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Exploring the potential and limitations of weak‐constraint 4D‐Var
Author(s) -
Laloyaux P.,
Bonavita M.,
Chrust M.,
Gürol S.
Publication year - 2020
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.3891
Subject(s) - constraint (computer aided design) , forcing (mathematics) , set (abstract data type) , computer science , homogeneous , mathematics , mathematical analysis , geometry , combinatorics , programming language
The standard formulation of 4D‐Var assumes random zero‐mean errors for all sources of information used in the analysis. This assumption is usually not well verified in real‐world applications. The performance of a weak‐constraint 4D‐Var formulation ("forcing" formulation) is studied in this paper in a simplified experimental setting using additive model errors of different length‐scales and observing systems of different coverage and accuracy. A set of twin experiments is carried out and results show that weak‐constraint 4D‐Var can accurately estimate the actual model errors and the initial state only when background and model errors have different spatial scales and when the observations are unbiased and spatially homogeneous. We also present preliminary results from a different weak‐constraint 4D‐Var formulation ("state" formulation) which could in principle overcome some of these limitations, but at the cost of a substantial increase of computational and memory requirements. These findings help identify the potential but also the intrinsic limitations of the weak‐constraint 4D‐Var approach. They also help to clarify the experimental results seen in the operational ECMWF analysis system where the analysis and first‐guess temperature bias is reduced by up to 50 % in the stratosphere.