Multifractal theory provides a reliable method for the scientific quantification of the geomorphological features of basins. However, most of the existing research has investigated small and medium-sized basins rather than complex and large basins. In this study, the Yellow River Basin and its sub-basins were selected as the research areas, and the generalized fractal dimension and multifractal spectrum were computed and analyzed with a multifractal technique based on the slope distribution probability. The results showed that the Yellow River Basin and its sub-basins exhibit clear multifractal characteristics, which indicates that the multifractal theory can be applied well to the analysis of large-scale basin geomorphological features. We also concluded that the region with the most uneven terrain is the Yellow River Downstream Basin with the “overhanging river”, followed by the Weihe River Basin, the Yellow River Mainstream Basin, and the Fenhe River Basin. Multifractal analysis can reflect the geomorphological feature information of the basins comprehensively with the generalized fractal dimension and the multifractal spectrum. There is a strong correlation between some common topographic parameters and multifractal parameters, and the correlation coefficients between them are greater than 0.8. The results provide a scientific basis for analyzing the geomorphic characteristics of large-scale basins and for the further research of the morphogenesis of the forms.

Multifractal theory provides an effective method for the scientific quantification of the river network features. This method has been applied to estimate river network structure in previous research, but there are few temporal and spatial analysis studied for large river basins based on multifractals. In this study, the Yellow River Basin and its nine provinces were selected as the study area, and the generalized fractal dimension and multifractal spectrum of the study area during the period 2000–2020 were calculated and analyzed. We analyzed the response relationship between the river network changes and the urbanization process. Results indicated that the river network of the study area exhibited obvious multifractal properties, which were mainly affected by dense river networks. The complexity of the studied river network has shown a tendency to decrease over time. The rate of change in the river network structure has a high positive correlation with urbanization, that is, the higher the rate of urbanization, the greater the impact on the river network structure. Additionally, the changes of the river network structure are more affected by urbanization during the rapid urbanization stage. We applied multifractal analysis to study the river network structure changes, which is of great significance for scientifically quantifying fluvial characteristics and studying the development and evolution of river networks.

In the process of global information construction, different fields have built their own discrete global grid systems (DGGS). With the development of big data technology, data exchange, integration, and update have gradually become a trend, as well as the associative integration of different DGGS. Due to the heterogeneity of DGGS and the different encoding rules, how to build the encoding conversion rules and data mapping relationship between the same object in various DGGS is an effective support and key technology to achieve the interoperability of DGGS. As a kind of multipurpose DGGS, the quaternary triangular mesh (QTM) has become an effective spatial framework for constructing the digital earth because of its simple structure. At present, there are many schemes for QTM encoding research, which plays a key role in the development of QTM, but at the same time, it also leads to difficulties in the communication and integration of QTM under different encoding. In order to solve this problem, we explore the characteristics of QTM encoding, and put forward three conversion algorithms: resampling conversion algorithm, hierarchical conversion algorithm, and row–column conversion algorithm.

Three-dimensional (3D) buffer analysis is among the basic functions of 3D spatial analysis, and it plays an important role in 3D geographic information systems. The rapid development of the 3D Discrete Global Grid System (DGGS) provides a new method for the 3D spatial analysis of geographic information. According to the spatial topology characteristics of the 3D DGGS and the concept of dimensionality reduction, a 3D buffer analysis method based on the spatial grid of the Earth system is proposed to solve the problem of the buffer algorithm of a space object being unsatisfactory at present. In this paper, we present a method to calculate the distance between cells based on the side length of the spherical grids according to the geometric characteristics of the grids. For the grids of a geographic object, we describe the Euclidean distance expansion algorithm and the radial elevation expansion algorithm that helped us to obtain its 3D buffer. Finally, in terms of algorithm complexity and visualization effect, compared with the traditional raster buffer algorithm, the method presented in this paper has lower complexity, an improved visualization effect, and stronger generality.