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.

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.

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.

Data interpolation methods are important statistical analysis tools that can fill in data gaps and missing areas by predicting and estimating unknown data points, thereby improving the accuracy and credibility of data analysis and research. Different interpolation methods are widely used in related fields, but the error between different interpolation methods and their interpolation fusion optimization have a significant impact on the interpolation accuracy, which still deserves further exploration. This study is based on two different types of point data: PM_2.5 (PM_2.5 refers to particulate matter in the atmosphere with a diameter of 2.5 μm or less, also known as inhalable particles or fine particulate matter) in Xinyang City, Henan Province, and the elevation of typical gullies in Yuanmou County, Yunnan Province. Using relative difference coefficients and hotspot analysis methods, the differences in error characteristics among four interpolation methods, ordinary kriging (OK), universal kriging (UK), inverse distance weighted (IDW), and radial basis functions (RBFs), were compared, and the influence of interpolation fusion methods on the accuracy of interpolation results was explored. The results show that after interpolation of PM_2.5 concentration and gully elevation, the error difference between OK and UK is the smallest in both datasets. For PM_2.5 concentration data, IDW and UK interpolation errors have the largest difference; for elevation data, the differences between RBF and UK interpolation are the largest. The weighted fusion results show that the interpolation error accuracy of PM_2.5 concentration data with an interpolation point density of 0.009 points per square kilometer is improved, and the root mean square error (RMSE) after fusion is reduced from 0.374 μg/m³ to 0.004 μg/m³. However, the error accuracy of the elevation data of the gully with an interpolation point density of 0.76 points/m² did not improve significantly. This indicates that characteristics such as the density of the original data are important factors that affect the accuracy of interpolation. In the case of sparse interpolation points, it is possible to consider fusing the interpolation results with different error patterns to improve their accuracy. This study provides a new idea for improving the accuracy of interpolation errors.