Related papers: A cheap data assimilation approach for expensive n…

Continuous data assimilation addresses time-dependent problems with unknown initial conditions by incorporating observations of the solution into a nudging term. For the prototypical heat equation with variable conductivity and the Neumann…

In this article, we prove that data assimilation by feedback nudging can be achieved for the three-dimensional quasi-geostrophic equation in a simplified scenario using only large spatial scale observables on the dynamical boundary. On this…

The large underlying assumption of climate models today relies on the basis of a "confident" initial condition, a reasonably plausible snapshot of the Earth for which all future predictions depend on. However, given the inherently chaotic…

This chapter describes a novel approach for the treatment of model error in geophysical data assimilation. In this method, model error is treated as a deterministic process fully correlated in time. This allows for the derivation of the…

Shallow water equations are extensively considered in the domains of oceans, atmospheric modelling, and engineering research (Franca et al., 2022), which play significant roles in floods and tsunami governance. Nonetheless, the accurate…

Complex nonlinear turbulent dynamical systems are ubiquitous in many areas. Recovering unobserved state variables is an important topic for the data assimilation of turbulent systems. In this article, an efficient continuous in time data…

This paper introduces a method for spatial interpolation of extreme values, and in particular targets the case in which conventional data, resulting from a measurement for example, are available at only a few locations. To overcome this the…

We propose two new methods based/inspired by machine learning for tabular data and distance-free localization to enhance the covariance estimations in an ensemble data assimilation. The main goal is to enhance the data assimilation results…

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…

Machine learning models have shown great success in predicting weather up to two weeks ahead, outperforming process-based benchmarks. However, existing approaches mostly focus on the prediction task, and do not incorporate the necessary…

Additive spatial statistical models with weakly stationary process assumptions have become standard in spatial statistics. However, one disadvantage of such models is the computation time, which rapidly increases with the number of data…

In this paper, we introduce a new, local formulation of the ensemble Kalman Filter approach for atmospheric data assimilation. Our scheme is based on the hypothesis that, when the Earth's surface is divided up into local regions of moderate…

This paper applies variational data assimilation to inundation problems governed by the shallow water equations with wetting and drying. The objective of the assimilation is to recover an unknown time-varying wave profile at an open ocean…

How will the climate system respond to anthropogenic forcings? One approach to this question relies on climate model projections. Current climate projections are considerably uncertain. Characterizing and, if possible, reducing this…

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…

Extreme weather events epitomize high cost: to society through their physical impacts, and to computer servers that simulate them to assess risk and advance physical understanding. It costs hundreds of simulation years to sample a few…

We introduce a mathematical formulation of feature-informed data assimilation (FIDA). In FIDA, the information about feature events, such as shock waves, level curves, wavefronts and peak value, in dynamical systems are used for the…

We introduce a data assimilation strategy aimed at accurately capturing key non-Gaussian structures in probability distributions using a small ensemble size. A major challenge in statistical forecasting of nonlinearly coupled multiscale…

Data assimilation is the process to fuse information from priors, observations of nature, and numerical models, in order to obtain best estimates of the parameters or state of a physical system of interest. Presence of large errors in some…

Weather prediction is a critical task for human society, where impressive progress has been made by training artificial intelligence weather prediction (AIWP) methods with reanalysis data. However, reliance on reanalysis data limits the…