Open AccessA new data assimilation method for high-dimensional models
Author(s) -
Guangjie Wang,
Xiaoqun Cao,
Xun Cai,
Jingzhe Sun,
Xiaoyong Li,
Heng Wang
Publication year - 2018
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0191714
Subject(s) - data assimilation , computation , mathematics , adjoint equation , automatic differentiation , nonlinear system , tangent , computer science , algorithm , regularization (linguistics) , mathematical optimization , partial differential equation , mathematical analysis , physics , artificial intelligence , meteorology , geometry , quantum mechanics
In the variational data assimilation (VarDA), the typical way for gradient computation is using the adjoint method. However, the adjoint method has many problems, such as low accuracy, difficult implementation and considerable complexity, for high-dimensional models. To overcome these shortcomings, a new data assimilation method based on dual number automatic differentiation (AD) is proposed. The important advantages of the method lies in that the coding of the tangent-linear/adjoint model is no longer necessary and that the value of the cost function and its corresponding gradient vector can be obtained simultaneously through only one forward computation in dual number space. The numerical simulations for data assimilation are implemented for a typical nonlinear advection equation and a parabolic equation. The results demonstrate that the new method can reconstruct the initial conditions of the high-dimensional nonlinear dynamical system conveniently and accurately. Additionally, the estimated initial values can converge to the true values quickly, even if noise is present in the observations.