A new data assimilation method for high-dimensional models

Abstract

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.

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

“…By exploiting common features of biogeochemical model, we can reduce this cost significantly, though an evaluation of the dual number-based adjoint model remains more costly than its hand-coded reference version, resulting in a 10%-15% increase in runtime for our full data assimilation system. (Options to speed up the code, such as storing the tangent linear matrices computed in the tangent linear model and reusing them in the adjoint model [17] or basing the full data assimilation system on dual numbers as in [9] are associated with a much larger coding effort and are not examined here.) We maintain that the ease of implementation and reduced risk to incorporate errors into the code outweigh this disadvantage for many applications.…”

“…Variational data assimilation uses the adjoint method for cost function minimization, requiring tangent linear and adjoint models which are based on the derivative of the nonlinear model [12]. If applied to the full model, dual numbers allow for the direct computation of the derivative of the cost function, avoiding the requirement for tangent linear and adjoint code altogether [9]. In many applications, however, parts of the complex data assimilation machinery are already in place and just need to be extended to accommodate a new model component.…”

Amazon Hydrology From Space: Scientific Advances and Future Challenges

“…Rainfall estimations by RS since the 1980s in the Amazon basin have depicted more amounts of rain in the north, particularly during the wet season (Espinoza, Ronchail, et al., 2019; Pacada et al., 2020; G. Wang et al., 2018) and lower amounts in the south, particularly during the dry season (Espinoza, Ronchail, et al., 2019; Leite‐Filho et al., 2019). This north‐south contrasting pattern is translated to the hydrological behavior of the main basins that show an intensification of the hydrological regime in the main course of the Amazon (Barichivich et al., 2018; Espinoza Villar, Guyot, et al., 2009; Heerspink et al., 2020).…”

“…Rainfall estimations by RS since the 1980s in the Amazon basin have depicted more amounts of rain in the north, particularly during the wet season Pacada et al, 2020;G. Wang et al, 2018) and lower amounts in the south, particularly during the dry season Leite-Filho et al, 2019).…”