New method for assessing the potential hazardousness of glacial lakes in the Cordillera Blanca , Peru

Introduction Conclusions References

objectivity; (c) principle of repeatability; and (d) principle of multiple results.Potential hazardousness is assessed based on a combination of decision trees for clarity and numerical calculation for objectivity.A total of seventeen assessed characteristics are used, of which seven have yet to be used in this context before.Also, several ratios and calculations are defined for the first time.We assume that it is not relevant to represent the overall potential hazardousness of a particular lake by one result (number), thus the potential hazardousness is described in the presented method by five separate results (representing five different glacial lake outburst flood scenarios).These are potentials for: (a) dam overtopping resulting from a dynamic slope movement into the lake; (b) dam overtopping following the flood wave originating in a lake situated upstream; (c) dam failure resulting from a dynamic slope movement into the lake; (d) dam failure following the flood wave originating in a lake situated upstream; and (e) dam failure following a heavy earthquake.All of these potentials theoretically range from 0 to 1.The presented method was verified on the basis of assessing the pre-flood conditions of seven lakes which have produced ten glacial lake outburst floods in the past and ten lakes which have not.A comparison of these results showed that the presented method successfully identifies the potentially hazardous lakes.

Phenomenon of GLOFs and the Cordillera Blanca
Glacial lakes of all types represent a significant threat for the inhabitants of highmountain regions worldwide (e.g.Clague et al., 2012), including the most heavily glacierised tropical range of the world -the Cordillera Blanca of Peru (Vilímek et al., 2005).A sudden release of retained water causes floods, so-called "glacial lake outburst floods" -GLOFs.These extreme hydrological processes are characterised by discharges several times higher than the discharges reached during "classical" hydrometeorological floods (e.g.Cenderelli and Wohl, 2001;Costa and Schuster, 1988).From the geomorphological point of view, these are one of the most significant fluvial processes influencing glacial valleys in the period of deglaciation in highmountain regions (Richardson and Reynolds, 2000).
Since the end of the Little Ice Age, whose second peak culminated in the Cordillera Blanca in the 19th Century (Solomina et al., 2007;Thomson et al., 2000), catastrophic GLOFs originating from moraine-dammed or bedrock-dammed lakes have claimed thousands of lives and caused considerable damage within the region of the Cordillera Blanca (e.g.Ames and Francou, 1995;Carey et al., 2012;Lliboutry et al., 1977;Zapata, 2002).Many of the largest lakes have been remediated since the early 1950s (Carey, 2005), however the number of outburst floods has increased over the last decade.This fact is connected to the ongoing progressive deglaciation and to the associated increase in the overall number of lakes within the Cordillera Blanca (Emmer et al., 2014).Besides the formation and rapid evolution of new potentially hazardous lakes, the volume of already existing proglacial lakes often increases due to continuing glacier retreat beneath the water level or by lake deepening caused by melting of ice cores incorporated in submerged basal moraine (Vilímek et al., 2005).The greater the volume of water retained in the lake, the greater the volume of water available for potential flooding, depending on the cause and mechanism of water release.Repeated Introduction

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Full bathymetric measurement is thus quite important for registering the dynamic evolution of a particular lake.
There are several causes and mechanisms of GLOFs (e.g.Clague and Evans, 2000;Richardson and Reynolds, 2000).Dynamic slope movements into the lake (icefall, landslide, or rockfall) producing a displacement wave, which may overtop or break the lake dam (depending on the particular lake type), are the main cause of GLOFs within the region of the Cordillera Blanca (Emmer and Cochachin, 2013).GLOFs following large earthquakes and GLOFs occurring when a flood wave originating from a lake situated upstream reaches a downstream situated lake were recorded in this region (Lliboutry et al., 1977;Zapata, 2002).It is clear that the occurrence of GLOFs is a highly complex question, which, besides the lake and dam settings, is closely connected with the wider settings of the lake's surroundings (e.g.glaciological setting of the mother glacier, slope stability of moraines surrounding the lake, etc.).Assessing the possibility of GLOF occurrence (potential hazardousness of glacial lake) is thus quite a challenging scientific problem, which requires an interdisciplinary approach as well as cooperation.

Previous research and methods for assessing the potential hazardousness of glacial lakes
"Potential hazardousness" relating to GLOFs is understood in this article to mean the possibility of a sudden release of water following dam failure or overtopping.
Analogically, the assessment of potential hazardousness is interpreted as being the estimation of the likelihood of a sudden release of water from a given lake.Therefore, we do not deal with the magnitude (maximal discharge) of a potential flood in any way.Generally, there are three types of glacial lakes, distinguished according to the dam material: moraine-dammed, bedrock-dammed and ice-dammed.In this article, icedammed lakes are excluded because they do not reach significant volumes within the Cordillera Blanca and thus do not represent a threat and there is no need to take them into the account in this context.The way that the water is released depends on Introduction

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Full the lake type: both dam failure and dam overtopping are possible scenarios in the case of moraine-dammed lakes, while dam overtopping is the only possible scenario in the case of bedrock-dammed lakes.Thus, assessing the potential hazardousness of bedrock-dammed lakes requires the same procedure as assessing the potential hazardousness of moraine-dammed lakes with the difference being that a dam stability assessment is not required for bedrock-dammed lakes, as the dam is always considered to be stable.
Several methods for assessing the potential hazardousness of glacial lakes can be found in the literature.These methods distinguish themselves by type of method construction, number and selection of assessed characteristics, required input data, and rate of subjectivity.Some of them are regionally-focused and some are designed to be adaptable (see Table 1).The only method focused directly on the region of the Cordillera Blanca was presented by Reynolds (2003).Nevertheless, as we have shown in our previous research, this method is designed as a case study, which is based on a subjective expert evaluation of selected lakes (glaciers) and does not provide any coherent methodological concept or complex results (Emmer and Vilímek, 2013).The demands on the input data and the rate of subjectivity of methods are generally considered as the fundamental obstructions to their repeated use.The methods presented by McKillop and Clague (2007a, b), Wang et al. (2011Wang et al. ( , 2012) ) limit subjectivity by determining the thresholds of all of the assessed characteristics.These methods are regionally-focused on different mountain environments and they are not suitable for use within the Cordillera Blanca (Emmer and Vilímek, 2013).

Reasons and objectives of the study
We have the following reasons for this study: firstly, as shown in our previous research -existing methods are not wholly suitable for use within the Cordillera Blanca from the perspective of the assessed characteristics and the account of regional specifics (especially the share and representation of various triggers of GLOFs, climate settings).Secondly, the majority of these methods are at least partly subjective (based on Introduction

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Full an expert assessment without giving any thresholds), thus different observers may reach different results even when the same input data are used.Repeated use is thus considerably limited and we consider this to be the fundamental drawback of the present methods as well as a research deficit.Due to the above-mentioned reasons, the main objective of this work is to provide a comprehensive and easily repeatable methodological concept for the objective assessment of the potential hazardousness of glacial lakes within the Cordillera Blanca, with regard to the regional specifics of GLOFs in this region.The impacts of glacial lake outburst floods cannot ever been completely eliminated; nevertheless, reliable assessment of the potential hazardousness is a necessary step in the spatialand cost-effective flood hazard and consequently risk management and mitigation, therefore it is of great importance.

Creation of new method
The presented method is designed to meet four principles which were consider as being crucial based on an analysis of the drawbacks of the existing methods (Emmer and Vilímek, 2013).Firstly, the principle of regional focus -the causes and mechanisms of GLOFs within the Cordillera Blanca significantly differ from GLOFs in other glacierised mountain ranges worldwide (Emmer and Cochachin, 2013) and an account of the regional specifics is thus essential for a relevant assessment of the potential hazardousness.Secondly, the principle of objectivity, which eliminates all doubts during assessments performed by different assessors (the same input data should provide the same results).The principle of objectivity directly corresponds with the third principle of repeatability, which along with the objectivity is subordinated to the availability of the required input data.The fourth principle is the principle of multiple results for different GLOF scenarios.Multiple results provide a more detailed view of the potential hazardousness of an assessed lake and also allowed any gaps in the availability of the input data to be filled.If it is not possible to gain any of Introduction

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Full the required characteristics (and thus calculate the result for a particular scenario), the other results may still be calculated.The principle of multiple results also allows individual characteristics important in each scenario to be targeted.Creation of a new method for assessing the potential hazardousness of glacial lakes generally requires four stages: (1) selection of the type of construction of the method; (2) selection of the appropriate characteristics to be assessed (this stage includes analysis of regional specifics and also subordination to the data availability); (3) determination of thresholds and weightings of the assessed characteristics (it is essential to determine the thresholds (critical values) because of the objectivity of the results and repeatability of the method used); and (4) method verification.

Type of construction of the method
Each method for assessing the potential hazardousness of glacial lakes usually has its own specific construction.Generally, we can distinguish between: pointsbased methods, calculation-based methods, decision tree-based methods, matrixbased methods and their combinations.A combination of decision trees for clear illustrative representation of the assessment procedures and calculations for objectivity and simple repeatability was used in the presented method.
Recorded mechanisms of GLOFs within the Cordillera Blanca of Peru (Emmer and Cochachin, 2013) have been shown to be dam overtopping or dam failure (only in case of moraine-dammed lakes), both following various triggers.Therefore, we feel it is necessary to strictly distinguish between these two dissimilar mechanisms in the potential hazardousness assessment, because the processes affecting the characteristics and also volumes of released water significantly differ.Dam overtopping within the Cordillera Blanca has been described as a result of: (a) dynamic slope movement into the lake; or (b) flood wave from a lake situated upstream.Dam failures have been described as a result of: (a) dynamic slope movement into the lake; (b) flood wave from a lake situated upstream; or (c) heavy earthquake.Introduction

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Full We feel it is not meaningful to describe the overall potential hazardousness of a particular lake with the use of a single number, as has been done by many authors before.The presented method thus assesses the potentials for the five above-mentioned scenarios separately, whereby providing five separate results.These results are designed as a product of two or three components for each scenario (Table 2).Richardson and Reynolds (2000) showed that it is necessary to include two components: (a) dam stability; and (b) potential for initializing event.This more or less corresponds to the components presented in this method.It is clear that some of the scenarios include similar components, e.g. both Scenario 1 and Scenario 3 include the components "potential for dynamic slope movement into the lake" and "potential for dam overtopping by displacement wave"; however, Scenario 3 also includes the component "dam erodibility".
The obtained results theoretically range from 0 to 1 for each component and thus also from 0 (zero potential) to 1 (maximal potential) for each scenario.Naturally, this allows for both the identification of the most hazardous lakes and the most likely scenario of the GLOF for a particular lake (scenario with the highest potential).

Assessed characteristics and their thresholds
According to previous research (Emmer and Cochachin, 2013;Emmer and Vilímek, 2013), five essential groups of characteristics which need to be taken into account in a regionally based method for assessing the potential hazardousness of glacial lakes within the Cordillera Blanca were estimated.These are groups of characteristics related to: (a) the possibility of dynamic slope movement into the lake; (b) the distinction between a natural dam and a dam with remedial works (more generally dam stability); (c) the dam freeboard (ratio of dam freeboard); (d) the possibility of a flood wave from a lake situated upstream; and (e) the possibility of a dam rupture following a large earthquake.
Individually assessed characteristics in the new method (requiring input data) were chosen to meet the following criteria: (1) they fit into the five above-mentioned groups Introduction

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Full of characteristics; and (2) they are subordinated to data availability.Some of the characteristics were repeated in several of the scenarios (e.g.dam freeboard for Scenarios 1-4) and some are specific for an individual scenario (e.g.piping for Scenario 5).Most of the characteristics have already been mentioned in previous studies but we have also defined seven characteristics which have not been mentioned in this context before (Table 3).
Objective determination of thresholds is quite a delicate scientific problem, on the other hand it is highly desirable to determine all of the thresholds in order to eliminate the subjective component (presence of an "expert assessment") and for repeatability of the method.We aimed to eliminate the need of threshold estimation, thus continuous variables and various ratios were used as much as possible.It is clear that it is not wholly possible to limit or quantify qualitative discrete variables (e.g.dam type, piping occurrence, or type of remedial work).Therefore, qualitative discrete variables are clearly used in decision trees, but not in the calculations.

Decision trees and calculations
As we have explained above, five separate assessment procedures (decision trees) for five different GLOF scenarios are included in the presented method.These are: (a) potential for dam overtopping resulting from a dynamic slope movement into the lake; (b) potential for dam overtopping following the flood wave originating in a lake situated upstream; (c) potential for dam failure resulting from dynamic slope movement into the lake; (d) potential for dam failure following the flood wave originating in a lake situated upstream; (e) potential for dam failure following a heavy earthquake.The first and second scenarios (dam overtopping) are possible for all lake types, whereas the other scenarios (dam failures) may occur exclusively in the case of moraine-dammed lakes.Introduction

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Full It has been shown that GLOFs most frequently result from dynamic slope movement into the lake, producing a displacement wave (e.g.Costa and Schuster, 1998;Clague and Evans, 2000;Awal et al., 2010).There are two components that need to be taken into consideration when assessing the potential for dam overtopping resulting from a dynamic slope movement into the lake.These are: (a) potential for dynamic slope movement into the lake; and (b) potential for dam overtopping by a displacement wave.
The overall potential for dam overtopping resulting from a dynamic slope movement into the lake is consequently derived by combining both of these components.
The group of characteristics describing the first component (potential for dynamic slope movement into the lake) includes characteristics related to the various types of dynamic slope movements, which may enter the lake and consequently cause a displacement wave resulting in dam overtopping.These are especially characteristics related to the possibility of: (a) calving into the lake; (b) icefalls from hanging glaciers into the lake; and (c) landslides on steep lateral moraines surrounding the lake.Thus, the potential for dynamic slope movement into the lake includes three subcomponents.For the final assessment of the potential for dam overtopping resulting from a dynamic slope movement into the lake, the higher subcomponent is used.
The first step in assessing the potential for icefall into the lake is to determine whether a glacier is situated above the lake or the valley is already completely deglaciated.If the valley is already completely deglaciated, the potential for icefall into the lake is naturally equal to 0. If there are glaciers above the lake, the first of the assessed characteristics related to the potential for icefalls from calving or hanging glaciers into the lake is the distance between the lake and the glacier (D is [m]).This characteristic provides information on whether the lake is in direct contact with the glacier (calving occurs) or not.If the assessed lake is in direct contact with a glacier (D is = 0 m), then the ratio of the width of the calving front to the maximal lake width (r Clw/Lw [unitless]) is calculated Introduction

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Full as follows: where C lw is the width of the calving front (C lw [m]) and Lw is the maximal lake width (L w [m]).The potential for icefall into the lake is equal to 1 if the ratio of the width of the calving front to the maximal lake width is equal or greater to 1.If it is less than 1, then the resulting value is used as the potential for icefall into the lake (Fig. 1).
If lake is not in direct contact with the glacier (D is > 0 m), the topographical susceptibility for icefall (T SI [unitless]) should be calculated as follows: where the mean slope between the lake and the glacier (S LG [ • ]) and the mean slope of the last 500 m of the glacier tongue (S G500 [ • ]) are used.A sinus function was chosen to describe the non-linear increasing potential with increasing slope.We feel that it is not necessary to include the distance between the lake and the glacier in the equation, because the question of whether a broken block of ice will finally hit the lake or not is primarily controlled by the slope between the lake and the glacier.Moreover, the distance between the lake and the glacier is used in the previous step in the decision tree.
To assess the potential for a landslide of a moraine into the lake, it is first necessary to decide whether there are unstable moraine slopes in the lake surroundings.It is recommended to make a decision on the basis of manual expert analysis of high resolution optical images, or geomorphological (geological) maps, if available.If there are moraines surrounding the lake, then the potential for a landslide into the lake is described by a single characteristic in the presented method, as follows: where S Mmax is the maximal slope of a moraine surrounding the lake (S Mmax [ • ]).We suppose that the use of the maximal slope instead of the mean slope, which is generally Introduction

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Full used, is more representative for this assessment procedure, because the possibility of a landslide occurrence is generally not controlled by the mean slope but by the maximal slope.The decision tree describing the procedure for assessing the potential for dynamic slope movement into the lake provides three results: potential for calving into the lake, potential for icefall from hanging glaciers into the lake and potential for a landslide of a moraine into the lake.The higher value is typically used for the final assessment of the potential for dam overtopping following dynamic slope movement into the lake.
The second component for assessing the potential for dam overtopping following dynamic slope movement into the lake is the potential for dam overtopping by a displacement wave.It is necessary to decide whether the displacement wave generated by the slope movement into the lake would overcome the dam freeboard (D f -vertical distance between the lake level and the lowest point on the dam crest; D f [m]) or would be captured within the lake.The first step in this part of the decision tree is therefore an assessment of the dam freeboard.If the assessed lake has surface outflow (D f = 0 m), then the potential for dam overtopping following dynamic slope movement into the lake is maximal (= 1).If D f > 0 m, the ratio of dam freeboard to the cube root of the lake volume (r Df/V ) is calculated.This ratio was chosen for several reasons.Firstly, this ratio provides a continuous variable therefore it is not necessary to determine any thresholds.Secondly, this ratio increases with increasing dam freeboard and decreases with the same dam freeboard and greater lake volume.Thirdly, there is no need to estimate the volume of potential slope movement.
It is clear that the lake volume is an essential input value for the calculation of dam freeboard to the cube root of the lake volume ratio.The relation between lake surface area (A [m 2 ]) and lake volume (V [m 3 ]) of 35 glacial lakes of various types (both moraine-dammed lakes and bedrock-dammed lakes) and sizes (from 0.02 × 10 6 m 3 to 49.63 × 10 6 m 3 ) within the Cordillera Blanca was used for this purpose.Input data were gained from Authoridad Nacional del Agua bathymetries (Cochachin et al., 2010;Cochachin and Torrés, 2011).The empirical power function formula for deriving lake Introduction

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Full volume (V ) from easily measured lake surface area (A) was estimated as follows: where A is the lake surface area (A [m 2 ]).This formula is used for calculating all of the lake volumes in the presented method.With this input data it is possible to calculate the ratio of dam freeboard to the cube root of lake volume (r Df/V [unitless]) as follows: where D f is dam freeboard (D f [m]); and V is lake volume (V [m 3 ]; Eq. 4).The cube root function was used for the purpose of unifying the units.

Potential for dam overtopping following the flood wave originating in a lake situated upstream (Scenario 2)
An outburst flood from a lake situated downstream following an outburst flood originating from a lake situated upstream is a possible scenario in the cascade systems of the lakes within the Cordillera Blanca.Hand in hand with ongoing deglaciation, new unstable lakes in high elevation about 5000 m a.s.l. are forming and rapidly growing (Emmer et al., 2014) and pose possible triggers for outburst floods from lakes situated downstream (great lakes in main valleys).Assessment of the potential for dam overtopping following a flood wave originating in a lake situated upstream generally requires the following two components to be included: (a) retention potential of a lake situated downstream (assessed lake); (b) potential for a flood wave from a lake situated upstream.Due to their interconnection and for reasons of clarity, both of these components are incorporated in the decision tree simultaneously (are not distinguished) (Fig. 2).
An assessment of the potential for a flood wave from a lake situated upstream is only meaningful when the ratio of the upstream lake volume to downstream lake retention potential (r V/Vret [unitless]) is higher than 1 (see Fig. 2).This ratio describes whether Introduction

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Full the lake volume of the upstream situated lake is greater than the retention potential of the downstream situated (assessed) lake or not.In this ratio, Eq. ( 4) is used for estimating the volume of the upstream situated lake(s).The second component of the ratio is the retention potential of a downstream situated (assessed) lake (V ret [m 3 ]).Based on a simplified geometric model, the formula for calculating the retention potential was estimated as follows: where ).The ratio of the upstream lake volume to downstream lake retention potential has the following form: where V is the volume of the lake situated upstream (V [m 3 ]; Eq. 4), and V ret is the retention potential of the lake situated downstream (V ret [m 3 ]; Eq. 6).The result of the upstream lake volume to downstream lake retention potential ratio calculation is limited: 0< r V/Vret < ∞.If the lake volume of the lake situated upstream is higher than the retention potential of the lake situated downstream (r V/Vret > 1), then the flood wave originating from this upstream lake may subsequently also cause an outburst flood from the lake situated downstream.In this case, it is necessary to assess the potential hazardousness of the lake separately.The potential for dam overtopping is therefore equal to the potential hazardousness of the upstream situated lake (the whole assessment procedure is needed).In cases where the retention potential of a downstream situated lake is higher than the volume of upstream situated lake, the potential flood wave would be absorbed by the downstream situated lake and the potential for dam overtopping is thus equal to zero (Fig. 2).
It is clear that the calculation of r V/Vret is not relevant for lakes with surface outflow (D f = 0 m; V ret = 0; r V/Vret → ∞).In this cases, it is necessary to estimate the minimal Introduction

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Full volume or the critical lake area (A crit [m 2 ]), which needs a separate assessment procedure (to avoid assessing all of the small lakes situated upstream).For this purpose, a simple equation was estimated: where A is the surface area of the assessed lake (A [m 2 ]).A constant (0.05) was chosen on the basis of analyzing previous events (e.g. the 2012 event in Artizon (Santa Cruz) valley; Emmer et al., 2014) and expert assessment.Should a lake situated upstream exceed the calculated critical lake area, then it is necessary to assess the potential hazardousness (whole procedure) of this lake.The potential hazardousness of the assessed downstream situated lake is then equal to this result (Fig. 2).

Potential for dam failure resulting from a dynamic slope movement into the lake (Scenario 3)
As it was mentioned in the introduction, an assessment of the potential for dam failure resulting from a dynamic slope movement into the lake requires the same procedure as the assessment of the potential for dam overtopping resulting from a dynamic slope movement into the lake, with the difference being that the dam erodibility has to be taken into consideration.This term is used to describe the "immunity" of a moraine dam (its outflow) to the extreme flow rate resulting from a displacement wave overtopping a moraine crest.Therefore, three components need to be incorporated (Table 2): (a) potential for dynamic slope movement into the lake; (b) potential for dam overtopping by a displacement wave; and (c) dam erodibility.The overall potential for dam failure following dynamic slope movement into the lake is calculated as a product of these three components and the overall procedure is shown in detail in Fig. 3.The procedure for estimating the components (a) and (b) is similar to the one described in the first scenario (Fig. 1).Introduction

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Full For estimating dam erodibility (third component) on the basis of remotely-sensed high resolution images and digitam terrain model, without any field survey, it is generally necessary to include the characteristics of dam material, dam geometry and peak discharge.With reduced demands on input data, the dam material is only characterised by dam type (moraine dam × bedrock dam).Dam geometry is represented by the maximal slope of the distal face of the dam (S DFDmax ; see below) and peak discharge is calculated in the form of a peak discharge factor (P DF ).The calculation of the peak discharge factor is different for the different scenarios.Therefore, P DFS3 is used for Scenario 3 (dam failure following dynamic slope movement into the lake), while P DFS4 is used in Scenario 4 (dam failure following a flood wave originating in a lake situated upstream).
The presented method does not quantify the volume of potential slope movement(s) into the lake, thus P DFS3 is designed to simplistically describe the peak discharge for an idealised unitary dynamic slope movement into the lake.In this scenario, P DFS3 is calculated as follows: where r Df/V is the ratio of the dam freeboard to the cube root of the lake volume (r Df/V [unitless]; Eq. 5).After that, erodibility of the dam for Scenario 3 (E RDBS3 ) is estimated as follows: where S DFDmax is the maximal slope of the distal face of the dam (S DFDmax [ • ]), simplistically describing the dam geometry and susceptibility to erosion (erodibility).
The maximal slope of the distal face of the moraine was used to capture the most vulnerable part of the moraine dam as we suppose that this is more predicative than the use of the mean slope (in contrary to methods presented by Wang et al., 2008Wang et al., , 2011;;Mergilli and Schneider, 2011).P DFS3 is the peak discharge factor for Scenario 3 (P DFS3 [unitless]; Eq. 9).Introduction

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Full It is generally necessary to take three components into the account for a meaningful assessment of the possibility of a flood wave from a lake situated upstream causing dam failure and GLOF from a lake situated downstream (Table 2).These are: (a) retention potential of a lake situated downstream (assessed lake); (b) potential for a flood wave from a lake situated upstream; and (c) dam erodibility of a downstream situated (assessed) lake.The overall procedure (decision tree) for assessing the potential for dam failure following a flood wave originating in a lake situated upstream is described in Fig. 4. The procedure for the estimation of components (a) and (b) is similar to the one described in the second scenario (Fig. 2).
Analogically to the previous scenario, dam failure may only occur in the case of moraine-dammed lakes.Therefore, the first step in assessing the potential for dam failure following a flood wave originating in a lake situated upstream is to distinguish between the different dam types (Fig. 4).The peak discharge factor for Scenario 4 (dam failure following a flood wave originating in a lake situated upstream) is calculated as follows: where V is the volume of the lake situated upstream (V [m 3 ]; Eq. 4), V ret is the retention potential of a downstream situated (assessed) lake (V ret [m 3 ]; Eq. 6), and A is the area An assessment of the potential for dam failure following a heavy earthquake requires the following two components to be included (Table 2).These are: (a) potential for a heavy earthquake; and (b) dam instability.The Cordillera Blanca is generally considered to be one of the most active seismic regions of the contemporary world.
It is clear that the potential for a heavy earthquake in comparison with other regions of the world needs deeper evaluation; on the other hand, the potential for a heavy earthquake on a regional scale (assessing the differences between each parts of this mountain range) is not needed.A South American seismic hazard map presented by USGS (Giardini et al., 1999;Rhea et al., 2010) shows that whole region of the Cordillera Blanca is categorized as a zone with maximal peak ground acceleration (PGA) of between 3.2 and 6.4 m s −2 .Although most earthquakes have their origin in the subduction zone of the Pacific Ocean, we suppose that there is no significant difference in the maximal PGA between the west and east side of the Cordillera Blanca.Therefore, the whole region of Cordillera Blanca has a equivalent (similar) potential for heavy earthquakes and it is not necessary to take characteristics of potential earthquake into account on a regional scale during the assessment of the potential hazardousness of glacial lakes in the presented method.Thus, the first component in the assessment of the potential for dam failure following a heavy earthquake (potential for heavy earthquake) is always equal to 1 (the whole region is susceptible to a heavy earthquake).
The second component (dam instability) firstly requires an assessment of dam type.It is clear that dam failure following a heavy earthquake is not a possible scenario for bedrock-dammed lakes, because bedrock dams are generally considered to be stable (dam instability = 0 and overall potential for dam failure following a heavy earthquake = 0; see Fig. 5).
It has been shown that moraine dam failure following a large earthquake occurs due to changes in the internal structure of the dam and consequent internal erosion (piping), Introduction

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Full which cyclically increases its rate due to the increasing discharge (positive feedback mechanism; Lliboutry et al., 1977;Yamada, 1998).In extreme cases, increasing piping may lead to dam rupture.Therefore, a crucial characteristic in assessing the potential for dam failure following a large earthquake is information about the internal structure of the dam, represented in this study by piping through the dam.If piping occurs, the estimation of dam instability (D I [unitless]) requires the following procedure, which starts with a calculation of the ratio between the dam height and the dam width (r Dh/Dw [unitless]) as follows: where ).Then, dam instability (D I [unitless]) is calculated as follows: where r Dw/Dh is the ratio between the dam height and the dam width (r Dh/Dw [unitless]; Eq. 13), and γ is the piping gradient (γ [ • ]).The piping gradient provides information about the slope between the water level and piping springs.A double value is used to emphasize the role of γ, which is rarely higher than 20 • .In the case that there is no evidence of piping, dam instability (D I = [unitless]) is calculated as follows: where r Dh/Dw is the ratio between the dam height and the dam width (r Dh/Dw [unitless]; Eq. 13).The power of two was used to emphasise that no piping occurs.

Input data
We believe that the method for assessing the potential hazardousness of glacial lakes and incorporating the assessed characteristics should always be partly subordinated Introduction

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Full to data availability, in order to provide applicability and repeatability of the method.
The presented method focuses on a wide range of users and thus is designed for broadly available input data.All of the assessed characteristics are easily driveable from high resolution optical images (e.g.Google Earth Digital Globe, 2013) and digital terrain models.Characteristics which need field survey (e.g.geological setting, detailed glaciological setting or characteristics describing the internal dam structure such as buried ice presence/absence) are not incorporated.
3 Method verification

General principle
It is always a highly important to verify the relevance of a new method, to prove its functionality and limit all possible doubts.The main idea of the presented method verification is the potential hazardousness assessment of several lakes, of which some have produced GLOFs since the end of Little Ice Age and some have not.Seven lakes from the region of Cordillera Blanca, which have produced ten GLOFs, were selected so that different lake types, different causes and different scenarios of GLOFs are represented.Another criterion was data availability for historical events (publications, reports from ANA archive; Huaráz, Peru).Ten lakes which have yet to produce GLOFs were chosen to be assessed to prove the presented method in comparison with GLOF-producing lakes.These ten lakes were selected so that different lake types and settings are represented.Therefore, a total number of twenty lakes (pre-flood conditions respectively) were examined.
An assessment of the pre-flood conditions of the lakes which have already produced GLOFs should show whether the presented method allows us to identify the most likely GLOF scenario for a particular lake (comparison with real cause) and if these lakes will have a higher potential than lakes which have yet to produce GLOFs.A comparison between the pre-GLOF conditions of the lakes which have produced GLOFs with those Introduction

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Full which have not should highlight the most susceptible lakes for each scenario.The assumption is that the presented method should clearly distinguish between lakes which have already produced GLOFs and those which have not.

Input data
Input data for assessing the pre-GLOF conditions of the examined events as well as input data for assessing the potential hazardousness of lakes which have yet to produce GLOFs were gained from various sources: (a) remotely sensed images (Google Earth Digital Globe, 2013 covering the Cordillera Blanca region since 1970; three sets of old aerial photographs for the periods 1948-1950, 1962-1963 and 1970)

Results
The results of the method can generally be verified from two points of view: (a) the most likely scenario for a particular lake; and (b) the most susceptible lake for each scenario.A combination of both of these results provides quite a good overview of the potential hazardousness of the examined lakes.

The most likely scenario for a particular lake
Verification of the most likely scenario of a GLOF for particular lakes is relevant only in the case of lakes which have already produced GLOFs (10 examined pre-flood conditions).It is important to stress that the potential for dam overtopping following dynamic slope movement into the lake or flood wave originating in a lake situated upstream is always higher than the potential for dam failure resulting from these Introduction

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Full causes, because dam overtopping is a prerequisite for dam failure.We feel it is relevant to distinguish between these mechanisms of GLOFs, the reasons for subsequent flood modelling and an estimation of the volume of potentially released water.
The presented method successfully identifies real GLOF triggers in 9 out of 10 cases (the only exception was the Lake Safuna Alta 1970 event; see Table 5).The condition of Lake Safuna Alta before a catastrophic earthquake occurred on 31 May 1970 indicted that the most likely GLOF scenario was dam overtopping by a displacement wave caused by calving of the glacier into the lake.The real cause of the flood was earthquake-induced piping.In fact, Lake Safuna Alta was assessed as the lake with the highest potential for dam failure following a heavy earthquake of all of the assessed lakes.From this point of view, it is also quite important to compare results within each scenario.

The most susceptible lake for each scenario
The results of the assessment of the potential for each scenario were ranked from the highest to the lowest potential for a GLOF (see Table 6).In general, the presented method reliably distinguishes between lakes which later produced GLOFs to those which did not.Detailed results for each scenario are described below.
Scenario 1: it can be clearly seen that the potential hazardousness of pre-flood conditions of lakes which have produced GLOFs resulting from dynamic slope movement into the lake reached the seven highest potentials for Scenario 1 (Fig. 7).
Three conditions reached the maximal potential of 1.00.These were the conditions of Lake Artesoncocha, before it produced GLOFs in July and October 1951 and Lake Palcacocha before it produced GLOF in 1941.Four other lakes which have already produced GLOFs reached a potential for dam overtopping caused by dynamic slope movement into the lake higher than 0.95.After that, a significant decrease in the reached potentials is evident and lakes which have yet to produce GLOFs are ranked.
The presented method works perfectly until the thirteenth position.After that there are two evident disharmonies -the Lake Safuna Alta 2002 event (14th position) and Introduction

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Full the Lake No. 513 2010 event (20th position).We have the following explanation for this phenomenon: firstly, both of these events were caused by an extraordinary highvolume slope movement, which cannot be reliably identified or accurately predicted without detailed field glaciological and geological survey.Secondly, both of these lakes have a dam freeboard in the order of tens of meters, which would help to significantly limit the expected low-or middle-scale events and thus decrease the susceptibility for dam overtopping in the presented method.From another point of view, the largescale dynamic slope movement can be characterised as a "quasi-random" event (see Sect. 4.2) and a GLOF following its potential impact on the affected lake may occur elsewhere, even from an ostensibly safe lake (e.g.Lake No. 513, which was generally considered as safe before the 2012 event; Carey, 2012).Scenario 2: the presented method reliably identified the only event that involved dam overtopping following a flood wave originating in a lake situated upstream (Fig. 8).This was dam overtopping and subsequent dam failure of Lake Atizon Bajo following a flood wave from Lake Artizon Alto in 2012 (potential 0.996).Two other lakes have significantly large lake situated upstream in their catchment area, and thus have a nonzero potential for Scenario 2 (Churup and the upstream situated Lake Churupito; Auquiscocha and the upstream situated Lake Checquiacocha).Both of these systems have yet to produce a GLOF and this was confirmed by them reaching significantly lower potentials (0.574 and 0.553, respectively) in comparison with the Atizon system.
On the other hand, the low number of the examined events of this scenario is a potential shortcoming, with the Artizon 2012 event being the only well-documented event of Scenario 2 (Scenario 4, respectively) from the Cordillera Blanca region.
Scenario 3: the results of the potential for dam failure following dynamic slope movement into the lake reliably identified the dam failures of Lake Palcacocha in 1941 (potential 0.559) and Lake Jancarurish in 1951 (potential 0.554; see Fig. 9).The remaining two dam failures of Lake Artesoncocha reached a substantially lower potential (0.259 and 0.225, respectively) than the potentials reached by lakes which have yet to produce GLOFs (Quitacocha, Checquiacocha).These lakes we interpret Introduction

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Full as being susceptible to dam failure following dynamic slope movement into the lake.It is important to realise that dam erodibility (a component of this scenario) is quite a complex issue, which is always estimated with a degree of uncertainty and approximation when the assessment is based on remotely sensed photos and DTMs without any field survey.If we take this fact into the account then the provided results are quite representative.Scenario 4: our investigation showed that the only lake susceptible to dam failure following a flood wave originating in a lake situated upstream is Lake Artizon Bajo (its pre-flood condition, respectively) with a potential of 0.207 (Fig. 10).This lake produced a GLOF in this way in 2012.No other lake from the examined lakes is susceptible to this scenario (there are no lakes significant in size situated upstream of the assessed moraine-dammed lakes).The presented method reliably identifies the potential hazard in this case.As in the case of Scenario 2, the low number of examined events (dam failures following this mechanism) is unfortunately taken into consideration, with the Artizon 2012 event being the only well-documented event of Scenario 4 from the Cordillera Blanca region.
Scenario 5: lakes with a higher potential for dam failure following a heavy earthquake were also identified successfully (Fig. 11).The only case of this scenario from the examined events (piping of Lake Safuna Alta after a heavy earthquake in 1970) reached the highest potential of 0.231, followed by the condition of Lake Palcacocha before the 1941 outburst with a potential of 0.217.Afterwards there was a significant decrease in potential, with the third position being occupied by the pre-flood condition of the Safuna Alta 2003 event as well as lakes Churupito and Mullaca.

Potentially hazardous lakes
Based on a comparison of the results obtained from the potential hazardousness assessment of ten pre-flood conditions of lakes which have already produced GLOFs and ten conditions of lakes which have yet to produce GLOFs, we recommend interpreting "hazardous lakes" as lakes which reach more than 0.9 in Scenario 1, more Introduction

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Full than 0.5 in Scenario 3; or more than 0.2 in Scenario 5.In the case of Scenarios 2 and 4, we recommend using similar values depending on the most likely scenario of a GLOF originating from a upstream situated lake.The relatively low number of examined events should also be taken into consideration.

Interpretation of results
It is highly important not to misinterpret the obtained results with regard to the character of the presented method.Therefore, we would like to emphasize that the presented method provides information about the likelihood of a sudden water release from a particular glacier lake (potential hazardousness) following five different scenarios of GLOFs, which were have been recorded in the studied region before.On the other hand, the presented method does not reflect any other possible GLOF scenario (e.g.dam failure following melting of buried ice reported from mountain ranges of Central Asia; Ives et al., 2010).The presented method also does not take into account the magnitude of potential outburst floods (as well as e.g. the volume of potential dynamic slope movement into the lake), or downstream impacts (downstream hazard assessment).

Potential sources of errors
It is not possible to predict the behaviour of the complex Earth system exactly and analogically the occurrence of GLOFs cannot be exactly predicted because this question is also highly complex.We are able to modify the spatial component or time component of the assessment but we are not able to refine both of these components simultaneously.This fact is connected with the so called "quasi-randomness" of the triggering events, e.g.spatio-temporal occurrence and magnitude of dynamic slope movements, spatio-temporal occurrence and magnitude of earthquakes and Introduction

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Full occurrence of extreme weather (O'Connor et al., 2001).The quasi-randomness and complexity of GLOF occurrence thus limit the reliability of each method, including presented one, and may pose a potential source of errors.On the other hand, modification of all of the existing approaches and particular methods for use on a regional scale is an attractive scientific challenge.Beside the quasi-randomness and partial unpredictability of the complex Earth system behaviour, potential sources of errors are especially connected to the acquisition and interpretation of input data.Therefore, we recommend using comprehensive and uniform input data, if possible).

(Dis)advantages of presented method
We feel that the main advantages of the presented method are as follows: a. repeatability, which allows both retrograde, present and also near-future potential hazardousness assessment and its evolution of selected lakes; b. objectivity, which allows different observers to gain equal results in the case of the same input data; c. principle of multiple results, which allows characteristics which do not play a role in a defined specific case to be omitted (scenarios, decision trees).
On the other hand, the presented method also has certain disadvantages, which mainly result from the type of construction of the method.These are: a. compromise between demands on input data, objectivity and repeatability and the relevance of the obtained results on the other side; b. need for a partial manual assessment (especially for qualitative discrete characteristics such as a distinction between different types of dams, identification of evidence of piping or type of remedial work); c. time-consuming acquisition of input data for a higher number of assessed lakes (17 characteristics needed for each lake).Introduction

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Full Glacial lake outburst flood (GLOF) is a highly important fluvial process, which represents a significant threat to the inhabitants of the Cordillera Blanca region, Peru.In these days of global climate change and subsequent glacier retreat, the threat of GLOFs is actually increasing.Reliable assessment of the potential hazardousness is a necessary step in the application of spatial-and cost-effective mitigation tools.In this paper, a new objective and easily repeatable method for assessing the potential hazardousness of glacial lakes within the Cordillera Blanca region is presented.
In contrast with existing methods, this regionally-focused method is based on an assessment of five separate potentials for five different GLOF scenarios, which have been recorded in the studied region.Assessment of pre-GLOF conditions of lakes which have produced GLOFs in the past and a comparison of these results with an assessment of lakes which have yet to produce GLOFs showed that this method has great potential for identifying the most likely GLOF scenario for a particular lake and also for identifying potentially the most hazardous lake(s) within a group of lakes for each scenario.The actual cause was successfully identified in nine out of ten preflood conditions.A distinction between lakes which have already produced GLOFs from those which have not was successful in all five scenarios.We believe that the presented method will serve as an integrated methodological concept for repeated assessment of the potential hazardousness of glacial lakes within the Cordillera Blanca region.Shortest distance between the assessed lake (its lakeshore) and the closest glacier situated above the lake D is = 0 m -direct contact between the lake and glacier; D is > 0 m -continuous variable e.g.Grabs and Hanisch (1993); Yamada (1993) Width of calving front

S1, S3
Horizontal distance between the left and right margins of a calving glacier .Assessed lakes and their potential for Scenario 4 ranked from the highest to the lowest (please note that empty columns represent lakes with a zero potential for this scenario; the results of particular lakes are listed in Table 6.).
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Screen / Esc Printer-friendly Version Interactive Discussion Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | of the assessed lake (A [m 2 ]).The power of two was used to emphasize the non-linear trend in the flow rate increase.If P DFS4 > 1, P DFS4 = 1 is used in the following calculation of dam erodibility for Scenario 4 (E RDBS4 = [unitless]): E RDBS4 = sin(S DFDmax ) • P DFS4 (12) where S DFDmax is the maximal slope of the distal face of the dam (S DFDmax [ • ]), and P DFS4 is the peak discharge factor for Scenario 4 (PDFS4 [unitless]; Eq. 11).
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ; (b) unpublished research reports from the archive of Authoridad National del Agua (Huaráz, Peru); (c) data and information gained during a field survey performed in May/June 2012 and June/July 2013; and (d) contemporary and historical groundbased photos from the studied sites.A comprehensive list of input data used for the assessment is presented in Supplement.
Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

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future work we recommend especially: a. a more detailed investigation for more precise specification of thresholds and calculations, based on an analysis of previous GLOFs as well as a field survey (geophysical measurements for estimating the stability of moraine slopes, measurements elucidating the internal structure of moraine dams, etc.); b. extension of the method for all types of high-mountain lakes (especially for the landslide-dammed lakes which have reached significant volumes in the studied region)Discussion Paper | Discussion Paper | Discussion Paper | Carey, M.: Living and dying with glaciers: people's historical vulnerability to avalanches and outburst floods in Peru, Global Planet.Change, 47, 122-134, doi:10.1016/j.gloplacha.2004.10.007,2005.Carey, M., Huggel, C., Bury, J., Portocarrero, C., and Haeberli, W.: An integrated socioenvironmental framework for glacial hazard management and climate change adaptation: Discussion Paper | Discussion Paper | Discussion Paper | types of glacial lakes; LD: landslides-dammed lakes; MDL: moraine-dammed lakes.DTM: digital terrain (elevation) model; EAM: earthquake activity maps; FS: field survey; GM: geological maps; MS: meteorological situation; MSI: multi-spectral images; OI: optical images.Discussion Paper | Discussion Paper | Discussion Paper |

Fig. 1 .Fig. 2 .Fig. 3 .Fig. 6 .Fig. 7 .Fig. 8 .Fig. 9 .
Fig. 1.Decision tree for assessing the potential for dam overtopping resulting from a dynamic slope movement into the lake.The overall potential is derived as a product of the highest partial potentials of the first and second components.

Table 1 .
List of methods for assessing the potential hazardousness of glacial lakes.

Table 3 .
Individually assessed characteristics (input data) used in the presented method.