Identification of an Optimal Derivatives Approximation by Variational Data Assimilation

TL;DR

This paper explores using variational data assimilation to identify optimal derivative approximations near boundaries in one-dimensional wave equations, aiming to improve numerical schemes for ocean modeling in coastal regions.

Contribution

It demonstrates how variational data assimilation can correct boundary derivative errors and guides the development of optimal numerical schemes for coastal ocean models.

Findings

Errors in derivative approximations can be effectively corrected.

The method provides insights into boundary error correction.

Potential application in improving coastal ocean simulations.

Abstract

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 us to discuss in detail as the development of the adjoint model and assimilation results. It is shown what kind of errors can be corrected by this control and how these errors are corrected. This study is carried out in view of using this control to identify optimal numerical schemes in coastal regions of ocean models.