Learn · NPTEL

Course11110608240 lectures

Dynamic Data Assimilation: an introduction

Prof. S. Lakshmivarahan · IIT Madras

Start with lecture 1 At NPTEL

Lectures

Introduction

  1. An Overview Video
  2. Data Mining, Data assimilation and prediction Video
  3. A classification of forecast errors Video

Mathematical Tools

  1. Finite Dimensional Vector Space Video
  2. Matrices Video
  3. Matrices Continued Video
  4. Multi-variate Calculus Video
  5. Optimization in Finite Dimensional Vector spaces Video

Deterministic, Static Inverse Problems

  1. Deterministic, Static, linear Inverse (well-posed) Problems Video
  2. Deterministic, Static, Linear Inverse (Ill-posed) Problems Video
  3. A Geometric View – Projections Video
  4. Deterministic, Static, nonlinear Inverse Problems Video
  5. On-line Least Squares Video
  6. Examples of static inverse problems Video

Numerical Algorithms for solving Least Squares Problems

  1. Interlude and a Way Forward Video
  2. Matrix Decomposition Algorithms Video
  3. Matrix Decomposition Algorithms Continued Video
  4. Minimization algorithms Video
  5. Minimization algorithms Continued Video

Deterministic, Dynamic Inverse Problems

  1. Inverse problems in deterministic Video
  2. Inverse problems in deterministic Continued Video
  3. Forward sensitivity method Video
  4. Relation between FSM and 4DVAR Video

Principles of Statistical Estimation

  1. Statistical Estimation Video
  2. Statistical Least Squares Video
  3. Maximum Likelihood Method Video
  4. Bayesian Estimation Video
  5. From Gauss to Kalman-Linear Minimum Variance Estimation Video

Stochastic, Static Inverse Problems

  1. Initialization Classical Method Video
  2. Optimal interpolations Video
  3. A Bayesian Formation-3D-VAR methods Video

Stochastic, Dynamic Inverse Problems

  1. Linear Stochastic Dynamics - Kalman Filter Video
  2. Linear Stochastic Dynamics - Kalman Filter Continued Video
  3. Linear Stochastic Dynamics - Kalman Filter Continued. Video
  4. Covariance Square Root Filter Video
  5. Nonlinear Filtering Video
  6. Ensemble Reduced Rank Filter Video

Nudging Methods

  1. Basic nudging methods Video

Predictability

  1. Deterministic predictability Video
  2. Predictability A stochastic view and Summary Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Madras
Department
Mathematics
Teacher
Prof. S. Lakshmivarahan
Level
Undergraduate
Language
English
Subjects
Mathematics
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
Who can watch
NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed