Synthetic Hydrographs Generation Downstream of a River Junction Using a Copula Approach for Hydrological Risk Assessment in Large Dams

Abstract

Peak flows values (Q) and hydrograph volumes (V) are obtained from a selected family of historical flood events (period 1957-2017), for two neighboring mountain catchments located in the Ebro river basin, Spain: rivers Ésera and Isábena. Barasona dam is located downstream of the river junction. The peaks over threshold (POT) method is used for a univariate frequency analysis performed for both variables, Q and V, comparing several suitable distribution functions. Extreme value copulas families have been applied to model the bivariate distribution (Q, V) for each of the rivers. Several goodness-of-fit tests were used to assess the applicability of the selected copulas. A similar copula approach was carried out to model the dependence between peak flows of both rivers. Based on the above-mentioned statistical analysis, a Monte Carlo simulation of synthetic design flood hydrographs (DFH) downstream of the river junction is performed. A gamma-type theoretical pattern is assumed for partial hydrographs. The resulting synthetic hydrographs at the Barasona reservoir are finally obtained accounting for flow peak time lag, also described in statistical terms. A 50,000 hydrographs ensemble was generated, preserving statistical properties of marginal distributions as well as statistical dependence between variables. The proposed method provides an efficient and practical modeling framework for the hydrological risk assessment of the dam, improving the basis for the optimal management of such infrastructure. flood hydrographs and, in particular, the frequency analysis of maximum peaks and volumes of hydrographs for a given river or hydrological system. Among others, the works of [8-13] stand out.This type of approach is very appropriate to assess and quantify the hydrological risk of large dams, since it allows the synthetic generation of maximum hydrographs with infinite combinations of flow and volume (Q, V). The subsequent application of dam routing processes allow to translate that hydrological input into hydrological risk variables for the infrastructure, which basically depend on the maximum level reached in the reservoir during the flood event, as well as on the maximum released flow during the event [4,6,14].When the dam is located downstream of the river junction of two rivers where gauge stations exist, the problem becomes significantly more complicated since the corresponding flow peaks do not generally occur at the same time. This problem has been researched by several authors in the past [15][16][17][18][19][20].The statistical analysis of peak flow time lag is a central matter in this case of river junction. Although hydrograph volumes are essentially additive, it is obviously not the case when it comes to flow peaks. In order to generate synthetic hydrographs at the desired point, it becomes necessary to incorporate time lags in a suitable way and assume a theoretical time pattern which allows to superimpose both hydrographs in time.The present study describes and applies a method for the synthetic generation ...

Effect of Seasonality on the Quantiles Estimation of Maximum Floodwater Levels in a Reservoir and Maximum Outflows

“…Such methodology follows exactly the same modelling steps used in [14], including marginal distributions analysis and copula modelling.…”

“…Copula modelling comprises the analysis of the empirical statistical dependence among the two variables involved (Q and V), the copula selection, copula fitting, and finally a goodness-of-fit assessment. Details of the procedure applied herein can be found in [14].…”

“…The results of (Q, V) bivariate analysis based on copula modelling resulted from the application of the method described in Section 2.2.1, comprising the following steps: analysis of the observed statistical dependence among variables, copula selection, copula fitting, and goodness-of-fit assessment. The procedure is carried out exactly in the same manner for each of the three samples analyzed herein (summer season, winter season, and whole year period), following the modelling steps in [14] where further details about copula modelling can be found.…”

“…Although the time pattern and hydrograph duration are also relevant variables to take into account, data availability in many real-world applications do not allow to incorporate successfully such descriptors in the analysis, which is the case of the study presented in this research, where the statistical analysis of flood hydrographs is restricted to peak flow (Q) and total hydrograph volume (V). Extreme value copula families have been applied to model the bivariate distribution (Q, V) for each of the selected seasons, following the method proposed by [14]. According to the method, a Monte Carlo simulation of synthetic design flood hydrographs (DFHs) is performed, making use of a gamma-type theoretical pattern to define them.…”

“…According to this seasonal approach, and following the modelling steps in [14], a 50,000 hydrographs ensemble was generated for each of the seasons considered, preserving in each case the seasonal statistical properties of marginal distributions as well as statistical dependence between variables.…”