Simulating glacier mass balance in the cross-border Poiqu/Bhotekoshi Basin, China and Nepal

To assess the change of glacier mass balance (GMB) in the Poiqu/Bhotekoshi basin in the context of global warming, this study applied a conceptual Hydrologiska Bryans Vattenbalansavdelning (HBV) hydrological model to quantify the GMB in the area. The HBV model was trained and validated based on in-situ hydro meteorological data from 10 weather stations in the basin. The dataset, which consists of the daily observations for both rainfall and air temperature, was partitioned into two decades, 1988–1998 and 1999–2008 for calibration and validation, respectively. The calibrated model was adopted to restore the daily runoff depth and then estimate the annual changes of GMB in Poiqu/Bhotekoshi basin over the period of 1988–2008. Results show that the Nash–Sutcliffe efficiency coefficient (Reff) of the daily runoff depth simulation after the runoff calibration process was above 0.802. Therefore, the simulated values of the HBV model are reliable and can be used to estimate the GMB of Himalayan cross-border glacial mountain basins with huge elevation difference, and provide scientific data support for water resources management. Furthermore, the result demonstrated a slow year-by-year rise of snow water equivalent because of global warming, and it highly correlates with the soil moisture, the spring temperature and the summer precipitation.


INTRODUCTION
In many mid-latitude mountain regions, glaciers act as a temporal water storage such that new snow falls to nourish the glaciers in winter and then melts in summer (Jansson et al. ). Normally, the glaciers in these regions can keep a balance between the melting and nourishing, however such balance is at risk due to the climate change. Recently, glacier shrinkage has become increasingly serious and has drawn much attention from the public. The most crucial concern is that the shrinking glaciers are likely to cause water loss and stream-flow variability, particularly during the dry seasons of At transnational level, the concerns regarding the mid-latitude glacier shrinkage mainly concentrate on the accessibility of water resources, which has caused disputes and even conflicts among countries. Poiqu/Bhotekoshi basin, a mid-latitude transnational region between China and Nepal, is currently confronting the imbalance between glacier recharging and discharging (Fujita & Ageta ). A quantitative assessment of the glacier loss is urgently needed in order to support environmental decision making.
In this study, a hydrological conceptual framework is considered to support the quantification of the glacier loss. The conceptual model used by this study is different from the physical model. The physical model is based on the hydrological process research using experimental methods. However, some measured data of cross-border basins are very difficult to obtain. The conceptual model generalizes the physical basis of the basin, and then combines the hydrological empirical formula to approximate the flow process of the basin. The basic idea is to model the runoff during the melting season as compared to the rainfall or snow nourishment such that the GMB can be estimated. The main challenges of this study come from several aspects. First, the existing hydrologic models that are mostly developed for estimating the contribution of melted ice sourced from the mountain snow peak, which could not provide a straightforward inference for estimating the runoff caused by mid-latitude glacial melting. It is worth noting that many scholars have made great progress in the study of glacial runoff at very high altitudes in recent years (Zhu et al. ; Yin et al. ), especially in the estimation of runoff using the improved HBV model at a glacierized alpine catchment (Wang et al. ). Second, the runoff in high elevation upstream basins can be contributed by either ice or snow, and therefore an analytical separation is required to identify the flows from the melting glaciers. In addition, the bad transportation conditions in the study area led to the rarity of in-situ hydrological data. Despite the dataset being adequate in the context of temporal information, only 12 weather stations were sparsely distributed over the basin. To resolve the abovementioned concerns, a runoff model that provides separate estimations for ice and snow and is capable of handling 'small' datasets is significantly necessary (Kulkarni et al. ; Zhao et al. ; Sun et al. ).
A large number of previous studies have shown that the methodological development in glacial hydrology has gone through three stages, namely empirical statistical modeling, analytical modeling, and numerical modeling (Chen et al. ). The first two stages appeared in the 1970s and have no obvious temporal order in the application to estimate glacier runoff. Since the early 1990s, simple statistical models started fading in the applications of simulating glacier runoff.
On the other hand, the conceptual glacier hydrological model was in development on the basis of formulating the physical process of the glacier runoff. Until the late 1990s, Arnold et al. ()  As one variation of the conceptual HBV model, the glacier melt runoff was rescaled by elevations in order to be adapted to simulate the Heihe mountain runoff in the north of China (Kang et al. , ). Despite Kang et al. (, ) computing the runoff contributions from ice/snow and rain separately, their description of the runoff formation process was incomplete, for instance, the infiltration and melt water refreezing were not considered. This study added infiltration and melt water refreezing factors to the model, and a complete conceptual HBV model was proposed and then applied in the Poiqu/Bhotekoshi basin to simulate the runoff process and assess the changes of GMB.
The objectives of this paper are: (a) to establish a conceptual hydrology model that simulates the glacier melt runoff in the cross-border region between the Poiqu basin, China, and Bhotekoshi basin, Nepal; (b) to estimate the sensitivity of simulation factors for this model in a glacier-feed zone transitioning from a higher altitude to a lower altitude; and (c) to assess the change of GMB in Poiqu/Bhotekoshi basin and support the environmental decision making.

Study area
Poiqu/Bhotekoshi, a tributary of the Cauchy River in the Ganges upstream, is one of the main water resources of Nepal, and since it flows across three countries, it is an important and invaluable topic in transnational environmental management (Figure 1). Poiqu/Bhotekoshi river, which originates in Nyalam County, China (85 25 0 -E86 30 0 E, 27 30 0 -N28 35 0 N), is 117 km long covering an area of 2,018.41 km 2 . In this river basin, the altitude changes rapidly from 4,554 to 616 m, which leads to a convergence of various climate, soil types, and landscapes. The precipitation in Poiqu/Bhotekoshi basin is spatially imbalanced; the northern Himalayas have 300-400 mm yearly rainfall, while the annual precipitation usually stays between 1,000 and 1,500 mm in the south (subtropical and tropical area).
The annual rainfall in the middle Poiqu/Bhotekoshi basin can also reach more than 1,000 mm, however a large amount of annual evaporation is observed. The ecological degradation, population concentration and the unbalanced distribution of precipitation, which in turn lead to serious soil erosion, attribute a dry characteristic to the valley area. The basins are widely spread from the most southern region to Zhangmu-Nyalamu region (above 5,000 m), and the corresponding surface soil content changes from southern alluvial soil and mountain red soil to the yellow brown soil and cold desert soil. From south to north, the vegetation type changes from coniferous/broad-leaved to shrub/meadow. In this study area, the relative elevation difference is large, so the simple statistical model is not suitable for glacier runoff simulation. The introduction of conceptual glacier hydrological model HBV focuses on the physical process of glacier runoff formation, which is helpful for the accuracy of simulating runoff and material balance.

Data
Due to the complexity of the conceptual HBV model, various factors (model input) are required, including daily average temperature, daily precipitation, monthly potential evaporation, temperature gradient, and annual precipitation gradient. In this study, the daily precipitation, daily tempera-  By using the Thiessen polygon method, the spatio-temporal interpolation of continuous daily precipitation value was conducted based on the precipitation data of six stations (Nyalum, Gumthang, Barhabise, Dhap, Nawalpur and Chautara). Then, the temperature data in two of the stations (Nyalum and Panchkhal) were used to estimate the daily average temperatures of the Poiqu/Bhotekoshi basin.

Water input calculation
In the study area, glacier melting, snow melting and rainfall are the main sources of basin runoff. Note that rainfall was considered as snowfall if the air temperature was below a threshold temperature T 0 ( C). After the accumulated snow on top of the glacier has melted completely, the amount of glacier melting is termed as an ice melting volume (Equations (1) and (2)) ( Table 1) (Hottelet et al. ; Konz & Seibert ):

Quantify soil water and evaporation
According to the concept of HBV, the soil moisture layer (SML) is defined as the layer that is below the soil surface and above the depth of active permafrost or water table.
In Equation (3), WR (mm) is the amount of seepage water that travels to the glacier and SML from different sources, and RO is the soil infiltration depth that calculates the water flux from soil to groundwater aquifer (Seibert & Vis ). Their relationships are given as (Table 1): A soil-box experimental model of evaporation, E p , is given as: when SM is less than L p , the ratio of actual evapotranspiration (E p ) to potential evapotranspiration (E) is linear with soil moisture; when the SM is greater than L p , E p is equal to E.

Model evaluation criteria
The R eff and coefficient of determination (r 2 ) (Equations (8) and (9)) were employed in this study to test the model accuracy (Nash & Sutcliffe ; Seibert ). While interpreting both indices, 1 indicates perfect performance and 0 is poor (Table 1).

Glacier mass balance
In accordance with the basin precipitation, runoff, and soil evaporation data were obtained by the model (Equation (10)), and are based on the principle of the water balance (Table 1): Model settings The daily  To prevent duplication, the data from closely adjacent stations were aggregated and allocated to the lower reaches of the basin. To avoid the high computational cost, the altitude was discretized into three levels: <1,800, 1,800-3,000, and 3,000-5,000 m. The land cover types were organized into two major ecosystemsglacier and forest (Table 2).

Model parameter calibration
To calibrate the model parameters, we combined a genetic algorithm (GA) with a trial and error method, along with  (1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998) was used for the parameter calibration in order to obtain a comprehensive model parameter ( Table 2). The sensitivity of the model was tested for 15 parameters (Table 3), and it was found to be significantly sensitive to recession coefficient K 1 , the snow adjustment factor and the soil field waterholding capacity, and also relatively sensitive to threshold temperature (TT), refreezing meltwater (CFR), a certain portion of the water equivalent of the snow pack (CWH), lower base flow recession coefficient (K 2 ) and max percolation to lower zone (PERC). In order to test the model efficiency, the calibrated parameters were used to conduct the nonparameter calibration. In this study, the data from 1999 to 2008 were adopted to validate the model test. The value of the first 10 years is used to calibrate the simulation model, and the second 10 years is used to verify the accuracy of the future prediction. The accuracy of calculation results is relatively high, which denotes that the model is feasible.
The R eff of the observed value and simulated value were 0.84 and 0.80, respectively (Figure 3).

Simulation result test
After the model simulation, the simulation results and the efficiency coefficient of each year were obtained. The best R 2 was 0.84 and the worst year reached 0.80, indicating that the model could explain more than 80% of the flow generation process in the basin (Figure 3). In terms of simulation accuracy, our model was successful in the study area. This benefits from the setting that the model takes into account both the glacier melting runoff in summer and snow water equivalent in winter, which results in the simulated values being close to the actual observed value.
However, the degree-day factor method of the glacier melting simulation in the model had insurmountable defects.
For example, with the increase of the time resolution, the simulation precision lowered (Hock ). Therefore, when comparing the model simulation with the observed monthly runoff depth (Table 4 and Figure 4), the effect was higher than the precision of the daily runoff depth. In addition, the correlation R 2 between the simulated monthly runoff depth and the observed value was as high as 0.98. In contrast with the annual runoff depth, the error in the maximum annual runoff depth was less than 6% during the model validation (Table 4). Since there is no practical significance for analyzing other months because of the dry season with less runoff, the precision was considered to be acceptable.
In summary, the model performs better in the simulation of monthly runoff depth than daily runoff depth, indicating that the changes in the monthly runoff depth obtained by the model were more acceptable.

RESULTS AND DISCUSSION
Besides the influence of precipitation and temperature, the

Temperature
Based on the in-situ meteorological observations, kriging interpolation was implemented to map the annual high,  1988-1998; and (b) validation period: 1999-2008. annual average, and annual low temperature. After that, a comparison was made among these temperature estimations. The daily temperature changes also followed the annual cycle. The difference between the annual maximum and minimum temperature was 0.22-39.56 C. However, the temperature increased with the altitude decline. At altitudes between 3,800 and 4,300 m, the annual average temperature was around 3.25-3.82 C ( Figure 6). However, a warming trend was shown on the northern Himalayas, where the temperature tendency rate was 0.32 C × 10 a -1 . This may contribute to the accelerated snow melting in that region.
When the altitude was approximately 2,000 m, the annual average temperature reached 14.56 C. At altitudes between 1,300 and 1,400 m, the annual average temperature was 17-18.56 C, which was higher than that at 2,000 m by 4 C, and its maximum reached 36 C. Furthermore, the temperature tendency rate was only 0.006 C × 10 a -1 , and the elevation showed a slowly increasing trend. At the altitude of 900-1,000 m, the average annual temperature was 21.34 C. At altitudes below 100 m near the equator, the temperature was very high, with the maximum temperature being as high as 39.56 C, and the minimum temperature 2.35 C.
The multiple regression method was adopted to obtain the daily average temperature of the Poiqu/Bhotekoshi basin based on the observation data of weather stations.
At the same time, the daily precipitation data were also obtained. Through mathematical statistics, it was determined that in the last two decades the basin temperature and the precipitation showed upward trends with average changing rates of 0.15 C × a -1 and 0.97 mm × a -1 , respectively.    year by year; on the other hand, the stable snow area is expanding and perennial snow cover is shrinking, which may be influenced by global warming.

Soil moisture storage and soil infiltration depth
Because the soil water content between the upper and lower layers is highly correlated, the soil water content in the upper layer can be estimated by using soil moisture storage in the lower layers through the HBV model. Soil moisture storage showed a nonlinear increasing trend in its depth

Analysis of basin runoff in upper and lower layer
The basin runoff needs to be considered in two soil conditions, high permeability and low permeability. In the high permeability of the upper layer, the water level descends following the decreasing rainfall and soil infiltration without interception, then we define the storage threshold of the upper layer as UGL (Equation (5)). When the upper groundwater storage is greater than UGL, the runoff is determined by the coefficient K 0 . If it is less than UGL, the value will be determined by K 1 . In the low permeability of the lower layer, the groundwater level is no longer declining, or decreasing slowly, even if the rainfall and other factors are still dropping. The runoff in the lower layer is determined by the coefficient K 2 . water level rises, the underwater pressure increases, the water infiltration increases, and the peak value of groundwater runoff curve will be higher. In the season of heavy rainfall, the infiltration of rainwater also increases, and the peak value of groundwater runoff curve will be higher.
One of the reasons is that the water level of the storage in upper groundwater is always greater than the lower, which leads the groundwater to flow downwards to the soil aquifer.
Another reason is that part of the water flows into the sea due to the hydraulic gradient.

Basin runoff
In this study, the runoff was represented by the runoff depth.
The daily runoff in the simulated annual cycle shows a similar overall trend. It increases in early January, peaks in August, and then declines in October. In August 1988, the maximum runoff reached 714 mm, and the maximum of other years ranged from 300 to 470 mm (Figure 4).
According to the spatial pattern of the runoff depth in the Poiqu/Bhotekoshi basin, the runoff depth gradually increased from north to south. The runoff depth on the northern slope of the Himalayas was relatively lower   and October-December, as shown in Figure 5.

Calculation of basin water balance
The change of permafrost in the river basin contributes to less than 1% of the water balance (Zhang & Yao ). Therefore, it is reasonable to assume that the annual average soil moisture content in the study area did not change. In the calculation, the impact of the precipitation gradient was considered in the precipitation (P) (Equation (10) This model can now be used to perform some monthly mountainous traffic trail forecasting based on the Poiqu/ Bhotekoshi basin, which is located in a particular zone transitioning from a higher altitude to a lower altitude.
From the analysis of glacier/snow modules, soil modules and groundwater module, the days of snow accumulation in the Himalayas was decreasing, in particular, the permanent snow area is shrinking with an annual rate of -1.00 × 10 3 m 3 a -1 because of global warming. The stable snow area was increasing, which results in a slow rise of snow water equivalent. The annual soil moisture storage was mainly affected by air temperature, and the correlations between soil moisture and temperature in spring, and soil moisture and rainfall in summer were the most significant. The model also simulated the storage and runoff of the most important groundwater response area. The simulation was performed on two soil layers, and then the water mass balance values were calculated. The R eff of the daily runoff depth simulation after the runoff calibration process was above 0.80. Therefore, the HBV model had a good simulation efficiency on the annual daily runoff depth in the Himalayan cross-river glacial mountains. The water and heat conditions of glaciers in the Himalayas are constantly fluctuating, and the annual material balance is also different. Sometimes the accumulated amount is greater than the melting amount, and a positive balance appears, which is conducive to the development of Himalayan glaciers; otherwise, it will produce negative balance, leading to glacier shrinking.
The results show that the simulated values of the HBV model are reliable and can be used to estimate the GMB of cross-border mountain basins with huge elevation difference, and provide scientific data support for water resources management. However, in this study, hydrological observation data and evapotranspiration data were inadequate, and more abundant model-driven data can further improve the simulation accuracy. In addition, hydrological and underlying surface data can be used to regionalize the parameters and provide scientific data support for hydrological forecasting in the future study.