Multilevel ensemble Kalman filtering for spatially extended models

2016/08/30 by Alexey Chernov, Haakon Hoel, Chernov, Alexey +7
Computer Science · Earth and Planetary Sciences · Physics and Astronomy · #FOS: Mathematics #Meteorological Phenomena and Simulations #Numerical Analysis (math.NA) #Scientific Research and Discoveries #Target Tracking and Data Fusion in Sensor Networks

paper · pdf · doi:10.48550/arxiv.1608.08558

openalex publication_date 2016/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

This work embeds a multilevel Monte Carlo (MLMC) sampling strategy into the Monte Carlo step of the ensemble Kalman filter (EnKF), thereby yielding a multilevel ensemble Kalman filter (MLEnKF) which has provably superior asymptotic cost to a given accuracy level. The development of MLEnKF for finite-dimensional state-spaces in the work [20] is here extended to models with infinite-dimensional state- spaces in the form of spatial fields. A concrete example is given to illustrate the results.

Citations

• Data Assimilation: A Mathematical Introduction
• Forward and Inverse Uncertainty Quantification using Multilevel Monte Carlo Algorithms for an Elliptic Nonlocal Equation
• A Hierarchical Multilevel Markov Chain Monte Carlo Algorithm with Applications to Uncertainty Quantification in Subsurface Flow

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