/Optimization_Data_Assimilation_MAE_5010

Python codes for Data Assimilation course MAE-5010

Primary LanguagePython

Python codes developed for MAE 5010 Data Assimilation course.

These codes require understanding of Linear Algebra, Adjoint Optimization, and Probability theory**

  1. HW1--Satellite radiance problem :

    1. Solve using LU (normal equation approach by Grammian)
    2. Solve using QR approach
    3. Solve using SVD approach
    4. 2D interpolation using bilinear least squares

  2. HW2-4D-VAR/Adjoint Optimisation(ODE-Lorenz Systerm):

    1. Linear 4D-VAR):
    2. Nonlinear 4D-VAR

  3. HW3-Gradeint based Optimisation:

    1. Newton/Gradient Method.
    2. Conjugate Gradient.
    3. Broyden–Fletcher–Goldfarb–Shanno (BFGS) Algorithm.

  4. HW4-4D-VAR/Adjoint Optimisation(PDE)

    1. Linear advection equation.

  5. HW5-Forward Sensistivity Model

    1. Lagrangian forecast air temperature model.

  6. HW6-3DVAR

    1. Initialization Classical Method.
    2. Optimal interpolation (bicubic).
    3. Bayesian Formulation.

  7. HW7-nonlinear dynamics describing a falling body (Julier, Uhlmann, Durrant-Whyte, IEEE Transactions on Automatic Control Volume 45, 2000)

    1. zeroth-order filter (linearized Kalman filter)
    2. first-order filter (Extended Kalman Filter)
    3. second-order filter (Gauss filter).

  8. HW8-Lorenz 96 (L96) problem

    1. stochastic Ensemble Kalman filter (EnKF).
    2. Deterministic EnKF.
    3. Reduced-rank square root (RRSQRT) filter.
    4. Unscented Kalman Filter method.

  9. Project- Deterministic and stochastic ensemble KF approaches for 1D nonlinear Korteweg de Vries (KdV) PDE.