Resolution of sharp fronts in the presence of model error in variational data assimilation

M. A. Freitag, N. K. Nichols, C. J. Budd

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

We show that the four-dimensional variational data assimilation method (4DVar) can be interpreted as a form of Tikhonov regularization, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularization recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularization. We apply this idea from stationary inverse problems to 4DVar, a dynamical inverse problem, and give examples for an L1-norm penalty approach and a mixed total variation (TV) L1–L2-norm penalty approach. For problems with model error where sharp fronts are present and the background and observation error covariances are known, the mixed TV L1–L2-norm penalty performs better than either the L1-norm method or the strong-constraint 4DVar (L2-norm) method. A strength of the mixed TV L1–L2-norm regularization is that in the case where a simplified form of the background error covariance matrix is used it produces a much more accurate analysis than 4DVar. The method thus has the potential in numerical weather prediction to overcome operational problems with poorly tuned background error covariance matrices.
Original languageEnglish
Pages (from-to)742-757
Number of pages16
JournalQuarterly Journal of the Royal Meteorological Society
Volume139
Issue number672
Early online date14 Aug 2012
DOIs
Publication statusPublished - Apr 2013

Fingerprint

data assimilation
inverse problem
matrix
norm
method
penalty
weather
prediction

Cite this

Resolution of sharp fronts in the presence of model error in variational data assimilation. / Freitag, M. A.; Nichols, N. K.; Budd, C. J.

In: Quarterly Journal of the Royal Meteorological Society, Vol. 139, No. 672, 04.2013, p. 742-757.

Research output: Contribution to journalArticle

@article{428a7aa4f1ec44fa937cdcf0b1f72b2a,
title = "Resolution of sharp fronts in the presence of model error in variational data assimilation",
abstract = "We show that the four-dimensional variational data assimilation method (4DVar) can be interpreted as a form of Tikhonov regularization, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularization recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularization. We apply this idea from stationary inverse problems to 4DVar, a dynamical inverse problem, and give examples for an L1-norm penalty approach and a mixed total variation (TV) L1–L2-norm penalty approach. For problems with model error where sharp fronts are present and the background and observation error covariances are known, the mixed TV L1–L2-norm penalty performs better than either the L1-norm method or the strong-constraint 4DVar (L2-norm) method. A strength of the mixed TV L1–L2-norm regularization is that in the case where a simplified form of the background error covariance matrix is used it produces a much more accurate analysis than 4DVar. The method thus has the potential in numerical weather prediction to overcome operational problems with poorly tuned background error covariance matrices.",
author = "Freitag, {M. A.} and Nichols, {N. K.} and Budd, {C. J.}",
year = "2013",
month = "4",
doi = "10.1002/qj.2002",
language = "English",
volume = "139",
pages = "742--757",
journal = "Quarterly Journal of the Royal Meteorological Society",
issn = "0035-9009",
publisher = "Wiley-Blackwell",
number = "672",

}

TY - JOUR

T1 - Resolution of sharp fronts in the presence of model error in variational data assimilation

AU - Freitag, M. A.

AU - Nichols, N. K.

AU - Budd, C. J.

PY - 2013/4

Y1 - 2013/4

N2 - We show that the four-dimensional variational data assimilation method (4DVar) can be interpreted as a form of Tikhonov regularization, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularization recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularization. We apply this idea from stationary inverse problems to 4DVar, a dynamical inverse problem, and give examples for an L1-norm penalty approach and a mixed total variation (TV) L1–L2-norm penalty approach. For problems with model error where sharp fronts are present and the background and observation error covariances are known, the mixed TV L1–L2-norm penalty performs better than either the L1-norm method or the strong-constraint 4DVar (L2-norm) method. A strength of the mixed TV L1–L2-norm regularization is that in the case where a simplified form of the background error covariance matrix is used it produces a much more accurate analysis than 4DVar. The method thus has the potential in numerical weather prediction to overcome operational problems with poorly tuned background error covariance matrices.

AB - We show that the four-dimensional variational data assimilation method (4DVar) can be interpreted as a form of Tikhonov regularization, a very familiar method for solving ill-posed inverse problems. It is known from image restoration problems that L1-norm penalty regularization recovers sharp edges in the image more accurately than Tikhonov, or L2-norm, penalty regularization. We apply this idea from stationary inverse problems to 4DVar, a dynamical inverse problem, and give examples for an L1-norm penalty approach and a mixed total variation (TV) L1–L2-norm penalty approach. For problems with model error where sharp fronts are present and the background and observation error covariances are known, the mixed TV L1–L2-norm penalty performs better than either the L1-norm method or the strong-constraint 4DVar (L2-norm) method. A strength of the mixed TV L1–L2-norm regularization is that in the case where a simplified form of the background error covariance matrix is used it produces a much more accurate analysis than 4DVar. The method thus has the potential in numerical weather prediction to overcome operational problems with poorly tuned background error covariance matrices.

UR - http://www.scopus.com/inward/record.url?scp=84897958535&partnerID=8YFLogxK

UR - http://dx.doi.org/10.1002/qj.2002

U2 - 10.1002/qj.2002

DO - 10.1002/qj.2002

M3 - Article

VL - 139

SP - 742

EP - 757

JO - Quarterly Journal of the Royal Meteorological Society

JF - Quarterly Journal of the Royal Meteorological Society

SN - 0035-9009

IS - 672

ER -