Abstract
Abstract. In many hydrological models, such as those derived by analytical probabilistic methods, the precipitation stochastic process is represented by means of individual storm random variables which are supposed to be independent of each other. However, several proposals were advanced to develop joint probability distributions able to account for the observed statistical dependence. The traditional technique of the multivariate statistics is nevertheless affected by several drawbacks, whose most evident issue is the unavoidable subordination of the dependence structure assessment to the marginal distribution fitting. Conversely, the copula approach can overcome this limitation, by dividing the problem in two distinct parts. Furthermore, goodness-of-fit tests were recently made available and a significant improvement in the function selection reliability has been achieved. Herein the dependence structure of the rainfall event volume, the wet weather duration and the interevent time is assessed and verified by test statistics with respect to three long time series recorded in different Italian climates. Paired analyses revealed a non negligible dependence between volume and duration, while the interevent period proved to be substantially independent of the other variables. A unique copula model seems to be suitable for representing this dependence structure, despite the sensitivity demonstrated by its parameter towards the threshold utilized in the procedure for extracting the independent events. The joint probability function was finally developed by adopting a Weibull model for the marginal distributions.
Highlights
The simplest stochastic models utilized in the representation of the precipitation point process usually employ individual event random variables, that consist in the rainfall volume, or the average intensity, the wet weather duration and the inter arrival time, whose probability functions have to be fitted according to recorded time series (Beven, 2001, 265–270 pp.)
Since the publication of this seminal paper, these hypotheses have been assumed in a number of other works aimed at various purposes. Focusing only on those exploiting the derived distribution theory, probability functions were developed for hydrological dependent variables such as the runoff volume (Chan and Brass, 1979; Eagleson, 1978b), the annual precipitation (Eagleson, 1978a), the annual water yield (Eagleson, 1978c), the runoff peak discharge in urban catchments (Guo and Adams, 1998) and in natural watersheds (Cordova and Rodrıguez-Iturbe, 1985; Dıaz-Granados et al, 1984), the flood peak discharge routed by a detention reservoir (Guo and Adams, 1999) and the pollution load and the runoff volume associated with sewer overflows (Li and Adams, 2000)
In this work the possibility of analysing the stochastic structure of the rainfall point process by a quite simple trivariate joint distribution has been clearly demonstrated. Such a distribution is based on three random variables able to represent the storm main features, the rainfall volume, the wet weather duration and the interevent period
Summary
The simplest stochastic models utilized in the representation of the precipitation point process usually employ individual event random variables, that consist in the rainfall volume, or the average intensity, the wet weather duration and the inter arrival time, whose probability functions have to be fitted according to recorded time series (Beven, 2001, 265–270 pp.). The first hydrological application of the event based statistics is due to Eagleson (1972), who derived the peak flow rate frequency starting from those featuring the average intensity and the storm duration, by assuming the two random variables independent and exponentially distributed. Since the publication of this seminal paper, these hypotheses have been assumed in a number of other works aimed at various purposes Focusing only on those exploiting the derived distribution theory, probability functions were developed for hydrological dependent variables such as the runoff volume (Chan and Brass, 1979; Eagleson, 1978b), the annual precipitation (Eagleson, 1978a), the annual water yield (Eagleson, 1978c), the runoff peak discharge in urban catchments (Guo and Adams, 1998) and in natural watersheds (Cordova and Rodrıguez-Iturbe, 1985; Dıaz-Granados et al, 1984), the flood peak discharge routed by a detention reservoir (Guo and Adams, 1999) and the pollution load and the runoff volume associated with sewer overflows (Li and Adams, 2000). Test statistics were conducted to evaluate the goodness-of-fit of the proposed functions with the observed samples, both for the copulas and the margins
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