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A radar wind analysis system (RWAS) has been developed for nowcast applications. By ingesting real-time wind observations from operational WSR-88D radars and surface mesonet, this system can produce and display real-time vector winds at each selected vertical level or on each conical surface of radar scans superimposed on radar reflectivity or radial-velocity images. An early version of the system has been evaluated and used to provide real-time winds to drive high-resolution emergency response dispersion models. This paper presents the detailed formulations of background error correlation functions used in each of the three steps of vector wind analysis performed in the RWAS and the method of solution used in each step of vector wind analysis. The performances of the RWAS are demonstrated by illustrative examples.