Programme of the ALATNET Seminar on Numerical Methods and NWP applications

Welcome and ALATNET presentation

Numerical Analysis (Joze Rakovec and Tomaz Vrhorec, Si), 5 hours

Historical and practical goals of Numerical Analysis
• Main methodologies with examples
• Solving linear problems: why and how?
• Partial Differential Equations: space discretisation techniques
• PDE: Time marching schemes and their properties
• Different types of instabilities
• NWP-oriented synthesis

Dynamics (Petra Smolikova, Cz), 5 hours

System of equations (hydrostatic, anelastic and fully compressible models)
• Integration schemes (Eulerian versus semi-Lagrangian)
• Discretization methods (spectral, finite elements, finite differences)
• Time discretization (explicite, implicite, semi-implicite correction)
• Horizontal discretization as a consequence of other choices
• Vertical discretization as a consequence of other choices

Physics (Jean-Francois Geleyn, F), 5 hours

Feed-back, multiple equilibrium states, stationnary vs. average solutions
• Numerical constraints on the parameterisation work
• Flux and tendencies, the dilemma
• Physical time-stepping (classical & with "passive" prognostic physical quantities)
• Linear instabilities and split-implicit solutions
• Stiffness and splitting
• Non-linear instabilities and upstream differencing
• Synthesis

Variational methods (Yves Bouteloup, F), 4 hours

Principles of variational methods
• Application to optimal control
• Other applications (singular vectors, optimisation of orography, ...)
• About minimizer

Numerical Filters (Gabor Radnoti, Hu and Piet Termonia, Be) 4 hours

Generalities
• Slowing down waves by space filters
• Damping waves by time filters
• The specific LAM coupling problem seen as a filter
• The data assimilation side of the problem
• Overview

Stochastic aspects (Claude Fischer, F), 3 hours

Introduction to predictability
• Usual techniques for defining the ensemble
• Products from ECMWF/EPS used at medium range
• How to improve probabilistic products
• Short range ensemble forecast at Meteo-France
• Application to a LAM

Data Management and scripts (Claude Fischer, F), 1 hour

Debriefing