.F- AIR FORCE (National Science Foundation); C.N.R.S (Centre National de la Recherche
Scientifique, France); U.N.S.A (Université de Nice-Sophia-Antipolis); Conseil Général des Alpes Maritimes; Conseil
Régional PACA
2. Report on Second event
Weather risk: predictability, uncertainty and modelling
During the week of Sept 10, 2001, academics, forecasters and forecast users in government and industry met in
Pembroke College, Oxford, to discuss the insights and limitations of
(i) current mathematical and physical methods in geophysical modelling,
(ii) statistical models of likely impact, and
(iii) financial modelling of related risk.
The discussion focused on weather time-scales (hours to months), but longer term phenomena were also considered.
The format of the meeting was brief presentations on each target area followed by extended discussion of target
questions. Ample time for more detailed follow-up discussions was made. This meeting was sponsored by the EU, the
London School of Economics, the Smith Institute and Pembroke College (Oxford). A major aim of the meeting was to
identify areas where proof of value experiments are currently justified, in harmony with the Smith Institute Faraday
Partnership on End-to-End Forecasting.
Lead presenters included:
2Harold Brooks, National Severe Storms Laboratory (US)
Joseph Hrgovcic, Enron
Julian Hunt, University College London
Steve Jewson, Risk Management Solutions
Ken Mylne, UK Met Office
Tim Palmer, European Centre for Medium-range Weather Forecasts
Mark Roulston, Oxford University
Leonard Smith, London School of Economics
Participants included representatives from the following institutions:
Academic: LSE, Oxford University, Max Plank (Dresden), Potsdam University, UCL, UMIST
Forecasting: American, British and European, Weather Centres
Industry: Deutsche Bank, Enron, Foundation for Science and Technology, London Electricity, METRA, National Grid
Company, Risk Management Solutions, Royal Dutch Shell
Aims
-Disseminate knowledge of the state of the art forecast philosophy and products as well as open questions regarding
their use.
- solate specific questions to be targeted in proof of value experiments.
- mprove dialogue between users, forecasters and academics interested in Predictability and Risk.
- Identify specific applications for which quantitative historical data exists.
- Determine the aspects of statistics, mathematical finance, and physical modelling in which advances are most
urgently needed for improved quantification of risk.
- Establish a general Academic/Industrial framework for continued communication of results, applications, and new
ideas over the next 4 years.
Target questions:
Advances in computer modelling of mathematical geophysics now allow forecast models with applications from
minutes to, perhaps, decades. Open questions abound regarding (1) the time and spatial scales on which current models
contain useful information, (2) the value of information to potential forecast uses and (3) how to best translate forecast
uncertainty into event/economic risk.
Our aim was to engender frank discussions of current methods, problems, and likely avenues of solution in a number of
target areas; discussions at the meeting were organised with respect to the time scales involved. Specific questions were
tailored to each session, but the following broad questions were addressed in each session.
From a government agency or industrial viewpoint:
- What quantities, exactly, are of interest? on which space and time scales? and at which lead times?
- Is risk management in this area best addressed by hedging, taking direct action, of some combination of strategies?
From a statistical viewpoint:
- On which time scales does a given forecast system add value beyond that of historical observations? how are these
limiting time-scales best identified?
- When should first principles models (simulation models) be used for downscaling? When are statistical models to be
preferred? is there an optimal mix?
From a mathematical or modelling viewpoint:
- What currently limits the predictability: uncertain starting data? computational power? model inadequacy?
- Might current methods increase the value of a forecast? For example, could targeted observations (selected for a
particular forecast goal) better quantify risk?
- To what degree can real-time on site modelling be used in conjunction with large-scale forecast products?
- For a given quantity of interest, is it likely that useful information is currently available at the required spatio-
temporal resolution and lead time? How can the existence of useful information best be established, particularly
when the forecast time-scale is long compared to the model lifetime?
- What background information would most enhance the likelihood that a given forecast system will be of practial
use? How are 'improvements' in a forecast system best quantified? Is this answer independent of the viewpoint of
the modeller? of the user?
Target Areas
1) Time Scales:
a) Short term forecasts (hourly/daily diagnostics)
b) Medium range forecasts (day to weeks)
c) Long range forecast possibilities (Seasonal/Climate)
2) Forecast methodology:
3a) Probabilistic (ensemble) and Best Guess (traditional) Forecasts
b) End-to-End Forecasts
c) Historical (Analogue) and purely Statistical Forecasts
3) High Impact Events:
a) Rare, perhaps extreme, events
b) Identifying windows of opportunity
c) Prolonged duration, cumulative events
4) Trading risk:
a) A user's perspective on pricing risk (real time hedging and direct action)
b) A market maker's perspective on likely cost of risk
Explicit Examples
Wind Energy Production
Electricity Demand
Forecasting: From Physics to Utility
Hedging From a User's Perspective
Data Assimilation
Product Demand
Short-term Severe Weather Hazards
Drought/Heat wave/Flood Warning
Industry/Academic Research Partnerships
Designing Proof of Value Experiments
General Background
The conference was organised on the basis of the strong belief of the organisers that weather (days/weeks/months
ahead) information is underused at present, (certainly on a timescale of hours to days, and probably with lead times of
months). There are several obvious areas for improving the use for weather information, most requiring some
underpinning research beforehand. Weather forecasting has now reached a state where information on the variety of
most likely weather conditions is now available over a period of weeks, perhaps seasons. There are a number of open
mathematical and statistical issues on how to best postprocess this model output, in order both (1) to identity the time
horizons at which the current forecasts have skill and (2) to extract information of economic and social value.
This conference has thus brought together forecasters, users from government and industry, and academics to address
these issues of mathematical geophysics in a variety of concrete contexts. A major aim of the meeting was to establish a
number of 'proof of value' experiments to be executed over the next two years, ideally in real-time.
Modern operational weather forecasts now include information on the likelihood of various weather events, usually
determined through ensemble prediction systems (EPS) like those of the European Centre for Medium-Range Weather
Forecasts ECMWF and the American National Center for Environmental Prediction NCEP. This approach propagates
our (hopefully small) uncertainty in the initial state of the atmosphere forward in time, yielding information on the
(potentially large) uncertainty of the forecast itself. Seeing variations in the day to day uncertainty provides information
of significant value for risk management. Application of the EPS output is significantly more complex than the use of
traditional 'best guess' forecasts. For instance, nonlinearities imply that decisions based on the mean forecast may differ
significantly from the decisions based on the distribution of forecasts; many open questions remain both on theoretical
interpretation and on practical best use of this information. The lead time at which forecasts add little to statistical
methods based only on historical data is hotly disputed.
This conference has provided a forum for the discussion of how state of the art forecasts can be analysed to give useful
and timely information for use in real time. The duration over which current forecasts are skilful depends on the space
and time scales on which information is required. Given that these scales vary with different applications (wind energy
forecasts are very local, electricity demand is determined over larger scales, agricultural and retail questions often
revolve on integrated effects and longer lead time scales), a variety of discussions focused on different space and time
scales have been held. Note that industrial information on, for example, weather related electricity demand may in fact
contain useful information for data assimilation in weather models. We have adopted a broad view of likely future
developments casted within particular current contexts.
Four different kinds of application have been of interest. The first kind require forecasts every day (e.g. demand
forecasting, expected production), others target specific high impact events which may be extreme events (e.g. tornados,
hurricanes) or relatively mild events the cumulative effect of which has significant impact (heat waves). Alternatively, a
third kind of application would look for "window's of opportunity", a period of many days over which some undesirable
effect does not occur, regardless of the average or 'most likely' values on each day within the window. Regardless of
how good the forecasts are today, there will be applications which request information not available in current state-of-
the-art forecasts; the use of weather derivatives in these areas has been a fourth focus of discussion, both their use
beyond the current skill horizon and the impact of skilful forecasts on the pricing of these new financial instruments.
4CONCLUSION
These two conferences have been very fruitful in many ways for the European and international participants. First, they
have attacked an original theme on the predictability of large and extreme events in a variety of fields of the
geosciences with strong connections with and applications to societal and economic problems. These two conferences
can be in a sense considered as precursors of the growing awareness of and need to focus science on extreme events.
Second, these two conferences have brought together a strong multidisciplanarity panel of scientists who have been able
to exchange their latest research results and their view points on the future possibilities of this difficult but very exciting
and important field of investigation. Third, by the participation of a large fraction of students, post-doctoral fellows and
more generally of young researchers from the European countries, these two conferences have provided a unique forum
for the education of a next generation of scientists who will more and more have to address and confront themselves
with acute societal problems linked with their scientific fields of investigations. Overall, we as the organisers feel that
these two conferences have served the community and the European countries well and we feel pleased and rewarded
by the many excellent comments and praised received from participants. These conferences have also led to direct
returns in the form of many novel collaborations that have been fostered by the interactions provided by these two
conferences and several papers in international referred journals can be directly attributed in direct line to the impact of
the conferences.
Identification:
Scientist in charge: Dr Didier Sornette
Address: Laboratoire de Physique de la Matière Condensée,
CNRS UMR6622 and Université des Sciences, B.P. 70,
Parc Valrose, 06108 Nice Cedex 2, France
Tel.: ++33 (0) 492076799
Fax: ++33 (0) 492076754
E-mail: Anne@unice.fr; sornette@unice.fr
Contractor: CNRS
Contract n°: FMMA-CT98-00485
Publications:
www site:
- for events: http://www.maths.ox.ac.uk
- of contractor:
- other relevant:
TMR Home Page CORDIS Programme Home Pages
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