Terrain feature points, such as the peaks and saddles, are the basic framework of surface topography and its undulations, which significantly affect the spatial distribution of surface topography. In the past, terrain feature points were extracted separately for each type, while the internal connections between the terrain feature points were ignored. Therefore, this work proposes an integrated algorithm for extracting terrain feature-point clusters, including the peaks, saddles and runoff nodes, based on the DEM data. This method includes two main processes: positive terrain-constrained ridgeline extraction and terrain feature-point cluster extraction. Firstly, a threshold determination method of flow accumulation in the hydrological analysis is proposed by combining morphological characteristics with runoff simulation, and the ridgelines are extracted based on this threshold. Subsequently, the peaks and their control areas are extracted by space segmentation. Meanwhile, the saddles and runoff nodes are obtained by spatial intersection. Finally, the integrated terrain feature-point clusters are obtained by merging the three extracted terrain feature points. This method was experimented with in the six typical sample areas in Shaanxi Province and verified its results by contour lines and optical images. It shows that the spatial positions of the extracted terrain feature clusters are accurate, and the coupling relationships are great. Finally, the experiments show that the statistical attributes of point clusters and their spatial distribution trends have an obvious correlation with geomorphic types and geomorphic zoning, which can provide an important reference for geomorphic zoning and mapping.

Gully erosion is well-developed in the Jinsha dry-hot valley region, which has caused serious soil losses. Gully volume is regarded as an effective indicator that can reflect the development intensity of gully erosion, and the evolutionary processes of gullies can be predicted based on the dynamic variation in gully volume. Establishing an effective prediction model of gully volume is essential to determine gully volume accurately and conveniently. Therefore, in this work, an empirical prediction model of gully volume was constructed and verified based on detailed morphological features acquired by elaborate field investigations and measurements in 134 gullies. The results showed the mean value of gully length, width, depth, cross-section area, volume, and vertical gradient decreased with the weakness of the activity degree of the gully, although the decrease in processes of these parameters had some differences. Moreover, a series of empirical prediction models of gully volume was constructed, and gully length was demonstrated to be a better predictor than other morphological features. Lastly, the effectiveness test showed the model of V = aL^b was the most effective in predicting gully volume among the different models established in this study. Our results provide a useful approach to predict gully volume in dry-hot valley regions.

Slope length is an important factor in soil erosion modeling, and the reasonable automatic extraction of slope length is of great significance in soil erosion research. However, previous studies have mainly focused on the regional scale, and how to effectively extract slope length at the slope scale deserves further research. In this study, a slope length extraction algorithm based on slope streamlines method (SSM) is proposed for the slope length extraction problem in geomorphology, and it is compared with three existing slope length calculation methods. The experimental results show that the new method can quickly calculate the length of slope streamlines, and the extracted slope lengths have better accuracy; the coefficients of determination demonstrates a better overall fitting effect of the four extraction methods, with coefficients of determination exceeding 0.7; this indicates that the use of SSM has similar accuracy and stability to other methods in calculating slope lengths. Among all the calculation methods, SSM has a better overall fitting effect for slope length calculation, and the obtained slope length value domain range is relatively small and concentrated in a small range, which expresses the slope length better.

To measure and present urban size urban spatial forms, in solving problems in the rapid urbanization of China, urban territorial scope identification is essential. Although current commonly used methods can quantitatively identify urban territorial scopes to a certain extent, the results are displayed using a continuous and closed curve with medium- and low-resolution images. This makes the acquisition and interpretation of data challenging. In this paper, by extracting discretely distributed urban settlements, road intersections in OpenStreetMap (OSM), electronic maps, and urban expansion curve based on fractal thoughts have been used to present urban territorial scope and spatial form. Guangzhou, Chengdu, Nanjing, and Shijiazhuang cities were chosen as the identification targets. The results showed that the distance threshold corresponding to the principal curvature point of the urban expansion curve plays a vital role in the extraction of urban settlements. Moreover, from the analysis, the optimal distance thresholds of urban settlements in Guangzhou, Chengdu, Nanjing, and Shijiazhuang were 132 m, 204 m, 157 m, and 124 m, respectively, and the corresponding areas of urban territorial scopes were 1099.36 km², 1076.78 km², 803.07 km², and 353.62 km², respectively. These metrics are consistent with those for the built-up areas.

Improving the accuracy of DEMs is a critical goal in digital terrain analysis. The combination of multi-source data can be used to increase DEM accuracy. Five typical geomorphic study areas in the Loess Plateau in Shaanxi were selected for a case study and a 5 m DEM unit was used as the basic data input. Data from three open-source databases of DEM images, the ALOS, SRTM and ASTER, were obtained and processed uniformly through a previously geographical registration process. Three methods, Gram–Schmidt pan sharpening (GS), weighted fusion and feature-point-embedding fusion, were used for mutual enhancement of the three kinds of data. We combined the effect of these three fusion methods in the five sample areas and compared the eigenvalues taken before and after the fusion. The main conclusions are as follows: (1) The GS fusion method is convenient and simple, and the three combined fusion methods can be improved. Generally speaking, the fusion of ALOS and SRTM data led to the best performance, but was greatly affected by the original data. (2) By embedding feature points into three publicly available types of DEM data, the errors and extreme error value of the data obtained through fusion were significantly improved. Overall, ALOS fusion resulted in the best performance because it had the best raw data quality. The original eigenvalues of the ASTER were all inferior and the improvement in the error and the error extreme value after fusion was evident. (3) By dividing the sample area into different areas and fusing them separately according to the weights of each area, the accuracy of the data obtained was significantly improved. In comparing the improvement in accuracy in each region, it was observed that the fusion of ALOS and SRTM data relies on a gentle area. A high accuracy of these two data will lead to a better fusion. Merging ALOS and ASTER data led to the greatest increase in accuracy, especially in the areas with a steep slope. Additionally, when SRTM and ASTER data were merged, the observed improvement was relatively stable with little difference.

Resource-based cities, characterized by a prolonged dependence on resource extraction and persistent urban expansion, frequently exhibit significant imbalances between the supply and demand of ecosystem services (ESs). Understanding how various types of resource-based cities respond to urbanization in terms of ESs supply–demand relationships is crucial for advancing sustainable urban development. This study examines three representative resource-based cities in Sichuan Province—Nanchong (growing), Luzhou (declining), and Panzhihua (mature)—to analyze changes in six key ESs from 2000 to 2020, including soil retention, carbon sequestration, water yield, habitat quality, food production, and recreational services. Ordinary least squares (OLS) regression and random forest (RF) models were employed to evaluate the effects of gross domestic product (GDP) density, construction land proportion (CLP), and population (POP) density on the ecosystem service supply–demand ratio (ESDR), and to explore variations in sensitivity among these cities. The results demonstrate that (1) ESs’ supply–demand patterns differ significantly among the three city types. Nanchong exhibited a declining supply and increasing demand for regulating services; Luzhou displayed improvements in its water yield and recreational services but persistent degradation of habitat quality; and Panzhihua achieved notable gains in carbon sequestration and habitat quality. (2) Urbanization generally reduced the ESDR across all three cities. However, the GDP density positively influenced the ESDR in Nanchong, while the CLP and the POP density exerted widespread negative effects. In Luzhou, the ESDR was primarily constrained by the CLP, whereas in Panzhihua, both the CLP and the POP density significantly reduced the ratio. (3) The sensitivity analysis revealed distinct response patterns: Nanchong was most sensitive to CLP, Luzhou responded most strongly to GDP density, and Panzhihua was highly sensitive to both GDP density and POP density. These findings underscore the necessity of formulating city-type-specific development strategies—such as land restoration, population control, and industrial upgrading—tailored to different types of resource-based cities, in order to reconcile urbanization with ecosystem service dynamics, promote green transformation, and contribute to the achievement of the Sustainable Development Goals (SDGs).