Dual number-based variational data assimilation: Constructing exact tangent linear and adjoint code from nonlinear model evaluations
Autoři:
Jann Paul Mattern aff001; Christopher A. Edwards aff001; Christopher N. Hill aff002
Působiště autorů:
Ocean Sciences Department, UC Santa Cruz, Santa Cruz, CA, United States of America
aff001; Department of Earth, Atmospheric and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, United States of America
aff002
Vyšlo v časopise:
PLoS ONE 14(10)
Kategorie:
Research Article
doi:
https://doi.org/10.1371/journal.pone.0223131
Souhrn
Dual numbers allow for automatic, exact evaluation of the numerical derivative of high-dimensional functions at an arbitrary point with minimal coding effort. We use dual numbers to construct tangent linear and adjoint model code for a biogeochemical ocean model and apply it to a variational (4D-Var) data assimilation system when coupled to a realistic physical ocean circulation model with existing data assimilation capabilities. The resulting data assimilation system takes modestly longer to run than its hand-coded equivalent but is considerably easier to implement and updates automatically when modifications are made to the biogeochemical model, thus making its maintenance with code changes trivial.
Klíčová slova:
Chlorophyll – Mathematical functions – Oceans – Programming languages – Tangents – Biogeochemistry – Fortran – Ocean modeling
Zdroje
1. Edwards CA, Moore AM, Hoteit I, Cornuelle BD. Regional Ocean Data Assimilation. Annual Review of Marine Science. 2015;7(1):21–42. doi: 10.1146/annurev-marine-010814-015821 25103331
2. Mattern JP, Song H, Edwards CA, Moore AM, Fiechter J. Data assimilation of physical and chlorophyll a observations in the California Current System using two biogeochemical models. Ocean Modelling. 2017;109 : 55–71. doi: 10.1016/j.ocemod.2016.12.002
3. Martins JRRA, Hwang JT. Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models. AIAA Journal. 2013;51(11):2582–2599. doi: 10.2514/1.J052184
4. Griewank A, Walther A. Evaluating derivatives: principles and techniques of algorithmic differentiation. Vol. 105. Siam, 2008.
5. Giering R, Kaminski T. Recipes for adjoint code construction. ACM Transactions on Mathematical Software. 1998;24(4):437–474. doi: 10.1145/293686.293695
6. Giering R. Tangent linear and adjoint biogeochemical models. Inverse methods in global biogeochemical cycles. Vol. 114; 2000. p. 33–48. doi: 10.1029/GM114p0033
7. Leuck H, Nagel HH. Automatic differentiation facilitates OF-integration into steering-angle-based road vehicle tracking. In: Proceedings. 1999 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (Cat. No PR00149). IEEE Comput. Soc; 1999. p. 360–365.
8. Yu W, Blair M. DNAD, a simple tool for automatic differentiation of Fortran codes using dual numbers. Computer Physics Communications. 2013;184(5):1446–1452. doi: 10.1016/j.cpc.2012.12.025
9. Wang G, Cao X, Cai X, Sun J, Li X, Wang H. A new data assimilation method for high-dimensional models. PLOS ONE. 2018;13(2):1–15. doi: 10.1371/journal.pone.0191714
10. Orr JC, Epitalon JM, Dickson AG, Gattuso JP. Routine uncertainty propagation for the marine carbon dioxide system. Marine Chemistry. 2018;207 : 84–107. doi: 10.1016/j.marchem.2018.10.006
11. Harkin AA, Harkin JB. Geometry of Generalized Complex Numbers. Mathematics Magazine. 2004;77(2):118–129. doi: 10.1080/0025570X.2004.11953236
12. Le Dimet F, Talagrand O. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus A. 1986;38A(2):97–110. doi: 10.3402/tellusa.v38i2.11706
13. Haidvogel DB, Arango HG, Budgell WP, Cornuelle BD, Curchitser EN, Di Lorenzo E, et al. Ocean forecasting in terrain-following coordinates: Formulation and skill assessment of the Regional Ocean Modeling System. Journal of Computational Physics. 2008;227 : 3595–3624. doi: 10.1016/j.jcp.2007.06.016
14. Kishi MJ, Kashiwai M, Ware DM, Megrey BA, Eslinger DL, Werner FE, et al. NEMURO—a lower trophic level model for the North Pacific marine ecosystem. Ecological Modelling. 2007;202(1-2):12–25. doi: 10.1016/j.ecolmodel.2006.08.021
15. Thépaut JN, Courtier P. Four-dimensional variational data assimilation using the adjoint of a multilevel primitive-equation model. Quarterly Journal of the Royal Meteorological Society. 1991;117(502):1225–1254. doi: 10.1002/qj.49711750206
16. Courtier P, Thépaut JN, Hollingsworth A. A strategy for operational implementation of 4D-Var, using an incremental approach. Quarterly Journal of the Royal Meteorological Society. 1994;120(519):1367–1387. doi: 10.1002/qj.49712051912
17. Mattern JP, Edwards CA. A simple finite difference-based approximation for biogeochemical tangent linear and adjoint models. Journal of Geophysical Research: Oceans. 2019;124(1):4–26.
18. Mattern JP. GitHub repository with dual number example implementation. GitHub:https://github.com/jpmattern/dualnum.
19. Doyle JD, Jiang Q, Chao Y, Farrara J. High-resolution real-time modeling of the marine atmospheric boundary layer in support of the AOSN-II field campaign. Deep-Sea Research Part II: Topical Studies in Oceanography. 2009;56(3-5):87–99. doi: 10.1016/j.dsr2.2008.08.009
20. Moore AM, Arango HG, Broquet G, Powell BS, Weaver AT, Zavala-Garay J. The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems. Part I—System overview and formulation. Progress in Oceanography. 2011;91(1):34–49. doi: 10.1016/j.pocean.2011.05.004
21. Mattern JP, Edwards CA, Moore AM. Improving Variational Data Assimilation through Background and Observation Error Adjustments. Monthly Weather Review. 2018;146(2):485–501. doi: 10.1175/MWR-D-17-0263.1
22. Hoffman MD, Gelman A. The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo. Journal of Machine Learning Research. 2014;15 : 1593–1623. ArXiv:1111.4246.
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