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Dual number-based variational data assimilation: Constructing exact tangent linear and adjoint code from nonlinear model evaluations

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  • Jann Paul Mattern
  • Christopher A Edwards
  • Christopher N Hill

Abstract

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.

Suggested Citation

  • Jann Paul Mattern & Christopher A Edwards & Christopher N Hill, 2019. "Dual number-based variational data assimilation: Constructing exact tangent linear and adjoint code from nonlinear model evaluations," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-10, October.
  • Handle: RePEc:plo:pone00:0223131
    DOI: 10.1371/journal.pone.0223131
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    References listed on IDEAS

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    1. Guangjie Wang & Xiaoqun Cao & Xun Cai & Jingzhe Sun & Xiaoyong Li & Heng Wang, 2018. "A new data assimilation method for high-dimensional models," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-15, February.
    2. Kishi, Michio J. & Kashiwai, Makoto & Ware, Daniel M. & Megrey, Bernard A. & Eslinger, David L. & Werner, Francisco E. & Noguchi-Aita, Maki & Azumaya, Tomonori & Fujii, Masahiko & Hashimoto, Shinji & , 2007. "NEMURO—a lower trophic level model for the North Pacific marine ecosystem," Ecological Modelling, Elsevier, vol. 202(1), pages 12-25.
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    1. Aristizabal, Mauricio & Hernández-Estrada, José L. & Garcia, Manuel & Millwater, Harry, 2023. "Solution and sensitivity analysis of nonlinear equations using a hypercomplex-variable Newton-Raphson method," Applied Mathematics and Computation, Elsevier, vol. 451(C).

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