Narrow Results

The simulation of the variation of the erosion or sedimentation and the sediment-carrying capability of the water on the river segments, as it changes from the lower-water season to the higher-water season, is performed by a dynamical model of the sediment transport on a river network. The model is constructed by considering that the sediment-carrying capability of the water in one segment is modulated by the undergone state of it and that of its neighbor segments. The calculated results can simulate the relative variations occuring in the natural river when the water seasons alternate.

A sediment transport dynamic model, based on the consideration of streams confluence and/or diversion, is proposed to investigate the influence of water diversion on the mainstream. The simulated results accord qualitatively with the observed or experimental phenomenon in the Yellow River, that is, sedimentation will get more in the main channel as the water is diverted. Some interesting scaling laws describing the behavior of the erosion–sedimentation state in the process of sediment transport are observed, which may help us to get some understandings of sediment transport dynamics in a river network.

This work develops a preliminary method for coding random self-similar patterns as a series of numbers and investigates the corresponding algorithm to calculate the topological distance between starting point and the link in the generated fractal pattern from the code series. With reference to the wide range of stochastic property in natural patterns, a process for generating fractal patterns with various generating probabilities of the pattern links denoted as separately random self-similar generation or separately random fractal is proposed. To assess the adaptability of the process, the coding method is applied to the generation of a random self-similar river network and the corresponding algorithm for calculating topological distance of the links is used to determine the width function of the pattern. The width function-based geomorphologic instantaneous unit hydrograph (WF-GIUH) model is then applied to estimate the runoff of the Po-bridge watershed in northern Taiwan. The results show that the separately random self-similar generating algorithm can be implemented successfully to calculate hydrologic responses.

This work discusses the random self-similar tree generation by employing multiple basic patterns, and investigates the character code and standardization algorithm for multiple basic patterns. With reference to the wide range of various basic patterns in natural shapes, the general coding method and the corresponding algorithm to calculate the topological distance is developed for random self-similar tree with multiple basic patterns. To assess the adaptability of the process, the general coding method is applied to transfer the generated river network to a code series and the corresponding algorithm for calculating topological distance of the links is used to determine the width function of the pattern. Finally, the width-function based geomorphologic instantaneous unit hydrograph (WF-GIUH) model is then applied to estimate the runoff of the Po-bridge watershed in northern Taiwan. The results reveal that the random self-similar tree with multiple basic patterns proposed in this study can be implemented successfully to calculate hydrologic responses.

Horton’s laws have long served as fundamental principles for fractal organization of a drainage basin. Scaling ratios of stream number, length, area, and side tributary have been proposed but the definitions of these basic variables are inconsistent. The concept of eigenarea can be utilized to resolve this issue. Here, we investigated the relationships among Hortonian scaling ratios using the concept of eigenarea. We found that the eigenarea ratio, likewise other scaling ratios, is invariant within a stream network, the law of eigenarea. We analytically revealed that the eigenarea ratio is equivalent to the stream length ratio. Our examination implies that Horton’s original two ratios of stream number and length can represent most Hortonian scaling ratios except Tokunaga ratio.