Flow-Reduction-Function in Ungauged Basins: A Regionalisation Method with Application in North-Western Italy

In the design of flood attenuation works based on temporary volume accumulation the volume associated to the design flood plays a key role. Once the hydrograph shape cannot be neglected, the volume of a future flood wave can be obtained by a so-called flow reduction function (FRF), sometimes known as flow duration volume curve. The FRF ε_D,1 for a single year represents the maximum mean discharge in a window of duration D divided by the peak flow of that year. Over all the available years, the mean value for each duration divided by the average peak flow represent the flow reduction ratio ε_D=E(Q_D)/E(Q_p). Empirical formulas for the FRF are proposed in literature, with 1 or 2 parameters to estimate on available data. Nerc, 1975, derived a 2 parameters equation ε_D=(1-D/b)^-c. Typically b=1/t_c (where t_c is the basin time of concentration) and c=1-n (n is the exponent of the intensity duration curve written as h=adⁿ).

Many authors direct their efforts to obtain flood – volume relation for gauged basins using stochastic, Monte-Carlo or copula approaches, but very few papers address the topic of FRF estimation in ungauged basins. Here a regionalisation method is proposed, to link parameters b and c to geomorphoclimatic characteristics of the basin. Flood volume data and morpho-climatic descriptors from 110 basin located in the North West of Italy have supported the analysis.

A pruning routine applied to geomorphoclimatic characteristics have reduced the number of non-correlated descriptors from 92 to 34. All possible combination of 2 and 3 descriptors have been considered in the framework of linear multi-regression models. Also canonical correlation analysis (CCA) and Alternating Conditional Expectation algorithms (ACE) have been tested. Results obtained allow to practically derive the FRF in ungauged basins over a 25.000 square kilometres region with a good degree of confidence.

[1] NERC (1975). Estimation of flood volumes over different duration. Flood Studies Report, I:352–373.