Accounting for an imperfect model in 4D‐Var

2006/10/01 by Yannick Tr'emolet, Yannick Trémolet · 263 citations
Earth and Planetary Sciences · Environmental Science · Mathematics · #Applied mathematics #Atmospheric and Environmental Gas Dynamics #Climate variability and models #Computer science #Constraint (computer-aided design) #Control variable #Data assimilation #Errors-in-variables models #Forcing (mathematics) #Mathematics #Meteorological Phenomena and Simulations #Meteorology #Physics #Representation (politics) #State variable #Statistics #Variable (mathematics)

paper · doi:10.1256/qj.05.224

published in Quarterly Journal of the Royal Meteorological Society 132(621), 2483-2504 (Wiley)

openalex publication_date 2006/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

Abstract In most operational implementations of four‐dimensional variational data assimilation (4D‐Var), it is assumed that the model used in the data assimilation process is perfect or, at least, that errors in the model can be neglected when compared to other errors in the system. In this paper, we study how model error could be accounted for in 4D‐Var. We present three approaches for the formulation of weak‐constraint 4D‐Var: estimating explicitly a model‐error forcing term, estimating a representation of model bias or, estimating a four‐dimensional model state as the control variable. The consequences of these approaches with respect to the implementation and the properties of 4D‐Var are discussed. We show that 4D‐Var with an additional model‐error representation as part of the control variable is essentially an initial‐value problem and that its characteristics are very similar to that of strong constraint 4D‐Var. Taking the four‐dimensional state as the control variable, however, leads to very different properties. In that case, weak‐constraint 4D‐Var can be interpreted as a coupling between successive strong‐constraint assimilation cycles. A possible extension towards long‐window 4D‐Var and possibilities for evolutions of the data assimilation system are presented. Copyright © 2006 Royal Meteorological Society

Cited by

• Implicit and explicit treatments of model error in numerical simulation
• Absolutely Minimising Generalised Solutions to the Equations of Vectorial Calculus of Variations in L^∞
• Uncertainty-aware data assimilation through variational inference
• Control-Augmented Autoregressive Diffusion for Data Assimilation
• Deep Learning for Physical Processes: Incorporating Prior Scientific Knowledge
• Model Training, Data Assimilation, and Forecast Experiments with a Hybrid Atmospheric Model that Incorporates Machine Learning
• 3D-VAR for Parametrized Partial Differential Equations: A Certified Reduced Basis Approach
• A New Approach for 4DVar Data Assimilation
• An Introduction to Solving the Least-Squares Problem in Variational Data Assimilation
• PhyDA: Physics-Guided Diffusion Models for Data Assimilation in Atmospheric Systems
• Appa: Bending Weather Dynamics with Latent Diffusion Models for Global Data Assimilation
• Model Error Covariance Estimation for Weak Constraint Data Assimilation
• Uncertainty quantification and optimal decisions. [europepmc]
• The Quest for Model Uncertainty Quantification: A Hybrid Ensemble and Variational Data Assimilation Framework. [europepmc]
• Data assimilation and agent-based modelling: towards the incorporation of categorical agent parameters. [europepmc]

Related

• Handling errors in four-dimensional variational data assimilation by balancing the degrees of freedom and the model constraints: A new approach
• A New Approach for 4DVar Data Assimilation
• Model Error Covariance Estimation for Weak Constraint Data Assimilation
• Variational Data-Consistent Assimilation
• Reduced basis approximation and a~posteriori error bounds for 4D-Var data assimilation