{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/impact-of-non-stationarity-on-hybrid-ensemble","title":"Impact of non-stationarity on hybrid ensemble filters: A study with a doubly stochastic advection-diffusion-decay model","arxiv_id":"1708.08794","date":"2017-08-29","proceeding":null,"authors":["Michael Tsyrulnikov","Alexander Rakitko"],"abstract":"Effects of non-stationarity on the performance of hybrid ensemble filters are studied (by hybrid filters we mean those which blend ensemble covariances with some other regularizing covariances). To isolate effects of non-stationarity from effects due to nonlinearity (and the non-Gaussianity it causes), a new doubly stochastic advection-diffusion-decay model (DSADM) is proposed. The model is hierarchical: it is a linear stochastic partial differential equation whose coefficients are random fields defined through their own stochastic partial differential equations. DSADM generates conditionally Gaussian spatiotemporal random fields with a tunable degree of non-stationarity in space and time. DSADM allows the use of the exact Kalman filter as a baseline benchmark. In numerical experiments with DSADM as the \"model of truth\", the relative importance of the three kinds of covariance blending is studied: with static, time-smoothed, and space-smoothed covariances. It is shown that the stronger the non-stationarity, the less useful the static covariance matrix becomes and the more beneficial the time-smoothed covariances are. Time-smoothing of background-error covariances proved to be systematically more useful than their space-smoothing. Under non-stationarity, a filter that extends the (previously proposed by the authors) Hierarchical Bayes Ensemble Filter and accommodates the three covariance-blending techniques is shown to outperform all other configurations of the filters tested. The R code of the model and the filters is available from github.com/cyrulnic/NoStRa.","url_abs":"http://arxiv.org/abs/1708.08794v3","url_pdf":"http://arxiv.org/pdf/1708.08794v3.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"impact-of-non-stationarity-on-hybrid-ensemble","repo_url":"https://github.com/cyrulnic/NoStRa","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}