A line search algorithm for Wind field adjustment with incomplete data and RBF approximation
For geophysical fluid dynamics and meteorology, this work offers a novel algorithmic approach to wind field reconstruction, though it is incremental as it builds on Sasaki's classical method.
The paper proposes a line search algorithm for constructing divergence-free wind fields from scattered horizontal data, using a PDE-constrained least squares approach with adjoint-based descent directions and RBF approximation. Numerical results demonstrate the method's effectiveness for wind field adjustment.
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.