# Explainable Machine Learning for Mapping Rainfall-Induced Landslide Thresholds in Italy
## 1 Introduction  
Rainfall-induced landslides are a significant geological hazard that poses severe threats to human lives and property [1]. Some countries have particularly high frequencies of suchlandslides due to their unique geographical locations, geological structure, and climatic conditions [2; 3; 4; 5]. Therefore, diverse strategies for landslide prediction and prevention are being actively explored and implemented globally to answer the crucial question of \"how much rainfall is required to trigger a landslide\". To address this issue, previous studies have proposed empirical statistical models, primarily in the form of rainfall intensity-duration (I-D) curves [6] and cumulative rainfall-duration (E-D) curves [7]. These models establish regional rainfall threshold criteria by describing the statistical relationship between rainfall parameters and landslides, with the aim of determining the minimum rainfall required to trigger landslides in specific geological and climatic regions. Due to the ease of data acquisition and simple computation, these methods allow for the establishment of straightforward and practical early warning standards. Most empirical threshold models typically develop a single universal threshold for the entire study area, ignoring the comprehensive influence of factors such as soil type, vegetation cover, and topography [8; 9; 10]. Although some studies have successfully refined thresholds based on individual factors as division criteria [11; 12], the comprehensive consideration of multiple geological and environmental conditions could further refine the thresholds and enhance their predictive performance. It has been demonstrated by numerous studies that landslide-triggering thresholds vary significantly depending on diverse regional geological and climatic conditions [13; 14; 15], suggesting that more accurate and regionally appropriate threshold models could be achieved through an approach that incorporates various environmental factors. In recent years, machine learning techniques have shown remarkable potential in geohazard prediction accuracy by effectively integrating multiple influencing factors and significantly reducing the economic costs of prediction processes [16; 17], while demonstrating superior performance in handling large-scale datasets to address complex geospatial modeling challenges [18]. Currently, their application is most prevalent in landslide susceptibility mapping. For instance, [PERSON] et al. incorporated 11 topographic factors (e.g., slope) in Lower Austria and systematically compared the performance of six models, including support vector machines (SVM) and random forests (RF) [19]. [PERSON] et al. proposed a heterogeneous ensemble learning (HEL) framework based on foundational models such as deep belief networks (DBN), convolutional neural networks (CNN), and residual networks (ResNet) to enhance modeling efficacy [20]. However, existing studies predominantly rely on static terrain features, neglecting dynamic triggers such as rainfall, which limits real-time early warning capabilities. To address this gap, researchers have begun integrating rainfall factors: [PERSON] et al. used rainfall time series as the sole input variable with long short-term memory (LSTM) networks to predict landslide probability [21], while [PERSON] et al. developed a spatio-temporally coupled landslide prediction framework for rainstorm scenarios by comparing empirical and machine learning approaches [22]. With the increasing complexity of these machine learning models, \"black box\" problems have emerged as a significant concern, making it difficult to understand the model's decision-making rationale [23]. Therefore, researchers have attempted to employ explainable techniques to enhance model transparency by quantifying the contribution of input variables [24; 25].