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Image /page/13/Figure/2 description: A flowchart detailing a methodology for assessing Glacial Lake Outburst Flood (GLOF) susceptibility. The flowchart has two main pathways. The first pathway takes "Historical GLOF events", "Glacier", and "Glacial lake" data, performs a "Statistical analysis" to determine "Spatiotemporal differentiation characteristics", and results in an understanding of "GLOFs in response to climate change". The second pathway uses machine learning. It starts with inputs of "Randomly selected glacial lakes" and "Conditioning factors" (which include Glacial lake area, Glacial lake replenishment area, Distance to glaciers, Elevation, Elevation variation coefficient, Topographic Wetness Index, Peak ground acceleration, and Distance to potential icefall). This data is split into a "Training sample 80%" and a "Validation sample 20%". The training sample is fed into a "Machine learning algorithm" to create an "Evaluation model of GLOF susceptibility (SVM)" and an "Evaluation model of GLOF susceptibility (MLP)". These models help determine the "Importance of conditioning factors". The validation sample is used for an "ROC test". Both the machine learning algorithm and the ROC test contribute to a "GLOF susceptibility index". This index is then processed by a "Natural breakpoint method" to identify "GLOF-prone lakes".

data/('Predicting glacial lake outburst susceptibility on the southern Tibetan Plateau with historical events and machine learning methods', '.pdf')_extraction.md

3 Data and methodology
3.3 GLOF modeling and model evaluation
3.3.3 Model evaluation


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Fig. 3 Flowchart of the methodology employed for GLOF susceptibility analysis

GLOF susceptibility, while ROC and AUC provide robust criteria for model selection and reliability assessment.


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The study area contains a total of 34,151 glaciers, distributed as follows: 18,460 glaciers in the western subzone, 6759 in the central subzone, and 8932 in the eastern subzone. The elevation range of glacier spans from 2741 m to 6716 m, as shown in Fig. 4a. In this figure, the horizontal axis represents glaciers sequentially numbered from west to east. Overall, glaciers at the eastern and western ends of the southern Tibetan Plateau are found at lower elevations, while those in the central section are distributed at higher elevations. The interquartile range (25–75%) of glacier elevations is between 5110 m and 5601 m, with an average elevation of 5339 m (Fig. 4b). The primary glacier flow direction across the study area is northward, followed by northeast and northwest, while southwestward flow is the least common, followed by southward flow. The three subzones exhibit distinct glacier flow patterns: in the western subzone, the dominant direction is northward, consistent with the overall trend, while southwestward flow is the least common; in the central subzone, the dominant flow direction is westward, followed by southeastward, with northwestward flow being the least frequent; in the eastern subzone, the primary flow direction is northeastward, followed by southwestward (Fig. 4c). The overall glacier slope in the study area predominantly falls within the range of 10°-35°, with the highest concentration (22%) in the 20°-25° range. The slope distribution pattern is similar across all three subzones, with the 20°-25° interval being the most common (Fig. 4d).

In 2018, a total of 10,173 glacial lakes were identified in the study area. The western subzone, despite having the highest concentration of glaciers, contained the fewest glacial lakes, with only 1861. In contrast, the central subzone had 3573 glacial lakes, while the


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Graph a is a scatter plot showing Elevation (m) on the y-axis (from 3000 to 7000) versus ID on the x-axis (from 0 to over 30000). The plot is divided into a Western subzone, a Middle subzone, and an Eastern subzone. The elevation points in the Western subzone generally increase from west to east. The Middle subzone shows a high concentration of points at high elevations, mostly between 5500 m and 6500 m. The Eastern subzone shows a general decrease in elevation from west to east.

Graph b is a box plot summarizing the total elevation data. The y-axis is the same as in graph a. The box, representing the 25%-75% interquartile range (IQR), is approximately between 5000 m and 5500 m. The median is around 5300 m, and the mean is slightly higher. Whiskers extend up to about 6500 m and down to 4000 m, with numerous outliers shown as dots.

Graph c is a radar chart showing the Contribution ratio (%) on the radial axis (from 0 to 20) versus direction in degrees (0 to 360). It compares the total data (black line) with the Western (blue), Middle (purple), and Eastern (magenta) subzones. The Western subzone peaks around 330 degrees, the Middle subzone peaks around 270 degrees, and the Eastern subzone has peaks around 30 and 150 degrees.

Graph d is a polar plot showing the Contribution ratio (%) on the radial axis (from 0 to 25) versus an angle from 0 to 90 degrees. It uses the same color scheme as graph c. All four lines show an increasing contribution ratio with the angle, peaking between 20 and 30 degrees before decreasing. The Eastern subzone shows the highest peak contribution ratio, over 10%.

**Fig. 4** Elevation, orientation and slope of glaciers. (a) Elevation of glaciers from west to east; (b) Box chart of elevation distribution of all glaciers; (c) Radar map of glacier flow direction; (d) Slope map of glaciers


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) on the radial axis ( from 0 to 25 ) versus an angle from 0 to 90 degrees . It uses the same color scheme as graph c . All four lines show an increasing contribution ratio with the angle , peaking between 20 and 30 degrees before decreasing . The Eastern subzone shows the highest peak contribution ratio , over 10 % . * * Fig . 4 * * Elevation , orientation and slope of glaciers . ( a ) Elevation of glaciers from west to east ; ( b ) Box chart of elevation distribution of all glaciers ; ( c ) Radar map of glacier flow direction ; ( d ) Slope map of glaciers

eastern subzone had the highest number, with 4739. The elevation of these glacial lakes ranged from 2174 m to 6078 m, as shown in Fig. 5a. The horizontal axis represents the sequence of glacial lakes numbered from west to east. Generally, the elevation of the glacial lakes decreases linearly from west to east. The elevation distribution of the glacial lakes predominantly fell within the interquartile range (25–75%) between 4568 m and 5232 m, with an average elevation of 4891 m (Fig. 5b), which is slightly lower than the overall elevation distribution of glaciers. The areas of the glacial lakes mainly ranged from 5400 m2 to 58,137,579 m2. The western subzone featured smaller glacial lake areas, while the central subzone had the largest average glacial lake area, at 92,880 m2. The median area of glacial lakes in the eastern subzone was nearly the same as in the central subzone, with values of 28,934 m2 and 28,258 m2, respectively (Fig. 5c). In terms of glacial lake types, Iceuncontacted Lakes represented the largest proportion at 46.39%, while Supraglacial Lakes accounted for the smallest proportion at 3.88%. Non-Glacier-Fed Lakes made up approximately 40.59% (Fig. 5d). From 1990 to 2018, both the number and area of glacial lakes in the three subzones showed an upward trend. The central subzone had the highest rate of increase, with a growth of 11.41% in number and 5.33% in area. The western subzone exhibited a 9.19% increase in the number of glacial lakes and a 1.38% increase in area. The eastern subzone showed an 8.73% increase in the number of glacial lakes and a 2.82% increase in area. Additionally, glacial lakes in the study area generally begin to thaw gradually at the end of April and refreeze by October.


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Chart (a) is a scatter plot showing the elevation of glacial lakes. The y-axis, 'Elevation (m)', ranges from 3000 to 6500. The x-axis, 'Glacial Lake ID', ranges from 0 to over 10000 and is divided into 'Western subzone', 'Middle subzone', and 'Eastern subzone'. The data points are concentrated between 4000 and 6000 meters.

Chart (b) is a box plot of the elevation data from chart (a). The y-axis is 'Elevation (m)' from 3000 to 6500. The box shows an interquartile range from approximately 4700 to 5200 m, with a median around 5000 m.

Chart (c) consists of three box plots comparing the 'Area (m²)' of lakes in the 'Western subzone', 'Middle subzone', and 'Eastern subzone'. The y-axis ranges from 0 to 200000. All three subzones show a median area below 50000 m² but have numerous outliers with larger areas. A legend explains the components of the box plot: 25%-75%, 1.5IQR, Median, Mean, and Outliers.

Chart (d) is a pie chart showing the distribution of lake types by percentage. The categories are: 'Ice-uncontacted Lake' (46.39%), 'Non-Glacier-Fed Lake' (40.59%), 'Ice-contacted' (9.14%), and 'Supraglacial Lake' (3.88%).

Chart (e) is a grouped bar chart showing the percentage of the total number and area of lakes in each subzone. The y-axis is 'Percentage (%)' from 0 to 12. For the 'Western subzone', the number is about 9.2% and the area is about 1.5%. For the 'Middle subzone', the number is about 11.2% and the area is about 5.2%. For the 'Eastern subzone', the number is about 8.8% and the area is about 2.8%.

**Fig. 5** Elevation, area, type and expansion trend of glacial lake. (a) Elevation of glacial lakes from west to east; (b) Box chart of elevation distribution of all glacial lakes; (c) Box chart of glacial lake areas; (d) Pie chart of glacial lake types; (e) The number and area changes of glacial lakes from 1990 to 2018


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The earliest documented GLOF in the study area occurred on August 28, 1935 (Tibetan calendar), at Lumu Lake in Bomi County. As of 2024, a total of 66 GLOF events have been recorded in the area, as detailed in Table 1. Among these, Cirenmacuo Glacial Lake and Ayacuo Glacial Lake each experienced three outbursts, while Dig Tsho Glacial Lake and Upper Luggye Glacial Lake each experienced two outbursts. Geographically, these historical GLOF events are primarily concentrated in the central and eastern subzones of the study area. Among the three subzones, the western subzone recorded the fewest GLOF events, with only three events, while the central subzone experienced the most, with 44 events, and the eastern subzone had 19. To further evaluate the spatial distribution characteristics of these events, a spatial autocorrelation analysis using the Global Moran's I index was conducted. The results showed a Moran's I value of 0.239, a Z-score of 1.69, and a p-value of 0.091, indicating a weak spatial clustering pattern of GLOF events. However, the clustering was not statistically significant at the 95% confidence level, although marginal significance was observed at the 90% confidence threshold. Regarding temporal trends, a higher number of GLOF events occurred during the 1960s and from 1990 to 2020 (Fig. 6a). The majority of these GLOFs occurred between June and October, coinciding with the rainy season on the Tibetan Plateau (Fig. 6b). The primary causes of these events (Fig. 6c) include icefalls (48.48%), moraine dam destabilization (18.18%), and heavy rainfall (6.06%). With global warming, the frequency and variety of GLOFs on the Tibetan Plateau have increased. These


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Image /page/16/Figure/2 description: An image displaying three charts labeled a, b, and c, analyzing the frequency and causes of certain events. Chart a is a line graph showing the number of events per decade from the 1930s to the 2020s. The y-axis, labeled 'Number', ranges from 0 to 18. The data points are: 1930s (2), 1940s (1), 1950s (4), 1960s (10), 1970s (1), 1980s (7), 1990s (18), 2000s (12), 2010s (10), and 2020s (approximately 1). The peak occurred in the 1990s. Chart b is a bar chart showing the number of events per month. The y-axis, labeled 'Number', ranges from 0 to 14. The values for each month are: April (2), May (3), June (9), July (11), August (11), September (9), October (7), and N/A (14). The highest frequency is in July and August. Chart c is a pie chart illustrating the percentage distribution of event causes. The largest portion is 'Icefall' at 48.48%. Other causes include 'Moraine dam destabilization' (18.18%), 'N/A' (16.67%), 'Heavy rainfall' (6.06%), 'Landslide' (4.55%), 'Rock/Snow avalanche' (3.03%), 'Upstream inflow' (1.52%), and 'Earthquake' (1.52%). A legend below the pie chart provides the key for each colored segment.


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**Fig. 6** The timing and triggering factors of historical GLOF events. (a) Chronological distribution map of historical GLOF events; (b) Monthly distribution map of historical GLOF events; (c) Pie chart of triggering factors of historical GLOF events

events mainly result in debris flows or floods, causing extensive damage to infrastructure such as highways, bridges, and power stations. They also lead to the silting of farmland, forests, and homes, disrupting transportation and local production, and inflicting severe economic losses. For example, the 1988 Guangxie Glacial Lake outburst destroyed 23 km of the Sichuan-Tibet highway, causing a road closure that lasted more than 200 days. Some GLOFs resulted in significant casualties. For example, the 1954 Sangwang Glacial Lake outburst claimed the lives of 400 people.


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The descriptive statistics for each conditioning factor in all positive samples (historical GLOF events) are presented in Table 2. Among these factors, elevation has the smallest coefficient of variation, approximately 0.089, while glacial lake area exhibits the largest coefficient of variation at 2.32. Other factors with relatively smaller coefficients of variation include the ECV, TWI, and PGA, indicating that historical GLOF events are more concentrated around these factors. For both positive and negative samples, the conditioning factors were used as independent variables, with the occurrence of GLOF serving as the dependent variable. These variables underwent multicollinearity diagnostics, and the results are shown in Table 2. The highest VIF value is 1.768, which meets the requirement for multicollinearity diagnostics in susceptibility evaluation. Therefore, these eight factors were ultimately selected as the conditioning factors for GLOF susceptibility.

The importance of each conditioning factor in the modeling process using machine learning algorithms for training samples is shown in Fig. 7. Due to the differing principles of each algorithm, the importance values for the conditioning factors vary. Among these factors, Distance to Glaciers, TWI, and Distance to Potential Icefall have importance greater than 0.1 in two models. Additionally, the MLP model identified Glacial Lake Area, Glacial Lake Replenishment Area, and Elevation as the most important factors, with the ECV also surpassing an importance of 0.1. The SVM model assigned the highest importance to Distance


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Table: Table 2 Descriptive statistics and VIF of prepared conditioning factors

| Conditioning factors                 | Descriptive statistics |                    |             |         |           |             |                          | VIF   |
|--------------------------------------|------------------------|--------------------|-------------|---------|-----------|-------------|--------------------------|-------|
|                                      | Mean                   | Standard deviation | Total       | Minimum | Median    | Maximum     | Coefficient of Variation |       |
| Glacial lake area (m2)               | 354278.06              | 801444.42          | 19,485,300  | 6188.69 | 144929.57 | 5,813,520   | 2.32                     | 1.435 |
| Glacial lake replenishment area (m2) | 16,644,600             | 27,457,000         | 915,452,000 | 5690.98 | 6,553,840 | 160,366,000 | 1.73                     | 1.768 |
| Distance to glaciers (m)             | 728.68                 | 1519.38            | 40077.44    | 0       | 200.74    | 9039.55     | 2.02                     | 1.239 |
| Elevation (m)                        | 4928.64                | 429.48             | 271075.68   | 3829.14 | 5009.42   | 5708.42     | 0.089                    | 1.578 |
| ECV                                  | 0.0135                 | 0.00677            | 0.743       | 0.00111 | 0.013     | 0.0416      | 0.48                     | 1.580 |
| TWI                                  | 11.25                  | 2.26               | 618.96      | 6.159   | 11.37     | 17.263      | 0.22                     | 1.584 |
| PGA (m/s2)                           | 0.239                  | 0.0778             | 13.14       | 0.0974  | 0.246     | 0.415       | 0.34                     | 1.278 |
| Distance to potential icefall (m)    | 14300.79               | 22711.11           | 786543.62   | 523.74  | 6219.83   | 111382.88   | 1.63                     | 1.459 |

Conditioning factors
Descriptive statistics
VIF


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to Potential Icefall, with a value of 0.39. The mean importance value of Distance to Potential Icefall across both models was notably high, reaching 0.26.


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The SVM and MLP algorithms from the Scikit-learn library were invoked through Jupyter Notebook to calculate the conditioning factor values for the training and validation samples. Additionally, the GridSearchCV function was used for parameter optimization. After executing the models, the results were imported into the GIS platform. In the SVM model, optimal hyperparameters were obtained through GridSearchCV, with C=1000 and  $\gamma$ =0.003. The conditioning factors for each glacial lake unit in the study area were then input into the model to calculate the GLOF susceptibility index. The final GLOF susceptibility evaluation results are shown in Fig. 8a, with a value range of [0.026, 1]. Using the natural breakpoint method, the susceptibility index map was classified into five categories: very low, low, medium, high, and very high susceptibility. In the susceptibility index classification results (Table 3), 474 glacial lakes were identified as VHS, representing 4.7% of the total number of glacial lakes in the study area, with susceptibility index values ranging from 0.74 to 1.0. Additionally, 1297 glacial lakes were classified as HS, accounting for 12.7% of the total number of glacial lakes, with index values ranging from 0.528 to 0.740. In the MLP model, a three-layer neural network was constructed, consisting of an input layer, a hidden layer, and an output layer. The optimal configuration was achieved through parameter optimization, resulting in 30 neurons in the hidden layer with the Tanh activation function. The GLOF susceptibility evaluation results based on this model are illustrated in Fig. 8b, with a value range of [0.12, 0.937]. In the susceptibility index classification results (Table 3), 1286 glacial lakes were classified as VHS, accounting for 12.6% of the entire study area, with susceptibility index values ranging from 0.616 to 0.937. Additionally, 2548 glacial lakes were identified as HS, representing 25% of the study area, with index values ranging from 0.505 to 0.616. In terms of modeling accuracy, the MLP algorithm exhibits slightly higher accuracy, with an AUC value of 0.96 compared to the SVM's AUC of 0.90.

4 Results
4.2 Generating GLOF susceptibility maps
4.2.2 GLOF susceptibility maps


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The formation of glacial lakes is closely tied to glacial movements (Liu et al. 2019). These lakes typically form at the leading edges of glaciers or in other low-lying areas, with their dams primarily composed of moraine, ice, debris, and occasionally bedrock. Over time, moraine dams can become unstable, leading to outburst events when they can no longer withstand rising water levels within the lake. This phenomenon is particularly common during warmer seasons or periods of climate warming. Global warming has led to increased temperatures in alpine and glacial regions, accelerating the melting of ice. Glaciers worldwide are retreating at an alarming rate, with many regions experiencing significant thinning and retreat (Ding et al. 2021; Jobanpreet and Chitradevi 2024). The meltwater from these glaciers replenishes glacial lakes, resulting in substantial lake expansion and destabilizing the surrounding glaciers. The debris-free glaciers on the Tibetan Plateau have retreated at

5 Discussion
5.1 GLOFs in response to climate change


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Image /page/19/Figure/2 description: A horizontal bar chart titled "Conditioning factors" shows the importance of various factors based on three different metrics: SVM (purple), MLP (green), and Mean (orange). The x-axis represents "Importance (%)" and ranges from 0.00 to 0.40. The y-axis lists the conditioning factors. The data presented is as follows:
- Glacial lake area: SVM is approximately 0.07, MLP is 0.16, and Mean is 0.12.
- Glacial lake replenishment area: SVM is approximately 0.08, MLP is 0.13, and Mean is 0.11.


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- Distance to glaciers: SVM is approximately 0.17, MLP is 0.13, and Mean is 0.14.
- Elevation: SVM is approximately 0.07, MLP is 0.13, and Mean is 0.10.
- ECV: SVM is approximately 0.04, MLP is 0.12, and Mean is 0.08.
- TWI: SVM is approximately 0.15, MLP is 0.12, and Mean is 0.13.
- PGA: SVM is approximately 0.06, MLP is 0.06, and Mean is 0.06.
- Distance to potential icefall: SVM is approximately 0.39, MLP is 0.14, and Mean is 0.26.
The chart indicates that "Distance to potential icefall" is the most important factor, especially for the SVM model. The top of the image includes a citation: "Natural Hazards (2023) 121:17677–17705".

Fig. 7 Importance of GLOF susceptibility conditioning factors


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Image /page/19/Figure/4 description: A figure displaying two maps, labeled 'a' and 'b', that show the Glacial Lake Outburst Flood (GLOF) susceptibility for a mountainous region. The maps cover a geographical area from 90°0'0"E to 90°30'0"E longitude and 28°0'0"N to 28°10'0"N latitude. Both maps feature a grayscale elevation background, with light blue areas indicating glaciers. A north arrow is in the top right, and a scale bar indicating 0 to 10 km is in the bottom right.


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Map 'a' is titled "GLOF susceptibility (SVM)". Its legend indicates an elevation range from a low of 1406 m to a high of 7452 m. The susceptibility is categorized into five levels:
- VLS (Very Low Susceptibility): 0.026 - 0.256 (Green)
- LS (Low Susceptibility): 0.256 - 0.392 (Light Green)
- MS (Medium Susceptibility): 0.392 - 0.528 (Yellow)
- HS (High Susceptibility): 0.528 - 0.740 (Orange)
- VHS (Very High Susceptibility): 0.740 - 1 (Red)

Map 'b' is titled "GLOF susceptibility (MLP)". It shares the same glacier and elevation legend as map 'a'. Its susceptibility categories are:
- VLS (Very Low Susceptibility): 0.120 - 0.283 (Green)
- LS (Low Susceptibility): 0.283 - 0.397 (Light Green)
- MS (Medium Susceptibility): 0.397 - 0.505 (Yellow)
- HS (High Susceptibility): 0.505 - 0.616 (Orange)
- VHS (Very High Susceptibility): 0.616 - 0.937 (Red)

Both maps show various colored polygons representing the susceptibility levels of different glacial lakes, with red and orange areas indicating high to very high susceptibility.

Fig. 8 Partial Map of GLOF Susceptibility Evaluation Results. (a) GLOF Susceptibility Evaluation Result based on SVM. (b) GLOF Susceptibility Evaluation Result based on MLP

an accelerated pace due to climate warming, with a reduction in area from  $94.59 \times 10^3$  km2 to  $61.16 \times 10^3$  km2 from 1988 to 2022 (Zhao et al. 2024). In the Himalayas, glaciers have shrunk by 20–30% (Nie et al. 2021). The retreat of glaciers increases the volume of glacial lakes at the glacier terminus and raises water levels, thereby increasing the risk of dam


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Table

| Susceptibility classification | SVM         |                            |                   | MLP         |                               |                             |
|----------------------------------|-------------|----------------------------|-------------------|-------------|-------------------------------|-----------------------------|
|                                  | Interval    | Number of glacial lakes | Percentage (%) | Interval    | Number of glacial lakes | Per- cent- age (%) |
| VHS                              | 0.740~1     | 474                        | 4.7               | 0.616~0.937 | 1286                          | 12.6                        |
| HS                               | 0.528~0.740 | 1297                       | 12.7              | 0.505~0.616 | 2548                          | 25.0                        |
| MS                               | 0.392~0.528 | 5047                       | 49.6              | 0.397~0.505 | 2602                          | 25.6                        |
| LS                               | 0.256~0.392 | 1349                       | 13.3              | 0.283~0.397 | 2142                          | 21.1                        |
| VLS                              | 0.026~0.256 | 2006                       | 19.7              | 0.120~0.283 | 1595                          | 15.7                        |


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failure. Marine glaciers, in particular, are highly sensitive to global warming, undergoing intense ablation, thinning, and retreat (Christian et al. 2022). This leads to the expansion of glacial lakes and the weakening of their dams, ultimately triggering GLOFs. This underscores the critical dependence of GLOF events on glacial dynamics.

Climate change can significantly impact precipitation patterns, leading to increased intensity and frequency of rainfall events (Maity and Maity 2022). Such changes may result in a rapid rise in glacial lake levels, elevating the risk of outbursts (Liu et al. 2014). Additionally, climate change influences glacier dynamics, accelerating both forward and lateral glacier movements, which in turn increases the frequency of glacial lake formation and the likelihood of outburst events. GLOFs exhibit pronounced cyclicality and trends under varying climatic conditions. The 1960s, regarded as one of the coldest decades in Tibet (Gong et al. 2022), provided favorable climatic conditions for glacier accumulation and advance. However, extreme weather events and unusual climatic fluctuations during this transitional period increased the risk of GLOFs. This was particularly evident during warmer transitional years when icefalls into glacial lakes became a significant trigger for multiple outburst events. As the climate warmed in the 1970s and 1980s, the frequency of GLOFs declined considerably due to diminished conditions for glacier accumulation. Icefalls and associated factors remained the primary triggers during this time. By the 1990s, intensified glacier ablation, thinning, and retreat—driven by mean annual temperatures exceeding multi-year averages—resulted in new dynamics. The period from 2000 to 2016 marked the warmest 16 years in Tibet's recorded history (Chen et al. 2022; Gong et al. 2022). During this era of accelerated global warming, GLOF events surged dramatically. In addition to icefalls, triggers expanded to include landslides, heavy rainfall, and the melting of buried ice. These non-icefall-related factors accounted for more than half of the GLOF events during this period, underscoring the increasing climate sensitivity of GLOFs.

The spatial differentiation of glaciers, glacial lakes, and historical GLOFs across the three subzones of the study area reveals distinct regional characteristics. The western subzone hosts the highest number of glaciers, reflecting its lower temperatures and drier climatic conditions. Its greater distance from the Indian Ocean and reduced water vapor transport result in less snowfall; however, the cooler climate supports longer glacier survival. In contrast, the eastern and central subzones, being closer to the Indian Ocean (Fig. 9), benefit from stronger water vapor transport and higher precipitation levels, creating favorable conditions for the formation of glacial lakes. The relatively lower elevation of glacial lakes in the eastern subzone is likely due to the higher water vapor content and warmer climate, which promote greater ice melt at glacier termini, facilitating glacial lake forma-


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Image /page/21/Figure/2 description: A topographical map of the Tibetan plateau and surrounding regions, illustrating elevation and major atmospheric circulation patterns. The elevation is represented by a color scale in the bottom left, ranging from low (green, 0 m) to high (brown and white, 8848 m). The central feature is the snow-covered Tibetan plateau, with its southern edge divided into a 'Western subzone', 'Middle subzone', and 'Eastern subzone'. Several cities are marked, including New Delhi, Lasa, Dacca, Wulumuqi, Xining, Chengdu, and Guangzhou. Arrows indicate key weather systems: blue arrows from the northwest show the 'Westerlies circulation', purple arrows from the southwest represent the 'Indian Ocean monsoon', and blue arrows from the southeast depict the 'Southeast Asian monsoon'. A pink arrow points to the Bay of Bengal, labeled 'Study area'. The map also includes latitude lines for N20°, N30°, and N40°, and distance markers such as '~1200km' and '~545km' related to the monsoon paths.


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Fig. 9 Schematic diagram of climate background of the study area

tion. The occurrence of GLOF events also varies spatially. The western subzone experiences the fewest GLOFs. In contrast, the eastern and central subzones have a higher frequency of GLOFs, driven by the greater number and larger size of glacial lakes and the higher rates of temperature increase. The varying distances from the Indian Ocean among the three subzones play a crucial role in shaping the spatial variability of water vapor transport and precipitation. The eastern and central subzones, being closer to the Indian Ocean, are more sensitive to climate change. Conversely, the western subzone, farther from the Indian Ocean and located at relatively higher latitude, experiences a drier and colder climate. Its climate is more influenced by the southern branch of the westerly circulation, resulting in a delayed response of glacial lakes to climate change. This highlights the climate sensitivity of GLOFs from another perspective.


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Section: 5 Discussion > 5.2 GLOF-prone lakes and model performance
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In the GLOF susceptibility evaluation, various machine learning models were employed to predict GLOF susceptibility and to calculate the weights of each evaluation factor. The accuracy of the models and their ability to effectively identify areas with high susceptibility demonstrated that both SVM and MLP are suitable for training with small datasets. Notably, all glacial lakes classified as HS and VHS by the SVM model were also classified as such in the MLP model. The MLP model, however, provided more conservative results, identifying a broader range of HS and VHS glacial lakes, accounting for 37.6% of the total. In contrast, the SVM model identified 17.4% of glacial lakes as HS and VHS. Figure 10 presents histograms of the susceptibility indices for all glacial lakes derived from both models. Although neither dataset passed the normal distribution test, the figure clearly shows that the


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Image /page/22/Figure/2 description: The image contains two histograms, labeled 'a' and 'b', presented side-by-side. Both plots have a y-axis labeled 'Count' and an x-axis ranging from 0.0 to 1.0. Plot 'a' is a histogram for 'SVM' with orange, diagonally hatched bars. Its y-axis ranges from 0 to 1600. The data distribution is skewed to the right, with the highest count reaching approximately 1500 in the bin corresponding to an x-value of about 0.35. There are vertical dashed lines at x-values of approximately 0.25, 0.35, 0.5, and 0.7. Plot 'b' is a histogram for 'MLP' with purple, diagonally hatched bars. Its y-axis ranges from 0 to a value above 1200. The data distribution is more symmetric, resembling a bell curve, with its peak count of approximately 1300 in the bin corresponding to an x-value of about 0.5. There are vertical dashed lines at x-values of approximately 0.3, 0.5, and 0.6.


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Fig. 10 Histogram of outburst susceptibility indices for each glacial lake (The vertical dashed lines represent the threshold values for susceptibility classification based on the natural break method). (a) Outburst susceptibility indices based SVM. (b) Outburst susceptibility indices based MLP

overall mean of the MLP results is higher, further confirming the conservatism of the MLP model's outcomes. Overall, this analysis reveals that these glacial lakes with HS and VHS ratings are predominantly located in the central and eastern subregions of the study area, highlighting spatial patterns of GLOF risk. Field validation further supports the reliability of the model predictions. In particular, Rongxia Zangbu Glacial Lake, which was investigated during field surveys, was identified as highly susceptible to GLOF. The SVM model assigned it a susceptibility score of 0.992, while the MLP model yielded a score of 0.78, both indicating a high risk of outburst. This moraine-dammed lake, formed by glacial deposition at an elevation of approximately 5050 m, has exhibited significant changes in recent years. Field observations reveal that its surface area expanded from 1,714,497 m2 in 2019 to 1,887,616 m2 in 2023. Concurrently, the width of the terminal moraine dam decreased dramatically from 939 m in 2019 to 166 m in 2023. Given the continuous expansion of the lake area and the substantial narrowing of the moraine dam, Rongxia Zangbu Glacial Lake shows clear signs of destabilization and poses a substantial potential risk of future outburst. Similarly, although the Gebumaco Glacial Lake has been historically outburst (Wang et al. 2011), it still covers an area of 445,722 m2, and the glacier which it originates has developed ice crevasses that are at risk of triggering ice avalanches. In this assessment, the SVM result is 0.545 and the MLP result is 0.517, both indicating moderate susceptibility. These findings are largely consistent with field observations, underscoring the practical applicability of the model-based susceptibility evaluation.

The most critical factors influencing GLOFs are Distance to Glaciers, TWI, and Distance to Potential Icefall, highlighting their pivotal role in GLOF dynamics. These factors are physically meaningful, as they directly reflect glacier—lake interactions and the likelihood of sudden mass movements impacting lake stability. Subsequently, factors such as Glacial Lake Area, Glacial Lake Replenishment Area, Elevation, and ECV further underscore the combined influence of geographic and climatic conditions on GLOF susceptibility. This aligns with the physical mechanisms underlying GLOF formation, which commonly involve rapid meltwater influx, direct calving of glaciers into lakes, or impacts from icefalls on moraine-dammed basins (Ahmed et al. 2021). Among all factors, Distance to Glaciers and Distance to Potential Icefall are especially significant, emphasizing the intrinsic link between glacial activity and lake instability. Glacial lakes predominantly form in close proximity to glaciers,


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as their genesis and hydrological input are tied to glacier melt and retreat (Ahmed et al. 2021). Moreover, historical analyses confirm that icefalls frequently act as immediate triggers for GLOF events, especially in high-relief regions such as the Himalayas and Andes. Despite relatively high coefficients of variation revealed in statistical analyses for these two proximity-related factors, their physical relevance to GLOF initiation remains indisputable, marking them as essential indicators of hazard potential. Topographic factors, including TWI, Elevation, and the ECV, also play crucial roles. These factors exhibit smaller coefficients of variation in statistical analyses, indicating that historical GLOF events tend to occur within specific ranges of TWI, elevation, and ECV, enhancing their discriminative power. TWI represents the hydrological accumulation potential of a landscape, being influenced by slope, catchment water accumulation, and terrain (Chowdhury 2023). Both TWI and ECV, as topographic derivatives, reflect terrain wetness and relief, respectively, capturing the hydrological and geomorphological context in which glacial lakes evolve. Similarly, Glacial Lake Area and Replenishment Area jointly influence the lake's hydrological budget, with their effects on stability modulated by glacier proximity and elevation. Specific elevation ranges are more conducive to the formation and persistence of glacial lakes, often coinciding with climatic and glaciological thresholds relevant to GLOF risk. The Glacial Lake Replenishment Area significantly impacts the rate and volume of water accumulation in a glacial lake, with larger areas corresponding to higher potential GLOF risks. In conclusion, GLOFs are typically triggered by a combination of interrelated factors. These critical variables not only shape the formation mechanisms of GLOFs but also profoundly influence the likelihood and scale of such disasters.

This study primarily focuses on analyzing historical records to identify the characteristics and susceptibility of GLOFs. Although the study is centered on the Southern Tibetan Plateau, the proposed methodological framework—integrating historical GLOF inventories, geomorphological indicators, and machine learning classifiers—can be adapted to other regions, provided that appropriate regional datasets are available. However, the uncertainty of the current analysis is also constrained by several data- and model-related constraints. First, it does not incorporate projections or scenario modeling to assess potential trends in glacial lake expansion and GLOFs under future climate change scenarios. Given that climate change can profoundly influence glacier retreat rates, glacial lake expansion, and the frequency of GLOFs, the absence of such dynamic considerations may lead to an underestimation of future GLOF risks. Second, the spatial coverage and accuracy of historical GLOF event records are uneven, often biased toward more accessible regions with longer observation histories, introducing potential geographic bias into model training. Furthermore, the limited number of known GLOF cases creates challenges for machine learning classifiers. Although SVM and MLP demonstrate some robustness in dealing with fewer samples, their generalization ability remains limited due to the risk of overfitting. Consequently, future research should consider integrating global or regional climate models, such as the CMIP6 dataset, to project the evolution of glaciers and glacial lakes under various greenhouse gas emission scenarios. Combining these modeling results with remotely sensed monitoring and in situ observational data could facilitate the construction of a multi-source data-driven dynamic risk assessment system.


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This study presents a comprehensive analysis of glaciers, glacial lakes, and historical GLOF events within the southern Tibetan Plateau. The findings reveal that glaciers in the study area are abundant and widely distributed, with elevations displaying a distinct pattern: lower levels in the eastern and western extremities. Glacier flow predominantly occurs northward, with slopes most commonly ranging between 20° and 25°. Accompanying the retreat of glaciers in the region, the number of glacial lakes has shown a steady year-on-year increase, particularly in the central and eastern subzones, where both the number and area of glacial lakes have grown significantly. Glacial lake areas vary considerably, with the central subzone exhibiting the largest average glacial lake area. Historically, 66 documented GLOF events have occurred within the study area, most frequently between June and October. These events were primarily triggered by icefall (48.48%), moraine dam destabilization (18.18%), and heavy precipitation (6.06%). The impact of climate warming on GLOFs has been particularly pronounced, notably during the 1960s and from 1990 to 2020, when rising temperatures and shifting precipitation patterns intensified the frequency of these events. The study underscores the significant dependence of GLOF events on glacial dynamics and their sensitivity to climatic variations, emphasizing the interplay between glacier changes and climate shifts in shaping the risk and occurrence of these hazardous events.

The study employed two machine learning algorithms, SVM and MLP, to predict the GLOF susceptibility based on historical events. The evaluation results indicated that approximately 17.4% of glacial lakes were classified into HS and VHS, with higher susceptibility predominantly observed in the central and eastern subzones. The MLP model demonstrated slightly better accuracy than the SVM model, achieving AUC values of 0.96 and 0.90, respectively. Additionally, further analysis highlighted that the MLP model produced more conservative predictions regarding GLOF susceptibility.

Overall, climate warming and glacier retreat have intensified the expansion and instability of glacial lakes, leading to an increased frequency and severity of GLOF events. The findings highlight the spatial and temporal patterns of GLOF events and their connection to climate change, providing valuable insights for guiding the prevention and mitigation efforts. The integration of machine learning technology has deepened our understanding of the complex nonlinear relationships between environmental factors and GLOF occurrences, providing an advanced and effective method for risk assessment in the region. Moving forward, future research should focus on integrating real-time remote sensing data, in situ observations, and advanced forecasting techniques to establish dynamic monitoring frameworks and early warning systems. These efforts will provide a robust scientific foundation for disaster prevention and management in alpine glacier regions.

**Acknowledgements** This study was supported by the Central Guidance for Local Science and Technology Development Foundation of China (Grant No.2024ZYD0159), Open Project of Major Hazard Measurement and Control Key Laboratory of Sichuan Province (Grant No.KFKT-202306) and the Talent Introduction Project of Xihua University (Grant No.Z231013).

**Funding** Sichuan Science and Technology Program (2025YFNH0008). Open Project of Major Hazard Measurement and Control Key Laboratory of Sichuan Province (KFKT-202306). Talent Introduction Project of Xihua University (Z231013).


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**Competing interests** The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Document: Predicting the Risk of Glacial Lake Outburst Floods in Karakorum
Type: text

**Abstract.** Glacier snouts respond to climate change by forming proglacial meltwater lakes, thereby influencing glacier mass balance and leading to advancements and surges. The positive feedback of climate change results in more frequent ice-dammed glacial lake outburst floods (GLOFs) in the Karakorum and surrounding regions, often facilitated by englacial conduits. However, the complex and multi-factor processes of conduit development are challenging to measure. Determining the lake depths that might trigger GLOFs and the numerical model specifications for breaching are still being determined. Empirical estimates of lake volumes, along with field-based monitoring of lake levels and depths and the assessment of GLOF risks, enable warnings and damage mitigation. Using historical data, remote sensing techniques, high-resolution imagery, crosscorrelation feature-tracking, and field-based data, we identified the processes of lake formation, drainage timing, and triggering depth. We developed empirical approaches to determine lake volume and trigger water pressure leading to a GLOF. The correlation of glacier surge and lake volume reveals that glacier surge velocity plays a crucial role in lake formation and controlling the size and volume of the lake. Lake volume estimation involves geometric considerations of the lake basin shape. A GLOF becomes likely when the lake's non-dimensional depth (n') exceeds 0.60, correlating with a typical water pressure on the dam face of 510 kPa. Additionally, we identified the critical risk zone of lakes, where all lake outburst floods occur, as the point where the lake volume reaches or exceeds 60% of its capacity. These field-based and empirical findings not only offer valuable insights for early warning procedures in the Karakorum but also suggest that similar approaches can be effectively applied to other mountain environments worldwide where GLOFs pose a hazard.

data/('Predicting the Risk of Glacial Lake Outburst Floods in Karakorum', '.pdf')_extraction.md


Document: 30 1. Introduction
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Globally, glacier shrinkage is a strikingly visible sign of climate change. However, within High Mountain Asia (HMA), particularly the Karakorum, Kunlun Shan, and Eastern Pamirs, the glaciers have been gaining mass since 1970 (Berthier and Brun, 2019; Gardelle et al., 2012; Kääb et al., 2015; Minora et al., 2013; Yao et al., 2012). This positive response to climate change consequently influences glacier dynamic behaviours, with the HMA glaciers thickening, increasing glacier surges, and


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advancing glacier termini throughout the region (Bhambri et al., 2013; Bolch et al., 2017). This behaviour contrasts neighbouring regions with negative glacier mass budgets, such as the Himalayas, Hindukush, and Tibet (Bazai et al., 2021; Bolch et al., 2011; Frey et al., 2014). In the latter areas, glaciers continue to shrink, thinning and reducing volume, showing no significant glacier advance (Dehecq et al., 2019; Farinotti et al., 2020; Yao et al., 2012). As a result, the Moraine Lake formation has increased the number of GLOFs in the glacier-retreating regions (Yong et al., 2017) as well as the number of glacier avalanches as increased (Byers et al., 2023; Kääb and Girod, 2023; You and Xu, 2022). However, in the glacier advance regions, the positive variation in regional climate feedback has prompted the rapid formation of ice-dammed lakes accompanied by sudden releases of meltwater originating from these lakes (Carling, 2013; Hewitt, 1982; Hewitt, 1998; Hewitt and Liu, 2010).

The mechanisms and frequency of ice dam glacial lake outburst floods (GLOFs) still need to be better understood, hindering accurate prediction (Bazai et al., 2021; Cook et al., 2016; Harrison et al., 2018; Richardson and Reynolds, 2000). Recent studies have investigated changes in frequency due to climate change (Rick et al., 2023; Veh et al., 2023) and conducted global assessments of flood volume and risk (Rick et al., 2023). Despite these efforts, understanding the drainage and predicting flood events from ice-dammed lakes remain challenging. Predicting these events is crucial due to their potential to cause devastating impacts on human lives and livelihoods, ecosystems, infrastructure (*e.g.*, roads, bridges, hydropower systems), river channel stability, and effects on agriculture and fisheries (Carrivick and Tweed, 2016; Cook et al., 2016; Emmer, 2017; John et al., 2000; Neupane et al., 2019; Zhang et al., 2022).


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flood volume and risk ( Rick et al . , 2023 ) . Despite these efforts , understanding the drainage and predicting flood events from ice - dammed lakes remain challenging . Predicting these events is crucial due to their potential to cause devastating impacts on human lives and livelihoods , ecosystems , infrastructure ( * e . g . * , roads , bridges , hydropower systems ) , river channel stability , and effects on agriculture and fisheries ( Carrivick and Tweed , 2016 ; Cook et al . , 2016 ; Emmer , 2017 ; John et al . , 2000 ; Neupane et al . , 2019 ; Zhang et al . , 2022 ) .

Ice-dammed Lake floods represent the dominant hazard in cryospheric regions, comprising 70% of GLOFs. In contrast, moraine-dammed lakes contribute only 9% (with the remaining 16%, 3%, and 2 % triggered by unknown dam types, volcanic activity, and bedrock, respectively) (Carrivick and Tweed, 2016). GLOFs have been recorded causing damage up to 120 km from moraine-dammed lakes (Richardson and Reynolds, 2000) and around 500 km from ice-dammed lakes (Hewitt and Liu, 2010). The resulting impacts include hundreds of human fatalities and the other impacts noted above (Carrivick and Tweed, 2016; Cui et al., 2014; Cui et al., 2015; Kreutzmann, 1994; Mason, 1929; Stuart-Smith et al., 2021; Zhang, 1990; Zheng et al., 2021). While attempts have been made to explore the breaching mechanisms of moraine lake outburst floods, triggered by ice or debris falls, strong earthquake shaking, internal piping, or overtopping waves that exceed the shear resistance of the dam (Emmer and Vilímek, 2013; Richardson and Reynolds, 2000), the understanding of the complex and unclear mechanisms of ice dam lake outburst floods remains a challenge (Werder et al., 2010), making a prediction using complex modelling currently impossible. Therefore, there is an urgent need for simplified approaches to GLOF prediction to mitigate downstream impacts.

Despite the uncertainty related to the detail of GLOF initiation, sudden glacier advances during surge cycles have a prominent role in the formation of ice-dammed lakes by creating an ice barrier in the valleys, particularly at narrow valley floor sections and at confluences (Bazai et al., 2021; Bhambri et al., 2019), damming minor and major rivers. Glacier surges are the main


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agents related to the formation of ice-dammed lakes in the Swiss Alps (Haeberli, 1983), Northern Norway (Xu et al., 2015), Argentinian Patagonia (Vandekerkhove, 2021), Alaska (Trabant et al., 2003), Karakorum, and in the Pamir (Bazai et al., 2021; Hewitt and Liu, 2010) and Tianshan regions (Ng, 2007; Shangguan et al., 2017). Recent studies reveal that the draining processes of ice-dammed lakes potentially involve subglacial breaching, overspill, rapid ice mass instability, and slow deformation of subglacial cavities (Björnsson, 2003; Haemmig et al., 2014; Round et al., 2017). Several attempts have been made to explore the drainage behaviour of ice-dammed lake outburst floods (Hewitt and Liu, 2010). However, due to the remoteness, danger, and inhospitable terrain where such lakes can be found, real-time data are few, and significant gaps remain in our knowledge of these processes.

In the Karakorum, ice-dammed lakes are found in five major valleys, three of which are densely populated and highly vulnerable to unexpected GLOF events. Recent advances in understanding have been made (Bazai et al., 2021) concerning the formation of episodic ice-dammed lakes, which, due to ice mass transfer variations, are linked to the changes in the glacier surface velocity and fluctuations in the crevasse density during the surge cycle (Rea and Evans, 2011; Sharp, 1985). Despite these advancements in knowledge, globally, the techniques for measuring and estimating lake volume (the volume of the lake before an outburst), the critical depth (for GLOF release), and timely prediction of ice-dammed lakes remain largely unexplored and unidentified (Round et al., 2017; Shangguan et al., 2016; Steiner et al., 2018). Very limited ice-dammed lake volume data are available. Still, these ice-dam lake volumes were measured either while the lake was empty (after the GLOF events) or partially filled and thus shallow (Round et al., 2017; Shangguan et al., 2016; Steiner et al., 2018). The downstream threat from those lakes is extremely high, while their full lake volumes are unknown. To measure the flood volume and flood magnitude for a deep and potentially full lake, the lake volume measurement is recognized as a critical variable that needs to be accurately calculated or at least well-estimated (Bazai et al., 2021; Bazai et al., 2022). An accurate estimate of lake volume will also help explore the timing, triggering depth of the lake, and frequency of ice-dammed lake outburst floods in relation to surge cycles. Timing information can be approximated by correlating glacier velocities and GLOF occurrences (Bazai et al., 2021; Bazai et al., 2022). The current research focuses of Bazai and colleagues aims to leverage historical records, regular field investigations, and remote sensing techniques to develop a comprehensive understanding, which should lead to better prediction of GLOFs through modelling dam failure mechanisms. Herein, the primary objective is to enhance predictive capabilities regarding GLOF event timing by refining empirical lake volume estimation and identifying critical depths for future risk reduction.


Document: 30 1. Introduction
Section: 2. Methodology: > 2.1. Data acquisition
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The identification and detection of the Shishper, Khurdopin, and Kyager ice-dammed lakes was accomplished using all available open and commercial satellite imagery sources from 1970 to 2022. The datasets include 590 images of Landsat 2-5, 7-9 and 45 images from Sentinel-2, downloaded from the United States Geological Survey (USGS) website


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(https://earthexplorer.usgs.gov/) (Table S1). The commercial high-resolution images consisted of 35 images from Gaofen-1 (GF-1) and Gaofen-2 (GF-2), 11 images from SPOT-6 and SPOT-7 and five images from Global Planet (https://data.cresda.cn/#/2dMap, https://earth.esa.int/eogateway and https://www.planet.com/products/planet-imagery, respectively). The following DEM datasets have been used for measuring lake volume, depth and dam height: the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) and the Phased Array type L-band Synthetic Aperture Radar (PALSAR)-DEM data scenes from the National Aeronautics and Space Administration (NASA) Earth Science Data Center website (https://search.earthdata.nasa.gov/). KH-9 and Shuttle Radar Topography Mission (SRTM) data were downloaded from http://earthexplorer.usgs.gov/ (Table S2). For more precise and high-resolution data, a field survey of the Shishper and Khurdopin glacier lakes was conducted in 2018, 2019, 2021, and 2022 and used Unmanned Aerial Vehicles (UAV) to determine annual lake extents, lake depths, glacier heights, and thickness, termini positions, and glacier surface displacements. The glacier outlines were obtained from the Randolph Glacier Inventory (RGI 6.0) (Consortium, 2017) and modified according to surge movements with time (https://www.planet.com/products/planet-imagery/).


Document: 30 1. Introduction
Section: 2. Methodology: > 2.2. Glacier Lake mapping and glacier surface velocity
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Satellite imagery had a spatial resolution of 0.8 to 30 m (Table S1). The images were selected based on the visibility of the glacier surface and lake areas, and overall, 23 ice-dammed lakes from eight surge events were identified through optical images related to the Khurdopin, Kyager, and Shishper glaciers (Table 1). The presence of lakes was determined based on the Normalized Difference Water Index (NDWI) (McFeeters, 1996), and the outlines of all 23 lakes were digitized manually using Landsat false-color composites (near-infrared, red, and green bands) to distinguish water bodies from other objects (Huggel et al., 2002). The extent of six lakes from Shishper and Khurdopin that occurred after 2017 were obtained in the field using GPS (G639; Accuracy: Single: 1 ~ 3m; SBAS: 0.6m) survey points along the lake shorelines (Fig.1a-d), as well as from Unmanned Aerial Vehicle (UAV) generated Digital Surface Models (DSMs). Field trips were conducted for Khurdopin in 2017 and 2018 and for Shishper in 2019, 2021 and 2022. Alternatively, high-resolution satellite imagery from Planet (3 m) and GF-1 and 2 (0.8 m to 4 m resolution, respectively) and SPOT-6 and SPOT-7 (1.5 m) were used to extract the lake boundaries. The use of high-resolution imagery aims to obtain accurate lake surface levels, and the latter is used for measuring volume and lake depth. The coupled lake extent and polygon help reduce the uncertainty of the lake extent obtained for Landsat 2-5 images. The above method was used to extract the extent of the previous lakes of Khurdopin and Kyager glacier, previously published (Bazai et al., 2021; Bazai et al., 2022), which data are incorporated into the current analysis, and the same method was used to extract the extent of Shishper lakes. These lake polygons and extents were further used to measure lake volume and depth mediated by field derived lake levels as appropriate (Bazai et al., 2022).


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Document: 30 1. Introduction
Section: 2. Methodology: > 2.2. Glacier Lake mapping and glacier surface velocity
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Panel (a) is titled "Shishper Lake March 2019" and shows an aerial view of a murky green glacial lake surrounded by rocky, snow-dusted slopes. A blue arrow points across the water, and a dotted rectangle labeled "Panel b" highlights a section of the shoreline.

Panel (b), titled "Shishper Lake Shoreline," shows a close-up of the rocky shoreline. Four colored dashed lines indicate the receding water levels from 2019 (blue, highest), 2020 (red), 2021 (green), to 2022 (light green, lowest).

Panel (c), titled "Khurdopin Lake February 2018," shows a river flowing through a valley filled with jagged glacial ice. A blue wavy arrow indicates the direction of water flow.

Panel (d), titled "Khurdopin Lake March 2018," shows the same area as panel (c) a month later, where the river has formed a lake with a surface of broken ice chunks.

Panel (e), titled "Khurdopin Lake Shoreline," shows the shoreline of the lake against the glacier. Two dashed lines indicate the water levels for 2017 (black, lower) and 2018 (red, higher), with a blue wavy arrow pointing towards the lake.

**Fig. 01** Shishper and Khurdopin glacial lake view in the field. a) Oblique view from a helicopter in 2019 (image captured in March 2019 during lake monitoring (Image by Gilgit-Baltistan Disaster Management Authority (GBDMA)); b) Shishper shoreline elevations of four lakes that outburst in the given years (image captured in June 2022); c and d are the regular monitoring views of the lake in the field: e) are the lake elevations in the given years. The Khurdopin Lake elevations were identified in the field in April 2018.

The surface velocities of the Khurdopin, Shishper, and Kyager glaciers from 1990 to 2022, highlighting the quiescent and surge phases, were obtained from published data (Bazai et al., 2021; Bazai et al., 2022) using image-to-image correlation open-source software COSI-Corr (Leprince et al., 2012; Leprince et al., 2007). The software effectively assesses the glacier surface velocity (Leprince et al., 2012; Steiner et al., 2018). Utilizing a displacement calculation, this technique was used to co-register and correlate surface features (Bazai et al., 2021; Steiner et al., 2018). The surface velocity and overall movement during the surge were monitored by observing changes in the GPS-registered glacier front positions every three months from March 2019 and measured for three years for the Shishper glacier in the field. When coupled with COSI-Corr measure velocities, these latter procedures gave precise results. The velocity estimation procedure generally yields an accuracy of ¼ of a pixel (Sattar et al., 2019). We estimated velocity root-mean-square errors (RMSE) to justify the image processing accuracy.


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The Shishper, Khurdopin and Kyager glaciers are surge-type glaciers (Copland et al., 2011; Hewitt, 1998). Since 1972, eight surge events have been occurred from Khurdopin (three surges), Kyager (three surges), and Shishper (two surges) (Table 1) at an interval of 17–20 years for three glaciers. The Landsat 2-4 images from 1970 to 1990 have errors in the selected glacier area. Therefore, the initial surges for Khurdopin and Kyager between 1970 and 1989 were not considered for estimating the annual velocity. Orthorectified Landsat scenes from TM to OLI–2 and sentinel 2 were used to estimate the yearly and event-based velocities of all three glaciers from 1989 to 2022 to obtain information about the surge events and glacier front changes. Within this period (1989 to 2022), some satellite images were absent, and for precise results, cloud-free images were chosen each year.


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Section: 2. Methodology: > 2.3. Field observation and lake volume measurement
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Field observations were performed in the Shimshal and Shishper Valley for the Khurdopin glacier in 2017, 2018, and for 155 Shishper in 2019, 2021, and 2022 to investigate glacier surges, glacier front dynamics, and ice-dammed lakes: lake level and lake depth. The latter value is from shoreline elevations and the elevation of the ice dam at its lowest point (Table 1 and Figure 1). Six lakes were regularly monitored: four from the Shishper Glacier and two from the Khurdopin Glacier. 23 GLOF events from eight surge cycles that occurred during the first year of the surge, or following, are presented in Table 1, with lakes resealing after GLOFs. The field data for six events from the Khurdopin and Shishper glaciers helped to reduce the uncertainty 160 and error for the data related to 17 lake extractions through remote sensing techniques noted above. All the previously recorded lakes from Khurdopin and Shishper were drained via single subglacial conduits with stable inlets and varying outlet positions and lengths. As closely as possible, we identified the inlet and outlet positions of the drainage conduits. The inlet position of the conduit in the ice-dammed lake basin is always in the deepest position, an important factor in determining the lake's depth. 165 The lowest ice dam height also tended to be in the vicinity of the conduit. The inlet positions were geolocated in empty lake basins using GPS, and the lake depth was calculated for these locations. From the field survey, we identified the approximate position of conduits from the presence of surface depressions in the glacier. We estimated the curvilinear conduit lengths between the inlet and outlet.


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180 **Table 1:** GLOF and Surge date and Lake volume measurement since 1970 using remote sensing technique. The average surge velocity of each of the 23 GLOFs from eight surge cycles is presented.


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Table

| No. s | Glacier Name | Date       | Sensor | Lake Area km2 | Aster/UAV Lake Volume Estimate (106 m3) | Lake Vol Uncertainty (+/-106 m3) | Vol. after [106 m3] | Average velocity (m/d) | Date of next clear image after GLOF | Type of drainage Complete (C) Partial (P) | Surge cycle and Resealed GLOF | Surge Duration in months            |
|----------|-----------------|------------|--------|---------------------|-----------------------------------------------------|----------------------------------------|------------------------|------------------------------|----------------------------------------------|-------------------------------------------------------|----------------------------------------|-------------------------------------------|
|          | Khurdopin       | 20/08/1977 | LM02   |                     |                                                     |                                        |                        |                              |                                              | P                                                     | 1977–1979                              | May 1977– Aug 1979; 27 Months       |
| 1        | Khurdopin       | 15/8/1999  |        |                     |                                                     |                                        |                        | 0.33                         |                                              | C                                                     | 1998-1999                              | Jan 1995 to Sep 2002; 92 Months     |
| 2        | Khurdopin       | 05/30/2000 | L5 TM  | 1.87                | 186                                                 | 2.1                                    | x                      | 0.33                         | 08/26/2000                                   | C                                                     | Resealed                               |                                           |
|          | Khurdopin       | 04/07/2001 | LE07   | 0.295               | 19.5                                                | 1.5                                    | x                      | 0.44                         | 06/26/2001                                   | C                                                     | Resealed                               |                                           |
| 4        | Khurdopin       | 07/15/2002 | LE07   | 0.60                | 52.1                                                | 1.6                                    | 2.2                    | 0.87                         | 08/16/2002                                   | P                                                     | Resealed                               |                                           |
| 5        | Khurdopin       | 07/28/2017 | LE07   | 0.180               | 16.2                                                | 1.4                                    | x                      | 1.41                         | LC 08 08/01/2017                          | C                                                     | 2016-2018                              | June 2006 to Aug 2009: 38 months |
| 6        | Khurdopin       | 03/18/2018 | LC08   | 0.402               | 19.8                                                | 0.9                                    | x                      | 0.53                         | 02/25/2018                                   | C                                                     | Resealed                               |                                           |
| 7        | Kyager          | 08/01/1977 | LM02   | 1.181               | 40.73                                               | 5.8                                    | x                      |                              | 10/14/1977                                   | C                                                     | 1976-1977                              | Jan 1975 to Aug 1978; 43 Months     |
| 8        | Kyager          | 07/18/1978 | LM02   | 2.17                | 82.12                                               | 15.6                                   | x                      |                              | 06/07/1979                                   | C                                                     | Resealed                               |                                           |
| 9        | Kyager          | 03/08/1997 | L5 TM  | 3.30                | 127.3                                               | 2.9                                    | x                      | 0.4                          | 04/09/1997                                   | C                                                     | 1994-1996                              | Jan 1995 to Sep 2002; 92 Months     |
| 10       | Kyager          | 09/10/1998 | L5 TM  | 3.32                | 133.5                                               | 3.5                                    | x                      | 0.3                          | 10/11/1998                                   | C                                                     | Resealed                               |                                           |
| 11       | Kyager          | 09/07/1999 | L7ETM+ | 2.19                | 86.12                                               | 1.23                                   | x                      | 0.46                         | 08/17/1999                                   | C                                                     | Resealed                               |                                           |
| 12       | Kyager          | 06/25/2000 | L7ETM+ | 0.91                | 23.48                                               | 1.12                                   | x                      | 0.49                         | 08/03/2000                                   | C                                                     | Resealed                               |                                           |
| 13       | Kyager          | 09/08/2002 | L7ETM+ | 2.93                | 115.19                                              | 1.09                                   | x                      | 1.29                         | 10/09/2002                                   | C                                                     | Resealed                               |                                           |
| 14       | Kyager          | 06/14/2008 | L5 TM  | 1.45                | 94.95                                               | 1.65                                   | x                      | 0.61                         | 23/06/2008                                   | C                                                     | Resealed                               | June 2006 to Aug 2009: 38 months |
| 15       | Kyager          | 07/28/2009 | L5 TM  | 1.39                | 91.35                                               | 1.56                                   | x                      | 0.56                         | 04/08/2009                                   | C                                                     | Resealed                               |                                           |
| 16       | Kyager          | 07/16/2015 | L8 OLI | 1.56                | 53.5                                                | 0.87                                   | x                      | 1.14                         | 05/08/2015                                   | C                                                     | Resealed                               | Jan 2013 to Aug 2018: 67 months     |
| 17       | Kyager          | 07/14/2016 | L7ETM+ | 1.63                | 45.89                                               | 1.49                                   | 2.9                    | 0.53                         | 30/07/2016                                   | P                                                     | 2014-2016                              |                                           |
| 18       | Kyager          | 07/31/2016 | L7ETM+ | 1.48                | 44.32                                               | 1.23                                   | x                      | 0.38                         | 08/09/2016                                   | C                                                     | Resealed                               |                                           |
| 19       | Kyager          | 08/10/2017 | L8 OLI | 2.91                | 113.99                                              | 0.73                                   | 11.9                   | 0.38                         | 26/08/2017                                   | P                                                     | Resealed                               |                                           |
| 20       | Kyager          | 08/06/2018 | L8 OLI | 2.38                | 87.98                                               | 0.53                                   | x                      | 0.29                         | 08/29/2018                                   | C                                                     | Resealed                               |                                           |
| 21       | Shishper        | 06/23/2019 | L8 OLI | 0.37                | 24.10                                               | 2.1                                    | x                      | 0.95                         | 07/13/2019                                   | C                                                     | 2017-2019                              | Dec 2018 to June 2022: 41 Months    |
| 22       | Shishper        | 05/29/2020 | L8 OLI | 0.50                | 24.90                                               | 1.5                                    | x                      | 0.46                         | 06/22/2020                                   | C                                                     | Resealed                               |                                           |
| 23       | Shishper        | 05/16/2021 | L8 OLI | 0.52                | 25.77                                               | 1.4                                    | x                      | 0.29                         | 07/15/2021                                   | C                                                     | Resealed                               |                                           |
|          | Shishper        | 05/07/2022 | L8 OLI | 0.41                | 27.66                                               | 1.1                                    | x                      | 0.24                         | 05/10/2022                                   | C                                                     | Resealed                               |                                           |


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In addition, we used a UAV (DJI Mavic 2 Pro) equipped with a high-resolution camera (4000 pixels × 2250 pixels) to obtain multiple aerial photographs with a minimum of 85% image overlap (Entwistle and Heritage, 2017; Entwistle and Heritage, 2019; Tonkin and Midgley, 2016). The UAV flew at a low uniform height (500 m - to reduce the image distortion) to generate high-resolution orthomosaics and DSMs of the glacier lake surfaces, empty lake basins, and glacier termini. The integral of the difference between the elevation of the lake surface and the elevation of the bottom in the extent of the lake obtains the volume. The lake volume data for the glacial lakes of Khurdopin and Kyager were presented previously (Bazai et al., 2021; Bazai et al., 2022), and the same approach was applied to obtain the Shishper glacier lake volume and depth data (Table 1). In addition to UAV data, we utilized data from KH-9 (1974), ASTER (2000-2019), PALSAR-DEM (June 2008), and SRTM (February 2000) for the computation of lake volumes (Table S2). The SRTM DEM without voids serves as the reference dataset, and the vertical uncertainties of the SRTM DEM are reported to be ±10 m (Rodriguez et al., 2006). The corrected DEMs from Karakorum regions were used by Bazai et al. (2021) and Gardelle et al. (2013).


Document: 30 1. Introduction
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Considering that the lake area in satellite images often exhibits a triangular planform (e.g., Fig 1a), we explored the possibility of using a geometric shape to approximate the volume of the lake basin. It is imperative to accurately extract boundary parameters, including lake elevation, length, width, and depth, and this information was manually acquired. Employing NDWI, we identify lake outliers through Landsat false-color composites, which use near-infrared, red, and green bands to distinguish water bodies from other features. We employ standard connected component analysis to (Dillencourt et al., 1992) to manually calculate the area and the perimeter and determine other dimensions of each lake. Initial calculations are pixel-based and later converted to metric units by multiplying pixel counts with their respective pixel sizes. The pixel size for high-resolution images varied from 0.8 to 3m and was cross-validated with Khurdopin and Shishper glacier lakes UAV data having a pixel size of 0.063m as well as with field survey evidence. Trials demonstrated that the known volume of the lakes determined using DEMs of the lake basins once drained could be approximated if the length of the lake from the upstream inlet to the ice-dam face (Z) and the breadth of the lake at the ice dam (C) are known. Improved estimates are obtained if the lake's depth (h) is known at the deepest point close to the dam face, which value can be obtained from a DEM of the drained basin. Alternatively, where a lake is present, this latter parameter can be obtained by plumbing the depth from a boat.

The first consideration was whether the valley sides might be considered to provide a V-shaped lake cross-section. Each lake volume (V) was approximated by an irregular tetrahedron (Fig. 2a left-hand panel) where the depth (h) is unknown, but the distance from A to B (X in Fig. 2a) and the length C are known values. Assuming the lake surface is an isosceles triangle, and the vertical face at the dam wall is an equilateral triangle, the volume can be obtained from:

$$V = \sqrt{V^2}$$
 (1)

$$V^{2} = \frac{1}{144} \left[ Y_{1}^{2} D^{2} (Z_{2}^{2} + X^{2} + C^{2} + E^{2} - Y_{1}^{2} - D^{2}) + Y_{2}^{2} E^{2} (Y_{1}^{2} + X^{2} + C^{2} + D^{2} - Y - E^{2}) + Z^{2} C^{2} (Y_{1}^{2} + Y + D^{2} + E^{2} - Z^{2} - C^{2}) - Y_{1}^{2} Y_{2}^{2} C^{2} - Y_{2}^{2} Z^{2} D^{2} - Y_{1}^{2} Z^{2} E^{2} - C^{2} D^{2} E^{2} \right]$$

2. Methodology:
2.4. Geometry of lake basin


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Where the values for lakeside lengths  $Y_1$  and  $Y_2$ , the main length Z, lakeside length D, and lakeside length E are defined in Fig. 2a and obtained from geometry.


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Panel (a) displays two diagrams of a three-dimensional shape, likely representing a lake basin formed by an ice dam. The diagrams show an irregular tetrahedron with vertices labeled A, B, C, D, and E. The shape is divided horizontally by a dashed line, separating the 'OPEN VALLEY' from the 'ICE DAM'. Various dimensions are labeled, including Y1, Z, X, and h. An arrow indicates 'Inflow' at the top vertex A.

Panel (b) is a scatter plot comparing two methods of volume calculation. The y-axis is labeled 'Lake Volume from DEM, V\_DEM (M m^3)' and ranges from 0 to 200. The x-axis is labeled 'Volume of Irregular Tetrahedron/10, V\_Tet (M m^3)' and ranges from 0 to 100. The plot contains data points for three locations: Shishper (black circles), Khurdopin (blue circles), and Kyager (red circles). A light blue dotted line represents a 1:1 ratio. A red dotted trend line is fitted to the data with the equation V\_DEM = 1.3525V\_Tet and an R-squared value of R^2 = 0.88.

**Fig. 02** (a) Definition diagram for calculating the volume of the lakes assuming (left) an irregular tetrahedral shape and (right) an irregular pentahedral shape. The blue shading represents the horizontal surface of the lake, and the white area represents the vertical ice wall. Panel (b) Relationship between the volumes of irregular tetrahedrons/10, derived from Eq. 1, and the volumes of the lakes determined using DEMs.

In passing, it can be noted that the volumes of the irregular tetrahedrons in most cases were not dissimilar to the volumes of regular tetrahedrons (*i.e.*, triangular-based pyramids), the equation for which is simple, in contrast to Equation 1. Nevertheless, using equation 1, the volume of the 'tetrahedron' lakes was around 10 times greater than the volume of the lakes determined using the DEMs (Fig. 2b). This result indicates that the actual depth of the lake (*h*) must be much less than that value associated with an equilateral triangle of side length C (Fig. 2a left-hand side).


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The relationship between the glacier surge velocity of (Khurdopin, Kyager, and Shishper) and 23 GLOFs is presented in Figure 3a-d and its triggering time or month in the year. In panels a to c, the GLOF occurred after the peak of the glacier surge, and the resealed lake formed while the surge velocity declined. These responses to slowing of the glacier velocity lasted 2-4 years after the surge peak. The relationship between the timing of glacier surges and the timing of GLOFs is shown in Fig. 3d. The three Karakorum glaciers can be used as regional exemplars of surge behavior controlling GLOF occurrence as there is a temporal relationship between the occurrence of periods of glacier surging and the occurrence of GLOFs (Fig. 3a-d). GLOFs occur towards the end of a surge period or immediately afterward; the detail is presented in Table 1. This pattern of behaviour prompted the hypothesis that glacier thickening and thinning during surging might control the development of ice-dammed


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