engleski

The Applicability of Functional Clustering in Analyzing Historical Floods of the Sava River in Zagreb

The Sava River Basin, as the largest river basin in Croatia, is of great importance for the water resources management and hydrological research in Croatia. The general intensification of extreme climatic conditions increases the number of flood events worldwide, which may indirectly affect the morphodynamical behavior in the riverbed. Valuable information on the flood-generation mechanisms may be contained in the flood hydrograph shapes, which can be expressed as continuous functions using a functional data approach [1]. In this research, we performed a preliminary analysis of annual flood events at the gauging station (GS) Zagreb by applying a clustering mechanism based on functional data to identify a set of representative hydrograph shapes that contain valuable information for future research on scour in the vicinity of bridges. Flood events that capture river’s flood regime can be represented as classical multivariate data or functional data, to be subsequently classified by applying a clustering algorithm. The functional analysis can provide a more objective and reproducible definition of the actual hydrological phenomena than the classical multidimensional analysis because it avoids the subjective selection of a set of hydrograph characteristics. Functional data analysis starts by considering the discrete data observations as part of a finite- dimensional space spanned by a set of basis functions and coefficients that define their linear combination. In addition, the choice of the appropriate order of polynomial segments and the number and placement of the knots are determined to represent the main characteristics of the hydrograph shapes. Finally, the resulting set of coefficients is used as an input for clustering. Since the hydrograph shape clusters can only be validated by their interpretability and usefulness, their evaluation was performed graphically [1, 2]. The input data for the analysis was a historical time series of daily discharge data from the Zagreb gauging station in the Sava River basin for the reference period 1960-2019, provided by the Croatian Meteorological and Hydrological Service. The time series consists of 21878 observations (60 years of data). The annual maxima method was applied to the time series to extract independent flood events corresponding to the maximum annual peak discharge values. For each event the flood volume and duration were determined over a fixed window corresponding to the longest duration of the rising and falling limb of all considered flood events, resulting in 16 days before and 38 days after the peak discharge (55 daily observations). The baseflow was separated from the direct flow using the R package “lfstat”, with the direct flow component normalized by dividing the ordinate of each hydrograph with the total volume of the flood event. Finally, a functional data analysis was performed by spanning B-spline functions of differing ranks onto the resulting direct flow data observations followed by implementing a k- means clustering algorithm to separate flood events into different clusters. For each cluster, a median was determined to represent three distinct types of hydrograph shapes. For this analysis the B-spline rank of 25 and the K value of 3 were ultimately chosen. This approach resulted in identifying three distinct types of flood events: (1) slow events described as both elongated rising and falling limbs, (2) intermediate events with steep rising limbs and moderately steep falling limb, and (3) fast events with steep rising and falling limbs of the hydrographs. This preliminary analysis was conducted in order to exploit the valuable process information contained in flood hydrograph shapes, which can be of great value for the future research within the R3PEAT project (“Remote Real- time Riprap Protection Erosion Assessment on large rivers”, UIP-2019-04-4046) supported by Croatian Science Foundation, that explores influences on the riverbed erosion around structure of bridges crossing large rivers in Croatia [3].

Functional clustering ; discharge ; Sava River Basin

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