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A shot noise process consisting of a series of events at random times and of random magnitudes, each of which produces a fixed shaped rise and recession, is used as the basis for describing continuous time streamflows. This type of model is chosen for its ability to model recessions. Recession shapes consisting of one or two exponential curves are considered. The fitting of the models to multisite daily data and the generation of synthetic daily data are described. The application of the models to some English streamflow data is illustrated.