PhD Position F/M Inverse problems for stochastic models under location uncertainty applied to ocean dynamics

1000scholars; Rennes; On-site; EUR 23,000 - 28,000; Full time

Job summary

Inria Rennes, within the Odyssey team, invites applications for a PhD thesis on modelling under location uncertainty in geophysical fluid dynamics. The work combines stochastic modelling, inverse problems, and numerical simulation of deep convection in ocean models using CROCO.

Collaboration with multiple teams will enrich the research environment. The candidate will develop theory, implement algorithms (adjoint and ensemble methods), and assess covariance estimation against reference

Qualifications

• Background in applied mathematics, fluid mechanics, or oceanography.
• Strong interest in numerical simulation.
• Basic programming skills in Python or Julia and Fortran or C++ would be an advantage.

Responsibilities

• The candidate will work with stochastic models for deep convection.
• Implement reference simulations using the CROCO model.
• Formulate inverse problems to determine covariances of stochastic noise.
• Explore adjoint and ensemble methods for parameter estimation.
• Assess scalability on high-dimensional ocean models.

Skills

Applied mathematics

Fluid mechanics

Oceanography

Numerical simulation

Python

Julia

Fortran

C++

Tools

Python

Julia

Fortran

C++

Job description

Context

The PhD thesis will be supervised by Gilles Tissot (Inria Rennes) and Quentin Jamet (SHOM), and directed by Étienne Mémin (Inria Rennes), within the Inria “Odyssey” team in Rennes. The thesis is part of the ANR “NOUILLES” project, in collaboration with the Inria “AIRSEA” team (Grenoble), the “Odyssey” team (Rennes), IGE (Grenoble), SHOM (Brest), and IRD-LEGOS (Toulouse). The inter-institutional “Odyssey” team, which brings together researchers from Ifremer, the Laboratory of Physical and Spatial Oceanography (UMR 6523), IMT Atlantique in Brest, and the Inria center at the University of Rennes, will provide the candidate with a particularly rich research environment and numerous opportunities for collaboration. The team aims to develop innovative and cross-disciplinary research directions combining satellite observations, physical modelling, applied mathematics, and numerical methods, with the goal of analysing observational and numerical modelling data and improving our understanding and knowledge of ocean dynamics.

Assignment

Modelling under location uncertainty considers a budget of conserved quantities (mass, momentum, and energy) submitted to a fluid displacement perturbed by Brownian motion. Applying this principle leads to a generalization of the equations governing geophysical fluid dynamics, in which the stochastic terms make it possible to model unresolved subgrid-scale processes that need to be parameterized in ocean models. The specification of the covariance of the stochastic noise nevertheless remains an open question. The objective of this PhD thesis is to formulate inverse problems aimed at determining these covariances, such that the stochastic model reproduces, according to a criterion to be defined, the behaviour of a reference simulation. The stochastic nature of the models makes the formulation of such inverse problems non-trivial. Furthermore, numerical scalability of the proposed methods to the high dimension of numerical ocean models will be a crucial challenge. Deep convection will be considered as a case study in this thesis. This phenomenon occurs when water masses cool at the surface, increase in density, and sink in the form of plumes due to gravitational instability. Although these processes occur at scales too small to be resolved by climate models, they nevertheless play a major role in global ocean circulation. The methodologies developed during this thesis could thus provide a basis for parameterizing these processes while combining mathematical rigour with physical consistency.

Main activities

This PhD project will involve theoretical developments, physical modelling, and their numerical implementation. The candidate will become familiar with stochastic models applied to deep convection events. They will work with reference numerical simulations using a Large-Eddy Simulation (LES) approach, performed with the operational CROCO model. They will theoretically formulate inverse problems tailored to this class of models. Adjoint and ensemble methods will be considered, and different choices of control parameters and cost functions will be compared. Determining the covariance of the stochastic noise conditioned on environmental parameters, such as surface heat flux or stratification, will be a major focus, both from a theoretical perspective and in terms of physical applications. To assess the scalability of the developed methods, a canonical three-dimensional turbulent channel flow configuration, without rotation or stratification, may also be considered.

Skills

A background in applied mathematics, fluid mechanics, or oceanography, together with a strong interest in numerical simulation, is required. Basic programming skills in Python or Julia and Fortran or C++ would be an advantage.