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The problem of concern in this work is the construction of free divergencefields given scattered horizontal components. As customary, the problem isformulated as a PDE constrained least squares problem. The novelty of ourapproach is to construct the so called adjusted field, as the unique solutionalong an appropriately chosen descent direction. The latter is obtained by theadjoint equation technique. It is shown that the classical adjusted field ofSasaki's is a particular case. On choosing descent directions, the underlyingmass consistent model leads to the solution of an elliptic problem which issolved by means of a Radial Basis Functions method. Finally some numericalresults for wind field adjustment are presented.

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