Description du sujet de thèse

In the current context of rapid climate change, numerical models are important tools for predicting climate change and assisting decision making by policy makers (e.g. in terms of protection of marine areas, land use or definition of fishing quotas). Two major challenges for the coming years are, on the one hand, to improve climate projections on a regional scale (what will be the local evolutions?) and, on the other hand, to estimate the uncertainty on these regional projections.
A climate model is a complex numerical system combining several components (e.g. ocean model, atmospheric model, ice model, vegetation model, etc.). These components depend on multiple parameters (inputs of the numerical simulation) that can be categorised as internal (i.e. values to be set within the model equations) and external (i.e. linked to contingencies external to the model, e.g. a greenhouse gas emission scenario).

The huge complexity of the climate models and their generally very high numerical cost make an exhaustive exploration of the parameter space, corresponding to all possible scenarios and all model internal options, completely illusory. The object of this work is therefore to exploit statistical tools for the design of experiments. These tools make possible the identification of specific combinations of parameters that provide maximum information on a given quantity of interest (for example an indicator of ecosystem health) calculated from the performed simulations. Such quantity of interest can also be a risk measurement, e.g. a probability that a temperature exceeds a given threshold. \\

Such an identification relies on the construction of a metamodel that corresponds to an approximated, almost inexpensive, function mapping a combination of parameters value to the quantity of interest. Such a metamodel is usually built with Gaussian processes. It can be built using multi-fidelity theory, from pre-existing simulations, possibly coming from different models of varying complexity. This is particularly appropriate in the case of regional climate modeling. Indeed, a remarkable feature of climate models is the organised archiving at international level of the results of several models of heterogeneous structure and quality. However, these archives, in particular
for regional simulations, are rarely used in this kind of context of exploration of the
space of parameters. The tendency is rather to work only with the most recent versions of the models.\\

In this context, the main objective of this PhD is to design a methodology for making the most of archived simulations carried out with models that are disparate in nature and quality, in order to improve the quality of metamodels, and thus the accuracy of the quantity of interest (or the risk measurement). The developments will be proposed and tested in the context of regional climate simulations.

From a statistical point of view, the theoretical tools for addressing these issues are sequential design of experiments, enrichment strategies, active learning and multi-fidelity Gaussian process regression.

Contexte de travail

This PhD thesis will take place in the AIRSEA team, at Jean Kuntzmann Lab (LJK), Grenoble, in close collaboration with the entire advising team. AIRSEA is a research team in applied mathematics, which scientific activities are focused on the design of mathematical and numerical methods for numerical forecast systems of the ocean and the atmosphere.
This phd is financed by IMPT (Institut des Mathématiques pour la Planète Terre).