A revised 4D-Var algorithm

Outline

Used Data

ECMWF forecast model geometry

The current operational 4D-Var system

A few 4D-Var Characteristics

The incremental formulation of 4D-Var

Approximations at inner iterations

The outer iterations

Slide 10

Slide 11

Test of incremental approximation

Evolution of TL model error

Impact of TL model resolution

Small scales

Impact of TL model resolution (adiab.)

Hessian eigenvector preconditioning

Trajectory (in)consistency

The revised 4D-Var algorithm: Motivation

The revised 4D-Var algorithm: Specification

Conjugate Gradients and Lanczos Algorithms

Conjugate Gradients and Lanczos Algorithms

Preconditioning

Preconditioning

Preconditioning

Preconditioning

Preconditioning: Spectrum of Hessian

Multi-incremental: RMS of T analysis increments

Conjugate-gradient: Reduction of Norm of gradient

C.G. and Lanczos Summary

Slide 31

Interpolated trajectory

Performance: Jo cost function

Scores

Performance: CPU cost

Conclusions