The determination of the optimal random field element (RFE) size is crucial in soil slope reliability analysis as it governs the trade-off between precision in failure probability calculations and computational efficiency. Given the substantial computational burden associated with smaller RFE sizes, studies on their impact on slope failure probability are scarce. This research examines the influence of RFE size on failure probability and safety factor, employing the Karhunen–Loève expansion to generate random fields and integrating the simplified Bishop method with particle swarm optimization (PSO) to assess slope stability. Through Monte Carlo Simulation (MCS), this study investigates the effects of the ratio of slope height to RFE size (H/D_e) on slope reliability metrics across two illustrative cases. Results reveal a notable influence of H/D_e on the distribution of safety factors (F_s) and failure probability (PF), with overestimation observed at smaller H/D_e ratios. When H/D_e exceeds 10 for Example 1 and 15 for Example 2, the F_s distribution patterns in both scenarios stabilize significantly, displaying minimal variability. The PF of Example 1 and Example 2 decreases with the increase of H/D_e and remains basically unchanged when H/D_e exceeds 10 and 15, respectively. Consequently, a recommended H/D_e ratio of 20 is proposed based on the analyzed cases, facilitating accurate calculations while mitigating computational overhead.

This study examines the intricate relationship between water resource dynamics and drought indices in the Yinchuan Plain, China, by integrating multi-source remote sensing data with advanced deep learning techniques. Using data from 2002 to 2022, we applied Long Short-Term Memory (LSTM) networks to model the spatiotemporal dynamics of water resources and their relationships with the Standardized Precipitation Index (SPI), Standardized Precipitation Evapotranspiration Index (SPEI), and Palmer Drought Severity Index (PDSI). Our findings reveal a strong correlation between total water resources and the SPEI (r = 0.81, p < 0.001), underscoring the pivotal role of evapotranspiration in this region’s water balance. The LSTM model outperformed traditional statistical methods, achieving a Root Mean Square Error of 0.142 for water resource predictions and 0.118 for drought index forecasts. Spatial analysis indicated stronger correlations in the northern Yinchuan Plain, likely influenced by its proximity to the Yellow River and regional water management practices. Wavelet coherence analysis identified significant coherence at the 6–12-month scale, highlighting the importance of seasonal to inter-annual strategies for water resource management. These results provide a robust foundation for developing effective water management policies and drought mitigation strategies in arid and semi-arid regions. The methodologies presented are broadly applicable to similar water-scarce regions, contributing to global efforts in sustainable water resource management under changing climatic conditions.