nach oben

Journal of Scientific Computing

Erschienen in:

01.11.2014

A Scalable Approach for Variational Data Assimilation

verfasst von: Luisa D’Amore, Rossella Arcucci, Luisa Carracciuolo, Almerico Murli

Erschienen in: Journal of Scientific Computing | Ausgabe 2/2014

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

Data assimilation (DA) is a methodology for combining mathematical models simulating complex systems (the background knowledge) and measurements (the reality or observational data) in order to improve the estimate of the system state (the forecast). The DA is an inverse and ill posed problem usually used to handle a huge amount of data, so, it is a large and computationally expensive problem. Here we focus on scalable methods that makes DA applications feasible for a huge number of background data and observations. We present a scalable algorithm for solving variational DA which is highly parallel. We provide a mathematical formalization of this approach and we also study the performance of the resulted algorithm.

Nächster Artikel Parallel Domain Decomposition Methods with Mixed Order Discretization for Fully Implicit Solution of Tracer Transport Problems on the Cubed-Sphere

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

It was shown [28] that incremental 3D-Var is equivalent to a GaussNewton method [10] (i.e. an approximation to a Newton iteration, in which the second-order terms of the Hessian are neglected) applied to the full nonlinear regularization functional.

The idea of using the L-BFGS method in variational data assimilation is not new because of its modest storage requirements and its high performance on large-scale unconstrained convex minimization [39, 46]. L-BFGS method is a Quasi–Newton method that can be viewed as extension of conjugate-gradient methods in which the addition of some modest storage serves to accelerate the convergence rate. The L-BFGS update formula generates the matrices approximating the Hessian using information from the last \(m\) Quasi-Newton iterations, where \(m\) is determined by the user (generally \(3 \le m \le 30\)). After having used the \(m\) vector storage locations for \(m\) quasi-Newton updates, the approximation of the Hessian matrix is updated by dropping the oldest information and replacing it by the newest information. Hence, time complexity of the L-BFGS increases linearly with the size of the \(m\) vectors [30].

Antonelli, L., Carracciuolo, L., Ceccarelli, M., D’Amore, L., Murli, A.: Total Variation Regularization for Edge Preserving 3D SPECT Imaging in High Performance Computing Environments. Lecture Notes in Computer Science (LNCS), vol. 2330, pp. 171–180, Springer-Verlag, Berlin, Heidelberg (2002)

Auroux, D., Blum, J.: Back and forth nudging algorithm for data assimilation problems. C. R. Acad. Sci. Ser. I 340(340), 873–878 (2005)MathSciNetCrossRefMATH

Blum, J., Le Dimet, F.X., Navon, I.M.: Data Assimilation for Geophysical Fluids, Volume XIV of Handbook of Numerical Analysis, chapter 9. Elsevier, Amsterdam (2005)

Carracciuolo, L., D’Amore, L., Murli, A.: Towards a parallel component for imaging in PETSc programming environment: a case study in 3-D echocardiography. Parallel Comput. 32, 67–83 (2006)MathSciNetCrossRef

Delahaies, S., Roulstone, L., Nichols, N.K.: Regularization of a Carbon-Cycle Model-Data Fusion Problem. Preprint University of, Reading, MPS-2013-10 (2013)

D’Amore, L., Arcucci, R., Marcellino, L., Murli, A.: A parallel three-dimensional variational data assimilation scheme. In: Numerical Analysis and Applied Mathematics, AIP C.P. vol. 1389, pp. 1829–1831 (2011)

D’Amore, L., Arcucci, R., Marcellino, L., Murli, A.: HPC computation issues of the incremental 3D variational data assimilation scheme in OceanVar software. J. Numer. Anal. Ind. Appl. Math. 7(3–4), 91–105 (2012)MathSciNet

D’Amore, L., Arcucci, R., Carracciuolo, L., Murli, A.: OceanVAR software for use with NEMO: documentation and test guide. In: CMCC Research Papers Issue RP0173 (2012)

D’Elia, M., Perego, M., Veneziani, A.: A variational data assimilation procedure for the incompressible Navier–Stokes equations in hemodynamics. J. Sci. Comput. 1–20 (2011)

10.

Dennis, J.E. Jr., Schnabel, R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice Hall Series in Computational Mathematics. Prentice Hall Inc., Englewood Cliffs, NJ (1983)

11.

Dobricic, S., Pinardi, N.: An oceanographic threedimensional variational data assimilation scheme. Ocean Modell. 22, 89–105 (2008)CrossRef

12.

Freitag, M., Budd, C.J., Nichols, N.K.: Tikhonov regularization for large inverse problems. In: 17th ILAS Conference. Braunschweig, Germany (2011)

13.

Fox, G.C., Williams, R.D., Messina, P.C.: Parallel. Computing Works!. Morgan Kaufmann Publishers Inc., Los Altos, CA (1994)

14.

Foster, I.: Designing and Building Parallel Programs. Addison-Wesley, Reading, MA (1995)MATH

15.

Ghil, M., Malanotte-Rizzoli, P.: Data Assimilation in Meteorology and Oceanography, Advances in Geophysics, vol. 33. Academic Press, New York (1991)

16.

Golub, G.H., Heath, M., Wahba, G.: Generalized cross-validation as a method for choosing a good ridge parameter. Technometrics 21(2), 215–223 (1979)

17.

Haben, S.A., Lawless, A.S., Nichols, N.K.: Conditioning of the 3DVAR Data Assimilation Problem, Mathematics Report 3/2009. Department of Mathematics, University of Reading (2009)

18.

Haben, S.A., Lawless, A.S., Nichols, N.K.: Conditioning of Incremental Variational Data Assimilation, with Application to the Met Office System. Preprint University of Reading, MPS-2010-22 (2010)

19.

Haben, S.A., Lawless, A.S., Nichols, N.K.: Conditioning and preconditioning of the variational data assimilation. Comput. Fluids 46, 252–256 (2011)CrossRefMATH

20.

Haben, S.A., Lawless, A.S., Nichols, N.K.: Conditioning of incremental variational data assimilation, with application to the Met Office system. Tellus A 63, 782–792 (2011)

21.

Kalman, R.E.: A new approach to linear filtering and prediction problems. Trans. ASME J. Basic Eng. 82(Series D), 35–45 (1960)

22.

Kalnay, E.: Atmospheric Modeling, Data Assimilation and Predictability. Cambridge University Press, Cambridge, MA (2003)

23.

Keyes, D.E.: How scalable is domain decomposition in practice? In: Proceedings of the International Conference Domain Decomposition Methods, Greenwich, pp. 286–297 (1998)

24.

Koivunen, A.C., Kostinski, A.B.: The feasibility of data whitening to improve performance of weather radar. J. Appl. Meteorol. 38, 741–749 (1999)CrossRef

25.

Kostinski, A.B., Koivunen, A.C.: On the condition number of Gaussian sample-covariance matrices. IEEE Trans. Geosci. Remote Sens. 38, 329–332 (2000)CrossRef

26.

Johnson, C., Hoskins, B.J., Nichols, N.K.: A singular vector perspective of 4-DVar: filtering and interpolation. Q. J. R. Meteorol. Soc. 131, 120 (2005a)CrossRef

27.

Johnson, C., Nichols, N.K., Hoskins, B.J.: Very large inverse problems in atmosphere and ocean modelling. Int. J. Numeric. Methods Fluids 47, 759771 (2005b)MathSciNet

28.

Lawless, A.S., Gratton, S., Nichols, N.K.: Approximate iterative methods for variational data assimilation. Int. J. Numer. Meth. Fluids 47, 1129–1135 (2005)MathSciNetCrossRefMATH

29.

Le Dimet, F.X., Talagrand, O.: Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus 38A, 97–110 (1986)CrossRef

30.

Liu, D.C., Nocedal, J.: On the limited memory BFGS method for large scale optimization. Math. Programm. 45, 503–528 (1989)MathSciNetCrossRefMATH

31.

Marx, B. A., Potthast, R.W.E.: On Instabilities in Data Assimilation Algorithms. University of Reading, Department of Mathematics and Statistics, Preprint MPS-2012-06 (2012)

32.

Miyoshi, T.: Computational Challenges in Big Data Assimilation with Extreme-Scale Simulations, Talk at BDEC Workshop. Charleston, SC (2013)

33.

Mogensen, K., Alonso Balmaseda, M., Weaver, A.: The NEMOVAR ocean data assimilation system as implemented in the ECMWF ocean analysis for System 4. Research Department, CERFACS, Toulouse (2012)

34.

Moler, C.: Experiments with MATLAB (2011)

35.

Morozov, V.A.: Methods for Solving Incorrectly Posed Problems. Wien. Springer, New York (1984)CrossRef

36.

Murli, A., D’Amore, L., Carracciuolo, L., Ceccarelli, M., Antonelli, L.: High performance edge-preserving regularization in 3D SPECT imaging. Parallel Comput. 34(2), 115–132 (2008)

37.

NEMO, http://www.nemo.ocean.eu

38.

Navon, I.M.: Data assimilation for numerical weather prediction: a review. In: Park, S.K., Xu, L. (eds.) Data Assimilation for Atmospheric, Oceanic and Hydrologic Applications. Springer, Berlin (2009)

39.

Navon, I.M., Legler, D.M.: Conjugate gradient methods for large-scale minimization in metereology. Mon. Weather Rev. 115, 1479–1502 (1987)

40.

Nerger, L., Hiller, W. and Schrter, J. The Parallel Data Assimilation Framework PDAF—a flexible software framework for ensemble data assimilation, EGU General Assembly, April 23–27, 2012, Vienna, Austria (Geophysical Research Abstracts, vol. 14, EGU2012-1885)

41.

Nocedal, J., Byrd, R.H., Lu, P., Zhu, C.: L-BFGS-B: fortran subroutines for large-scale bound-constrained optimization. ACM Trans. Math. Softw. 23(4), 550–560 (1997)MathSciNetCrossRefMATH

42.

Potthast, R., Graben, P.: Inverse problems in neural field theory. SIAM J. Appl. Dyn. Syst. 8(4), 1405–1433 (2009)MathSciNetCrossRefMATH

43.

Stewart, L.M., Dance, S., Nichols, N.K.: Data assimilation with correlated observation errors: experiments with a 1-D shallow water model. Tellus A. 65, 19546 (2013)

44.

Tikhonov, A.N.: Regularization of incorrectly posed problems. Sov. Math. Dokl. 4, 1624–1627 (1963)MATH

45.

Vanoye, A., Mendoza, A.: Application of direct regularization techniques and bounded-variable least squares for inverse modeling of an urban emissions inventory. Athmosferic Pollut. Res. 5 (2014)

46.

Zou, X., Navon, I.M., Berger, M., Phua, K.H., Schlick, T. LeDimet, F.X.: Numerical experience with limited-memory quasi-Newton and truncated Newton methods. SIAM J. Optim. 3, 582–608 (1993)

Titel: A Scalable Approach for Variational Data Assimilation
verfasst von: Luisa D’Amore
Rossella Arcucci
Luisa Carracciuolo
Almerico Murli
Publikationsdatum: 01.11.2014
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 2/2014
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-014-9824-2

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 2/2014

Numerical Anisotropy Study of a Class of Compact Schemes

Atmospheric Sound Propagation Over Large-Scale Irregular Terrain

An Analysis of Solution Point Coordinates for Flux Reconstruction Schemes on Triangular Elements

An Efficient Lattice Boltzmann Model for Steady Convection–Diffusion Equation

A $$P_N P_M{-} CPR $$ P N P M - C P R Framework for Hyperbolic Conservation Laws

Improved Accuracy of High-Order WENO Finite Volume Methods on Cartesian Grids