Differentiation and correlation of spatial pattern and multifunction in rural settlements considering topographic gradients: Evidence from Loess Hilly Region, China

In the process of rapid industrialization and urbanization, China's rural settlements are undergoing rapid differentiation and reorganization. Their spatial pattern and multifunction have attracted much attention. In the Loess Hilly Region of China, topographic factors are deeply involved in the formation and evolution of the spatial pattern and multifunction in rural settlements. Therefore, this paper proposed a new method of topographic gradient analysis based on micro-geomorphic units. Taking Tianshui City in Longzhong Loess Hilly Region as an example, we analyzed the gradient differentiation and spatial correlation of the spatial pattern and multifunction in rural settlements. The results indicated that: (1) The topographic gradient differentiation of spatial pattern in rural settlements was distinct. As the topographic gradients rose, the numerical distributions of TA, AREA_CV, MPI, PR, and SHDI were generally concentrated from high to low values. The numerical distribution of LFI was generally scattered from low to high values. In addition, the numerical distribution of AWMSI and AWMPFD showed the "arch bridge" pattern. (2) The topographic gradient differentiation of multifunction in rural settlements was distinct. The overall level of LF was relatively low, and the numerical difference was small. It had the characteristics of concentrated distribution and marginal distribution in geographical space. The overall level of PF was low, and the spatial distribution had strong urban directivity and significant topographic gradient differences. The overall level of EF was relatively low, and the spatial distribution had significant horizontal zonality and topographic gradient differences. (3) Rural settlements' scale, distribution, and structure were generally synergistic with LF and PF, but there were trade-off relationships with EF. Moreover, the trade-off/ synergy relationships between spatial pattern and multifunction had significant spatial heterogeneity in terms of spatial distribution. This paper is significant for formulating settlement development and construction plans, guiding spatial reconstruction and functional reorganization, improving settlement living environment, and promoting rural revitalization.