Data assimilation in Earth system models combines high-dimensional, coupled, nonlinear models with large volumes of in situ and remotely sensed observational data. The dynamics and observations are nonlinear, the distributions are non-Gaussian, and the cost of simulation is high. The goal of the minisymposium is to provide a forum for this diverse group to discuss and share ideas for advancing the science of DA in climate modeling or any of its components (e.g. atmosphere, ocean, ice sheets, land models, or sea ice). Topics of interest include coupled data assimilation; strategies for estimating and mitigating model errors; strategies for addressing strong nonlinearities and non-Gaussianity; multiscale, multilevel, or multifidelity methods; and machine learning methods for data assimilation.
08:30
Implicitly localized MCMC sampler to cope with nonlocal/nonlinear data constraints in large-size inverse problems
Jean-Michel Brankart | Universite Grenoble Alpes | France
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Jean-Michel Brankart | Universite Grenoble Alpes | France
Many practical applications involve the resolution of large-size inverse problems, without providing more than a moderate-size sample to describe the prior probability distribution. In this situation, additional information must be supplied to augment the effective dimension of the available sample, for instance using a covariance localization approach. In this study, it is suggested that covariance localization can be efficiently applied to an approximate variant of the Metropolis/Hastings algorithm, by modulating the ensemble members by the large-scale patterns of other members. Modulation is used to design a (global) proposal probability distribution (i) that can be sampled at a very low cost, (ii) that automatically accounts for a localized prior covariance, and (iii) that leads to an efficient sampler for the augmented prior probability distribution or for the posterior probability distribution. The resulting algorithm is applied to an academic example, illustrating (i) the effectiveness of covariance localization, (ii) the ability of the method to deal with nonlocal/nonlinear observation operators and non-Gaussian observation errors, (iii) the reliability, resolution and optimality of the updated ensemble, using probabilistic scores appropriate to a non-Gaussian posterior distribution, and (iv) the scalability of the algorithm as a function of the size of the problem. The codes are openly available from github.com/brankart/ensdam.
09:00
Bayesian inversion using a variational approach
Andreas Stordal | NORCE | Norway
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Andreas Stordal | NORCE | Norway
Sampling from a posterior density is challenging in high dimensions and complex systems where the likelihood is often only available numerically, and the computational resources are limited. In the Bayesian framework, sampling the posterior can be seen as an optimal transport problem. In this context I will present a variational gradient descent algorithm, known as Stein Variational Gradient Descent (SVGD) which is defined a kernel reproducing Hilbert space.
The implementation of SVGD with and without an adjoint code will be presented, as well as a discussion on the choice of the kernel reproducing Hilbert space. Examples from reservoir characterization will be given.
09:30
- CANCELED - Parametric Bayesian estimation of point-like pollution sources of groundwater layers
Boujemaa Ait-El-Fquih | King Abdullah University of Science and Technology (KAUST) | Saudi Arabia
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Boujemaa Ait-El-Fquih | King Abdullah University of Science and Technology (KAUST) | Saudi Arabia
Jean-François Giovannelli | IMS (Univ. Bordeaux, CNRS, Bordeaux INP) | France
Nicolas Paul | Électricité de France (EDF) | France
Alexandre Girard | Électricité de France (EDF) | France
Ibrahim Hoteit | King Abdullah University of Science and Technology (KAUST) | Saudi Arabia
This talk is devoted to the estimation of point-like pollution sources of groundwater layers. To cope with the ill-posed character of this problem, a parametric Bayesian framework has been recently established. In this framework, where the priors for the source parameters are either uniform or Gaussian and the observation noise is homogeneous, a stochastic Markov Chain Monte Carlo (MCMC) algorithm has been proposed to compute the posterior distribution of both source parameters and noise variance. Here, we consider a more general model with truncated-Gaussian priors for pollution quantity and spreading time parameter, which gathers advantages of uniform and Gaussian choices, and an inhomogeneous noise, which accounts for the spatial diversity among sensors. For this model, we extend the existing stochastic algorithm, then propose a concurrent deterministic algorithm based on the variational Bayesian (VB) approach. This approach designs an approximation of the posterior law based on a separable from. The proposed MCMC and VB algorithms target the exact posterior and the approximated posterior, respectively. It is further shown that the former is more accurate, while the latter is computationally more efficient. Results of numerical experiments conducted using an experimental platform to compare the performances of the proposed schemes will be presented.
10:00
- CANCELED - Developing data assimilation algorithms for the analysis and prediction of geophysical flows across many scales
Yue (Michael) Ying | National Center for Atmospheric Research | United States
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Yue (Michael) Ying | National Center for Atmospheric Research | United States
One of the biggest scientific challenges of our time is the accurate prediction of geophysical flows across many scales. Data assimilation plays an important role in furthering the understanding of these dynamical systems by combining the knowledge from observations and model forecasts. For a multiscale system, smaller scales feature more rapid and nonlinear error growth, which causes suboptimal performance for methods based on linearization such as the ensemble Kalman filter. High dimensionality of a multiscale system also limits the efficient use of nonlinear methods such as the particle filter. In this seminar talk, I will introduce a multiscale ensemble data assimilation method designed to crack these problems. The method is based on the idea of finding solution incrementally from large to small scales in an iterative manner, which is inspired by the computer vision literature. Consider when nonlinearity at small scales gives rise to position/timing errors of coherent features in the model state, the multiscale method performs data assimilation in large scale first, taking advantage of the fact that larger scales are more linear, and then utilize the analysis increments at larger scales to reduce the position errors (nonlinearity) at smaller scales. As a proof of concept, the multiscale method is tested with a quasi-geostrophic model. I will discuss the future development of multiscale methodology and its potential application to solving Earth-system prediction problems.