Le Gall, Philomène

Climate Change in the hydrometeorological series using rigorous statistical methods
The work of this PhD concerns the study of Climate Change in the hydrometeorological series using rigorous statistical methods. By its nature, the project is interdisciplinary because it requires for its short and long-term success, specialized expertise to both in theoretical statistics and hydrology/climatology. More specifically, the concerns are: multivariate nonparametric statistics and modeling of the dependence using copula; change point tests; statistical hydrology and statistical climatology. We aim at proposing new probabilistic and statistical concepts as well as methods for modeling climatic and environmental risks in a non stationary framework. More precisely, the objective is the detection and modeling of temporal non stationarities in extremes. Extremes and maxima of stationary sequences under various mixing conditions have been studied intensively. However still little is known in the framework of non stationarity, induced by climate changes for example.
The work will first focus on the Lombard’s test, which is quite flexible as it is able to detect abrupt changes, linear trends or onset-of-trends. Even in the univariate context, few tests have been dedicated to the detection of changes for extremes. Nonparametric techniques, such as Mann- Kendall test for trend or Pettitt test for change point, have a long tradition of use in geosciences, even if they are inefficient for extremes. It could be adapted for more flexible trend, by nonparametric or semi parametric modeling. However, the main issue is that such tests have not been specifically developed for extremes. Indeed, the Lombard test is based on the rank score which corresponds to the normalization of a square-integrable transformation of the rank. The challenge of adapting such tests for our purpose is thus to design new statistics, efficient for detecting extremes.
Copulas model the dependence between several random variables, in our context, for example statistical indices of detecting changes in extremes or output of climate models. This approach has been proved to be successful these last years, where several statistical models of copulas have been developed. However the emergency of copulas to detect breaks is very recent. At short term we will propose improvements to existing methods; in addition we will consider a very general framework where data can be issued from a stochastic process with a temporal link.

Publié le 16 mai 2019