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Ensemble data assimilation methods such as the Ensemble Kalman Filter (EnKF) are a key component of probabilistic weather forecasting. They represent the uncertainty in the initial conditions by an ensemble which incorporates information…

Applications · Statistics 2018-10-17 Sylvain Robert , Daniel Leuenberger , Hans R. Künsch

The ensemble Kalman filter (EnKF) is a widely used methodology for state estimation in partial, noisily observed dynamical systems, and for parameter estimation in inverse problems. Despite its widespread use in the geophysical sciences,…

Numerical Analysis · Mathematics 2016-09-21 Claudia Schillings , Andrew M. Stuart

The stability properties of intermediate-order climate models are investigated by computing their Lyapunov exponents (LEs). The two models considered are PUMA (Portable University Model of the Atmosphere), a primitive-equation simple…

Atmospheric and Oceanic Physics · Physics 2018-06-07 Lesley De Cruz , Sebastian Schubert , Jonathan Demaeyer , Valerio Lucarini , Stéphane Vannitsem

The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations…

Probability · Mathematics 2015-06-17 D. T. B. Kelly , K. J. H. Law , A. M. Stuart

Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For…

Numerical Analysis · Mathematics 2020-08-26 Jana de Wiljes , Xin T. Tong

Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally, our limited knowledge of the underlying processes.…

Numerical Analysis · Mathematics 2017-07-21 Lun Yang , Akil Narayan , Peng Wang

Contemporary data assimilation often involves more than a million prediction variables. Ensemble Kalman filters (EnKF) have been developed by geoscientists. They are successful indispensable tools in science and engineering, because they…

Probability · Mathematics 2017-05-26 Andrew J. Majda , Xin T. Tong

This study considers the data assimilation problem in coupled systems, which consists of two components (sub-systems) interacting with each other through certain coupling terms. A straightforward way to tackle the assimilation problem in…

Atmospheric and Oceanic Physics · Physics 2015-06-22 Xiaodong Luo , Ibrahim Hoteit

Compared with linear time invariant systems, linear periodic system can describe the periodic processes arising from nature and engineering more precisely. However, the time-varying system parameters increase the difficulty of the research…

Signal Processing · Electrical Eng. & Systems 2023-03-16 Jiachen Qian , Zhisheng Duan , Peihu Duan , Zhongkui Li

Data assimilation plays a key role in large-scale atmospheric weather forecasting, where the state of the physical system is estimated from model outputs and observations, and is then used as initial condition to produce accurate future…

Methodology · Statistics 2018-02-13 Azam Moosavi , Ahmed Attia , Adrian Sandu

Data assimilation (DA) aims at optimally merging observational data and model outputs to create a coherent statistical and dynamical picture of the system under investigation. Indeed, DA aims at minimizing the effect of observational and…

Data Analysis, Statistics and Probability · Physics 2022-01-05 Yumeng Chen , Alberto Carrassi , Valerio Lucarini

Ensemble Kalman methods were initially developed to solve nonlinear data assimilation problems in oceanography, but are now popular in applications far beyond their original use cases. Of particular interest is climate model calibration. As…

Data Analysis, Statistics and Probability · Physics 2025-11-21 Rebecca Gjini , Matthias Morzfeld , Oliver R. A. Dunbar , Tapio Schneider

The accuracy of Earth system models is compromised by unknown and/or unresolved dynamics, making the quantification of systematic model errors essential. While a model parameter estimation, which allows parameters to change…

Methodology · Statistics 2023-10-04 Yohei Sawada , Le Duc

Accurate knowledge of time-variation in meridional flow-speed and profile is crucial for estimating a solar cycle's features, which are ultimately responsible for causing space climate variations. However, no consensus has been reached yet…

Solar and Stellar Astrophysics · Physics 2014-08-22 Mausumi Dikpati , Jeffrey L. Anderson , Dhrubaditya Mitra

The majority of data assimilation (DA) methods in the geosciences are based on Gaussian assumptions. While these assumptions facilitate efficient algorithms, they cause analysis biases and subsequent forecast degradations. Non-parametric,…

Methodology · Statistics 2025-05-12 Hristo G. Chipilski

Data assimilation techniques, such as ensemble Kalman filtering, have been shown to be a highly effective and efficient way to combine noisy data with a mathematical model to track and forecast dynamical systems. However, when dealing with…

Dynamical Systems · Mathematics 2023-05-17 Stephen A Falconer , David J. B. Lloyd , Naratip Santitissadeekorn

Working with a two-stage ice sheet model, we explore how statistical data assimilation methods can be used to improve predictions of glacier melt and relatedly, sea level rise. We find that the EnKF improves model runs initialized using…

Dynamical Systems · Mathematics 2023-05-23 Emily Corcoran , Logan Knudsen , Talea Mayo , Hannah Park-Kaufmann , Alexander Robel

Data assimilation (DA) methods combine model predictions with observational data to improve state estimation in dynamical systems, inspiring their increasingly prominent role in geophysical and climate applications. Classical DA methods…

Numerical Analysis · Mathematics 2025-10-23 Lizuo Liu , Tongtong Li , Anne Gelb

We explore the potential of three-dimensional data assimilation for assimilating sparsely-distributed 2-metre temperature observations across the coupled atmosphere-land interface into the soil moisture. Using idealised twin experiments…

Atmospheric and Oceanic Physics · Physics 2022-09-29 Tobias Finn , Gernot Geppert , Felix Ament

We examine the problem of time delay estimation, or temporal calibration, in the context of multisensor data fusion. Differences in processing intervals and other factors typically lead to a relative delay between measurement updates from…

Systems and Control · Electrical Eng. & Systems 2021-11-18 Jonathan Kelly , Christopher Grebe , Matthew Giamou