A line search algorithm for Wind field adjustment with incomplete data and RBF approximation

TL;DR

This paper introduces a novel line search algorithm for wind field adjustment using RBF approximation, solving a PDE-constrained least squares problem with a unique adjusted field via adjoint techniques.

Contribution

It presents a new line search method for wind field adjustment that incorporates RBF approximation and adjoint equations, extending Sasaki's classical approach.

Findings

The proposed method effectively adjusts wind fields with incomplete data.

Numerical results demonstrate the accuracy of the RBF-based adjustment.

The approach efficiently solves the elliptic problem inherent in the model.

Abstract

The problem of concern in this work is the construction of free divergence fields given scattered horizontal components. As customary, the problem is formulated as a PDE constrained least squares problem. The novelty of our approach is to construct the so called adjusted field, as the unique solution along an appropriately chosen descent direction. The latter is obtained by the adjoint equation technique. It is shown that the classical adjusted field of Sasaki's is a particular case. On choosing descent directions, the underlying mass consistent model leads to the solution of an elliptic problem which is solved by means of a Radial Basis Functions method. Finally some numerical results for wind field adjustment are presented.