Technical note: Design flood under hydrological uncertainty

Abstract

Abstract. 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.

Uncertainty Assessment of Synthetic Design Hydrographs for Gauged and Ungauged Catchments

“…Serinaldi () stated that many joint distributions and copulas can be fitted to small samples because goodness of fit tests cannot discriminate between alternative models due to the lack of power. An increase in the length of relatively short samples could noticeably reduce the uncertainty of design variable quantiles (Botto et al, ) and therefore, as shown in our study, the uncertainty of the whole design hydrograph. The problem of a limited sample size could for practical applications be partially overcome by temporal, spatial, or causal information expansion.…”

Corrección de las crecientes de diseño por incertidumbre hidrológica

“…El criterio de costo-beneficio mínimo se puede consultar en Campos-Aranda (2015). Botto, Ganora, Claps y Laio 2017 Botto et al (2017) lograron concretar los resultados del UNCODE en un procedimiento muy simple, que corrige la CD estimada a través del AFC, mediante un factor correctivo, función del tamaño del registro (n) y del periodo de retorno (Tr). El resultado es una estimación de la CD 2020, Instituto Mexicano de Tecnología del Agua Open Access bajo la licencia CC BY-NC-SA 4.0 (https://creativecommons.org/licenses/by-nc-sa/4.0/) 406 Tecnología y ciencias del agua, ISSN 2007-2422, 11(6), 400-425.…”

“…Estimación del factor correctivo Botto et al (2014) han demostrado que la CD obtenida aplicando el UNCODE ( * ) siempre es un valor mayor que la estimada (QTr) con el AFC, a la que llaman libre de incertidumbres (uncertainty-free). Por otra parte, Botto et al (2017) han definido que la diferencia relativa entre ambos valores corresponde con el factor de corrección (y), esto es:…”

“…(1) 2020, Instituto Mexicano de Tecnología del Agua Open Access bajo la licencia CC BY-NC-SA 4.0 (https://creativecommons.org/licenses/by-nc-sa/4.0/) 407 Tecnología y ciencias del agua, ISSN 2007-2422, 11(6), 400-425. DOI: 10.24850/j-tyca-2020-06-10 Según Botto et al (2017), el valor de y aumenta con el Tr debido al incremento de la incertidumbre de la estimación de QTr y para un Tr fijo también crece con la variabilidad en la distribución de probabilidades que permite estimar QTr, la cual es la función del tamaño (n) del registro disponible de gastos máximos anuales utilizado en el AFC. A partir de la Ecuación (1) se puede obtener la estimación buscada de ̂ * , como:…”

“…Los coeficientes a0, a1 y a2 se citan en la Tabla 1 y dependen de la distribución de probabilidades utilizada en el AFC; se evaluaron aplicando de manera extensiva el UNCODE. Botto et al (2017) 2020, Instituto Mexicano de Tecnología del Agua Open Access bajo la licencia CC BY-NC-SA 4.0 (https://creativecommons.org/licenses/by-nc-sa/4.0/) Tabla 1. Coeficientes de la Ecuación (3) y sus propiedades estadísticas adimensionales: coeficiente de determinación (R 2 ), error absoluto medio (EAM) y error estándar medio (EEM).…”