Planning and verification of hydraulic infrastructures require a design estimate of hydrologic variables, usually provided by frequency analysis, and neglecting hydrologic uncertainty. However, when hydrologic uncertainty is accounted for, the design flood value for a specific return period is no longer a unique value, but is represented by a distribution of values. As a consequence, the design flood is no longer univocally defined, making the design process undetermined.

The Uncertainty Compliant Design Flood Estimation (UNCODE) procedure is a novel approach that, starting from a range of possible design flood estimates obtained in uncertain conditions, converges to a single design value. This is obtained through a cost–benefit criterion with additional constraints that is numerically solved in a simulation framework. This paper contributes to promoting a practical use of the UNCODE procedure without resorting to numerical computation. A modified procedure is proposed by using a correction coefficient that modifies the standard (i.e., uncertainty-free) design value on the basis of sample length and return period only. The procedure is robust and parsimonious, as it does not require additional parameters with respect to the traditional uncertainty-free analysis.

Simple equations to compute the correction term are provided for a number of probability distributions commonly used to represent the flood frequency curve. The UNCODE procedure, when coupled with this simple correction factor, provides a robust way to manage the hydrologic uncertainty and to go beyond the use of traditional safety factors. With all the other parameters being equal, an increase in the sample length reduces the correction factor, and thus the construction costs, while still keeping the same safety level.

Illustrative example (without uncertainty) of the application of the
cost–benefit framework to compute the design flood. Two generic cost and
damage functions are reported in

The flood frequency curve is commonly used to derive the design flood as the
quantile

To face this problem

The UNCODE approach is founded on the joint use of the cost–benefit approach
of Eq. (

It is worth noting that, as a consequence of the inherent equivalence of
Eq. (

To simplify the UNCODE application, which requires the use of numerical
computation of

The UNCODE design flood,

The coefficients

The parent distribution

The sample length

We generated 100 records for each combination of

Coefficients to be used to estimate

Coefficients

Comparison between the exact,

Values of the correction factor

The reliability of the approximated correction factor

A synthesis of the obtained results is shown in Fig.

The UNCODE approach to flood frequency analysis provides a solution to
quantify the design flood estimate when considering the uncertainty of the
distribution quantile; however, application of the full UNCODE procedure may
be cumbersome and computationally demanding for the practitioner. An
approximate but reliable framework has been proposed here to allow easy
computation of the UNCODE design flood value from the standard value using a
correction factor,

The extensive simulation analysis at the base of this study shows that the
coefficients relating the UNCODE value

The obtained results demonstrate that an increase in the length of relatively
short samples has a noticeable impact in terms of reduction of

The work is based on simulated data. The results can be reproduced by randomly generating datasets as described in the text of this paper.

The authors declare that they have no conflict of interest.

Funding from ERC Consolidator Grant 2014 no. 647473 “CWASI – Coping with water scarcity in a globalized world” is acknowledged. Daniele Ganora also acknowledges the RTD Starting Grant from Politecnico di Torino. Edited by: Giuliano Di Baldassarre Reviewed by: Alessio Pugliese and one anonymous referee