Optimization of wind field retrieval procedures Luther White a, * , Alan Shapiro b a Department of Mathematics, University of Oklahoma, Norman, OK 73019, USA b School of Meteorology, University of Oklahoma, Norman, OK 73019, USA Abstract We study the formulation of the problem to retrieve wind fields from radar data. Our formulation allows us to consider the retrieved wind fields as a function of radar loca- tions. We examine the properties of this function with the objective of determining ‘‘best’’ locations for observations. Problems are then posed to determine radar locations to minimize certain criteria involving retrieval errors over a class of test wind fields. A numerical study is presented illustrating the theory developed. Ó 2005 Elsevier Inc. All rights reserved. 1. Introduction The wind field retrieval problem seeks to estimate three dimensional vector fields representing wind fields in a three dimensional domain X from data consisting of measurements of radial velocities from n radar sites supple- mented with constraints based on physical laws. The retrieval problem may 0096-3003/$ - see front matter Ó 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.amc.2005.01.033 * Corresponding author. E-mail addresses: lwhite@ou.edu (L. White), ashapiro@ou.edu (A. Shapiro). Applied Mathematics and Computation 171 (2005) 25–52 www.elsevier.com/locate/amc