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[Objective] Rainfall erosivity serves as an indicator to assess the potential impact of rainfall on soil erosion, playing a crucial role in evaluating regional soil erosion risk. Therefore, analyzing the temporal and spatial variations of rainfall erosivity in Beijing from 1981 to 2020 holds significant importance for scientifically assessing and preventing regional soil erosion risks. [Methods] This study employed Kriging interpolation, Mann-Kendall non-parametric test, and wavelet analysis based on daily precipitation data collected from 119 rainfall stations in Beijing and its surrounding areas between 1981 and 2020. These methods were utilized to analyze the spatial distribution, trend changes, and periodic fluctuations of annual rainfall erosivity as well as erosivity associated with moderate rain (10~25 mm), heavy rain (25~50 mm), and extreme rain (≥50 mm) in Beijing. [Results] The annual rainfall erosivity in Beijing ranged from 1 691.51 to 3 914.89 (MJ·mm)/(hm2·h·a) during the period from 1991 to 2020. The spatial distribution characteristics of annual rainfall erosivity exhibited similarities with heavy rain and rainstorm but differed from moderate rain patterns. Overall, there was a decreasing trend observed from northeast regions towards the surrounding areas. Over the past four decades, moderate rainfall erosivity demonstrated a significant increasing trend in Beijing; however, no significant mutations or trends were observed for annual rainfall erosivity, heavy rain events, rainstorms or July-August summer precipitation erosivity. Notably large decreasing trends were identified for annual rainfall erosivity within local areas such as Miyun and Pinggu districts. The main cycle for both annual rainfall erosivity and medium-to-heavy intensity precipitation lasted approximately twenty-five years with two to three alternating “low-high” changes. [Conclusion] The study can offer a scientific foundation for soil and water conservation, agricultural practices, and ecological preservation in Beijing.

Prediction of the rate of penetration (ROP) is integral to drilling optimization. Many scholars have established intelligent prediction models of the ROP. However, these models face challenges in adapting to different formation properties across well sections or regions, limiting their applicability. In this paper, we explore a novel prediction framework combining feature construction and incremental updating. The framework fine-tunes the model using a pre-trained ROP representation. Our method adopts genetic programming to construct interpretable features, which fuse bit properties with engineering and hydraulic parameters. The model is incrementally updated with constant data streams, enabling it to learn the static and dynamic data. We conduct ablation experiments to analyze the impact of interpretable features' construction and incremental updating. The results on field drilling datasets demonstrate that the proposed model achieves robustness against forgetting while maintaining high accuracy in ROP prediction. The model effectively extracts information from data streams and constructs interpretable representational features, which influence the current ROP, with a mean absolute percentage error of 7.5% on the new dataset, 40% lower than the static-trained model. This work provides a theoretical reference for the interpretability and transferability of ROP intelligent prediction models. [ABSTRACT FROM AUTHOR]