Dependence of the sediment delivery ratio on scale and its fractal characteristics

The sediment delivery ratio (SDR) is an indicator used to determine the capacity for eroded sediment to be delivered to the outlet of a particular basin. Based on systematic reviews of SDR studies in China and abroad during the last 50 years, this study analyzes whether the SDR has scale-dependent characteristics and discusses the fractal characteristics of the SDR. In addition, the SDR in various watersheds in China and abroad showed correlations with temporal and spatial scales, which means that the SDR depends on watershed scale. Moreover, the SDR can be quantitatively expressed and scaled using fractal dimension under certain temporal and spatial scales. Within a nested watershed, a proposed SDR scale transfer model was constructed using the SDR at a typical watershed unit scale with an area of approximately 1 km2 (SDR′) and a fractal dimension of the SDR at a nested watershed scale (D). This research also points out that the study and calculation of the SDR cannot be correct without considering its scale dependence. It is a valid and useful approach to construct SDR scaling models by using fractal dimension, which could be an interesting research topic regarding SDR scaling in the future.