Flow–sediment relationship as functions of spatial and temporal scales in hilly areas of the Chinese Loess Plateau

Little information is available on the scale behavior of the flow–sediment relationship despite numerous studies on the scale behavior of sediment yield. Based on data observed at 19 gauging stations and 10 runoff experimental plots, we examined the flow–sediment relationship in the context of spatio‐temporal scales for hilly loess areas, China. Distinct from many rivers around the world, sediment concentration in runoff is totally independent of flow discharge at any spatial scale for hilly loess areas. At the intra‐event timescale, the relationship between flow discharge and sediment discharge can be well fitted by a proportional function especially at the entire slope (a combination of the hill slope and the channel side slope) and the larger scale. At the inter‐event timescale, the variability of mean sediment concentration for a single runoff event decreases dramatically with increasing spatial scale. Accordingly, the proportional model of event runoff volume and sediment yield proposed in Zheng et al. (2007a and 2008) is applicable over a wide range of spatial scales from the hill slope to the large‐sized watershed (up to 110, 000km2). Both proportional models of the intra‐ and inter‐event timescales are corroborated by the nonlinear regression technique, which yields a power fit with an exponent extremely close to 1. In a fully physical sense, however, the runoff–sediment yield relationship at the watershed scale should be linear with a negligible constant term due to the presence of base flow. At the annual timescale, the relationship between annual runoff volume and annual sediment yield at the watershed scale becomes linear with an indispensable constant term due to the higher proportion of base flow. The widely used power function is inappropriate for fitting the flow–sediment relationship in hilly loess areas at any spatio‐temporal scales we examined. A comparable result was also obtained for the Walnut Gulch Experimental watershed of USA, suggesting that the proportional model may be universal for regions where sediment supply is sufficiently available. ► The flow–sediment relationship at multiple spatio-temporal scales in hilly loess areas, China. ► A proportional relationship between flow discharge and sediment discharge and between event runoff volume and sediment yield. ► The nonlinear regression yields a power fit with an exponent extremely close to 1. ► A linear relationship between annual runoff volume and annual sediment yield at the w