Flow duration curve estimation in ephemeral catchments in Portugal

Abstract

The flow regime of a river can be described using the flow duration curve (FDC), which represents the frequency distribution of flows and can be derived from gauged data. Many resource assessments are required where gauged data are limited or unavailable, thus models for predicting FDCs in ungauged catchments are required. In semiarid environments, such as parts of southern Portugal, river flows often become zero for significant periods of time. This makes modelling the discontinuities in the flow regime using commonly used continuous distributions more difficult. This paper presents the derivation of a regionalized model (from a data set of 67 catchments) for predicting FDCs for ungauged catchments in Portugal, which may be ephemeral. The approach uses the theory of total probability to combine a model for predicting the percentage of time the river is dry with a model for predicting an FDC for the non-zero period. These component parts can be modelled separately, relating them to catchment characteristics such as hydrogeology and climate.Key words theory of total probability; multiple regression analysis; flow duration curve; ungauged catchments; ephemeral streams; Portugal Estimation de la courbe des débits classés pour des bassins versants éphémères du PortugalRésumé: Le régime d'écoulement d'une rivière peut être décrit par la courbe des débits classés (CDC), qui représente la distribution de fréquence des débits et qui peut être déduite de données jaugées. Cependant, de nombreuses évaluations de la ressource sont requises en des sites où les données jaugées sont limitées ou non disponibles, ce qui rend nécessaires des modèles de prédétermination des CDC en bassins versants non jaugés. Dans des environnements semi-arides, comme par exemple dans certaines régions du sud du Portugal, les écoulements des cours d'eau deviennent souvent nuls pendant des laps de temps significatifs. Cela rend la modélisation des discontinuités du régime d'écoulement plus difficile avec les approches basées sur les distributions continues couramment utilisées. Cet article présente la déduction d'un modèle régional (en utilisant un jeu de données de 67 bassins versants) pour prédéterminer les CDC de bassins non jaugés au Portugal, y compris de bassins à écoulement éphémère. L'approche est basée sur la théorie de la probabilité totale pour combiner un modèle prédéterminant le pourcentage de temps pendant lequel le cours d'eau est sec, et un modèle prédéterminant une CDC relative à la période où les débits sont non nuls. Ces différentes parties peuvent être modélisées séparément, en les reliant aux caractéristiques des bassins versants comme l'hydrogéologie ou le climat.

Regional models of flow-duration curves of perennial and intermittent streams and their use for calibrating the parameters of a rainfall–runoff model

“…To solve this problem, Haan (1977, in Crocker et al 2003 suggested the use of the total probability theorem, according to which the probability of an event A, belonging to the sample space S consisting of K mutually and collectively exclusive events B i , with i ≤ K, is given by:…”

Regional flow duration curves for ungauged sites in Sicily

“…Ganora et al (2009) observed that theoretically FDC could not be interpreted as a probability curve since discharge is correlated between successive time intervals and discharge characteristics are dependent on the season. However the FDC is often interpreted as probability distribution and the most used distribution is the log-normal, which has been proposed by Beard (1943) and successfully used by several authors (Fennessey and Vogel, 1990). Other authors used different distributions as the beta (Iacobellis, 2008) or the kappa (Castellarin et al, 2007).…”

“…Often these studies regard large catchments with perennial streamflows, as Canada (Leboutillier and Waylen, 1993), India (Singh et al, 2001), Italy (Castellarin et al, 2007Castellarin et al, 2004;Franchini and Suppo, 1996;Iacobellis, 2008;Ganora et al, 2009), Greece (Niadas, 2005), Taiwan (Yu et al, 2002), Philippines (Quimpo et al, 1983), South Africa (Smakhtin et al, 1997) and United States (Fennessey and Vogel, 1990). It is important to point out that analysis of FDC for small catchments with ephemeral streamflows, as in Portugal (Croker et al, 2003) are less frequent than studies for perennial streamflows. Nevertheless small catchments are often of great interest for the development of local water resources especially when exploited by diversions to integrate larger water management systems.…”

Belli̇ Aşilma Olasiğina Sahi̇p Debi̇leri̇n Bölgesel Regresyon Denklemleri̇ni̇n Eldesi̇ Ve Doğu Karadeni̇z Havzasi Örneği̇

“…Bu amaçla maksimum yağışların değişimi incelenebildiği [8] gibi, debilerin değişimi de incelenebilmektedir. Kanada [9], Yunanistan [10], Hindistan [11], İtalya [12], Tayvan [13], Filipinler [3], Portekiz [14], Güney Afrika [15], Amerika [16] …”