Modeling Glacier Mass Balance and Runoff in the Koxkar River Basin on the South Slope of the Tianshan Mts . during 1959 to 2009 , China

Water resources provided by alpine glaciers are an important pillar for people living in the arid regions in the west of China. In this study, the HBV (Hydrologiska Byrans Vattenavdelning) light model was applied to simulate glacier mass balance and runoff in the Koxkar River Basin (KRB) on the south slope of Mt. Tumur, western Tianshan Mts.. Daily temperature and precipitation were calculated by multiple linear regressions and gradient-inverse distance weighting, respectively, based on in-situ observed data by automatic weather stations (AWSs) in the basin (2007–2009) and at four meteorological stations neighbering the basin (1959–2009). Observed daily air temperature and precipitation were taken as input data for the HBV model, which was calibrated using runoff in 2007/08 and 2009/10, and validated in 2008/09 and 2010/11. Generally, the model could simulate runoff very well. The annual glacier mass balance and runoff were calculated using the HBV model driven by interpolated meteorological data for the period of 1959–2009. The simulated glacier mass balance were reasonable when compared with those observed values at nearby glaciers, indicating a decrease trend of mass balance in the basin with an average value of –370.4 mm a-1 since 1959. The annual runoff showed a slight increase trend (5.51 mm a-1). Futher analysis indicated that the runoff is more sensitive to temperature than precipitation amuont in the Koxkar river basin.


Introduction
Glaciers concentrated in mountain regions are important water resources and an oasis of economic lifeblood in arid and semi-arid areas in western China [1][2][3].Rising temperatures have resulted in the loss of more than half of the glacier volume in Asia since 1900 [4].In the northwestern arid area of China, the importance of meltwater is particularly prominent, meltwater runoff accounts for 22% of the runoff from mountains.andglacier meltwater from Tianshan Mts.supplies 38.5% of the total runoff in the Tarim River basin [5].Since 1980s, streamflow significantly increase which flow out from Tianshan Mts., the retreat of glaciers has a major impact on water resources in arid regions [6].
Hydrology in the arid region has become an important topic of research [7]and hydrological model can simulate hydrological processes and is of great practical significance and scientific value for exploring new ideas about integrated river basin management of water resources [8].However, due to the extremely high altitude and difficult environment of the Tianshan Mts., hydro-meteorological data for this inaccessible area are rare, especially in the glaciated watersheds.Additionally, there has been few application of hydrological models to the south slope of Mt.Tumur, Tianshan Mts.. Therefore, it is urgent to investigate water resources from glaciers in this area.
The HBV (Hydrologiska Byrans Vattenavdelning) model was developed by the Swedish Meteorological and Hydrological Institute (SMHI) for the cold regions in 1973.The HBV model, with its strong practical aspects and improved simulation results, has been applied successfully to forecast runoff for more than 200 river basins in Sweden and has been successfully applied in more than 40 countries of the world to study hydrological processes under climate change, changes of permafrost, and changes of land use [9][10][11][12][13][14].The HBV model is a semi-distributed conceptual model that requires less data input and produces better simulation results [15].It has also been successfully used in different watersheds in the cold region of western China.Kang et al. (2002) established a conceptual hydrological model for upstream of Hei river in Qilian Mts. of western China based on the principle of the HBV model.The model is in accordance with the characteristics of formation of mountain runoff in study area, where the basin was divided into two basic landscape zones, alpine tundra-snow and mountain vegetation, and the simulation were well [16].In addition, the model has applicability to glaciated watersheds in the Tibetan Plateau, where it also achieved well, the HBV light model includes glacier module which is more applicable for mountain regions where glacier distributed [17].

Study Area
The KRB is located in the southern Mt.Tumur, western Tianshan Mts., and is one of the source regions of the Akesu river (Fig. 1).The KRB has a total area of 116.5 km 2 with glacier area of 89.6 km 2 (76.9%), and its elevation ranges from 2960 to 6342 m a.s.l..The length of Koxkar glacier is 25.1 km, and the ice volume is 15.79 km 3 .Annual precipitation is about 533 mm in the KRB which is supplied mainly by moisture from the Atlantic and Arctic.Of the precipitation, 50% occurs from June to August, 70% occurs from May to September, and about 30% occurs during the cold season.Annual precipitation near the snow line is 750-850 mm [18][19][20].There are one automatic weather station (AWS) and one hydrological station located in the terminal of the glacier (Base Camp) (2974 m a.s.l.) (Fig. 1), and other four AWSs located in the glacier with elevations of 3200, 3400, 3700, and 4200 m a.s.l., respectively (Fig. 1).

Geographical data
The HBV light model requires geographical data including digital elevation model (DEM), aspect, and land cover.The 30-m-resolution Global DEM (http://datamirror.csdb.cn)and a digital vector map of modern glaciers were obtained from the Chinese Glacier Inventory [20].
The basin was divided by altitude zones, aspect zones, and zones with and without glacier (Fig. 2).The land cover data were taken from the Science Data Center for Cold and Arid Regions (http://westdc.westgis.ac.cn/).The land cover types include bare land, shrub, grassland, snow cover, glacier, and water (

HBV Model
The HBV model is a semi-distributed model, which means that a catchment can be separated into different elevation and vegetation zones as well as into different subcatchments [22].The HBV light conceptual runoff model, as presented here, is based on the HBV model [23].It was coupled with a more detailed snow and glacier melt subroutine employing the degree-day approach [24].The subroutine has a physical basis.For this study, the HBV light model, which takes into account various aspect classes in each elevation belt and couples Monte Carlo and genetic algorithms to calibrate the parameters automatically [25,26], was applied to model runoff depth, glacier runoff, and GMB in the KRB.The model is composed mainly of the input data, which were processed semi-distributed by four modules: the glacier ablation module, soil module, response module, and flow concentration module (Fig. 3) [22].The main formulae of each module are described as follows.The model simulates daily discharge using daily rainfall and temperature as input.Precipitation is simulated to be either snow or rain depending on whether the temperature is above or below a threshold temperature, TT [ ] ℃ .All precipitation simulated to be snow, i.e., falling when the temperature is below TT, is multiplied by a snowfall correction factor, SFCF.In the snow and glacier routine, the amount of meltwater is calculated by the degree-day method [27], which uses positive degree days (while daily mean temperature is above 0 ) multiplied by a factor.℃ This model also considers the influence of different aspect and different melt intensity of glacier and snow [25](Eq.2).Meltwater and rainfall are retained within the snowpack until the amount exceeds a certain fraction, CWH, of the water equivalent of the snow.Refreezing of meltwater is also considered in this model [28][29][30].Liquid water within the snowpack refreezes according to Eq. and TCALT [ºC/100 m] (Eqs.8 and 9).The long-term mean of the potential evaporation, Epot, M, for a certain day of the year can be corrected to its value at day t, Epot(t), by using the deviations of the temperature, T(t), from its long-term mean, TM, and a correction factor, CET [°C -1 ] (Eq.10) [31,32].
The formulae are as follows (Eqs 11 and 12).

Reconstruction of temperature
There are many methods to interpolate temperature, e.g., inverse distance weight, trend surface, kriging interpolation, cokring interpolation, and these methods are usually used to interpolate the spatial distribution of temperature.However, they require a high number of data points for calculation.In this study, we had only four NMSs for interpolation (Table 2).
Thus, the previous temperature data were interpolated by the statistical method of multiple regression analysis, which depended only on the temperature recorded at the four stations.
Two equations were formulated because the four stations had records of various length.
Reff was 0.88 from 2007 to 2009 which is fairly satisfactory considering the great varying of precipitation in the mountainous regions.By applying the above method, the annual precipitation at Camp-AWS from 1959 to 2009 was reconstructed (Fig. 7).The precipitation increased by 4.8 mm a -1 (p < 0.05), consistent with those of other studies [34].

Model calibration and validation
Except for meteorological data, there are 13 parameters in the HBV model that need to be calibrated (Table 3).To obtain a proper set of parameters, we gave every parameter a reasonable range according to the literature.A set of parameters representing the   mm a -1 (p < 0.01), and it increased more significantly after the 1990s than before the 1990s.The simulated result is consistent with the results for other watersheds in which runoff is observed in the Tianshan Mts.[39].Evaporation increased by 3.5 mm a -1 in the KRB.On the basis of the water balance principle (Eq.( 16)), the change in water volume in the basin (ΔS) equals the total precipitation (P) minus the runoff (R), soil evaporation and sublimation (Es), and evaporation at the glacier surface (Eg).Peer-reviewed version available at Water 2017, 9, 100; doi:10.3390/w9020100 ΔS is the sum of the soil moisture change (ΔSS) and the GMB (B), as shown in Eq. ( 17).The long-term GMB can be calculated according to Eq. (18).Because there is no permafrost in the KRB, it can be assumed that ΔSS did not change.The contribution of the change in ice content in permafrost to the water balance is less than 1% on a yearly scale [40].Precipitation was calculated by considering the precipitation gradient, ES was simulated, and Eg was regarded as constant at 137.2 mm (Fig. 10c) [41].Because there is no long-term observation of GMB in the KRB, we chose the two nearest glaciers (No. 1 in the headquarter of the Urumuqi river and Tuyuksu) in the Tianshan Mts., which have been observed in situ, to compare from 1959 to 2009.As can be seen from Table 4, the GMB value for Koxkar Glacier is between the values for the No. 1 and Tuyuksu glaciers, thus the simulated result is reasonable and credible.Glacial ablation in the KRB increased at a rate of 4.2 mm a -1 (p < 0.01) from 1959 to 2009, and the average elevation of glacier decreased by 18.53 m (16.68 m w.eq.), or at a rate of 370 mm a -1 (Fig. 10c).

Sensitivity analysis of runoff
In this study, we used the HBV model to analyze the sensitivity of runoff to changes of temperature and precipitation in the KRB.Climate change in the area is manifested mainly as changes in temperature and precipitation, and it has had a significant impact on the hydrological processes of the watershed, which is partly covered by glacier.Since the required input of the HBV model is daily data and the time interval of predicted meteorological data is monthly, in order to quantitatively study the sensitivity of runoff to changes in temperatures and precipitation, we assumed that the set of parameters and the glacier did not change into the future.Thus, the temperature was increased by 1 , ℃ 2 , and ℃ 4 , respectively, the precipitation was increased by 10%, 20%, and 30%, respectively, and the ℃ runoff was simulated by the HBV model.
When the temperature was increased by 1 to 4 , the amounts of change of monthly ℃ ℃ runoff differed, and the amount of annual runoff increased by 27.4%, 56.2%, 127%, respectively (Fig. 11, Table 5).As can be seen from Fig. 12, in the case of rising temperature, increases in the amount of runoff occur mainly from May to October.The month with the largest runoff is August, which shows that the runoff was supplied mainly by meltwater from the glacier.The distribution of internal annual runoff changes when temperature is higher (Fig. 11).Significantly increased runoff normally appears in May, and significantly decreased runoff normally appears in October; however, when temperature is higher, the significantly increased and decreased runoff shift to an earlier and later date, respectively.When precipitation increases by 10%, 20%, and 30%, monthly runoff increases by 6.1%, 11.3%, and 19.8%, respectively (Fig. 12, Table 6).Increased amounts of runoff occur mainly in the ablation season (from May to October).However, when precipitation is increased, the runoff does not increase very significantly.This is mainly because the runoff of Tianshan Mountain-based snowmelt is limited by temperature conditions; when only precipitation increases, runoff does not have a significant increase.Under the precipitation increases, increased runoff is concentrated mainly in June, July, and August.Within this period of time, radiation is sufficient and increased precipitation on the glacier leads to melting, which leads to increased runoff in the watershed.Increased precipitation causes a reduction in runoff from October to April (Fig. 12).

Discussion
Uncertainty of reconstructed meteorological data.Precipitation determines the accumulation of a glacier, and temperature determines the melting.Additionally, the amount and distribution of interannual variability of precipitation affects the supply and activity of a glacier [42].In this study, we used polynomial regression and IDW based on gradients to reconstruct temperature and precipitation in the KRB from 1959 to 2009.The accuracy of the reconstructed temperature is higher than that of precipitation; this is mainly due to the temperature being influenced by single factors in the mountainous region [43].The accuracy of the reconstructed monthly precipitation is better than that of daily precipitation.
Precipitation in mountains is influenced by many factors, e.g., elevation, slope, aspect, surface conditions, etc. [44,45].We considered only the influence of elevation in this paper and did not consider other factors.However, although the interpolated accuracy of precipitation was influenced, the result can reflect the long-term trend of precipitation.
Temporal and spatial differences of gradients of temperature and precipitation.Gradients of precipitation and temperature are important input data for the HBV model, and these are fixed values in the model.However, gradients of precipitation and temperature have some differences under different altitudes and surface conditions [46].Results show that the gradient of temperature has significant differences in areas of human activity, forest vegetation zones, and glaciated areas in each month, which can be up to 0.62 100 m ℃ -1 at the same altitude in different months [47].In the KRB, there are only six types of land cover and there is no human activity.Additionally, the area of glacier accounts for 76.9% of the watershed, so we assume that differences in surface conditions have little influence on the temperature gradient.In the Tianshan Mts., the gradient of precipitation is more complex than the gradient of temperature.Differences in lapse rate of precipitation are not only in a different aspect, but in a different aspect of the same month it is also significantly different, that is to say the gradient of precipitation of different month have differences in different elevation [45,48].Because of limitations from observation conditions, the gradients of precipitation and temperature in the KRB are averages, which makes the simulated process of runoff uncertain at the daily scale.
Temporal and spatial differences of degree-day factor.The degree-day factor of glacier and snow was an average value in the HBV model when we simulated runoff in the KRB.The degree-day factor is a key parameter in the degree-day model, and, with improved time resolution, the accuracy of the degree-day factor decreases [38].The degree-day factor is a sensitive parameter in the HBV model when runoff in a watershed having glacier cover is simulated.It is influenced by temperature, altitude, slope, and aspect [49,50].Previous studies have indicated that the degree-day factor shows temporal and spatial differences in the Tianshan Mts. and Tibetan Plateau [19,51,52].The area of the KRB is 116.7 km 2 , and the value of degree-day factor is 9.5 mm/day. in the model.Therefore, the monthly runoff is ℃ Peer-reviewed version available at Water 2017, 9, 100; doi:10.3390/w9020100more accurate than the daily runoff, which was simulated by the HBV model.The trend of the GMB results is consistent with increased glacier ablation in the Tianshan Mts. and is reasonable and credible at the annual scale.

Conclusion
In this study, variations of runoff and glacial characteristics over the past 50 years were simulated and the sensitivities of runoff under different temperature and precipitation variations in the KRB were analyzed.Temperature and precipitation were found to increase by 0.32 °C (10a) -1 and 4.8 mm a -1 , respectively, from 1959 to 2009 at Camp-AWS in the KRB.
Runoff depth increased at 5.6 mm a -1 .The simulated GMB of the KG was approximately 370 mm a -1 .The glaciers thinned 18.53 m from 1959 to 2009.The runoff is more sensitive to variation of temperature than variation of precipitation.Increases in precipitation and temperature will lead to changes in the internal annual distribution of runoff.
In this study, the HBV light model and the principle of water balance were employed to simulate the change in runoff depth, evaporation, glacier mass balance (GMB), and glacier runoff in the Koxkar river basin (KRB) during 1959 to 2009.The work aims to reconstruct climate change in the past 50 years in the region, to understand changes in glacier mass balance and runoff in response to climate change.This work may provide knowledge for water resource management in the arid regions of central Asia.

Fig. 1
Fig. 1 Locations of the Koxkar glacier and observation sites areas.Four meteorological stations around the Koxkar river basin are shown at top right

Fig. 2
Fig. 2 Elevation and aspect in the Koxkar river basin

Fig. 3
Fig. 3 Schematic structure of the HBV light model

3 .
Rainfall and snowmelt (P) are divided into water filling the soil box and groundwater recharge depending on the relation between water content of the soil box (SM [mm]) and its largest value (FC [mm]) (Eq.4).Actual evaporation from the soil box equals the potential evaporation if SM/FC is above LP, whereas a linear reduction is used when SM/FC is below LP (Eq.5)(Bergström 1973).Groundwater recharge is added to the upper groundwater box (SUZ [mm]).PERC [mm d-1 ] defines the maximum percolation rate from the upper to the lower groundwater box (SLZ [mm]).Runoff from the groundwater boxes is computed as the sum of two or three linear outflow equations depending on whether or not SUZ is above a threshold value, UZL [mm] (Eq.6).This runoff is finally transformed by a triangular weighting function defined by the parameter MAXBAS (Eq.7) to give the simulated runoff [mm d-1 ].If different elevation zones are used, the changes in precipitation and temperature with elevation are calculated using the two parameters PCALT [%/100 m] Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted: 31 October 2016 doi:10.20944/preprints201610.0139.v1Peer-reviewedversion available at Water 2017, 9, 100; doi:10.3390/w9020100

Fig. 6 Fig. 7
Fig. 6 Comparison of simulated and observed monthly precipitation (P) at Camp-AWS from 2007 to 2009

PreprintsFig. 10 Table 4
Fig. 10 Simulated annual runoff depth (a), evaporation (b), and annual glacier mass balance (GMB) and GMB (c) in the Koxkar river basin during 1959-2009 Table 4 Comparison of simulated and observed glacier mass balance accumulation between Koxkar Glacier and adjacent glaciers

PreprintsFig. 11
Fig. 11 Sensitivity of runoff under various temperature variations relative to 2007 to 2011

Fig. 12
Fig. 12 Sensitivity of runoff under different precipitation variations relative to 2007 to 2011

Table . 2
Details of the Camp-AWS and the four national meteorology stations (NMS) around the Koxkar

Reconstruction of temperature and precipitation data
Undstanding the climate, discharge, and GMB in past decades is important for predicting future trends.In this work, we used the HBV hydrological model to simulate runoff and GMB from 1959 to 2009.Long-term observed data are unavailable for the basin, so it was necessary to reconstruct the historical runoff and GMB.The daily air temperature and precipitation in

Table 3
Definition of and set of optimized parameters of HBV for the Koxkar river basin

Table 5
Change of runoff under various changes of temperature

Table 6
Change of runoff under various changes of precipitation