An investigation of incremental 4D‐Var using non‐tangent linear models

• Published in: Quarterly journal of the Royal Meteorological Society Vol. 131; no. 606; pp. 459 - 476
• Main Authors: Lawless, A. S., Gratton, S., Nichols, N. K.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 01.01.2005; Wiley
• Subjects: Earth, ocean, space; Exact sciences and technology; External geophysics; Gauss–Newton; Incremental formulation; Mathematics; Meteorology; Tangent linear; Variational data assimilation; Weather analysis and prediction; Lagrangian model; Weather forecast; Gauss Newton method; Iterative method; Perturbation; Tangent linear model; Gauss-Newton Incremental formulation Tangent linear Variational data assimilation; Convergence rate; Variational calculus; Four dimensional model; Numerical forecast; Data assimilation; Shallow-water equations
• ISSN: 0035-9009; 1477-870X
• DOI: 10.1256/qj.04.20

We investigate the convergence of incremental four‐dimensional variational data assimilation (4D‐Var) when an approximation to the tangent linear model is used within the inner loop. Using a semi‐implicit semi‐Lagrangian model of the one‐dimensional shallow water equations, we perform data assimilation experiments using an exact tangent linear model and using an inexact linear model (a perturbation forecast model). We find that the two assimilations converge at a similar rate and the analyses are also similar, with the difference between them dependent on the amount of noise in the observations. To understand the numerical results, we present the incremental 4D‐Var algorithm as a Gauss–Newton iteration for solving a least‐squares problem and consider its fixed points. Copyright © 2005 Royal Meteorological Society.