Introduction: Numerical Weather Prediction as an Initial Value Problem, Filtering Problem, Finite Difference techniques for various partial differential equations (parabolic, hyperbolic and elliptic), Time integration schemes, Explicit, Implicit, and semi-implicit Schemes.

Consistency and stability [CFL condition], Von Newmann stability analysis for various finite difference schemes, Staggered grid, Nonlinear instability,Arakawa Jacobians, Semi lagrangian methods, Spectral Technique, Galerkin methods, Introduction to Hierarchy of numerical models: Barotropic models, Equivalent barotropic model, Two level baroclinic model, Shallow water model, Primitive equation models, Brief overview of sub-grid scale processes (convection, boundary layer, radiation, land surface), Objective analysis, Initialization schemes, Data assimilation, Variational schemes, Kalman Filter schemes , High resolution regional modelling- Nested grids, Boundary conditions , Ensemble forecasting

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