1,382 research outputs found
Reduced-order 4D-Var: a preconditioner for the Incremental 4D-Var data assimilation method
This study demonstrates how the incremental 4D-Var data assimilation method
can be applied efficiently preconditione d in an application to an
oceanographic problem. The approach consists in performing a few iterations of
the reduced-order 4D-Var prior to the incremental 4D-Var in the full space in
order to achieve faster convergence. An application performed in the tropical
Pacific Ocean, with assimilation of TAO temperature data, shows the method to
be both feasible and efficient. It allows the global cost of the assimilation
to be reduced by a factor of 2 without affecting the quality of the solution
A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilation
The effect of preconditioning linear weighted least-squares using an
approximation of the model matrix is analyzed, showing the interplay of the
eigenstructures of both the model and weighting matrices. A small example is
given illustrating the resulting potential inefficiency of such
preconditioners. Consequences of these results in the context of the
weakly-constrained 4D-Var data assimilation problem are finally discussed.Comment: 10 pages, 2 figure
A Practical Method to Estimate Information Content in the Context of 4D-Var Data Assimilation. II: Application to Global Ozone Assimilation
Data assimilation obtains improved estimates of the state of a physical system by combining imperfect
model results with sparse and noisy observations of reality. Not all observations used in data assimilation
are equally valuable. The ability to characterize the usefulness of different data points is important
for analyzing the effectiveness of the assimilation system, for data pruning, and for the design of future
sensor systems.
In the companion paper (Sandu et al., 2012) we derive an ensemble-based computational procedure
to estimate the information content of various observations in the context of 4D-Var. Here we apply
this methodology to quantify the signal and degrees of freedom for signal information metrics of satellite observations used in a global chemical data assimilation problem with the GEOS-Chem chemical
transport model. The assimilation of a subset of data points characterized by the highest information
content yields an analysis comparable in quality with the one obtained using the entire data set
Estimating model evidence using data assimilation
We review the field of data assimilation (DA) from a Bayesian perspective and show that, in addition to its by now common application to state estimation, DA may be used for model selection. An important special case of the latter is the discrimination between a factual modelâwhich corresponds, to the best of the modeller's knowledge, to the situation in the actual world in which a sequence of events has occurredâand a counterfactual model, in which a particular forcing or process might be absent or just quantitatively different from the actual world. Three different ensembleâDA methods are reviewed for this purpose: the ensemble Kalman filter (EnKF), the ensemble fourâdimensional variational smoother (Enâ4DâVar), and the iterative ensemble Kalman smoother (IEnKS). An original contextual formulation of model evidence (CME) is introduced. It is shown how to apply these three methods to compute CME, using the approximated timeâdependent probability distribution functions (pdfs) each of them provide in the process of state estimation. The theoretical formulae so derived are applied to two simplified nonlinear and chaotic models: (i) the Lorenz threeâvariable convection model (L63), and (ii) the Lorenz 40âvariable midlatitude atmospheric dynamics model (L95). The numerical results of these three DAâbased methods and those of an integration based on importance sampling are compared. It is found that better CME estimates are obtained by using DA, and the IEnKS method appears to be best among the DA methods. Differences among the performance of the three DAâbased methods are discussed as a function of model properties. Finally, the methodology is implemented for parameter estimation and for event attribution
A reduced-order strategy for 4D-Var data assimilation
This paper presents a reduced-order approach for four-dimensional variational
data assimilation, based on a prior EO F analysis of a model trajectory. This
method implies two main advantages: a natural model-based definition of a mul
tivariate background error covariance matrix , and an important
decrease of the computational burden o f the method, due to the drastic
reduction of the dimension of the control space. % An illustration of the
feasibility and the effectiveness of this method is given in the academic
framework of twin experiments for a model of the equatorial Pacific ocean. It
is shown that the multivariate aspect of brings additional
information which substantially improves the identification procedure. Moreover
the computational cost can be decreased by one order of magnitude with regard
to the full-space 4D-Var method
- âŠ