The Center for Collaborative Adaptive Sensing of the Atmosphere (CASA) is a National Science Foundation Engineering Research Center created in fall 2003. Led by the University of Massachusetts at Amherst with several partners including the University of Oklahoma, CASA is establishing a revolutionary new paradigm in which systems of distributed, collaborative, and adaptive sensor (DCAS) networks are being developed to overcome fundamental limitation in current approaches particularly in the inability to sample the lower parts of the atmosphere.

In the first phase of its research program, CASA is emplacing test beds of small, inexpensive, low-power Doppler weather radars sited on existing infrastructures such as cell phone towers to test the DCAS concept. The first such network, called NETRAD and consisting of 4 dual-polarization, mechanically-scanning Doppler radars, will begin operating in central Oklahoma in summer 2005. This network will be expanded to 9 phased-array radars in late 2006. Unique to these systems is their ability to adjust dynamically their scanning strategies and other attributes in a collaborative manner with neighboring radars, to sense multiple atmospheric phenomena while simultaneously meeting multiple end user needs all in a theoretically optimal manner.

In order to be more concrete by what is meant by “optimal,” we focus on the formulation of the problem to retrieve wind fields from radar data with conservation of mass side constraints. The retrieval problem itself is posed as a variational minimization problem, the solution of which depends on parameters in its formulation. In this initial work, the parameters are the location of radar sites used to observe radial wind field velocities. Thus, the specific problem is to design optimally a network that may include many radar sites. In this application an optimal design is one that minimizes retrieval error.

Our approach first studies the dependence of the retrieved solutions on radar site locations to determine basic continuity properties. A retrieval operator is then defined that is a mapping from the ensemble of possible test wind fields into itself. A retrieval error function comparing hypothetical wind fields with the associated retrieved wind fields is defined. This error depends not only on the hypothetical input wind fields but problem parameters as well. Thus, various families of test input wind fields are posed and the minimization of retrieval error with respect to those wind fields is considered. These test ensembles can be tailored to the needs of end users. For this application the “optimal” site configuration is a configuration minimizing the retrieval error functional (evaluated with respect to the test wind fields) over admissible configurations of radar sites. Numerical studies are described and results are reported that indicate optimal configurations of networks of radar sites for various numbers of radars. It is shown that optimal adaptive adjustment strategies have analogous formulations and the results obtained in this work extend to a variety of design and operational applications.