Forewarning Model for Glacial Lake Outburst in Southeast Tibet

Abstract

The southeast region of Tibet experiences frequent glacial lake outburst disasters, and disaster warning systems are thus crucial for disaster prevention and mitigation in the area. In this study, based on remote sensing images and historical data, 20 glacial lakes in southeast Tibet were selected as samples for risk analysis. A probability model of glacial lake outburst floods (GLOFs) in southeast Tibet was established using logistic regression for seven selected prediction indexes. By calculating the sensitivity and specificity of the model, the probability of identifying GLOFs was found to be 60%, with an identification degree of 86%. The under the ROC (receiver operating characteristic) curve index was prominently larger than 0.5, indicating the applicability of logistic regression for predicting GLOFs in southeast Tibet. The probability equation of the model shows that the area of the glacial lake, the distance of the glacial lake from the glacier, the slope of the glacier, the slope of the glacier tongue, and the dam backwater slope have a great influence on the probability of GLOFs. The results can provide a reference for the local governments to prevent disasters and reduce the damage of GLOFs.

1. Introduction

Glacial lakes are lakes of glacial origin and they commonly occur in high mountain areas. Under the action of multiple factors, glacial lakes can suddenly release large amounts of water, which can have devastating effects on lives and livelihoods. Outbursts from glacial lakes have repeatedly caused the loss of human lives as well as severe damage to local infrastructure. However, the hazard potential of glacial lakes remains uncertain in several high mountain ranges around the world, especially in the context of the accelerating rates of glacier retreat as a result of atmospheric warming [1,2].

As a consequence of global warming, the rates of glacier retreat and melting have increased, further leading to the increase and expansion of glacial lakes [3,4,5]. As glaciers recede in response to climatic warming, the number and volume of potentially hazardous moraine-dammed lakes in high mountain areas are increasing [6]. These lakes develop behind unstable ice-cored moraines and have the potential to burst catastrophically, producing devastating glacial lake outburst floods (GLOFs). In the past 50 years, there have been at least 20 major outbursts in the Himalayas, most of which are concentrated in Tibet [7]. Therefore, it is of great practical significance for the social and economic development of Tibet to carry out the disaster assessment of glacial lake outbursts.

GLOFs are the result of the comprehensive effects of the climatic background and geological conditions [8]. Chinese and international scholars have conducted extensive research on GLOFs. Researchers usually divide relevant evaluation indexes into qualitative, quantitative, and semi-quantitative according to the characteristics of the glacial lake concerned [9,10]. Lv et al. [11] evaluated GLOFs according to the heat index and glacial lake outburst risk index. Huang et al. [12] used the fuzzy evaluation method to select eight indicators for evaluating the risk of GLOF in Luozha County. Guo et al. [13] used Landsat TM satellite remote sensing data to evaluate the risk of glacial lakes in the southern section of the Sichuan–Tibet highway by means of onsite investigation, interviewing, and surveying. McKillop [14] selected 188 glacial lakes in Columbia as samples and established a probability equation of glacial lake outburst risk using logistic regression and four indexes. Liu et al. [15] used the fuzzy matter-element extension method to comprehensively evaluate the risk of GLOFs in the Parlung Zangbo River basin.

In the risk assessment and modeling of GLOFs, it is of great significance to select an appropriate model corresponding to the influence factors of glacial lakes, which would ensure the accurate and reliable estimation of the hazard level index [16,17,18]. The logistic regression model is a regression model based on the maximum likelihood estimation method. It is an excellent and widely used model for evaluating landslide susceptibility. It can be used to effectively determine the correspondence between landslides and non-landslides (1-0) and nonlinear correlations between landslides and impact factors. This model has simple calculation steps and offers high adaptability to evaluation factors required by independent variables. Evaluation factors can be either discretely distributed or continuously distributed [19]. Scholars in China and abroad have also made useful attempts and explorations using logistic regression models to evaluate the susceptibility of moraine lakes to outbursts [20,21,22]. Litan et al. [23] described the probability of glacial lake formation on a pixel basis for Himalayan glaciers using logistic regression. DiAngelis et al. [24] developed a logistic regression predictive model for estimating the hazard probability of the Grasshopper Glacier Lake. Robin et al. [25] also used logistic regression to classify the drained/undrained lakes in the southern Coast Mountains of British Columbia, Canada. Moraine lake outburst disasters are non-periodic sudden natural disasters affected by the geographical climate and environment. Considering its high accuracy and rationality, this study applied logistic regression to establish a model for assessing the outburst susceptibility of moraine lakes in southeast Tibet.

Southeast Tibet lies in the eastern part of the Himalayas, and it is characterized by a dense distribution of glacial lakes. This area is dominated by moraines, which have high glacier activity and poor stability and are sensitive to climate change. Glacial avalanches, glacial mudslides, and GLOFs caused by glacier retreat have become the main natural disasters in this area. This study aimed to establish a risk evaluation and prediction model of GLOFs in southeast Tibet. To this end, the morphological characteristics of typical glacial lakes in southeast Tibet were investigated, the evaluation indexes of the GLOF probability were summarized and selected, and the mechanism and influence of GLOFs were identified using the logistic regression method. The findings have reference value for disaster prevention and mitigation in Tibet.

2. Materials and Method

2.1. Study Area

Southeast Tibet generally includes two regions, Nyingchi and Qamdo. The main mountain system in the region is the Nyainqentanglha Mountains. This mountain system has a wide range. Moreover, it has the widest distribution of glacial lakes on the Qinghai–Tibet Plateau. On the whole, the terrain of the region is high and steep, with an average elevation of more than 4000 m and a maximum elevation of more than 6000 m (Figure 1).

Under the influence of the Indian monsoon, numerous terminal moraine lakes have developed in this area. Glaciers and ice lakes are mainly distributed in the Nyainqentanglha Mountains. Although this region has more than 8500 glaciers, they are rapidly receding due to climate change. Consequently, glacial activity is intense and a large amount of meltwater is produced, leading to a large number of glacial lakes. Most of the glacial lakes in this area are moraine-blocked lakes, including terminal moraine-blocked lakes and lateral moraine-blocked lakes.

2.2. Data Sources

The data regarding glacial lakes in the study area were obtained from the 2008–2017 High Asia 30 m resolution annual glacial lake data established by the Institute of Aerospace Information Innovation, Chinese Academy of Sciences. This data set integrates images from Landsat and high-resolution satellites, and uses adaptive threshold methods and artificial digitization methods to provide high-resolution Asian glacial lake products of 30 m resolution at an annual scale, including the location, type (four categories), altitude, distance from the parent glacier, area, perimeter, and other information.

Information on the slope of the glacier, slope of the glacier tongue, and dam backwater slope was acquired from the National Tibetan Plateau Scientific Data Center. This data set is mainly the fourth version of the SRTM terrain data obtained by CIAT (International Center for Tropical Agriculture) using a new interpolation algorithm. The interpolation algorithm was used to fill in the data missing from SRTM90 [20].

2.3. Evaluation Method

In order to avoid the subjectivity of the evaluation method and the complexity of the semi-quantitative method, we adopt the logistic regression method to establish the prediction model.

The logistic regression model is a multivariate nonlinear statistical analysis model, β, which is suitable for the multivariable control dichotomy problem, and is a typical supervised learning model. In the logistic analysis, the binary variable Y is used to describe the state of the moraine lake. Y = 1 indicates the occurrence of GLOF, and Y = 0 indicates no GLOF. The specific principles of logistic regression can be found in the literature [14,25].

The logistic regression formula is:

$$\mathrm{Y}=\mathrm{Logis}\left(\mathrm{P}\right)=\frac{1}{1+{\mathrm{e}}^{-\left(\mathrm{a}+{\mathsf{\beta }\mathrm{x}}_1+{\mathsf{\beta }}_2{\mathrm{x}}_2+......+{\mathsf{\beta }}_{\mathrm{n}}{\mathrm{x}}_{\mathrm{x}}+\mathrm{L}\right)}}$$

In the formula, P is the probability value of the occurrence of the dependent variable calculated from the independent variable, that is, the outburst probability of the moraine lake, and its range is 0–1. X₁, X₂, X₃, ..., X_n are various evaluation factors, namely, independent variables; n is the number of evaluation factors; and a is the intercept. ${\beta }_1,{\beta }_2,{\beta }_3...... {\beta }_n$ represent the independent variable regression coefficients computed by the logistic regression model.

2.4. Model Validation

The result of logistic regression is probability, and a threshold is thus used to divide positive and negative values. Each threshold will produce a set of eigenvalues of false positive rate (FPR) and true positive rate (TPR). After selecting multiple groups of threshold values, the receiver operating characteristic (ROC) curve is formed. FPR = FP/(FP + TN), namely, the number of negative samples predicted to be positive/the actual total number of negative samples, and TPR = TP/(TP + FN), namely, the number of positive samples predicted to be positive/the actual total number of positive samples. The higher the TPR and lower the FRP, the better the results. Accordingly, the top left corner of the graphic canvas is the most ideal result. FPR = 0 and TPR = 1 correspond to a larger area under the ROC curve (AUC), which is ideal [26].

3. Results

3.1. Selection of Pre-Evaluation Factors

The evaluation indexes are generally summarized from the characteristics of the glacial lake concerned, and different indexes are selected for the research areas. Nevertheless, the selection of indexes is mainly based on three principles: (1) field survey data and the degree of difficulty of the prediction indexes; (2) weight analysis of previous prediction indexes; and (3) comprehensive conditions inducing GLOFs and their modes.

In most studies, prediction indexes are divided into four categories, namely, climate factors, glacier parameters, glacial lake parameters, and dam parameters. According to the difficulty of obtaining the index in Tibet, combined with the weight analysis of Zhuang et al. [27] on the prediction index of GLOFs, in order of importance, were the dam crest width, distance of glacial lakes from glacier tongue front, combination of water and heat, area of glacial lakes, alimentation of glacier areas, development degree of glacial fissures, slope of the glacier tongue, average longitudinal slope of glacier snow area, dam backwater slope, degree of collapse on both sides, and degree of scouring by side gullies. In this study, seven indexes, namely, the area of the glacier, area of the glacial lake, distance of the glacial lake from the glacier tongue front, slope of the glacier, slope of the glacier tongue, ratio of height from glacial lake surface to dam crest to dam body height, and ratio of width to thickness of the dam body were selected, and these indexes are expressed by X₁, X₂, X₃, X₄, X₅, X₆, and X₇, respectively (

Table 1. Data of glacial lake samples in the study area.

ID	Longitude	Altitude	X1/km2	X2/km2	X3/km	X4/‰	X5/‰	X6	X7
1	88.92	27.85	26.00	0.56	0.02	0.01	0.02	0.10	0.02
2	90.10	28.25	46.00	6.38	1.95	0.00	0.00	0.17	0.00
3	87.93	27.97	6.49	0.92	0.60	0.00	0.01	0.07	0.00
4	90.53	28.47	2.30	0.52	0.00	0.00	0.03	0.16	0.04
5	96.14	29.60	3.14	0.42	0.58	0.13	0.06	0.18	0.01
6	97.37	29.20	0.07	0.16	0.08	0.12	0.11	0.03	0.25
7	97.27	29.44	0.13	0.01	0.16	0.16	0.11	0.04	0.19
8	97.25	29.47	0.06	0.01	0.30	0.08	0.08	0.11	0.05
9	97.16	29.46	0.19	0.07	0.05	0.13	0.06	0.07	0.01
10	96.40	29.46	35.56	0.03	0.28	0.18	0.27	0.14	0.04
11	96.81	29.22	0.22	0.50	0.00	0.04	0.03	0.20	0.03
12	96.84	29.26	4.32	0.03	3.23	0.08	0.11	0.07	0.01
13	96.82	29.30	0.05	2.38	0.00	0.04	0.03	0.18	0.05
14	96.83	29.24	1.18	2.01	1.45	0.02	0.06	0.15	0.10
15	97.02	29.39	0.35	0.17	0.48	0.22	0.17	0.19	0.08
16	96.56	29.62	0.30	0.01	0.17	0.09	0.30	0.05	0.20
17	96.38	29.57	0.03	0.23	0.27	0.20	0.07	0.13	0.03
18	96.18	29.57	0.78	0.02	0.62	0.20	0.12	0.09	0.03
19	96.77	29.59	0.08	0.15	0.24	0.12	0.24	0.10	0.07
20	96.62	29.73	0.41	0.07	0.00	0.27	0.00	0.07	0.14

).

3.2. Establishment of an Assessment Model for Glacial Lake Susceptibility

In this study, the susceptibility evaluation model was established using MATLAB with X₁, X₂, X₃, X₄, X₅, X₆, and X₇ as independent variables and C as the dependent variable. Before establishing a logistic regression model, the evaluation factors need to be analyzed for collinearity (

Table 2. Collinearity diagnosis results of glacial lake variables.

Variable	Collinearity Diagnosis
	VIF	TOL
Area of glacier	1.23	0.77
Area of glacial lake	1.26	0.71
Distance of glacial lakes to glacier tongue front	1.52	0.56
Slope of glacier	1.09	0.89
Slope of glacier tongue	1.33	0.65
Ratio of height from glacial lake surface to dam crest to dam body height	1.47	0.61

). Two commonly used important diagnostic methods were employed, namely, the variance inflation factor (VIF) and tolerance (TOL). When the variance inflation factor (VIF) is less than 10 and tolerance (TOL) is greater than 0.10, the independent variables do not exhibit collinearity. In other words, the linear correlation between the independent variables is not strong.

Samples of glacial lake outburst in southeast Tibet are limited, and the threshold value was set according to the Sigma principle. The specific calculation method is shown in the literature [28]. The independent variables were iteratively calculated using the forward step-by-step conditional likelihood ratio test. The dam backwater slope (X₇) of the terminal moraine dams was eliminated because its Sig value was larger than 0.05 at 0.174. The Sig values of the other six evaluation factors were all less than 0.05. Therefore, the constructed moraine lake outburst susceptibility evaluation model is as follows:

$$\mathrm{P}=\frac{1}{1+{\mathrm{e}}^{-\left(-0.872-2.589{\mathrm{x}}_1-0.066{\mathrm{x}}_2+0.994{\mathrm{x}}_3-0.955{\mathrm{x}}_4+0.099{\mathrm{x}}_5+0.731{\mathrm{x}}_6\right)}}$$

In the formula: X₁ is the supply glacier area, X₂ is the glacial lake area, X₃ is the distance from the glacial lake to the glacier, X₄ is the glacier slope, X₅ is the glacier tongue slope, and X₆ is the ratio of the height of the glacial lake from the water surface to the dam crest and the height of the dam body.

3.3. Model Checking

Considering the limited number of samples of moraine lakes with and without historical outbursts in the study area, the sample probability value calculated by the model and the actual value were used to cross-validate the evaluation model.

According to the normal distribution diagram, the probability of the sample was 0.73. The average values of μ and σ were 0.41 and 0.3, respectively. According to the threshold equation T = μ + Kσ, the threshold was set as 40%. When the P-value is greater than or equal to 40%, the sample is classified as the outburst class; when the P-value is less than 40%, the sample is classified as the non-outburst class. As shown in

Table 3. Calculated and actual values of outburst and non-outburst samples of glacial lakes in southeast Tibet.

ID	Y/Observed	Y/Forecast	ID	Y/Observed	Y/Forecast
1	1	1	11	0	0
2	1	1	12	0	1
3	1	1	13	0	0
4	1	0	14	0	0
5	1	0	15	0	0
6	0	0	16	0	0
7	0	0	17	0	0
8	0	0	18	0	0
9	0	0	19	0	0
10	0	1	20	0	0

, the number of correctly classified glacial lake outbursts is 13, and the number of wrongly classified glacial lake outbursts is 2. By calculating the sensitivity, specificity, and other indexes, the probability of identifying glacial lake outburst events is 60%, and the identification degree of non-outburst glacial lakes is 86%.

To further verify the accuracy of the model, the ROC curve was applied. The ROC curve is the standard for assessing a model. The abscissa represents specificity, that is, the false alarm rate, and the ordinate represents sensitivity. The closer the abscissa is to zero and the larger the ordinate, the higher the accuracy rate. As shown in Figure 2, the accuracy of the logistic regression model was close to 70%. Owing to the limited number of samples, the learning curve is not smooth enough. The closer the ROC curve is to the upper left corner, the higher the accuracy of the model evaluation results. AUC is an indicator of model quality, with a numerical range of 0.5–1. When the AUC is less than 0.5, the prediction fails; between 0.5 and 0.7, the prediction is good; and above 0.7, the prediction is very good. In the figure below, the AUC area is prominently greater than 0.5, indicating that logistic regression prediction plays a certain role in the prediction of GLOFs in southeast Tibet. The AUC of the evaluation model was 0.874, indicating that the model has good evaluation ability.

4. Discussion

According to the equation of the probability of glacial lake outburst in southeast Tibet, with other factors remaining unchanged, the area of glacier lake, distance of the glacial lake from the glacier, slope of the glacier, and slope of the glacial tongue are all equally proportional to the probability of glacial lake outburst, indicating that when the above-mentioned index value is larger, the probability of glacial lake outburst is higher. When the slope of the glacier and slope of glacial tongue are large, the topography of the glacier snow area shows greater fluctuations. The high and steep terrain provides potential energy conditions for glacial action. Higher slopes are more conducive to the accumulation and release of glacier energy in glacial lake areas. Relevant studies reported that the slope of glacier areas generally ranges between 7° and 12°. Slopes greater than 7° are conducive to the occurrence of glacial lake outbursts. The steeper the glacial tongue slope, the more likely it is to fracture, leading to poor instability and the increase of water pressure on the terminal moraine dam [29,30,31]. The area of the glacial lake is also an important condition for the occurrence of a glacial lake outburst. The larger the area of the glacial lake, the greater the water storage capacity of the glacial lake, and the greater the hydrostatic pressure on the terminal moraine dam. Some researchers refer to glacial lakes with an area greater than 0.2 km² as large glacial lakes, which are dangerous [32]. The ratio between the height of the glacial lake from the top of the dam to the height of the dam and the area of the glacier are inversely proportional to the probability of glacial lake outburst. Therefore, the smaller the two indexes, the greater the probability of glacial lake outburst. In this study, the average area of outburst glacial lakes was 1.76 km², the average slope of the glacier tongue was 13°, and the distance between the glacial lakes and the glacier was 0.028 km, which agree with the results of previous research. Regarding non-outburst glacial lakes, the average area of glacial lakes was 0.41 km², and the area of glacial lakes greater than 0.2 km² accounted for more than 50% of the total area. The average slope of the glacier tongue and glacier was 11°, and most glacial lakes are at risk of outburst.

Temperature and precipitation are also important factors affecting glacial lake outbursts. Therefore, it is necessary to develop the logistic regression predictive model based on climate variables [24,33]. The number of prediction indicators selected will also affect the prediction results. Robin et al. [25] put forward 18 prediction indexes for the evaluation of the risk of glacial lake outburst. Pratidina et al. [34] evaluated landslide susceptibility using 11 prediction indexes. Therefore, more predictive indicators should be considered in future work [35]. In addition, due to the limited number of samples in the regression analysis and errors in the sample data, these factors will directly affect the evaluation effect of the model.

5. Conclusions

The Qinghai–Tibet Plateau features many high and extremely high mountains, where glaciers and glacial lakes have widely developed. In this area, 35 GLOF disasters have been recorded, which threatened human life and property. With the change of the global climate and ecological environment, the frequency of GLOF disasters is increasing. In particular, debris flow from glacial lake outbursts in some cross-border basins have caused certain damage to local areas and downstream countries, creating international disaster events. Therefore, this study developed a model for predicting the possibility of glacial lake outburst by employing logistic regression. The following conclusions can be drawn.

(1) The prediction model of glacial lake outburst risk was established by selecting seven indexes: the glacier area, area of glacial lake, distance of the glacial lake from the glacier, slope of the glacier, slope of the glacial tongue, ratio of glacial lake water surface to dam crest height to dam body height, ratio of dam body width to thickness, and dam backwater slope. The indexes can truly reflect the risk of glacial lake outburst.

(2) The ROC curve and AUC were used to test the accuracy of the model. The ROC curve showed a correct rate of 70%, and the AUC was greater than 0.5, indicating the high accuracy and generalization ability of the model.

(3) According to the probability equation of the model, the area of the glacial lake, the distance of the glacial lake from the glacier, the slope of the glacier, the slope of the glacier tongue, and the dam backwater slope are all directly proportional to the possibility of glacial lake outburst. Therefore, larger index values indicate a higher possibility of glacial lake outburst.