Changes in glacial lakes in the Poiqu River Basin in the central Himalayas

The Poiqu River Basin contains 162.2 km 2 of ice and 19.9 km 2 of glacial lakes. The 7 remote sensing data over the last 40 years have been used to identify 147 glacial lakes in the basin 8 and clearly revealed the retreat of glaciers and the growth of glacial lakes at accelerating rates, in 9 parallel to warming climate in the Himalayas. Based on remote sensing images and digital 10 elevation model (DEM) analysis, the area and water changes in glaciers and glacial lakes are 11 analyzed in detail, and a water balance equation (WBE) is proposed to account for the mechanism 12 of lake growth. The WBE includes water supplies from rainfall runoff, ice and snow ablation, 13 glacial retreat, and water losses due to infiltration and evaporation. As each water contribution 14 item specifically depends on local weather and morphology, the WBE provides a direct link 15 between glacier and glacial lake changes and climate changes under local conditions. Operation of 16 the WBE for five major glacial lakes in the Poiqu River Basin has revealed that water from 17 glaciers and snow cover dominates the growth of lakes. Lakes are found to vary in different ways 18 even with similar backgrounds, depending strongly on local weather and geomorphology 19 conditions. The WBE is not only applicable for predicting future changes in glacial lakes under 20 climate warming conditions but is also useful for assessing water resources from rivers in the 21 central Himalayas. 22 23

images. Fig. 4 displays the images with characteristic marks, and Table 2 lists the signs for 23 identifying types of glaciers and glacial lakes. In practice, these elements are combined with 24 morphology and DEM data to delineate the boundary of lakes or glaciers. Moreover, moraines, 25 deposits, and colluvium are also identified by their marks and spectral features. 26 In particular, glaciers are located near mountain tops and limited to certain elevations. Glaciers 27 usually have tongue-shaped fronts with flow lines, and the uppermost boundary coincides with the 28 mountain edge, with ice cracks on the trailing edge, which are shown in black in the image.  Table 2 Interpretation signs for glaciers and glacial lakes(Six pictures are from Google 3 Earth images and two pictures are from GF-2 images. They are signed in the lower right 4 corner) 5

Results of interpretation 6
A total of 147 glacial lakes and related glaciers have been identified in the Poiqu River Basin, 7 with a glacier area of 162.2 km 2 and a glacial lake area of 19.9 km 2 . Table 3 lists the types and 8 numbers of each lakes. Most of these lakes are end moraine lakes. 9 10 Table 3 Types of glacial lakes in the Poiqu River Basin 11 12 These lakes have areas ranging between 1.6610 4 ~ 5.50 km 2 , and 125 lakes are smaller than 13 0.1 km 2 . More than 60% of lakes are located at altitudes between 5000 ~ 5500 m. Lakes larger 14 than 0.1 km 2 are mainly in the tributaries of Keyapu,Rujiapu,and Chongduipu in upper Poiqu and 15 in Zhangzangbu in middle Poiqu. As listed in Table 4, more than half of the lake area is located in 16 Chonduipu, approximately 9.51 km 2 , and the second largest is Keyapu at approximately 5.44 km 2 . 17 These lakes account for 83% of the total area of glacial lakes. The table also lists the distance of 18 the lake to its connected glacier, indicating that most lakes are nearly linked to the glacier and thus 19 their changes are expected to be well correlated. Rujiapu tributary (Fig. 5D), where we have relatively large glacial lakes for consideration, i.e., 26 Galongco Lake (5.50 km 2 ), Gangxico Lake (4.60 km 2 ), Jialongco Lake (0.60 km 2 ), Longmuqieco 27 Lake (0.52 km 2 ), and Cirenmaco Lake (0.33 km 2 ). The features of the tributaries are as follows: 28 29 https://doi.org/10.5194/hess-2020-20 Preprint. Discussion started: 3 March 2020 c Author(s) 2020. CC BY 4.0 License. Glaciers are mainly distributed in the upper reaches, and Cirenmaco Lake is located in a tributary 10 in the eastern source area.  Table 5 lists basic parameters of the tributaries, which are crucial for the formation and 20 evolution of the lakes, and parameters for the major lakes in the present state, based on 21 interpretation of 2018 images, are listed in Table 6. 22 23   Table 5 Parameters of the glacial lake tributaries 24 Table 6 Basic parameters for major glacial lakes in the Poiqu River Basin 25 26 4 Changes in glaciers and glacial lakes 27

Variations in glaciers and glacial lakes 28
Interpretations of the multisource images allow for detailed scrutiny of changes in glaciers 29 and glacial lakes. In this way, we obtain the areas of glaciers and glacial lakes in recent decades. 30 https://doi.org/10.5194/hess-2020-20 Preprint. Discussion started: 3 March 2020 c Author(s) 2020. CC BY 4.0 License. Fig. 6 shows the total changes in glacier and glacial lake areas in Poiqu since 1977, where the 1 dotted line means that the curve is inferred only because of the lack of data before 1999. Despite 2 the possible uncertainty before 1999, the gross tendency of glacier loss and glacial lake growth is 3 clear. The retreat rate of glacier area reaches 43.6%, which is approximately 2.98 km 2 /a; 4 accordingly, the glacial lake area has expanded by 169%, which is approximately 0.19 km 2 /a. 5 Since 2004, the retreat rate has reached as high as 7.2 km 2 /a, while the growth rate of the lake has 6 reached 0.44 km 2 /a (in Table 7). 7 This finding is comparable to the results from the literature. For example, from 1975to 2010, 8 glaciers decreased by 19% in area (Xiang et al., 2014, while glacial lake area increased by 83% 9 (approximately 0.26 km 2 /a) from 1976-2010 (Wang et al., 2015). In 1986In -2001, the glacial area 10 increased by 47% (approximately 0.37 km 2 /a) (Chen et al., 2007). 11 For comparison, glacial lakes increased by 29.7% in the entire Chinese Koshi River (including 12 Poiqu and six other tributary rivers) in 1976-2000(Shrestha and Aryal, 2011Wang et al., 2012) at 13 a rate of approximately 1.6 km 2 /a. In the Koshi River, the glacier area has decreased by 19% 14 (approximately 23.48 km 2 /a) (Shangguan et al., 2014;Xiang et al., 2018), and the glacial lake area 15 has increased by 10.6%. In 2000-2010, the glacial lake increased by 6% in area (approximately 16 0.72 km 2 /a) (Wang et al., 2015). This result means that Poiqu undergoes more dramatic changes in 17 glaciers and glacial lakes. In particular, the Galongco and Gangxico Lakes have increased up to 18 500% and 107%, respectively, following area decreases in their connected glaciers by 40%. 19 20

Table 7 Area variations and annual speeds of glaciers and glacial lakes in Poiqu river 21
Basin since 1977 22  Figs. 7-10 show pictures for the five major lakes and their connected glaciers (or the so-called 27 "mother glaciers", because they are the sources of generation for the connected glacial lakes) in 28 different years between 1977 and 2018. It is easy to calculate the area of glaciers and glacial lakes 29 in each stage, as listed in Table 8. (The data sources for the images in different years are listed in 30 https://doi.org/10.5194/hess-2020-20 Preprint. Discussion started: 3 March 2020 c Author(s) 2020. CC BY 4.0 License. Table 1 and Table 2). 1 For more details, we construct the annual variation in the lakes from the historical data; Fig.  2 11 shows the variation in Galongco Lake since 1977, which increased abruptly from 1.77 to 5.50 3 km 2 between 1977 and 2018. The retreat-growth correlation can be seen more clearly from the large lakes mentioned above, 19 as shown in Table 9 and Fig. 12. The gross tendency of glacial retreat and glacial lake growth is 20 also remarkable here. Notably, there was a sudden decrease in area in 1981, simply because there 21 was an outburst (Xu and Feng, 1988). Thus, historical anomalies in glacial lake areas may be 22 caused by lake outbursts. 23 24   Table 9 Annual rates of change in 5 typical glacial lakes and their glaciers 25 The five major lakes, Cirenmaco Lake, Galongco Lake, Gangxico Lake, Jialongco Lake, and 30 Longmuqieco Lake, have increased up to 30%, 74%, 40%, 200%, and 54% at rates of 0.01 km 2 /a, 31 Earth and the right image about the Galongco Lake is from UAV image) 16 https://doi.org/10.5194/hess-2020-20 Preprint. Discussion started: 3 March 2020 c Author(s) 2020. CC BY 4.0 License. 0.13 km 2 /a, 0.07 km 2 /a, 0.02 km 2 /a, and 0.01 km 2 /a, respectively, from 1977 to 2018. 1 Corresponding to the decrease in glaciers, the variations in glacial lakes under consideration 2 have presented three patterns in recent years: 3 1) Fluctuation in area, as in the case of Cirenmaco and Jialongco (Tables 8 and 9 and Fig.  4 12A). 5 Both lakes are located at relatively low altitudes (Jialongco is at 4306 m and Cirenmaco is at 6 4639 m), are sensitive to temperature and both experienced an outburst in this episode (in 1981 7 and 2002, respectively) and then increased steadily. Jialongco Lake even experienced a sudden 8 rise during 2006 and2008 (Fig. 13), when the local temperature reached its 50-year peak. 9 Moreover, a field survey indicates that Jialongco has an overflow at 0.3 m 3 /s in the rainy season, 10 meaning that the lake has reached its maximum and thus fluctuates, similar to ordinary lakes 11 undergoing seasonal changes. This finding implies that small amounts of variation in glacial lakes 12 do not mean that the related glaciers also vary by small amounts. Dramatic change in glaciers 13 results in a great loss of water but does not necessarily increase the size of the connected lake. 2) Remarkable increase in area, as in the case of Galong Lake and Longmuqieco Lake 17 (Tables 8 and 9 and Fig. 12B). 18 Historic remote sensing data (1954 ~ 2018) indicate that Galongco formed in the late 1960s 19 as a result of a warming climate. Then, the lake increased steadily, with no marks of historic 20 outburst and no overflow events based on recent UAV images. Indeed, the lake level is still 10 m 21 below the front moraine bank, and it is only at 1 km downstream that the water flows from 22 infiltration. Thus, the lake has had little loss of water and increases steadily. Despite no field 23 survey data, the same case can be expected for Longmuqieco, which has similar altitude and water 24 supply areas and connected glaciers. 25 3) Gentle increase in area, as in the case of Gangxico (Tables 8 and 9 and Fig. 12C). Gangxico is supplied by the back glacier. As the glacier is small, the lake grows slowly. Moreover, 27 Gongxico is hydraulically connected near Gongco and Galongco, and its water enters Gongco in 28 the southern area through infiltration, while the water of Gongco infiltrates into Galongco (Fig.  29   14). As Gongco has remained steady in last 50 years, Gongxico is also in a balanced state and 30 shows a small tendency to increase. 1 These observations suggest that glacial lakes change in various patterns even under the same 2 local conditions. Furthermore, little variation in glacial lake area does not necessarily mean that 3 there are no changes in related glaciers. In this sense, glaciers are more sensitive to changes in 4 weather or climate.

Influences of temperature and precipitation 9
As glaciers are sensitive to temperature, it is reasonable to consider the effects of weather on the 10 changes in glaciers and glacial lakes. Unfortunately, weather stations are very sparse in the 11 Himalayas, and no stations in the tributaries are under consideration; only records from nearby 12 stations are accessible. Near the study area, we have three weather stations in Nylamu, Quxiang,13 and Zhangmu at altitudes of 3900 m, 3300 m, and 2200 m, which not only represent the vertical 14 variations in weather but also the variations from north to south. Chongpudui and Rujiapu are in 15 the northwestern and northeastern areas of Nylamu, respectively, and both rivers are similar to the 16 whole county in terms of weather conditions, so the temperature and precipitation for lakes (i.e., 17 Galongco, Jialongco, and Longmuqieco) in these tributaries can be interpolated from the records 18 in Nylamu. Similarly, the weather of the Zhangzangbu (for Cirenmaco Lake) River is interpolated 19 from the records in Quxiang. 20 Combining the data from the three stations may comprehensively reflect the weather features 21 of the study area. The key factor for interpolation is the gradient of temperature (R T ) and 22 precipitation (R P ) varying with elevation. To obtain the R T and R P , we take the records of Nylamu 23 and Zhangmu in 2016. The daily R T is defined as follows: 24 where T N and T Z are the daily temperatures recorded in Nylamu and Zhangmu, respectively, and 26 Al N and Al Z are the altitudes of the two stations. This gives an R T of -6.1º C/km. As precipitation in 27 the study area is also governed by altitude, R P can be obtained in a similar way, i.e., the 28 precipitation difference divided by the altitude difference between the two stations, which gives a 29 value of -10 mm/km. The minus symbol means a decrease with altitude. Fig. 15 displays the 30 interpolated temperature and precipitation for the glacial lakes under consideration. Then, both the 1 interpolated temperature and precipitation for the target point can be obtained in the same way: 2 where the subscript H means the altitude of the target points (i.e., the tributary rivers or the glacial 4 lakes) and 0 indicates the recorded values.  and glacial lakes, indicating that the temperature is negatively and positively related to glaciers 15 and glacial lakes. Fig. 17 shows the precipitation series in contrast to the areas of glaciers and 16 glacial lakes, indicating that the tendency of precipitation is negatively associated with glaciers but 17 positively associated with glacial lakes. On the other hand, it is found that precipitation is well 18 correlated with temperature, with a correlation coefficient larger than 0.5. In short, the growth of 19 glacial lakes following the retreat of glaciers is governed by warming conditions. Despite the remarkable fluctuation in various episodes, the weather conditions present a gross 4 tendency in parallel to the retreat of glaciers and growth of glacial lakes. In fact, the temperature in 5 the Tibet plateau increased at a rate of approximately 0.3-0.4C per ten years, nearly two times the 6 global rate. For the case of the present study, the lake area increases by approximately 40% at a 7 rate of 0.28 km 2 /a, which is clearly higher than the other regions in the Himalayas (Nie et al., 8 2017). 9 In the following section, we propose a procedure to calculate the water balance for typical 10 glacial lakes, illustrating the weather effects on the changes in glaciers and glacial lakes in 11 different ways. 12 13 5 Water balance for glacial lakes 14

Volume of glacial lakes 15
To understand changes in glacial lakes, it is necessary to find the changes in water volume in 16 the lakes. Then, we must find the lake volume from the area. This procedure can be done using 17 ArcGIS tools. First, we create the DEM of the lake bottom using images at the time the lake 18 formed and the following periods. Meanwhile, we interpret the annual water level from a series of 19 images, which record the evolution of the lake (cf. Fig. 11). In detail, we create irregular triangle 20 nets (ITNs) under the control of contour lines and obtain the DEM since the formation of the lake. 21 Then, the average elevation of the lake boundary (i.e., the water level) can be obtained for many 22 years. Finally, we compare the DEM derived from the water level and the DEM before lake 23 extension and obtain the variation in the water level with the water volume (Fig. 18). For example, 24 Galongco has the following relationship between lake volume and area: V lake = 5.0A 1.72 (10 6 m 3 ), 25 where A is the lake area (in units of km 2 ). 26 27 Fig. 18 Terrain reconstruction of GB Lake below the water level 28

Water balance equation (WBE) 29
The observations above indicate that the expansion of glacial lakes is well related to the retreat 30 of glaciers, which in turn relies on changes in temperature and precipitation (rainfall and snow) in 1 recent years. Then, it is possible to propose the following water balance equation (WBE) for a 2 glacial lake: 3 where V, P, G, I, and E are the water quantities of the glacial lake, the water supplies from 5 precipitation (rainfall and snow), glacier loss and ice-snow melting, and water loss through 6 infiltration and evaporation, respectively;  represents the annual increment. 7 In detail, the items in WBE are closely related to weather and geomorphologic conditions and 8 can only be determined empirically. 9 1) Water supplies from precipitation (P R , P S ) 10 This involves rainfall and snowfall. The water supply from rainfall (P R ) is governed by the 11 hydrological process in the valley. For a given valley, the runoff depends on the rainfall process 12 (often featured by intensity R and quantity Q R ), the drainage area contributing to the lake (S), and 13 the geomorphologic factors such as slope , vegetation cover, and permeability K. In general, this 14 can be expressed as follows: 15 Water supplies from snowfall (P S ) also depend on temperature T, solar radiation I R , snow 17 density  S , and snow permeability k, in addition to the geomorphologic factors: 18 Then, the water supplied from precipitation is as follows: 20 2) Water supplies from glaciers (G) 22 The major controlling factors are temperature T, solar radiation I R , glacier density  G , fracture 23 density , and geomorphologic factors:

3) Water loss from infiltration (I) 26
Infiltration mainly depends on the permeability of the materials constituting the lake, and in the 27 present case, the materials are mainly moraines, which are generally poorly graded in terms of 28 grain composition and have high porosity. Infiltration also occurs underground and depends on the 29 substrate sediment of the valley channel downstream of the lake. 30 where GSD describes the granular features of moraines and sediments (Li et al., 2013(Li et al., , 2017 in 32 terms of grain size distribution, and J is the hydraulic slope between the water level and seepage 33 https://doi.org/10.5194/hess-2020-20 Preprint. Discussion started: 3 March 2020 c Author(s) 2020. CC BY 4.0 License.

points. 1
In addition, when the lake is "saturated", i.e., the capacity reaches the maximum due to the 2 limitation of the local landform, the lake will not increase in area, and the water supplies 3 exceeding the capacity will be lost through overflow. In such a case, the supply is balanced by the 4 loss. 5

4) Water loss from evaporation (E) 6
Theoretically, evaporation is controlled by temperature, solar radiation, lake area A, wind speed 7 v, surface saturated vapor pressure p, and turbulent energy  (Lu et al., 2017): However, for the present case, the effect due to evaporation is much smaller and is usually 10 ignorable compared with the other contributing terms. 11

Practical operation of the balance equation 12
In practice, each item introduced in the WBE can be empirically estimated, especially in the 13 present case, where we suffer from a severe lack of basic solar radiation and local weather data. In 14 the following section, we provide a practical routine for the calculations. 15

1) Water supplies from rainfall and snow 16
In principle, the supply is equal to the runoff drainage to the lake, which is calculated using 17 the standard hydrologic method for each rainfall event, depending on the temporal process and 18 spatial distribution of the rainfall over the drainage area. However, for the case of glacial lakes, we 19 have only annual area variation and weather data from nearby stations, and it is impossible to 20 perform standard hydrograph calculations; instead, we reduce the calculation to the runoff of the 21 slope (Gao et al., 2019): 22 where P R is the runoff and employed here as the water supply from rainfall, S is the drainage 24 area contributing to the lake, R a is the annual rainfall, and  is the coefficient, depending on local 25 conditions of the drainage slope, such as the material properties and vegetation cover, which is 26 empirically determined as follows (Liang et al. 2018): 27 where  is the slope angle, and ALs varies among arid, semiarid, semihumid, and humid areas.

29
As the Poiqu River Basin is located in the semiarid area but has sufficient moisture content in air, 30 ALs can be taken as the upper limit of 0.75. Then,  is mainly governed by the slope gradient of 31 the drainage area to the lake. 32 2) Melt water from ice and snow melt 33 There have been various methods used in glacial hydrology (Braithwaite and Olesen, 1989). 34 Physical models have incorporated many influencing factors, such as temperature and radiation 35 intensity; thus, these models have high calculation accuracy. However, they do not apply to areas lacking a sufficient database, as in the case in the Himalayas. Instead, empirical methods are 1 widely employed, among which the Degree-Day Model (DDM) is generally most used to calculate 2 the melting of glaciers and snow cover (Kayastha et al., 2005;Zhang et al., 2006;3 Pradhananga et al., 2014). The DDM is practical, simple and well-accepted, considering the 4 influence of the degree-day factor (DDF) and the normal accumulated temperature. Following the 5 method, the melted thickness of the glacier (M) is determined by the production of DDF and the 6 positive cumulative temperature in a certain period (PDD, in units of dC): 7 where DDF is in units of mmd -1 C -1 , and varies with elevation (Liu et al., 2014). PDD can be 9 directly calculated from the daily temperature record, i.e., the cumulative temperature of the days 10 with temperatures higher than 2C. In fact, the PDD involves two components applied to the melt 11 of snow cover and glaciers, PDD S and PDD G . In other words, only the residual cumulative 12 temperature PDD G applies to glacial melting. 13 Then, the melt water quantity is the production of M and the glacier area (A G ): 14 Similarly, this also applies to the water supply from snow cover melting. DDF is generally hard 16 to obtain, but in Poiqu, we may make a reference to the results in the nearby area, 80 km away at 17 Mt. Everest. According to previous studies, the DDF is 16.9 for the Kunbu glacier at an altitude of 18 5350 m (86°52′E，27°59′N) (Kayastha et al., 2005), and the DDF is 8.21 for the Rongbu glacier at 19 the same altitude (Liu et al., 2014). Then, we take the average value, 12.6, as the overall DDF for 20 glaciers in Poiqu, and for individuals, we make some corrections depending on the slope 21 orientations of the glaciers. For the west-oriented slope (e.g., Cirenmaco Lake), the melt is 22 relatively more intense than the east-oriented slope (e.g., the Galongco and Gangxico Lakes); for 23 the cases of Jialongco and Longmuqieco, the slopes are north-oriented, the sunshine is shielded, 24 and the melt is relatively weak. Based on these results, we obtain a corrected DDF for each glacier 25 (Table 9). 26 According to studies on the snow cover of the Dokriani Glacier in the Indian Himalayas 27 et al., 2000), the DDF for snow is approximately 30% less than that for 28 glaciers. As this is geographically similar to the Poiqu area, a reduction rate of 30% can be used 29 for determining the DDF of snow cover for the glaciers and glacial lakes under consideration, as 30 listed in Table 6. 31 On the other hand, not all meltwater can reach the connected lake; some infiltrates into the 32 bed through the crevasses. This creates a loss of water supplies from melt water, and a reduction 33 coefficient, R c , is considered when the water supplies are estimated (cf. Table 5). 34

3) Evaporation 35
The Poiqu River is located at high altitude, where the stored water is in a liquid state only in 36 reference. The lake is located in the tributary of Chongduipu, similar to Galongco and Gangxico, 1 and at similar altitudes (5173, 5075 and 5218 m, respectively). However, it is distinctive in that the 2 Gangco does not receive a water supply from glaciers; the major water supplies come from rainfall. 3 Notably, Gongco has not increased in area, remaining at approximately 2.1 km 2 in recent years. It 4 is possible that the water supplies are balanced by the water losses due to infiltration and 5 evaporation. Since Gongco receives seepage flow from Gangxico and simultaneously feeds 6 Galongco through seepage, the supplies from rainfall can be considered balanced by evaporation. 7 However, according to the estimation, water supplies from rainfall are generally very small 8 compared with those from the meltwater of glaciers and snow cover. Therefore, evaporation is 9 negligible in the Poiqu River. 10

4) Infiltration 11
Water loss due to infiltration is controlled by the permeability of the moraine bank of the lake 12 and the sediment in the valley channel. As it is inaccessible to most glacial lake areas, we can only 13 trace the marks of infiltration through remote sensing images (including UAV and Google Earth) 14 (cf. the case of Galongco in Fig. 19). 15 For the permeability coefficient K, we conducted experiments on material samples from the 16 moraines and sediments, and it was found that K (cm/s) is well related to the grain size distribution 17 (GSD) of the loose granular materials: 18 where D c and μ are GSD parameters (Li et al., 2013;2017), which can be directly obtained 20 from the granulometric analysis of moraine and sediment samples for each lake. Then, the 21 infiltration discharge can be calculated by Darcy's law: 22 where J is the hydraulic slope and A is the infiltration area. For a given valley, the water loss 24 from infiltration is I = QT, with T as the effective time for infiltration, which is mainly the rainy 25 season when the valley has flow water. 26 Based on the discussions above, we obtain a working list of parameters for calculating the WBE 27 (Table 10). 28

Exemplification of Galongco 32
Now, we apply the WBE to the five major lakes to see how the area has increased in recent 33 decades. For this procedure, we first take glacial Lake Galongco in 2006 as an example to show 34 the calculation process. 35

1) Geomorphologic background and related parameters 36
As mentioned above, Galongco Lake is located in a small tributary of Chongduipu, at an 37 altitude of 5075 m, in an area 5.5 km 2 , and the drainage area to the lake, including slopes around 38 https://doi.org/10.5194/hess-2020-20 Preprint. Discussion started: 3 March 2020 c Author(s) 2020. CC BY 4.0 License. the lake, is 22.33 km 2 . Two glaciers are directly connected to the lake in the northwestern and 1 western parts of the upstream area, with a total area of 13.5 km 2 according to the GF-2 satellite 2 images in 2018. 3 In 2006, the lake area was 3.93 km 2, and the glacier area was 13.06 km 2 (Fig. 19). Based on 4 the DEM, the angle of the draining slope is estimated to be 23.7° on average, and thus, the runoff 5 coefficient is 0.56 according to Eq. (13). 6 Following the background of the lake and glaciers, the DDFs for glaciers and snow cover are 7 12.6 and 8.3, respectively, and the reduction coefficients for glaciers and snow cover are 0.61 and 8 0.56, respectively (cf. Table 9). respectively, and the cumulative temperature was 282.3C. Based on the DDM, the cumulative 18 temperature for snow cover melt is 128.3C, and thus the cumulative temperature for glacial melt 19 is 153C. 20

3) Infiltration 21
According to samples of moraine materials in the lake tributary, the GSD parameter μ is 0.03 22 and D C is 11.2 mm, which yields a permeability coefficient K of 0.088 cm/s. According to Google 23 Earth images, the infiltration area is approximately 8426 m 2 , and the hydraulic slope is 0.13, 24 which gives a discharge of infiltration of 0.96 m 3 /s. Considering that only July and August have 25 positive temperatures higher than 2C, infiltration only occurs in these months. 26

4) Water supplies and losses 27
Based on the parameters described above and using formulas (6)-(9), we obtain the water 28 supplies and losses: 29 (i) the water supply from rainfall (P R ) is 1.5610 5 m 3 ; 30 (ii) the water supply from glacial melting (P S ) is 1.9010 6 m 3 ; 31 (iii) the water supply from snow melting (G) is 8.1110 6 m 3 ; and 32 (iv) the water loss from infiltration is (I)5.9210 6 m 3 . 1 Therefore, the WBE provides a water supply of 4.2510 6 m 3 to the lake in 2006, which 2 accounts for the area increase of 0.33 km 2 . 3 In the same way, we can calculate the water balance for other years. Notably, for some years, 4 no data are available for glaciers or lakes (e.g., only three sets of data are available between 1988 5 and 2004); for these situations, we use an extrapolation method. Considering that the changes in 6 glaciers and glacial lakes have steady near-linear tendencies in recent years, we can assume that (R 2 =0.8779), which provides a baseline for extrapolation in recent years. 12 Using the methods above, we obtain the water balance for Galomngco between 1988 and 2018, as 13 listed in Table 10, and the symbols in Table 11 are listed as follows: 14 T ccumulative temperature; 15 T cGcumulative temperature for glacial melting; 16 T cScumulative temperature for snow melting, which is T c -T cG ; 17 M G -melt thickness of a glacier; 18 W Gwater supply from glaciers; 19 W snowwater supply from snow cover; and 20 W total -total quantity of water supplies. 21 22 Table 11 Water balance for Galongco Lake between 1988 and 2018 23 24

Water balance for typical lakes 25
Similarly, we can perform balance calculations for other lakes, from which we obtain the 26 variation in water quantity for the lakes since 1988 using the parameters listed in Table 6. Table 12  27 displays the comparison between the calculated water quantity and the observed quantity for the 28 five selected lakes. changes in the connected glacier (cf. Fig. 13). As the WBE does not consider the glacial dynamics 7 and dramatic changes in local conditions, the calculation cannot incorporate the sudden changes. 8 This means that the WBE operation should be further improved to incorporate the water variations 9 due to catastrophic processes. 10 However, the gross agreement between the calculation and observation does suggest that the 11 WBE has provided a practical and functional framework for understanding the characteristics of 12 changes in individual glacial lakes. Moreover, it provides a practical method for quantitatively 13 assessing the growth of glacial lakes. In particular, the calculation reveals that the lakes in Poiqu 14 have undergone different water supply balance proportions, which makes it possible to distinguish 15 among the local conditions of the lakes. 16 Table 13 lists the average fraction of water supplies from glaciers, snow, and rainfall over the 17 calculation period. It is obvious that lakes at relatively low elevations (i.e., below approximately 18 5000 m) are mainly supplied by glaciers, and lakes at high elevations are mainly supplied by 19 snowfall. For all these lakes, the water supplies from rainfall are much smaller, even below 5%, 20 and this can almost be ignored considering the accuracy of the estimation. This clearly reflects the 21 altitude effect on glaciers. At low altitudes, the cumulative annual temperature is positive and 22 directly melts the glaciers. At high altitudes, glaciers are covered by snow, and the positive 23 temperature mainly acts on snow cover. Indeed, several years have shown near-zero cumulative 24 temperatures for Gangxico Lake and Longmuqieco Lake, which results in a small fraction of 25 glacial ablation. 26 27 Table 13 Fractions of various water supplies to the lakes 28 29 Then, the WBE not only provides a method to account for the water supplies to glacial lakes 30 but also reveals differences between lakes. Although glaciers are sensitive to temperature, the lake 31 grows in various ways depending on local conditions, especially altitude and basin circumstances 32 (e.g., morphology and moraine materials).  2) Mass balance for glaciers and ice caps is of great importance in Earth's hydrological cycle 14 and response to climate change (Aizen and Aizen, 1997;Haeberli et al., 1999;Valentina Radić and 15 Hock, 2013;Lambrecht and Mayer, 2009;Huss, 2011;Huss and Hock, 2018). The results of this 16 study provide a detailed scenario of water balance for individual lakes through operation of WBE 17 for typical glacial lakes, revealing details in water supplies from precipitation, glaciers, and snow 18 cover and water losses from infiltration. The WBE provides the mechanism for lake growth and 19 agrees well with the observations and image interpretations, and the calculation for individual 20 lakes has made up for the deficiencies in previous studies, which only gave an overall view of lake 21 expansion at the regional scale (e.g., Nie et al., 2017). In addition, the WBE operation has also 22 discovered that glacial lakes under similar background conditions may vary in different ways, 23 depending on local elements at small scales, which would be inevitably neglected in studies at 24 large scales. The lake may remain at their greatest sizes (e.g., at the maximal area of extension) 25 even if the glaciers undergo dramatic changes. 26 3) Furthermore, WBE operation is crucial to gain a better understanding of water supplies for 27 glacierized river basins. Near the study area, there are many rivers originating in the high Asian 28 mountains, such as the rivers of Yarlong Zangbo (Brahmaputra), Indus, Ganges, Nujiang (Salween) 29 and Lancangjiang (Mekong), but the quantification of water sources is usually highly uncertain because of a lack of understanding of the hydrological regimes and runoff calculations (Winiger et 1 al., 2005;Bookhagen and Burbank, 2010;Immerzeel and Bierkens, 2012;Miller et al., 2012;Lutz 2 et al., 2014;Hassan et al., 2017). The proposed WBE calculation has revealed the variety of water 3 supplies from glaciers, snow cover, and precipitation for individual glacial lakes; thus, this 4 calculation is expected to be applicable for estimating glaciohydrologic processes in large 5 glacierized rivers. 6 4) Admittedly, the WBE for glacial lakes is proposed here only at the annual scale, which makes 7 it difficult to be accurate when considering individual lakes during a given period. This is mainly 8 due to the lack of data and ignorance of specific water supply and loss processes. For example, 9 runoff should be calculated for the tributary watershed using records for individual rainfall events, 10 which strongly depend on the watershed conditions (i.e., conditions of slope, channel, vegetation, 11 and soils or sediments, especially moraines for the lakes) and the rainfall pattern. However, in the 12 study area, and even in the Himalayas, only annual (and usually incomplete) weather records are 13 available at several points, and it is only possible to provide a gross estimate of the runoff simply 14 by the production of rainfall and watershed area. Similarly, water quantities from other sources 15 can only be best estimated for accuracy in terms of order of magnitude. 16 On the other hand, the WBE does not consider the dynamical processes of glaciers (Copland 17 et al., 2011;Dowdeswell et al., 1995), such as glacial surging, its hydrologic consequences or the 18 possible dramatic changes in morphology, such as the collapse of lakes or other surface processes 19 (e.g., icefalls, landslides, or debris flows due to earthquakes or extreme weather events), which 20 may bring dramatic changes that overwhelm the steady, gentle changes that occur over tens or 21 even hundreds of years. Therefore, the model cannot explain the sudden changes in glaciers and 22 glacial lakes, as in the case of Jialongco. In addition, the parameters involved for these items are 23 highly uncertain in practice, and systematic and detailed scrutinization is required to improve the 24 accuracy of the operation. 25

Conclusion 26
This study employed multisource images and identified 147 glacial lakes in the Poiqu River in 27 the central Himalayas and explored the detailed changes in major glacial lakes. Tracing the 28 evolutions of glaciers and glacial lakes over the last 40 years, we find that the glaciers have 29 undergone increasing retreat while the glacial lakes grew and expanded. The major lakes have increased by up to 30% ~ 200% in area, at rates between 0.01 km 2 /a and 0.13 km 2 /a, which make 1 the Poiqu River an area of high levels of glacier and glacial lake changes in recent decades. 2 3 Detailed analysis of individual glacial lakes indicates that the lake grows in various patterns, 4 depending on local conditions of weather and geomorphology, or even occasional dramatic events 5 such as a lake outburst, icefall, or glacial surging. As these events are always inaccessible and 6 usually cannot be identified from images, abnormalities in glacial lake growth may provide hints 7 for those catastrophic occurrences. Meanwhile, small variations in lakes do not necessarily imply 8 no changes in glaciers and lakes. 9 Based on the changes in glacial lake area and DEM analysis, we abstracted the water change in the 10 lakes and proposed a WBE that governs the growth of the lake. As each item of the water 11 contribution specifically depends on local weather and morphology, the balance equation provides 12 a direct link between glacier and glacial lake changes and climate changes under local conditions. 13 Operation of the WBE for the five major glacial lakes in the tributaries of Poiqu River has 14 shown that individual lakes vary in different ways and receive water supplies from glaciers, snow 15 cover, and precipitation in different fractions. The results clearly reveal the altitude effect on 16 changes in glaciers and glacial lakes. At low altitudes, temperature is more effective for glacier 17 ablation, and lakes are mainly supplied by melted water from glaciers. At high altitudes, 18 temperature acts more on snow cover, and melted snow becomes the major water supply to lakes. 19 The difference between water supplies from glaciers and snow cover is as high as 50%, according 20 to the present cases. This implies that it is insufficient to apply weather or climate conditions to 21 individual glacial lakes at a large scale to determine climate effects on glacial lake changes. Zhang, G.Q., Bolch, T., Allen, S., Linsbauer, A., Chen, W.F., and Wang, W.C.: Glacial lake evolution and 10 glacier-lake interactions in the Poiqu River basin, central Himalaya, 1964-2017. J. Glaciol., 65, 347-365, 11 https://doi.org/10.1017/jog.2019.13, 2019 Zhang, Y., Liu,S. Y., and Ding.,Y. J., Spatial Variation of Degree-day Factors on the Observed Glaciers in Western 13 China. Acta Geographica Sinica., 61, 89-98, 2006. (     Note: EM--End moraine-dammed lake; ER--Glacial erosion lake; V-Glacial valley lake.