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A hypsometric integral (HI) is a topographical index with important geomorphological meaning. It can both describe the development state of the watershed and reflect the strength of activity in the geological structure. Based on this index, the integral curve method was used to analyze the HI characteristics of watersheds in the region west of the Lvliang Mountains on the Loess Plateau of Shanxi Province, China, in combination with 30-m resolution Shuttle Radar Topography Mission data. In order to accurately characterize erosion development within the watershed, the HI characteristics of each topographic feature object in the watershed were comprehensively analyzed. The results of HI scale effects show that HI was not strongly dependent on the spatial resolution of Digital Elevation Model (DEM) data, but had some scale dependence on the stable area of the watershed. The spatial distribution of the HI shows that the HI values of the watersheds in the southern loess residual tableland were the largest, and the degree of erosion was the weakest; the HI values of the watersheds in the north-central part of the loess hilly-gully region were relatively small, and the degree of erosion was stronger. This result is consistent with the results of the spatial distribution of sediment yield in literatures. The reasons for the spatial distribution of the HI were analyzed in terms of geological formations and climatic environments. The results show that for the study area, tectonic activity, formation lithology, rainfall, and agrotype were not the main factors affecting the HI values. The structure of the paleotopography and erosion cutting due to the uplift of the Lvliang Mountains and later water erosion controlled the spatial distribution state of HI. Thus, for the study area, the HI value cannot reflect the strength of tectonic activity. The combination of topographic feature object method and the HI index further quantified the erosion development state of the watershed.

The Hypsometric Integral Based on Digital Elevation Model for the Area West of Lvliang Mountains in Loess Plateau, Shanxi, China