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.

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.

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.

The development of loess landforms is controlled by underlying, pre-existing paleotopography. Previous studies have focused on the inheritance of loess landform and the control of underlying paleotopography on modern terrain based on the digital elevation model (DEM), while the similarities and differences between modern terrain and underlying paleotophotography have not been directly spatialized. In this study, areas with high and coarse sediment yield (AHCSY) in the Loess Plateau of China were selected to form the study area, and the DEM of the study area’s underlying paleotophotography was reconstructed using detailed geological maps, loess thickness maps, and underlying paleotopographic information. The hypsometric integral (HI) and spatial similarity analysis methods were used to compare the spatialized difference between underlying and modern terrain of the Loess Plateau from the perspectives of the landform development stage and surface elevation, respectively. The results of the HI method demonstrate that essentially, there are similarities between the geomorphologic development stages of underlying and modern terrain, and only some local differences exist in some special areas. The results regarding the spatialized coefficient of relative difference and the Jensen–Shannon divergence demonstrate that the thicker the loess is, the weaker the similarity is, and vice versa. Meanwhile, according to the present loess landform division, the order of regional similarity from low to high is as follows: loess tableland, broken loess tableland, hilly regions, dunes, and the Yellow River Trunk. The use of the similarity analysis method to analyze similarities between underlying and modern terrain plays an important role in revealing the inheritance of loess landforms.