9,966 research outputs found
Data Driven Computing by the Morphing Fast Fourier Transform Ensemble Kalman Filter in Epidemic Spread Simulations
The FFT EnKF data assimilation method is proposed and applied to a stochastic
cell simulation of an epidemic, based on the S-I-R spread model. The FFT EnKF
combines spatial statistics and ensemble filtering methodologies into a
localized and computationally inexpensive version of EnKF with a very small
ensemble, and it is further combined with the morphing EnKF to assimilate
changes in the position of the epidemic.Comment: 11 pages, 3 figures. Submitted to ICCS 201
Variational assimilation of Lagrangian data in oceanography
We consider the assimilation of Lagrangian data into a primitive equations
circulation model of the ocean at basin scale. The Lagrangian data are
positions of floats drifting at fixed depth. We aim at reconstructing the
four-dimensional space-time circulation of the ocean. This problem is solved
using the four-dimensional variational technique and the adjoint method. In
this problem the control vector is chosen as being the initial state of the
dynamical system. The observed variables, namely the positions of the floats,
are expressed as a function of the control vector via a nonlinear observation
operator. This method has been implemented and has the ability to reconstruct
the main patterns of the oceanic circulation. Moreover it is very robust with
respect to increase of time-sampling period of observations. We have run many
twin experiments in order to analyze the sensitivity of our method to the
number of floats, the time-sampling period and the vertical drift level. We
compare also the performances of the Lagrangian method to that of the classical
Eulerian one. Finally we study the impact of errors on observations.Comment: 31 page
Morphing Ensemble Kalman Filters
A new type of ensemble filter is proposed, which combines an ensemble Kalman
filter (EnKF) with the ideas of morphing and registration from image
processing. This results in filters suitable for nonlinear problems whose
solutions exhibit moving coherent features, such as thin interfaces in wildfire
modeling. The ensemble members are represented as the composition of one common
state with a spatial transformation, called registration mapping, plus a
residual. A fully automatic registration method is used that requires only
gridded data, so the features in the model state do not need to be identified
by the user. The morphing EnKF operates on a transformed state consisting of
the registration mapping and the residual. Essentially, the morphing EnKF uses
intermediate states obtained by morphing instead of linear combinations of the
states.Comment: 17 pages, 7 figures. Added DDDAS references to the introductio
Displacement Data Assimilation
We show that modifying a Bayesian data assimilation scheme by incorporating
kinematically-consistent displacement corrections produces a scheme that is
demonstrably better at estimating partially observed state vectors in a setting
where feature information important. While the displacement transformation is
not tied to any particular assimilation scheme, here we implement it within an
ensemble Kalman Filter and demonstrate its effectiveness in tracking
stochastically perturbed vortices.Comment: 26 Pages, 9 figures, 5 table
Optimal boundary conditions at the staircase-shaped coastlines
A 4D-Var data assimilation technique is applied to the rectangular-box
configuration of the NEMO in order to identify the optimal parametrization of
boundary conditions at lateral boundaries. The case of the staircase-shaped
coastlines is studied by rotating the model grid around the center of the box.
It is shown that, in some cases, the formulation of the boundary conditions at
the exact boundary leads to appearance of exponentially growing modes while
optimal boundary conditions allow to correct the errors induced by the
staircase-like appriximation of the coastline.Comment: Submitted to Ocean Dynamics. (27/02/2014
The Kalman-Levy filter
The Kalman filter combines forecasts and new observations to obtain an
estimation which is optimal in the sense of a minimum average quadratic error.
The Kalman filter has two main restrictions: (i) the dynamical system is
assumed linear and (ii) forecasting errors and observational noises are taken
Gaussian. Here, we offer an important generalization to the case where errors
and noises have heavy tail distributions such as power laws and L\'evy laws.
The main tool needed to solve this ``Kalman-L\'evy'' filter is the
``tail-covariance'' matrix which generalizes the covariance matrix in the case
where it is mathematically ill-defined (i.e. for power law tail exponents ). We present the general solution and discuss its properties on
pedagogical examples. The standard Kalman-Gaussian filter is recovered for the
case . The optimal Kalman-L\'evy filter is found to deviate
substantially fro the standard Kalman-Gaussian filter as deviates from 2.
As decreases, novel observations are assimilated with less and less
weight as a small exponent implies large errors with significant
probabilities. In terms of implementation, the price-to-pay associated with the
presence of heavy tail noise distributions is that the standard linear
formalism valid for the Gaussian case is transformed into a nonlinear matrice
equation for the Kalman-L\'evy filter. Direct numerical experiments in the
univariate case confirms our theoretical predictions.Comment: 41 pages, 9 figures, correction of errors in the general multivariate
cas
- …