Related papers: On Variational Data Assimilation in Continuous Tim…

Data assimilation method consists in combining all available pieces of information about a system to obtain optimal estimates of initial states. The different sources of information are weighted according to their accuracy by the means of…

This paper focuses on continuous data assimilation (CDA) for the Navier-Stokes equations with nonlinear slip boundary conditions. CDA methods are typically employed to recover the original system when initial data or viscosity coefficients…

Data assimilation is a central problem in many geophysical applications, such as weather forecasting. It aims to estimate the state of a potentially large system, such as the atmosphere, from sparse observations, supplemented by prior…

Data assimilation addresses the general problem of how to combine model-based predictions with partial and noisy observations of the process in an optimal manner. This survey focuses on sequential data assimilation techniques using…

Data assimilation addresses the problem of identifying plausible state trajectories of dynamical systems given noisy or incomplete observations. In geosciences, it presents challenges due to the high-dimensionality of geophysical dynamical…

Data assimilation, in its most comprehensive form, addresses the Bayesian inverse problem of identifying plausible state trajectories that explain noisy or incomplete observations of stochastic dynamical systems. Various approaches have…

Variational data assimilation technique applied to identification of optimal approximations of derivatives near boundary is discussed in frames of one-dimensional wave equation. Simplicity of the equation and of its numerical scheme allows…

The four-dimensional variational data assimilation (4D-Var) has emerged as an important methodology, widely used in numerical weather prediction, oceanographic modeling, and climate forecasting. Classical unconstrained gradient-based…

Model errors are increasingly seen as a fundamental performance limiter in both Numerical Weather Prediction and Climate Prediction simulations run with state of the art Earth system digital twins.This has motivated recent efforts aimed at…

In this paper, the Ensemble Kalman Filter is compared with a 4DVAR Data Assimilation System in chaotic dynamics. The Lorenz model is chosen for its simplicity in structure and its dynamical similarities with primitive equation models, such…

Data Assimilation is the process in which we improve the representation of the state of a physical system by combining information coming from a numerical model, real-world observations, and some prior modelling. It is widely used to model…

We provide a clear and concise introduction to the subjects of inverse problems and data assimilation, and their inter-relations. The first part of our notes covers inverse problems; this refers to the study of how to estimate unknown model…

In data assimilation, the model may be subject to uncertainties and errors. The weak-constraint data assimilation framework enables incorporating model uncertainty in the dynamics of the governing equations. We propose a new framework for…

Data assimilation aims to estimate the states of a dynamical system by optimally combining sparse and noisy observations of the physical system with uncertain forecasts produced by a computational model. The states of many dynamical systems…

We prove consistence, convergence and stability of the Domain Decomposition in space and time method of 4DVAR Data Assimilation problem. We introduce the condition number of the problem and validate the theoretical analysis through…

An intrinsic property of almost any physical measuring device is that it makes observations which are slightly blurred in time. We consider a nudging-based approach for data assimilation that constructs an approximate solution based on a…

In this paper, numerical analysis is carried out for a class of history-dependent variational-hemivariational inequalities arising in contact problems. Three different numerical treatments for temporal discretization are proposed to…

This study demonstrates how the incremental 4D-Var data assimilation method can be applied efficiently preconditione d in an application to an oceanographic problem. The approach consists in performing a few iterations of the reduced-order…

Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…

Data assimilation (DA) is widely used to combine physical knowledge and observations. It is nowadays commonly used in geosciences to perform parametric calibration. In a context of climate change, old calibrations can not necessarily be…