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