Related papers: Boundary conditions control for a Shallow-Water mo…

We evaluate the influence of local resolution, eddy viscosity, coastline structure, and boundary conditions on the numerical representation of boundary currents in a finite element shallow-water model. The use of finite element…

We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary…

Accurate mapping of ocean bathymetry is a multi-faceted process, needed for safe and efficient navigation on shipping routes and for predicting tsunami waves. Currently available bathymetry data does not always provide the resolution to…

A 4D-Var data assimilation technique is applied to the rectangular-box configuration of the NEMO in order to identify the optimal parametrization of boundary conditions at lateral boundaries. The case of the staircase-shaped coastlines is…

We present a new continuous data assimilation algorithm based on ideas that have been developed for designing finite-dimensional feedback controls for dissipative dynamical systems, in particular, in the context of the incompressible…

The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…

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…

The goal of this paper is to solve the global sensitivity analysis for a particular control problem. More precisely, the boundary control problem of an open-water channel is considered, where the boundary conditions are defined by the…

We describe a spectrally-filtered discrete-in-time downscaling data assimilation algorithm and prove, in the context of the two-dimensional Navier--Stokes equations, that this algorithm works for a general class of interpolants, such as…

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 apply two data assimilation (DA) methods, a smoother and a filter, and a model-free machine learning (ML) shallow network to forecast two weakly turbulent systems. We analyse the effect of the spatial sparsity of observations on accuracy…

This paper is a contribution in the context of variational data assimilation combined with statistical learning. The framework of data assimilation traditionally uses data collected at sensor locations in order to bring corrections to a…

Variational data assimilation is a technique for combining measured data with dynamical models. It is a key component of Earth system state estimation and is commonly used in weather and ocean forecasting. The approach involves a…

The shallow water equations (SWE) are a widely used model for the propagation of surface waves on the oceans. We consider the problem of optimally determining the initial conditions for the one-dimensional SWE in an unbounded domain from a…

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…

Extensive numerical evidence shows that the assimilation of observations has a stabilizing effect on unstable dynamics, in numerical weather prediction and elsewhere. In this paper, we apply mathematically rigorous methods to showing why…

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…

Data assimilation is uniquely challenging in weather forecasting due to the high dimensionality of the employed models and the nonlinearity of the governing equations. Although current operational schemes are used successfully, our…

While the formulation of most data assimilation schemes assumes an unbiased observation model error, in real applications, model error with nontrivial biases is unavoidable. A practical example is the error in the radiative transfer model…

The paper is devoted to deriving necessary optimality conditions in a general optimal control problem for dynamical systems governed by controlled sweeping processes with hard-constrained control actions entering both polyhedral moving sets…