Using negative exponential function to characterize built-up land density along slope gradient for 19 urban areas in China

In China, numerous cities are expanding into sloping land, yet the quantitative distribution patterns of urban built-up land density along the slope gradient remain unclear, limiting the understanding of sloping land urbanization. In this paper, a simple negative exponential function was presented to verify its applicability in 19 typical sloping urban areas in China. The function fits well for all case urban areas (R²≥0.951, p < 0.001). The parameters of this function clearly describe two fundamental attributes: initial value a and decline rate b. Between 2000 and 2020, a tends to increase, while b tends to decrease in all urban areas, confirming the hypothesis of mutual promotion between flatland densification and sloping land expansion. Multiple regression analysis indicates that the built-up land density and the ruggedness of background land can explain 70.7% of a, while the average slope ratio of built-up land to background land, the built-up land density and the built-up land area can explain 82.1% of b. This work provides a quantitative investigative tool for distribution of urban built-up land density along slope gradient, aiding in the study of the globally increasing phenomenon of sloping land urbanization from a new perspective.