Abstract
This study focuses on the return period evaluation for design hyetographs, which is usually estimated by adopting a univariate statistical approach. Joint Return Period (JRP) and copula-based multivariate analysis are used in this work to better define T-year synthetic rainfall patterns which can be used as input for design flood peak estimation by means of hydrological simulation involving rainfall-runoff (RR) models. Specifically, a T-year Design Hyetograph (DH) is assumed to be characterized by its peak H, at the chosen time resolution Δt, and by the total rainfall height W, cumulated on its critical duration dCri, which has been a priori fixed. As stated in technical literature, the choice of the expression for JRP depends on which event is deemed as critical for the investigated system; the most important cases are: (i) all the variables must exceed a certain magnitude to achieve critical conditions; or (ii) at least one variable must be greater than a threshold; or (iii) critical conditions are induced by all the events with a joint Cumulative Density Function (CDF) overcoming an assigned probability threshold. Once the expression for JRP was chosen, the relationship among multivariate T-year design hyetographs and T-year design flood peak was investigated for a basin located in Calabria region (southern Italy). Specifically, for the selected case study, a summary diagram was obtained as final result, which allows the main characteristics of T-year DHs to be estimated, considering both the univariate and the copula based multivariate analysis, and the associated T-year design flood peaks obtained through the simulation with a RR model.
Highlights
Many hydrological issues require the use of design rainfall models in order to evaluate the effects of intense precipitation events over a basin or urban area
Different expressions can be obtained depending on which event is deemed as critical for the investigated system [11,12]; the most important cases are: (i) all the variables must exceed a certain magnitude to achieve critical conditions; or (ii) at least one variable must be greater than a threshold; or (iii) critical conditions are induced by all the events with a joint Cumulative Density Function (CDF) overcoming an assigned probability threshold
The design hyetograph from the univariate analysis should correspond to a return period greater than 200 years in order to get, by using the chosen RR model, a peak discharge equal to Q50 ; the bivariate analysis allows for obtaining Q50, Q100, and Q200 with design hyetographs whose pairs can be associated to return periods TOR equal to the T of the peak discharges and, in any case, considerably less than those obtained from the univariate analysis; on the basis of Equation (13), the adoption of other forms for Joint Return Period (JRP) (TAND, TKEN, TCOND ) would imply T values for the Design Hyetograph (DH) greater than those obtained with TOR
Summary
Many hydrological issues require the use of design rainfall models in order to evaluate the effects of intense precipitation events over a basin or urban area. All of the above listed quantities related to a DH are characterized by an intrinsic variability, and as such a multivariate approach should be more suitable For this reason, in this paper the authors carried out a multivariate analysis by using copula functions [9], with the aim of assessing the impact of different DHs in the estimation of design flood peak. The basin of Corace at Grascio (located in Calabria region, southern Italy) was selected as case study In this analysis, all the DHs are assumed to have the rainfall peak H in correspondence of dCrit /2, while Wn is uniformly distributed on all the remaining time intervals with a resolution ∆t = 20 min.
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