5 research outputs found
An Optimization Framework to Improve 4D-Var Data Assimilation System Performance
This paper develops a computational framework for optimizing the parameters
of data assimilation systems in order to improve their performance. The
approach formulates a continuous meta-optimization problem for parameters; the
meta-optimization is constrained by the original data assimilation problem. The
numerical solution process employs adjoint models and iterative solvers. The
proposed framework is applied to optimize observation values, data weighting
coefficients, and the location of sensors for a test problem. The ability to
optimize a distributed measurement network is crucial for cutting down
operating costs and detecting malfunctions
A Time-parallel Approach to Strong-constraint Four-dimensional Variational Data Assimilation
A parallel-in-time algorithm based on an augmented Lagrangian approach is
proposed to solve four-dimensional variational (4D-Var) data assimilation
problems. The assimilation window is divided into multiple sub-intervals that
allows to parallelize cost function and gradient computations. Solution
continuity equations across interval boundaries are added as constraints. The
augmented Lagrangian approach leads to a different formulation of the
variational data assimilation problem than weakly constrained 4D-Var. A
combination of serial and parallel 4D-Vars to increase performance is also
explored. The methodology is illustrated on data assimilation problems with
Lorenz-96 and the shallow water models.Comment: 22 Page
Robust data assimilation using and Huber norms
Data assimilation is the process to fuse information from priors,
observations of nature, and numerical models, in order to obtain best estimates
of the parameters or state of a physical system of interest. Presence of large
errors in some observational data, e.g., data collected from a faulty
instrument, negatively affect the quality of the overall assimilation results.
This work develops a systematic framework for robust data assimilation. The
new algorithms continue to produce good analyses in the presence of observation
outliers. The approach is based on replacing the traditional \L_2 norm
formulation of data assimilation problems with formulations based on \L_1 and
Huber norms. Numerical experiments using the Lorenz-96 and the shallow water on
the sphere models illustrate how the new algorithms outperform traditional data
assimilation approaches in the presence of data outliers.Comment: 25 pages, Submitted to SIS
Numerical Linear Algebra in Data Assimilation
Data assimilation is a method that combines observations (that is, real world
data) of a state of a system with model output for that system in order to
improve the estimate of the state of the system and thereby the model output.
The model is usually represented by a discretised partial differential
equation. The data assimilation problem can be formulated as a large scale
Bayesian inverse problem. Based on this interpretation we will derive the most
important variational and sequential data assimilation approaches, in
particular three-dimensional and four-dimensional variational data assimilation
(3D-Var and 4D-Var) and the Kalman filter. We will then consider more advanced
methods which are extensions of the Kalman filter and variational data
assimilation and pay particular attention to their advantages and
disadvantages. The data assimilation problem usually results in a very large
optimisation problem and/or a very large linear system to solve (due to
inclusion of time and space dimensions). Therefore, the second part of this
article aims to review advances and challenges, in particular from the
numerical linear algebra perspective, within the various data assimilation
approaches.Comment: 31 pages, 2 figure