3 research outputs found
A Derivative-Free Trust Region Framework for Variational Data Assimilation
This study develops a hybrid ensemble-variational approach for solving data
assimilation problems. The method, called TR-4D-EnKF, is based on a trust
region framework and consists of three computational steps. First an ensemble
of model runs is propagated forward in time and snapshots of the state are
stored. Next, a sequence of basis vectors is built and a low-dimensional
representation of the data assimilation system is obtained by projecting the
model state onto the space spanned by the ensemble deviations from the mean.
Finally, the low-dimensional optimization problem is solved in the
reduced-space using a trust region approach; the size of the trust region is
updated according to the relative decrease of the reduced order surrogate cost
function. The analysis state is projected back onto the full space, and the
process is repeated with the current analysis serving as a new background. A
heuristic approach based on the trust region size is proposed in order to
adjust the background error statistics from one iteration to the next.
Experimental simulations are carried out using the Lorenz and the
quasi-geostrophic models. The results show that TR-4D-EnKF is an efficient
computational approach, and is more accurate than the current state of the art
4D-EnKF implementations such as the POD-4D-EnKF and the Iterative Subspace
Minimization methods
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