Abstract
The mathematical properties of the normalized diffusive hydrograph allow for easy determination of intrinsic basin characteristics. These include lag times between storm events and peak flow, recession rate, and the total, temporally integrated flow volume, all in terms of a single parameter, the basin time constant “b”. This simple function displays surprising fidelity to measured hydrographs of springs and hundreds of streams and small rivers. We explain this fidelity by showing that the curvature of the theoretical hydrograph matches that of the natural hydrographs better than several alternate models, and by demonstrating that the simple hydrograph function can be integrated over a range of time constants (0 to b max ) to represent the hierarchy of flow paths of varying lengths that exist in real watersheds. Surprisingly, the unwieldy analytical results from this integration are almost numerically indistinguishable from a simple hydrograph using a single, suitably-weighted average for the time constant. The peak flow times are shifted slightly. The accuracy with which the simple hydrograph approximates the integrated results for hierarchies of hydrographs representing individual flow paths explains why the former can realistically describe the discharge behaviors of complex natural watersheds.
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Criss, R.E., Winston, W.E. Properties of a Diffusive Hydrograph and the Interpretation of Its Single Parameter. Math Geosci 40, 313–325 (2008). https://doi.org/10.1007/s11004-008-9145-9
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DOI: https://doi.org/10.1007/s11004-008-9145-9