A First-order Method to Identify Potentially Dangerous Glacial Lakes in a Region of the Southeastern Tibetan Plateau

Abstract Though glacial lake outburst floods have become an urgent issue on the Tibetan Plateau, no standardized methods have been proposed so far to identify and prioritize potentially dangerous glacial lakes (PDGLs). Here, we developed a first-order approach to identify PDGLs in the Boshula Mountain Range, southeastern Tibetan Plateau. Five variables—mother glacier area, distance between lake and glacier terminus, slope between lake and glacier, mean slope of moraine dam, and mother glacier snout steepness—were selected to identify PDGLs on the basis of four criteria we suggested. A fuzzy consistent matrix method was then applied to determine the weight of variables, and characteristic statistical values were used as thresholds to classify each variable. Out of 78 moraine-dammed lakes studied, we identified 8 glacial lakes as potentially very highly dangerous. We also validated our approach with 6 drained glacial lakes inside and outside our study area. Successfully identifying them as potentially very highly and/or highly dangerous lakes demonstrates the validity of the method.


Introduction
There are many glacial lakes on the Tibetan Plateau, and some of them have drained suddenly in recent years, producing glacial lake outburst floods (GLOFs) (Xu 1988;Ding and Liu 1992;Chen et al 1999). Such floods mainly occurred in the drainage basins of the Brahmaputra, Pumqu, and Poiqu rivers in south and southeast Tibet (Cheng et al 2008), where Tibetans live and where the climate is significantly influenced by the Asian summer monsoon. It is thus important to evaluate the potential risk of GLOFs in this region.
Several researchers have already developed approaches to assess glacial lake hazards worldwide, including remote sensing (Huggel et al 2002;Kä ä b et al 2005;Allen et al 2008;Fujita et al 2008), geographic information systems (GIS) (Huggel et al 2003(Huggel et al , 2004b, and/or statistical (McKillop and Clague 2007b) and empirical (Huggel et al 2004a;McKillop and Clague 2007a) methods. Among these methods, remote sensing is regarded as the best way to extensively investigate glacial lakes and the impact of GLOFs in inaccessible glacier mountainous areas (Bolch et al 2008). Note that although these remote sensing-based methods are usually developed to evaluate glacial lakes in particular regions of concern (eg Huggel et al 2002(eg Huggel et al , 2003 in the Swiss Alps; Clague 2007a, 2007b in British Columbia;and Hegglin and Huggel 2008 in the Cordillera Blanca), their applicability to other mountainous regions, such as the southeastern Tibetan Plateau, warrants further study. In addition, some data of high quality in the aforementioned studies are not available or are difficult to acquire for the Tibetan Plateau area because of various factors. Using limited available data to assess the hazards of expanding glacial lakes in Tibet is therefore a challenge.
Here, we used readily available remotely sensed datatopographic maps; digital elevation models (DEMs); and Landsat, ALOS (Advanced Land Observing Satellite) AVNIR-2 (Advanced Visible and Near Infrared Radiometer type 2) imageries (Table 1) -to qualitatively evaluate the status of 78 moraine-dammed lakes whose area is larger than 0.02 km 2 in the Boshula Mountain Range (Wang et al 2011;96.25u-96.75uE, 29.5u-30uN), southeastern Tibetan Plateau (Figure 1). Our endeavor lies in developing a first-order method to detect

Selecting variables to identify PDGLs
Though GLOFs have recently become one of the primary natural hazards on and around the Tibetan Plateau, no uniform criteria have been introduced to identify PDGLs. Previous studies have indicated that the possibility of a glacial lake outburst is a function of several variables (Chen et al 1999;Lü 1999;RGSL 2003;Bajracharya et al 2007;McKillop and Clague 2007b;Wang et al 2008). Based on previously drained glacial lakes on the Tibetan Plateau, Lü (1999) suggested 7 variables for predicting PDGLs in Tibet (Table 2). McKillop and Clague (2007b) listed 18 variables on the basis of previously published accounts of moraine dam failures all over the world (Table 3). However, some of those proposed variables can only be detected from high-resolution satellite images or through field observation. It seems to be impracticable for a regional glacial lake evaluation on the Tibetan Plateau because we cannot laboriously investigate each lake in the field, taking into consideration that the remoteness and harsh weather conditions may hamper our measurements on the ground.
We therefore propose 4 criteria to filter candidate variables to identify PDGLs in our study area. First, variables should be measured using readily available, remotely sensed data (eg topographic maps, medium resolution of Landsat, ALOS imageries, and DEMs). Therefore, variables such as lake water volume, width of the moraine dam crest (Lü 1999), glacier calving front width (Richardson and Reynolds 2000) and moraine height-to-width ratio (Clague and Evans 2000;Huggel et al 2002) were exempted from our consideration, as they can only be measured on high-resolution data or in the field. Second, only variables proposed according to characteristics of previously outburst lakes on the Tibetan Plateau were included. With this criterion, such variables as lake freeboard (Blown and Church 1985) and lake freeboard-to-moraine crest height ratio (Huggel et al 2004a) were abandoned because they were based on drained lakes in the Swiss Alps and British Columbia. Third, the data type of variables had to be continuous rather than nominal, because the quantitative values were used to classify variables (Table 3, see also next section). Fourth, variables should act independently and should not be reproducible from each other. For example, only 2 variables of lake-glacier proximity, lake-glacier relief, and slope between lake and glacier snout can calculate the other one, which was thought to be redundant.
Five variables met the 4 criteria, including (1) mother glacier area, (2) distance between lake and glacier terminus, (3) slope between lake and glacier, (4) mean slope of moraine dam, and (5) mother glacier snout steepness. Among these, mother glacier area reflects the area of accumulation and glacier snout and suggests the magnitude of snow and ice avalanche if it happens. Distance and slope between lake and mother glacier help project the possibility of ice avalanche into the glacial lake. The mean slope of the moraine dam dictates the dam's stability, and the steepness of glacier snout reflects the potentiality that the glacier tongue might crack.
The 5 variables were easily obtained from available satellite images and DEM. Mother glacier area and the distance between mother glacier and lake can be measured using ALOS imagery. Slope between lake and glacier was calculated based on the height difference between glacier terminus and the nearest lakeshore as well as the distance between mother glacier and lake. For the case where the glacier terminus was directly connected with the lake, it was represented by mother glacier snout steepness. A 100-m buffer zone outward from the glacial lake was approximately defined as moraine dam because most dam breaches are within this range (Lü 1999), and the horizontally lower most 500 m of glacier, where ice avalanche most likely occurs (Alean 1985), was defined as glacier snout. The mean slope of moraine dam and glacier snout can be calculated automatically after defining the outline of moraine dam and glacier snout in the slope grid generated from DEM with a resolution of 25 m.

Determining the weights of variables
It is necessary to assign a weight to each variable because they have a different influence on the potential risk of a glacial lake outburst. We used a fuzzy consistent matrix (FCM) method (Yao and Zhang 1997) to estimate the relative weights of each of the 5 variables. FCM, (A ij ) m*n , is a matrix of pairwise comparison of the importance of variables, where 0 # A ij # 1 and A ij + A ji 5 1. A ij is the membership of the importance of variable A i with regard to A j , so the larger A ij is, the more important A i is than A j .
If A ij 5 0.5, variable A i is as equally important as A j (Huang et al 2005). We constructed FCM (Table 4) based on outburst causes of historically drained glacial lakes in Tibet (Table 5) combined with empirical knowledge. Triggering mechanisms for GLOFs in Tibet can be overtopping induced by ice avalanches slumping into the lake or piping due to thawing of buried dead ice beneath the moraine dam (Table 5). The former mechanism has dominated in the past. Therefore, distance and slope between lake and glacier as well as mother glacier snout steepness-which reflect the probability of ice avalanche-were thought to be more important than the other 2 variables. The weights of each of the 5 variables (w 1-5 ) were thus calculated, respectively, as 0.07, 0.27, 0.22, 0.195, and 0.245, using the following formula (Huang et al 2005): Slope of accumulation area of mother glacier (6) 7-12 .7 Slope of glacier tongue (6) 3-20 .8 Distance between glacier and lake (m) 8-500 ,500 Lake water volume (10 8 m 3 ) 0.03-2.5 .0.01 Width of crest of moraine dam (m) 3-1,000 ,60 Slope of downstream face of moraine dam (6) 25-33 .20 Mother glacier snout steepness.  where

Classification of variables
Each glacial lake was labeled with a unique identity number from GL1 to GL78 (Figure 1). Figure 2 shows the values of 5 variables for all of the 78 moraine-dammed lakes in the study area. We then classified each variable into 4 intervals on the basis of the data's statistical distribution. The 25th percentile, median, and 75th percentile of each variable were used as cutoff values to equally screen the number of glacial lakes into each group, and then each group was assigned a danger value (V) from 0.25 to 1 (Table 6). Finally, the total value (P) of each glacial lake was calculated as: FIGURE 2 Mother glacier area (A), distance between lake and glacier terminus (B), slope between lake and glacier (C), mother glacier snout steepness (D), and mean slope of moraine dam (E) for the 78 moraine-dammed glacial lakes. Middle of the box is median and box width is defined by interquartile range (25th and 75th percentiles). Whiskers are 10th and 90th percentiles. Holly squares and stars are mean and min-max values.

MountainResearch
where w i is the weight of variable A i and V i is the danger value in Table 6. With the breaks in the cumulative curve and statistical characteristic values of P's distribution (Figure 3), we classified outburst potential for a glacial lakes as very high (P . 0.8), high (P 5 0.7-0.8), medium (P 5 0.5-0.7) and low (P , 0.5) to select approximately 10%, 15%, 50%, and 25% in each group. With these thresholds defined, we identified 8 glacial lakes as having a very high outburst potentiality. The details of these 8 glacial lakes are given in Supplemental data, Appendix S1 (http://dx.doi. org/10.1659/MRD-JOURNAL-D-10-00059.S1).

Validation of the method
To validate our method of identifying PDGLs, we applied the method to the drained glacial lakes inside and outside our study area. Only 2 glacial lakes in the study area had a previous outburst, as revealed by satellite images (see Figure 7 in Wang et al 2011), so the sample may not be sufficient to validate the method. We therefore added another 4 drained glacial lakes along the Himalayan region to supplement our validation database (see also Table 5).
We did not take all lakes listed in Table 5 in our validation database because no remotely sensed data were available to represent the status of these glacial lakes before outburst. We used topographic maps (1970s) and corresponding DEMs (constructed from topographic maps) to measure the 5 variables of these 6 drained glacial lakes to obtain the status of lakes before outburst (Supplemental data, Appendix S1; http://dx.doi.org/10.1659/MRD-JOURNAL-D-10-00059. S1). According to our methods, the 6 lakes are identified as having a very high and/or high risk of being PDGLs (P . 0.7), which is consistent with the fact that they drained in the past, and thus verifying the validity of our method to Mother glacier area (km 2 ) ,0.5 0.5-1 12.5 .2.5 Distance between lake and glacier terminus (m) .600 300-600 80-300 ,80 Slope between lake and glacier (6) ,12 12-17 17-21 .21 Mean slope of moraine dam (6) ,10 10-14 14-22 .22 Mother glacier snout steepness (6) ,14 1419 19-26 .26 The total value (P) for all 78 moraine-dammed lakes. The line is the cumulative curve of the distribution of P. Frame on the right: the box and whisker plot shows the statistical characteristic values. Symbols represent same meaning as in Figure 2. P . 0.8, P 5 0.7-0.8, P 5 0.5-0.7, and P , 0.5 were classified, respectively, as very high, high, medium, and low potentially dangerous lakes.

Discussion and conclusion
We provided an easy way to qualitatively evaluate the degree of danger of glacial lakes using 5 suggested variables. Though it is certainly not possible to accurately predict when glacial lakes will outburst, our method can evaluate the status of glacial lakes in the study area and prioritize the potentially unstable glacial lakes for further assessment. Note, however, that some glacial lakes labeled as medium and low potentially dangerous lakes using our method (P , 0.7) may also produce catastrophic floods in the future, as other factors (eg extreme precipitation in the monsoon season, geotechnical characteristics of the moraine dam) can lead to the breach of these glacial lakes. Also, the evolution of glacial lakes is a dynamic process.
With lake expansion and glacier melt, glacial lakes with a low hazard potentiality can evolve into potentially highly dangerous ones. However, the increasing frequency of GLOFs on the Tibetan Plateau (Richardson and Reynolds 2000) and limited manpower and resources in Tibet compel us to first resolve the problems posed by glacial lakes with a visibly high-hazard potential. Meanwhile, we need to intensify our monitoring of glacial lakes, to acquire the latest satellite imagery so as to identify new PDGLs as soon as possible.
We chose the 5 variables in our method based on 4 criteria. Among them, 2 of the variables (mother glacier area and glacier snout steepness) are related to the glacier, 2 (distance and slope between lake and glacier) to the lakeglacier relation, and 1 (mean slope of moraine dam) to the moraine dam. From historical documents on previously outburst glacial lakes, the dominant factor leading to GLOFs in Tibet has been overtopping induced by ice avalanche (Table 5). For this type of glacial lake, the 5 variables seem to be sufficient for evaluating their potentially dangerous status as the variables have already combined the status of the glacier and glacial lake, the instability of the moraine dam, and the triggering mechanism. However, for other causes of glacial lake outbursts-such as melt of dead ice and presence of ice core beneath the moraine dam-variables other than the 5 variables presented here may be more suitable to predict PDGLs. Therefore, applying the method to predict this type of glacial lake may not be as accurate as the former type. But considering the fact that more than three quarters of outburst glacial lakes in Tibet were caused by ice avalanches ( We assigned a weight to each variable according to characteristics of historically drained glacial lakes combined with empirical knowledge. The applied FCM method can convert the qualitative description into quantitative numbers when conducting pairwise comparison of variables. We ranked the variables in order of importance: distance from lake to glacier, mother glacier snout steepness, slope between lake and glacier, mean slope of moraine dam, and mother glacier area. Close study of most of the potentially very highly dangerous glacial lakes in the southeast Tibet (Supplemental data, Appendix S1; http://dx.doi.org/10.1659/MRD-JOURNAL-D-10-00059.S1) showed that the terminus of the mother glacier with a precipitous glacial tongue is very close or directly connected to the moraine-dammed glacial lake. In addition, we also divided each variable into 4 groups with critical values (ie 25th percentile, median, and 75th percentile) to make sure that each interval had the same number of glacial lakes. This is also applicable in the Himalayas where an inventory of glaciers and glacial lakes was available (ICIMOD 2005). With the attribute database of glaciers and glacial lakes in the Himalayas and ASTER Global Digital Elevation Model, we reclassified the 5 variables on the basis of numerical distribution characteristics (ie 25th percentile, median, and 75th percentile) and reanalyzed the PDGLs in Nepal and Bhutan identified by the International Centre for Integrated Mountain Development (ICIMOD). Of 44 analyzed PDGLs, 32 were labeled as potentially very highly and/or highly dangerous. Discrepancies may be caused by the different criteria defined in identifying PDGLs as ICIMOD gave greater importance to glacial lake area, whereas our method did not take this variable into consideration at all.
Our method is simple and the variables described in our method can be easily obtained from mediumresolution remotely sensed data and DEM. This is especially suitable in Tibet, where high-resolution satellite images and DEMs are sometimes not available or are available only at a high cost. Previous comprehensive methods of assessing GLOF hazards provided by Huggel et al (2002Huggel et al ( , 2004a and Clague (2007a, 2007b) were mainly based on outburst floods in the Swiss Alps or British Columbia, and they also relied on high resolution of remote sensing data (eg IKONOS satellite image or aerial photograph) or field observation. However, the data applied in this study are relatively easy to access, so the applicability of our method to other regions of the Tibetan Plateau may be promising.

Supplemental data
APPENDIX S1 Potentially very highly dangerous glacial lakes (P . 0.8) identified in our study area and their corresponding parameters (8 glacial lakes). Lake area uncertainties are obtained with a shoreline length multiplied by half a cell resolution of the ALOS image. Also shown are the characteristics of 6 drained glacial lakes obtained from topographic maps and corresponding DEMs.