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The fundamental problem in hydrology, in both the theoretical and the applied sense, is the prediction of streamflow. While there have been the usual stepwise improvements in our understanding of the mechanisms of the various components of the hydrologic cycle that transfer rainfall into streamflow, the overall problem of prediction must be viewed in a stochastic sense. There are great uncertainties in the processes, the parameters, and the measured inputs and outputs. The study of stochastic hydrology attempts to provide a theoretical framework for the prediction of floods and droughts, the design of hydraulic structures, and the optical management of water resource systems. During the past decade there has been a burst of research activity that has placed increased emphasis on the application of the powerful techniques of time-series analysis in the study of hydrologic phenomena. One of the leaders in this effort has been Ignacio Rodriguez-Iturbe, who is now to be honored as a recipient of the James B. Macelwane Award.