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.
16:30
Data assimilation for constructing stabilized POD models
Adrian Sandu | Virginia Tech | United States
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Authors:
Adrian Sandu | Virginia Tech | United States
Andrey A Popov | Virginia Tech | United States
Changhong Mou | Virginia Tech | United States
Traian Iliescu | Virginia Tech | United States
Reduced order modeling is the process of developing low-dimensional systems that capture the most important characteristics of a high-dimensional dynamical system. General techniques such as proper orthogonal decomposition (POD) can lead to reduced order models that do not inherit the stability or the physical conservation properties of the full order model. We present the construction of stabilized POD models where the stabilization terms are constructed via data assimilation algorithms.
17:00
Solving weak constraint variational data assimilation problems using a low-rank approach
Melina Freitag | University of Potsdam | Germany
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Authors:
Melina Freitag | University of Potsdam | Germany
Dan Green | University of Bath | United Kingdom
Weak constraint four-dimensional variational data assimilation is an
important method for incorporating data into a model. The system arising
within the minimisation process can be formulated as a saddle point
problem. In this talk, we present a low-rank approach which exploits the
structure of this system using techniques and theory from solving matrix
equations. Numerical experiments with the linear advection-diffusion
equation, and the nonlinear Lorenz-95 model demonstrate the
effectiveness of a low-rank Krylov subspace solver.
17:30
- CANCELED - Data Thinning Strategies for Global Assimilation of Large Number of Radio Occultation Profiles
Răzvan Ştefănescu | Spire Global, Inc. | United States
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Authors:
Răzvan Ştefănescu | Spire Global, Inc. | United States
Matthew Hei | Spire Global, Inc. | United States
Dusanka Zupanski | Spire Global, Inc. | United States
Vladimir Irisov | Spire Global, Inc. | United States
Paul Madden | Spire Global, Inc. | United States
Alexander MacDonald | Spire Global, Inc. | United States
Radio occultation observations provide a significant positive impact on weather forecast skills. Their use
in the data assimilation NWP systems also results in smaller and more accurate bias corrections in
infrared and microwave observations. The Radio Occultations are usually available in the form of
bending angle or refractivity profiles whereas the most popular observation operator follows the Abel
integral formulation. With an increased number of available radio occultation profiles, there is a need to
take into account observation errors correlations into the community GSI data assimilation system. This
study represents the first step towards this goal, and we are going to implement horizontal and vertical
thinning strategies based on unsupervised machine learning techniques and quantify their impact on the
quality of the forecasts of the global NOAA FIM model.
18:00
Model error covariance estimation using the Expectation-Maximization algorithm in sequential Monte Carlo and ensemble Kalman filters
Manuel Pulido | Universidad Nacional del Nordeste | Argentina
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Authors:
Manuel Pulido | Universidad Nacional del Nordeste | Argentina
Tadeo Javier Cocucci | Universidad Nacional del Nordeste | Argentina
Magdalena Lucini | Universidad Nacional del Nordeste | Argentina
A standard methodology to estimate model parameters from observations in data assimilation techniques is to augment the state space. This methodology presents an overall success when estimating deterministic physical parameters. The posterior density model error covariances or stochastic parameters posterior distribution within the augmented state approach collapses in both ensemble Kalman filters and particle filters. To overcome this, I will give an overview on a statistical learning method that combines the Expectation-Maximization (EM) algorithm with sequential Monte Carlo and ensemble Kalman filters to estimate statistical parameters that give the maximum of the observation likelihood given a set of observations. A batch EM algorithm and an online EM algorithm that work with particle filters are introduced. Both methods take approximations to avoid the need of smoothing, using the innovation likelihood in the former and neglecting the influence of current observations in the latter. Numerical experiments with the 40 variable Lorenz-96 system will be shown, in which the method is applied to infer model error covariances from noisy observations. The methods are able to converge using the perturbed observation ensemble Kalman filter and the variational mapping particle filter with good accuracy under moderate observational noise. The methods show promising results and ongoing work is focused on the extension of the methodology for very high-dimensional geophysical models