Document: 30 1. Introduction
Section: 3. Result:
Type: figure
Figure

Image /page/9/Picture/2 description: The logo for EGUsphere, a preprint repository. The logo features the text "EGUsphere" in blue. The letters "EGU" are bold and enclosed in a blue circular gear-like shape. The word "sphere" follows, with a blue arch and a gray arch curving over it. Below the main text, the words "Preprint repository" are written in a smaller, gray font. The background is white.


Document: 30 1. Introduction
Section: 3. Result:
Type: text

lakes (Bazai et al., 2022). Lake volumes would increase when the speed of the ice was low such that ice mass would be conserved or increased, and fracturing of the ice would reduce. The corollary pertains to when the ice speed increases, the glacier thins, and the fracturing of the ice mass increases, providing hydraulic drainage conduits.

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


Document: 30 1. Introduction
Section: 3. Result:
Type: figure
Figure

Image /page/9/Figure/4 description: The image contains four charts, labeled (a), (b), (c), and (d), which analyze glacier velocity and related events over time.


Document: 30 1. Introduction
Section: 3. Result:
Type: text

Charts (a), (b), and (c) are line graphs plotting 'Average Velocity m y⁻¹' against 'Years'. Each chart has a secondary y-axis on the right labeled 'GLOF Triggered' with months from March to November. These charts show periods of increased velocity called 'Surge periods' highlighted with a grey background.

- Chart (a) displays data from 1986 to 2020. The average velocity is shown by a red line, with a dashed blue line at an average of 79 m y⁻¹. There are two surge periods: 1998-2002, with an average peak velocity of 343 m y⁻¹, and 2016-2020. GLOF events are marked with blue circles.

- Chart (b) covers the years 1989 to 2020. The average velocity is 29.9 m/y. It shows two main surge periods: 1994-1998 (average peak velocity 289 m/y) and 2013-2016 (average peak velocity 423 m/y). A smaller 'Mini Surge' is noted around 2008. GLOF events are marked with orange circles.

- Chart (c) spans from 1989 to 2022. The average velocity is 87 m/y. It highlights two surge periods: 1997-2002 (average peak velocity 310 m/y) and 2017-2020. GLOF events are marked with grey circles.

- Chart (d) is a timeline starting from 01/01/1990, with a numerical x-axis from 2000 to 12000. It plots events for different locations: Khurdopin (blue dots), Kayager (orange dots), and Shishper (grey dots). Horizontal lines indicate the season: blue for Winter and orange for Summer.

Fig. 03 Relationship between glacier surge and GLOF, with annual glacier velocity analysis during the surge and quiescent phases for three glaciers: (a) Khurdopin, (b) Kyager, and (c) Shishper glacier. GLOFs for these glaciers occurred between the months of March to November. The combined analysis is presented in (d), illustrating the occurrences of GLOFs (dots) in relation to periods of glacier surging (bars). Some points are plotted below the timeline to avoid coincident positions. The blue and red lines show the winter (from October to April) and summer (May to September) seasons in which the GLOF occurred dominantly in the summer months.

As a first attempt to relate glacier behaviour in a predictive sense to lake formation, we sought to determine the resultant lake volume from the prior surge speed. In Fig. 03, the relationship between surge and GLOF was developed using annual velocity data for ease of trend comprehension. However, daily measurements of glacier velocity were conducted to assess its impact on lake volume, given the velocity sensitivity to the triggering time of GLOFs. Consequently, the glacier's daily velocity was specifically recorded on the day when the GLOF was initiated, as detailed in Table 01. Despite a broad data spread, a least-squares regression analysis, with four outliers excluded from the analysis, defines a statistically significant negative power (-1) relationship between surge speed and lake volume (Fig. 4). Raising the glacier surge speed to the power of -2.0 and multiplying by 10 reproduced well the data trend for low glacier surge speeds. Similarly, -0.8 and a -3.0 power functions define the lower and upper limits of the data spreads. These results, although clearly not definitive, were a spur to investigate if there


Document: 30 1. Introduction
Section: 3. Result:
Type: figure
Figure

Image /page/10/Picture/1 description: The image shows the Creative Commons Attribution (CC BY) license icon. It is a rectangular icon with a grey upper section and a black lower section. On the grey section, there are two white circles. The left circle contains the letters "CC" in black, and the right circle contains a black icon of a person. The black section at the bottom has the letters "BY" in white.


Document: 30 1. Introduction
Section: 3. Result:
Type: figure
Figure

Image /page/10/Picture/2 description: The image shows the logo for EGUsphere, a preprint repository. The logo consists of the text "EGUsphere" in blue. The letters "EGU" are enclosed within a blue, gear-like circle. Above the word "sphere," there are two swooshes, one blue and one gray. Below the main text, the words "Preprint repository" are written in a smaller, gray font. The background is white.


Document: 30 1. Introduction
Section: 3. Result:
Type: text

might be a theoretical geometric relationship between the volume of the lake and the control on lake water level exerted by the surge speed. The physical basis for such a relationship is that an increase in surge speed should cause the glacier to thin and fracture after a period of ice thickening and lake volume increase. During surging, the height of the ice barrier impounding the lake would reduce, and fracturing in the ice would increase, both lowering the lake level and reducing the lake surface area. Therefore, surge speed should control lake depth, volume, and potential GLOF volumes.


Document: 30 1. Introduction
Section: 3. Result:
Type: figure
Figure

Image /page/10/Figure/4 description: A scatter plot showing the relationship between Glacier surge speed (U\_s) on the x-axis and Lake Volume (V\_DEM) on the y-axis. The x-axis, labeled "Glacier surge speed, U\_s (m d⁻¹)", ranges from 0 to 1.6. The y-axis, labeled "Lake Volume, V\_DEM (M m³)", ranges from 0.0 to 200.0.


Document: 30 1. Introduction
Section: 3. Result:
Type: text

The plot displays data points for different glaciers, indicated by a legend:
- Shishper: black circles
- Khurdopin: blue circles
- Kyager: red circles
- Khurdopin drained: blue triangles
- Kyager drained: red triangles

Most of the circular data points fall within a light blue shaded area, suggesting an inverse relationship where lake volume decreases as glacier surge speed increases. Several dotted curves representing different power-law models are overlaid on the data:
- V\_DEM = 30U\_s⁻³ (brown dotted line)
- V\_DEM = 25U\_s⁻¹ R² = 0.33 (black dotted line)
- V\_DEM = 10U\_s⁻²·⁰ (green dotted line)
- V\_DEM = 10U\_s⁻⁰·⁸ (light blue dotted line)

The text above the plot reads, "therefore, surge speed should control lake depth, volume, and potential GLOF volumes."

**Fig. 04** Variation in glacial lake volume as a function of the glacier surge speed. Data from three glaciers. Most lakes drained completely, but three had residual volumes (triangles). Outliers are shown as black-ringed symbols. A -0.8-power function defines the lower limit to the data spread, whilst a -2.0-power function defines the central tendency of the data trend, and a -3-power function defines the upper limit to the data spread (see text for explanation).

Most of the lakes investigated occur in steep-walled side valleys, the ice dam forming one side of a roughly triangular water surface (Fig. 5a-b). Projecting the valley walls downwards, the geometry of the lake basin can be considered to be either: 1) an irregular tetrahedron, with the lake surface defined as an isosceles triangle (Fig. 5a-b); and the vertical cross-section at the ice dam defined by an equilateral three-sided triangle; or, 2) an irregular pentahedron whereby the vertical cross-section at the ice dam is defined by a quadrilateral (Fig. 2a). In the former case, only the length of the lake (X) and the breadth of the lake


Document: 30 1. Introduction
Section: 3. Result:
Type: figure
Figure

Image /page/11/Picture/1 description: A Creative Commons Attribution (CC BY) license icon. The icon is a rectangle with a grey top section and a black bottom section. The grey section contains two white circles. The left circle has the letters 'CC' in black, and the right circle has a black stick figure icon, representing attribution. The black bottom section has the letters 'BY' in white.


Document: 30 1. Introduction
Section: 3. Result:
Type: figure
Figure

Image /page/11/Picture/2 description: The logo for EGUsphere, a preprint repository. The logo features the text "EGUsphere" in blue. The letters "EGU" are inside a blue circular gear-like symbol. Above the word "sphere", there are two swooshes, one blue and one gray. Below the main text, the words "Preprint repository" are written in a smaller, gray font. The background is white.


Document: 30 1. Introduction
Section: 3. Result:
Type: text

270 (C) at the ice dam are needed to estimate the lake volume, whereas for the second case, the depth (h) of the lake at the ice dam is required as well. The values for X and C are obtained from remote sensing imagery of the lake surface. Before a GLOF, the depth h can be obtained by deploying a plumb-line or echo-sounder in the lake or estimated through a topographic survey of the bounding slopes. Subsequent to GLOF drainage, h can be measured from a DEM or field survey. Assuming an irregular tetrahedron (Equation 1) implies the valley walls form a V-shaped cross-section to the lake at the ice dam face. In contrast, 275 assuming an irregular pentahedron implies the valley walls form a square-shaped section, which is more akin to typical Ushaped glacial valleys.

Given the idealized geometric properties of the water mass, and assuming C and X vary little in contrast to h, the lake's volume increases as a function of  $h^3$  (tetrahedron) or  $h^2$  (pentahedron). Given the assumption that depth reduces as surge speed increases provides an explanation for the potential -2 to -3 power function relationships between surge speeds and lake volumes. For example, concerning a tetrahedron, assuming the equilateral geometry is maintained as water depth (h) in the lake increases, then, considering Pythagoras' theorem, the volume of the lake increases as the cube of the depth and by corollary as the -3 power of the surge speed. This later function is shown in Fig. 4, and the trend closely defines the upper limit of the empirical data, whilst the -2 relationship, which should pertain to pentahedral volumes, follows the approximate trend of the central tendency of the data spread. Thus, the geometrical properties assumed in the analysis delimit both an upper limit to the relationship between surge velocity and lake volume as well as the main trend.

The appropriateness of assuming geometric shapes for the lake volume was checked by comparing the calculated geometric volumes with the measured DEM lake volumes. Utilizing Eq. 1 and only the values X and C, the volume of the 'tetrahedron' lakes was around 10 times greater than the volume of the lakes determined using the DEMs (Fig. 2a). 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.

290 Nevertheless, this procedure provides a means to estimate lake volume from plan-view data alone.


Document: 30 1. Introduction
Section: 3. Result:
Type: figure
Figure

Image /page/12/Picture/1 description: A rectangular Creative Commons license icon, divided horizontally. The top section is gray and contains two white circles. The left circle has the letters 'CC' in black, and the right circle has a black icon of a person. The bottom section is black and has the letters 'BY' in white.


Document: 30 1. Introduction
Section: 3. Result:
Type: figure
Figure

Image /page/12/Figure/3 description: The image contains three panels labeled (a), (b), and (c). Panels (a) and (b) are photographs of glacial dammed lakes. Panel (a) is an aerial view of a large, light-blue glacial lake surrounded by dark, rocky terrain. Panel (b) is a closer view of a similar lake, showing chunks of ice or rock floating in the water within a steep valley. Panel (c) is a scatter plot comparing two volume calculation methods. The y-axis is labeled 'Lake Volume from DEM, V\_DEM (M m³)' and the x-axis is labeled 'Volume of Pentrahedron, V\_Pen (M m³)'. Both axes range from 0.0 to 250.0. The plot shows about 20 grey circular data points that form a strong positive linear trend. A grey dotted line represents the linear regression, with the equation 'V\_DEM = 0.8828 V\_Pen' and 'R² = 0.93' written next to it. A blue dotted line labeled '1:1' is also shown for reference. The caption below the figure reads: 'Figure 5: Examples of Shishper glacial dammed lakes exhibiting roughly triangular surface 2D shapes and overall pyra...'


Document: 30 1. Introduction
Section: 3. Result:
Type: text

**Fig. 05:** Examples of Shishper glacial-dammed lakes exhibiting roughly triangular surface 2D shapes and overall pyramidal-shaped volumes (see Fig. 2a); (a) oblique aerial view towards the ice dam; (b) oblique aerial view from the ice dam axially up the impounded valley (image captured in March 2019 during lake monitoring (Image by (Image by Gilgit-Baltistan Disaster Management Authority (GBDMA)). Panel (c) Relationship between the volumes of irregular tetrahedrons/10, derived from Eq. 1, and the volumes of the lakes determined using DEMs.

In contrast to the assumption of a tetrahedron, improving lake volume estimates were obtained considering the measured DEM-derived values of *h* along with the values of *X* and *C*. Once again, assuming an irregular tetrahedron as in Fig. 2a, the analysis demonstrated that the tetrahedral lake volume was roughly half that of the DEM volume (not illustrated). Rather, considering


Document: 30 1. Introduction
Section: 3. Result:
Type: figure
Figure

Image /page/13/Picture/1 description: A Creative Commons Attribution (CC BY) license icon. The icon is a rectangle with a light gray top half and a black bottom half. On the gray half, there are two white circles with black symbols inside. The left circle contains the letters 'CC', and the right circle contains a stick figure person icon. On the black half, below the person icon, the letters 'BY' are written in white.


Document: 30 1. Introduction
Section: 3. Result:
Type: figure
Figure

Image /page/13/Picture/2 description: The logo for EGUsphere, a preprint repository. The logo features the text "EGUsphere" in a blue sans-serif font. The letters "EG" are inside a blue circular gear-like shape. Above the "sphere" part of the text, there are two swooshes, one blue and one gray. Below the main text, the words "Preprint repository" are written in a smaller, gray font.


Document: 30 1. Introduction
Section: 3. Result:
Type: text

the valley-cross section to be U-shaped (roughly quadrilateral) rather than V-shaped means that doubling the area of the triangular dam face section to form a quadrilateral gives a lake volume defined as an irregular pentahedron (square-based pyramid) (Fig. 2a right-hand side) in contrast to an irregular tetrahedron (Fig. 2a left-hand side). The volume of an irregular pentahedron is:

$$V = \frac{1}{3} (C h) X \tag{2}$$

which is more amenable to solving than Equation 1.

The relationship shown in Fig. 5c is preferable to that shown in Fig. 2a as it lies close to the 1:1 relationship between  $V_{Pen}$  and  $V_{DEM}$  but requires knowledge of the parameters as height or depth: h, length; X, and width; C. In contrast, the less exact relationship in Fig. 2a requires only X and C. If assuming a rectangular base to the pentahedron exactly matched the DEM volume, then the coefficient value would be unity. Thus, the coefficient of 0.8986 reflects the deviation of the cross-sectional shape of the lake at the dam face from a rectangle. Note that the relationships between both determinations of lake volume progressively deviate from a 1:1 relationship as lake volume increases. This trend might indicate that larger lakes are less well-defined as tetrahedrons or pentahedrons as the volumes increase.


Document: 30 1. Introduction
Section: 3. Result: > 3.1. Predicting the Timing of GLOF Events
Type: text

The timing of a GLOF remains difficult to determine, but the main driver is the critical depth. The critical depth is that depth that exerts sufficient pressure at the ice dam wall to induce completed connectivity within the sub-glacial GLOF drainage conduit. For the cases of the glacial lakes (Shishper, Khurdopin, and Kyager), the glacial lake depths (h) have been normalized by dividing by the minimum value of the ice dam height to give values (n') that range between 0 for a fully-drained lake to a hypothetic value of 1 if the lake level reached the height of the ice barrier. At the approximate time of GLOF occurrence, the resultant values of n' range between 0.32 and 0.95 (Fig. 6a-c). Most GLOFs occur for a range of n' values between 0.61 and 0.95 (Fig. 6d). Thus, n' = 0.60 can be regarded as a warning level value with the risk of a GLOF occurring imminently increasing as n' approaches unity.

As the water pressure (P) at the dam face increases linearly with water depth in each lake, any variation in the pressure with n' that deviates from the linear trend reflects changes in the height of the ice dam (Fig. 6d). Thus, for example, the values of pressure for the Shishper lakes around an n' value of 0.8 reflect greater overall ice dam heights in contrast to the Kyager lakes for similar values of n'. The two values of low pressure for n' < 0.6 reflect low ice dam heights and presumably low structural integrity within the ice mass, allowing ready conduit development. Low values of n' (< 0.6) likely are associated with shallow lakes of low hazard potential. Overall, the Kyager data (Fig. 6d) indicate that a minimum water pressure of around 500 kPa should be regarded as a threshold for general concern for GLOF occurrence in the region.


Document: 30 1. Introduction
Section: 3. Result: > 3.1. Predicting the Timing of GLOF Events
Type: figure
Figure

Image /page/14/Picture/1 description: A Creative Commons Attribution (CC BY) license icon. The icon is a rectangle with a grey top section and a black bottom section. On the left side of the grey section is the Creative Commons logo, which consists of the letters 'CC' inside a white circle. To the right of that is the attribution symbol, a stick figure inside a white circle. In the black section at the bottom, the letters 'BY' are written in white.


Document: 30 1. Introduction
Section: 3. Result: > 3.1. Predicting the Timing of GLOF Events
Type: figure
Figure

Image /page/14/Figure/3 description: A four-panel figure, labeled (a) through (d), analyzing glacier lake characteristics. Panels (a), (b), and (c) show cross-sectional profiles of lakebeds, while panel (d) shows a scatter plot of water pressure versus lake depth.


Document: 30 1. Introduction
Section: 3. Result: > 3.1. Predicting the Timing of GLOF Events
Type: text

Panel (a) is a cross-section of the Shishper Glacier lakebed. The x-axis represents the cross-section in meters (0-2100), and the y-axis shows elevation in meters (2520-2660). A secondary top x-axis shows volume in 10^6 m^3 (0-32). The plot displays the lakebed profile, the glacier, and lake levels for years 2019 (E=2650, V=24.10), 2022 (E=2641, V=27.66), 2021 (E=2638, V=25.77), and 2020 (E=2636, V=24.90). An inset map shows the glacier and lake outlines.

Panel (b) is a cross-section of the Khurdopin Glacier lakebed. The x-axis is cross-section in meters (0-3400), and the y-axis is elevation in meters (3360-3440). The top x-axis shows volume in 10^6 m^3 (0-180). It shows lake levels for years 2000 (E=3440, V=186), 2002 (E=3420, V=52.1), 2018 (E=3418, V=19.80), 2001 (E=3416, V=19.5), and 2017 (E=3415, V=16.2). An inset map is included.

Panel (c) is a cross-section of the Kyager Glacier lakebed. The x-axis is cross-section in meters (0-6500), and the y-axis is elevation in meters (4750-4830). The top x-axis shows volume in 10^6 m^3 (0-130). It displays numerous lake levels from 1977 to 2018, with a detailed legend providing the year, elevation (E), and volume (V) for each.

Panel (d) is a scatter plot of Water Pressure (P) in kPa versus Normalized glacier lake depth (n'). The x-axis ranges from 0.0 to 1.0, and the y-axis from 0 to 1600. Data points are shown for Shishper (black circles), Khurdopin (blue circles), and Kyager (red circles). Linear trendlines are fitted to each dataset with the equations: P = 1514.9 n' for Shishper, P = 977.1 n' for Khurdopin, and P = 835.5 n' for Kyager. A light blue shaded area from n' ≈ 0.6 to 1.0 is labeled 'Critical range'.

**Fig. 06:** The relationship between lake volume and elevation and the critical depth for GLOFs. a) Shishper; b) Khurdopin; c) Kyager; d) Water pressure at dam face as a function of n'. The cross sections are denoted by (A' and A). The date of each lake flood event is shown as L, E is the lake's elevation, and V is the lake volume. The straight, solid red lines relate specific lake elevations to volumes. The UAV photographs captured in the field were used for panel a, and the images captured by the GF-2 were used for panel b.


Document: 30 1. Introduction
Section: 4. Discussion:
Type: text

Although predictive models related to ice-dam lake development and subsequent GLOF risk would best be based on modelling the physics of the systems, the controlling parameters are numerous and complex. For example, the mechanisms of glacial sliding, over-burden pressure, tensile and driving stresses require consideration, as do flexure and ice fracture mechanics, thermal erosion, and water pressure, amongst other controls (Carrivick et al., 2020). Few of these controls are well-understood, and, importantly, even where there is an adequate theory, the field data required to inform modelling are absent for specific potential GLOF locations. Consequently, there is an urgent need for simpler methods to predict the likely volume of ice-dammed lakes and the probable triggering water levels that lead to GLOFs. Given that requirement, it is acknowledged that


Document: 30 1. Introduction
Section: 4. Discussion:
Type: figure
Figure

Image /page/15/Picture/1 description: A Creative Commons Attribution (CC BY) license icon. The icon is a rectangle with a grey top half and a black bottom half. The grey section contains two white circles with black outlines. The left circle has the letters 'CC' in black, and the right circle has a black icon of a person. The black section has the letters 'BY' in white.


Document: 30 1. Introduction
Section: 4. Discussion:
Type: figure
Figure

Image /page/15/Picture/2 description: The logo for EGUsphere, a preprint repository. The logo features the text "EGUsphere" in blue. The letters "EGU" are bold and enclosed in a blue circular gear-like shape. The word "sphere" follows, with a blue arch and a gray arch curving over it. Below the main text, the words "Preprint repository" are written in a smaller, gray font. The background is white.


Document: 30 1. Introduction
Section: 4. Discussion:
Type: text

the relationships proposed herein are empirical and apply specifically to glaciers within the Karakorum region. However, there is no reason to suppose that similar functions based on geometric considerations and critical depth (Zhao et al., 2017) might not be developed elsewhere, including for moraine-dammed lakes (Yao et al., 2010). Below, the approach is explored for glacially dammed lakes worldwide.


Document: 30 1. Introduction
Section: 4. Discussion:
Type: figure
Figure

Image /page/15/Figure/4 description: The image contains three plots, labeled (a), (b), and (c), which analyze data related to ice-dammed glacier lakes and Glacial Lake Outburst Flood (GLOF) events.


Document: 30 1. Introduction
Section: 4. Discussion:
Type: text

Plot (a) displays the maximum volume level of several glacier lakes against their elevation. The y-axis represents 'Elevation (m.a.s.l)' and the x-axis represents 'Volume M m³'. Each lake (Kyager, Khurdopin, Merzbacher, Chilinji, Medvezhiy, Shishper) is shown as a horizontal bar divided into a 'Safe lake level' (light blue) and a 'Triggering lake level' (red). Black dots indicate the volume and elevation of past 'GLOF Event's. An inset shows similar data for the Russel and Rio Colonia lakes. Each lake has an associated n' value: Kyager n'=0.67, Khurdopin n'=0.76, Merzbacher n'=0.83, Chilinji n'=0.60, Medvezhiy n'=0.71, Shishper n'=0.67, Russel n'=0.80, and Rio Colonia n'=0.79.

Plot (b) is a vertical bar representing the 'Normalized Glacier Lake depth (n')'. The bar is divided into a 'Safe Zone' (light blue, for n' values below 0.6) and a 'High Risk and Critical Zone' (red, for n' values above 0.6). Dotted lines connect the n' values of various lakes to their corresponding position on this risk scale. Merzbacher, Russell, Rio Colonia, Khurdopin, and Medvezhiy fall into the high-risk zone, while Kyager, Shishper, and Chilinji are in the safe zone.

Plot (c) is a scatter plot comparing 'Reference Volume (M m³)' on the y-axis to the 'Volume of Irregular Tetrahedron (M m³)' on the x-axis for various glaciers around the world. The data points, color-coded by location (e.g., Medvezhiy-Pamir, Grænalón-Iceland, Merzbacher-TianShan), show a strong positive linear correlation. A dashed line of best fit is shown with the equation y = 1.0689x and an R² value of 0.9865.

**Fig. 07:** (a) Represents the maximum volume level of ice-dammed glacier lakes that experience outbursts based on specific volume and elevation criteria. In this representation, the red signifies each lake's triggering level, depth, or zone, where all GLOF events were initiated. Among these lakes, n' values represent the non-dimensional relationship between lake depth and glacier height; panels (b) illustrate each lake's normalized critical lake depth and the high-risk and critical zones for Glacial Lake Outburst Floods (GLOFs). It also highlights the high-risk and critical zones for each lake, where values exceeding n' 0.6


Document: 30 1. Introduction
Section: 4. Discussion:
Type: figure
Figure

Image /page/16/Picture/1 description: A rectangular icon representing the Creative Commons Attribution license, also known as CC BY. The icon is divided horizontally into two sections. The top, larger section is grey and contains two white circles with black outlines. The circle on the left has the letters 'CC' in black, and the circle on the right has a black pictogram of a person. The bottom, smaller section is black and has the letters 'BY' in white.


Document: 30 1. Introduction
Section: 4. Discussion:
Type: figure
Figure

Image /page/16/Picture/2 description: The image shows the logo for EGUsphere, a preprint repository. The logo consists of the text "EGUsphere" in blue. The letters "EGU" are inside a blue, gear-like circle. Above the word "sphere," there are two swooshes, one blue and one gray. Below the main text, the words "Preprint repository" are written in a smaller, gray font. The background is white.


Document: 30 1. Introduction
Section: 4. Discussion:
Type: text

indicate a critical threshold for the potential occurrence of an ice-dammed lake outburst flood. Panel (c) shows the relationship between the referenced volume and measured volume through a geometric approach to the location of glaciers presented in Fig. S1.

Glacially dammed lakes worldwide exhibit consistent behavior in terms of lake formation, filling, and volume gain in response to low glacier velocity (Bazai et al., 2021). Additionally, specific pressure, volume, and critical lake depth values for initiating outburst floods are evident (see Figure 6). Building upon the information presented in Figure 6 for the Karakorum, Figure 7, based on 50 GLOF events from glacial dammed lakes, offers a depiction of the conditions under which glacier lake volume measurements are successfully estimated with high accuracy. Among the 50 GLOF events, 27 examples are given from Pamir, Tianshan, Greenland, and northern Patagonia (see Figure 7a-c). These relevant data are limited, often with only estimates or measurements of lake volume available. Figures 7a and b serve as key components and summaries for this discussion. identifying the lake volumes, elevations, and the critical depth values for GLOF outbursts. The measured lake volumes and the related water surface elevations are shown in Fig. 7a, together with critical depth values (n'). Critical depth values (n')exceed 0.60 in all cases of GLOFs (Fig. 7b), from which we infer that a safe lake level can be defined as  $\leq$  0.60, and the trigger level is  $\geq 0.60$ . Values of values n' < were associated only with slow, non-catastrophic, lake drainage. Therefore, in the case of future ice-dammed lakes, values of critical depth (n') exceeding 0.60 should be a cause for concern and would serve as a warning level. The geometric procedure outlined herein to estimate lake volume produced an excellent correlation with measured lake volumes (R2 value of 0.986; Fig. 7c). These findings suggest that future exploration should concentrate on specific volume and depth parameters to determine critical thresholds associated with depth, elevation, or volume for future predictive purposes.

Estimating the volume of an undrained ice-dammed lake from a field survey is dangerous due to floating ice (Fig. 05b), rugged terrain, and sudden drawdowns. The utilization of DEM measurements for lake volume estimation may also introduce high uncertainties or errors due to the difficulty in defining the lake depths (Carrivick et al., 2020; Emmer, 2018). However, for rapid response or mitigation policy purposes, the empirical model (Eq. 1) used in the current study proves to be quite efficient when applied to measure the lake volume before a GLOF.


Document: 30 1. Introduction
Section: 4. Discussion:
Type: text

, elevation , or volume for future predictive purposes . Estimating the volume of an undrained ice - dammed lake from a field survey is dangerous due to floating ice ( Fig . 05b ) , rugged terrain , and sudden drawdowns . The utilization of DEM measurements for lake volume estimation may also introduce high uncertainties or errors due to the difficulty in defining the lake depths ( Carrivick et al . , 2020 ; Emmer , 2018 ) . However , for rapid response or mitigation policy purposes , the empirical model ( Eq . 1 ) used in the current study proves to be quite efficient when applied to measure the lake volume before a GLOF .

Understanding glacier surges, lake formation, and the interactions between lakes and glaciers is crucial for advancing knowledge and developing empirical or numerical GLOF models in mountainous regions (Carrivick et al., 2020; Quincey and Luckman, 2014). In this study, the glacier and lake interactions and their relationship have been explored, and their effect on lake volume and draining processes has been examined. Glacier surge speed is routinely determined using remote-sensing imagery (Paul, 2015), as is lake surface area (Quincey and Luckman, 2014). Thus, remote sensing provides a means to develop images similar to Fig. 4 for specific locations around the globe where ice-dammed lakes form due to glacier surging. Although the data within Fig. 4 are scattered, a negative relationship between surge velocity and lake volume is strongly implied. Specifically, data points scatter around a median trend according to a theoretical -2 power function. Most values fall below a theoretical -3 power function (Fig. 4). Clearly, more data points within Fig. 4 would be desirable. Although GLOFs cannot be predicted from this approach, the likely volume of water that might be released catastrophically can be determined. For sites


Document: 30 1. Introduction
Section: 4. Discussion:
Type: figure
Figure

Image /page/17/Picture/1 description: A Creative Commons Attribution (CC BY) license icon. The icon is a grey rectangle with a black bar at the bottom. On the grey section, there are two white circles with black symbols inside. The left circle contains the letters 'CC', and the right circle contains the attribution symbol, which is a stylized person. On the black bar at the bottom, the letters 'BY' are written in white.


Document: 30 1. Introduction
Section: 4. Discussion:
Type: figure
Figure

Image /page/17/Picture/2 description: The image shows the logo for EGUsphere, a preprint repository. The logo consists of the word "EGUsphere" in blue. The letters "EGU" are enclosed within a blue, gear-like circle. Above the "sphere" part of the word, there are two swooshes, a blue one on top and a gray one below it. Underneath the main logo, the text "Preprint repository" is written in a smaller, gray font. The background is white.


Document: 30 1. Introduction
Section: 4. Discussion:
Type: text

that are deemed to pose a threat to human life and infrastructure, once the lake volume is better constrained, either through DEM analysis or geometric considerations, the value of n for any specific lake provides a ready indicator of the probability of an imminent GLOF. In contrast to the lower trend for water pressures associated with the Kyager lakes, the higher water pressures required to cause the Khurdopin and Shishper lakes to empty may reflect greater structural integrity, possibly related to a greater downstream extent of the glacier dams. These structural issues can be examined in the future. Still, at this stage, if n' exceeds 0.6, an initial general warning could be issued to communities downstream of the ice dam. In principle, the estimated volume of a potential GLOF can then be routed downstream using standard hydrodynamic flood routing procedures to determine the timing, depth, and extent of flooding at locations where inundation is forecast. Thus, the severity of the likely impact on humankind can be determined, and specific warning times can be derived from the rate of travel of the GLOFs. These results represent a step forward from the observations made by Carrivick et al. (2020), who proposed the exploration of the interaction between lake water and glaciers to understand the lake formation process and identify lake depth, level, and volume. Based on this understanding, empirical models can be generated to predict GLOFs in a timely manner. The current study offers a comprehensive explanation and advanced knowledge building upon the findings of Carrivick et al. (2020). The study revealed that glacier surge and GLOF development relationship indicates that glacier dynamics control lake volume. Furthermore, the study explores the lake-draining process and identifies the relative depth above which an ice-dammed lake's sudden draining may occur. Future research should further investigate the range of n' values and the nature of ice-failure mechanisms connecting lake drawdown and GLOF progression.


Document: 30 1. Introduction
Section: 410 5. Conclusion:
Type: text

The hazards associated with glacier lake outburst floods (GLOFs) in cryospheric regions are increasing worldwide in response to climate change, posing a significant threat to inhabitants in densely populated areas, particularly in the Himalayan Karakoram and Hindu Kush regions. Year on year there is a rise in human casualties and losses to residences, infrastructure, the energy sector, and local and international trade. Despite the escalating risk, the understanding of these hazards remains limited. It is imperative to determine the causes of these hazards, make timely predictions, and formulate new mitigation policies to minimize losses. This research identified the critical depth, lake volume, pressure, and elevation of ice-dammed lakes worldwide associated with GLOFs. An inverse relationship between lake volume and glacier surge speed was observed, indicating that surge speed controls lake depth, volume, and potential GLOF volumes. Comparing surveyed lake volumes with geometric estimates for 23 GLOF events from the Karakoram and 27 events from around the world, a linear regression ( $R^2 = 0.95$ ) demonstrated that geometric estimates can be robust in the absence of detailed field or remote-sensing surveys. A GLOF will likely occur when the lake's non-dimensional depth (n') exceeds 0.60, corresponding to a typical water pressure on the dam face of 510 kPa.


Document: 30 1. Introduction
Section: 425 Acknowledgements
Type: text

This study was supported by the Second Tibet Plateau Scientific Expedition and Research Program (STEP) (Grant No. 2019QZKK0906) and the National Natural Science Foundation of China (Grant no. 42350410445). Special thanks to the monitoring team of Gilgit-Baltistan Disaster Management Authority (GBDMA), Quaid-i-Azam University, and Karakoram International University for their support and data sharing, and thanks to the Special Research Assistant program of the Chinese Academy of Sciences.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Type: text

Rabindra Osti,\* Shinji Egashira and Yognath Adikari

International Centre for Water Hazard and Risk Management, Public Works Research Institute, Minamihara 1-6, Tsukuba 305-8516, Japan

data/('Prediction and assessment of multiple glacial lake outburst floods scenario in Pho', '.pdf')_extraction.md


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan > Abstract:
Type: text

In this study, the characteristic of multiple glacial lake outburst floods (GLOFs) in the Pho Chu River basin in Bhutanese Himalayas is evaluated to help assess the potential impact. Thorthormi Cho (TC) and Lugge Cho (LC) in the east branch and two unnamed lakes labelled A and B in the west branch of Pho Chu are chosen for the study. Numerical models were employed to simulate different involved processes. The results show that the peak sediment discharge in the east branch of the Pho Chu River by the TC dam breach reached about 5000 m3/s (during the first GLOF) at 4 km whereas by the LC dam breach is about 600 m3/s (second GLOF) at 6 km. However, the highest peak hydrographs (sediment and water mixture) calculated during the first and second GLOF are about 10 000 m3/s at the 18-km section and about 23 000 m3/s at the 10-km section, respectively. In the west branch of Pho Chu, erosion and depositions are the frequent intermittent local processes during the first GLOF event from Lake A. Because the first event stabilized the irregular river bed profile, there is not much sediment discharge developed during the second GLOF from Lake B. At the 17-km section of the west branch, the peak hydrograph reached about 9000 m3/s during the first event against the peak of about 800 m3/s during the second event. The results suggest that even if multiple dam breaches occur simultaneously, GLOF surges pass through the main river channel at different times with very different flood characteristics. The differences in travel time and flood characteristics mostly depend on the distributions of bed slope and potential erosion depth along the reach. Further, the amount of sediment accumulated in and transported by each surge is reliant on the temporal geomorphologic setting of the river and therefore on the impact of the previous GLOF on riverbed profile and potential erosion depth. The robustness in peak GLOF hydrographs is associated with sediment flow dynamics. As a consequence, serious inundation of Punakha, Lobeysa and major portion of Wangdue Phodrang is anticipated. Copyright © 2011 John Wiley & Sons, Ltd.

KEY WORDS moraine dam breach; GLOF; simulation; prediction; assessment; Bhutan

Received 18 November 2010; Accepted 16 September 2011


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: INTRODUCTION
Type: text

Geologically weak, high snow-fed mountains around the globe are known as global hotspots of natural hazards. In recent decades, frequency and magnitude of high mountain hazards especially glacial hazards are increasing (Evans and Clague, 1994; Beniston et al., 1997; Kääb et al., 2005; Haeberli et al., 2007; Science Daily, 2008; Osti and Egashira, 2009; UNEP-United Nations Environment Programme, 2010) due to accelerated hydrometeorological changes resulting to glacier melting (IPCC, 2007; UNEP, 2007). Melting process leads to the development of new lakes or expansion of existing glacial lakes, increasing water volume behind fragile moraine dams. As a consequence, moraine dams of such glacial lakes can abruptly breach due to increased statistic pressure, seepage and overflow triggered by avalanches, earthquakes, landslides and other factors (Post and Mayo, 1971; Clague, 2003; RGSL, 2003; Hambrey and Alean, 2004) and in various modes e.g. head cutting, overtopping, landslides and so on (Costa and Schuster, 1988; Grabs and Hanisch, 1993; Wahl, 1998; Osti

E-mail: osti55@pwri.go.jp

et al., 2011). The breach of moraine dam does not necessarily mean that the lake becomes stable but it is more likely that the unstable dam may burst many times together with the refilling of dam (Dussaillant et al., 2010). Moraine dam breaches pose immediate threats of landslide, debris flow, flash flood and inundation risk to downstream communities. Floods caused by the glacial lake outbursts are widely known as glacial lake outburst floods (GLOFs). Among different glacial hazards listed by Richardson and Reynolds (2000), GLOFs are considered the most damaging glacial hazard in the Hindu Kush Himalaya (UNEP, 2007).

In a changing natural, sociocultural and economical environment, GLOFs are now added threats to human life and physical infrastructures and therefore to the socioeconomic state of mountain regions (Ives, 2004; Sperling and Szekely, 2005). The increased number and magnitude of GLOF hazards and their impacts have already been reported by many researchers such as Watanabe *et al.* (1994); Beniston *et al.* (1997); ICIMOD-UNEP (2001); Kääb *et al.* (2005) and Haeberli *et al.* (2007). Although many studies have been conducted to understand triggering mechanisms as well as dam failure modes and GLOF impacts, there are only a handful of researches that really describe the mechanics of GLOF development processes, which are fundamental for prediction, assess-

<sup>\*</sup>Correspondence to: Rabindra Osti, International Centre for Water Hazard and Risk Management, Public Works Research Institute, Minamihara 1-6, Tsukuba 305-8516, Japan.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: INTRODUCTION
Type: text

al . * ( 1997 ) ; ICIMOD - UNEP ( 2001 ) ; Kääb * et al . * ( 2005 ) and Haeberli * et al . * ( 2007 ) . Although many studies have been conducted to understand triggering mechanisms as well as dam failure modes and GLOF impacts , there are only a handful of researches that really describe the mechanics of GLOF development processes , which are fundamental for prediction , assess - < sup > \ * < / sup > Correspondence to : Rabindra Osti , International Centre for Water Hazard and Risk Management , Public Works Research Institute , Minamihara 1 - 6 , Tsukuba 305 - 8516 , Japan .

ment and mitigation of GLOF hazards. An attempt made by Osti and Egashira (2009) to evaluate the Tam Pokhari GLOF development process in the Khumbu Region, Nepal by comparing the results from hydrodynamic models for water only and water-sediment mixture flows pointed out that the magnitude of GLOF primarily depends on the amount of sediment accumulated during the GLOF development process and therefore on the river morphology. Besides, GLOF risk in any GLOF-prone area could not be only associated with individual outbursts that are usually described in the literature but also with the possibility of simultaneous breaches of several moraine dams and therefore the multiple surges of GLOFs. There are no known hydrodynamic studies on the consequences of simultaneous moraine dam breaches triggered by any external forces such as high magnitude earthquakes. In fact, high mountain regions such as the Himalayas that consist of fragile geology are highly prone to earthquakes. Beside other reasons, the possible multiple breaches of dams due to seismic movement are discussed by Chandra (1978) and Bilham et al. (1997) and its sensitivity to the breach process was described by Tryggvason (1960), Post and Mayo (1971) and Costa and Schuster (1988). However, potential risk associated with such multiple GLOFs in a basin is rarely understood among scientists and practitioners.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: INTRODUCTION
Type: text

hydrodynamic studies on the consequences of simultaneous moraine dam breaches triggered by any external forces such as high magnitude earthquakes . In fact , high mountain regions such as the Himalayas that consist of fragile geology are highly prone to earthquakes . Beside other reasons , the possible multiple breaches of dams due to seismic movement are discussed by Chandra ( 1978 ) and Bilham et al . ( 1997 ) and its sensitivity to the breach process was described by Tryggvason ( 1960 ) , Post and Mayo ( 1971 ) and Costa and Schuster ( 1988 ) . However , potential risk associated with such multiple GLOFs in a basin is rarely understood among scientists and practitioners .

There are many unanswered questions in GLOF prediction such as what happens if two or more lakes at different locations in the same basin breach simultaneously? At any downstream locations, will the magnitude and other characteristics of GLOF triggered by each breach in such a multi-hazard scenario be the same as that predicted in a single-hazard scenario because river morphology could have been changed significantly due to multiple and consequential surges? The foremost thing to understand is that the conventional method for predicting individual GLOF events as water only flow by using river flow models (Jingshi and Fukushima, 1999; Bohorquez and Darby, 2008) may not produce a reliable result as many GLOF events observed in the past resembled debris flows (Xu and Feng, 1994; Huggel et al., 2004; Osti and Egashira, 2009). However, river flow models are useful for predicting floods due to GLOF in the downstream regions mainly in lower basin, where debris flow does not exist. Furthermore, GLOF prediction based on a debris flow model as applied by Osti and Egashira (2009) can address the problems but should be applied in a multi-hazard scenario, i.e. multiple dam breaches. In addition to that, there is a need to identify the transitional boundary where the debris flow changes into river flow after sediment deposition so that coupling two different models, i.e. debris flow model and inundation model is possible. In this paper, the GLOF prediction model developed and field tested by Osti and Egashira (2009) was applied to a multi-hazard scenario mainly to check how the characteristics of GLOF hazard change as a consequence of multiple loading of peak flows and thereby temporal variation of riverbed morphology at any downstream locations. It is hoped that the result produced through this research will be helpful to predict GLOF hazard, access

corresponding impacts and propose control measures in multiple GLOF hazards conditions of the Pho Chu River basin in Bhutan.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: STUDY AREA
Type: text

The Puna Tshang Chu River in western Bhutan originates in the glacier-capped eastern Himalayas near the China (Tibet) border and flows down the Himalayan slopes crossing the border of Bhutan flowing into India and finally draining into the Bay of Bengal after mixing in the Brahmaputra River. The Puna Tshang Chu basin is characterized by three major rivers inside Bhutan: Mo Chu, Pho Chu and Dang Chu. In this study, we consider only Pho Chu (Figure 1). Among three major rivers in the basin, the Pho Chu sub-basin is highly GLOF-prone. A total of 154 glaciers and 549 lakes exist in the Pho Chu basin only (ICIMOD-UNEP, 2001). Most glacial lakes are located near the present glacier terminal at about 4150-4200 m in Lunana area, northern Pho Chu basin. The Pho Chu main (TM) stream has two branches, a western (TW) and eastern (TE) branches. Tarina and Lunana glaciers feed the western branch (TW) and the eastern branch (TE), respectively. The total catchment area of the Pho Chu River at the junction of the two tributaries is about  $1000 \,\text{km}^2$  ( $T_W = 410 \,\text{km}^2$  and  $T_E = 590 \,\text{km}^2$ ). The lengths of the eastern and western branches up to the merging point are 39.5 and 27 km, respectively. The length of the main river reach up to the Bhutan-India border is 185 km. There are about eight different potentially dangerous lakes only in the Pho Chu River basin (Karma, 2006). Raphstreng Tsho (28°06′16″, 90°14′45″), Thorthormi Cho (26°06′07″, 90°15′46″) and Lugge Cho (28°05′41″, 90°17′ 36") in the eastern branch and two unnamed Lakes A  $(28^{\circ}06'45'',\,89^{\circ}54'30'')$  and B  $(28^{\circ}06'15'',\,89^{\circ}53'56'')$  in the western branch of the Pho Chu River are considered highly dangerous (ICIMOD-UNEP, 2001). Thorthormi Cho is aligned along the main TE about 4 km downstream from the Lugge Cho, whereas the Lake A is located about 0.5 km river distance away from Lake B in Tw. The river stations showing locations of different flood-prone villages are shown in Figure 2. For clarity, distances are measured from Bhutan India border (Figure 2a) and also from the river heads (Figure 2b).

The Pho Chu basin area experienced at least four recorded GLOFs in the past (Karma, 2006). The first in 1950, which destroyed Punakha Dzong (a monastery fortress), the second in summer 1960 together with high rainfall runoff discharge, the third one in 1968 which washed away a temple and bridges and killed 12 people and the latest one was the historic Lugge Cho (partial burst) GLOF in 1994 which incurred huge damage in the Pho Chu basin (Watanabe and Rothacher, 1996). The 1994 GLOF event is the only event which is well documented in Bhutan.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: STUDY AREA
Type: text

from the river heads ( Figure 2b ) . The Pho Chu basin area experienced at least four recorded GLOFs in the past ( Karma , 2006 ) . The first in 1950 , which destroyed Punakha Dzong ( a monastery fortress ) , the second in summer 1960 together with high rainfall runoff discharge , the third one in 1968 which washed away a temple and bridges and killed 12 people and the latest one was the historic Lugge Cho ( partial burst ) GLOF in 1994 which incurred huge damage in the Pho Chu basin ( Watanabe and Rothacher , 1996 ) . The 1994 GLOF event is the only event which is well documented in Bhutan .

A survey of the 1994 Lugge Cho GLOF conducted by the Department of Geology and Mines, Government of Bhutan (Leber *et al.*, 2002; Brauner *et al.*, 2003) from 20 to 23 October 1994 states that 23 lives were lost and 91 households were affected on top of other damages. The peak discharge of about 2539 m3/s measured at


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: STUDY AREA
Type: figure
Figure

Image /page/2/Figure/2 description: A multi-panel figure illustrating the location and features of a river basin. The figure is divided into three parts labeled (a), (b), and (c).


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: STUDY AREA
Type: text

Part (a) consists of two Google satellite images. The left image shows two glacial lakes, labeled Lake-A and Lake-B, in a mountainous, snowy region. The right image shows the Rapstreng lake and the Thorthormi and Lugge glaciers. An arrow points from this area to the headwaters of a river in part (c).

Part (b) displays a map of a country with its administrative boundaries outlined in red. A specific region, corresponding to the river basin, is overlaid with a black dotted grid. A scale bar at the bottom indicates distances of 0, 45, and 90 kilometers. An arrow connects this map to the more detailed map in part (c).

Part (c) is a detailed elevation map of the river basin. A grayscale legend indicates elevation ranging from a low of 104 to a high of 7056. The main river, shown in blue, is formed by two tributaries, the Mo-Chu and the Pho-Chu. Downstream, the river is labeled Dang Chu and Puna Tshang Chu. Key points along the river are marked as A, B, C, D, and E. Punakha Town is located at point D. A legend for 'Reach Length' provides the following distances: A-C = 40 km, B-C = 35 km, C-D = 55 km, and D-E = 130 km. A scale bar at the bottom shows distances of 0, 15, and 30 kilometers.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: STUDY AREA
Type: figure
Figure: Figure 1. Location map of Pho Chu River basin in Bhutan and locations of glacial lakes on it

Figure 1. Location map of Pho Chu River basin in Bhutan and locations of glacial lakes on it


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: STUDY AREA
Type: figure
Figure

Image /page/2/Figure/4 description: The image displays two diagrams, labeled (a) and (b), illustrating a river system. Diagram (a) is a map of the Mo Chu River Basin, showing the Puna Tshang Chu River. The river is marked with distances in kilometers, starting from 0.0 at the bottom and increasing upwards. Key locations are marked, including Wangdue Phodrang, Lobeysa, and Punakha Town at km 129.2. Further upstream, at km 184.2, the river splits into the Western Branch of Pho Chu (Tw) and the Eastern Branch of Pho Chu (Te). This upper section is circled, and an arrow points to diagram (b) for a more detailed view. Diagram (b) is a schematic of the headwaters. The Eastern Branch of Pho Chu (Te) originates from Lugge Cho (km 0.0) and Thorthormi Cho (km 3.8), with subsequent markers at 1.8, 11.0, 16.8, 19.0, and 24.0 km. The Western Branch of Pho Chu (Tw) originates from Lake A (km 0.0) and Lake B, with markers at 0.5, 8.2, 14.0, 17.5, and 18.0 km. The two branches merge, and the river continues with markers at 27.0 and 39.5.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: STUDY AREA
Type: figure
Figure: Figure 2. Flood-prone village locations and river stations along Pho Chu River measured from (a) Bhutan-India border and (b) tributaries' heads

Figure 2. Flood-prone village locations and river stations along Pho Chu River measured from (a) Bhutan-India border and (b) tributaries' heads


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: STUDY AREA
Type: text

Wangdue Phodrang hydrological station (85 km downstream from the Lugge Cho Lake) destroyed Punakha Dzong and surrounding areas about 5 km upstream from the hydrological station (Figure 2). The GLOF scoured the valley floor and banks, triggering landslides and bringing down much sediment and woody debris. In the process, the GLOF accumulated loose sediment slowly, gaining the volume and energy of the flow and compounding the damage downstream. Lugge Cho's flood reached about 200 km downstream from the lake, i.e. somewhere near to Bhutan–India border causing 2-m-high flood waves (Richardson and Reynolds, 2000). Watanabe and Rothacher

(1996) highlighted the cause of the 1994 GLOF due to excess melting of glaciers and excess water accumulation behind a moraine dam that collapsed later due to excessive hydrostatic pressure escorted by the pool of water. Lugge Cho Lake grew very fast due to the retreat of the Lugge Cho glacier about 160 m/year from 1988 to 1993 (SAARC, 2007). The glacier melting and volume expansion apply to almost all lakes in the region, which means all lakes are vulnerable. External forces such as high magnitude earthquake can also play a significant role in breaching such vulnerable moraine dams at any time as the area is highly earthquake prone. The overall moraine structure of almost

all dams is resting over loose ice and sediment materials that will create a havoc if hit by a serious earthquake.

Bhutan is located in highly fragile earthquake zone. A review article by Kuensel (2009) shows that about 19 major earthquakes have hit Bhutan since 1713. The biggest events were in 1897, 1934 and 1950, measuring 8 or above on the Richter scale. There are still ongoing debates on what will be the worst scenario of earthquake in Bhutan, however the article (Kuensel, 2009) emphasized by quoting some past researches the probability of occurrence of an earthquake of above 8.1–8.3 magnitude in a highly seismic-risk zone of Bhutan. The most recent earthquake event in Bhutan was recorded on 24 September 2009 with the magnitude of 6.1 Richter scale (BBC, 2009). Since 1980, there have been four similar quakes in the Pho Chu River basin in Bhutan, and the alarming situation is that the upstream of the Pho Chu basin in the Lunana area is identified as a very high earthquakerisk zone (Meyer et al., 2006), which is also the home for many potentially dangerous lakes in the country. The depth and surface size of these lakes also increased in recent years (Leber et al., 2002; Brauner et al., 2003), and if these lakes burst simultaneously due to such high tremor by an earthquake, then the released volume of water and accumulated bed sediment mass could translate into a gigantic GLOF. As an aftermath the human and economic loss could be many folds of the 1994 Lugge GLOF. It is to note that the Punakha–Wangdue valley is relatively highly populated region and is under rapid development in Bhutan. There are three major hydropower stations located within the basin.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: METHODOLOGY
Type: text

In this study, three different types of models, i.e. moraine dam breach, debris flow and river flow models are employed to simulate and check the effect of simultaneous dam breaches and sequential occurrences of GLOFs in the Pho Chu River basin.

In the upstream area, a numerical model is used to reproduce the debris flows, which generally form when unstable saturated non-cohesive riverbed materials entrain into the flow body. In order to determine the upstream boundary conditions to the debris flow model in the form of a dam breach hydrographs, dam breach analyses were performed using different types of dam breach models. It is considered that earthquake-triggered breaches of moraine dams occur simultaneously. However depending on several factors such as the amount of water volume released from each lake, channel geometry, sediment budget, distance between lakes and GLOF characterization including timing and magnitude of surges, the potential impact in downstream areas may vary from place to place.

The moraine dam breaches of Thorthormi Cho and Lugge Cho draining into torrent  $T_E$  and Lake A and Lake B into torrent  $T_W$  are considered for modelling. The Raphstreng Tsho Lake, which also drains into torrent  $T_E$ , shows a stable shore line and is considered stable (Leber *et al.*, 2002; Brauner *et al.*, 2003) and therefore excluded in the modelling. The characteristic of a debris flow caused by GLOFs in each case is evaluated up to the location, from

where the erosion and deposition is not active, which is usually the place where the river gradient changes from steeper to mild slope region. Because the water flow continued further downstream even after the release of sediment by deposition, there is a chance of flooding further downstream. Therefore the hydrographs at the section, from which the sediment concentration reduced to a minimum level, are taken as input to the inundation model to check the inundation extent up to the Bhutan–India border.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: METHODOLOGY
Type: text

, 2003 ) and therefore excluded in the modelling . The characteristic of a debris flow caused by GLOFs in each case is evaluated up to the location , from where the erosion and deposition is not active , which is usually the place where the river gradient changes from steeper to mild slope region . Because the water flow continued further downstream even after the release of sediment by deposition , there is a chance of flooding further downstream . Therefore the hydrographs at the section , from which the sediment concentration reduced to a minimum level , are taken as input to the inundation model to check the inundation extent up to the Bhutan – India border .

The total water volume discharged during the event was calculated based on the assumed sink depth and the approximate area of the lake surface visible in Google Earth image and calculated with the help of a geographical information system software namely ArcGIS. The sink depth (40 m) is considered same for all the breaches and decided based on the suggestions made by the survey report (Leber et al., 2002; Brauner et al., 2003) as well as the tendency of moraine dam failures in a similar environment of Bhutan and Nepal (ICIMOD-UNEP, 2001; Mool, 2007; Osti and Egashira, 2009). The top width of the 100-m-high moraine dams is estimated at 50 m (Leber et al., 2002; Brauner et al., 2003). The longitudinal bed profiles of torrents TE and TW and the topography of the area were derived from the digital elevation model (DEM) provided by the Shuttle Radar Topography Mission (SRTM) (USGS, 2004). The SRTM data are sampled at 3", which is about 90 m in resolution. The uncertainty lies in the vertical accuracy of SRTM-DEM, which can only be reduced by using precise DEM data that are not available for the region at present. The hydrology modelling, an extension of the ArcGIS software, is used to delineate the watershed at the Bhutan–India border and to plot the centrelines of the river as well as the tributaries. The river reach/station distances are measured relative to the distance from the tributaries' heads for all runs of simulations (Figure 2b). The time to start the breaching of individual dam and therefore the start of GLOF propagation is set at zero value for each run of simulation independently, i.e. start time of breach hydrograph is set as a start time of GLOF. The HEC-GeoRAS extension in ArcGIS is used to extract all the necessary geometric data describing the river profile and cross-sections for flood-routing purpose. Some of the typical river cross-sections are illustrated in Figure 3.

Dam breach modelling

In general, it is numerically difficult to reproduce moraine dam breach phenomena and therefore to predict a breach hydrograph because there are many unknown variables that may contribute to the failure of moraine dams. However, a peak dam breach flow is estimated by comparing the results from three different models namely (1) simple dam break equation, (2) the Hydrologic Engineering Center River Analysis System (HEC-RAS) and (3) the Simplified Breach Analysis (SIMBA).

Simple dam break equation. A simple dam break Equation (1) is developed by the National Weather Service (NWS) of the USA, although the dam break context considered in the equation is different. This equation is


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: METHODOLOGY
Type: figure
Figure

Image /page/4/Figure/2 description: A figure displaying four line graphs in a 2x2 grid. Each graph plots Elevation in meters (m) on the y-axis against Station in meters (m) on the x-axis, representing different topographical cross-sections.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: METHODOLOGY
Type: text

Top-left graph: Labeled "200 km in T\_W". The y-axis ranges from 1700 to 2200 m, and the x-axis ranges from 0 to 3500 m. The line shows a U-shaped valley, starting at an elevation of approximately 2180 m, descending to a minimum of about 1750 m near station 1700, and then ascending to about 2200 m.

Top-right graph: Labeled "205 km in T\_E". The y-axis ranges from 1800 to 2200 m, and the x-axis ranges from 0 to 3000 m. The line shows a U-shaped valley, starting at an elevation of approximately 2180 m, descending to a minimum of about 1850 m near station 1600, and then ascending to about 2100 m.

Bottom-left graph: Labeled "130 km". The y-axis ranges from 600 to 900 m, and the x-axis ranges from 0 to 8000 m. The line starts at an elevation of about 900 m, descends to a minimum of about 610 m near station 3500, and then gradually ascends with some fluctuations to about 820 m.

Bottom-right graph: Labeled "18 km". The y-axis ranges from 0 to 600 m, and the x-axis ranges from 0 to 8000 m. The line shows a small peak of about 520 m near the start, then descends to a wide, low-elevation area around 100 m between stations 3000 and 5000, followed by a gradual, bumpy ascent to about 250 m.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: METHODOLOGY
Type: figure
Figure: Figure 3. Typical cross-sections along Pho Chu River extracted from SRTM-DEM (distances measured from Bhutan-India Border)

Figure 3. Typical cross-sections along Pho Chu River extracted from SRTM-DEM (distances measured from Bhutan-India Border)


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: METHODOLOGY
Type: text

based on the concept of the falling head weir flow used in the NWS full dam break model (Wetmore and Fread, 1984):

$$Q_{\rm w} = Q_{\rm o} + 3.1 B_{\rm r} \left[ C / \left( T_{\rm f} + C / \sqrt{H} \right) \right]^3$$
 (1)

where  $Q_{\rm w}$  is the peak water flow, i.e. the breach flow and the non-breach flow (ft³/s),  $Q_{\rm o}$  is the non-breach flow (ft³/s),  $B_{\rm r}$  is the final average breach width (ft), C is a coefficient that can be calculated as  $C = 23.4 * A_{\rm s}/B_{\rm r}$ ,  $A_{\rm s}$  is a reservoir surface area (acres) at the maximum pool level, H is the failure depth (ft) above the final breach elevation, and  $T_{\rm f}$  is the time to failure (h). Because the dam breach shape, especially width and height, is measured in the field, only the time of the breach must be calculated. To accomplish this, a statistically derived predictor (Equation 2) for the time of dam failure developed by Froehlich (1995) is used. From the work of Froelich in which the properties of 63 types of dam breaches ranging in height from 4 to 90 m were considered, the following predictor equation was obtained:

$$T_{\rm f} = 0.59 (V_{\rm s}^{0.47}) / (H^{0.91})$$
 (2)

where  $T_{\rm f}$  is the time of failure (h) and only includes the vertical erosion of the dam,  $V_{\rm s}$  is the storage volume (ac-ft), and H is the height (ft) of water above the bottom of the breach.

Hydrologic Engineering Center River Analysis System. The estimated peak flow by Equation 1 can be used to compare with the peak flow of a hydrograph produced by a dam breach model component of a hydrodynamic model named the HEC-RAS developed by the HEC of the US Army Corps of Engineers (U.S. Corps of Engineers, 2002). One of the parameters that need to be estimated for the input to HEC-RAS is the duration of the full dam breach formation, which is determined using Equation 2. The dam breach model in the HEC-RAS is used in the overtopping

failure mode; therefore, the geometry of the breached portion of the lake is critical in the calculation. Available DEMs could not accurately generate lake bottom surface profiles; therefore, the lake volumes in this study were modelled using manually drawn cross-sections that were partially extrapolated from the lake area assuming all lakes as bowl shape. HEC-RAS can perform a full unsteady flow routing through a reservoir pool and downstream of a dam (U.S. Corps of Engineers, 2002).


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: METHODOLOGY
Type: text

the full dam breach formation , which is determined using Equation 2 . The dam breach model in the HEC - RAS is used in the overtopping failure mode ; therefore , the geometry of the breached portion of the lake is critical in the calculation . Available DEMs could not accurately generate lake bottom surface profiles ; therefore , the lake volumes in this study were modelled using manually drawn cross - sections that were partially extrapolated from the lake area assuming all lakes as bowl shape . HEC - RAS can perform a full unsteady flow routing through a reservoir pool and downstream of a dam ( U . S . Corps of Engineers , 2002 ) .

Simplified Breach Analysis. In addition to HEC-RAS, a physically based model, namely, SIMBA developed at the US Department of Agriculture is also used to produce breach hydrographs. The SIMBA model is originally developed to analyse laboratory dam breach experiment and aimed at its application in flood control and watershed protection (Hanson et al., 2005; Temple et al., 2005). In SIMBA, overtopping mode is considered and the erosion processes are divided into four primary stages, e.g. head-cut formation, deepening, upstream advancement and lateral widening. The inflow to the reservoir is an input value, which is considered minimum annual average flow 5 m3/s both in Thorthormi Cho and Lugge Cho, whereas it is assumed at 2 m3/s for Lake A and Lake B (Leber et al., 2002). The outflow and volumes can be calculated as a function of reservoir water surface elevation, which is governed by the dam erosion process. In this method, all outflow over the dam or through the breach area can be calculated by assuming negligible hydrostatic pressure exerted at the breach section and energy loss within the reservoir flow. The erosion rate of the dam can be calculated by considering normal flow depth combined with a stressbased detachment rate method (Temple et al., 2005). The erodibility coefficient of 2 cm3/N s as an input parameter for SIMBA model is used for the most erodible soil in the classification of Hanson and Simon (2001).

GLOF modelling


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: METHODOLOGY
Type: text

elevation , which is governed by the dam erosion process . In this method , all outflow over the dam or through the breach area can be calculated by assuming negligible hydrostatic pressure exerted at the breach section and energy loss within the reservoir flow . The erosion rate of the dam can be calculated by considering normal flow depth combined with a stressbased detachment rate method ( Temple et al . , 2005 ) . The erodibility coefficient of 2 cm < sup > 3 < / sup > / N s as an input parameter for SIMBA model is used for the most erodible soil in the classification of Hanson and Simon ( 2001 ) . GLOF modelling

In order to simulate a GLOF, the debris model is used with governing equations for the flow of water and sediment mixture. In order to describe water and sediment mixture flows, different approaches are usually used; some describe debris flows but some describe wash, suspension and bed loads. However, there are only a few approaches which really consider such sediment flows as a unified problem that can be described by a single set of equations. Also, many constitutive equations for the evaluation of the sediment-water mixture flow have been proposed, and they can be roughly classified into four groups (Egashira, 2007): (1) Coulomb-type shear stress (Savage and Hutter, 1989, 1991; Iverson and Denlinger, 2001), (2) Bingham type (Chen, 1988; O'Brien and Julien, 1988; Julien and Lan, 1991), (3) fluid type (Takahashi, 1980, 1991; Tsubaki et al., 1982) and (4) Coulomb-type shear plus fluid type (Egashira and Ashida, 1992; Egashira et al., 1997). There are advantages and disadvantages to each of these groups (Osti and Egashira, 2009). In this study, we employ the D-type solution as this can provide not only a steady-state solution but also can distinguish between flow over a rigid bed or an erodible bed and can explain how the flow body stops. The formulae described by Egashira et al. (1997), which are type D, are employed in the study. The model was developed to describe the flow of a mixture of water and coarse sediment under the assumption that turbulent suspension is negligible. These formulae can distinguish differences in flow over erodible and rigid beds and also be used to evaluate profiles of velocity and sediment concentration as the flow changes from a bed load layer to debris flow in response to a monotonic change in the flux sediment concentration.

Osti and Egashira (2008, 2009) employed 1-D governing equations proposed by Egashira *et al.* (1997) to simulate GLOF. The constitutive equations and erosion rate formula developed by Egashira *et al.* (1997, 2001) were used to solve the governing equations.

The equations of mass conservation describing the water-sediment mixture and sediment only can be expressed as

$$\frac{\partial h}{\partial t} + \frac{1}{B} \frac{\partial \bar{u}hB}{\partial x} = \frac{E}{c_*} \tag{3}$$

$$\frac{\partial \bar{c}h}{\partial t} + \frac{1}{B} \frac{\partial \gamma \, \bar{c}\bar{u}hB}{\partial x} = E \tag{4}$$


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: METHODOLOGY
Type: text

$ $ \ frac { \ partial h } { \ partial t } + \ frac { 1 } { B } \ frac { \ partial \ bar { u } hB } { \ partial x } = \ frac { E } { c_ * } \ tag { 3 } $ $ $ $ \ frac { \ partial \ bar { c } h } { \ partial t } + \ frac { 1 } { B } \ frac { \ partial \ gamma \ , \ bar { c } \ bar { u } hB } { \ partial x } = E \ tag { 4 } $ $

The equations for momentum conservation and bed elevation are as follows:

$$\frac{\partial h\bar{u}}{\partial t} + \frac{\partial \beta h\bar{u}\bar{u}}{\partial x} = gh\sin\theta - gh\cos\theta\frac{\partial h}{\partial x} - \frac{\tau_b}{\bar{\rho}_m}$$
 (5)

$$\frac{\partial z_{b}}{\partial t} = -\frac{E}{c_{c} \cos \theta} \tag{6}$$

where h is the flow depth, t is the time, x is the coordinate toward the flow direction, E is the erosion rate of the bed sediment (its negative value denotes deposition),  $\bar{c}$  is the

depth-averaged and volumetric sediment concentration,  $c_*$  is the sediment concentration of the underlying sediment bed,  $\bar{u}$  is the depth-averaged velocity of the mixture, B is the river bed width, g is the acceleration due to gravity, and  $\bar{\rho}_{\rm m}$  is the depth-averaged mass density of the sediment-water mixture, which is defined as

$$\bar{\rho}_{\rm m} = (\sigma - \rho)\,\bar{c} + \rho \tag{7}$$

where  $\sigma$  is the mass density of the sediment particle,  $\rho$  is the mass density of water including fine sediment,  $\tau_b$  is the bed shear stress,  $z_b$  is the bed elevation from a reference level, and  $\theta$  is the bed slope, which is expressed as

$$\theta = \sin^{-1} \left[ -\frac{\partial z_b}{\partial x} \right] \tag{8}$$

$\gamma=(1/A)\int_A \{(c\,u)/(\bar c\,\bar u)\}\,\mathrm{d}A$  in Equation (4) is a correction factor with a value that ranges from 0 to 1 for sediment transportation, depending on the bed slope and interparticle friction angle.  $\beta$  in Equation (5) is the momentum-correction factor, which has a value from 1.10 to 1.40 for debris flow. The following equations for the bed shear stress and erosion rate are also employed:


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: METHODOLOGY
Type: text

$ \ gamma = ( 1 / A ) \ int_A \ { ( c \ , u ) / ( \ bar c \ , \ bar u ) \ } \ , \ mathrm { d } A $ in Equation ( 4 ) is a correction factor with a value that ranges from 0 to 1 for sediment transportation , depending on the bed slope and interparticle friction angle . $ \ beta $ in Equation ( 5 ) is the momentum - correction factor , which has a value from 1 . 10 to 1 . 40 for debris flow . The following equations for the bed shear stress and erosion rate are also employed :

$$\tau_{\rm b} = \tau_{\rm v} + \rho f \, \bar{u}^2 \tag{9}$$

$$\frac{E}{\bar{u}} = c_* \tan(\theta - \theta_e) \tag{10}$$

where  $\tau_y$  is the yield stress caused by particle-to-particle contacts, f is the friction factor,  $\theta$  is the bed slope, and  $\theta_e$  is the equilibrium bed slope corresponding to the sediment concentration  $\bar{c}$  of a debris flow. Parameters  $\tau_y$ ,  $\tan\theta_e$  and f are expressed as follows:

$$\tau_{y} = \left(\frac{\bar{c}}{c_{*}}\right)^{1/5} (\sigma - \rho) \,\bar{c} \, g \, h \cos\theta \tan\varphi_{s} \tag{11}$$

$$\tan \theta_{\rm e} = \frac{(\sigma/\rho - 1)\,\bar{c}}{(\sigma/\rho - 1)\,\bar{c} + 1}\,\tan \varphi_{\rm s} \tag{12}$$

$$f = \frac{25}{4} \left[ k_{\rm f} \frac{(1-\bar{c})^{5/3}}{\bar{c}^{2/3}} + k_{\rm d} \left( \frac{\sigma}{\rho} \right) (1-e^2) \,\bar{c}^{1/3} \right] \left( \frac{h}{d} \right)^{-2} \tag{13}$$


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: METHODOLOGY
Type: text

frac { 25 } { 4 } \ left [ k_ { \ rm f } \ frac { ( 1 - \ bar { c } ) ^ { 5 / 3 } } { \ bar { c } ^ { 2 / 3 } } + k_ { \ rm d } \ left ( \ frac { \ sigma } { \ rho } \ right ) ( 1 - e ^ 2 ) \ , \ bar { c } ^ { 1 / 3 } \ right ] \ left ( \ frac { h } { d } \ right ) ^ { - 2 } \ tag { 13 } $ $

where d is the particle diameter,  $k_{\rm f}$ =0.16,  $k_{\rm d}$ =0.0828, and e and  $\phi_{\rm s}$  are the restitution coefficient (e=0.85) and the interparticle friction angle of sediment particles, respectively. In this study, parameters such as flow width, physical properties of the sediments and potential erosion depths were determined by field surveys and, in some instances, expert knowledge or data from secondary sources. The physical properties of the bed material were as follows: particle size diameter d=20 cm, interparticle friction angle of the sediment particles  $\phi_{\rm s}$ =38°, mass density of sediment  $\sigma$ =2.65 g/cm³, mass density of interstitial fluid with suspended sediment  $\rho$ =1.33 g/cm³ and the sediment concentration of the underlying stationary sediment bed  $c_*$ =0.52. The potential erosion depth ( $D_{\rm p}$ ), which is defined

as a depth of unstable sediment overlaying the bedrock was estimated to be an average of 10 m throughout the reach based on field observations (Leber *et al.*, 2002; Brauner *et al.*, 2003). In the simulation, riverbed slopes steeper than 18° are considered naturally stable as unstable saturated bed sediment cannot exist in such a steep slope. The riverbed width (*B*) varies throughout the river zones; however it is considered constant in a temporal scale. For simplicity, an average bed width for each 100-m river reach was assigned (ranges from 50 to 300 m). The finite leapfrog difference scheme was employed for computations with  $\nabla x = 20$  m and  $\nabla t = 0.012$  s. The computational time for each simulation was started from zero without any influence from other simulations.

In some instances, flux sediment concentrations of sediment flow could be lower than those of generally accepted debris flows. However, the word debris flow is used for simplicity because it has been explained by Egashira *et al.* (1997) that the dynamic characteristics of the debris flow change monotonically with sediment concentration and the sediment concentration can be determined uniquely in an erodible bed if sediment particles composed of the flow body are so coarse that turbulent suspension cannot take place.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: METHODOLOGY > Flood inundation modelling
Type: text

The output of the debris flow model provided the upstream boundary conditions, i.e. the peak flood hydrograph for delineating the inundation in downstream areas up to the Bhutan–India border (Figure 4). The location of upstream boundary for each simulation is set at the location where the sediment concentration is reduced to a lowest level without rebounding its value at any downstream sections, and this is usually the place where the riverbed slope changes from steeper to milder

slope. One-dimensional river flow model developed by the US Corps of Engineers namely HEC-RAS was used to perform one-dimensional unsteady flow calculations under mixed flow regime condition, providing upstream boundary condition as calculated hydrographs and the downstream boundary as normal water depth. All simulations were performed under mixed flow regime, which utilizes local partial inertia technique. The local partial inertia technique applies a reduction factor to the two inertia terms in the momentum equation as the Froude number goes toward 1.0 (U.S. Corps of Engineers, 2002). The model solves the Saint Venant equations formulated for natural channels using the wellknown four-point implicit box finite difference scheme. The upstream boundary conditions, i.e. the highest peak flood hydrographs, due to either first or second surge of debris flow (GLOF) in each tributary, i.e. TE and TW, are considered for inundation simulations. There are some limitations in 1-D simulation, which are well described by comparing results by 1-D and 2-D river flow models by Carling et al. (2009). However, they suggested that the difference is less significant when 1-D model deals with peak flow conditions.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: text

The satellite images provided the basic geometrical feature of four different lakes in the Pho Chu River basin (Table 1). Lakes Lugge and Thorthormi are two largest glacial lakes in  $T_{\rm E}$ , whereas the two other unnamed lakes A and B in  $T_{\rm W}$  are smaller in size. The NWS model (Equations 1 and 2) resulted in the peak dam breach discharge of over  $10\,000\,{\rm m}^3/{\rm s}$  in Lugge Cho and Thorthormi but about  $5\,000\,{\rm m}^3/{\rm s}$  in Lakes A and B. The estimated dam breach peak flows are then compared with the results produced by


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure

Image /page/6/Figure/9 description: A diagram illustrating a hydrological model of two river systems originating from glacial lakes. On the left, a river flows from Lake A and Lake B. A corresponding graph shows the discharge (m³/sec) over time (s) at a downstream point T\_WX. This hydrograph displays two peaks: a larger one for the "Lake A Burst" at time T\_W1, and a smaller one for the "Lake B Burst" at time T\_W2. On the right, another river system originates from two lakes named "Thorthormi Cho" and "Lugge Cho". A second hydrograph shows the discharge at a downstream point T\_EY. This graph also has two peaks: a smaller one for the "Thorthormi Cho Burst" at time T\_E1, and a larger one for the "Lugge Cho Burst" at time T\_E2. The two river systems are shown merging further downstream. An arrow points from the right-side lakes, indicating they provide the "Upstream boundary conditions for inundation analysis" with the condition specified as (T\_W2=T\_E1=0).


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure: Figure 4. Sketch of the upstream boundary conditions at arbitrary debris flow termination sections $T_{WX}$ and $T_{EY}$ in $T_{W}$ and $T_{E}$ , respectively, for the worst inundation scenario

Figure 4. Sketch of the upstream boundary conditions at arbitrary debris flow termination sections  $T_{WX}$  and  $T_{EY}$  in  $T_{W}$  and  $T_{E}$ , respectively, for the worst inundation scenario


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: table
Table

| Table I. Features | of selected | glacial lakes | in Pho | Chu river bas | in |
|-------------------|-------------|---------------|--------|---------------|----|
|                   |             |               |        |               |    |

Table I. Features
of selected
glacial lakes
in Pho
Chu river bas
in


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: table
Table

| Lake name   | Lake area (m2) | Breached depth (m) | Volume (m3) | Breach time (h) | Peak Flow (m3/s) |
|-------------|----------------|--------------------|-------------|-----------------|------------------|
| Lugge       | 1 674 000      | 40                 | 66 950 000  | 1.18            | 14 000           |
| Thorthormi  | 1 410 000      | 40                 | 56 387 000  | 1.08            | 12 300           |
| B (unnamed) | 424 000        | 40                 | 16 956 000  | 0.62            | 5800             |
| A (unnamed) | 253 000        | 40                 | 10 107 000  | 0.49            | 4000             |

Lake name
Lake area (m2)
Breached depth (m)
Volume (m3)
Breach time (h)
Peak Flow (m3/s)


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: text

the HEC-RAS and SIMBA models, which in the case of Lugge Cho are plotted in Figure 5. The results produced by NWS equations that are listed in Table 1, closely match the results produced by HEC-RAS and SIMBA models (Figure 5). Dam breach hydrographs of all selected glacial lakes calculated by SIMBA are plotted in Figure 6. These hydrographs were used as upper boundary conditions for GLOF modelling in each tributary for each case of GLOF from each lake. The timing of moraine dam breaches could be same for all selected lakes but because of relative downstream locations of the Thorthormi Lake in TE and Lake B in TW, the first surges of GLOF in TE and TW are supposed to be caused by the dam breaches at Thorthormi Lake and Lake A respectively.

In the case of Thorthomi Cho in  $T_E$ , the sediment discharge at 0.5, 4, 8, 9 and 18 km (measured from the lake mouth as shown in Figure 2b) sections as well as the sediment and water mixture hydrographs at 18 km are plotted in Figure 7a–f. The upstream reaches are debris flow development and transportation regions, and the river reaches especially 9–14 and 18–21 km are mild slope regions where the debris flow usually deposits mainly for the first run of simulation. Therefore, the total hydrographs


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure

Image /page/7/Figure/6 description: A line graph comparing two models, SIMBA and HEC-RAS, plotting Discharge (m³/s) on the y-axis against Time (min) on the x-axis. The x-axis ranges from 0 to 300 minutes, with labels at intervals of 50. The y-axis ranges from 0 to over 15000 m³/s, with labels at 0, 5000, 10000, and 15000. The SIMBA curve shows a sharp peak, reaching a maximum discharge of over 15000 m³/s at approximately 25 minutes before declining. The HEC-RAS curve has a broader peak, reaching its maximum discharge of just over 15000 m³/s at approximately 65 minutes before declining. The SIMBA curve peaks earlier and higher than the HEC-RAS curve.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure: Figure 5. Calculated moraine dam breach hydrograph at Lugge Cho Lake

Figure 5. Calculated moraine dam breach hydrograph at Lugge Cho Lake


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure

Image /page/7/Figure/8 description: A line graph plots Discharge in cubic meters per second (m³/s) on the y-axis against Time in minutes (min) on the x-axis. The y-axis ranges from 0 to over 15,000, with major gridlines at 5,000, 10,000, and 15,000. The x-axis ranges from 0 to 300, with major gridlines every 50 minutes. The graph displays four curves, each representing a different location: Lugge, Thorthomi, Lake B, and Lake A. All four curves show a rapid increase in discharge to a peak, followed by a more gradual decrease. The 'Lugge' curve has the highest peak, reaching approximately 17,000 m³/s at around 25 minutes. The 'Thorthomi' curve peaks slightly lower, at about 15,000 m³/s, also around 25 minutes. The 'Lake B' curve peaks at approximately 6,000 m³/s around 20 minutes. The 'Lake A' curve has the lowest peak, just over 5,000 m³/s, also around 20 minutes. All four curves show the discharge decreasing and approaching zero by the 300-minute mark.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure: Figure 6. SIMBA-calculated moraine dam breach hydrographs at four selected glacial lakes

Figure 6. SIMBA-calculated moraine dam breach hydrographs at four selected glacial lakes


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: text

at these locations need to be compared and the worst case needs to be considered for inundation modelling. The results reveal that the GLOF developed as a debris flow acquired the peak value of sediment discharge of about 4500 m3/s at 4-km section (Figure 7b). Figure 7a-e indicates that the debris flow development is significant along the initial reach of 0–6 km. The sediment discharge gradually reduced from 6 to 11 km (debris flow deposition zone) and significantly reduced after the 18-km section after depositing the sediment in relatively mild slope region between 16.5 and 18 km (Figures 7e and 8a–b). In Figure 8b, the calculated final erosion and deposition situation due to the GLOF is plotted, which however does not exactly agree with the slope distribution as shown in Figure 8a. This is why the erosion and deposition take place corresponding to a temporally changed local bed slope and sediment concentration of debris flow body as shown in Equation 10. The calculated total hydrograph (sediment and water mixture) at 18 km shows that the peak flow, which characterizes the inundation and damage in downstream areas, is still very high and as high as the peak of the dam breach hydrograph at the lake location. The robustness in hydrograph exists because of accumulated sediment by riverbed erosion and sediment transportation in increased channel capacity by erosion. This is how the calculated results assuming the rigid bed river is different from the realities as described by Osti and Egashira (2009). The total hydrograph at 18 km by the first GLOF event will be compared with the second GLOF surge of Lugge Cho so that the worst case of the inundation of downstream locations can be developed.

In TE and for the simulation of the second GLOF event from the Lugge Cho Lake, the final riverbed profile calculated from the first simulation of GLOF from Thorthormi lake, potential erosion depth (+/-ve) formed during the first GLOF from Thorthormi Lake and a dam breach hydrograph at the Lugge Cho Lake are taken as initial and boundary conditions. The results are presented in Figure 9. The graphs show that the amount of sediment supplied during the second GLOF event at almost every downstream cross-section of the river is very small (Figure 9a and b) in comparison with the first event except for the initial 4-km reach in-between the Thorthormi and Lugge Cho Lakes, which was not considered in the first run simulation. In the 4-km initial reach, debris flow developed significantly but remained at minimum values in downstream sections. However, the result of second GLOF was surprising as the peak discharge of mixture flow  $(Q_T)$ , i.e. sediment and water at 10-km section exceeds 23 000 m3/s (Figure 9c), which is almost double the value of the peak breach flow at the Lugge Cho dam breach site and the peak


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure

Image /page/8/Figure/2 description: The image displays six line graphs, labeled (a) through (f), showing discharge over time at different downstream distances. Each graph plots discharge on the y-axis against time (T) in seconds on the x-axis.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: text

Graph (a) is for a distance of 500m. The y-axis, Qs (m³/sec), ranges from 0 to 4000. The x-axis, T (sec), ranges from 0 to 1000. A sharp peak occurs around T=200 sec, reaching over 3000 m³/sec, followed by a rapid decrease with smaller fluctuations.

Graph (b) is for a distance of 4000m. The y-axis, Qs (m³/sec), ranges from 0 to 5000. The x-axis, T (sec), ranges from 0 to 1000. Multiple sharp peaks appear between T=400 and T=500 sec, with the highest peak reaching approximately 4500 m³/sec.

Graph (c) is for a distance of 8000m. The y-axis, Qs (m³/sec), ranges from 0 to 800. The x-axis, T (sec), ranges from 0 to 1000. A single prominent peak of about 750 m³/sec occurs around T=650 sec, followed by smaller peaks.

Graph (d) is for a distance of 9000m. The y-axis, Qs (m³/sec), ranges from 0 to 600. The x-axis, T (sec), ranges from 0 to 1000. The main peak is around 500 m³/sec at T=700 sec, with a smaller secondary peak following.

Graph (e) is for a distance of 18000m. The y-axis, Qs (m³/sec), ranges from 0 to 50. The x-axis, T (sec), ranges from 0 to 1500. The discharge peaks at approximately 45 m³/sec around T=1050 sec.

Graph (f) is also for a distance of 18000m but shows total discharge, QT (m³/sec), where QT = Qs + Qw. The y-axis ranges from 0 to 10000. The x-axis, T (sec), ranges from 0 to 3000. There is a series of very high, sharp peaks between T=1000 and T=1300 sec, with the maximum peak approaching 10000 m³/sec, followed by a long tail with multiple smaller peaks.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure: Figure 7. (a–e) Calculated sediment discharge graphs at different locations in $T_E$ and (f) Total hydrograph ( $Q_T$ ) at 18 km during the first GLOF event by Thorthormi Cho

Figure 7. (a–e) Calculated sediment discharge graphs at different locations in  $T_E$  and (f) Total hydrograph ( $Q_T$ ) at 18 km during the first GLOF event by Thorthormi Cho


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure

Image /page/8/Figure/4 description: The image contains two line graphs, labeled (a) and (b), plotted on a shared horizontal axis representing "Distance (m)" from 0 to 25000.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: text

Graph (a) shows "Bed-slope (degrees)" on the y-axis, which ranges from 0 to 25. The black line plot is highly variable, with numerous sharp peaks. The bed-slope is generally higher and more volatile from 0 to about 8000m and again from 15000m to 25000m, with several peaks approaching 20 degrees. In the intermediate section, from roughly 8000m to 15000m, the bed-slope is much lower, mostly staying below 5 degrees.

Graph (b) shows "Erosion and Deposition (m)" on the y-axis, ranging from -15 to 15. Positive values indicate deposition, while negative values indicate erosion. The red line plot shows significant fluctuations. From 0 to about 6000m, there are several instances of erosion, reaching down to -10m. A period of net deposition occurs from about 6000m to 11000m, peaking at approximately 5m. This is followed by a major erosional phase from about 11000m to 17000m, where the value drops below -10m. For the remainder of the distance, the plot shows smaller fluctuations around the zero line.


Document: Prediction and assessment of multiple glacial lake outburst floods scenario in Pho Chu River basin, Bhutan
Section: RESULTS AND DISCUSSION
Type: figure
Figure: Figure 8. (a) Bed slope distribution, and (b) erosion and deposition along TE

Figure 8. (a) Bed slope distribution, and (b) erosion and deposition along TE