Accuracy is always at odds with efficiency in the context of Data Assimilation on complex dynamical system. Such systems often involve large amounts of variables, with impactful non-linearities, and poorly understood stochastic behaviour. Tackling these problems in an efficient manner is the key to unlocking the next generation of algorithms. The discussion of directions such as exploiting the time-dependent structure of natural systems, reduced order modeling, accounting for model error, and efficient ways to solve the underlying optimization problem, are just some of the topics of fundamental importance in the next few years of research, that will be covered.
14:00
Data-driven Reduced Order Model Control Variates in a Multilevel Ensemble Kalman Filter
Andrey A Popov | Virginia Tech | United States
Show details
Authors:
Andrey A Popov | Virginia Tech | United States
Changhong Mou | Virginia Tech | United States
Traian Iliescu | Virginia Tech | United States
Adrian Sandu | Virginia Tech | United States
The use of lower cost models with no loss of accuracy is appealing. In the context of large-scale dynamical systems, POD models have proven to be of great usefulness in the understanding of dominant linear dynamics. Their use in an online context, however has been limited by their poor long-term predictive behaviour. We aim to lift this barrier by using the reduced order model as acting on a control variate, thus exploiting the power of their short-term feature predictions, while relying on a full space model for the majority of the heavy lifting and stabilization. We apply this idea to a multilevel EnKF, and test on a Quasi-Geostrophic model to show greater accuracy and stability of the method.
14:30
Model error with time-autocorrelation and its effect in data assimilation
Javier Amezcua | University of Reading | United Kingdom
Show details
Authors:
Javier Amezcua | University of Reading | United Kingdom
Haonan Ren | University of Reading | United Kingdom
Peter Jan van Leeuwen | Colorado State | United States
The data assimilation problem is quickly moving into a weak-constraint scenario, i.e. allowing for imperfections in the model (not only initial conditions and observations). The weak-constraint formulation allows for the explicit treatment of model error, which can come from many sources: the discretisation in time and space, the lack of understanding of some processes, the inability to represent all scales of a system, and the mismatch in resolution of model and observations. A common practice is to assume the model error to have no auto-correlation in time. In this talk we illustrate how scale interaction can lead to model error with a non-trivial structure in time. We also discuss the consequences of time-auto-correlated model error in the data assimilation process.
15:00
- NEW - A Data-Driven Localization Method for Ensemble Based Data Assimilation
Elias D. Nino-Ruiz | Universidad del Norte | Colombia
Show details
Authors:
Luis Guzman-Reyes | Universidad del Norte | Colombia
Elias D. Nino-Ruiz | Universidad del Norte | Colombia
Daladier Jabba-Molinares | Universidad del Norte | Colombia
In this paper, we propose a dynamic localization method for ensemble-based data assimilation via a modified Cholesky decomposition. The method exploits the information brought by ensemble members to estimate optimal radius lengths of model components. This estimation process is performed by using Bayes' Theorem; our prior beliefs and likelihood functions are modeled via Gamma distributions: in priors, hyper-parameters are fixed based on our prior knowledge of error dynamics while to build likelihood functions, model parameters are fitted with empirical statistics from background ensembles at assimilation steps. Once the optimal radius lengths are estimated, a modified Cholesky decomposition is employed to estimate precision covariances of background error distributions. The assimilation process is then performed similarly to that of the EnKF based on a modified Cholesky decomposition (EnKF-MC). Experimental tests are performed by using the Lorenz-96 model. To compare our results, we employ an EnKF-MC implementation with different structures of background error correlations. In terms of $\ell_2$-norm of errors, the proposed filter implementation can outperform the EnKF-MC method for fixed radius lengths across all model components, and even more, different hyper-parameters can be tried in our filter formulation without degrading its convergence.
15:30
Ensemble methods for nonparametric drift estimation and model selection
Paul J. Rozdeba | University of Potsdam | Germany
Show details
Authors:
Paul J. Rozdeba | University of Potsdam | Germany
Nikolas Nüsken | University of Potsdam | Germany
Sebastian Reich | University of Potsdam | Germany
One faces the significant challenge of making predictions in the face of model error
in a wide variety of scientific problems. For example, unresolved physical contributions to a
dynamical model with random forcing, such as those encountered in atmospheric dynamics,
may lead to a misspecification of the model drift function which must be estimated from
observations. In this context, nonparametric methods of statistics treat these as unknown
parameters that are elements of function spaces. In the Bayesian framework they are viewed
as stochastic processes conditioned on data, and posterior inference becomes a task of
infinite-dimensional parameter estimation, resulting in high-dimensional computational
problems. I will discuss the application of particle-based filtering methods of data assimilation
(DA) to nonparametric drift estimation, motivated by the success of algorithms such as the
ensemble Kalman filter (EnKF) in high-dimensional systems, as well as developments in
nonlinear filters that share a similar feedback-control structure. A modified EnKF for
simultaneous state and drift estimation in the presence of observation noise, leading to non-
Gaussian posterior distributions, is derived and shown to be robust to the presence of noise. I
will also discuss aspects of posterior consistency and contraction under ensemble
approximations and DA methods such as localization and inflation, as well as model selection
which is of critical concern in nonparametric estimation.