Welcome to the "AssimilEx"'s home page,
a three-year ANR project that focuses on developing new
statistical models to improve the assimilation
of extreme events in geosciences.
This project is sponsored by the French agency
ANR (Agence Nationale de la Recherche)
and it has four members:
June 23rd-26th 2008 -
ANR AssimilEx Lecture & Workshop on Extremes :
Statistical modeling of extremes in data assimilation and filtering approaches
The AssimilEx project summary
Loss of life and economic damage from extreme weather and climate events has been recurrent in
human history. Although the mean behaviour of most climatic processes is well understood, the
statistical modelling of extreme events in time and space remains a difficult mathematical
challenge. This is mainly due to the intrinsic rarity of extreme events, their non-Gaussian
amplitudes and the different spatio-temporal scales involved.
In this inter-disciplinary project (mathematics and geosciences), we propose to develop new
statistical models for one important geophysical research topic: data assimilation of extreme
events. The fundamental problem of data assimilation may be simply stated as follows: given the
state of the atmosphere at one time, what is the state of the atmosphere at a later time if one
knows the observational data with the underlying dynamical principles governing the system under
observation? Mathematically, this corresponds to a state-space formulation in which the state
equation drives the dynamics of the system and the observational equation integrates measurements
with the state variables. The originality of this project is to combine the expertise of climate
scientists and statisticians in order to propose innovative statistical models that are capable
of accurately representing the distribution of extreme events when implementing a statistical
data assimilation procedure.
We aim at taking advantage of recent developments in the field of Extreme Value Theory (EVT) and
to offer mathematically sound models. More precisely, we plan on focusing on maxima and
consequently, to build statistical models based on the multivariate mixture extremes class
proposed recently by Fougeres et al. (2005). This EVT family offers the flexibility to perform
spatio-temporal extrapolation and easy interpretation by suitable choices of the mixing variables.
These two characteristics are essential for data assimilation. Besides proposing these new EVT
models, we will study their statistical properties, derive inference schemes and test the
validity of our approach on simulated data and real applications, e.g. annual maxima precipitation
and pollution peaks.
The overall benefits of the proposed activity are three fold. First, this research will lead to
an enhanced understanding of climate extremes. Second, the new mathematical methods will not only
allow to solve similar problems in Earth sciences, but it will also be beneficial to other fields
based on applied mathematics. Extending state-space modelling techniques in a spatial-temporal
EVT framework is novel and will provide new tools for spatio-temporal analysis. Finally, research
collaborations between atmospheric scientists and applied mathematicians will be strengthened by
providing better statistical models to the climate community, new algorithms to statisticians and
directing a post-doctoral fellow at the intersection of two fields.
- Naveau P., and Poncet P.
State-space Models for Maxima Precipitation. Submitted.
- R codes or packages related to the assimilation of extremes will be posted here.
Extreme Value Theory