Data Assimilation

Atmospheric Science · Part 7

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Table of Contents

  1. 1.Bayesian Framework
  2. 2.Optimal Interpolation (OI)
  3. 3.3D-Var: Three-Dimensional Variational Assimilation
  4. 4.4D-Var: Four-Dimensional Variational Assimilation
  5. 5.Ensemble Kalman Filter (EnKF)
  6. 6.Hybrid Ensemble-Variational Methods
  7. 7.Observation Types and Quality Control
  8. 8.Fortran: Optimal Interpolation for 2D Temperature Field
  9. 9.Background Error Covariance B
  10. 10.Observation Error Covariance R

Key Equations

$$p(\mathbf{x}|\mathbf{y}) \propto p(\mathbf{y}|\mathbf{x})\,p(\mathbf{x})$$
$$\mathbf{K} = \mathbf{BH}^T(\mathbf{HBH}^T + \mathbf{R})^{-1}$$
$$J(\mathbf{x}_0) = \frac{1}{2}(\mathbf{x}_0 - \mathbf{x}^b)^T \mathbf{B}^{-1}(\mathbf{x}_0 - \mathbf{x}^b) + \frac{1}{2}\sum_{i=0}^{N}(\mathbf{y}_i - H_i(\mathbf{x}_i))^T \mathbf{R}_i^{-1}(\mathbf{y}_i - H_i(\mathbf{x}_i))$$
$$\mathbf{x}_k^a = \mathbf{x}_k^b + \mathbf{K}(\mathbf{y}_k^o - H(\mathbf{x}_k^b)), \quad \mathbf{K} = \mathbf{P}^b\mathbf{H}^T(\mathbf{HP}^b\mathbf{H}^T + \mathbf{R})^{-1}$$

Equations are rendered with MathJax in the PDF with professional LaTeX typesetting.

Course Context

This PDF is part of the Atmospheric Science course on CoursesHub.World. Study the physics of weather and climate from atmospheric thermodynamics to planetary atmospheres. Covers atmospheric dynamics, synoptic meteorology, clouds and precipitation, radiation budgets, clima...

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