Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 1. Introduction
Type: table
Table: Table 1 Case study examples of different types of outburst floods from glacial sources.

| Outburst type                         | Example                                                                                | Description                                                                                | References                                                                                |
|---------------------------------------|--------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|--------------------------------------------------------------------------------------------------------------------|
| Glacial Lake Outburst Flood (GLOF) | Dig Tsho, 1985 (Nepal Himalaya)                                                               | Failure triggered by overtopping from ice avalanche-triggered displacement waves. Reconstructed peak discharges of >2000 m3 s-1. Five fatalities, hydroelectric power station destroyed.                                                                                | Vuichard and Zimmerman (1987), Cenderelli and Wohl (2001), Richardson and Reynolds (2000a)                   |
|                                       | Sabai Tsho, 1998 (Nepal Himalaya)                                                             | Moraine destabilisation and failure believed to have been triggered by earthquake. Reconstructed GLOF peak discharge of 10,000 m3 s-1. 4.4 × 105 m3 of sediment deposited within 14 km of breach.                                                                                | Osti and Egashira (2009), Osti et al. (2011)                                                                       |
|                                       | Luggye Tsho, 1994 (Bhutan Himalaya).                                                          | Partial drainage of glacial lake, ~48 × 106 m3 of water drained into the Pho Chhu river, producing a flood wave >2 m high 200 km from the source lake. 23 fatalities and widespread damage to buildings up to 84 km downstream.                                                                                | Watanabe and Rothacher (1994), Richardson and Reynolds (2000b)                                                     |
|                                       | Queen Bess Lake, 1997 (British Columbia)                                                      | Moraine dam overtopped by ice avalanche-triggered displacement wave. 8 × 106 m3 water released. Peak discharges >1000 m3 s-1. Elevated water stage noticeable >100 km from source.                                                                                | Clague and Evans (2000), Kershaw et al. (2005)                                                                     |
| Glacier outburst (Jökulhlaup)      | Grímsvötn lake, 1996 (Vatnajökull, Iceland) Kverkfjöll, Holocene (Vatnajökull, Iceland) | Largest documented Icelandic jökulhlaup. Triggered by subglacial eruption. Peak discharges 4 × 104 m3 s-1, total volume of water released 3.2 km2. Source of some of the largest Icelandic Holocene jokulhlaups. Reconstructed peak discharges of 0.5–10 × 104 m3 s-1. Fluvial erosion of bedrock and geomorphic work comparable to late Pleistocene 'megafloods'. | Guðmundsson et al. (1995), Russell et al. (1997), Björnsson (2002) Carrivick (2007), Carrivick et al. (2004) |
| Glacier-dammed lake outburst       | Indus and Yarkand rivers, (Karakoram Himalaya)                                                | Numerous examples of glacier advance and damming of headwater rivers. Peak discharges believed to exceed 105 m3 s-1, causing significant erosion, sedimentation and secondary slope failure.                                                                                | Hewitt (1982), Hewitt and Liu (2010).                                                                              |
|                                       | S. Tahoma Glacier, 1967– (Mt. Rainier, WA, USA)                                               | Frequent outbursts recorded since 1967. Damage to infrastructure.                                                                                | Walder and Driedger (1994)                                                                                |
|                                       | Altai Mountains (~13 ka BP) (Southern Siberia)                                                | Quaternary ice-dammed lake outbursts producing 'megafloods' with maximum discharges of 10–18 × 106 m3 s-1. Last outburst believed to have occurred ~13 ka BP; peak discharge > 1 × 106 m3 s-1.                                                                                | Rudoy (2002), Carling et al. (2009)                                                                                |
|                                       | Hubbard Glacier, 1986, 2002, (Alaska, USA.)                                                   | Glacier temporarily blocked entrance to Russell Fjord twice in recent history. In 1986, catastrophic failure of ice dam resulted in the release of ~5.4 km3 of water, with peak discharges of up to 1 × 105 m3 s-1.                                                                                | Mayo (1989), Motyka and Truffer (2007), Ritchie et al. (2008)                                                   |

Outburst type
Example
Description
References


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 1. Introduction
Type: text

compromised, and water is released through the newly-formed outflow channel. Depending on factors including the cohesiveness of the dam material, breaching may be rapid, or more prolonged, and will result in either the partial or full breaching of the dam structure. The ultimate outcome is the downstream propagation of an outburst flood wave, which may take the form of a 'clearwater' low-viscosity flow, or, as has been more commonly documented, a high-viscosity, hyperconcentrated (sediment comprising ~20% of flow volume) or debris flow arising from the entrainment of vast quantities of debris sourced from the eroded dam structure and unconsolidated channel and floodplain material (e.g. Lliboutry et al., 1977a; Blown and Church, 1985;

Clague et al., 1985; Vuichard and Zimmerman, 1987; Clague and Evans, 2000; O'Connor et al., 2001; Kershaw et al., 2005).

Our understanding of the conditioning factors required for lake development and expansion has advanced considerably in recent decades, and can be largely attributed to advances in the capabilities of spaceborne sensor technology and Geographic Information Systems (GIS) (e.g. Wessels et al., 2002; Quincey et al., 2005, 2007; Bolch et al., 2008), combined with field-based investigations of the morphology, sedimentology and internal structure of contemporary dams using ground-penetrating radar, self-potential or resistivity techniques (e.g. Pant and Reynolds, 2000; Richardson and Reynolds, 2000a,b; Haeberli

data/('Modelling outburst floods from moraine-dammed glacial lakes', '.pdf')_extraction.md


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 1. Introduction
Type: figure
Figure

Image /page/2/Figure/7 description: A diagram illustrates the process of a glacial lake outburst flood (GLOF) in a mountainous region. On the left, a large glacier, labeled A, terminates in a proglacial lake, labeled a. An arrow points from the glacier into the lake, indicating calving or meltwater input. At the base of the glacier is a label F. Higher in the mountains, another glacier, labeled B, and a landslide, labeled C, are also shown with arrows pointing towards the lake, indicating them as sources of water or displacement waves. The lake is contained by a natural moraine dam, labeled d. An arrow labeled 1 shows water movement within the lake. In the ground beneath the lake, a symbol for seismic activity is labeled G. The dam is shown being breached at point b, with a large arrow labeled 2 indicating the outflow of water. This creates a massive debris flow, labeled D/1, which travels down a valley. A third arrow, labeled 3, shows the direction of the flow towards a small village of four houses situated in the valley downstream. There is also a label c/E within the lake.


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 1. Introduction
Type: text

Fig. 1. Schematic of a hazardous moraine-dammed glacial lake. Potential triggers, conditioning factors, and key 'phases' in a GLOF event are highlighted. Potential triggers include: (A) contact glacier calving; (B) icefall from hanging glaciers; (C) rock/ice/snow avalanches; (D) dam settlement and/or piping; (E) ice-cored moraine degradation; (F) rapid input of water from supra-, en-, or subglacial (including subaqueous) sources; (G) seismicity Conditioning factors for dam failure include (a) large lake volume; (b) low width-to-height dam ratio; (c) degradation of buried ice in the moraine structure; (d) limited dam freeboard. Key stages of a GLOF include (1) propagation of displacement or seiche waves in the lake, and/or piping through the dam; (2) breach initiation and breach formation; (3) propagation of resultant flood wave(s) down-valley. Adapted from Richardson and Reynolds (2000a)

et al., 2001; Reynolds, 2006; Hambrey et al., 2009; Langston et al., 2011; Moore et al., 2011; Reynolds, 2011; Thompson et al., 2012a,b) (Fig. 2), and surveys of expanding supraglacial lake systems (Benn et al., 2000; Richardson and Reynolds, 2000b; Benn et al., 2001; Thompson et al., 2012a) (Fig. 3).

This review considers the various modelling approaches that have been used for the reconstruction of palaeoGLOF (historical, typically ungauged) dynamics, and the prediction of potential future GLOF events. We first provide a detailed overview of the hazard, before considering hazard assessment of the lake basin and the modelling of potential triggering mechanisms. Dam overtopping and breach initiation and growth are then considered, before available hydrodynamic modelling approaches are introduced and discussed. The review concludes with a discussion of the advantages and limitations of various models and modelling approaches, including the identification of key areas for future research.


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 2. Moraine-dammed lakes > 2.1. Neoglacial moraine dams
Type: text

Moraine-dammed glacial lakes are found in the majority of alpine and high-mountain regions, with concentrations in the Andes (e.g. Lliboutry et al., 1977a; Reynolds, 1992; Emmer and Vilímek, 2013), the Hindu–Kush–Himalaya (HKH) arc (e.g. Richardson and Reynolds, 2000a; Mool et al., 2001; Komori, 2008; Bajracharya and Mool, 2009), the Tien Shan (Janský et al., 2010) and western Cordillera of North America (e.g. Clague and Evans, 1994; Evans and Clague, 1994; Clague and Evans, 2000; Kershaw et al., 2005). The majority of lateral and terminal moraine complexes, which impound present-day proglacial lakes were constructed during the 'Little Ice Age'; a globally-synchronous period of glacial advance extending from the 15th century to the end of the 19th century (Grove, 2004).

The main factors dictating the type of moraine dam that exists at a particular location are the longitudinal elevation profile of the parent glacier, or glaciers, and the availability of debris for supraglacial, englacial, or subglacial transport. Short, steep glaciers will respond to mass balance variations by advancing and retreating considerable distances. In contrast, long valley glaciers with shallow longitudinal profiles will respond to changes in mass balance by thickening and thinning, while the snout position remains relatively stable (Richardson and Reynolds, 2000a). Large, wide moraines thus tend to be associated with the latter glacier style, with steep, dynamic glaciers often lacking any significant terminal ridge at all. The mobilisation of supraglacial debris onto the former subglacial surface will result in the formation of 'dump' moraines (Benn and Owen, 2002). Most moraine-dams possess steep proximal and distal

slopes, which may exceed angles of 40°, are typically devoid of any substantial vegetation cover, and are composed of poorly consolidated, unsorted, and uncohesive sediment (Costa and Schuster, 1988) (Fig. 4). Width-to-height ratios are controlled by the volume of material delivered to the glacier snout through the pathways mentioned above, and the length of time the terminus location remains stationary.

2. Moraine-dammed lakes
2.1. Neoglacial moraine dams


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 2. Moraine-dammed lakes > 2.2. Lake formation
Type: text

Provided the moraine is sufficiently consolidated and stable, glacial meltwater will pond in the deglaciated basin between the glacier terminus and moraine. This development pathway typically requires the presence of an overdeepened glacier bed (Frey et al., 2010). In the absence of a glacial overdeepening, the ponding of glacial meltwater may not be effective enough to produce a fully formed morainedammed lake. Depending on the permeability of the moraine, the lake will either continue to increase in volume until overtopping or piping occurs, or its volume will be naturally regulated as water seeps through the structure or over the dam crest (e.g. Lliboutry et al., 1977a; Costa and Schuster, 1988; Rana et al., 2000; Hubbard et al., 2005). In the case of the latter, a stable drainage regime will persist indefinitely if flow discharge is unable to entrain the coarser fraction of morainic material, resulting in natural armouring of the outflow channel (Costa and Schuster, 1988).

Alternatively, in situ glacier downwasting may result from the presence of inverted ablation gradients in the lower reaches as a result of downglacier increases in surface debris cover. This leads to a decrease in driving stresses and glacier velocity and causes, in turn, glacier stagnation (Benn et al., 2001, 2012). This, in turn, promotes the development of supraglacial ponds which, if drainage through englacial or supraglacial conduits is avoided, may coalesce to form a 'proto' moraine-dammed lake (Hochstein et al., 1995; Reynolds, 2000; Sakai et al., 2000; Benn et al., 2001; Wessels et al., 2002; Röhl, 2008; Sakai et al., 2009; Sakai and Fujita, 2010; Benn et al., 2012; Thompson et al., 2012a) (Fig. 3). Lakes that have originated in this way are particularly associated with debris-covered glaciers (Benn et al., 2000; Reynolds, 2000; Benn et al., 2001; Thompson et al., 2012a), as the irregular surface topography and typically low surface gradients of the glacier tongue are conducive to supraglacial lake formation (Reynolds, 1981, 2000; Quincey et al., 2007). Geometrically, moraines that have developed from the surface lowering of glacier tongues with thick supraglacial debris are typically large, complicated complexes with steep outwash fans (see geomorphological and sedimentological analyses in Hambrey et al., 2009, and Benn and Owen, 2002), whereas moraines and outwash fans formed by comparatively 'clean' glaciers are somewhat more subdued (Benn and Owen, 2002).

2. Moraine-dammed lakes
2.2. Lake formation


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 2. Moraine-dammed lakes > 2.2. Lake formation
Type: figure
Figure

Image /page/3/Figure/12 description: A scientific graph showing a cross-section of model resistivity with topography. The vertical axis represents Elevation in meters (m), ranging from approximately 4940 to 5000. The horizontal axis shows distance, with markers at 0, 80, 160, 240, and 320 m. The main part of the graph is a color-coded plot representing resistivity. A color key at the bottom indicates "Resistivity in ohm-metres," with values ranging from 2052 (blue) to 619729 (dark red/purple). The top of the plot is a black line showing the surface topography. Below the surface, a white dashed line is labeled "Top of ice," separating an upper layer of lower resistivity (greens and yellows) from a lower layer of higher resistivity (reds and purples). The high-resistivity areas are labeled "Ice." The graph also notes a "Unit electrode spacing 5 m."


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 2. Moraine-dammed lakes > 2.2. Lake formation
Type: text

Fig. 2. Electrical resistivity profile along a transect across the terminal moraine complex of Imja Glacier, Khumbu Himal, Nepal, revealing the presence of buried ice (modified from fig. 7c, Revnolds. 2006).


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 2. Moraine-dammed lakes > 2.2. Lake formation
Type: figure
Figure

Image /page/4/Picture/2 description: A figure from a scientific publication by M.J. Westoby et al. shows two photographs, labeled A and B, depicting glacial landscapes. Photograph A displays a glacier terminus with a steep ice cliff next to a partially frozen, light-blue proglacial lake. A vertical scale bar indicates the cliff height is 10 meters. The surrounding area is covered in rocky moraine, with snow-capped mountains in the background. Photograph B shows a wider view of a larger system of interconnected glacial lakes filled with floating icebergs. A horizontal scale bar indicates a width of 50 meters across one section of the lake. The landscape is characterized by moraine, patches of snow, and some brown vegetation in the foreground.


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 2. Moraine-dammed lakes > 2.2. Lake formation
Type: text

Fig. 3. The temporal evolution of supraglacial ponds on Ngozumpa Glacier, Khumbu Himal, Nepal; (A) supraglacial pond with calving ice face; (B) coalesced melt ponds and subsequent development of a 'proto' glacial lake.


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 2. Moraine-dammed lakes > 2.3. Trigger mechanism
Type: text

Many documented GLOFs have been initiated by overtopping waves caused by external triggers (e.g. Lliboutry et al., 1977a; Clague and Evans, 2000; Richardson and Reynolds, 2000a; Kershaw et al., 2005). Triggers include (often combined) ice and rock avalanches or landslides (e.g. Vuichard and Zimmerman, 1987; Harrison et al., 2006), or discrete glacier calving events (both sub-aerial and sub-aqueous) (e.g. Lliboutry et al., 1977a; Blown and Church, 1985). Additional triggers include dam settlement, piping, and lateral moraine collapse as a result of seismic activity (e.g. Osti et al., 2011), temporary blockage of an overflow channel (e.g. Huggel et al., 2004; Mergili and Schneider, 2011) or the flotation of submerged dead ice, resulting in water displacement (Richardson and Reynolds, 2000b). A number of conditioning factors may also predispose a particular moraine dam to fail, such as low freeboard, a high height-to-width dam ratio (Huggel et al., 2002a; McKillop and Clague, 2007; Quincey et al., 2007; Emmer and Vilímek, 2013), and sedimentological and structural characteristics (e.g. loosely consolidated, saturated sediment), as well as the presence of degrading permafrost or a massive buried ice core (Watanabe et al., 1995; Richardson and Reynolds, 2000b) (Fig. 2). A consideration of approaches to model the various triggers is presented in Section 3.1.

2. Moraine-dammed lakes
2.3. Trigger mechanism


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling
Type: text

A number of methods can be used to model the various stages or 'components' of a GLOF (Fig. 1), either empirically, analytically, or

numerically. We classify these components according to their physical location and temporality in the GLOF modelling cascade, and define them as follows:

- 1. Trigger mechanism
- 2. Breach initiation and development
- 3. Downstream routing of the outburst flood wave(s)


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.1. Trigger mechanism > 3.1.1. Ice, snow, and rock avalanching
Type: text

The increasing capability of Geographic Information Systems (GIS), coupled with the wide availability and affordability of multi-temporal imagery and topographic data products from space- and airborne platforms has facilitated the production of largely desk-based natural hazard assessments (e.g. Huggel et al., 2002a, 2004; Salzmann et al., 2004; Kääb et al., 2002, 2005; Quincey et al., 2005; Huggel et al., 2005; McKillop and Clague, 2007; Allen et al., 2008). Potential triggering events, such as avalanche or landslide starting zones in close proximity to glacial lakes, can be identified using a relatively straightforward procedures including spectral band segmentation, thresholding, and DEM-derived slope classification, in combination with detailed aerial photography or high-resolution satellite imagery (Margreth and Funk, 1999; Salzmann et al., 2004; Quincey et al., 2005; Huggel et al., 2006; Allen et al., 2008).

The identification of potentially dangerous glaciers or rock slopes, followed by the mapping of potential avalanche run-out tracks, and

3. Approaches to modelling
3.1. Trigger mechanism
3.1.1. Ice, snow, and rock avalanching


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.1. Trigger mechanism > 3.1.1. Ice, snow, and rock avalanching
Type: figure
Figure

Image /page/5/Picture/2 description: A figure from a scientific paper, cited as "M.J. Westoby et al. / Earth-Science Reviews 134 (2014) 137–159", composed of three photographs labeled A, B, and C, showing a glacial landscape.


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.1. Trigger mechanism > 3.1.1. Ice, snow, and rock avalanching
Type: text

Panel A is a wide-angle view of a mountainous, rocky terrain with a glacial lake in the upper right. A large moraine dam, which appears to have been breached, is prominent. A black arrow points to a section of the dam's inner wall. The slopes are covered with scree and patches of snow.

Panel B shows a view from a lower elevation, looking up at a bouldery landscape with a sharp moraine ridge in the middle ground. In the background are snow-covered mountains under a light sky.

Panel C is a close-up view of the side of the moraine dam, with annotations illustrating its structure. An arrow points to the top edge, labeled "Original moraine dam surface". Below this, a bracket indicates a large section of "Exposed morainic material". At the bottom, another bracket labels the accumulated debris as "Post-GLOF stone-fall and slumping". Snow-capped mountains are visible in the background.

**Fig. 4.** Breached moraine dams in the Khumbu Himal, Nepal: (A) Dig Tsho. An ice avalanche, originating from the hanging remnants of Langmoche Glacier, entered the lake. Displacement wave(s) subsequently overtopped the terminal moraine (Vuichard and Zimmerman, 1987). A sizeable breach (centre, foreground) was formed by the escaping floodwaters. Black arrow indicates area shown in C; (B) Chukhung Glacier terminal moraine. For scale, maximum breach top width is –90 m. Little is known about the dam failure dynamics of this GLOF, although it is estimated that approximately 5.5 × 105 m³ of water was impounded before failure, based on reconstructed pre-GLOF dam and lake geometry (M Westoby, unpublished data); (C) Panoramic photograph of exposed sediment in the central section of a moraine dam breach, Dig Tsho, Nepal. Widespread, post-GLOF deposits are present at the base of the exposure. In this example, large boulder- and cobble-sized clasts are supported in a poorly-sorted, unconsolidated sand-gravel matrix. Total section is 150 m in length and 11 m high at the point of annotation.

the identification of potentially hazardous process combinations, such as an avalanche or landslide entering a glacial lake can then form the basis for more detailed investigation (Salzmann et al., 2004). The identification of subtle features such as bedrock tension cracks and jointing or overhanging glacial seracs which may provide clues as to the location of potential rock or ice avalanche starting zones remains challenging, particularly in the absence of very fine-resolution spaceborne or airborne imagery for many areas of interest (e.g. Huggel et al., 2006). GIS-based identification of contemporary or, in light of climate warming, potential future avalanche or landslide starting zones (see, e.g. Frey et al., 2010) remains the most viable approach. Mass movement trajectory modelling based on statistical parameters (e.g. Alean, 1985; Huggel et al., 2004) one-dimensional centre-of-mass models (e.g. Mergili et al., 2012), or more advanced physically based distributed models (e.g. Hungr, 1995; Sampl and Zwinger, 2004) may be used to


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.1. Trigger mechanism > 3.1.1. Ice, snow, and rock avalanching
Type: text

et al . , 2006 ) . GIS - based identification of contemporary or , in light of climate warming , potential future avalanche or landslide starting zones ( see , e . g . Frey et al . , 2010 ) remains the most viable approach . Mass movement trajectory modelling based on statistical parameters ( e . g . Alean , 1985 ; Huggel et al . , 2004 ) one - dimensional centre - of - mass models ( e . g . Mergili et al . , 2012 ) , or more advanced physically based distributed models ( e . g . Hungr , 1995 ; Sampl and Zwinger , 2004 ) may be used to

predict plausible avalanche run-out distances and inundation areas, although advanced two- and three-dimensional models based on computational fluid dynamic (CFD) theory are required if dynamic behaviour such as deformation and lateral spreading of the avalanche or landslide body are to be realistically simulated (e.g. Sampl and Zwinger, 2004; Sailer et al., 2008). Progress in our understanding of the dynamics of rock-ice avalanches has been made in recent years by workers including Schneider et al. (2010), who used a two-dimensional numerical model, RAMMS (Christen et al., 2010), in combination with seismic data recordings to infer a proportional relationship between the latter and the frictional work rate of an avalanche.


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.1. Trigger mechanism > 3.1.2. Glacier calving
Type: text

Prediction of calving rates, or more importantly for hazard assessment, the prediction of volumes of discrete calving events and

characteristics of triggered impulse waves is far from straightforward. Progress in understanding the glaciological (e.g. Benn et al., 2007) and limnological factors governing thermo-erosional notch development (e.g. Röhl, 2006) has improved in recent years, and has provided insights into the prediction of future calving rates under future warming scenarios. Long-term monitoring of calving frequency, including impulse wave heights, may aid prediction of the likely occurrence of waves capable of overtopping terminal moraine structures. Alternatively, an artificial reduction in dam freeboard through manual intervention, specifically lake level lowering (e.g. Grabs and Hanisch, 1993), has been carried out at sites in the Peruvian Andes (e.g. Lliboutry et al., 1977a; Reynolds, 1992, 1998a,b; Reynolds et al., 1998) and Nepal Himalaya (e.g. Reynolds, 1998a,b; Yamada, 1998). As well as reducing hydrostatic pressure in the moraine dam complex, this also serves to increase the minimum wave amplitude required for overtopping, though at the risk of increasing calving activity via decreased ice-tongue support by buoyancy forces, with potentially disastrous consequences (Lliboutry et al., 1977a).

3. Approaches to modelling
3.1. Trigger mechanism
3.1.2. Glacier calving


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.1. Trigger mechanism > 3.1.3. Wave overtopping
Type: text

Many documented moraine dam failures have been initiated by overtopping by waves generated from landslides or ice avalanches (e.g. Lliboutry et al., 1977a; Costa and Schuster, 1988; Clague and Evans, 2000; Richardson and Reynolds, 2000a). Numerous moraine dams, both failed and intact, show evidence of overtopping by displacement waves (Lliboutry et al., 1977a,b; Blown and Church, 1985; Costa and Schuster, 1988; Clague and Evans, 2000; Richardson and Reynolds, 2000a; Hubbard et al., 2005; Kershaw et al., 2005). Whilst these waves might not technically be a trigger for moraine-dam failure in their own right, as a preceding initiation mechanism must have occurred, it is often the erosive power of their run-up and passage across a moraine-dam that may initiate its failure.

Waves generated by sub-aerial mass flows such as landslides or avalanches fall into one of two categories. The first is a solitary displacement wave formed by the 'pushing' of the top level of the water column. The second is classified as a standing wave, or 'seiche', formed when the volume and entry velocity of the external mass is large enough to trigger the mobilisation of the entire water column (Fig. 5). Resultant 'sloshing' of the water in the enclosed moraine basin causes the repeated run-up of water at the lake boundaries and may be highly effective at eroding the dam structure (e.g. Hubbard et al., 2005; Balmforth et al., 2008). Based on geomorphological evidence, Hubbard et al. (2005) undertook a comprehensive reconstruction of seiche dynamics in a moraine-dammed glacial lake in Peru. On 22 April 2002 a rock avalanche deposited 8–20 × 106 m³ of material onto the surface

of the terminus of Glaciar Pucajirca,  $\sim 5 \times 10^6$  m³ of which directly entered moraine-dammed Laguna Safuna Alta and triggered a seiche. The lake had been artificially lowered prior to the event, though still posed a potential failure risk. The initial overtopping wave height is estimated to have exceeded 100 m. The presence of multiple erosion discontinuities on the proximal face of the latero-terminal moraine complex suggests that at least ten seiche waves reached the moraine dam, with at least one wave becoming entirely airborne. Whether more than one wave overtopped the dam structure is unknown. Following two failures in 1951 (Reynolds, 1992), evidence of multiple wave run-ups was also observed by Lliboutry et al. (1977a) at Artesoncocha, another Peruvian moraine-dammed lake.

3. Approaches to modelling
3.1. Trigger mechanism
3.1.3. Wave overtopping


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.1. Trigger mechanism > 3.1.3. Wave overtopping
Type: text

lake had been artificially lowered prior to the event , though still posed a potential failure risk . The initial overtopping wave height is estimated to have exceeded 100 m . The presence of multiple erosion discontinuities on the proximal face of the latero - terminal moraine complex suggests that at least ten seiche waves reached the moraine dam , with at least one wave becoming entirely airborne . Whether more than one wave overtopped the dam structure is unknown . Following two failures in 1951 ( Reynolds , 1992 ) , evidence of multiple wave run - ups was also observed by Lliboutry et al . ( 1977a ) at Artesoncocha , another Peruvian moraine - dammed lake .

The dimensions and propagation rate of a displacement wave are determined by the mass, geometry, velocity (both subaerial and subaqueous), and angle of entry of material into a standing body of water, as well as the lake area and bathymetry (e.g. Fritz et al., 2003a; Walder et al., 2003). For obvious reasons, empirical equations to represent impulse wave characteristics have been derived almost exclusively from physical scale, laboratory-based experiments (e.g. Fritz et al., 2003a,b; Walder et al., 2003; Ataie-Ashtiani and Nik-Khah, 2008; Balmforth et al., 2008, 2009). As a result, such experiments are typically not able to simulate the effects of, for example, observed, complex basin bathymetry on wave propagation and run-up (Synolakis, 1987). Few studies also appear to have taken into consideration the effects of lateral spreading where the source of the landslide or avalanche is the valley flanks (e.g. Risley et al., 2006), though such problems may be overcome by the use of numerical flow models (e.g. Cannata et al., 2012).

From a hazard development perspective, the interaction of a displacement wave, or a series of seiche waves with the moraine dam structure is important. Required, therefore, are estimates of overtopped water volumes and inundation depths with which to force breach erosion and flood-routing models. Of note are recent scaled experiments conducted by Balmforth et al. (2008, 2009), who used a combination of physical and theoretical modelling to assess the impact of large displacement waves on moraine dam structures. Their results demonstrated that initiation of the breaching process ultimately amounts to a competition between erosion and rates of lake drainage and seiche damping. A threshold was identified whereby the amplitude of the initial wave, or rate of erosion, should exceed a critical value for catastrophic dam failure to be initiated (Balmforth et al., 2009).


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.1. Trigger mechanism > 3.1.4. Atmospheric triggers
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Heavy precipitation (e.g. Worni et al., 2012) or a glacial outburst flood from an adjacent ice mass may trigger a rapid increase in lake volume and level and the subsequent enlargement and down-cutting of an

3. Approaches to modelling
3.1. Trigger mechanism
3.1.4. Atmospheric triggers


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.1. Trigger mechanism > 3.1.4. Atmospheric triggers
Type: figure
Figure

Image /page/6/Figure/11 description: A diagram illustrating a cross-section of a proglacial lake system. On the left, a light blue glacier is shown next to a body of water labeled "Proglacial lake". The lake is contained on the right by a brown landform labeled "Moraine dam". Several processes are indicated by numbered arrows. Number 1 points to two small black arrows indicating material falling from the glacier. Number 2 is a large black arrow pointing up from the lake surface near the dam. Number 3 is a curved black arrow going over the top of the moraine dam. Number 4 is a dashed white arrow pointing down into the lake near the dam, indicating sedimentation. Other unlabeled arrows show a solid black arrow pointing down from the glacier into the lake and a dashed white arrow pointing up from the submerged part of the glacier.


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.1. Trigger mechanism > 3.1.4. Atmospheric triggers
Type: text

**Fig. 5.** Dynamics of a standing wave or 'seiche': (1) input of external mass to the lake system (e.g. a large glacier calving event); (2) mobilisation of the entire water column, and; (3) subsequent overtopping of dam structure, followed by (4) continuing, but attenuating, oscillations of the water body, which may or may not result in further overtopping. Black triangle represents the water surface pivot point, around which the standing wave oscillates. Note: figure dimensions for illustrative purposes only and not necessarily to scale.

existing spillway, or the initiation of a new channel (Clague and Evans, 1992, 2000). Quantifying the minimum volume of water required to fill a lake is relatively straightforward if basin perimeter and freeboard are known and seasonal variations in water level are taken into account (e.g. Janský et al., 2010). However, it is difficult to predict the timing and volume of water released, particularly where historical outbursts from the glacier in question have not been documented.


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.1. Trigger mechanism > 3.1.5. Ice-cored moraine degradation
Type: text

Modelling the degradation of ice-cored moraine complexes is challenging. Subsidence caused by the melting of interstitial ice or a massive ice core reduces the structural integrity of a dam, thereby increasing the propensity for failure (Richardson and Reynolds, 2000b). Consequently, dam freeboard is reduced through lowering of the dam crest, thereby reducing the minimum amplitude of displacement waves required to overtop the dam, or reducing the additional volume of glacially- or meteorologically-derived water required to fill the reservoir and overflow the dam. Quantification of moraine surface lowering has been achieved either by in situ monitoring (e.g. Reynolds, 1992; Watanabe et al., 1995; Pant and Reynolds, 2000; Janský et al., 2009), or the assessment of multi-temporal, high-resolution digital terrain models (DTMs) (cf. Irvine-Fynn et al., 2011; Bennett and Evans, 2012; Sawagaki et al., 2013). The disadvantage of the former is that it is typically extremely challenging from a logistical perspective, whilst DTM errors associated with the latter should not exceed the anticipated change in moraine surface elevation over the investigation timescale, which is often small.

3. Approaches to modelling
3.1. Trigger mechanism
3.1.5. Ice-cored moraine degradation


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.1. Trigger mechanism > 3.1.6. Earthquake-triggered dam failure
Type: text

Modelling the response of a glacier-moraine-dammed lake system to an earthquake (Dai et al., 2005; Strasser et al., 2008) is incredibly difficult, not least because of the unpredictability associated with estimating the timing and magnitude of a seismic event (and its seismic signature in the vicinity of a glacial lake, which may be hundreds of kilometres from the earthquake epicentre). Analysis of geological maps may help to identify whether an area that contains morainedammed lakes lies close to active faults, and is therefore at an elevated risk of experiencing earthquake-induced GLOFs. However, by their very nature, many mountain ranges are tectonically active, and so it might be argued that this trigger should be automatically considered as a trigger in the majority of cases. Detailed field investigation in support of geotechnical characterisation of a moraine-dam may provide an indication of its susceptibility to settlement and piping in the event of an earthquake, whilst semi-quantitative analysis of the structural characteristics of calving faces of lake-terminating glaciers from field investigation or remotely sensed imagery may aid prediction of the likelihood of mass failure and the estimation of displacement wave dimensions. However, this is far from an exact science.

3. Approaches to modelling
3.1. Trigger mechanism
3.1.6. Earthquake-triggered dam failure


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.2. Dam-breach > 3.2.1. Breach initiation
Type: text

Sudden or gradual overtopping and inundation, or internal failure as a result of piping and seepage may result in the development of a breach through the moraine dam (Fig. 4). In the case of the former, overtopping water is likely to traverse the width of the dam crest as a uniform sheet (e.g. Kershaw et al., 2005). Alternatively, flow through an existing outlet will be augmented (Costa and Schuster, 1988). Erosion of the dam will occur if the increased boundary shear stresses exerted by the overtopping or channelized flow exceed the cohesive strength of the surface material (Korup and Tweed, 2007). This permits increased discharge from the lake, which in turn may result in runaway incision. Incision will cease when one of the following occurs: i) the base-level of the moraine is reached; ii) a bedrock abutment (or a significant decrease in material erodibility) is encountered; or iii) the outflow

channel becomes sufficiently armoured to halt down-cutting (e.g. Clague and Evans, 1992).

Breaches initiated by internal failure of the dam structure are considerably less well understood, although the underlying principle is that saturation and subsequent seepage of lake water through the dam structure causes the finer fraction of the sediment to be removed, forming 'pipes' and thereby reducing the local physical strength of the dam material (Clague and Evans, 2000; Korup and Tweed, 2007). In addition, thermokarst degradation of buried ice contained within the moraine structures has been observed (Richardson and Reynolds, 2000b). Collapse of subsurface cavities may lead to a lowering of dam crest elevation, thereby increasing the likelihood of an overtopping failure. The transition to open breach formation is initiated through slumping and mechanical failure and collapse of the overlying material.

The detailed simulation of breach formation processes is central to an assessment of the downstream hazards posed by a GLOF, since the shape of the breach hydrograph (Fig. 6, Table 2) will determine, in the first instance, the peak discharge at the flood source. This hydrograph will typically be used as an upstream boundary condition for subsequent flood routing. In order of increasing complexity, models used in published simulations of moraine dam failure events may be generally classed as one of the following: i) empirical regression models; ii) analytical and parametric models; iii) physically-based, numerical models.

3. Approaches to modelling
3.2. Dam-breach
3.2.1. Breach initiation


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.2. Dam-breach > 3.2.2. Empirical dam-breach models
Type: text

Empirical models represent the simplest approach to dam-break modelling (Table 3). These models are not process-based and comprise a single or series of regression relationships derived from test case studies or observed historical dam failures (e.g. Macdonald and Langridge-Monopolis, 1984; Blown and Church, 1985; Costa and Schuster, 1988; Froehlich, 1995; Wahl, 1998). Examples of empirical equations used for dam-break modelling are provided in Wahl (2004), who also undertook a comprehensive investigation of uncertainty estimates surrounding the use of such equations, and also Thornton et al. (2011). Input parameters typically include a combination of the following: dam width, height, lake area and volume. If unknown, lake volume may also be approximated using a separate empirically-derived equation (see e.g. Huggel et al., 2002a,b). Model output typically comprises a single discrete value, such as peak discharge  $(Q_p)$  (e.g. Hagen, 1982; Walder and O'Connor, 1997) or time to peak  $(T_p)$  (e.g. MacDonald and Langridge-Monopolis, 1984; Froehlich, 1995). Such models have been widely used in the glacial hazards literature. One of the earliest examples is presented by Clague and Mathews (1973), who discovered that the magnitude of the peak discharge of a glacial outburst flood arising from the failure of an ice-dammed lake is approximately proportional to the available volume of stored water. An applied example of the use of empirical models is provided by Vuichard and Zimmerman (1986, 1987), who applied the relationships of Hagen (1982), MacDonald and Langridge-Monopolis (1984), and Blown and Church (1985) to

3. Approaches to modelling
3.2. Dam-breach
3.2.2. Empirical dam-breach models


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.2. Dam-breach > 3.2.2. Empirical dam-breach models
Type: figure
Figure

Image /page/7/Figure/15 description: A line graph plots Discharge (Q) on the vertical y-axis against Time (T) on the horizontal x-axis. The graph shows a curve that starts at a low, relatively constant discharge level from time T0 to T2. At time T2, the discharge begins to rise, increasing sharply after T3. The curve reaches its maximum value, the peak discharge labeled Qp, at time T4. After this peak, the discharge decreases until time T5. The area under the main part of the curve, representing the increased flow, is shaded in light blue. Several points on the curve are marked with a star: at time T2 corresponding to discharge Q2, at time T3 corresponding to discharge Q3, at the peak at time T4, and on the descending part of the curve at time T5. Dotted lines connect these marked points to their corresponding values on the axes.


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.2. Dam-breach > 3.2.2. Empirical dam-breach models
Type: text

**Fig. 6.** Generic dam breach outflow hydrograph. Axis annotation is explained in Table 2. Modified from fig. 2.7, Morris et al. (2009).


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.2. Dam-breach > 3.2.2. Empirical dam-breach models
Type: table
Table: Table 2 Description of phases comprising a generic dam breach outflow hydrograph (see Fig. 7) and qualitative description of our ability to model them. Adapted from Morris et al. (2009).

| Time  | Description                                                                                | Modelling ability |
|-------|--------------------------------------------------------------------------------------------------------------------|-------------------|
| T0    | No breach initiation                                                                                | -                 |
| T1    | Start of breach initiation. Seepage over or through dam begins.                                                    | Limited           |
| T1–T2 | Breach initiation phase. Q typically low. May last hours–months (Q2)                                               | Poor              |
| T2–T3 | Critical transition to breach formation. Erosion reaches upstream face of dam, initiating rapid breach growth (Q3) | Limited           |
| T3–T5 | Breach formation. Rapid vertical erosion dominates initially, followed by continued vertical and lateral erosion.  | Poor–moderate     |
| T4    | Peak discharge (Qp)                                                                                | Good              |


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.2. Dam-breach > 3.2.2. Empirical dam-breach models
Type: text

estimate the peak discharge (6–8000  ${\rm m}^3/{\rm s}$ ) of the 1985 Dig Tsho GLOF, Nepal.

However, such relations are limited in their suitability for predictive purposes, as they neglect the inclusion of basic hydraulic principles pertaining to breach initiation and enlargement and are typically derived from a range of failed dam types and settings, including artificial constructs (Walder and O'Connor, 1997). In their appraisal of preexisting empirical relations, Walder and O'Connor (1997) maintained that such relationships were flawed in their assumption that  $Q_n$  may be simply approximated as the product of volume of water released and the resulting drop in lake level, instead recognizing that hydraulic principles and constraints, such as breach erosion rate, are equally as important. Though theoretically more robust than standard empirical equations, this approach assumes that the user is able to quantify breach erosion rates. The impracticalities of quantifying the physical processes at work during breach formation are numerous, and although experimental progress in this field has been made in recent years (e.g. Morris et al., 2007), in practice these parameters are generally unknown and extremely challenging to quantify in the field. Providing the geometric characteristics of the dam structure and attendant lake basin are known, empirical relations represent an expeditious and simple approach to estimating Qp, and, at first glance, would appear suitable for relatively basic hazard assessment. Taking the above into account and without reliable estimates of time to peak flow and consideration of the form of rising and falling limbs of the outflow hydrograph, such data have limited value for the assembly of inundation maps and reach-specific hydrograph and flood attenuation data. However, whilst the derivation of individual hydrographs may be appropriate for reconstructive GLOF modelling efforts, where detailed process analysis and

geomorphological inference might be applied to constrain model boundary conditions and input parameters, the merits of adopting a deterministic approach for predictive GLOF modelling is questionable given the inherent variability of material properties and model boundary conditions. We consider the extent and significance of uncertainty in the GLOF model chain in Section 5.


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.2. Dam-breach > 3.2.3. Analytical and parametric dam-breach models
Type: text

Analytical and parametric models are semi-physically based, given their consideration of simplified physical processes (Morris et al., 2009b). These models incorporate simplified numerical treatments of the physical processes involved during the breach development phase (e.g. Capart, 2013), and typically assume that the rate of breach growth is purely time-dependent. Accordingly, the user is required to enter morphometric boundary conditions including final breach geometry (e.g. base width and side slope angle) and the time required for full formation. The model then proceeds to iteratively calculate the outflow hydrograph as the breach develops. Another assumption is that weir equations can be used to represent flow over the dam. Such equations typically assume the form:

$$Q = Cd L H^{\frac{3}{2}}$$
 (1)

with:

$$H = h_w + \frac{V^2}{2g} \tag{2}$$


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.2. Dam-breach > 3.2.3. Analytical and parametric dam-breach models
Type: table
Table: Table 3 Empirical equations used to estimate peak discharge $(Q_p)$ for natural dam failures. Examples marked with an asterisk (\ ) have been derived entirely from case studies of moraine-dam failure

|                                       | Reference                                | Type     | R2 (if known) | No. case studies |           | Empirical equation                   |
|---------------------------------------|------------------------------------------|----------|------------------|------------------|-----------|--------------------------------------|
|                                       |                                          |          |                  | Real             | Simulated |                                      |
| Height of water equations             | Kirkpatrick (1977)                       | Best fit | 0.790            | 13               | 6         | $Qp = 1.268(Hw + 0.3)2.5$            |
|                                       | US Soil Conservation (1981)              | Envelope | -                | 13               |           | $Qp = 16.6(Hw)1.85$                  |
|                                       | US Bureau of Reclamation (1982)          | Envelope | 0.724            | 21               |           | $Qp = 19.1(Hw)1.85$                  |
|                                       | Singh and Snorrason (1982)               | Best fit | 0.488            |                  | 8         | $Qp = 13.4(Hd)1.89$                  |
|                                       | * Walder and O'Connor (1997)             | Best fit | 0.620            | 9                |           | $Qp = 0.045(V)0.66$                  |
|                                       | Pierce et al. (2010)                     | Best fit | 0.633            | 72               |           | $Qp = 0.784(H)2.668$                 |
|                                       |                                          | Best fit | 0.640            | 72               |           | $Qp = 2.325 ln(H)6.405$              |
| Storage equations                     | Singh and Snorrason (1984)               | Best fit | 0.918            |                  | 8         | $Qp = 1.776(V)0.47$                  |
|                                       | Evans (1986)                             | Best fit | 0.836            | 29               |           | $Qp = 0.72(V)0.53$                   |
|                                       | * Walder and O'Connor (1997)             | Best fit | 0.090            | 9                |           | $Qp = 60.3(V)0.84$                   |
| Height of water and storage equations | Hagen (1982)                             | Envelope | -                | 6                |           | $Qp = 0.54(V Hw)0.5$                 |
|                                       | Macdonald and Langridge-Monopolis (1984) | Best fit | 0.788            | 23               |           | $Qp = 1.154(V Hw)0.412$              |
|                                       |                                          | Envelope | 0.156            | 23               |           | $Qp = 3.85(VwHw)0.411$               |
|                                       | Costa (1985)                             | Best fit | 0.745            | 31               |           | $Qp = 0.763(V Hw)0.42$               |
|                                       | * Costa and Schuster (1988)              | Best fit | 0.780            | 8                |           | $Qp = 0.00013 (PE)0.60$              |
|                                       |                                          | Envelope | -                |                  |           | $Qp = 0.063 (PE)0.42$                |
|                                       | Froehlich (1995)                         | Best fit | 0.934            | 22               |           | $Qp = 0.607(V0.295 Hw1.24)$          |
|                                       | * Walder and O'Connor (1997)             | Best fit | 0.490            | 9                |           | $Qp = 0.19(Hw V)0.47$                |
|                                       | Pierce et al. (2010)                     | Best fit | 0.844            | 87               |           | $Qp = 0.0176(VH)0.606$               |
|                                       |                                          | Best fit | 0.850            | 87               |           | $Qp = 0.038(V0.475H1.09)$            |
| Other                                 | Thornton et al. (2011)                   | Best fit | 0.909            | 14               |           | $Qp = 0.1202(L)1.7856$               |
|                                       |                                          | Best fit | 0.871            | 25               |           | $Qp = 0.863(V0.335H1.833 Wav-0.663)$ |
|                                       |                                          | Best fit | 0.991            | 14               |           | $Qp = 0.012(V0.493H1.205L0.226)$     |

Reference
Type
R2 (if known)
No. case studies
Empirical equation


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.2. Dam-breach > 3.2.3. Analytical and parametric dam-breach models
Type: text

and:

$$V = \frac{Q_a}{A} \tag{3}$$

where Q is flow discharge (m³ s<sup>-1</sup>), Cd is a weir coefficient, L is the width of the weir,  $h_w$  is the hydraulic head of the impounded water above the dam crest, V is the average velocity (m/s) of flow immediately upstream of the weir,  $Q_a$  is the actual flow rate, and A is the cross-sectional channel area (m²). Cd can be determined by dividing  $Q_a$  by the theoretical flow rate,  $Q_t$ . Where one or more input parameters must be approximated, there exists an associated danger of over- or underestimation of dam-breach peak discharge or time to peak (or both), making sensitivity analyses of input parameter combinations an essential undertaking.

Early flood routing models developed by the United States National Weather Service (NWS), including DAMBRK (Fread, 1988a) and FLDWAV (Fread, 1993), utilise the parametric model BREACH (Fread, 1988b) to compute an upstream hydrograph. GLOF modelling studies that have adopted semi-physical breach models include Meon and Schwarz (1993), who used DAMBRK to reconstruct the 1981 GLOF from Zhangzanbo Lake, Nepal, and Shrestha et al. (2010), who used BOSS-DAMBRK (an enhanced version of the original DAMBRK model) to estimate patterns of flood inundation in the Sun Koshi basin, Nepal. Osti and Egashira (2009) used the NWS Simplified Dam Break (SMPDBK) model (see Whetmore et al., 1991), combined with an empirical predictor of failure duration (Froehlich, 1995) to reconstruct the 1998 GLOF from Sabai Tsho glacial lake in the Khumbu Himal, Nepal. Dam-breach modelling undertaken fails to account for dead ice and the heterogeneous nature of the moraine dam structure, and thereby precluding an accurate simulation of the moraine breaching process.


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.2. Dam-breach > 3.2.4. Fully physically based numerical models
Type: text

Complex numerical models are based predominantly on the physical processes observed during failure, including breach flow hydraulics and sediment transport, as well as soil erodibility relationships and structural models to simulate breach widening (e.g. Mohamed et al., 2002; Worni et al., 2012). Purely numerical models have not seen widespread use in the dam-breach literature. This may be attributed in part to their comparatively high computational cost, although with the rapid advent of affordable, high-end desktop computers this should cease to be an issue in the near future. With respect to outbursts from moraine-dammed lakes, the most commonly used numerical models have been NWS DAMBRK (Carling and Glaister, 1987; Fread, 1988a) and BREACH (Fread, 1988b; O'Connor et al., 2001; Bajracharya et al., 2007; Xin et al., 2008; Shrestha et al., 2010), although the adoption of advanced models appears to be becoming more commonplace.


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.3. Glacial Lake Outburst Flood routing
Type: text

Floods from sudden dam failures, often termed 'dam-break outburst floods', are characterised by the often short-lived passage of high-magnitude floodwaters and associated transient flow hydraulics (Marren, 2005; Carrivick, 2010). The rate and style of breach formation, which, in the first instance, determines breach hydrograph form (Fig. 6), exerts a dominant control on flood dynamics in the 'near field', or through immediate downstream reaches. However, with increasing distance from the flood source, valley characteristics including topography (e.g. channel slope, bends, and channel geometry), vegetation (e.g. Lancaster et al., 2003) and sediment availability play a more dominant role (Richardson and Reynolds, 2000a). Floods which entrain vast quantities of uncohesive sediment, sourced from the moraine dam and deposits on the valley floor and sides may become transformed into debris flows (Clague et al., 1985; Evans, 1986; Rickenmann, 1999;

Clague and Evans, 2000). Such flows are capable of achieving far greater runout distances than typical clearwater flows, owing to the increased momentum afforded by the combination of fluid and solid forces (and resultant transition to a non-Newtonian flow regime) and continuing addition of material through bed and bank erosion (Iverson, 1997). However, evidence from historical GLOFs and debris flows suggests such flows are unlikely to form or be sustained on slopes of less than 10–15° (e.g. Clague and Evans, 1994; O'Connor et al., 1994; Clague and Evans, 2000; Procter et al., 2010).


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.3. Glacial Lake Outburst Flood routing > 3.3.1. Palaeohydraulic reconstruction
Type: text

The simplest form of hydraulic modelling involves the use of palaeocompetence and palaeohydraulic techniques to reconstruct flood stage and discharges, typically at the reach scale (e.g. Costa, 1983; Williams, 1984; Kershaw et al., 2005; Bohorquez and Darby, 2008). Using this method, empirical equations are used to relate clast size to hydraulic parameters. When combined with measures of crosssectional channel geometry, longitudinal channel slope, and roughness coefficients of the reach in question (known as the 'slope-area' method), these relationships are capable of providing estimates of peak discharge and flood velocity for 'steady' hydraulic conditions, where it is assumed that hydraulic variables including flow depth, velocity, and discharge may vary at successive points downstream, but are considered as remaining temporally constant (Riggs, 1976; Williams, 1978; Costa, 1983; Baker, 1988; Baker, 2000). In reality, GLOFs are inherently 'unsteady' and are typically characterised as exhibiting spatially and temporally varying flow discharges, velocities, stage and sediment transport conditions.


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.3. Glacial Lake Outburst Flood routing > 3.3.2. GIS-based methods
Type: text

The simplest computational models are GIS-based flow-routing algorithms, which transfer flow sequentially downslope across a digital elevation model (DEM) (e.g. Desmet and Govers, 1996; Liang and Mackay, 2000). Modified single-flow (MSF) models assign flow from a cell to one of its eight neighbours (the 'D8' method), based on the direction of steepest descent (O'Callaghan and Mark, 1984). The obvious limitation of this method is its inability to transfer flow to more than one adjacent cell (Tarboton, 1997). Accordingly, more advanced algorithms are capable of allocating the contents of a given cell to its neighbours (the 'multiple-flow direction' (MF) model, weighted according to slope angle. MSF and MF models also assume a critical slope angle, below which runout will cease (Huggel et al., 2003). Such models have seen an appreciable amount of use in the natural hazards literature, most likely as a result of their general applicability to many types of gravitational flows (e.g. Huggel et al., 2008). Their use in GLOF simulation has been rather more limited. Relevant studies include the work of Huggel et al. (2002b, 2003), who used a combination of MSF and MF modelling to simulate outbursts from a number of lakes in the Swiss Alps and the Peruvian Andes, and Allen et al. (2009), who used MSF modelling to investigate potential ice avalanche-debris flow interactions and flood hazard in Mount Cook National Park, New Zealand.


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.3. Glacial Lake Outburst Flood routing > 3.3.3. One-dimensional numerical modelling
Type: text

Numerical models used for flood reconstructions may be broadly subdivided according to their dimensionality. One-, two- and three-dimensional models (hereafter referred to as 1-, 2-, and 3-D, respectively) are more process- and physically-based than their GIS counterparts, and attempt to solve modified versions of the Navier–Stokes equations (see Batchelor, 1967). 1-D flood routing models are based on a one-dimensional version of the St-Venant, or 'shallow water' equations (SWE) (Barré de St-Venant, 1871):

$$\frac{\partial Q}{\partial x} + \frac{\partial A}{\partial t} = 0 \tag{4}$$

$$\frac{1}{A}\frac{\partial Q}{\partial t} + \frac{1}{A}\frac{\partial}{\partial x}\left(\frac{Q^2}{A}\right) + g\frac{\partial h}{\partial x} - g\left(S_0 - S_f\right) = 0 \tag{5}$$

where Eq. (4) and Eq. (5) are the conservation of mass and conservation of momentum equations respectively. Q is flow discharge, A the cross-section surface area, t is time, g is gravitational acceleration (9.81 m/s), h is the cross-sectional averaged water depth,  $S_0$  is the longitudinal bed slope, and  $S_f$  is the friction slope.


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.3. Glacial Lake Outburst Flood routing > 3.3.3. One-dimensional numerical modelling
Type: text

} \ right ) + g \ frac { \ partial h } { \ partial x } - g \ left ( S_0 - S_f \ right ) = 0 \ tag { 5 } $ $ where Eq . ( 4 ) and Eq . ( 5 ) are the conservation of mass and conservation of momentum equations respectively . Q is flow discharge , A the cross - section surface area , t is time , g is gravitational acceleration ( 9 . 81 m / s ) , h is the cross - sectional averaged water depth , $ S_0 $ is the longitudinal bed slope , and $ S_f $ is the friction slope .

One-dimensional models typically use the step-backwater procedure. This is essentially an automated, numerical adaptation of the slope-area method, with model output comprising energy-balanced water surface profiles (a function of discharge, channel roughness and channel geometry), cross-sectional averaged velocity and discharge (e.g. USACE, 2010). Cross-sectional profiles may be either derived from field surveys, or using a DEM with sufficiently high spatial resolution. Flow may be modelled as either subcritical (wave velocity > flow velocity), supercritical (wave velocity < flow velocity), or as a mixed regime. As well as predefined cross-sections, initial boundary conditions include either an input hydrograph at the uppermost cross-section, or, if unavailable, downstream water profiles calculated either from direct measurement during a flood event, or using palaeo-stage indicators (PSI). The latter approach has typically been used for GLOF reconstruction (e.g. Cenderelli and Wohl, 2003; Kershaw et al., 2005; Bohorquez and Darby, 2008), as high discharges and flow velocities, turbulence, and the inclusion of large clasts renders them virtually impossible to instrument, particularly in upper reaches. Consequently, the few directly measured GLOF hydrographs that exist are from locations tens or hundreds of kilometres downstream where relatively subdued flow dynamics permits instrumentation (Richardson and Reynolds, 2000a). Popular freely or commercially available 1-D models that have been used in the glacial hazards literature include HEC-RAS (Cenderelli and Wohl, 2001, 2003; Alho et al., 2005; Alho and Aaltonen, 2008; Carling et al., 2010; USACE, 2010), and the NWS DAMBRK (Meon and Schwarz, 1993) and FLDWAV models (Bajracharya et al., 2007).


Document: Modelling outburst floods from moraine-dammed glacial lakes
Section: 3. Approaches to modelling > 3.3. Glacial Lake Outburst Flood routing > 3.3.4. Higher-order numerical modelling
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Two-dimensional models are based on depth-averaged versions of the SWE, derived by integrating the Reynolds-averaged Navier-Stokes equations over the depth of the flow (Chanson, 2004; Hervouet, 2007). Advantages of using 2-D models include their ability to simulate multi-directional and multi-channel flows (in contrast, and as their name implies, 1-D models are only capable of routing flow in one direction, i.e. downstream), super-elevation of flow around channel bends, hydraulic jumps (i.e. in-channel transitions between supercritical and subcritical flow regimes) and turbulent eddying. These are dynamic characteristics intrinsic to GLOFs. Two-dimensional models are often capable of simulating non-Newtonian flow dynamics (e.g. Pitman et al., 2013) such as those observed when a GLOF has entrained a volume of debris from the moraine-dam and valley floor to sufficiently alter its flow rheology (see e.g. O'Brien, 2003; Rickenmann et al., 2006; Armanini et al., 2008; Stoltz and Huggel, 2008). Fully 3-D models are capable of solving the full Navier–Stokes equations, resulting in calculation of variations in flow velocity across both the flow width and depth. Despite their representation of the more complex hydraulic and sediment transport characteristics of catastrophic flooding, to date 2-D and 3-D modelling applications in the flow hazards literature are rare (e.g. Worni et al., 2012), with the majority of studies focusing on glacial outburst floods (jökulhlaups) (e.g. Carrivick, 2006, 2007; Alho and Aaltonen, 2008; Bohorquez and Darby, 2008), or mudflows (e.g. Stoltz and Huggel, 2008; Boniello et al., 2010). This paucity of 2-D and 3-D model applications to GLOF simulation most likely stems from the coupling of high computational cost and the lack of DEMs at sufficiently fine resolution in alpine areas to make their use tractable.


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From a modelling perspective, a high degree of uncertainty surrounds the breach formation stage. This is largely attributable to the lack of incorporation of detailed simulations of erosion and breach flow in existing breach models (Wahl, 1998, 2004). During breach formation, rates and patterns of erosion and outflow vary considerably. Recent reviews (Wahl, 1998; Mohamed et al., 2002; Morris et al., 2008, 2009b) highlight the importance of the 'breach initiation' phase, defined as a period of relatively minimal, but increasing discharge, during which dam integrity is yet to be compromised (Fig. 6). Through intervention, runaway breach expansion may be avoided at this stage. Though currently lacking, this information is central to the construction of hazard assessments that aim to quantify flood wave arrival times, discharge, and patterns of inundation, all of which are often subject to a significant degree of uncertainty due to the necessary assumptions made during model parameterisation. For overtopping-type failures, breach initiation is typically manifested as the progressive development of an outflow channel by sheet flow over the dam (for non-cohesive material) or a number of channels on the downstream face of the moraine dam (for cohesive material) (Balmforth et al., 2008; Morris et al., 2008). For cohesive material, subsequent overtopping promotes the progressive enlargement of one or more of these channels through headcutting. The breach initiation phase ceases once runaway incision of an outflow channel begins. The length of this period is controlled by a number of factors, including the water depth and return period of overtopping waves, as well as the erodibility of dam material (e.g. Broich, 2002; Balmforth et al., 2008, 2009). Empirical regression equations capable of providing estimates of time to peak (e.g. MacDonald and Langridge-Monopolis, 1984) have been derived almost exclusive from case study datasets of man-made embankment dams, and provide no estimate of breach initiation time.

The delineation of the breach initiation and breach formation phases for failures initiated by seepage and piping within a natural dam is extremely challenging (Wahl, 2004). With the exception of the work of, for example, Fell et al. (2003) and Wan and Fell (2004), our understanding of breach initiation via internal piping and seepage is rather limited, though it has been established that breach initiation via subsurface pathways are typically lengthy (potentially >24 h) and less evident to the casual observer than for overtopping-type failures. The transition from 'normal', clear-water seepage outflow to cloudy seepage with minimal variation in discharge indicates a developing pipe, and thus the beginning of breach initiation (Wahl, 2004). Catastrophic failure cannot be avoided once the overlying material collapses under its own weight and subsequent erosion in the style of an overtopping failure occurs (Mohamed et al., 2002).

4. Contemporary modelling challenges
4.1. Dam-breaching
4.1.1. Modelling breach initiation


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our understanding of breach initiation via internal piping and seepage is rather limited , though it has been established that breach initiation via subsurface pathways are typically lengthy ( potentially > 24 h ) and less evident to the casual observer than for overtopping - type failures . The transition from ' normal ' , clear - water seepage outflow to cloudy seepage with minimal variation in discharge indicates a developing pipe , and thus the beginning of breach initiation ( Wahl , 2004 ) . Catastrophic failure cannot be avoided once the overlying material collapses under its own weight and subsequent erosion in the style of an overtopping failure occurs ( Mohamed et al . , 2002 ) .

For moraine dams, the presence of interstitial ice, ice lenses, a massive ice core, or permafrost (e.g. Hambrey et al., 2009; Worni et al., 2012), introduce further challenges for modellers. Ice cores represent largely impermeable barriers along (or indeed, in the presence of structural discontinuities in the form of relict crevasses traces, through) which subsurface flows are concentrated and routed, accelerating thermal erosion of the ice and removal of overlying sediment (Watanabe et al., 1995; Richardson and Reynolds, 2000b; Janský et al., 2009). Following assessment of the extent of stagnant ice within moraine dams, achievable almost exclusively through the use of in situ geophysical techniques (e.g. Pant and Reynolds, 2000; Richardson and Reynolds, 2000a,b; Reynolds, 2006, 2011), dams may be treated as composite structures, much like artificial rock fill or clay-cored constructions, for the simulation of overtopping failures. However, there is little published evidence of theoretical, physical or computational experimental parameterisation of dam breach models and the exploration of the implications for failure dynamics.

Presently, the breach initiation phase is poorly represented or entirely neglected in breach models (Morris et al., 2008). As an example, the 'time to failure' boundary condition in DAMBRK (Fread, 1984) is defined as the time taken for final breach dimensions to develop once downstream face erosion and subsequent breaching of the upstream dam face has already been achieved. Thus, any detailed simulation or quantification of initiation time is neglected. However, the standalone NWS-BREACH model (nested within DAMBRK), is capable of providing information on elapsed time associated with the transition from erosion of the downstream to upstream face, which may, with caution, be taken as indicative of a switch from the breach 'initiation' to 'development' phase.


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Significant progress has been made in the last decade through the identification of issues with dam-break model physicality by international working groups, including the CADAM, IMPACT and FLOODsite projects (e.g. Mohamed et al., 2002; Morris et al., 2008, 2009b), as well as the ongoing work of the Dam Safety Interest Group (CEATI, 2012). Although these projects focused predominantly on modelling the failure of artificially-constructed earthen embankment dams, the models considered have seen widespread use in the glacial hazards literature, and so, with careful interpretation, many findings may be equally applicable to moraine dam failure scenarios. Concerning dam-breach formation, a range of issues pertaining to, for example, the mechanics of breach enlargement, side slope evolution and breach flow hydraulics have been identified. Mohamed et al. (2002) highlighted the inability of existing models to accurately simulate the processes of breach widening and enlargement. A constant shape, typically rectangular (e.g. Wetmore and Fread, 1984), trapezoidal (e.g. Cristofano, 1965; Fread, 1984; 1988b) or parabolic (e.g. Harris and Wagner, 1967), and a linear or user-specified rates of development of increase in breach width and depth, are assumed by the majority of existing models (Wahl, 1997). However, logic dictates that subaqueous and subaerial rates of erosion are far from identical, whilst field evidence and physical scale modelling demonstrates that breach side slopes approach near-vertical angles immediately following down-cutting (e.g. Mohamed et al., 2002; Morris et al., 2008). A transition towards a more parabolic or trapezoidal geometry occurs later in the breach formation stage as mass wasting and discrete block failure of the side slopes occurs. The heterogeneous composition and relatively non-cohesive nature of moraine dam material would suggest that maintenance of steep side slopes during breach development is less likely. However, recent large-scale physical dam-break experiments have demonstrated that steep-sided breaches develop for a range of dam compositions, including both non-cohesive and cohesive materials (e.g. Vaskinn et al., 2004).

Following recognition of the limitation of existing models, a number of advanced, commercially- or publicly-available, physically-based numerical breach models have been developed. Notable examples include HR-BREACH (Mohamed et al., 2002; Morris et al., 2008), SIMBA (Temple et al., 2005; Hanson and Hunt, 2007), and BASEMENT (Faeh et al., 2011). As an example of the improved physicality and dimensionality afforded by the use of such models, in combination with standard treatments of hydraulics, sediment transport and soil mechanics, HR-BREACH is capable of iteratively adjusting breach shape through the incorporation of an improved methodology for modelling lateral breach expansion through the simulation of both continuous erosion and discrete mass failure (Mohamed et al., 2002). With the exception of the work of Worni et al. (2012), advanced dam breach models have not been applied to the moraine dam failure problem, but have the potential to vastly improve our understanding of failure dynamics through improved physical representation of complex failure processes and outflow hydrodynamics.

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4.1. Dam-breaching
4.1.2. Breach enlargement


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Another key parameter, also often overlooked, is the erodibility of dam material (Hanson and Cook, 2004; Hanson and Hunt, 2007;

Morris et al., 2008). Sediment transport equations used within the majority of breach models consider the removal of dam material as a function of applied shear stress, water velocity, and particle diameter, which are unrepresentative of the true variables that dictate erodibility (Morris et al., 2008). Dam material texture (including soil cohesivity), compaction moisture content and compaction energy exert a profound influence over erodibility, and, along with dam geometry, determine headcut migration rates during breach initiation. Indeed, small changes in moisture content or compaction have been shown to result in orderof-magnitude changes in erodibility (Hanson and Hunt, 2007; Morris et al., 2008). Ideally, in situ investigation of the above variables is desirable, however, due to logistical challenges these are often estimated. Quantification of erodibility coefficients for materials typically used for the construction of embankment dams (soil/clay mixtures) has been attempted (Hanson and Hunt, 2007), though such material differs significantly from glacial moraine, which is typically non-cohesive, poorly consolidated, composed of a heterogeneous mixture of sand, gravel, cobbles, and boulders (e.g. Benn and Owen, 2002) (Fig. 4), and may contain discontinuous or continuous permafrost and cores of massive, relict ice (e.g. Hanisch et al., 1998; Reynolds, 2000; Richardson and Reynolds, 2000a; Delisle et al., 2003; Hambrey et al., 2009).

The potential presence of a range of permafrost concentrations and structures represents a significant modelling challenge. There is no evidence in the literature of experimental or field-based investigation into the erodibility of glacial moraine dam material, including the influence of ice content on breach development, having been undertaken to date. Recent research into the degradation of frozen river-bank sediment reveals complex degradational patterns between thawed, frozen and massive ice-cored material (Dupeyrat et al., 2011). Dupeyrat et al. (2011) discovered that the resistance of pure ice to thermal erosion by flowing water was greater than that of surrounding permafrost with lower ice content. Following the ablation of interstitial ice, cohesion and therefore substrate shear strength is vastly reduced, facilitating the rapid removal of sediment (Gatto, 1995). Equally, the importance of discrete mechanical instead of thermal erosion mechanisms increases with the bulk density of permafrost (Lick and McNeil, 2001; Dupeyrat et al., 2011). A critical ice content may therefore be identified, above which mechanical failure dominates, and below which progressive ablation and sediment removal is the main mode of erosion. At present, even the most advanced dam breach models are unable to account for the presence of permafrost or massive, 'pure' ice in the dam structure, though this may indeed prove to be a controlling factor on rates of breach development and should be a priority for future experimental and numerical modelling research.

4. Contemporary modelling challenges
4.1. Dam-breaching
4.1.3. Permafrost and massive ice


Document: Modelling outburst floods from moraine-dammed glacial lakes
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Most retrodictive or predictive GLOF modelling efforts have considered breach enlargement and the downstream routing of the escaping floodwaters as a single event. However, a number of historical GLOFs have been identified as multiple-phase events (e.g. Clague et al., 1985; Vuichard and Zimmerman, 1986; Clague and Evans, 2000; Kershaw et al., 2005). Depending on displaced water volume and the degree of flow attenuation as the moraine crest is traversed, single or multiple overtopping wave may represent self-contained flood events, regardless of whether this eventually leads to breach formation (e.g. Hubbard et al., 2005; Kershaw et al., 2005). To simulate this phenomenon, the modeller is first required to estimate the overtopping flood hydrograph for entry as an upstream boundary condition. Since contemporary dam breach or flood routing models are generally incapable of performing such calculations, overtopping volume and duration must be calculated independently using known (or estimated) input mass, basin and dam parameters applied to the empirically-derived equations of, for example, Muller (1995) or Walder et al. (2003). Results may then be used to force model applications to determine the flood characteristics of the initial escaping floodwaters. Similarly, the temporary armouring or blockage of the moraine breach by discrete mass failure of the breach sidewalls or blocks of ice (e.g. Worni et al., 2012) may contribute to the intermittency and 'pulsing' of the escaping floodwaters, such as that documented by Vuichard and Zimmerman (1986) for the 1985 Dig Tsho GLOF. Whilst physically based numerical dambreach models are capable of simulating discrete mass failure and the subsequent removal of this material by the breach flow, numerical reconstruction of the intermittency of breach expansion and hydrograph development remains challenging in a modelling environment which is typically unable to numerically resolve individual clasts and boulders.

A further complication for the preservation of flow hydraulics and sediment transport is the nature of model coupling. The NWS DAMBRK and FLDWAV codes comprise both dam breach and flow routing algorithms (Fread, 1993). Similarly, HEC-RAS permits the breaching of an inline structure, either at the source of the flood (e.g. at the exit of a reservoir or storage area), or at a user-defined point along the flow path (USACE, 2010). However, both approaches use parametric-type breaching models, which, for reasons discussed above, represent rather simplified approximations of the breaching process. More traditionally, standalone breach models have been used to produce the initial outflow hydrograph, which is then considered as an upstream input to subsequent hydrodynamic modelling efforts. At present, such an approach is standard practice, though it has implications for the conservation of flow momentum at the dam foundation-valley floor boundary. Here, flow accelerates under the combination of the effects of gravity and the pressure of the overlying water contained in the reservoir (the 'pressure head') (Carrivick, 2010). In a fully-coupled, higher order model, short-lived flow acceleration, and a resulting zone of intensely turbulent flow at the dam base would be preserved. However, such effects are not considered when breaching and flood routing models are decoupled. Consequently, near-dam flow velocities calculated using this method are likely to be underestimated.


Document: Modelling outburst floods from moraine-dammed glacial lakes
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though it has implications for the conservation of flow momentum at the dam foundation - valley floor boundary . Here , flow accelerates under the combination of the effects of gravity and the pressure of the overlying water contained in the reservoir ( the ' pressure head ' ) ( Carrivick , 2010 ) . In a fully - coupled , higher order model , short - lived flow acceleration , and a resulting zone of intensely turbulent flow at the dam base would be preserved . However , such effects are not considered when breaching and flood routing models are decoupled . Consequently , near - dam flow velocities calculated using this method are likely to be underestimated .

A related and equally important consideration is the conservation of sediment outflow dynamics at the exit of the breach, and use as input to hydrodynamic modelling. Many studies have largely failed to acknowledge or account for this, yet from a geomorphological perspective, and in combination with outflow discharge and flow hydraulics, the erosion and subsequent transport of morainic material from the breach controls the transience of patterns of erosion, deposition, and flow rheology (e.g. Kershaw et al., 2005; Worni et al., 2012), particularly in near-field locales. An example of a simulated sediment outflow time series for a Himalayan GLOF, produced using HR-BREACH, is displayed in Fig. 7. In


Document: Modelling outburst floods from moraine-dammed glacial lakes
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Figure

Image /page/12/Figure/5 description: A line graph with two y-axes plots sediment outflow and discharge against time. The x-axis is labeled 'T (mins)' and ranges from 0 to 200. The left y-axis is labeled 'Sediment outflow (Qs; m³ s⁻¹)' and ranges from 0 to 140. The right y-axis is labeled 'Discharge (Q; m³ s⁻¹)' and ranges from 0 to 1800. A jagged black line, representing sediment outflow, starts at zero, rises with significant fluctuations to a peak of approximately 100 m³/s around 90-100 minutes, and then generally decreases. Underneath the black line are thin gray vertical lines representing high-frequency data. A smooth, bell-shaped light blue curve, representing discharge, starts at zero, peaks at approximately 1700 m³/s around 135 minutes, and returns to zero around 180 minutes. The peak of the sediment outflow occurs before the peak of the discharge.


Document: Modelling outburst floods from moraine-dammed glacial lakes
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**Fig. 7.** Rates of sediment evacuation ( $Q_s$ ) during moraine breaching; in this instance an experimental reconstruction of the 1985 Dig Tsho event using HR-BREACH. Sediment outflow fluctuates significantly between successive 10 second time-steps, as a result of periodic discrete breach wall failure events, which represent considerable, though short lived 'pulses' of sediment to the developing outflow channel. It is worth noting that peak sediment outflow precedes peak discharge (Note: end of sediment time series data corresponds with cessation of breach outflow).

this particular instance, sediment evacuation rates were approximated by calculating the volumetric change of the breach between successive 10 second time steps over the full duration of the simulation. The significant variability in sediment outflow over extremely short time scales (often between individual time steps) is the result of instantaneous, discrete mass failure events which represent the main lateral expansion mechanism of the breach. Such behaviour would most likely be manifest in a hydrodynamic simulation of downstream flood propagation as a series of short-lived sediment 'pulses'. The rheological, hydraulic, and geomorphological effects of temporally-varying flow sediment concentrations are discussed in further detail in Section 4.2.3.


Document: Modelling outburst floods from moraine-dammed glacial lakes
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As with other sudden onset, sediment-laden outburst floods (e.g. Carrivick et al., 2010), GLOFs possess highly transient and spatially-varying flow regimes. From a modelling perspective, this introduces a range of challenges, including, but not limited to; an often rapid increase in discharge, high flow velocities and rapidly expansive patterns of inundation; the propagation of a translatory shock wave over initially 'dry' terrain; highly turbulent, typically overbank flow, the occurrence of flow super-elevation at sharp channel bends (often triggering secondary failure of colluvial slopes), and highly transitory flow rheology, which exerts a major control over intra- and post-flood channel reworking.

During breach development, escaping floodwaters accelerate under the combination of the effects of gravity and the pressure of the overlying water contained in the reservoir (Stansby et al., 1998). This acceleration is typically short-lived, as floodwaters descending the distal face of the moraine dam encounter comparatively shallow gradients in the proglacial environment. Given a wide, largely unconfined proximal zone, flow will expand laterally as sheet flow, with depth and velocity gradually decreasing with distance from the flood source (Cenderelli and Wohl, 2003; Hogg and Pritchard, 2004). Alternatively, the continuation of steep near-field topography will promote the convergence of floodwaters, producing a higher velocity initial flood wave. As the flood wave propagates downstream, time-varying flow discharges and depths, combining to determine the overall degree of inundation, will be dictated by the breach outflow hydrograph and topographic complexity.

4. Contemporary modelling challenges
4.2. Hydrodynamic modelling
4.2.2. Complex flow hydraulics


Document: Modelling outburst floods from moraine-dammed glacial lakes
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the distal face of the moraine dam encounter comparatively shallow gradients in the proglacial environment . Given a wide , largely unconfined proximal zone , flow will expand laterally as sheet flow , with depth and velocity gradually decreasing with distance from the flood source ( Cenderelli and Wohl , 2003 ; Hogg and Pritchard , 2004 ) . Alternatively , the continuation of steep near - field topography will promote the convergence of floodwaters , producing a higher velocity initial flood wave . As the flood wave propagates downstream , time - varying flow discharges and depths , combining to determine the overall degree of inundation , will be dictated by the breach outflow hydrograph and topographic complexity .

One-dimensional hydrodynamic models are unable to simulate many key characteristics of GLOFs. Energy losses through the effects of boundary friction and turbulent eddying is handled explicitly in 2-D and 3-D flow models, though are accounted for in 1-D models through representations of channel conveyance. This is typically undertaken through manual calibration of roughness coefficients, such as Manning's n, in order to produce optimal, or 'best-fit' water surface profiles to palaeo-stage evidence, or at-a-point hydrographs which closely mirror available observed data (usually unobtainable) (e.g. Cenderelli and Wohl, 2001; Bohorquez and Darby, 2008). No studies currently exist which directly compare the application of 1-D and 2-D hydraulic models to the GLOF phenomenon. However, analogous research has been undertaken for glacial outburst floods, including the work of Alho and Aaltonen (2008) and Bohorquez and Darby (2008). The former found that, for unsteady outburst flow simulations across a relatively wide, shallow Icelandic sandur, predicted inundation extents were broadly comparable, with the greatest discrepancies occurring when flow encountered a sinusoidal gorge (Alho and Aaltonen, 2008). On the face of it, and with careful calibration, these findings appear to encourage the use of expeditious, computationally undemanding 1-D models, though *sandar* are often far less topographically complex than steep, high relief and tortuous alpine channels. However, Bohorquez and Darby (2008) found that a 1-D model compared reasonably to a 2-D approach for a glacial outburst flood in a high mountain, alpine setting. Averaged discharge estimates produced using 1-D modelling were higher than equivalent data obtained through 2-D modelling (429- $557 \text{ m}^3 \text{ s}^{-1}$  and  $358-454 \text{ m}^3 \text{ s}^{-1}$  for 1-D and 2-D models, respectively),


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and tortuous alpine channels . However , Bohorquez and Darby ( 2008 ) found that a 1 - D model compared reasonably to a 2 - D approach for a glacial outburst flood in a high mountain , alpine setting . Averaged discharge estimates produced using 1 - D modelling were higher than equivalent data obtained through 2 - D modelling ( 429 - $ 557 \ text { m } ^ 3 \ text { s } ^ { - 1 } $ and $ 358 - 454 \ text { m } ^ 3 \ text { s } ^ { - 1 } $ for 1 - D and 2 - D models , respectively ) ,

attributable to the reconstruction of a recirculation zone in the 2-D model, which the 1-D model was unable to reproduce due to its inherent unidirectional treatment of flow direction (Bohorquez and Darby, 2008). This particular example was undertaken over a relatively short distance (<1 km), and for an outburst event with a peak discharge an order of magnitude lower than many documented GLOFs. The natural question arising from the above therefore becomes: how do spatio-temporal fluctuations in GLOF dynamics, including the timing and maximum extent of flood inundation, vary with model dimensionality? With the increasing use of advanced hydraulic codes, a comprehensive appraisal of 1-D, 2-D and 3-D approaches to GLOF prediction is a fundamental research priority, and will be of key interest to hazard assessment and disaster mitigation bodies who are considering the use of more advanced codes.

As far as possible, and regardless of model dimensionality, particular attention should be given to the numerical discretisation of the flow path in a sufficient level of detail (Fig. 8). A sufficiently detailed topographic representation of the flow path is central to the production of meaningful, robust estimates of flood duration, discharge, velocity, and inundation extent, and is a prerequisite for the use of 2-D and 3-D hydrodynamic models. This is of particular importance in upper reaches, where, for a range of hydrograph forms, flood dynamics may vary significantly. However, results of the intercomparison of coarse

(e.g. SRTM) versus fine (e.g. LiDAR) topographic data for flood inundation modelling (e.g. Sanders, 2007) have revealed that coarse-resolution elevation data possess remarkable value, particularly for rapid, 'first-pass' assessments. Similarly, Huggel et al. (2008) discovered that coarse SRTM and ASTER terrain data, in combination with GIS-based flood routing models, possess remarkable value for providing first-order hazard assessments of volcanically triggered lahars.


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where , for a range of hydrograph forms , flood dynamics may vary significantly . However , results of the intercomparison of coarse ( e . g . SRTM ) versus fine ( e . g . LiDAR ) topographic data for flood inundation modelling ( e . g . Sanders , 2007 ) have revealed that coarse - resolution elevation data possess remarkable value , particularly for rapid , ' first - pass ' assessments . Similarly , Huggel et al . ( 2008 ) discovered that coarse SRTM and ASTER terrain data , in combination with GIS - based flood routing models , possess remarkable value for providing first - order hazard assessments of volcanically triggered lahars .

The increasing availability of affordable, high-specification desktop computing resources means that the reconstruction and adoption of detailed floodplain topography (and higher order hydrodynamic models) is becoming increasingly viable (e.g. Alho and Aaltonen, 2008; Carrivick et al., 2010). However, the acquisition of fine-resolution topographic datasets is often significantly hindered in many remote, inaccessible, high-altitude regions due to logistical impracticalities. Recent advances in the development and provision of free, publicly-available and user-friendly photogrammetric methods (e.g. Westoby et al., 2012), and the increasing affordability of low-altitude tethered (e.g. Boike and Yoshikawa, 2003; Smith et al., 2009; Vericat et al., 2009) and autonomous surveying platforms (e.g. Lejot et al., 2007; Niethammer et al., 2012) are steadily making the production of high-resolution topographic data products for (geo)morphological analysis and grid-based representation of alpine valley floor topography more practical.