The Mathematics of Climate and the Environment
IHP, Paris, September 9 - December 21 2019
Deadline for financial support: March 15th, 2019
Registration is free however mandatory: http://www.ihp.fr/en/CEB/T3-2019
Course I Schedule
Course I: Mathematical methods in climate and geophysical fluid dynamics
16 Sept.– 4 Oct. 2019
The course will take place in the amphiteater of the Institut Henry Poincaré
11 Rue Pierre et Marie Curie, 75005 Paris, France
(a) Dynamical systems & climate applications
Franco Flandoli (SNS, Pisa) & M. Ghil (ENS)
(b) Numerical methods & climate applications
Darryl Holm (Imperial College London) & Thomas Dubos (Ecole Polytechnique)
Schedule
Monday, 16 Sept.
Michael Ghil
Morning, 10:30-12:30
General introduction to the course.
Classic bifurcation theory in autonomous DDSs; application to energy balance models
Afternoon, 15:00-17:00
Successive bifurcation trees; application to the wind-driven ocean circulation
Tuesday, 17 Sept.
Franco Flandoli
Morning, 10:30-12:30
Nonautonomous and random dynamical systems (NDSs & RDSs).
Pullback & random attractors (PBAs & RAs)
Afternoon, 15:00-17:00
Random invariant measures and link to classical Markov invariant measures
Advanced topics in NDSs & RDSs, like synchronization by noise
Wednesday, 18 Sept.
Darryl Holm
Morning, 10:30-12:30
Tutorial on the Infinite-Dimensional Geometry of Fluid Dynamics
Flows, Pull-backs, Differential k-forms, Lie derivatives and all that
What is advection, mathematically? Familiar fluid examples!
Deterministic Advection in Kelvin's Circulation Theorem
Hamilton's principle for Deterministic Advection by Lie Transport (DALT)
Thursday, 19 Sept.
Darryl Holm
Morning, 10:30-12:30
The path to the SALT algorithm for stochastic parameterisation
-- Kunita theorem for stochastic advection (1984)
-- VariationaI principle for stochastic advection by Lie transport
-- Example: stochastic magnetohydrodynamics
Friday, 19 Sept.
Darryl Holm
Morning, 10:30-12:30
The LA SALT Euler--Boussinesq (EB) fluid system in a vertical plane
-- Dynamics of Expectations (climate) + Fluctuations (weather) +
Variances (predictability)
-- Preparation for explaining analytical properties of 2D LA SALT EB
-- Global well-posedness of 2D LA SALT EB
Monday, 23 Sept.
Michael Ghil
Morning, 10:30-12:30
PBAs & RAs; applications to the El Niño–Southern Oscillation (ENSO) &
the wind-driven ocean circulation
Afternoon, 15:00-17:00
Ergodic theory of DDSs, NDSs & RDSs
Statistical methods for the comparative study of climate observations & simulations
Wednesday, 25 Sept.
Franco Flandoli
Morning, 10:30-12:30
SDE & SPDEs of fluid dynamics: well posedness, existence of RDS and RA
Afternoon, 15:00-17:00
Kolmogorov and Fokker-Planck equations associated to SPDEs
Friday, 26 Sept.
Thomas Dubos
Morning, 10:30-12:30
Numerical methods, I
Equations of motion in the atmosphere and ocean: Transport; Motion on a rotating Earth; Hydrostatic approximation
Friday, 26 Sept.
Thomas Dubos
Morning, 10:30-12:30
Numerical methods, II
Bousinesq-like approximations; Numerics for geophysical fluid models, linear and nonlinear topics
