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The unit hydrograph (UH) is a powerful conceptual tool for describing rainfall-runoff relationships. In the framework of discrete-time black-box systems, the assumptions of linearity, stationarity, and causality yield a convolution equation suitable for the machine computation of runoff from rainfall, once the UH is known. An algorithm based on linear programming (LP) produces an estimate of the UH that fulfills, by construction, the physical constraint of nonnegativity. Using the software Mathematica in the functional-programming style to implement this algorithm leads to a concise and user-friendly computer code. In two single-storm case studies the results obtained by the LP method prove to be highly competitive with those obtained by the O'Donnell method. Moreover, a third case study illustrates a peculiar feature of the LP method: the UH estimate can benefit of the simultaneous use of several pairs of rainfall-runoff data. Key words: Rainfall-runoff relationships, Unit hydrograph, Linear programming, Mathematica
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