State-of-the-art stochastic data assimilation methods for
                        high-dimensional non-Gaussian problems

Vetra-Carvalho, Sanita; Leeuwen, Peter Jan van; Nerger, Lars; Barth, Alexander; Altaf, Muhammad Umer; Brasseur, Pierre; Kirchgessner, Paul; Beckers, Jean-Marie

doi:10.1080/16000870.2018.1445364

Cited by 85 publications

(81 citation statements)

References 111 publications

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“…Because this transition occurs on horizontal dimensions that are smaller than the typical grid size of large-scale ice sheet models, many studies have focussed on the ability of the numerical model to properly simulate grounding line migration using synthetic experiments (e.g. Vieli and Payne, 2005;Durand et al, 2009;Gladstone et al, 2012;Seroussi et al, 2014). Two Marine Ice Sheet Model Intercomparison Projects (MISMIP) have allowed the identification of the minimum requirements to properly resolve GL motion: (i) inclusion of membrane stresses and (ii) a sufficiently small grid size or a subgrid interpolation of the GL (Pattyn et al, 2012(Pattyn et al, , 2013.…”

Section: Introductionmentioning

confidence: 99%

Assimilation of surface observations in a transient marine ice sheet model using an ensemble Kalman filter

Gillet-Chaulet

2020

The Cryosphere

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Abstract. Marine-based sectors of the Antarctic Ice Sheet are increasingly contributing to sea level rise. The basal conditions exert an important control on the ice dynamics and can be propitious to instabilities in the grounding line position. Because the force balance is non-inertial, most ice flow models are now equipped with time-independent inverse methods to constrain the basal conditions from observed surface velocities. However, transient simulations starting from this initial state usually suffer from inconsistencies and are not able to reproduce observed trends. Here, using a synthetic flow line experiment, we assess the performance of an ensemble Kalman filter for the assimilation of transient observations of surface elevation and velocities in a marine ice sheet model. The model solves the shallow shelf equation for the force balance and the continuity equation for ice thickness evolution. The position of the grounding line is determined by the floatation criterion. The filter analysis estimates both the state of the model, represented by the surface elevation, and the basal conditions, with the simultaneous inversion of the basal friction and topography. The idealised experiment reproduces a marine ice sheet that is in the early stage of an unstable retreat. Using observation frequencies and uncertainties consistent with current observing systems, we find that the filter allows the accurate recovery of both the basal friction and topography after few assimilation cycles with relatively small ensemble sizes. In addition it is found that assimilating the surface observations has a positive impact on constraining the evolution of the grounding line during the assimilation window. Using the initialised state to perform century-scale forecast simulations, we show that grounding line retreat rates are in agreement with the reference; however remaining uncertainties in the basal conditions may lead to significant delays in the initiation of the unstable retreat. These results are encouraging for the application to real glacial systems.

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Section: Introductionmentioning

confidence: 99%

Assimilation of surface observations in a transient marine ice sheet model using an ensemble Kalman filter

Gillet-Chaulet

2020

The Cryosphere

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“…For the SMC, we use an optimal particle filter, which takes advantage of the linear Gaussian observation model and the Gaussian transition density of the state variables in our current SEBM. More generally, when the observation model is nonlinear and the transition density is non Gaussian, the optimal particle filter can be replaced by implicit particle filters [12,35] or local particle filters [38,39]; we refer to [8,25,49] for other data assimilation techniques. The details of the algorithm are provided in Section 7.3.…”

Section: Sampling the Posterior By Particle Mcmc Methodsmentioning

confidence: 99%

“…When the true parameters are known, the Bayesian approach has demonstrated great success in state estimation, thanks to the developments in Monte Carlo sampling and data assimilation techniques (see e.g. [8,25,49]). However, the problem of joint state-parameter estimation, especially when the parameter estimation is ill-posed, has had relatively little success in nonlinear cases and remains a challenge [23].…”

Section: Introductionmentioning

confidence: 99%

Response to the second referee

Lu¹

2019

Preprint

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While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter estimation. To overcome the challenges, we introduce a strongly regularized posterior by normalizing the likelihood and by imposing physical constraints through priors of the parameters and states.We investigate joint parameter-state estimation by the regularized posterior in a physically motivated nonlinear stochastic energy balance model (SEBM) for paleoclimate reconstruction. The highdimensional posterior is sampled by a particle Gibbs sampler that combines MCMC with an optimal particle filter exploiting the structure of the SEBM. In tests using either Gaussian or uniform priors based on the physical range of parameters, the regularized posteriors overcome the ill-posedness and lead to samples within physical ranges, quantifying the uncertainty in estimation. Due to the ill-posedness and the regularization, the posterior of parameters presents a relatively large uncertainty, and consequently, the maximum of the posterior, which is the minimizer in a variational approach, can have a large variation. In contrast, the posterior of states generally concentrates near the truth, substantially filtering out observation noise and reducing uncertainty in the unconstrained SEBM.

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“…The general formulation (101) with the coefficients p * ij chosen appropriately 2 leads to a large class of socalled ensemble transform particle filters (Reich and Cotter 2015). Ensemble transform particle filters generally result in biased and inconsistent but robust estimates which have found applications to high-dimensional state space models (Evensen 2006, Vetra-Carvalho, van Leeuwen, Nerger, Barth, Altaf, Brasseur, Kirchgessner andBeckers 2018) for which traditional particle filters fail due to the 'curse of dimensionality' (Bengtsson, Bickel and Li 2008). More specifically, the class of ensemble transform particle filters includes the popular ensemble Kalman filters (Evensen 2006, Reich and Cotter 2015, Vetra-Carvalho et al 2018, Carrassi, Bocquet, Bertino and Evensen 2018 and so-called second-order accurate particle filters with coefficients p * ij in (101) chosen such that the weighted ensemble meanz…”

Section: Filteringmentioning

confidence: 99%

Data assimilation: The Schrödinger perspective

Reich

2019

Acta Numerica

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Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using probabilistic particle-based algorithms. In addition to surveying recent developments for discrete-and continuous-time data assimilation, both in terms of mathematical foundations and algorithmic implementations, we also provide a unifying framework from the perspective of coupling of measures, and Schrödinger's boundary value problem for stochastic processes in particular.

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State-of-the-art stochastic data assimilation methods for high-dimensional non-Gaussian problems

Cited by 85 publications

References 111 publications

Assimilation of surface observations in a transient marine ice sheet model using an ensemble Kalman filter

Assimilation of surface observations in a transient marine ice sheet model using an ensemble Kalman filter

Response to the second referee

Data assimilation: The Schrödinger perspective

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