Rainfall-Induced Landslide Prediction Models, Part I: Empirical–Statistical and Physically Based Causative Thresholds

Abstract

Introduction and Problem Statement: Landslides represent a significant geological hazard worldwide. One of the primary triggers for these landslides is rainfall, which is becoming more intense as a result of climate change. The available literature has produced extensive research. However, this largely overlooks the use of mixed methodologies. Furthermore, a comprehensive review combining empirical, physically based, deterministic, and phenomenological models is still rare. Objective and Method: This study (Part I of a two-part review) addresses this gap by employing a mixed review that integrates quantitative scientometric analysis with a qualitative systematic review. The primary objective of Part I is to deliver a critical assessment, focusing on empirical and physically based causative threshold models. Main Results and Validation: Macroscopically, our analysis reveals that antecedent rainfall is a more robust indicator than classical intensity–duration (I-D) thresholds, though the latter remains widely used due to its simplicity. Physically based models provide a critical bridge when geotechnical data is scarce, correlating rainfall with internal slope responses like displacement. At a microscopic level, hybrid artificial intelligence (AI) models consistently demonstrate superior predictive accuracy by capturing complex, nonlinear relationships missed by simpler models. These findings are validated through a systematic evaluation of performance metrics across the reviewed literature. Main Conclusions and Significance: We conclude that while empirical thresholds offer operational simplicity, the future of accurate prediction lies in sophisticated hybrid AI models trained on extensive monitoring data. This review synthesizes fragmented knowledge into a unified framework, providing a clear roadmap for model selection.

1. Introduction

“A landslide is the movement of a mass of rock, earth, or debris down a slope [1].” These events, which naturally occur in hilly regions and contribute to landscape evolution, are initiated when slope materials cannot resist the stresses from a variety of triggering factors. As a prevalent global hazard, they cause significant human and economic losses [2]. To quantify this impact, historic severity is highlighted by Froude and Petley [3], who reported that non-seismic landslides caused approximately 55,997 fatalities in 4862 incidents globally between 2004 and 2016. Figure 1a illustrates this global distribution, revealing a pronounced concentration of landslides in some regions (i.e., Asia), which underscores specific regional vulnerabilities. This long-term trend is consistent with the World Health Organization estimates of over 18,000 deaths from 1998 to 2017 (accessed 6 November 2025).

Beyond this historical context, the threat remains current, as demonstrated by a recent world map from the European Commission’s Directorate-General for European Civil Protection and Humanitarian Aid Operations (2022) detailing fatal landslide events from August to December 2020 (Figure 1b). The impact is not uniformly distributed, with regions like China experiencing disproportionately high losses; since 2000, the country has averaged about 600 landslide-related deaths annually, accounting for nearly 25% of its natural disaster mortality [4]. The persistent consequences, including extensive human casualties, destruction of critical infrastructure, and substantial economic losses [5], underscore the urgent need for reducing such catastrophic risk.

To systematically understand and mitigate this risk, it is essential to classify these events. Hungr et al. [6] extended the Varnes system and classified landslides into 32 distinct types based on material composition (such as rock, debris, or soil) and movement mechanisms (such as falls, topples, slides, and flows). This classification offers a more comprehensive framework for understanding different landslide mechanisms. These landslides can be triggered by various factors, including earthquakes, volcanic activity, floods, and intense rainfall. Among these triggers, rainfall is the most common cause of slope instability globally. Increasingly severe rainstorms, driven by climate change, are contributing to a higher frequency of catastrophic landslides [7,8].

With that in mind, for the purpose of this review, the focus is narrowed to rainfall-induced landslides due to their high frequency and destructive potential. Figure 2 visualizes a schematic view of the shallow rainfall-induced landslides. These landslides are typically shallow, with slip surfaces running parallel to the slope surface [9,10]. According to Caine [11], the depth of shallow landslides is generally less than 2 to 3 m, as mentioned by other studies [12,13,14]. The failure mechanism of these landslides involves the movement of soil or debris near the surface, and is characterized by their rapid onset and intensity [15].

To reduce these hazards, mitigation techniques such as stabilizing piles, soil nailing, drainage systems, and other strategies are crucial, particularly when the slope is exposed to unforeseen triggers like heavy rainfall [16]. However, such mitigation strategies should be prioritized and optimized to achieve both practicability, cost, and safety. A key prerequisite for such optimized mitigation is accurate prediction. In recent years, there has been an increased focus on leveraging landslide prediction models as a promising strategy to reduce risks. These models are vital for identifying prone areas and providing timely alerts, thereby minimizing impacts and facilitating the development of early warning systems [17,18].

Consequently, a diverse suite of prediction models has been developed, ranging from simple thresholds to advanced numerical simulation and deterministic models. The available literature offers extensive efforts to review these models, as outlined in Table 1. However, a critical analysis of this existing body of reviews reveals significant gaps. It is seen that many of the available reviews focus on a single methodology, and scientometric analysis has been infrequently applied in this context. Additionally, this knowledge (Table 1) is found to be fragmented, and the literature could be enriched by providing a comprehensive review to synthesize this fragmented knowledge into a unified framework, providing a clear roadmap for model selection.

Therefore, this paper aims to systematically bridge a critical gap in the current literature by conducting a comprehensive review of prediction models for rainfall-induced landslides. It is guided by the following overarching research questions: (a) What are the fundamental strengths and limitations of the predominant model types used in landslide prediction? (b) How can the accuracy and reliability of these models be evaluated and compared? (c) What future research directions are essential for advancing the field towards more robust and operational prediction systems? To answer these questions, this study utilizes a mixed-methods approach, integrating quantitative (scientometric) and qualitative (systematic) analyses. Scientometric mapping will objectively identify dominant research trends and collaborations, while the systematic review will provide a critical, in-depth evaluation of model methodologies and reported accuracies. Furthermore, a bibliometric analysis will be employed to assess and compare the documented performance of various statistical, AI, and probabilistic models identified in the literature. This integrated methodology ensures a holistic and evidence-based assessment of the landslide prediction landscape.

This review paper represents the first of two parts, concentrating on empirical–statistical thresholds and physically based causative models. The second part, which addresses deterministic models and landslide susceptibility assessments, has already been published [19]. Together, these two parties offer a complete overview of the different approaches for predicting rainfall-induced landslides. This two-part review explores the evolution of different approaches, starting with a macroscopic perspective based on input parameters and initial conditions, followed by a microscopic examination of alternative analysis models for the same method. The structure of this research is as follows: Section 2 outlines the research methodology; Section 3 highlights the scientometric analysis; Section 4 focuses on the systematic analysis, which is divided into two subsections—(1) empirical–statistical thresholds, and (2) physically based causative thresholds; Section 5 provides the discussion; Section 6 states the conclusions; and Section 7 proposes future work. The remaining sections summarize the notations and abbreviations and list the references.

Table 1. Available review articles for landslide prediction techniques.

Study	Content
Zhang et al. [12] *	Geotechnical and hydrological concepts related to rainfall-triggered landslides
Chae et al. [20] *	Landslide susceptibility, modeling of runout, monitoring, and early warning systems
Segoni et al. [21] *	Rainfall-based landslide thresholds
Merghadi et al. [22] *	Application of machine learning algorithms for assessing landslide susceptibility
Shano et al. [23] *	Overview of various prediction methods, emphasizing statistical models
Yanbin et al. [24] *	Use of machine learning techniques in landslide susceptibility analysis
Zou & Zheng [25] **	Scientometric review, limited physical prediction models, and case studies
Huang et al. [26] ***	Landslide susceptibility models based on Geographic Information System (GIS) data
Petrucci [27] *	Analysis of the main causes behind landslide-related fatalities
Vung et al. [28] *	Exploration of challenges, opportunities, and future research directions for rainfall-induced landslides
Ebrahim et al. [19] *	Deterministic and susceptibility-based landslide prediction models
Ebrahim et al. [29] *	Time series-based prediction models for landslides

Note: * Refers to systematic reviews; ** Scientometric analysis; *** Bibliometric approach.

Table 1. Available review articles for landslide prediction techniques.

Study	Content
Zhang et al. [12] *	Geotechnical and hydrological concepts related to rainfall-triggered landslides
Chae et al. [20] *	Landslide susceptibility, modeling of runout, monitoring, and early warning systems
Segoni et al. [21] *	Rainfall-based landslide thresholds
Merghadi et al. [22] *	Application of machine learning algorithms for assessing landslide susceptibility
Shano et al. [23] *	Overview of various prediction methods, emphasizing statistical models
Yanbin et al. [24] *	Use of machine learning techniques in landslide susceptibility analysis
Zou & Zheng [25] **	Scientometric review, limited physical prediction models, and case studies
Huang et al. [26] ***	Landslide susceptibility models based on Geographic Information System (GIS) data
Petrucci [27] *	Analysis of the main causes behind landslide-related fatalities
Vung et al. [28] *	Exploration of challenges, opportunities, and future research directions for rainfall-induced landslides
Ebrahim et al. [19] *	Deterministic and susceptibility-based landslide prediction models
Ebrahim et al. [29] *	Time series-based prediction models for landslides

Note: * Refers to systematic reviews; ** Scientometric analysis; *** Bibliometric approach.

2. Methodology of the Study

This study employs a mixed-methods approach combining quantitative scientometric analysis and qualitative systematic review to address the complex, interdisciplinary nature of landslide predictions. The systematic review provides a detailed critical analysis of specific models, while the scientometric analysis objectively maps research landscapes and emerging trends through data-driven techniques. The integrated approach yields complementary insights: the scientometric analysis reveals predominant patterns across the research domain, while the systematic review investigates how and why these patterns emerge. This dual perspective enables both macroscopic overview and microscopic analysis, following established practices in complex field reviews [30,31,32]. The methodological framework is illustrated in Figure 3 and Figure 4, which detail the systematic review and scientometric analysis procedures, respectively. The following subsections provide comprehensive descriptions of each methodological phase.

2.1. Search Strategy Design

Landslides can be classified based on various factors, such as geology, engineering, environmental science, ecology, meteorology, atmospheric science, geochemistry, geophysics, physical science, and water resources [25]. Additionally, as highlighted in the keyword mapping by Zou and Zheng and Ebrahim et al. [25,33], landslides are associated with a wide range of keywords. Therefore, the research h process begins with the identification of relevant studies on landslides, guided by the authors’ perspectives. This section outlines the use of keywords, search databases, and inclusion and exclusion criteria to filter the collected papers. The subsequent screening methodology follows the PRISMA framework in Section 5.

2.2. Database Selection and Search Execution

To ensure robust retrieval of relevant articles, the search was conducted across two premier bibliographic databases: Scopus and Web of Science. These platforms were selected for their extensive coverage of the peer-reviewed literature and their compatibility with scientometric analysis tools like VOSviewer (version 1.6.20). Google Scholar was utilized as a supplementary source for the snowballing process to identify additional studies not indexed in the primary databases. The core search was performed using the “landslide prediction” keyword to comprehensively target the relevant literature.

2.3. Screening and Eligibility Criteria

The retrieved studies were filtered using explicit inclusion and exclusion criteria to ensure the review’s focus and quality. The inclusion criteria were as follows: (1) studies primarily focused on landslide prediction with the aim outlined in Section 1; (2) publications from the year 2000 up to 2024; (3) articles published in peer-reviewed journals; (4) document types limited to research articles and review papers; and (5) availability of the final publication version. The exclusion criteria comprised (1) non-English publications, due to their minority within the relevant literature and limitations in translation resources; (2) studies with unavailable full text; (3) manuscripts from subject areas unrelated to engineering; and (4) publications from non-journal sources (e.g., conference proceedings, books). The application of this screening process is detailed in the PRISMA flow diagram (Figure 5).

2.4. Screening and Assessment of Collected Articles

The initial searches in Scopus and Web of Science yielded 88 and 99 articles, respectively. After removing 8 duplicate articles, 179 unique records remained for screening. The relatively low number of duplicates can be attributed to the different indexing criteria between Web of Science and Scopus databases, as well as the broad range of related keywords in this field. The systematic review and meta-analysis (PRISMA) procedure [34] was then applied to evaluate the collected articles (see Figure 5). This screening process led to the exclusion of 47 papers due to irrelevance or unavailability of full texts. After full-text evaluation of the remaining articles, 132 articles met the inclusion criteria.

Subsequently, backward and forward snowballing approaches [35] were employed to identify additional studies not captured by the database searches. The 132 included papers served as the starting set for these snowballing strategies. Backward snowballing involved examining reference lists of included papers, while forward snowballing identified new publications that cited these papers. This iterative process continued until no new relevant documents emerged, resulting in the discovery of 68 additional articles. Furthermore, 29 papers were included through manual searches during the full-text review phase, bringing the final total to 229 articles included in this study. The complete screening and evaluation process is summarized in Figure 5.

2.5. Limitations of the Methodology

While this mixed-methods approach provides comprehensive insights into landslide prediction research, several methodological limitations should be acknowledged: (a) The selected keywords, while informed by previous studies, may not fully capture the entire spectrum of the landslide prediction literature. Some relevant studies might use alternative terminology or focus on specific sub-domains not adequately represented by our search terms.

(b) The reliance on major indexed databases (Scopus and Web of Science), while necessary for scientometric analysis, potentially excludes relevant studies from non-indexed journals, conference proceedings, and regional publications. Furthermore, the review exclusively includes English-language publications due to practical translation constraints, which may overlook valuable research published in other languages.

(c) The scientometric analysis depends on the algorithmic capabilities of VOSviewer, which may occasionally struggle with author disambiguation and capturing the nuanced, interdisciplinary terminology characteristic of landslide prediction research. Additionally, the manual classification of 229 studies into specific model categories was beyond this study’s scope due to resource and time constraints, representing a valuable direction for future systematic annotation efforts.

3. Scientometric Analysis

This section provides a detailed analysis of the selected studies. The scientometric analysis was initiated following the completion of the screening process to examine relationships among authors, keywords, publications, and countries within specific research domains. This analysis was performed using the open-source VOSviewer software tool [36], a widely recognized visualization application employed in this study to analyze the results. The primary objective of the scientometric analysis is to ensure that the findings are meaningful and relevant for inclusion in the systematic review. A total of 229 manuscripts, identified through snowballing and manual searches, were analyzed using VOSviewer software.

3.1. The Trend in Annual Publications for Landslide Prediction

Figure 6 illustrates the annual publication trend in landslide prediction research, revealing distinct phases of activity. The period from 2000 to 2014 was characterized by a low, steady output of approximately three articles per year. A significant and sustained surge began around 2015, with annual publications rising sharply from 8 to a peak of 28 by 2023. This notable increase is not merely correlational; it can be causally linked to two key drivers: (1) the widespread adoption of advanced machine learning techniques, which provided new capabilities for analyzing complex geospatial and triggering data, and (2) growing research into the impacts of climate change, particularly the influence of more frequent and intense rainfall events on slope stability. The apparent decline to eight publications in 2024 is an artifact of the literature collection cutoff date for this analysis and does not reflect a genuine decrease in research interest. As this study’s literature search was concluded during this year, many relevant articles from 2024 were likely still in the publication pipeline or not yet indexed in the selected databases.

3.2. Leading Journals in Landslide Prediction Contributions

VOSviewer software was utilized to identify the leading journals in landslide prediction research, with the results presented in

Table 2. The top journals contributing to landslide prediction research: Ranked by document and citation counts (No.).

No.	Source	Documents (No.)	Citations (No.)	Total Strength Link
1	Landslides	32	4195	1190
2	Engineering Geology	19	1414	733
3	Bulletin of Engineering Geology and the Environment	11	317	625
4	Applied Sciences (Switzerland)	11	178	354
5	Géotechnique	8	6117	142
6	Geotechnical and Geological engineering	7	173	330
7	Sustainability (Switzerland)	7	76	253
8	Journal of Hydrology	6	1456	396
9	Geoenvironmental disaster	5	404	405
10	stochastic environmental research and risk assessment	5	290	172

. This analysis provides valuable guidance for researchers seeking reputable publication venues in this field. Two thresholds were established for the VOSviewer analysis: a minimum of five papers per journal and a minimum of ten citations per journal. The analysis was conducted using “sources” as the unit of analysis and employed “bibliographic coupling” as the analysis method. From an initial pool of 86 journals, 10 met the established criteria (Figure 7). It should be noted that there are no universally established standards for these threshold values [25]. In Figure 7, the node sizes reflect the journals’ relative influence based on publication volume, while the connecting lines represent citation relationships between journals, with total link strength indicating the intensity of these connections [36]. Table 2 reveals that “Landslides” emerges as the dominant journal in this field, with the highest number of publications (32 articles) and citations (4195), establishing it as one of the most influential publication venues for landslide prediction research.

3.3. Active Nations in Landslide Prediction

Understanding scientific collaboration networks in any field of study facilitates the identification of leading scientists, laboratories, organizations, authors, and nations, thereby greatly enhancing academic cooperation. In this analysis, the previously mentioned thresholds were applied using “countries” as the unit of analysis and “bibliographic coupling” as the analysis type. From a total of 44 countries analyzed, 15 met the established criteria. The node size in Figure 8 represents each country’s influence in the field, weighted by publication volume. China and Italy emerged as the most prolific contributors worldwide, with 77 and 31 publications, respectively, indicating their dominant research output in landslide prediction.

Table 3. The top five prominent and publishing countries relevant to landslide prediction.

Country	Documents	Citations	Total Link Strength
China	77	3896	7348
Italy	30	5007	5622
United States	26	5146	2963
United Kingdom	20	6299	2623
Japan	11	2351	2098

further details the top five countries contributing to landslide prediction research. This analysis of national collaboration networks benefits both academic and industrial practitioners seeking innovative landslide solutions by highlighting the geographic centers of research investment and expertise in this field.

3.4. Article Co-Citation Analysis in Landslide Prediction

The total number of citations a publication receives reflects its contribution to the field. Accordingly, this section highlights the most cited publications in landslide prediction research. Since these publications demonstrate limited bibliographic coupling, the top 10 cited articles were selected directly from the Scopus and Web of Science databases (Table 4). These influential works span from 2000 to 2024, representing key developments in the field over nearly a quarter-century. To address the inherent advantage older research possesses in accumulating citations compared to more recent work, this study employed a normalized citation measure. The citation count for each article was normalized by dividing by the average number of citations for all articles published in that year [36], thereby providing a more equitable assessment of research impact across different publication periods.

Table 4. Top 10 cited articles according to normalized citations (NS).

Author	Article	Journal	Citation	NS
Merghadi et al. [22]	Machine learning methods for landslide susceptibility studies: A comparative overview of algorithm performance	Earth-Science Reviews	603	8.20
Soga et al. [37]	Trends in large-deformation analysis of landslide mass movements with particular emphasis on the material point method	Géotechnique	383	5.80
Froude & Petley [3]	Global fatal landslide occurrence from 2004 to 2016	Natural Hazards and Earth System Sciences	1164	5.62
Ebrahim et al. [33]	Recent Phenomenal and Investigational Subsurface Landslide Monitoring Techniques: A Mixed Review	Remote Sensing	7	4.90
Hungr et al. [6]	The Varnes classification of landslide types, an update	Landslides	2274	4.32
Ikram et al. [38]	A novel swarm intelligence: cuckoo optimization algorithm (COA) and SailFish optimizer (SFO) in landslide susceptibility assessment	Stochastic Environmental Research and Risk Assessment	37	4.16
Zhang et al. [39]	Application of an enhanced BP neural network model with water cycle algorithm on landslide prediction	Stochastic Environmental Research and Risk Assessment	140	3.50
Mondini et al. [40]	Deep learning forecast of rainfall-induced shallow landslides	Nature communications	31	3.49
Chae et al. [20]	Landslide prediction, monitoring and early warning: a concise review of state-of-the-art	Geosciences Journal	267	3.03
Long et al. [41]	A multi-feature fusion transfer learning method for displacement prediction of rainfall reservoir-induced landslide with step-like deformation characteristics	Engineering Geology	47	2.94

Table 4. Top 10 cited articles according to normalized citations (NS).

Author	Article	Journal	Citation	NS
Merghadi et al. [22]	Machine learning methods for landslide susceptibility studies: A comparative overview of algorithm performance	Earth-Science Reviews	603	8.20
Soga et al. [37]	Trends in large-deformation analysis of landslide mass movements with particular emphasis on the material point method	Géotechnique	383	5.80
Froude & Petley [3]	Global fatal landslide occurrence from 2004 to 2016	Natural Hazards and Earth System Sciences	1164	5.62
Ebrahim et al. [33]	Recent Phenomenal and Investigational Subsurface Landslide Monitoring Techniques: A Mixed Review	Remote Sensing	7	4.90
Hungr et al. [6]	The Varnes classification of landslide types, an update	Landslides	2274	4.32
Ikram et al. [38]	A novel swarm intelligence: cuckoo optimization algorithm (COA) and SailFish optimizer (SFO) in landslide susceptibility assessment	Stochastic Environmental Research and Risk Assessment	37	4.16
Zhang et al. [39]	Application of an enhanced BP neural network model with water cycle algorithm on landslide prediction	Stochastic Environmental Research and Risk Assessment	140	3.50
Mondini et al. [40]	Deep learning forecast of rainfall-induced shallow landslides	Nature communications	31	3.49
Chae et al. [20]	Landslide prediction, monitoring and early warning: a concise review of state-of-the-art	Geosciences Journal	267	3.03
Long et al. [41]	A multi-feature fusion transfer learning method for displacement prediction of rainfall reservoir-induced landslide with step-like deformation characteristics	Engineering Geology	47	2.94

3.5. Keyword Co-Occurrence Mapping in Landslide Prediction

VOSviewer software was used to identify the most frequently used keywords by selecting “co-occurrence” as the analysis type and “all keywords” as the unit of analysis. For this study, a keyword was required to have a minimum of ten occurrences. Out of 1785 total keywords, 45 met this threshold, as visualized in Figure 9. The size of each node is proportional to the keyword’s frequency, with “landslide” and “landslides” appearing as the most dominant terms. The analysis reveals three distinct thematic clusters: a blue cluster associated with landslide susceptibility mapping, a red cluster focused on physical models, and a green cluster centered on physically based thresholds. This keyword mapping elucidates the primary research streams within the field, demonstrating that current work converges on susceptibility assessment, mechanistic modeling, and threshold determination. This objective, data-driven clustering helps researchers identify core topics and select effective keywords to enhance the discoverability of their future publications, complementing the more subjective conclusions derived from narrative and systematic evaluations [42].

4. Systematic Review

This section provides a comprehensive review of landslide prediction techniques. These techniques can be classified according to two primary criteria: (1) the scale of the investigated case study, and (2) the accessibility of inventory data. Landslide events can be examined from either local or national perspectives. The classification by scale is addressed by Oguz et al. [43], who categorized landslides into local and national scales. For clarification, Figure 10 presents a national map of Hong Kong alongside a specific local landslide from 2018. For local-scale analysis, empirical–statistical thresholds, triggering-physical thresholds, and physical–deterministic models can be implemented based on data availability and required prediction accuracy. Conversely, landslide susceptibility, risk, and vulnerability maps are typically utilized at the national scale. Figure 11 summarizes the complete review process based on this classification framework. This figure will be discussed in detail across both parts of this study: Part I (this manuscript) and the published Part II [19]. All figures and comparative analyses presented herein were developed by the authors to synthesize trends and findings from the literature. While based on previously published research, each appropriately cited in the text, direct attribution of all sources within figures is impractical due to the substantial number of studies included. Readers are referred to the relevant textual citations for detailed references.

4.1. Empirical–Statistical I-D Thresholds

4.1.1. Intensity–Duration Thresholds

Understanding the causal factors that trigger landslides is fundamental to effective hazard assessment. Among these factors, rainfall is the most prevalent and widely studied trigger. Historically, landslides have demonstrated a strong correlation with rainfall patterns, where slope failures frequently correspond to specific hydro-meteorological conditions. This relationship has led researchers to increasingly employ empirical rainfall thresholds for landslide prediction [11,45,46,47]. These thresholds are crucial for predicting potential landslides and form a core component of many landslide early warning systems. They are typically derived by analyzing historical data on rainfall intensity (I) and duration (D) for specific regions, beyond which landslide initiation becomes probable [48,49]. In other words, as illustrated by Guzzetti et al. [50], “Rainfall thresholds are defined by a minimum amount of rainfall that, when exceeded, can trigger landslides. With that in mind, several statistical approaches have been developed to define these thresholds. Early and site-specific formulations include the regression-based Equation (1) proposed by Caine [11] and Equation (2) by Hong et al. [45]. To enhance generalizability, Peruccacci et al. [51] proposed a more universal formulation (Equation (3)) for landslide-prone areas using the innovative CTRL-T methodology [47]. The CTRL-T framework represents an advanced approach for the automated extraction of rainfall data [52], thereby improving the precision and objectivity of threshold determinations. Building on these concepts, Ering and Babu [53] developed Intensity–Duration (I-D) thresholds using the Forecasting of Landslides Induced by Rainfall (FLaIR) model. A key advantage of the FLaIR model is its ability to process varied rainfall inputs through a gamma-type transfer function, denoted as Ξ(t) (Equation (4)).

$$I=14.82D^{-0.39}$$

(1)

$$I=15.58D^{-0.52}$$

(2)

$$E=(\epsilon \pm \Delta \epsilon )D^{(\xi \pm \Delta \xi )}$$

(3)

$$\Xi (t)=t^{\nu -1}\exp \left(-{\displaystyle \frac{t}{\mathrm{T}}}\right)/T^{\nu }\Gamma (\nu )$$

(4)

where E represents the rainfall event, ϵ is the scaling parameter, and ζ is the shape parameter, which defines the intercept and slope of the power law curve, respectively. Additionally, Δϵ and Δζ denote the uncertainties associated with these two parameters. υ denotes the dimensionless parameter, and T denotes the temporal scale.

Figure 12 demonstrates a critical limitation of intensity–duration (I-D) thresholds: while they can achieve high predictive accuracy, their operational effectiveness is substantially constrained by a significant rate of false positive alarms [49,54,55]. This limitation arises from the fundamental principle of the I-D method, which establishes a fixed critical rainfall intensity for a given duration, beyond which landslides are predicted. However, this binary approach often fails to account for complex antecedent conditions, such as variable soil moisture and regional hydrological characteristics, leading to warnings being triggered by rainfall events that meet the I-D criteria but simplify actual slope failures.

4.1.2. Antecedent Rainfall Thresholds

To address the limitations of conventional I-D thresholds, researchers have developed more sophisticated causal thresholds that account for the physical processes linking rainfall to slope failure. Rainfall influences landslide occurrence through multiple interconnected mechanisms, including increased ground saturation, elevated soil weight, rising groundwater levels, soil erosion, and reduced effective stress, all of which collectively diminish the slope safety factor [56]. When analyzing rainfall-induced landslides, antecedent rainfall plays a crucial role in preconditioning slopes for failure [54]. This factor helps incorporate other causative elements that contribute to landslide initiation [46,54,55,56]. The hydrological processes involved, including infiltration, storage, and evaporation, are primarily governed by the temporal dynamics of porewater pressure changes in subsurface soils [55]. However, the critical duration of antecedent rainfall that optimally predicts landslide occurrence remains uncertain [56]. To operationalize these concepts, Lee et al. [46] proposed the Antecedent Precipitation Index (API), quantified in Equations (5)–(7). Concurrently, Huang et al. [13] developed an alternative approach that integrates both maximum hourly rainfall intensity with cumulative current rainfall and precipitation from the preceding six days.

$$AP{I}_{30}=115+1.2\times {10}^{-12}{N}^{10.6}$$

(5)

$$E_3=-0.726AP{I}_{30}+295.0$$

(6)

$$E_3=-0.726AP{I}_{30}+194.3$$

(7)

where API₃₀ is the 30-day antecedent precipitation index, N is the number of rainy days within the 30 days concerned, and E₃ is the cumulative 3-day rainfall. Equation (6) is for a major landslide, and Equation (7) is for a medium landslide.

To enhance the analysis of antecedent rainfall, Hong et al. [54] applied inter-event time definitions (IETDs), the time interval separating distinct rainfall events, and determined that a 12 h IETD yielded the highest predictive accuracy, as visualized in Figure 13. Rather than relying on a single duration, Chhorn et al. [56] proposed that a combination of multiple antecedent periods improves forecast precision, identifying a specific combination of 1 h, 15 h, and 19 days that achieved a 58.5% probability of landslide occurrence. Concurrently, Uwihirwe et al. [55] employed a Bayesian probabilistic approach, finding that the most accurate model (AUC = 0.669) integrated rainfall from the event day with that of the preceding 10 days (Figure 14a). Further advancing the methodology, Zhao et al. [57] developed a modified API that accounts for variations in evaporation and maximum soil moisture capacity. This refined threshold demonstrated superior performance over the general I-D form proposed by Brunetti et al. [58] (Figure 14b). Supporting the value of extended antecedent periods, Aryastana et al. [59] concluded that a 30-day cumulative rainfall window could enhance traditional thresholds, achieving over 90% accuracy.

4.1.3. I-D Thresholds Prediction Accuracy

The accuracy of any landslide prediction model is contingent upon several factors, including data availability, rainfall parameters, and site-specific characteristics. Uwihirwe et al. [55] employed a Bayesian probabilistic approach, maximum true skill statistic, and minimum radial distance to evaluate various rainfall-triggering thresholds. As shown in Figure 14a, while rainfall event-based analysis achieved the highest accuracy (AUC), it was accompanied by a high false positive rate (FPR). In contrast, incorporating the simple causative antecedent rainfall index (API₁₀) significantly reduced the FPR. Similarly, Zhao et al. [57] demonstrated that a modified API outperforms conventional I-D models (Figure 14b). Collectively, these findings indicate that accounting for slope response through antecedent moisture dynamics enhances model accuracy compared to relying solely on rainfall data. Recent studies have increasingly adopted such trigger thresholds for landslide causation [13,46,54,56,60]. While these methods are straightforward and consider antecedent rainfall as a primary causative factor, further improvements in prediction accuracy require the integration of additional causative features, which will be explored in Section 5.2, “Physically Based Causative Thresholds”.

4.2. Physically Based Causative Thresholds and Prediction

A landslide occurring during a rainfall period where total precipitation reaches its peak defines the critical duration. However, if a landslide occurs when cumulative antecedent rainfall is not at its maximum, the failure is likely attributable to non-rainfall factors [56]. This highlights that the term physically based causative refers to an approach that integrates rainfall as the primary triggering factor with secondary indicators of slope instability to enhance prediction pacity and topography, explain why rainfall alone cannot deterministically predict landslides [49,54]. By complementing rainfall with physical precursors such as soil moisture content [57,61,62], topographic thresholds [63], displacement patterns [64], soil suction [65], and groundwater levels [66], models achieve more robust accuracy with lower false positive rates. Therefore, this section is organized according to the classification framework in Figure 15 to systematically review these integrated applications and provide a more holistic understanding of landslide dynamics.

4.2.1. Displacement Instability Performance and Prediction

Landslide displacement prediction follows a systematic framework comprising four fundamental processes: (1) data inventory and input parameter identification, (2) model selection, (3) data preparation involving sampling and decomposition techniques, and (4) model evaluation. This methodological workflow, illustrated in Figure 16, structures the subsequent detailed discussion of each component.

1.

Data inventory and input model parameters

When sufficient monitoring data are available, various mathematical approaches can effectively predict landslides with reasonable accuracy. Comprehensive site investigations, real-time monitoring, and laboratory tests provide critical early warning indicators. For instance, significant pore-pressure variations often precede substantial slope movements, serving as reliable precursors. However, the effectiveness of these methods depends heavily on both the precision of geotechnical data interpretation and the strategic selection of monitoring locations. Given that characterizing geotechnical and hydrological properties requires extensive effort and offers limited generalization capabilities [67], displacement monitoring presents a practical alternative to overcome these limitations [68]. Multiple researchers have employed continuously monitored displacement data using diverse technologies, including GPS [39,67,68,69,70,71,72], GNSS [73], optical fiber [74], and fiber Bragg grating [75]. The Three Gorges region along China’s Yangtze River represents one of the most extensively studied areas, where landslides are triggered by rainfall and reservoir level fluctuations [39,41,68,69,70,71,72,74,76,77,78,79,80,81,82]. Beyond historical displacement data, prediction models incorporate the various causative factors summarized in Table 5. These encompass rainfall parameters (up to 75 features) [73], antecedent and rolling rainfall with intensity and effective rainfall metrics [78], groundwater level indicators (up to 10 variables) [73], climate features [83], reservoir water level parameters (current value, antecedent change rate, average value, etc.) [39,72], and porewater pressure [64,84]. Figure 17 provides a schematic overview integrating these variables.

2.

Model selection

Regression analysis has been widely adopted in landslide prediction due to its advantages of not requiring prior information to establish functions, its straightforward interpretability, and its capacity to estimate input variable contributions [85]. For instance, Bednarczyk [64] used linear regression to correlate displacement magnitude with cumulative rainfall and pore pressure, while Chen et al. [86] applied it to examine the relationships between rainfall, reservoir levels, and displacement; however, such linear approaches often fall short because the relationships are inherently complex and nonlinear, primarily due to a variable time lag—ranging from six months to six days [86] (Figure 18)—between peak triggering events and peak slope response. This complexity is exemplified by Abolmasov et al. [87], who found a low correlation (R² = 0.145) when relating displacement to river level, even while accounting for time-lag and acceleration concepts (Figure 19). Consequently, more sophisticated regression techniques have been explored, such as the hyperbolic relationships used by Sasahara [84] to reasonably predict shear strain and displacement from pore water pressure, though this was demonstrated only on a uniform laboratory soil model, unlike complex natural slopes. Advancing beyond these methods, Li et al. [70] developed a novel Short-Term Forecasting of Landslides (STFL) model that achieved high accuracy (R² > 0.99) in predicting failure time (Equation (8), Figure 19) by utilizing displacement parameters in the tertiary stage (when the tangential angle exceeds 79°) and solving for unknowns with the Levenberg–Marquardt algorithm.

$$S=P_1(P_2^{P_{3}t}-1)/(P_0-t)$$

(8)

where P₀, P₁, P₂, and P₃ are the simulated parameters, t denotes time, and S denotes displacement.

Landslide deformation thresholds are highly site-specific and vary significantly between different landslides, making universal displacement thresholds unreliable for general application. To address this limitation, Shentu et al. [75] proposed using the direction angle of displacement as an alert criterion instead of absolute displacement values. However, this method presents its own challenges, as the tangential angle of the displacement curve becomes sensitive to changes in the scale of either the displacement or time axes. Consequently, Li et al. [70] recommended utilizing the displacement rate as a more robust indicator. Despite these methodological challenges, researchers continue to pursue displacement-based prediction methods aimed at forecasting slope behavior before actual failure, with the ultimate goal of establishing reliable displacement thresholds for early warning systems.

The advancement of intelligent algorithms has led to the increasing application of nonlinear models in landslide displacement prediction. Furthermore, investigating triggering factors enhances dataset quality, reduces randomness, and decreases computational demands [74]. Consequently, linear or empirical equations prove inadequate for simulating dynamic, nonlinear, and asymmetrical data [68,69]. Intelligent models provide an effective approach for managing such complex dynamic relationships. AI techniques can be categorized into regression [67], classification (supervised) [88], and clustering (unsupervised) methods [77,89]. Supervised learning techniques have become predominant in recent research [33]. Intelligent regression models can predict displacement [68], groundwater levels, and matric suction [65]. These models can be integrated with physical approaches to enhance performance [90], reduce uncertainty [79], and address missing data issues [89]. Classification models have been utilized for landslide susceptibility mapping [88], while artificial regression models have been primarily applied to regional-scale analyses, similarly to physical models and empirical–statistical thresholds. Concurrently, classification methods and landslide susceptibility mapping (LSM) have been mainly employed for large catchment areas to inform land-use planning [91]. This study first discusses regression intelligence models (Part I), while LSM is addressed in the published Part II (refer to Ebrahim et al. [19]). Figure 20 illustrates recently adopted methods for displacement prediction.

Various single AI models have been implemented, including ANN (BPNN) [78,89,92], RNN [69], ELM [69,76], GM(1,1) [69], SVM [76], RF [73,83], and MLR [83]. However, these individual models may require enhancement due to the dynamic nature of landslides and their influencing factors [68,69,70,80]. For instance, landslide displacement can be categorized into trend and periodic components, as depicted in Figure 21. The trend component primarily relates to the creep effect, influenced by lithology, structure, and stress state, while the periodic component corresponds to random factors, such as rainfall, reservoir level fluctuations, and groundwater variations. Predicting sudden displacement changes has attracted significant attention due to its critical implications [77]. Traditional models like ANN and SVM demonstrate limited accuracy in predicting such behavior because the volume of anomalous displacement points is substantially smaller than trend points. Additionally, periodic points consistently exhibit delayed responses to triggering factors (Figure 22). Therefore, Gao et al. [80] and Li et al. [70] recommend employing multi-data-driven models to address these complex behaviors.

To overcome the limitations of single models, researchers have developed various hybrid approaches including EEMD–ELM [68], LSTM-DMA [79], GM-ENN [80], KGM, MKGW, and WMKGM [70], WCA-BPNN [39], SSA-LSTM [93], EEMD-RNN, EEMD-GRU, EEMD-LSTM, EEMD-SVM, EMD-LSTM, and EEMD-ELM [67], ELM-RS-SVR [82], SVM-(MSI, BA, GWO, DA, WOA, GOA, SSA)-CEEMD [71], SVC-PSO-SVR [74], DES-VMD-(BLSTM, BGRU, BRNN), DES-(BLSTM, BGRU, BRNN) [72], and (GOA-GA-VMD)-GRA-(TempoVar-Transformer) [94]. Hybrid models integrate the advantages of multiple approaches to overcome the limitations inherent in single-model frameworks.

3.

Model decomposition and data preparation

Cumulative displacement can be decomposed into creep and accelerated components (Figure 22) using various analytical techniques, including high-pass (HP) filter analysis [39], double moving average (DMA), and single moving average (SMA) models [79]. Additional decomposition methods comprise empirical mode decomposition (EMD) [67], ensemble empirical mode decomposition (EEMD) [68], EEMD with kurtosis criterion [67], and complete ensemble empirical mode decomposition (CEEMD) [71]. The CEEMD method offers an advantage over EMD and EEMD by effectively handling residual terms that exhibit an initial decrease followed by an increase. For state classification, a support vector classifier (SVC) can distinguish between creep and acceleration phases [74]. Alternative approaches include DES-BDNN [72] and K-means clustering [77], which divide total displacement into stationary and mutational points. Variational mode decomposition (VMD) may also be employed to isolate displacement components, with optimization through the GroupWise coupling algorithm [94]. The final cumulative predicted displacement is obtained by superimposing results from both trend and periodic models. Notably, periodic displacement prediction utilizes factors such as rainfall, reservoir level, groundwater level, and prior periodic displacement data, while trend displacement is forecast using historical cumulative displacement records [67].

4.

Training and testing data split ratio

The ratio between training and testing datasets significantly influences prediction accuracy in landslide displacement modeling. Krkač et al. [73] evaluated various split ratios and determined that testing ratios up to 4% yield acceptable results (Figure 23). In another study, Krkač et al. [83] implemented 49 folds with a 98% training and 2% testing ratio. Wang et al. [72] developed a novel approach using Variational Mode Decomposition (VMD) and interpolation to reduce nonlinear displacement complexity and expand training data quantity, respectively. Most studies referenced in Table 5 partitioned monitoring data according to specific time periods or fixed measurement counts. For comparative analysis, when ratios are unspecified, we recommend calculating and rounding to approximately 5%. Common sampling ratios include 70%:30% [39,65,69,71,78,80,94] and 80%:20% [68,76,77,79,90,93], with additional configurations of 85%:15% [67,74], 90%:10% [70,82], 60%:40% [84], and 50%:50% [92] also being implemented across various studies.

5.

Missing data and training data shortage

Monitoring surface displacement involves complex challenges, including device failure, data noise, and signal loss, which often result in reduced forecast accuracy [75]. Furthermore, automated monitoring equipment operating in outdoor environments faces inevitable issues such as hardware deterioration, aging components, power supply interruptions, and other factors that contribute to incomplete datasets [81]. To address these limitations, researchers have employed various strategies, including removing incomplete data segments when developing complex intelligence models [89]; working with limited datasets [75]; applying statistical methods to fill missing data series [70,81]; and implementing fusion transfer learning approaches [41].

de Souza and Ebecken [89] combined artificial neural networks with statistical methods (correlation analysis and principal component analysis) and clustering techniques (K-means and Dendrogram) to reconstruct missing rainfall data, finding that PCA combined with correlation analysis and ANN yielded optimal results. Shentu et al. [75] utilized limited sample data with a novel multivariate gray model (Feedback Optimizing Background Grey Model FOBGM (1, N)) to predict deep displacement, demonstrating superior accuracy compared to GM (1,1), GM (1, N), OGM (1, N), and BPNN models. However, this study was conducted under controlled laboratory conditions and did not account for real-world complexities, while the use of small-sample datasets remains suboptimal [81].

Alternative approaches include the mean-based low-rank autoregressive tensor completion (MLATC) method for time series prediction of landslide displacement, specifically designed to address missing data in monitoring processes [81]. Li et al. [70] implemented cubic spline interpolation for data gap filling, Savitzky–Golay filters for noise reduction, and t-tests for outlier removal. A particularly innovative methodology was proposed by Long et al. [41], based on the premise that landslides in similar geographical and geological settings exhibit comparable deformation patterns despite magnitude variations. Their multi-feature fusion transfer learning (MFTL) approach incorporates data from neighboring locations with similar displacement characteristics to create robust training datasets, providing an effective solution for limited data scenarios. This framework considered influencing factors such as rainfall and reservoir level fluctuations to predict both mutation and creep displacements, with additional refinement for mutation displacement prediction through the integration of non-uniform weight error (NWE) with MFTL to enhance accuracy.

6.

Regression performance evaluation

Model accuracy in displacement prediction is commonly assessed using the coefficient of determination (R²) and root mean squared error (RMSE), supplemented by additional metrics including mean absolute error (MAE) and mean squared error (MSE). These evaluation parameters are calculated using Equations (9)–(12) [95]. For error-based metrics (RMSE, MAE, MSE), values approaching zero indicate superior predictive accuracy, while higher values reflect poorer model performance. In contrast, R² values closer to 1.0 represent a better model fit. The standard deviation ratio (SDR) provides another validation measure, where values nearest to zero signify the highest accuracy [96]. Pearson correlation coefficient (PRC) values range from −1 to +1, with +1 indicating perfect positive correlation and −1 representing perfect negative correlation [97].

$$R^2=1-\left({\displaystyle \sum _{i=1}^N{\left(X_i-Y_i\right)}^2}/{\displaystyle \sum _{i=1}^N{\left(Y_i-\overline{Y}\right)}^2}\right)$$

(9)

$$RMSE=\sqrt{{\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N{\left(X_i-Y_i\right)}^2}}$$

(10)

$$MAE={\displaystyle \frac{1}{N}}{\displaystyle \sum _{i=1}^N\left|X_i-Y_i\right|}$$

(11)

$$MSE={\left(RMSE\right)}^2$$

(12)

where Y_i is the specific value of the ith real data, $\overline{Y}$ is the average value of the real data, and X_i is the specific value of the ith predicted data.

7.

Displacement models’ prediction accuracy

The performance of prediction models depends not only on algorithmic sophistication but also on the underlying controlling factors. While physical models benefit from established theoretical relationships between input and output parameters, statistical and intelligent models derive their effectiveness from several critical factors: strong dependency relationships, dataset quality, sampling ratios, and inventory data accuracy. Table 5 provides a comprehensive comparison of these models, evaluating both final accuracy and overall performance, with Figure 24, Figure 25 and Figure 26 specifically highlighting models demonstrating superior results.

No universally superior model exists across all scenarios. Optimal prediction depends on a thorough investigation of influencing features and careful consideration of actual initial conditions, which can substantially enhance accuracy (Figure 21) [74,98]. Consequently, removing outdated or irrelevant features can improve model performance [76]. While studies indicate that BPNN [78] and MLR [83] provide reasonable accuracy, these simpler models often fail to capture dynamic nonlinear relationships, particularly when datasets closely represent physical mechanisms [78,83]. Marrapu et al. [90] demonstrated that ANNs trained on extensive datasets achieve higher accuracy than those using limited data, though models require refinement when datasets lack critical information [39].

Understanding physical behavior and initial conditions remains essential for appropriate model selection. For instance, Wang et al. [82] improved model suitability by categorizing displacement into trend and periodic components. When evaluating model accuracy independently of dataset characteristics and sampling ratios (Figure 24, Figure 25 and Figure 26), GM(1,1) achieved the minimum RMSE among single models for total displacement, while PSO-SVR-SVC recorded the minimum RMSE among hybrid models. For creep displacement, simple polynomial regression achieved the maximum R², while the LSTM-DMA hybrid model recorded the minimum RMSE. Regarding periodic displacement, RS-SVR achieved both maximum R² and minimum RMSE.

Generally, trend displacement can be accurately predicted using simple polynomial regression [39,82], gray models [80], or single models like ELM [82] and DES [72]. However, periodic displacement exhibits complex nonlinear behavior [70,80] that requires hybrid model analysis, such as RS-SVR, for short-term acceleration effect prediction.

Table 5. AI models for predicting landslide displacement (modified after Ebrahim et al. [29]).

Study	Key Features	Model with the Best Accuracy			Sampling Ratio (Training: Testing)	Model Performance: (R2) 1, RMSE (mm) 2, MAPE% 3, MSE (mm2) 4, Minimum Error% 5, Maximum Error % 6, MAE (mm) 7, MAPE (mm) 8
(Neaupane and Achet [92]; Yao et al. [69]; Cao et al. [76]; Liu et al. [78]; Krkač et al. [73]; Krkač et al. [83]; Li et al. [70]; Yang et al. [93])	- Trend features: Time series cumulative displacement. - Periodic features: Antecedent, rolling, and current data for rainfall, reservoir level, and groundwater level. - Infiltration and evaporation data to estimate effective rainfall.	Creep	Periodic	Decomposition	- Varied sampling ratio (refer to Section 4.2.1) - 70%:30% and 80%:20% are widely adopted	Creep displacement	Periodic displacement
		BPNN		-		0.891 1
		ELM		-		0.984 1
		RF		-		0.998 1 2.56 2
		MLR		-		3.06 2
		KGM		-		0.9998 1
		RNN-RC				0.07 2 0.04 3
		BPNN-PSO		-		38.4 4
		SSA-LSTM		-		0.965 1 1.307 2
(Lian et al. [68]; Gao et al. [80]; Xing et al. [79]; Niu et al. [67]; Zhang et al. [39]; Zhang et al. [71]; Han et al. [74]; Wang et al. [82]; Wang et al. [72]; Ye et al. [94])		PSO-SVR		SVC		0.08827 2 0.02105 8
		DES	VMD-BLSTM	DES-BDNN		0.983 1 7.224 2
		GM (1,1)	ENN	-		0.2 5	9.73 6
		ELM	RS-SVR	-		0.9991 1	0.9991 1 0.1993 2
		Polynomial	WCA-BPNN	High Pass (HP) filter		>0.991	40.60 3 9.47 2
		LSTM-DMA		DMA		7.28 2 6.02 7	6.92 2 5.7 3
		EEMD-ELM		EEMD		74.00 2	2.3944 3
		Polynomial	EEMD-LSTM	EEMD and the kurtosis criterion		1 1	0.998 1 0.25 3
		SVM-SSA		CEEMD		0.9998 1 22.766 4	0.762 1 13.589 2
		GRA-TempoVar-Transformer		GOA-GA-VMD		1.86 2 4.85 7

Note: The numbers in the table correspond to the following performance metrics: ¹: R², ²: RMSE (mm), ³: MAPE (%), ⁴: MSE (mm²), ⁵: Minimum Error (%), ⁶: Maximum Error (%), ⁷: MAE (mm), ⁸: MAPE (mm).

Table 5. AI models for predicting landslide displacement (modified after Ebrahim et al. [29]).

Study	Key Features	Model with the Best Accuracy			Sampling Ratio (Training: Testing)	Model Performance: (R2) 1, RMSE (mm) 2, MAPE% 3, MSE (mm2) 4, Minimum Error% 5, Maximum Error % 6, MAE (mm) 7, MAPE (mm) 8
(Neaupane and Achet [92]; Yao et al. [69]; Cao et al. [76]; Liu et al. [78]; Krkač et al. [73]; Krkač et al. [83]; Li et al. [70]; Yang et al. [93])	- Trend features: Time series cumulative displacement. - Periodic features: Antecedent, rolling, and current data for rainfall, reservoir level, and groundwater level. - Infiltration and evaporation data to estimate effective rainfall.	Creep	Periodic	Decomposition	- Varied sampling ratio (refer to Section 4.2.1) - 70%:30% and 80%:20% are widely adopted	Creep displacement	Periodic displacement
		BPNN		-		0.891 1
		ELM		-		0.984 1
		RF		-		0.998 1 2.56 2
		MLR		-		3.06 2
		KGM		-		0.9998 1
		RNN-RC				0.07 2 0.04 3
		BPNN-PSO		-		38.4 4
		SSA-LSTM		-		0.965 1 1.307 2
(Lian et al. [68]; Gao et al. [80]; Xing et al. [79]; Niu et al. [67]; Zhang et al. [39]; Zhang et al. [71]; Han et al. [74]; Wang et al. [82]; Wang et al. [72]; Ye et al. [94])		PSO-SVR		SVC		0.08827 2 0.02105 8
		DES	VMD-BLSTM	DES-BDNN		0.983 1 7.224 2
		GM (1,1)	ENN	-		0.2 5	9.73 6
		ELM	RS-SVR	-		0.9991 1	0.9991 1 0.1993 2
		Polynomial	WCA-BPNN	High Pass (HP) filter		>0.991	40.60 3 9.47 2
		LSTM-DMA		DMA		7.28 2 6.02 7	6.92 2 5.7 3
		EEMD-ELM		EEMD		74.00 2	2.3944 3
		Polynomial	EEMD-LSTM	EEMD and the kurtosis criterion		1 1	0.998 1 0.25 3
		SVM-SSA		CEEMD		0.9998 1 22.766 4	0.762 1 13.589 2
		GRA-TempoVar-Transformer		GOA-GA-VMD		1.86 2 4.85 7

Note: The numbers in the table correspond to the following performance metrics: ¹: R², ²: RMSE (mm), ³: MAPE (%), ⁴: MSE (mm²), ⁵: Minimum Error (%), ⁶: Maximum Error (%), ⁷: MAE (mm), ⁸: MAPE (mm).

4.2.2. Matric Suction and Groundwater Prediction

AI models provide effective solutions for predicting complex internal causative factors such as soil matric suction (SMS) and groundwater levels due to their ability to handle nonlinear relationships. Davar et al. [65] developed a hybrid intelligence model for predicting SMS, a key indicator of soil shear strength, that integrates extensive physical soil property datasets and evaluates three optimization algorithms: Bayesian Regularization Backpropagation (BR-BP), Particle Swarm Optimization (PSO), and Butterfly Optimization Algorithm (BOA). This approach addresses common ANN limitations, including slow learning rates and poor generalization. Utilizing comprehensive field monitoring and laboratory data encompassing soil depth, volumetric soil moisture content (VSMC), air temperature, rainfall, soil temperature, and suction measurements, the study determined that PSO-ANN achieved optimal performance.

Similarly, groundwater level fluctuations, closely associated with landslide triggers, exhibit complex behavior influenced by rainfall and reservoir level variations with temporal delays. Cao et al. [66] applied a Genetic Algorithm-Support Vector Machine (GA-SVM) hybrid model to capture nonlinear interactions between intrinsic and extrinsic factors, incorporating multiple features, including antecedent and current rainfall and reservoir levels. The results demonstrated GA-SVM’s superiority over BPNN, while both multi-feature models outperformed single-feature GA-SVM. Liu et al. [99] implemented a regression tree model using rainfall, soil moisture content, and water level parameters to predict groundwater level changes, accounting for factors such as surface runoff, vegetation, climate conditions, and soil structure. This approach surpassed ANN, SVM, ELM, and Gaussian Process Regression (GPR) with an RMSE of 0.0812. Ng et al. [100] introduced a novel multivariate long short-term memory (M-LSTM) model that simultaneously utilizes spatial and temporal pore water pressure (PWP) data from multiple measurement locations. However, such geotechnical models remain constrained by data scarcity, whereas displacement prediction benefits from more readily available surface monitoring data.

4.2.3. Moisture Content and Topographic Thresholds

Soil moisture content significantly enhances landslide prediction accuracy when integrated with rainfall analysis. Zhao et al. [57] employed a Bayesian probabilistic approach combining antecedent soil moisture content—calculated using the SHETRAN (Système Hydrologique Européen TRANsport) model—with recent rainfall data. Their analysis incorporated rainfall events, antecedent soil wetness, rainfall duration, cumulative precipitation, and landslide occurrences, demonstrating that probabilistic thresholds outperform conventional I-D thresholds.

De Luca and Versace [61] developed the Generalized FLaIR Model (GFM), applicable to both shallow and deep-seated landslides, which accounts for initial soil moisture conditions dependent on antecedent rainfall. The model offers multiple configurable thresholds (Equations (13) and (14)) and utilizes a lumped conceptual hydrological approach (Equation (15)) where production storage level (PSL) is calibrated using evaporation and discharge data to track wetness increase throughout rainfall events [62]. Adapted from the GR4J model [101] (Figure 27), the R-PSL threshold provides superior performance for long-duration rainfall compared to I-D thresholds, while short-duration events require alternative parameters, such as hourly rainfall data [62].

$$Y(t)={\displaystyle \underset{t - M}{\overset{t}{\int }}I(\mathrm{T})\Xi (t - \mathrm{T}})d\mathrm{T}$$

(13)

$$Y_{cr}(t)=\left(R^{*}{}_D(t - d)/D\right)+\left(f\left[R^{*}{}_D(t - d)\right]/d\right)$$

(14)

$$R=a*PSL+b$$

(15)

where Y is a mobility function, I is rainfall intensity, Ξ represents a filter function that can take different mathematical expressions, t is time, T is defined on the interval [t − M; t], M is the process’s temporal memory, and R^*_D is cumulative rainfall filtered on D and d durations and evaluated at the instants (t − d) and t, respectively.

Soil saturation dynamics are illustrated in Figure 28, where soil thickness above bedrock (H) comprises unsaturated (z) and saturated (h) zones [102]. When cumulative rainfall exceeds unsaturated zone capacity, saturated zone depth increases until complete soil saturation occurs [103]. Saturated thickness can be quantified using Equation (16) [104], while topographic influences are captured through Kirkby’s wetness index [105] (Equation (17)), enabling derived thresholds (Equations (18) and (19)) [63].

The topographic wetness index (TWI) correlates with soil moisture during wet conditions [106] and utilizes digital elevation models (DEMs) to represent surface soil spatial distribution [63,102,104]. High-resolution DEMs reduce slope geometry uncertainties [107], though accurate soil thickness remains essential for instability analysis [63,102,103,104,106,108]. Unlike TWI, the soil wetness index (SWI) incorporates dynamic rainfall conditions [109] and serves as a crucial landslide predictor [110]. SHETRAN’s finite difference hydrological model simulates soil moisture responses using three-dimensional grids, incorporating meteorological data (evapotranspiration, precipitation), topographic properties (TWI), land cover, and soil types [111]. SWI calculations utilize preceding-day rainfall data averaged across meteorological stations, with threshold exceedance triggering wet soil classification in warning zones [110].

$$h(t)=H-Z(t)-FRC\left[ATI-\ln \left({\displaystyle \frac{W}{\tan \beta }}\right)\right]$$

(16)

$$TWI=\ln (W/\tan \beta )$$

(17)

$$\tan \beta \ge \left[{\displaystyle \frac{C}{{\gamma }_{t}gH {\cos }^2 \beta }}+\tan \varphi \right] \mathrm{lower} \mathrm{thresholds}$$

(18)

$$\tan \beta <\left[{\displaystyle \frac{C}{{\gamma }_{t}gH {\cos }^2 \beta }}+\left(1-{\displaystyle \frac{{\gamma }_w}{{\gamma }_t}}\right)\tan \varphi \right]\mathrm{upper} \mathrm{thresholds}$$

(19)

where h(t) denotes the saturated water height at time t, H represents the soil thickness, W is the unit width collecting area, tanβ is the surface slope, and ATI refers to the average topographic index in the catchment. FRC is a model coefficient obtained through the flow recession records. C denotes the cohesion, g represents the gravitational acceleration, γ_t is the bulk density of the soil, γ_w is the density of water, H is the soil thickness measured vertically, β is the gradient of the hill slope, and φ is the angle of the soil’s effective friction.

5. Discussion

5.1. Synthesis of Findings and Comparative Analysis of Model Approaches

This mixed-methods review was guided by the overarching question of how different landslide prediction models compare in their principles, applications, and accuracy. The findings reveal a clear trade-off between model simplicity and mechanistic sophistication, directly addressing our research inquiries as follows: (a) Empirical-statistical thresholds operate on the premise that rainfall is the most critical causative factor for landslide occurrence [54]. This assumption provides advantages in scenarios where topographic, geotechnical, and hydraulic data are limited [53]. Due to their operational simplicity and minimal instrumentation requirements, these models are preferred for early warning systems (EWS) [61]. They offer a practical alternative to physically based models, which require extensive data monitoring, collection, and calibration, making the latter seldom used in operational EWS [62]. However, empirical-statistical thresholds face constraints. Their application is typically limited to specific case studies [13], and they struggle to provide accurate rainfall thresholds when historical landslide and rainfall data are sparse [48,112]. Although these models can achieve high accuracy in certain conditions, their forecasting reliability is often compromised by substantial false positive alarm rates [54,55]. (b) Physically based causative thresholds are constructed under the assumption that relationships between landslides and controlling factors remain relatively constant over time [73]. These models inherently assume that past events will recur without significant changes and that sudden failure mechanisms, such as strain-softening along sliding surfaces, will not occur. Since sudden failures are rarely captured in training datasets, these models cannot predict such events [71,79]. Additionally, they often neglect random triggers like wind and vehicle loads due to insufficient monitoring data [82]. Further limitations include prediction accuracy dependence on temporal resolution, with better performance achieved through smaller prediction steps [80]. Regression-based approaches are generally constrained to smaller areas due to their reliance on field monitoring data, unlike landslide susceptibility maps, which can cover broader regions. These models frequently focus on single parameters such as displacement or groundwater levels while overlooking spatial variations in land cover, soil composition, topography, and geotechnical attributes. Most are also restricted to historical training data, limiting their capacity for real-time prediction and adaptation to sudden changes [99]. Despite these limitations, physically based models offer advantages. AI implementations can analyze multiple causative factors using existing monitoring data, providing extended warning periods compared to theoretical models and superior accuracy to empirical–statistical thresholds. Furthermore, they represent a cost-effective alternative to comprehensive geotechnical investigations.

5.2. Consolidating Fragmented Knowledge

The mixed-review methodology proved essential for this holistic assessment, with the dual perspective culminating in the integrated framework presented in Figure 29. This framework delineates a structured progression from national-scale to local-scale modeling approaches, reflecting a hierarchical decision-making process where input parameters guide model selection as follows: (a) At the national scale, factors including geology, geomorphology, soil properties, and triggering elements such as rainfall facilitate the generation of landslide susceptibility maps (refer to Part II; [19]). These maps form the foundation for risk assessments employing multivariate models, AI techniques, and hybrid approaches, enabling the precise identification of high-risk areas and their potential impacts on infrastructure and human safety. (b) Transitioning to local scales, the framework incorporates more detailed models accounting for complex geometrical, hydrological, and soil conditions. Deterministic physical models simulate intricate landslide processes using site-specific conditions [19], while statistical regression, AI, and probabilistic models complement these analyses by predicting initiation based on slope responses, including displacement, groundwater levels, matric suction, and moisture content. Combined with I-D thresholds, these approaches enable increasingly accurate landslide forecasting.

A particularly innovative aspect of Figure 29 lies in its synthesis of fragmented knowledge into an effective visualization that systematically illustrates the interconnections between different modeling approaches. This framework integrates statistical regression, AI, and physical methods within a unified hybrid modeling paradigm. Such integration is crucial for enhancing predictive accuracy in complex rainfall-induced landslide scenarios, where single-method approaches often prove inadequate. Complementing this, the color-coded accuracy assessment (ranging from reasonable to perfect) provides an immediate evaluation of model reliability based on specific input parameters, establishing a multi-tiered framework that enables robust predictive capabilities that are adaptable from national-scale susceptibility mapping to site-specific risk assessment.

While this review provides a comprehensive synthesis, several limitations, as outlined in Section 2.5, should be acknowledged. The reliance on major databases, specific keywords, and English-language publications may have omitted some relevant studies. Furthermore, the vast number of studies precluded a manual, quantitative meta-analysis of accuracy by model type. This remains a significant gap and a critical recommendation for future work.

6. Conclusions

This study has demonstrated the value of a mixed-methods framework, integrating scientometric and systematic analyses, to provide a holistic and critical assessment of the landslide prediction research landscape. The dual-pronged approach allowed for both a macroscopic mapping of global research trends and a microscopic evaluation of model methodologies, offering a more complete picture than either method could alone.

The primary insight from this synthesis is the clear evolution and necessary trade-offs in prediction modeling. The field is advancing from simple, data-scarce empirical thresholds (I-D, API) towards complex, physically informed models, with hybrid AI architectures emerging as the new frontier for achieving high-fidelity predictions. These hybrid models represent a paradigm shift, effectively addressing the nonlinear and decomposed nature of landslide behavior, particularly for critical periodic displacement.

However, this review also conclusively shows that no universal model exists. The choice between empirical, physical, or hybrid approaches is fundamentally dictated by the specific application’s scale, the availability of data, and the required accuracy. Empirical models remain the pragmatic choice for regional early-warning systems, while physically based and hybrid models are indispensable for site-specific assessments.

Ultimately, this study underscores that the path toward more reliable landslide prediction lies not in seeking a single perfect model, but in the contextual application of a hierarchical modeling strategy, as visualized in Figure 29. Future progress hinges on building richer, multi-parameter datasets and developing more adaptable models that can bridge the critical gap between data-driven predictions and geotechnical reality. This review provides a structured framework and a clear identification of research gaps (

Table 6. Identified research gaps and corresponding recommendations.

Gap	Recommendations
High false-positive rates in I-D thresholds due to two primary oversights: (1) the influence of infiltration capacity and subsurface hydrology, and (2) the role of slope-specific properties (e.g., geometry, geotechnical parameters).	1. Conduct field experiments to quantitatively establish the relationship between rainfall, evaporation, infiltration, and surface runoff. 2. Perform sensitivity analyses to identify the dominant physical parameters, enabling the development of refined I-D thresholds that retain simplicity while improving accuracy.
Over-reliance on surface displacement data in physically based models, which fails to capture sudden failure mechanisms driven by subsurface processes (e.g., deep-seated displacement, tilting, suction stress, groundwater fluctuations).	Develop and deploy comprehensive subsurface monitoring systems to create high-resolution datasets. These datasets should be used to train hybrid AI models capable of predicting complex, nonlinear landslide mechanisms and precursor signals of sudden failure [113,114].
Inadequate consideration of practical field constraints, including data loss from sensor failure in harsh environments and limitations imposed by telecommunication data rates.	Implement robust data validation and gap-filling techniques. Furthermore, conduct sensitivity analysis to optimize the trade-off between data transmission rates, model complexity, and prediction reliability under realistic operational constraints.

) to guide these essential future endeavors.

7. Future Directions and Recommendations

This review has identified that while significant progress has been made, the development of next-generation landslide prediction models demands focused efforts on two critical fronts. First, feature selection must be guided by a deeper understanding of site-specific initial conditions, and second, model architecture must be suited to the complexity of the feature relationships. Despite advancements in statistical modeling, such as hybrid AI models, there are still some gaps that need to be addressed, as outlined in Table 6.