Fuzzy unit hydrograph

The unit hydrograph method, frequently used for representing the rainfall-runoff transformation, is subject to a number of uncertainties related both to the model assumption and data acquisition, despite them usually being disregarded. A methodology to account for these uncertainties based on the fuzzy approach is proposed and illustrated. It is assumed that the unit hydrograph can be represented through a fuzzy schematization, and effective precipitation is also considered a fuzzy series; by applying the extension principle to the convolution integral a fuzzy runoff is obtained. In particular, the Nash cascade parametric form of the unit hydrograph is used, and its parameters are considered fuzzy numbers. The general methodology and the assessment of the parameters are explained using a case study relevant to the subcatchments of the Neckar catchment (southwest Germany). The proposed procedure enables bands to be calculated that describe the range of possible hydrographs for predefined h levels. The uncertainty in the runoff calculation is thus represented in terms of fuzzy vagueness by the width of these bands. The bands decrease with the increase of the h level. The calibrated parameters are then used with the extension principle for calculating the vagueness of different runoff characteristics, such as flood peak discharge and time to peak, as fuzzy numbers.