Morphodynamic changes in the riverbed may be accelerated by the climate change-induced effects, mostly through the increase of the frequency of extreme climatic events such as floods. This can lead to scouring of the riverbed around the bridge substructure and consequently reduces its overall stability. In order to better understand hydromorphological processes at the local scale, the influence of floods on bridge scour requires a detailed analysis of several interacting flood hydrograph characteristics. This paper presents a multivariate analysis of the annual maximum (AM) flood discharge data at four gauging stations on the Drava and Sava Rivers in Croatia (Europe). As part of the hydrograph analysis, multiple baseflow separation methods were tested. Flood volumes and durations were derived after extracting the baseflow from measured discharge data. Sui63 marginal distribution functions were fitted to the peak discharge (Q), flood volume (V) and duration (D) data. Bivariate copula analyses were conducted for the next pairs: peak discharge and volume (Q–V), hydrograph volume and duration (V–D) and peak discharge and hydrograph duration (Q–D). The results of the bivariate copula analyses were used to derive joint return periods for different flood variable combinations, which may serve as a preliminary analysis for the pilot bridges of the R3PEAT project where the aim is to investigate the influences on the riverbed erosion around bridges with installed scour countermeasures. Hence, a design hydrograph was derived that could be used as input data in the hydraulic model for the investigation of the bridge scour dynamics within the project and a preliminary methodology is proposed to be applied. The results indicate that bivariate frequency analysis can be very sensitive to the selected baseflow separation methodology. Therefore, future studies should test multiple baseflow separation methods and visually inspect the performance.

中文翻译：

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使用 Copulas 对洪水水位线峰值、体积和持续时间进行联合建模——以欧洲克罗地亚的 Sava 和 Drava 河为例

气候变化引起的影响可能会加速河床的形态动力学变化，主要是通过增加洪水等极端气候事件的频率。这会导致桥梁下部结构周围的河床被冲刷，从而降低其整体稳定性。为了更好地了解局部尺度的水文形态过程，洪水对桥梁冲刷的影响需要对几个相互作用的洪水水文特征进行详细分析。本文介绍了克罗地亚（欧洲）德拉瓦河和萨瓦河上四个测量站的年最大 (AM) 洪水流量数据的多元分析。作为水文分析的一部分，测试了多种基流分离方法。洪水量和持续时间是在从测量的流量数据中提取基流后得出的。将 Sui63 边际分布函数拟合到峰值流量 (Q)、洪水量 (V) 和持续时间 (D) 数据。对接下来的对进行双变量 copula 分析：峰值流量和流量 (Q-V)、水位线体积和持续时间 (V-D) 以及峰值流量和水位线持续时间 (Q-D)。双变量 copula 分析的结果用于推导不同洪水变量组合的联合返回周期，这可以作为 R3PEAT 项目试点桥梁的初步分析，目的是调查对桥梁周围河床侵蚀的影响安装冲刷对策。因此，推导出了一个设计过程线，可用作水力模型中的输入数据，用于研究项目内的桥梁冲刷动力学，并建议采用初步方法。结果表明，双变量频率分析对所选的基流分离方法非常敏感。因此，未来的研究应该测试多种基流分离方法并目视检查性能。