59 research outputs found
Comparison of regularized ensemble Kalman filter and tempered ensemble transform particle filter for an elliptic inverse problem with uncertain boundary conditions
In this paper, we focus on parameter estimation for an elliptic inverse problem. We consider a 2D steady-state single- phase Darcy flow model, where permeability and boundary conditions are uncertain. Permeability is parameterized by the Karhunen-Loeve expansion and thus assumed to be Gaussian distributed. We employ two ensemble-based data assimilation methods: ensemble Kalman filter and ensemble transf
Parameter estimation for subsurface flow using ensemble data assimilation
Over the years, different data assimilation methods have been implemented to acquire improved estimations of model parameters by adjusting the uncertain parameter values in such a way that the mathematical model approximates the observed data as closely and consistently as possible. However, most of these methods are developed on the assumption of Gaussianity, e.g. Ensemble Kalman Filters, whic
Accounting for model error in Tempered Ensemble Transform Particle Filter and its application to non-additive model error
In this paper, we trivially extend Tempered (Localized) Ensemble Transform Particle Filter—T(L)ETPF—to account for model error. We examine T(L)ETPF performance for non-additive model error in a low-dimensional and a high-dimensional test problem. The former one is a nonlinear toy model, where uncertain parameters are non-Gaussian distributed but model error is Gaussian distributed. The latter one is
Statistical relevance of vorticity conservation with the Hamiltonian particle-mesh method
We conduct long-time simulations with a Hamiltonian particle-mesh method for ideal fluid flow, to determine the statistical mean vorticity field of the discretization. Lagrangian and Eulerian statistical models are proposed for the discrete dynamics, and these are compared against numerical experiments. The observed results are in excellent agreement with the theoretical models, as well as with the continuum statistical mechanical theory for ideal fluid flow developed by Ellis et al. (2002). In particular the results verify that the apparently trivial conservation of potential vorticity along particle paths within the HPM method significantly influences the mean state. As a side note, the numerical experiments show that a nonzero fourth moment of potential vorticity can influence the statistical mean
Statistical mechanics of Arakawa`s discretizations
The results of statistical analysis of simulation data obtained from long-time integrations of geophysical fluid models greatly depend on the conservation properties of the numerical discretization chosen. Statistical mechanical theories are constructed for three discretizations of the quasi-geostrophic model due to Arakawa (1966), each having different conservation properties. It is shown that the three statistical theories accurately explain the differences observed in statistics derived from the discretizations. The effect of the time discretization is also considered, and it is shown that projection is insufficient if the underlying spatial discretization is not conservative
Impact of the initialisation on the predictability of the Southern Ocean sea ice at interannual to multi-decadal timescales
In this study, we assess systematically the impact of different initialisation procedures on the predictability of the sea ice in the Southern Ocean. These initialisation strategies are based on three data assimilation methods: the nudging, the particle filter with sequential importance resampling and the nudging proposal particle filter. An Earth system model of intermediate complexity is used to perform hindcast simulations in a perfect model approach. The predictability of the Antarctic sea ice at interannual to multi-decadal timescales is estimated through two aspects: the spread of the hindcast ensemble, indicating the uncertainty of the ensemble, and the correlation between the ensemble mean and the pseudo-observations, used to assess the accuracy of the prediction. Our results show that at decadal timescales more sophisticated data assimilation methods as well as denser pseudo-observations used to initialise the hindcasts decrease the spread of the ensemble. However, our experiments did not clearly demonstrate that one of the initialisation methods systematically provides with a more accurate prediction of the sea ice in the Southern Ocean than the others. Overall, the predictability at interannual timescales is limited to 3 years ahead at most. At multi-decadal timescales, the trends in sea ice extent computed over the time period just after the initialisation are clearly better correlated between the hindcasts and the pseudo-observations if the initialisation takes into account the pseudo-observations. The correlation reaches values larger than 0.5 in winter. This high correlation has likely its origin in the slow evolution of the ocean ensured by its strong thermal inertia, showing the importance of the quality of the initialisation below the sea ice
Regularized shadowing-based data assimilation method for imperfect models and its comparison to the weak constraint 4DVar method
We consider a data assimilation problem for imperfect models. We propose a novel shadowing-based data assimilation method that takes model error into account following the Levenberg-Marquardt regularization approach. We illuminate how the proposed shadowing-based method is related to the weak constraint 4DVar method both analytically and numerically. We demonstrate that the shadowing-based method respects the distribution of the data mismatch, while the weak constraint 4DVar does not, which becomes even more pronou
Transform-based particle filtering for elliptic Bayesian inverse problems
We introduce optimal transport based resampling in adaptive SMC. We consider elliptic inverse problems of inferring hydraulic conductivity from pressure measurements. We consider two parametrizations of hydraulic conductivity: by Gaussian random field, and by a set of scalar (non-)Gaussian distributed parameters and Gaussian random fields. We show that for scalar parameters optimal transport based SMC performs comparably to monomial based SMC but for Gaussian high- dimensional random fields optimal transport based SMC outperforms monomial based SMC. When comparing to ensemble Kalman inversion with mutation (EKI), we observe that for Gaussian random fields, optimal transport based SMC gives comparable or worse performance than EKI depending on the complexity of the parametrization. For non-Gaussian distributed parameters optimal transport based SMC outperforms EKI
Application of ensemble transform data assimilation methods for parameter estimation in reservoir modeling
Over the years data assimilation methods have been developed to
obtain estimations of uncertain model parameters by taking into account a few
observations of a model state. The most reliable Markov chain Monte Carlo
(MCMC) methods are computationally expensive. Sequential ensemble methods
such as ensemble Kalman filters and particle filters provide a favorable
alternative. However, ensemble Kalman filter has an assumption of
Gaussianity. Ensemble transform particle filter does not have this assumption
and has proven to be highly beneficial for an initial condition estimation
and a small number of parameter estimations in chaotic dynamical systems with
non-Gaussian distributions. In this paper we employ ensemble transform
particle filter (ETPF) and ensemble transform Kalman filter (ETKF) for
parameter estimation in nonlinear problems with 1, 5, and 2500 uncertain
parameters and compare them to importance sampling (IS). The large number of
uncertain parameters is of particular interest for subsurface reservoir
modeling as it allows us to parameterize permeability on the grid. We prove
that the updated parameters obtained by ETPF lie within the range of an
initial ensemble, which is not the case for ETKF. We examine the performance
of ETPF and ETKF in a twin experiment setup, where observations of pressure
are synthetically created based on the known values of parameters. For a
small number of uncertain parameters (one and five) ETPF performs comparably
to ETKF in terms of the mean estimation. For a large number of uncertain
parameters (2500) ETKF is robust with respect to the initial ensemble, while
ETPF is sensitive due to sampling error. Moreover, for the high-dimensional
test problem ETPF gives an increase in the root mean square error after data
assimilation is performed. This is resolved by applying distance-based
localization, which however deteriorates a posterior estimation of the
leading mode by largely increasing the variance due to a combination of less
varying localized weights, not keeping the imposed bounds on the modes via
the Karhunen–Loeve expansion, and the main variability explained by the
leading mode. A possible remedy is instead of applying localization to use
only leading modes that are well estimated by ETPF, which demands knowledge
of which mode to truncate.</p
Investigating the consistency between proxy-based reconstructions and climate models using data assimilation: a mid-Holocene case study
The mid-Holocene (6 kyr BP; thousand years before present) is a key period to study the consistency between model results and proxy-based reconstruction data as it corresponds to a standard test for models and a reasonable number of proxy-based records is available. Taking advantage of this relatively large amount of information, we have compared a compilation of 50 air and sea surface temperature reconstructions with the results of three simulations performed with general circulation models and one carried out with LOVECLIM, a model of intermediate complexity. The conclusions derived from this analysis confirm that models and data agree on the large-scale spatial pattern but the models underestimate the magnitude of some observed changes and that large discrepancies are observed at the local scale. To further investigate the origin of those inconsistencies, we have constrained LOVECLIM to follow the signal recorded by the proxies selected in the compilation using a data-assimilation method based on a particle filter. In one simulation, all the 50 proxy-based records are used while in the other two only the continental or oceanic proxy-based records constrain the model results. As expected, data assimilation leads to improving the consistency between model results and the reconstructions. In particular, this is achieved in a robust way in all the experiments through a strengthening of the westerlies at midlatitude that warms up northern Europe. Furthermore, the comparison of the LOVECLIM simulations with and without data assimilation has also objectively identified 16 proxy-based paleoclimate records whose reconstructed signal is either incompatible with the signal recorded by some other proxy-based records or with model physics
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