Poster - Series of 6 seminar and tutorial introduction to data assimilation Richard Menard, ph.d. environment and climate change canada Montreal, Canada 1st week: introduction and mathematical background,2nd week: introdution to estimilation theory and concepts of data assimilation, 3rd week elementary data asssimilation methods, 4th week sequental/dynamical data assimilation methods, 5th week variational data assimilation methods 6th week ensemble methods Mondays from 10 am to 1pm (10:00 to 13:00) Starting on october 8th 2018 IGF room 511/516
poster - Introduction to data assimilation Richard Ménard, Ph.D. Environment and Climate Change Canada Montreal, Canada First week. Introduction and mathematical background General introduction to data assimilation. History of data assimilation. What data assimilation is really solving. Short review of applications in geophysics, engineering, and other fields. Review of underlying mathematical techniques: a) Linear algebra (only what is needed for data assimilation). b) Univariate and multivariate random variables. Second week. Introduction to estimation theory and concepts of data assimilation Basis of estimation theory and control theory: a) Bayes theorem, Maximum a Posteriori, Maximum likelihood. Conditional expectation. Minimum variance. b) Short review of dynamical system concepts: Observability, Controllability. Numerical methods to solve the advection equation with a 1D toy model. Concepts of tangent linear model and adjoint models. Third week. Elementary data assimilation methods Optimum interpolation. One observation experiment. Error covariance in physical space. Properties of an analysis. Estimation of error statistics (climatological): Hollingsworth-Lönnberg, Maximum likelihood, Desroziers method. Fourth week. Sequential/dynamical data assimilation methods Nudging and spectral nudging. Kalman filter. Exercises using the advection equation. Asymptotic solution. Statistical consistency (chi-square). Introduction to other deterministic methods such as Square root filtering, SEEK filters. Fifth week. Variational data assimilation methods 3D and 4D Var. Preconditioning. Kalman smoother and Weak constraint 4D Var. Review of operational schemes. How do we get the error statistics needed? Sixth week. Ensemble methods Stochastic vs deterministic approaches. Localization and inflation. Partial review of EnKF implementations.