Probability Analysis and Control of River Runoff–sediment Characteristics based on Pair-Copula Functions: The Case of the Weihe River and Jinghe River

Abstract

Analyzing the encounter frequency of high–low runoff and sediment yield is important for the appropriate dispatching of runoff–sediment resources, as well as river regulation. However, there have been no reports on the utilization of the pair-copula function in analyzing the runoff–sediment characteristics from a probabilistic perspective and conducting probability control on the runoff–sediment yields of different hydrologic stations. This paper builds marginal distribution functions on the basis of kernel distribution theory. In addition, this paper builds the joint distribution functions through pair-copula functions in order to analyze the encounter probability and the compensation characteristics of high–low runoff and sediment at different stations on the Weihe River in China, as well as the origins of runoff–sediment, to conduct probability control of river runoff–sediment resource allocation. The results show that, in different periods, the synchronous probability of high–low runoff of the Weihe River’s Xianyang and Huaxian Stations, and the Jinghe River’s Zhangjiashan Station differ, while that of high–low sediment at the three stations changes little—remaining at around 54%. Therefore, the sediment and runoff of the Weihe River apparently have different origins. In years of high and low runoff, if the runoffs of the Xianyang and Zhangjiashan Stations can be kept within a certain range, then the runoff of the Huaxian Station will be in a particular range, at a certain probability. Sediment at the Huaxian Station can be controlled, in a similar way. These results are of great significance for the water and sediment management department of the Weihe river, in order to reasonably allocate water and sediment resources.

Probabilistic Assessment of Correlations of Water Levels in Polish Coastal Lakes with Sea Water Level with the Application of Archimedean Copulas

“…One of the methods of their application is the analysis of synchronicity and asynchronicity of occurrences of phenomena. According to other authors, copula functions have proven efficient in comprehensive analyses of, e.g., dependencies between the discharge volume and volume of supplied debris [44,45]. They also permit the quantitative determination of the frequency of occurrence of phenomena or disasters and can be used to prevent undesirable events (i.e., drought and floods) and limit the risk of their occurrence, i.e., their use in shaping the rational management of water resources in a given area [43,[45][46][47].…”

“…According to other authors, copula functions have proven efficient in comprehensive analyses of, e.g., dependencies between the discharge volume and volume of supplied debris [44,45]. They also permit the quantitative determination of the frequency of occurrence of phenomena or disasters and can be used to prevent undesirable events (i.e., drought and floods) and limit the risk of their occurrence, i.e., their use in shaping the rational management of water resources in a given area [43,[45][46][47]. This paper presents the possibility of applications of synchronicity analyses in the analysis of the dependency of maximum water levels in coastal lakes on sea water levels, which can also contribute to an increase in the level of water management in coastal areas.…”

“…It concerns, for example, separate and combined probabilities of the occurrence of maximum water levels in lakes and the sea (probabilistic assessment of correlations of maximum water levels in lakes and the sea).The objective of this paper was the determination of correlations of water levels in coastal lakes of the South Baltic with water levels in the sea (through the application of the correlation coefficient) and the consideration of the possibility of simultaneous modeling of correlations between the selected variables (with the application of copula theory), which provided more possibilities for interpretation of the detected relations than traditional statistical tools did.The strength of the relationship between maximum water levels in lakes and the sea is presented in the form of the probability of occurrence of synchronous and asynchronous situations. This approach has so far been applied in research on, among other things, correlations between the volume of outflow and volume of supplied debris [43][44][45] and the volumes of outflow in rivers [46,47]. The results of Author Contributions: Conceptualization, D.W.; methodology, A.P.…”

“…The strength of the relationship between maximum water levels in lakes and the sea is presented in the form of the probability of occurrence of synchronous and asynchronous situations. This approach has so far been applied in research on, among other things, correlations between the volume of outflow and volume of supplied debris [43][44][45] and the volumes of outflow in rivers [46,47]. The results of Author Contributions: Conceptualization, D.W.; methodology, A.P.…”

On the Relationship between Suspended Sediment Concentration, Rainfall Variability and Groundwater: An Empirical and Probabilistic Analysis for the Andean Beni River, Bolivia (2003–2016)

“…Further developments on those empirical relationships are listed in Vercruysse et al [22] including data mining techniques like fuzzy logic, artificial neuronal networks and principal components analysis. Copula functions were tested in Slovenian rivers, to estimate event-based SSC [23] and in the Weine River in China to evaluate the variations in the runoff-sediment relationship [24,25]. On the other hand, more straightforward and direct empirical models can be established by using the rainfall in the equations, with the additional advantage that rainfall data is more widely available [26].…”