Geospatial Mudflow Risk Modeling: Integration of MCDA and RAMMS

Abstract

This article presents a comprehensive assessment of mudflow risk in the Talgar River basin through the application of Multi-Criteria Decision Analysis (MCDA) methods and numerical modeling using the Rapid Mass Movement Simulation (RAMMS) environment. The first part of the study involves a spatial assessment of mudflow hazard and susceptibility using GIS technologies and MCDA. The key condition for evaluating mudflow hazard is the identification of factors influencing the formation of mudflows. The susceptibility assessment was based on viewing the area as an object of spatial and functional analysis, enabling determination of its susceptibility to mudflow impacts across geomorphological zones: initiation, transformation, and accumulation. Relevant criteria were selected for analysis, each assigned weights based on expert judgment and the Analytic Hierarchy Process (AHP). The results include maps of potential mudflow hazard and susceptibility, showing areas of hazard occurrence and risk impact zones within the Talgar River basin. According to the mudflow hazard map, more than 50% of the basin area is classified as having a moderate hazard level, while 28.4% is subject to high hazard, and only 1.8% falls under the very high hazard category. The remaining areas are categorized as very low (4.1%) and low (14.7%) hazard zones. In terms of susceptibility to mudflows, 40.1% of the territory is exposed to a high level of susceptibility, 35.6% to a moderate level, and 5.5% to a very high level. The remaining areas are classified as very low (1.8%) and low (15.6%) susceptibility zones. The predictive performance was evaluated through Receiver Operating Characteristic (ROC) curves, and the Area Under the Curve (AUC) value of the mudflow hazard assessment is 0.86, which indicates good adaptability and relatively high accuracy, while the AUC value for assessing the susceptibility of the territory is 0.71, which means that the accuracy of assessing the susceptibility of territories to mudflows is within the acceptable level of model accuracy. To refine the spatial risk assessment, mudflow modeling was conducted under three scenarios of glacial-moraine lake outburst using the RAMMS model. For each scenario, key flow parameters—height and velocity—were identified, forming the basis for classification of zones by impact intensity. The integration of MCDA and RAMMS results produced a final mudflow risk map reflecting both the likelihood of occurrence and the extent of potential damage. The presented approach demonstrates the effectiveness of combining GIS analysis, MCDA, and physically-based modeling for comprehensive natural hazard assessment and can be applied to other mountainous regions with high mudflow activity.

1. Introduction

Mudflows are among the most hazardous hydrological phenomena, caused by disruption of the dynamic balance in the “water–slope–loose detrital material” system [1]. They are characterized by significant destructive potential, leading to extensive socio-economic and environmental consequences, including infrastructure damage, ecosystem degradation, and threats to human life. The occurrence of mudflows results from a combination of various factors, the influence of which varies depending on specific conditions, including surface morphology, intense precipitation, geological composition, and anthropogenic activity [2,3]. Their roles in the initiation and development of mudflows are unequal, as the frequency and intensity of the process are determined by the prevailing natural conditions of the region. In addition to the primary factors, additional triggering mechanisms such as seismic activity, tectonic movements, and degradation of soil and vegetation cover can also influence mudflow formation [4,5,6]. With global climate change and increasing urbanization in mountainous and foothill areas, both the frequency and intensity of mudflow events are on the rise [7], emphasizing the need for comprehensive assessment of mudflow hazard and risk.

Broadly, climate change impacts not only the number and intensity of natural disasters but also their nature [8,9]. This highlights the need for predictive models capable of forecasting such events and mitigating their impacts on populations and ecosystems. In Kazakhstan, as in many other mountainous countries, frequent mudflow episodes necessitate improved methodologies for risk assessment and damage mitigation.

Currently, the situation in Kazakhstan’s mountainous areas has changed significantly. New challenges, threats, and risks have emerged due to the intensification of development in mountain river valleys above existing mudflow protection structures. These include new infrastructure and industrial facilities (roads, bridges, power and communication lines, energy facilities, and water intake systems), as well as major social objects (tourism complexes and recreational zones, restaurants and cafes, residential buildings). Studies have shown that all of these facilities are subject to potential mudflow impacts [10].

Within Kazakhstani research, both qualitative and quantitative methods for mudflow risk assessment have been developed [9,11,12,13], based on hydrometeorological data analysis and statistical modeling. These methods involve mapping zones of increased mudflow activity and applying GIS technologies to analyze and identify the most mudflow-prone areas and regions with high mudflow risk. Mathematical models have been proposed to estimate the probability of critical values of precipitation intensity and duration, which trigger mudflows [14,15,16]. These studies have contributed to improving approaches for mudflow risk forecasting and management in Kazakhstan. In recent years, modern methods and approaches to mudflow hazard and risk assessment have been actively developing worldwide. They are based on geospatial modeling that integrates remote sensing data, GIS analysis, and mathematical modeling [17,18,19,20,21,22]. One of the most promising directions is the use of MCDA, particularly the AHP [23,24,25,26], which allows for a quantitative evaluation of the contribution of various factors to mudflow hazard and territorial susceptibility. However, their limitations lie in the static nature of the analysis, while the dynamic aspects of mudflow propagation remain underexplored. Therefore, integration of these results with physical models such as RAMMS, which take into account the dynamics of channel processes and mudflow parameters, can significantly enhance the accuracy of risk assessment [27]. Key parameters affecting the reliability of modeling include the volume of the outburst flood and initial debris mass, its velocity and travel distance, rheological properties (viscosity, density), and the dynamics of interaction with the channel substrate [28]. Erosion and accumulation processes significantly influence the formation and evolution of the flow, determining the degree of entrainment of loose material. The composition of the mudflow also plays a critical role: the front typically contains coarser material, while the tail part is dominated by the liquid fraction. Sedimentation processes of debris mass on alluvial cones and in channel depressions may transform into mud streams, debris floods, or channel breakthroughs, necessitating a comprehensive approach to mapping risk zones. The use of RAMMS in modeling and assessing mudflow risk allows consideration of a wide range of factors affecting mudflow dynamics and supports the development of more effective mudflow risk management strategies [29].

However, despite the significant body of research, questions of recipient susceptibility and mudflow prediction remain unresolved, especially in the context of climate change. Even with the use of advanced modeling technologies, much remains uncertain regarding the effects of changing climatic conditions, such as rising temperatures and increased precipitation, on the stability of moraine dams, mudflow sources, and the probability of lake outbursts [30,31,32,33]. Furthermore, there is a lack of studies that consider the local specificities of geological, hydrological, and climatic factors in the context of Kazakhstan, which complicates accurate risk assessment for individual regions of the country.

In the context of climate challenges, mudflow phenomena represent a serious threat not only to Kazakhstan but also to other mountainous regions of the world. Their study, modeling, and forecasting are key tasks for developing effective risk reduction measures, protecting populations, and sustainably managing vulnerable territories. The aim of this study is to develop a geospatial model for assessing mudflow risk by integrating AHP, MCDA, and numerical RAMMS modeling to improve the accuracy of hazard and susceptibility mapping and the analysis of potential mudflow development scenarios.

2. Study Area

The location of the Talgar River basin in the Ile Alatau Mountains is characterized by complex mountainous terrain. The northern slope of the basin is composed of several spurs of the main ridge, which act as watersheds for mountain rivers. The Talgar River basin has a total catchment area of 444 km², of which the Left Talgar accounts for 273 km², the Middle Talgar for 103 km², and the Right Talgar for 68.5 km² [34]. The upper reaches of these gorges are marked by extensive glaciation, comprising 92 glaciers with a total area of 117.9 km².

The catchment area of the basin is situated within a major glaciation center, known as the Talgar Mountain Node, which determines the clearly defined glacial-fed regime of the Talgar River. In the middle course of the Right Talgar River, it is joined by a major tributary—the Middle Talgar River—which originates from the Shokalsky Glacier. In its lower reaches, as it exits the mountains, the Left and Right Talgar Rivers merge into a single channel, thereby forming the Talgar River (Figure 1).

These rivers are characterized by steep gradients ranging from 6 to 11%. Their average width varies from 3 to 5 m, with depths ranging from 0.5 to 1.0 m. A distinctive feature of these rivers is the sharp variability in discharge, not only seasonally but also throughout the day, associated with fluctuations in air temperature.

High daytime temperatures during the summer months (June, July, August) cause intensive melting of glaciers and snowfields, resulting in the rapid filling of all water bodies and raising river water levels to a maximum around 5–6 PM [35]. The minimum water levels typically occur around 6–7 AM. In addition to glacial and snowmelt, rainfall of a convective character during summer months significantly contributes to increased discharge, often leading to catastrophic consequences in the form of mudflows [36]. Daily precipitation can reach up to 91 mm, with a monthly average norm of 46 mm [7].

Moraine-dammed lakes—almost all of glacial origin—are located in the high mountain zone (3000–3700 m above sea level), posing a potential mudflow hazard [37,38,39,40,41].

3. Materials and Methods

3.1. Data Sources

The assessment of mudflow hazard and risk in the Talgar River basin was conducted using an integrated approach that considers spatial, hydrometeorological, and socio-economic factors (Figure 2). The core data for this analysis were raster and vector datasets from various sources covering the Talgar River basin. Spatial data for the comprehensive analysis of natural and anthropogenic factors influencing mudflow conditions were obtained from a digital elevation model (DEM) with a spatial resolution of 12.5 m × 12.5 m (ALOS PALSAR), global LULC maps (Living ATLAS ESRI, 10 m resolution), satellite imagery (Sentinel-2, 10 m × 10 m resolution), and topographic maps (scale 1:200,000). For the analysis of morphometric and morphological characteristics of streams and catchments relevant to mudflow formation, data from the HydroSHEDs portal were used. The combination of spatial data and GIS analysis enabled automation of information processing necessary for analyzing mudflow conditions and simulating mudflow behavior.

Hydrometeorological data, including temperature and precipitation indicators for the study area, were obtained from the CHELSA-EarthEnv daily precipitation product. Precipitation and temperature are the main triggers for the initiation and propagation of mudflows. These datasets were selected based on their availability and accuracy [42], as well as their temporal coverage and provision of daily values, allowing for detailed analysis of selected observation points.

Soil and geological data were sourced from the Semirechye Soil Map (scale 1:500,000) and geological maps of Kazakhstan, as soil texture and lithology play a key role in slope stability.

Infrastructure and demographic data including population density, location of settlements, transportation networks, buildings, and mudflow protection structures were obtained from the Department for Emergency Situations of Almaty and open crowdsourcing platforms such as Humdata, OpenStreetMap, and DivaGIS.

3.2. Data Preparation

To prepare the DEM of the Talgar River basin, ArcGIS 10.x (ESRI Inc.) was used. In the initial stage, the DEM projection system was transformed from a surface-based to a planar rectangular coordinate system using the Asia North Equidistant Conic projection. This ensured spatial alignment and data accuracy, which is critical for further analysis and the definition of criteria affecting mudflow hazard and susceptibility. The coordinate system transformation was essential for correctly representing the geographic features of the terrain in the model, thereby improving the quality and reliability of DEM-derived data. Raster extraction along the boundaries of the Talgar River basin was performed in ArcGIS 10.x using the Spatial Analyst Tools, allowing for a focused analysis of the study area. In the final stage of DEM preparation, “sinks”—gaps caused by interpolation errors and elevation rounding—were eliminated using the Fill function in the Spatial Analyst module of ArcGIS 10.x. This ensured continuity and accuracy of the relief model for proper morphometric analysis and improved understanding of the basin’s geographic characteristics.

To assess the susceptibility of territories to mudflows, Sentinel land use imagery with 10 m resolution for 2023 was used. These data were projected into a unified coordinate system and processed in ArcGIS 10.x, where classification into nine land use/land cover (LULC) categories was conducted.

For data processing and cartographic visualization of results, ArcGIS 10.x was used. The analysis was based on maps (*.tif format) at a scale of 1:25,000. The investigated mudflow hazard criteria, such as slope, SPI, STI, drainage density (DD), and distance from hazardous objects (HOs), as well as susceptibility criteria, such as slope, elevation, TWI, and distances from HOs and rivers, were derived from the DEM using Spatial Analyst Tools.

For the evaluation of hydrometeorological conditions related to mudflow hazard, temperature and precipitation data were used. As critical indicators for identifying mudflow hazard, the cumulative temperature from 1 May to 31 July and daily precipitation values from 1 June to 31 August [1] over a 10-year period were selected.

The cumulative temperature for 1 May to 31 July period was selected because this is the time of intensive snow and ice melt, which increases the volume of water entering glacial-moraine lakes and accelerates mudflow formation. High temperatures during this period create conditions for substantial snowmelt and the activation of other triggering factors. To determine the potential landslide hazard in the Talgar River basin, daily air temperature values were extracted from the CHELSA database and presented in the form of raster data. Daily average air temperature values from 1 May to the date of analysis were processed in a GIS environment using the “Raster Calculator” tool by summing the temperature values for the specified period, which made it possible to obtain cumulative fields of temperature sums. In accordance with the methodological recommendations from [1], the criterion for assessing the level of mudflow hazard is the value of the sum of average daily air temperatures (Tᵢ, °C) exceeding 108% of the long-term average (∑Tₙ). For specific calendar dates of the mudflow hazard period, according to weather station data, threshold (critical) values of temperature sums are determined for the study area. For example, to determine the mudflow hazard in the Kishi Almaty River basin at the Mynzhylyk weather station starting from 1 May, by 30 June, the critical value is 284 °C, and by August 10, it is 655 °C.

Precipitation data were processed based on daily values recorded between 1 June to 31 August. Critical daily precipitation thresholds were defined by mountain zone categories according to [1]: 20 mm/day for low mountains and 40 mm/day for mid- and high mountains. These precipitation values represent threshold levels beyond which the probability of mudflow occurrence increases and adverse impacts on ecosystems and infrastructure emerge. The number of days with precipitation exceeding these thresholds was used to calculate hazard levels. The more days with exceedances, the higher the mudflow hazard is. Precipitation and temperature data were processed using ArcGIS Pro tools.

In selecting criteria for mudflow hazard and territorial susceptibility, the NDVI index was considered as a factor with significant influence on mudflow formation and development. NDVI was calculated from Sentinel satellite imagery (10 m resolution) in the ArcGIS 10.x environment using the raster calculator and the following mathematical expression (1) [43]:

NDVI = (NIR − Red)/(NIR + Red)

(1)

where NIR is the near-infrared band and Red is the red visible band. NDVI allows assessment of vegetation cover density, which can inhibit mudflow development processes, as well-developed vegetation strengthens the soil and reduces the likelihood of erosion.

The presence of mudflow protection structures mitigates the consequences of mudflows, thus reducing the risk of their formation and development. Information on the locations of such structures was mapped, and using Spatial Analyst Tools in ArcGIS 10.x, the distance from each site in the study area to the nearest protection structure was calculated. This enabled evaluation of the degree of protection from potential mudflows.

To assess territorial susceptibility to mudflows, additional parameters were used, such as distance from rivers, distance from infrastructure, and distance from objects posing technogenic, social, and ecological risks. These data were also processed using ArcGIS 10.x Spatial Analyst Tools.

One of the key criteria for determining slope stability with respect to mudflows is the soil cover of the study area. Soil data were processed using ArcGIS 10.x and the Georeferencing function. Geospatial referencing of the soil map was performed using control points matched with coordinates from existing topographic and satellite imagery, ensuring integration into the GIS environment for further spatial analysis of soil distribution characteristics.

All spatial layers were reprojected into a unified coordinate system to ensure their compatibility for subsequent analysis. This preprocessing was also applied to the soil map, which was transformed to a single coordinate system and clipped to the basin boundary, ensuring accuracy in geospatial analysis.

3.3. Analysis of Criteria Determining Mudflow Hazard in the Talgar River Basin

Mudflow hazard refers to the probability of occurrence of phenomena, events, and processes capable of causing damage [2,7,44,45].

Mudflow hazard is determined by a combination of factors that contribute to mudflow formation, which in turn influence the development and intensity of mudflows. According to the research [45], mudflows arise as a result of the breakdown of the “water–slope–loose detrital material” system.

1.

Hydrological component of mudflow hazard includes the following criteria: distance from hazardous objects (moraine lakes and mudflow centers), precipitation, air temperature, and drainage density, all of which define the probability and intensity of mudflow formation.

1.1.

Distance from hazardous objects is one of the criteria influencing the intensity and character of mudflow development. Using remote sensing data, aerial photographs, and topographic maps, the number and coordinates of moraine lakes and mudflow centers within the study basin were identified.

1.1.1.

Distance from glacial-moraine lakes. Glacial-moraine lakes are common in high-mountain areas with glaciation [46]. Under climate change conditions in the study area [47], new glacial-moraine lakes are forming, and existing lake basins are rapidly filling with glacial meltwater [48]. Lake outburst probability depends on morphometric characteristics, lake volume, dam composition, and the mechanical structure of surrounding materials. Several moraine lakes with such characteristics are found in the study area.

Sentinel-2 satellite imagery was used to calculate distances from moraine lakes. Glacial-moraine lakes were identified using the Normalized Difference Water Index (NDWI) (2), which enhances the detection of water bodies while minimizing vegetation and soil effects [49,50]:

NDWI = (Green − NIR)/(Green + NIR)

(2)

where NIR is the near-infrared reflectance and Green is the reflectance in the green spectral band.

As the distance from glacial-moraine lakes increases, the probability of glacial mudflow occurrence decreases, thereby reducing hazard levels. However, in areas directly exposed to potential outburst floods, the hazard increases due to the growth of expected flow parameters. For instance, on 6 July 1993, a first-category mudflow occurred in the Middle Talgar River basin due to an outburst from a lake near the Bezymianny Glacier. The event was not linked to hydrometeorological anomalies (e.g., high temperatures, intense melt, heavy rainfall). Lake No. 9 burst as a result of sub-moraine drainage channel collapse; the lake surface was 60% covered with floating snow masses. Observations from a monitoring post located more than 500 m away estimated peak discharges close to 1000 m³/s, while maximum flow at the destroyed Right Talgar-duplicate radio mudflow warning site reached 1340 m³/s; but within the urban area, maximum flows did not exceed 300 m³/s.

1.1.2.

Distance from mudflow centers. In addition to glacial mudflows, rainfall-induced mudflows are common in the study area [7]. According to Kazakhstan State Agency Mudflow Protection (KSAMP), approximately 70% of mudflows in the region are rainfall-induced. Mudflow centers are typically areas with large accumulations of loose material and slopes ranging from 10° to 55° [1]. A total of 91 mudflow centers were identified from aerial and satellite imagery. Most of these centers are located in mid- and high-mountain zones. Greater distance from mudflow centers is associated with lower likelihood of rainfall-induced flows and thus lower hazard.

1.2.

Precipitation. Precipitation is a critical factor increasing the likelihood of mudflow formation. Its spatial distribution depends not only on geography but also on elevation zones [51]. Mountain ranges oriented west to east serve as natural barriers to moist air masses, resulting in significant variations in precipitation distribution across regions [52].

Changes in the altitude of the zero-degree isotherm significantly affect precipitation distribution in the Ile Alatau River basins. In mountainous regions with significant altitudinal gradients, temperature and humidity vary with elevation, and the height of the zero isotherm plays a key role in determining the form of precipitation. When the isotherm rises, rainfall is more likely; when it drops, snowfall predominates. This is particularly relevant in summer, when intense rainfall combined with snowmelt can trigger mudflows [2].

1.3.

Temperature. Air temperature is a critical hydrological factor influencing mudflow hazard, especially in glacial-moraine environments. Rising temperatures intensify snow and ice melt, increasing melting and glacial runoff and contributing to lake filling and potential outbursts. Temperature variations also accelerate thermokarst processes, which destroy ice and soil layers, further increasing mudflow risk.

T.G. Tokmagambetov et al. [37] demonstrated that moraine lake outbursts correlate with exceedances in cumulative mean daily temperature relative to multiyear averages. According to KSAMP, 29 moraine lake outbursts occurred in the Talgar basin between 1960 and 2020. The research [46] showed that the most catastrophic glacial mudflows occurred during hot, sunny days in high-mountain areas, with air temperatures reaching 15–18 °C, and peak discharges during outbursts ranging from 18 to 250 m³/s, with total water releases from lakes of 0.1–0.2 million m³.

1.4.

Drainage density is the ratio of the total length of the river network within a basin to the basin area (D, km/km²). This criterion reflects the development degree of the hydrographic network across the study territory.

When calculating drainage density (3), both permanent and temporary rivers and tributaries must be considered. Excluding temporary rivers from the calculations will lead to incorrect results, especially for basins where only temporary streams predominate, since the drainage density for such basins will be zero. During floods, when both permanent and temporary streams are active, including all channels in density calculations is essential for realistic modeling [53]. Thus, for more accurate modeling of water processes and risk assessment, including the risk of mudflow formation, it is necessary to take into account all types of water flows active in different periods of time, including temporary flows that can significantly affect the dynamics and intensity of water phenomena.

D = L/A

(3)

where L is the total length of streams [km] and A is the area providing drainage [km²].

As drainage density increases, the infiltration capacity of soils decreases [53]. Areas with high drainage density become zones of mudflow formation and propagation [54]. Maximum drainage density is typical for high mountain areas with abundant precipitation.

2.

Terrain surface factors: slope and Stream Power Index (SPI) determine the movement characteristics and development of mudflows.

2.1.

Slope. Mudflows involve the downslope movement of water-saturated detrital material under gravitational force. Therefore, slope values are critical in assessing mudflow hazard and identifying vulnerable territories [55]. Steeper slopes correspond to higher mudflow velocities, density, and height. The most susceptible areas are mid- and high-mountain zones with slopes exceeding 25° [36].

2.1.1.

Stream Power Index (SPI) quantifies the erosive force of water flow and is used to characterize potential water erosion on a given topographic surface (4) [56].

As catchment area and slope increase, more water accumulates, and flow velocity rises. This intensifies channel erosion and sediment transport, increasing SPI and erosion hazard.

SPI = ln(A × tanβ)

(4)

where A is the specific catchment area and β is the slope gradient.

Since SPI depends on slope, it can be seen as a derivative of slope in modeling potential flow erosion. Thus, steeper areas of the basin correspond to higher SPI values.

3.

Geological factors determining mudflow hazard include various characteristics and properties of geological materials (soil, rock, soil horizons, etc.) that influence slope stability, runoff dynamics, and other processes contributing to mudflow formation. Mudflows are defined as channelized movements of debris-laden water that transport or deposit sediment [57].

3.1.

Soil cover. The granulometric and mineralogical composition of soil affects mudflow density and volume [36]. Infiltration and filtration characteristics of soil, combined with precipitation intensity, determine runoff behavior [58]. Low infiltration capacity combined with high-intensity rainfall causes surface runoff to exceed critical thresholds, triggering erosion-induced flows. High infiltration combined with prolonged rainfall saturates thick soil layers, initiating slope failures and flow. Complete soil saturation can lead to chain mudflow events.

3.1.1.

Sediment Transport Index (STI), described by Moore and Burch [59], identifies erosion-prone zones near channels and areas of sediment accumulation. High STI values occur on steep slopes and eroded lower catchments [19], while low values indicate slow sediment movement and promote deposition—commonly in upper catchment zones with dense vegetation. STI effectively reflects landscape-scale erosion and sediment transport from high mountain areas to depositional zones. The main factors influencing sediment transport within a drainage basin include gravity, terrain slope, and sediment concentration (5).

STI = (m + 1) × (A/22.13)^m × sin(β/0.0896)ⁿ

(5)

where A is the specific catchment area, β is the slope, m is the area exponent (typically 0.6), and n is the slope exponent (typically 1.3).

4.

Mitigating factors of mudflow hazard include both natural and artificial elements that can reduce the impacts of mudflows (e.g., protective structures, vegetation cover).

4.1.

Distance from mudflow protection structures. Structures such as dams, channels, barriers, and drainage systems help prevent or minimize mudflow impacts. Distance from such infrastructure or their absence increases hazard levels. These structures can also redirect flow and act as barriers to breaches. In the Talgar River basin, a reinforced concrete, cellular mudflow retention dam filled with soil was constructed between 1991 and 2005 to protect the town of Talgar and other settlements (pop. ~40,000). This infrastructure significantly reduces territorial susceptibility to mudflows.

4.2.

Normalized Difference Vegetation Index (NDVI) is a quantitative indicator reflecting the presence and condition of vegetation. Vegetation plays an anti-erosion role through its dense turf layer, which, together with tree and grass roots, reduces runoff impact and stabilizes diluvial and colluvial deposits [56]. Consequently, reduced erosion susceptibility results in lower mudflow energy. NDVI values are interpreted as follows: from –1 to 0: infrastructure, snow, water, bare soil, and rocks; from 0 to 1: vegetated surfaces [60].

3.4. Analysis of Criteria Determining Territorial Susceptibility to Mudflows in the Talgar River Basin

Territorial susceptibility to mudflows expresses the degree of potential losses resulting from a mudflow [61]. These losses typically involve human casualties, destruction of economic assets, including buildings, infrastructure, cultural heritage, property, and disruption of economic activity. Susceptibility is determined by the capacity of social, physical, and economic systems to withstand mudflow hazards [62].

Furthermore, according to the Intergovernmental Panel on Climate Change (IPCC) [63], susceptibility is defined as the propensity or predisposition of an area or specific location to be adversely affected. In Kazakhstani scientific literature [14,64], the concepts of mudflow hazard and risk are widely used; however, the issue of assessing territorial susceptibility to mudflows remains underexplored.

Susceptibility may be defined as the property of any material object to partially or fully lose its natural or intended functions due to the impact of a catastrophic process of a given genesis and intensity [65]. The assessment of object susceptibility to catastrophic processes is conducted at the level of individual elements (“bottom-up” approach). Susceptibility indicators are aggregated by integrating data on the elementary structural components of objects into higher-level composite indicators. The typology of objects for susceptibility assessment is based on the mechanism and nature of hazard impact and takes into account the required level of detail for each specific natural process.

Currently, identifying economic facilities exposed to mudflows remains challenging due to the lack of statistical data on mudflow-induced damages and the insufficient development of models that reflect the resistance capacity of objects located in affected zones across different assessment levels.

Susceptibility assessment is a critical aspect of studying and monitoring the effects of various natural and anthropogenic factors on different environmental components. Ultimately, susceptibility indicators for various elements are combined within a more complex, multi-component entity that is the territory.

In susceptibility analysis, special attention is given to the territory as a holistic unit where natural and anthropogenic components interact. One important aspect of this approach is the identification of risk zones for areas exposed to various exogenous natural threats, including mudflows.

For a detailed assessment of susceptibility in territories exposed to mudflows, a geomorphological zoning methodology was adopted. Within this framework, the territory is analyzed in terms of river basins, allowing for the identification of several key geomorphological zones: the initiation zone, the transformation zone, and the accumulation zone.

1.

Initiation zone is the area where the mudflow process begins. These are typically steep slopes susceptible to erosion and accumulation of loose debris, which can generate water flows carrying large volumes of sediment. The following criteria are used to assess susceptibility in this zone:

1.1.

Distance from hazardous objects: hazardous features such as mudflow centers and glacial-moraine lakes can significantly influence the intensity and speed of mudflow development, which determine the nature and calculated indicators of the mudflow.

1.2.

Slope defines the dynamics of water flow and its erosive capacity, including mudflow formation. Steeper slopes increase flow speed and intensity, raising the likelihood of high-energy mudflows.

2.

Transformation zone is where the mudflow begins to change its structure, lose its original energy and velocity. Redistribution of the solid fraction and changes in flow morphology occur here. The flow velocity and erosive power significantly decrease. The following criteria are considered to assess susceptibility in this zone:

2.1.

Distance from rivers: river channels act as natural conduits for mudflows. The distance from the mountain river channel in mudflow-prone areas directly correlates with the level of risk: the closer an object is, the higher its exposure risk is.

2.2.

Topographic Wetness Index (TWI) indicates areas where moisture accumulates, correlating with transformation zones’ geomorphology. Moisture accumulation increases susceptibility to erosion and flooding.

3.

Accumulation zone is characterized by the deposition of loose debris transported by mudflows. The flow stabilizes here, and sediment is partially deposited, affecting local ecosystems. The following criteria are used to assess susceptibility in this zone:

3.1.

Elevation (m) influences flow direction and intensity. Low-lying downstream areas are more prone to flooding and sediment deposition.

3.2.

Distance from mudflow protection structures: the presence of protective structures significantly mitigates mudflow impacts. Distance to such structures reflects the level of protection.

4.

Recipients: susceptibility also depends on the resilience of social, physical, and economic systems to mudflow hazards. Recipient-related components were grouped into a separate category:

4.1

Distance from economic facilities: economic objects such as private houses, resorts, utilities, hydropower stations, bridges, and canals may be damaged by mudflows. Their location helps estimate potential economic losses.

4.2

Land Use/Land Cover (LULC): land use type (e.g., agriculture, forests or urban areas) influences the area’s resistance to mudflows. Forested and agricultural lands may be more resilient than urbanized areas.

4.3

Distance from roads: proximity to roads increases the risk of transport infrastructure damage and hampers emergency and recovery efforts.

4.4

NDVI (Normalized Difference Vegetation Index) assesses vegetation cover. High NDVI values indicate dense vegetation, which contributes to water retention and reduces flow energy.

The integrated approach proposed by the authors assessing susceptibility through geomorphological zoning enables a more precise and detailed risk evaluation and supports the development of targeted protective measures against the adverse impacts of mudflows.

3.5. Evaluation of Criteria Significance Using the Analytic Hierarchy Process (AHP)

In this study, the Analytic Hierarchy Process (AHP), developed by T. Saaty [66], was applied to evaluate mudflow hazard and territorial susceptibility. AHP is a form of Multi-Criteria Decision Analysis (MCDA) widely used in spatial planning, natural hazard management, and risk assessment [26,66].

AHP allows the decomposition of complex problems into a hierarchically organized structure and provides a quantitative assessment of the importance (weights) of each criterion [67]. A two-level hierarchical structure was constructed in this study, including 10 indicators of mudflow hazard and 10 indicators of territorial susceptibility.

In the first step, a square pairwise comparison matrix A = [a_ij ] is built, where each a_ij element reflects the preference of i criterion over j criterion, based on the following relation (6):

$${\mathrm{a}}_{\mathrm{i}\mathrm{j}}={\displaystyle \frac{{\mathrm{w}}_{\mathrm{i}}}{{\mathrm{w}}_{\mathrm{j}}}}, {\mathrm{a}}_{\mathrm{i}\mathrm{i}}=1, {\mathrm{a}}_{\mathrm{j}\mathrm{i}}={\displaystyle \frac{1}{{\mathrm{a}}_{\mathrm{i}\mathrm{j}}}}$$

(6)

where $w_i$ and $w_j$ are the weights of the corresponding criteria.

To determine the criterion weights, the eigenvector $w_i$ satisfying Equation (7) is found:

$$A\times w={\lambda }_{max}\times w,$$

(7)

where ${\lambda }_{max}$ is the largest eigenvalue of matrix A. The vector w is then normalized so that the sum of all weights equals one (8):

$${\sum }_{i=1}^n{w}_i=1,$$

(8)

AHP is implemented by forming a square pairwise comparison matrix, where rows and columns correspond to the analyzed criteria. Relative weights are calculated using a numerical scale from 1 to 9, according to Saaty’s scale of importance (1993) (

Table 1. AHP pairwise comparison.

Intensity of Importance	Definition	Explanation
1	Equal importance	Two criteria contribute equally to the objective
3	Moderate importance	One criterion is slightly preferred
5	Strong importance	One criterion is strongly preferred
7	Very strong importance	One criterion is very strongly favored
9	Absolute importance	One criterion is overwhelmingly dominant
2, 4, 6, 8	Intermediate values	Compromise between the above preferences

). For each criterion, a value is selected from the importance scale, then compared to other criteria in the columns to determine relative priority. Based on these comparisons, the degree of importance of each criterion in relation to the criteria of the next level is determined and, ultimately, the combined influence of the criteria on the formation of mudflow hazard and the determination of the susceptibility of territories to mudflow phenomena is established.

In accordance with Saaty’s recommendations [66], individual expert judgments from 10 specialists were aggregated using the geometric mean to form the unified pairwise comparison matrix. To validate the consistency of expert judgments, the Consistency Index (CI) was applied to each comparison matrix. The CI is calculated as follows (9):

$$CR={\displaystyle \frac{{\lambda }_{max}-n}{n-1}},$$

(9)

where n is the number of criteria. The Consistency Ratio (CR) compares the CI to a Random Index (RI) (10):

$$CR={\displaystyle \frac{CI}{RI}}$$

(10)

If CR < 0.1, the consistency level is considered acceptable, and the derived weights are deemed reliable.

Criterion weights were determined through expert pairwise comparisons. A group of 10 experts in hazardous natural processes, hydrology, and risk management participated in the survey. Weights were calculated using Saaty’s matrix, and consistency was verified using the consistency index [68]. In each case, the CR value remained below the recommended 0.1 threshold, indicating acceptable consistency [66].

In the GIS environment, thematic layers were created for each criterion related to mudflow hazard and territorial susceptibility. Based on assigned hazard scores (ranging from 1 to 5) and calculated weight coefficients, these layers were overlaid using the index overlay method to perform an integrated assessment of mudflow hazard and exposure. This method enabled the combination of heterogeneous spatial data by standardizing their values and applying weighted summation, resulting in a composite map that reflects the spatial variability of both hazard intensity and territorial vulnerability.

The spatial implementation of AHP was carried out in GIS for subsequent cartographic visualization of results. Each criterion corresponded to a normalized spatial layer weighted accordingly. All layers were combined using a weighted overlay method to produce the final mudflow hazard map and the susceptibility map. These were then integrated to develop a mudflow risk map that reflects the combined influence of factors across the Talgar River basin.

3.6. Mudflow Risk Assessment in the Talgar River Basin

Mudflow risk assessment involves analyzing various factors, such as the probability of hazard occurrence and the susceptibility of the area to mudflows.

According to studies [61], natural risk refers to the expected losses (including human fatalities and injuries, property damage, and disruption of economic activity) resulting from the occurrence of a specific natural hazard in a given area over a defined period. Risk is calculated based on hazard and susceptibility assessments.

Mudflow risk can be understood as the probability of negative outcomes associated with mudflow events, which can be significantly reduced to an acceptable level. Mudflow risk management involves comprehensive consideration of all factors defining mudflow hazard and the susceptibility of the territory or object, with the aim of effectively regulating the risk level.

Mudflow risk assessment is based on analyzing the expected losses associated with the potential manifestation of mudflow hazard in a specific region within a given time frame [1].

Mudflow risk represents the degree of adverse impact of mudflows on the social, ecological, and economic spheres of a territory.

The magnitude of mudflow risk in a given area depends on both the probability of occurrence of mudflows of various magnitudes (hazard probability) and the potential damage they may cause to people, the environment, and economic infrastructure (impact risk) [11,45].

Mathematically, risk can be expressed as the product of the probability of an event and the magnitude of its potential consequences [69,70]. In the context of mudflows, this principle can be adapted as:

Mudflow Risk = Mudflow Hazard × Territorial Susceptibility to Mudflows

To assess the accuracy of the spatial evaluations of mudflow hazard and susceptibility, a quantitative validation was conducted using ROC AUC (Receiver Operating Characteristic—Area Under the Curve) analysis. A total of 74 georeferenced points representing actual mudflow events in the Talgar River basin, mapped from archival and literary sources [7], field observations, and visual interpretation of satellite imagery, served as the empirical reference.

Point selection was performed to ensure spatial representation across various morphological zones (highland, mid-mountain, and low-mountain sectors) to guarantee validation representativeness.

Model results were compared to empirical data by overlaying point coordinates onto the final maps and extracting corresponding raster cell values for analysis.

ROC curves and AUC values were generated using the ArcSDM (Spatial Data Modeller) module in ArcGIS 10.x, which allows statistical validation of models through binary pixel classification (mudflow event/non-event). The obtained AUC values provided an objective, quantitative evaluation of the models’ ability to distinguish between zones of varying hazard and susceptibility levels.

For quantitative assessment of mudflow parameters, the physically based RAMMS Mudflow model was employed. Simulations were performed for three cases: the historical mudflow events of 6 July 1993 and 17 July 2014, as well as a hypothetical scenario. These events differ in characteristics, making them suitable for comparative analysis and risk evaluation in the study area.

The methodological basis of the study was the integration of MCDA and numerical modeling of mudflows in the RAMMS software environment. This approach made it possible to combine expert assessment of spatial mudflow hazard with physically based modeling of flow dynamics. In the first stage, using MCDA, each factor was assigned a weight using the AHP method, and the criteria were combined using the overlay method in a GIS environment. The result was a map of potential mudflow hazard and vulnerability. At the second stage, scenario modeling of mudflow processes was performed in RAMMS based on DEM data, lake outburst parameters, and physical and mechanical characteristics of the sediment material. The modeling made it possible to determine the spatial distribution of flow height and velocity. The RAMMS results were converted into raster layers and compared with MCDA data for subsequent analysis of overlap and refinement of vulnerable areas along the riverbed identified in the first stage. Combined maps were created, combining probability and intensity, which made it possible to develop a final risk matrix that took into account both aspects—the probability of occurrence and the scale of impact.

4. Results and Discussion

The research results include three main stages: assessment of mudflow hazard, analysis of territorial susceptibility, and integration of these results to determine the overall risk level in the Talgar River basin, with refined floodplain delineation using the RAMMS software. The application of the AHP method allowed for a quantitative evaluation of the influence of different criteria on the formation of mudflow hazard and territorial susceptibility.

To determine the weights of the criteria influencing mudflow hazard and territorial susceptibility, pairwise comparison matrices were compiled in accordance with AHP methodology (

Table 2. (a) Pairwise comparison matrices for mudflow hazard assessment criteria. (b) Pairwise comparison matrices for territorial susceptibility to mudflows assessment criteria.

(a)
Criteria		Distance from HO	Precipitation	Drainage Density	Air Temperature	Slope	SPI	STI	Soil	Distance from MPS	NDVI
	Scale of importance	9	7	7	6	7	3	5	3	2	1
Distance from HO	9	1.00	1.29	1.29	1.50	1.29	3.00	1.80	3.00	4.50	9.00
Precipitation	7	0.78	1.00	1.00	1.17	1.00	2.33	1.40	2.33	3.50	7.00
Drainage Density	7	0.78	1.00	1.00	1.17	1.00	2.33	1.40	2.33	3.50	7.00
Air Temperature	6	0.67	0.86	0.86	1.00	1.00	2.00	1.20	2.00	3.00	6.00
Slope	7	0.78	1.00	0.86	1.00	1.00	2.33	1.40	2.33	3.50	7.00
SPI	3	0.33	0.43	0.43	0.50	0.43	1.00	0.60	1.00	1.50	3.00
STI	5	0.56	0.71	0.71	0.83	0.71	1.67	1.00	1.67	2.50	5.00
Soil	3	0.33	0.43	0.43	0.50	0.43	1.00	0.60	1.00	1.50	3.00
Distance from MPS	2	0.22	0.29	0.29	0.33	0.29	0.67	0.40	0.67	1.00	2.00
NDVI	1	0.11	0.14	0.14	0.17	0.14	0.33	0.20	0.33	0.50	1.00
(b)
Criteria		Distance from HO	Slope	Distance from Rivers	TWI	Elevation	Distance from MPS	Distance from EF	LULC	Distance from Roads	NDVI
	Scale of importance	3	3	7	2	3	1	9	8	5	4
Distance from HO	3	1.00	1.00	0.43	1.50	1.00	3.00	0.33	0.38	0.60	0.75
Slope	3	1.00	1.00	0.43	1.50	1.00	3.00	0.33	0.38	0.60	0.75
Distance from Rivers	7	2.33	2.33	1.00	3.50	2.33	7.00	0.78	0.88	1.40	1.75
TWI	2	0.67	0.67	0.29	1.00	0.67	2.00	0.22	0.25	0.40	0.50
Elevation	3	1.00	1.00	0.43	1.50	1.00	3.00	0.33	0.38	0.60	0.75
Distance from MPS	1	0.33	0.33	0.14	0.50	0.33	1.00	0.11	0.13	0.20	0.25
Distance from EF	9	3.00	3.00	1.29	4.50	3.00	9.00	1.00	1.13	1.80	2.25
LULC	8	2.67	2.67	1.14	4.00	2.67	8.00	0.89	1.00	1.60	2.00
Distance from Roads	5	1.67	1.67	0.71	2.50	1.67	5.00	0.56	0.63	1.00	1.25
NDVI	4	1.33	1.33	0.57	2.00	1.33	4.00	0.44	0.50	0.80	1.00

a,b). The criteria selection and rationale for hazard and susceptibility assessment are detailed in the Methods section. Each criterion was compared against the others based on its relative influence using Saaty’s 9-point scale, where 1 indicates equal importance and 9 denotes absolute dominance. For example, in hazard assessment, the criterion distance from hazard objects, including proximity to mudflow centers and glacial-moraine lakes in the Talgar River basin, was rated with a maximum weight of 9. In susceptibility assessment, distance from economic facilities was assigned the highest priority.

According to the AHP results, the most significant contributors to mudflow hazard were (Figure 3): distance from mudflow centers (0.19); mudflow-triggering precipitation (0.15); slope steepness (0.15), and cumulative air temperature (0.13). These results confirm the dominant role of morphometric and climatic factors in the formation of mudflows in the Talgar River basin.

For susceptibility assessment (Figure 4), the most influential criteria were: distance from economic facilities (0.20); LULC (0.18); distance from rivers (0.16), and distance from road networks (0.11). Damage or flooding of these components may lead to major socio-economic losses and severe ecological consequences. These elements are particularly sensitive to the physical impacts of mudflows and are critical to the population’s well-being and territorial resilience.

Based on the derived weights and spatial data calculated using the AHP method, maps of mudflow hazard and territorial susceptibility were developed. Visualization and quantitative interpretation of the resulting data are presented in the form of tables and thematic maps (

Table 3. Significance of mudflow hazard assessment criteria.

Mudflow Hazard Criteria	Units of Measurement	Hazard Levels of Criteria			Area of Hazardous Zones
		Value	Description	Category	%	km2
Water component
Distance from hazardous objects	km	0–1.9	Very Low	1	32.5	156.6
		1.9–3.8	Low	2	33.3	160.7
		3.8–5.8	Moderate	3	25.1	121.2
		5.8–7.7	High	4	7.8	37.6
		7.7–9.7	Very High	5	1.2	5.9
Precipitation	mm	1–3	Very Low	1	80.8	389.6
		3–5	Low	2	5.8	27.7
		5–7	Moderate	3	9.7	46.9
		7–9	High	4	2.3	11.3
		9–11	Very High	5	1.3	6.4
Air temperature	°C	876–887	Very Low	1	9.2	44.6
		865–876	Low	2	17.7	85.4
		832–843	Moderate	3	4.0	19.5
		854–865	High	4	28.1	135.6
		843–854	Very High	5	40.9	197.1
Drainage Density	km/km2	0–0.8	Very Low	1	57.6	278.8
		0.8–1.7	Low	2	13.9	66.8
		1.7–2.6	Moderate	3	14.1	67.8
		2.6–3.9	High	4	9.1	43.7
		3.9–4.4	Very High	5	5.4	25.9
Geomorphological component
Slope	°	0–14	Very Low	1	16.3	78.5
		14–24	Low	2	18.3	88.4
		24–32	Moderate	3	20.7	99.8
		32–40	High	4	24.4	117.6
		40–80	Very High	5	20.3	97.6
Stream Power Index		−34.6–−7	Very Low	1	1.1	5.2
		−7–−3.5	Low	2	5.8	28.0
		−3.5–−0.67	Moderate	3	7.2	34.7
		−0.67–1.4	High	4	55.2	266.1
		1.4–25.1	Very High	5	30.7	148.0
Geological component
Sediment Transport Index		0–46	Very Low	1	99.6	480.0
		46–219	Low	2	0.3	1.3
		219–488	Moderate	3	0.1	0.4
		488–869	High	4	0.0	0.2
		869–1185	Very High	5	0.0	0.1
Soil	Level	Mountainous-meadow alpine, subalpine peat	Very Low	1	20.0	96.5
		Eroded mountainous black soils	Low	2	11.3	54.5
		Steppe mountainous black soils	Moderate	3	7.4	35.7
		Mountain-forest black soil-like	High	4	23.0	111.0
		Glaciers, cliffs, screes	Very High	5	38.2	184.3
Mitigating component
Distance from MPS	km	0–6.7	Very Low	1	15.3	73.9
		6.7–13.3	Low	2	22.2	106.9
		13.3–19.9	Moderate	3	27.3	131.7
		19.9–26.6	High	4	18.7	90.1
		26.6–33.3	Very High	5	16.5	79.3
NDVI	Level	0.67–1	Very Low	1	25.7	123.7
		0.43–0.67	Low	2	13.1	63.4
		0.18–0.43	Moderate	3	10.6	51.1
		0.004–0.18	High	4	30.5	146.8
		−1–0.004	Very High	5	20.1	97.1

and

Table 4. Significance of susceptibility assessment criteria to mudflows.

Mudflow Hazard Criteria	Units of Measurement	Hazard Levels of Criteria			Area of Hazardous Zones
		Value	Description	Category	%	km2
Start zone
Distance from hazard objects	km	0–1.9	Very Low	1	1.2	5.9
		1.9–3.8	Low	2	7.8	37.6
		3.8–5.8	Moderate	3	25.1	121.2
		5.8–7.7	High	4	33.3	160.7
		7.7–9.7	Very High	5	32.5	156.6
Slope	°	0–14	Very Low	1	16.3	78.5
		14–24	Low	2	18.3	88.4
		24–32	Moderate	3	20.7	99.8
		32–40	High	4	24.4	117.6
		40–80	Very High	5	20.3	97.6
Transit zone
Distance from rivers	km	2.9–4.8	Very Low	1	5.7	27.3
		2.1–2.9	Low	2	14.7	70.6
		1.3–2.1	Moderate	3	22.6	108.9
		0.6–1.3	High	4	27.6	133.0
		0–0.6	Very High	5	29.5	142.2
TWI		0.9–4.2	Very Low	1	29.2	140.6
		4.2–5.8	Low	2	41.1	198.0
		5.8–7.8	Moderate	3	21.3	102.7
		7.8–11.4	High	4	6.7	32.3
		11.4–24.4	Very High	5	1.7	8.4
Accumulation zone
Elevation	m	1158–1700	Low	2	7.1	34.2
		1700–2900	Moderate	3	28.9	139.2
		2900–3300	High	4	17.4	83.9
		3300–4335	Very High	5	46.6	224.7
Distance from MPS	km	26.6–33.3	Very High	5	16.5	79.3
		19.9–26.6	High	4	18.7	90.1
		13.3–19.9	Moderate	3	27.3	131.7
		6.7–13.3	Low	2	22.2	106.9
		0–6.7	Very Low	1	15.3	73.9
Recipients
Distance from economic facilities	km	0–5.4	Very Low	1	14.9	71.7
		5.4–10.7	Low	2	16.9	81.4
		10.7–16	Moderate	3	21.4	103.1
		16–21.4	High	4	24.2	116.7
		21.4–26.8	Very High	5	22.6	109.1
LULC		Vegetation	Very Low	1	13.5	65.1
		Crops	Low	2	0.1	0.3
		Bare ground/rangeland	Moderate	3	66.1	318.6
		Water bodies	High	4	18.8	90.5
		Built area	Very High	5	1.5	7.4
Distance from roads	km	9–13.2	Very Low	1	9.8	47.3
		6.6–9	Low	2	13.7	66.0
		4.2–6.6	Moderate	3	23.8	114.6
		1.9–4.2	High	4	23.0	110.7
		0–1.9	Very High	5	29.8	143.5
NDVI	Level	0.67–1	Very Low	1	25.7	123.7
		0.43–0.67	Low	2	13.1	63.4
		0.18–0.43	Moderate	3	10.6	51.1
		0.004–0.18	High	4	30.5	146.8
		−1–0.004	Very High	5	20.1	97.1

).

The tables represent processed spatiotemporal data for the ten criteria used to assess the levels of mudflow hazard and territorial susceptibility. For each criterion, the unit of measurement, value ranges corresponding to five hazard/susceptibility categories (very low, low, moderate, high, very high), and the calculated area of territories falling within each category, both in absolute values (km²) and relative terms (%) of the total study area, are provided.

This approach allows for a preliminary geostatistical analysis of the spatial distribution of hazardous and vulnerable areas for each individual criterion and helps identify the most significant contributing factors and zones most exposed to mudflow impacts.

The observed variability in the distribution of hazardous and vulnerable areas across the criteria indicates differing levels of sensitivity to the formation and propagation of mudflows. Accordingly, the sensitivity of the criteria was differentiated proportionally to their influence on the final hazard and susceptibility maps, thereby enhancing the overall accuracy of the assessment (Figure 5).

Based on the integration of multicriteria information in the geoinformation environment, the spatial layers corresponding to each of the ten criteria were harmonized into a unified format and value scale. Geospatial data analysis enabled the combination of key factors influencing mudflow formation into a single, integrated assessment. As a result of comprehensive data processing and interpretation, including standardization, classification, and weighting of criteria, final maps of mudflow hazard and territorial susceptibility were produced. These maps illustrate the spatial distribution of the Talgar River basin classified into five levels of hazard and susceptibility.

According to the resulting mudflow hazard map (Figure 6a), the majority of the basin (50.2% (242.0 km²)) falls within the moderate hazard class. The map reveals a clear spatial pattern: zones of high and very high hazard are predominantly concentrated in the high-mountain area of the Talgar River basin, driven by a combination of adverse geomorphological conditions including steep slopes, high terrain dissection, and intense orographic precipitation. Conversely, the mid-mountain and especially low-mountain areas are mainly characterized by low and very low hazard levels due to gentler terrain, reduced precipitation accumulation, and relatively stable geological conditions. High hazard zones cover 31.2% (150.5 km²) of the basin, while low hazard zones occupy 13.9% (67.1 km²). Very low and very high hazard zones account for 2.1% (10.2 km²) and 2.5% (12.2 km²), respectively (

Table 5. Classification of mudflow hazard levels with corresponding values and area distribution.

Hazard Level	Value	Area (%)	Area (km2)
Very Low	1	1.8	8.6
Low	2	15.6	75.2
Moderate	3	52.5	252.8
High	4	28.4	136.8
Very High	5	1.8	8.6

).

This distribution confirms the key role of elevation zoning, morphometric parameters, and climatic conditions in mudflow formation, justifying the need for a differentiated approach to territorial risk management.

In contrast to the hazard map, the territorial susceptibility map (Figure 6b) reveals the opposite spatial trend. The high-mountain zones are predominantly characterized by low and very low susceptibility, owing to minimal anthropogenic pressure and the absence or extremely low density of infrastructure and economic activity. Conversely, in the low-mountain areas, zones of high and very high susceptibility prevail, due to the presence of settlements, engineering structures, transportation networks, and other socio-economically significant facilities.

This distribution highlights that susceptibility is determined less by natural conditions than by the degree of anthropogenic land use and the concentration of infrastructure elements exposed to potential mudflow impacts.

According to the mudflow susceptibility map (

Table 6. Classification of mudflow susceptibility levels with corresponding values and area distribution.

Susceptibility Level	Value	Area (%)	Area (km2)
Very Low	1	4.1	19.8
Low	2	14.7	70.9
Moderate	3	35.6	171.6
High	4	40.1	193.4
Very High	5	5.5	26.3

), high susceptibility zones cover 40.1% of the territory (193.4 km²). Moderate susceptibility zones account for 35.6% (171.6 km²), and low susceptibility zones cover 14.7% (70.9 km²). Very low and very high susceptibility zones occupy 4.1% (19.8 km²) and 5.5% (26.3 km²), respectively.

To refine the assessment of territorial susceptibility in the Middle Talgar River basin, numerical simulations were conducted using the RAMMS model. This basin was selected due to frequent glacial-moraine lake outburst events and recorded mudflows, along with steep slopes and glacial coverage. Within the framework of three scenarios (1. the 6 July 1993 event; 2. the 17 July 2014 event; 3. a hypothetical August 2024 event), spatial characteristics of mudflows were obtained, based on the scenario results matrix, which includes the combined values of flow height and velocity. Based on these parameters, impact intensity zones were classified, allowing refinement and detail enhancement of previously developed susceptibility maps. The parameters used for each scenario are presented in

Table 7. Simulation parameters.

Parameters	6 July 1993 Scenario	17 July 2014 Scenario	August 2024 Hypothetical Scenario
Grid resolution, m	25	25	25
Simulation time, s	4000	3500	3000
Dump step interval, s	100	100	100
Mudflow density, kg/m3	2200	2000	1800
Friction coefficients (Mu, Xi), m/s2	Mu = 0.02 Xi = 400	Mu = 0.03 Xi = 450	Mu = 0.04 Xi = 500

.

The resulting map integrates all scenarios and reflects both the potential intensity of mudflow impact and the degree of territorial susceptibility (Figure 7).

Analysis of the spatial distribution of hazard and susceptibility indicators confirms a high level of risk within the study area. This necessitates the implementation of preventive measures and the development of comprehensive risk management strategies.

The presented results are essential for understanding the spatial distribution of mudflow hazard and susceptibility, particularly under complex topographical conditions and increasing anthropogenic pressures. The discussion focuses on interpreting observed spatial patterns, analyzing the possible causes of distribution disparities, and evaluating the reliability of the resulting cartographic models.

To quantify the accuracy of the spatial models, the ROC (Receiver Operating Characteristic) metric was applied, which assesses a model’s diagnostic ability based on the ratio of true positive to false positive classifications.

The ROC curve and AUC value analysis were conducted to validate both the mudflow hazard and mudflow susceptibility maps using a dataset of 74 documented mudflow event locations registered between 1841 and 2014 (Figure 8) from [7]. These historical event samples served as ground truth data to evaluate the predictive performance of the models. The ROC curve was constructed by comparing model-predicted values with the actual occurrence of mudflow events, enabling the calculation of the True Positive Rate and False Positive Rate across various threshold levels. The confidence band on the ROC curve shows the range within which, with a given confidence level, the “true” ROC curve is likely to be found. It provides a means to assess the statistical reliability of the ROC curve. Such visualization is an important tool for a reasonable interpretation of the classification model’s effectiveness. In the context of assessing the hazard of mudflow and the susceptibility of an area to mudflows, the presence of a confidence band allows for possible variations in the classification results to be taken into account. The confidence band in the ROC curve graph contributes to a more complete and informed analysis of the data obtained and allows reliable conclusions to be drawn about the probability of areas being affected by mudflow processes.

The ROC analysis of the hazard map showed a high level of model reliability, with an Area Under the Curve (AUC) value of 0.86, indicating strong agreement between classified high-hazard zones and known/historically recorded mudflow occurrences.

For the susceptibility map, the AUC was 0.71, reflecting an acceptable level of model accuracy. The relatively lower value compared to the hazard map can be attributed to the more complex nature of susceptibility assessment, which depends on the spatial distribution of socio-economic assets, infrastructure, and land use. This complexity may introduce discrepancies between model assumptions and actual ground conditions.

Thus, the use of ROC analysis provided an objective means of evaluating the quality of the spatial models and confirmed their applicability for further risk assessment. High AUC values demonstrate the effectiveness of the proposed approach in integrating multiple criteria and validating the simulation results.

5. Conclusions

This study developed an integrated methodology for assessing mudflow hazard and territorial susceptibility based on the overlay of spatial criteria reflecting climatic, geological, and geomorphological characteristics of the region. The resulting thematic maps of hazard and susceptibility allowed for the identification of zones with varying levels of risk, including areas with high and very high potential susceptibility to mudflows.

The spatial analysis results show that more than 80% of the study area falls within the moderate to high mudflow hazard categories, with a significant portion also exhibiting medium to high susceptibility. These findings indicate a substantial risk of mudflow occurrence and highlight the need for preventive measures in the most vulnerable zones.

The results obtained are of high practical significance and can be used in the planning and implementation of measures to reduce mudflow risks. In particular, zoning of the territory according to hazard and susceptibility levels can be used as a basis for the development of urban planning documentation and territorial planning in the Talgar River basin. The identified high-risk zones should be included in the priority areas for monitoring, engineering protection, and emergency prevention. The developed approach is also recommended for use in other mountainous areas with similar natural conditions and a high probability of mudflow processes. Regular updating of input data and modeling scenarios will allow for timely updating of risk assessments in the context of climate change and anthropogenic impact.