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Implicit treatment of model error using inflated observation-error covariance
- Source :
- Quarterly Journal of the Royal Meteorological Society, Quarterly Journal of the Royal Meteorological Society, Wiley, 2017, 143 (707), pp.2496-2508. ⟨10.1002/qj.3102⟩
- Publication Year :
- 2017
- Publisher :
- HAL CCSD, 2017.
-
Abstract
- International audience; Data assimilation involving imperfect dynamical models is an important topic in meteorology, oceanography and other geophysical applications. In filtering methods, the model error is compensated for by inflation. In variational data assimilation, authors usually try to estimate it, which means that all uncertainty-loaded model inputs are included into the control vector. However, this approach suffers from implementation difficulties. In this paper we suggest an alternative method, motivated by the 'nuisance parameter' concept known in statistics. This method allows the model error to be treated implicitly by inflating the observation-error covariance. The equivalency theorem substantiating the method has here been proved. We also consider a case with a biased model error. In the corresponding mixed formulation, the spatially distributed mean error is included into the control vector, whereas the time-dependent fluctuations around the mean are subjected to the proposed implicit treatment. Numerical experiments for the 1D generalized Burgers' equation illustrate the presented theory. In these experiments the model error related to uncertainty in the advection coefficient has been considered.
- Subjects :
- Atmospheric Science
Mathematical optimization
UNCERTAINTY ANALYSIS
010504 meteorology & atmospheric sciences
Mean squared error
IMPERFECT MODEL
SYSTEMATIC ERRORS
NUMERICAL EXPERIMENTS
010103 numerical & computational mathematics
ERRORS
01 natural sciences
NUMERICAL MODEL
Data assimilation
VARIATIONAL DATA ASSIMILATION
DATA ASSIMILATION
IMPLEMENTATION DIFFICULTIES
CONTROL SYSTEM
SYSTEMATIC ERROR
Applied mathematics
Nuisance parameter
ACTIVE CONTROL
BURGERS' EQUATION
0101 mathematics
'IDLE' CONTROL
0105 earth and related environmental sciences
Mathematics
BURGERS' EQUATIONS
EXPERIMENTAL STUDY
STATISTICAL ANALYSIS
Covariance
TIME-DEPENDENT FLUCTUATIONS
Burgers' equation
Error correction model
OBSERVATIONAL METHOD
GEOPHYSICAL APPLICATIONS
RANDOM ERRORS
[SDE]Environmental Sciences
RANDOM ERROR
Errors-in-variables models
OCEANOGRAPHY
Round-off error
IMPERFECT MODELING
Subjects
Details
- Language :
- English
- ISSN :
- 00359009 and 1477870X
- Database :
- OpenAIRE
- Journal :
- Quarterly Journal of the Royal Meteorological Society, Quarterly Journal of the Royal Meteorological Society, Wiley, 2017, 143 (707), pp.2496-2508. ⟨10.1002/qj.3102⟩
- Accession number :
- edsair.doi.dedup.....e2974a472caa14bb9f6174165e59550c