Related papers: Deterministic treatment of model error in geophysi…

Data assimilation schemes are confronted with the presence of model errors arising from the imperfect description of atmospheric dynamics. These errors are usually modeled on the basis of simple assumptions such as bias, white noise, first…

This chapter provides various perspective on an important challenge in data assimilation: model error. While the overall goal is to understand the implication of model error of any type in data assimilation, we emphasize on the effect of…

Data assimilation plays a crucial role in numerical modeling, enabling the integration of real-world observations into mathematical models to enhance the accuracy and predictive capabilities of simulations. This approach is widely applied…

Using a dynamical model to make predictions about a system has many sources of error. These can include errors in how the model was initialised but also errors in the dynamics of the model itself. For many applications in data assimilation,…

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…

We commonly refer to state-estimation theory in geosciences as data assimilation. This term encompasses the entire sequence of operations that, starting from the observations of a system, and from additional statistical and dynamical…

A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…

Data assimilation refers to the problem of finding trajectories of a prescribed dynamical model in such a way that the output of the model (usually some function of the model states) follows a given time series of observations. Typically…

This paper contains the latest installment of the authors' project on developing ensemble based data assimilation methodology for high dimensional fluid dynamics models. The algorithm presented here is a particle filter that combines model…

Geological parameterization entails the representation of a geomodel using a small set of latent variables and a mapping from these variables to grid-block properties such as porosity and permeability. Parameterization is useful for data…

Ensemble data assimilation is a problem in determining the most likely phase space trajectory of a model of an observed dynamical sys- tem as it receives inputs from measurements passing information to the model. Using methods developed in…

Parametric prediction error methods constitute a classical approach to the identification of linear dynamic systems with excellent large-sample properties. A more recent regularized approach, inspired by machine learning and Bayesian…

Data assimilation is an iterative approach to the problem of estimating the state of a dynamical system using both current and past observations of the system together with a model for the system's time evolution. Rather than solving the…

The accuracy of simulation-based forecasting in chaotic systems is heavily dependent on high-quality estimates of the system state at the time the forecast is initialized. Data assimilation methods are used to infer these initial conditions…

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…

This tutorial provides a broad introduction to Bayesian data assimilation that will be useful to practitioners, in interpreting algorithms and results, and for theoretical studies developing novel schemes with an understanding of the rich…

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…

Numerical simulations of physical systems exhibit discrepancies arising from unmodeled physics and idealizations, as well as numerical approximation errors stemming from discretization and solver tolerances. This article reviews techniques…

An alternative data-driven modeling approach has been proposed and employed to gain fundamental insights into robot motion interaction with granular terrain at certain length scales. The approach is based on an integration of dimension…

We investigate model assessment and selection in a changing environment, by synthesizing datasets from both the current time period and historical epochs. To tackle unknown and potentially arbitrary temporal distribution shift, we develop…