Knowledge-based landslide hazard zonation, particularly in areas with limited field data, is an important approach to hazard management. However, the lack of a scientific mechanism for standardizing weights derived from heterogeneous studies represents a major challenge to such approaches. To address this gap, the present study implemented a relative-importance normalization framework in Mazandaran Province, Iran, and compared its performance with that of a median-weighting method. Based on their frequency of occurrence in seven reliable previous studies, nine criteria—slope, aspect, elevation, precipitation, distance to faults, roads, streams, and population centers, and land use—were selected and weighted. The results showed that slope, with a weight of 0.239, had the greatest influence, followed by distance to roads (0.133) and precipitation (0.121). The use of the median preserved the overall ranking of the criteria while reducing the weights assigned to elevation and land use. The weight of distance to population centers was also associated with uncertainty because this criterion appeared in only two studies. Compared with the median-based method, the relative-importance normalization method performed better, concentrating 10.5% of landslide points in the highest-hazard class and increasing the Frequency Ratio from 0.72 in the low-hazard class to 1.04 in the high-hazard class. In contrast, the median-based method concentrated 0.15% of landslide points in the highest-hazard class. The Area Under the Curve (AUC) values for the two methods were 0.477 and 0.592, respectively, indicating that this index alone is insufficient for performance evaluation. Validation using 674 landslide points confirmed the increasing trend of the Frequency Ratio. In addition, 34.2% of the provincial area was classified within the high- and very-high-hazard zones. This framework is suitable for hazard zonation in data-scarce mountainous regions.
Introduction
Landslides represent one of the most destructive natural hazards in mountainous and foothill regions worldwide, causing substantial annual economic losses and threatening critical infrastructure and human settlements. Mazandaran Province in northern Iran, situated within the active tectonic framework of the Alborz mountain range, is particularly susceptible due to its steep slopes, humid climate, and intense orographic precipitation. While knowledge-driven methods offer a practical approach for landslide hazard zonation especially in regions lacking comprehensive field data they face a fundamental challenge: the absence of a scientific mechanism for integrating and standardizing criterion weights derived from heterogeneous previous studies. Traditional expert-based methods like AHP are prone to subjective bias, whereas purely statistical approaches suffer from data quality issues. A critical review of both national and international literature highlights a major flaw in the common practice of simply averaging criterion weights. This approach introduces systematic error because previous studies differ considerably in their total number of criteria and employ heterogeneous scoring schemes. To address this methodological gap, the present study introduces and implements a systematic framework called "Relative Importance Normalization" (RIN) for landslide hazard zonation in Mazandaran Province. The RIN framework normalizes weights internally within each source study prior to final aggregation, thereby eliminating bias caused by varying numbers of criteria across studies. In parallel, a median‑based weighting approach commonly used in previous research was also applied to serve as a benchmark for comparative evaluation. Both weighting approaches were validated using 674 recorded landslide points and assessed through Frequency Ratio (FR) and Receiver Operating Characteristic (ROC) analysis. The comparative assessment of these two approaches forms the core contribution of this study, providing insights into the effectiveness of standardized weighting frameworks in knowledge‑based landslide susceptibility mapping.
Material and Methods
This study adopted a knowledge‑driven approach comprising three main steps. In the first step, nine conditioning factors slope, aspect, elevation, rainfall, distance to faults, distance to roads, distance to streams, land use, and distance to population centers were selected based on their highest frequency of occurrence in seven authoritative previous studies that employed pairwise comparison for landslide hazard assessment. The raw global weights for these criteria and their sub‑criteria were extracted from the literature. In the second step, two parallel weighting approaches were pursued. The first approach involved extracting the median weights for each criterion directly from the literature and applying them to the corresponding spatial layers. The second approach applied the Relative Importance Normalization (RIN) algorithm to eliminate bias caused by varying numbers of criteria across studies. For each study, the sum of weights for the nine target criteria was calculated. The relative importance of each criterion within a study was then obtained by dividing its global weight by this sum. Subsequently, for each criterion, the mean of the relative importance values was computed across all studies containing that criterion. Finally, these mean values were normalized to sum to unity, producing the final standardized weights. In the third step, for sub‑criterion standardization, a reference classification system was defined for each criterion based on frequent class intervals identified in the literature and local environmental characteristics. Mapped weights from different studies were normalized within each criterion, averaged across studies, and then multiplied by the corresponding final criterion weight to obtain absolute sub‑criterion weights. For model validation, 674 recorded landslide points were used. The Frequency Ratio (FR) index was calculated as the ratio of the percentage of landslide points in each hazard class to the percentage of area occupied by that class. Additionally, the Receiver Operating Characteristic (ROC) curve and the Area Under the Curve (AUC) were computed to quantitatively assess the performance of both weighting approaches. The AUC values for the median‑based method and the RIN method were compared to evaluate their respective capabilities in distinguishing high‑risk from low‑risk zones.
Results and Discussion
The findings revealed that slope, with a weight of 0.239, exerts the greatest influence on landslide occurrence in the region, followed by distance from roads (0.133) and precipitation (0.121). Distance from faults (0.105), land use (0.098), distance from streams (0.085), elevation (0.076), aspect (0.075), and distance from population centers (0.068) ranked subsequently. Sub‑criteria analysis revealed that among the evaluated factors, the most susceptible conditions were associated with the 30–45% slope class (absolute weight: 0.080), the 0–100 m road buffer (0.047), and the 500–650 mm precipitation range (0.039). Sensitivity analysis substituting the median for the mean showed a stable rank order, though elevation and land use weights decreased, indicating some influence from outlier data. Regional analysis for the Alborz cluster revealed an increased elevation weight (0.103), highlighting its local significance. To evaluate model performance, two parallel weighting approaches were compared: (1) a median‑based weighting method, and (2) the Relative Importance Normalization (RIN) framework. Validation using 674 recorded landslide points demonstrated that the RIN method concentrated 10.5% of the points in the very high hazard class (class 5), whereas the median‑based method placed only 0.15% of points in this class. The Frequency Ratio (FR) for the RIN method showed a consistent upward trend from the very low hazard zone (FR = 0.72) to the very high hazard zone (FR = 1.04), confirming the model's spatial correspondence with field reality. The highest FR value (1.15) belonged to the moderate hazard class (class 3), which can be explained by its extensive areal coverage (30.2%) and the concentration of instability factors such as 15–30% slopes and transitional elevations. Classes 4 and 5 together contained 34.1% of recorded landslide points within 34.2% of the total area, indicating a density ratio of approximately 1.5‑fold compared to the provincial average. Quantitative assessment using the Receiver Operating Characteristic (ROC) curve and the Area Under the Curve (AUC) yielded an AUC of 0.592 for the median‑based method and 0.477 for the RIN method. While the AUC of the median‑based method was higher, this value is misleading, as the majority of landslide points (77.6%) were concentrated in the low and moderate hazard classes (classes 2 and 3), with only 18% falling into high‑risk zones (classes 4 and 5). In contrast, the RIN method, despite its lower AUC, distributed 68.7% of the points across moderate to very high hazard classes (classes 3–5) and maintained a logical increasing FR trend. These findings indicate that AUC alone is insufficient for evaluating landslide susceptibility models and that the distribution of points within high‑risk classes serves as a more critical performance indicator. The final hazard zonation map, generated in a GIS environment through weighted overlay summation and classified using Natural Breaks into five classes, showed that high and very high hazard zones (classes 4 and 5) collectively cover 34.2% of the study area (7,469 km²), while moderate hazard covers 30.2% (6,573 km²).
Conclusion
This study introduces and implements the Relative Importance Normalization (RIN) framework as a systematic computational solution to the fundamental challenge of objective criterion weighting in knowledge‑based landslide hazard assessments. Unlike conventional statistical averaging—which introduces systematic bias when synthesizing heterogeneous studies with varying numbers of input criteria—the RIN framework normalizes weights internally within each source study prior to final aggregation, thereby enabling a more consistent and replicable weighting scheme. The framework was applied and validated in Mazandaran Province using 674 recorded landslide points. The validation results demonstrated a clear, monotonic increase in Frequency Ratio (FR) values from the very low hazard zone (FR = 0.72) to the very high hazard zone (FR = 1.04), confirming the model's spatial accuracy and reliability. Comparative analysis with a median‑based weighting approach further revealed that the RIN method significantly outperformed the conventional method in identifying high‑risk zones, concentrating 10.5% of landslide points in the very high hazard class, compared to only 0.15% for the median‑based approach. While the RIN framework offers strong theoretical transparency, high reproducibility, and flexibility for dynamic updates as new studies become available, certain limitations remain. These include the low representation of specific parameters (e.g., distance to population centers, which appeared in only two studies) and the coarse spatial resolution of some input layers. The quantitative assessment using the Area Under the Curve (AUC) yielded values of 0.592 for the median‑based method and 0.477 for the RIN method. Although the AUC of the median‑based method was higher, this value was misleading, as 77.6% of landslide points were concentrated in low and moderate hazard classes, whereas the RIN method, despite its lower AUC, distributed 68.7% of points across moderate to very high hazard classes and maintained a logical increasing FR trend. These findings indicate that AUC alone is insufficient for evaluating landslide susceptibility models and that the distribution of points within high‑risk classes serves as a more critical performance indicator. Future investigations should explore refining RIN‑derived weights using local expert knowledge and integrating them into hybrid models alongside data‑driven algorithms such as logistic regression or support vector machines. Finally, the resulting hazard maps serve as a dependable decision‑support tool for emergency management, infrastructure routing, and prioritizing mitigation measures in the landslide‑prone terrains of Mazandaran and analogous mountainous regions.
Acknowledgements
The authors sincerely thank the management and expert staff of the General Department of Natural Resources and Watershed Management of Mazandaran Province for providing the foundational spatial data layers, which played a fundamental role in advancing this research. It is also worth noting that the initial idea of this study originated from a master's thesis in Environmental Hazards, supervised by the corresponding author at the University of Birjand. Following extensive revisions in content, methodology, and results, the thesis was developed into the present article.