These are the slides of the first part of the course Big data, data assimilation and uncertainty quantification given by Dan Crisan, Omar Ghattas and myself, in the framework of the Institut Henri Poincaré (IHP) trimester The Mathematics of Climate and the Environment.

  • Lecture 1: Elementary principles of geophysical data assimilation. The Bayesian standpoint. Classical methods of data assimilation: 3D-Var, the Kalman filter, 4D-Var.
  • Lecture 2: The ensemble Kalman filter and its variants (focus on the algorithmic/mathematical aspects.)
  • Lecture 3: Recent advances: hybrid and ensemble variational techniques. Discussion on what to expect from machine learning/deep learning.

Details on the trimester can be found here.