Surface Mass Balance Modelling at Naradu Glacier, Western Himalaya

In view of climate change, Himalayan glaciers are losing its mass. In present study we analyzed 7 12 year long field based data series of surface mass-balance measurements performed between 2011/12 13 and 2017/18 at Naradu glacier, western Himalaya. The average specific mass balance for the studied 14 period was 0.83 m w.e. with a highest melting of 1.15 m w.e. The analysis of topographic features 15 showed that south and southeast aspect along with the presence of debris cover area and the slope 16 between 18 to 36 degree are the major factors which causes highest melting from a particular zone. 17 For better understanding of SMB variability and its causes, multiple linear regression analyses 18 (MLRA) was performed by taking temperature and precipitation as predictors. The temperature and 19 precipitation records were taken from NASA GIOVANNI website. The MLRA shows that 71% of 20 the variance of observed SMB can be explained by temperature and precipitation. The MLRA shows 21 the importance of summer half-year temperature. This variable alone explains the 64% variance of 22 observed SMB. The seasonal period analysis showed that with two predictor variables most of the 23 SMB variability is described by summer temperature and winter precipitation. All monthly 24 combinations show that SMB variance is best described by June temperature and September 25 precipitation. apart from providing the

observed SMB. The seasonal period analysis showed that with two predictor variables most of the 23 SMB variability is described by summer temperature and winter precipitation. All monthly 24 combinations show that SMB variance is best described by June temperature and September 25 precipitation. 26 27 28 The importance of glaciers cannot be overlooked as they are the key indicators of climate change 29 apart from providing the fresh water to the downstream population. Worldwide, an increased global 30 average temperature by 1.5 ˚C is causing the enhanced melting of glaciers [1]. Rapid glacier mass 31 loss may further cause changes in the landscape of mountains and Polar Regions that affects the 32 global albedo and gives positive feedback to the warming phenomenon. It also has a very real impact 33 on local hazards, regional water cycles, and global sea levels [2][3][4][5][6]. 34 For more than a century, World Glacier Monitoring Service (WGMS) along with its antecedent 35 organizations is collecting and publishing glacier fluctuation data obtained from its forty-one 36 scientific collaboration countries. This effort has been taken to gather long-term glacier observations 37 which would further give insight into processes of climatic change such as the formation of ice ages 38 total numbers of 15 stakes observations were used to calculate the melting and accumulation 92 observations were based on the 4 snow pits at the elevation range of 5132-5249 m a.s.l. The mass 93 balance for the year 2013/14 is based on the observations of 10 new stakes distributed between 4773 94 to 5017 m a.s.l. and earlier stakes which continued standing in this year while the accumulation 95 observations were based on two snow pits at an elevation of 5123 and 5170 m a.s.l. The mass 96 balance of the year 2014/15 has been calculated by using 12 stakes (4618 -5064 m a.s.l.) and two 97 pits (5128 & 5183 m a.s.l.). To estimate the ablation of the year 2015/16, 10 new stakes were 98 installed in the ablation zone and the previous year's stakes enhanced the network while two pits 99 have been dug at the elevation of 5156 and 5222m asl. The network of 10 stakes (with some old 100 stakes) has been used for 2016/17 and 2017/18 mass balance estimation. During the seven years of 101 analysis, the variation between lowest and highest melting was -0.04 m w.e. to -5.07 m w.e. The melting are glacier hypsometry, slope and aspect [42]. In view of this, we tried to study all the 105 possible topographic factor for Naradu glacier which may affect the melting and found that south 106 and southeast aspect along with the presence of debris cover area and the slope between 18 to 36 107 degree are the major factors which make this zone the highest melting zone for four discussed years. 108 The detailed map showing the aspect, debris area and slope of Naradu glacier has been presented    to Figure 4b) and may have a major impact on the melting of ice/snow depending on its thickness 146 [54]. MLRA does not include those SMB measurements which are from the stakes that were not able 147 to survive for the whole study period. The involvement of these kinds of measurements will surely 148 raise the biases due to the gap in their dada record [55].

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The stakes elevation change with time due to glacier flow and changes in local ice thickness [55][56][57]

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The individual stake measurement is shown through Figure 3 a & b. The annual SMB was more 157 than 500 cm w.e. for all the balance year except 2014/15 which showed a slightly lower value.

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Modelled SMB values clearly show a significant increasing trend over 7 years as the p value of F-159 test is much lower than α = 0.01. The standard deviation in SMB per stake per year varied between 160 0.2 -11.8 cm w.e. a -1 and does not show correlation with elevation (as R 2 = 0.07) (Figure 4). 161 For analysis, the modelled SMB measurements for each stake were converted to perturbations by 162 taking a 7-year stake's mean. The SMB perturbation has been shown through Figure 5. During 163 analysis, we found a perfect correlation between SMB perturbation and elevation for all three stakes.

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Further, no link has been found between meteorological parameters (i.e. temperature and precipitation) and annual SMB elevation gradient. This "no linkage" is a prerequisite condition for 166 our analysis and is in the line with many other studies like [49] and related studies [58][59][60][61].

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To find the relation between meteorological data and SMB perturbation, the MLRA approach has 168 been used [55,62] by considering below equation 2. This correlation analysis required the abandon 169 of the effect of measurement of different meteorological parameters in different units (here, the 170 temperature in degree C and precipitation in mm w.e.) and hence these parameters have been 171 standardised by converting the data to z-score.

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Where y = dependent/response variable and will indicate SMB perturbation in the present study. 'a' 175 and 'b' are the regression coefficients and x1, x2,……….xn are the independent/predictor variables.

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Here, 1 2 will be represented by the z-score of the meteorological parameters i.e. temperature The goal of the study is to describe the observed SMB (through MLRA) by using temperature and between precipitation and SMB (refer to Figure 6a and Table 2).

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Secondly, the year is sub-divided into two categories i.e. winter half-year (WHY) and summer half-  PWHY (-11) indicates relatively higher importance of the SHY temperature (Figure 6b).

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Thirdly, the predictors were split into seasonal components i.e. spring (AMJ), summer (JAS), MLRAs by using a temperature and precipitation as a predictor variable. In the seasonal analysis we 222 found that with two predictor variables most of the SMB variability is described by summer 223 temperature and winter precipitation (R 2 = 82%; p-values F-test = 0.032) (refer to Table 2).

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Depth analysis of all monthly combinations was also done and the results show that the SMB  Temperature Dominance. The analysis shows that the observed SMB and temperature are strongly 255 correlated. The same findings have been reported by [38], in which they have assessed the impact of 256 inter and intra annual meteorological parameters variation on Naradu glacier mass balance. Koul and 257 Ganjoo estimated that the rate of melting of the Naradu glacier is positively proportional to the 258 temperature which is a function of solar radiation that reaches the glacier body. [65]found that the

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The Naradu glacier starts losing its mass from April and the process continues till September or May 271 extend till mid-October. In these months, along with the high temperature, the absence/reduction of 272 the snow cover also plays an important role in glacier melting. In these months, the snow cover, 273 which protects the glacier by reflecting the radiation shrinks and the glacier ice area is now widely years showed significant mass loss [72,73] . Later on, the reconstruction of mass balance on the 300 same glacier has been done by [74] for the 2001/02 to 2007/08. In this reconstruction analysis, 301 Kumar and others showed a negative mass balance for five years whereas the glacier gained the which has the longest study series outside the Baspa basin is the Chhota Shigri glacier [76]. This 306 glacier is well-studied in many aspects. The glacier has been studied for mass balance, energy   extended throughout the Himalayan region [83]. The studies, analyzing the effect of temperature and 332 precipitation on SMB variation found that SMB is more sensitive to temperature rather than 333 precipitation [55,84] but the scenario may change depending on the spatial position of a glacier [82] 334 resulting in the change in the magnitude of various meteorological parameters. The same findings 335 have been reported by [85]. This study was done on Glacier AXOIO in the Nepalese Himalaya by 336 taking three predictors namely; air temperature, precipitation, and relative humidity. The results of 337 the study showed that mass balance is more sensitive to air temperature as apart from melting it also 338 controls the phase of precipitation (snow or rain). In 2017, [75] have done the same study by taking 348 [87] analysed four glaciers of Norway using the sensitivity formula given by [88]. In this analysis, 349 Engelhardt found that at a higher temperature, SMB sensitivity to temperature increases whereas 350 SMB sensitivity to precipitation decreases. This shows the sensitivity of SMB also depends on the 351 magnitude of temperature and precipitation, for example, higher temperature causes the reduction in 352 the accumulation period and consequently reduces the amount of precipitation to be fallen as snow.

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Our continuous monthly time period analysis shows a higher correlation compared with other studies 354 [55]. This may happen because their analysis was based on many variables i.e. May-June-July 355 temperature and winter precipitation (here we took June temperature and September precipitation).

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Apart from variation in no. of variables, the results also depend on the authenticity of the data source 357 (here we took meteorological data from NASA GIOVANNI and field based SMB data) and it's 358 processing before use like a validation of the satellite data with field data and checking of the 359 homogeneity.

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Conclusions. This study uses the most accurate glaciological method to estimate the mass balance of  June causes most of the snow to be melted out and exposed old ice surface is rooting poor albedo.

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Further, the type of precipitation (rain/snow) also influences the SMB over the Naradu glacier.

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Study Area. Naradu glacier is one among 89 glaciers of the Baspa basin, western Himalaya [89]. disturbance is the non-monsoonal precipitation driven by westerly which brings sudden winter rain.

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The moisture of the western disturbance originates over the Mediterranean Sea [97]. In winter 404 months, western disturbance use to go to their lowest latitudes, and during their way they cross north 405 and central parts of India in a phased manner from west to east, disturbing normal features of 406 circulation pattern [98] and causes snowfall in higher elevations of NW India and winter rainfall in 407 plains of northern and central India. Baspa Basin falls in the western Himalayan Range and hence 408 receives its precipitation during winter months due to westerly disturbances (WD). The study region 409 receives nearly 70% of annual precipitation in winter and springs in the form of snowfall, and only 410 30% as rainfall near snout and as dry snow in higher-up regions [38]. while the snow density was calculated at the different depths of the snow pit.

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The variation between the beginning and the end of a hydrologic year represents the mass balance 427 change for that year [100][101][102][103]. In order to know the ablation of Naradu glacier in a particular year, The length of the stakes above the glacier surface was measured every year from September 2014 to 449 September 2018 together with ice/snow density and the emergence difference gives the annual 450 ablation at that point. 451 The pits have been dug at several altitudes in the accumulation zone to measure the density of snow.

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The pit location on the glacier is presented through a map. The previous year's surface was identified 453 from the dirty ice of the last year. The mass of the sampled snow was estimated through a weighing 454 machine. Snow density (ρ) at specific depth intervals was calculated by using the below formula: Where, M is the mass of snow collected in a known volume, V

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The ablation and accumulation values have been integrated over the glacier to calculate the mass 459 balance. The overall mass balance, Bi is calculated according to: hence GIOVANNI data has been carefully analysed for homogeneity. ANOVA test has been used to 477 check the inhomogeneity in temperature data whereas due to non-availability of real annual 478 precipitation data, we were unable to apply the same on precipitation data. ANOVA test has been 479 applied by considering the field observations (through AWS) of annual temperature data for years Where SMB is the annual specific mass balance (m w.e.), elevation represents the stake elevation (m 492 asl) and the uncertainties correspond to the 95% confidence level. Based on this simple linear fit 493 approach, the average ELA for the period of 2011/12 -2017/18 is expected to occur at 5523 masl.

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Which is slightly over estimated compared to real observations.