Ruzayqat, Hamza;
Beskos, Alexandros;
Crisan, Dan;
Jasra, Ajay;
Kantas, Nikolas;
(2024)
Sequential Markov Chain Monte Carlo for Lagrangian Data Assimilation with Applications to Unknown Data Locations.
Quarterly Journal of the Royal Meteorological Society
10.1002/qj.4716.
(In press).
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Abstract
We consider a class of high-dimensional spatial filtering problems, where the spatial locations of observations are unknown and driven by the partially observed hidden signal. This problem is exceptionally challenging, as not only is it high-dimensional, but the model for the signal yields longer-range time dependences through the observation locations. Motivated by this model, we revisit a lesser-known and provably convergent computational methodology from Berzuini et al. (1997, Journal of the American Statistical Association, 92, 1403–1412); Centanniand Minozzo (2006, Journal of the American Statistical Association, 101, 1582–1597); Martin et al. (2013, Annals of the Institute of Statistical Mathematics, 65, 413–437) that uses sequential Markov Chain Monte Carlo (MCMC) chains. We extend this methodology for data filtering problems with unknown observation locations. We benchmark our algorithms on linear Gaussian state-space models against competing ensemble methods and demonstrate a significant improvement in both execution speed and accuracy. Finally, we implement a realistic case study on a high-dimensional rotating shallow-water model (of about 104–105 dimensions) with real and synthetic data. The data are provided by the National Oceanic and Atmospheric Administration (NOAA) and contain observations from ocean drifters in a domain of the Atlantic Ocean restricted to the longitude and latitude intervals [−51◦,−41◦], [17◦, 27◦], respectively.
| Type: | Article |
|---|---|
| Title: | Sequential Markov Chain Monte Carlo for Lagrangian Data Assimilation with Applications to Unknown Data Locations |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1002/qj.4716 |
| Publisher version: | https://doi.org/10.1002/qj.4716 |
| Language: | English |
| Additional information: | Copyright © 2024 The Authors. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. |
| Keywords: | high-dimensional filtering, Markov chain Monte Carlo, spatial filtering |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10188563 |
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