Comparative Study of Hydrology and Icemelt in Three Nepal River Basins Using the Glacio-Hydrological Degree-Day Model (GDM) and Observations From the Advanced Scatterometer (ASCAT)

An assessment of the water supply and its seasonal and annual changes over the century in the High Mountain Asia (HMA) region is of increasing interest due to its potential impact on one-sixth of the global population. In order to understand the changing hydrology and snow and ice melt, we used remotely sensed Advanced Scatterometer (ASCAT) observations of glacier melt (GM) and a distributed and gridded Glacio-hydrological Degree-day Model (GDM) in three river basins: Tamor, Trishuli and Marsyangdi. The GDM-estimated contribution of snowmelt, icemelt, rainfall and baseflow in river flows is found to be most accurate in the Trishuli River basin, with Nash-Sutcliffe efficiency (NSE) between the estimated and observed discharges of 0.81 and volume differences of −0.5%, and reasonably accurate in the Tamor River basin, with NSE of 0.69 and volume difference of −7.51%. Similarly, NSE of 0.81 and volume difference of 4.64% in Marsyangdi River basin. We find strong similarities in the timing of glacier melting using the GDM and from observations from the ASCAT GM, determining the seasonal start of glacier melting to within 6 days on average. In all basins ASCAT GM observes melting at higher elevations relative to GDM, average of 5,328 m a.s.l. Systematic differences in glacier melting area determined by modeling and satellite observations indicate ASCAT may have suboptimal resolution, view geometry and/or polarimetry for delineating glacier melting at the process-scale in complex topography, especially in the ablation zone. This is the first step in examining the remote sensing products that could potentially be incorporated into hydrologic models to increase the accuracy of the hydrologic flow as well as the ability to estimate river discharge in other basins with limited data.


INTRODUCTION
An assessment of the water resources and the seasonal and annual changes over the century in the High Mountain Asia (HMA) region is of increasing interest to scientists of multiple disciplines. The water supply in the upper reaches of the HMA is particularly sensitive to climate change (Wagnon et al., 2007;Immerzeel et al., 2010) and it share high percentage contribution from snow and glacier melt in river discharge (Koppes et al., 2015). The water supply in the upper reaches of the HMA is particularly sensitive to climate change because of the high share of river discharge contributed by snow and glacier melt. HMA contains the largest deposit of glacier ice outside of the North and South Pole regions; hence it is sometimes called the "Third Pole." The Himalayan range encompasses about 15,000 glaciers, which store about 12,000 km 3 of fresh water (IPCC, 2007). Many authors have suggested that the shrinking of glaciers in response to climate change might change the hydrological regime in these regions (Bolch et al., 2012;Immerzeel et al., 2012;Kääb et al., 2012). A decrease in glacier volume and area tends to influence the intensity of the seasons and the interannual variation on runoff (Juen et al., 2007). Glacier melt's contribution is projected to increase until 2050 and then decrease in the sub-basins (Immerzeel et al., 2013). Regionally, it is expected to increase discharge until 2050 and then decrease (Lutz et al., 2016). In western Himalaya, glacier melt's contribution to runoff is projected to increase by 16-50%, with a 1-3 • C increase in temperature (Singh and Kumar, 1997;Tahir et al., 2011;Sam et al., 2016). While about 53 million people inhabit the 2400 km of the Himalayas, more than one billion people living downstream depends on the water from HMA, for the food and energy production (Apollo, 2017). The changes in river flow are expected to directly affect the availability of water for hydropower generation, drinking, irrigation, industrial and other purposes affecting one-sixth of the global population.
Hydrologists and glaciologists started to use snowmelt and glacio-hydrological models in the 1990s to estimate river flows as well as the contribution of snow and glacier melt to the flows in the HMA region. The two melt-modeling approaches currently used to calculate the discharge of glacierized river basins are the energy balance model and the temperature index model. The energy balance approach explicitly models melt as a residual in the surface-energy-balance equation when accounting for sums of energy fluxes within the atmosphere and glacier boundary (Reid and Brock, 2010). The temperature-index-model, on the other hand, derives melt from the empirical relationship between air temperatures and melt rates (Braithwaite, 1995;Hock, 2003).
Although the energy balance approach best describes melt totals (Hock, 1999(Hock, , 2003, this approach is not always feasible for remote Himalayan glaciers, where input data availability is a major constraint (Kayastha et al., 2000). Several studies have used temperature index models in data-scarce Himalayan basins (Takeuchi et al., 1996;Kayastha et al., 2000Kayastha et al., , 2005Kayastha and Shrestha, 2019) to estimate river discharge at different temporal scales. Four main reasons for using the model are: (1) the wide availability of air temperature data, (2) the relatively easy interpolation and forecasting possibilities of air temperature, (3) generally good model performance despite its simplicity, and (4) computational simplicity (Hock, 2003).
On the other hand, several studies have modified the simple temperature index model by incorporating different parameters, such as albedo, shortwave radiation and melt factors, to improve the model's performance (Cazorzi and Fontana, 1996;Hock, 1999). Wortmann et al. (2016) incorporate glacier extents, volume and ice flow into the eco-hydrological soil and water integrated (SWIM) model (SWIM-G) to perform glaciohydrological modeling of the Upper Aksu catchment in Central Asia. Similarly, Douglas et al. (2016) modified a glacier evolution and runoff model (GERM) to incorporate debris cover and thickness and to redistribute mass losses according to observed surface elevation changes and used it to study the upper Khumbu catchment in Nepal. Ren and Su (2018) coupled an energybalance glacier-melt scheme with the variable infiltration capacity hydrology model (VIC-glacier) and applied the model in a catchment in eastern Pamir. This model provided a tool for sensitivity tests and for quantifying the response of glacier melt and discharge, enabling estimates of the impact of climate variability with a physically based method.
We examined a range of remotely sensed products that could potentially be incorporated into the Glacio-hydrological Degreeday Model (GDM) to increase the accuracy of the model as well as the ability to estimate river discharge in other basins with limited data. In this study, we made the first step toward incorporating remotely sensed data on glaciers melt estimation, and compare the model-based freeze, thaw, and melt in three river basins of HMA region with Advanced Scatterometer (ASCAT)-derived freeze, thaw, and melt.
Realizing the need for models at a higher spatial resolution to accurately represent the rugged topography of the HMA region, we present the recently developed gridded GDM, which is capable of providing melt data at 4.5 km × 4.5 km grid level. GDM is used to derive the sources of melt -icemelt (debriscovered ice, clean ice), snowmelt, rain and baseflow -in the river discharge. We then compared the results of glacier icemelt from GDM with icemelt estimated using ASCAT data in three basins in the HMA region.

Study Area
We compared GDM results with ASCAT in three river basins of Central Himalaya: Tamor, Trishuli, and Marsyangdi River basins (Figure 1), which are sub-basins of the Koshi and Narayani River basins in the Himalaya. While the climate of all three basins is dominated mostly by the Indian summer monsoon from June to September and occasionally by the westerly disturbance post monsoon (October-January), the basins differ in the location and the aspect (facing north or south) of the glaciated area at various elevation ranges and are exposed to different orographic effects. The part of Trishuli River basin that lies in Nepal (40%) is influenced by the Indian summer monsoon and orographic effects, while leeward phenomena prevail in the rest of the basin, which lies on the Tibetan plateau. Most of the Tamor River

Setup of the GDM
The GDM, Version 1.0 is a gridded and distributed glaciohydrological model capable of simulating the contribution of hydrological components in river discharge. GDM simulates four different runoff components in total discharge: snowmelt, glacier icemelt, rainfall and baseflow at daily time steps. A melt module is based on the degree-day approach, a simplification of a complex process (Braithwaite and Olesen, 1989) to estimate glacier ice and snow melts with minimal data requirements (Kayastha et al., 2005). The two-reservoir based modeling approach of the soil and water assessment tool (SWAT) (Luo et al., 2012) is adopted to simulate the hydrological response of the baseflow and rainfall runoff contribution to river discharge. In the case of the Trishuli River basin, the basin is divided into 4.5 × 4.5 km grids, and classified land class information from GlobeLand30 is extracted to each grid in order to match the grid size of the ASCAT data. Daily temperature and precipitation are extrapolated to each grid from the reference station for the discharge simulation. The threshold temperature (T T ) determines whether the precipitation is in the form of snow or rain in each grid in the respective time step: where T is the extrapolated daily air temperature for the grids and T T is threshold temperature, both in • C. In each grid, daily ice melt from debris-free and debriscovered ice and snow melt from glaciated and glacier free areas is calculated as: where M is the ice or snow melt in mm day −1 in each grid, T is daily air temperature in • C, and K d, Ks, and K b are the degreeday factors for debris-covered ice, snow and clean glacier ice in mm • C −1 day −1 . The model takes into account the multilayer melting of the snow above clean ice and debris-covered ice. Baseflow is calculated using a baseflow simulation approach, as in SWAT (Luo et al., 2012). The surface runoff (Q G ) in the model does not consider sub daily precipitation; the surface runoff consists of runoff from rainfall and snowmelt from each grid. The surface runoff component is calculated grid-wise based on the following equation: where Q r is discharge from rain and Q s is discharge from snowmelt and icemelt in m 3 s −1 , C r , and C s are the rain and snow runoff coefficients, and Q G is surface runoff component from each grid in m 3 s −1 . The total surface runoff contribution Q R from all grids and the total baseflow contributions Q B from all grids are expressed as: where Q b is the baseflow contribution from each grid and n is the number of grids. Total surface discharge Q R is then routed with the baseflow contribution Q B toward the outlet through the following equation: where k is the recession coefficient, Q d is total discharge in m 3 s −1 and d is the d th day. The recession coefficient k is obtained by solving Eq. 7 given by Martinec and Rango (1986). The constants x and y computed from this equation are 0.95 and 0.002, respectively, for all river basins.

Input Data
Daily air temperature, precipitation and stream flow data, which are the main input data of respective river basins to the model, are obtained from Department of Hydrology and Meteorology, Government of Nepal (Table 1). Air temperature and precipitation measured at the climatological station in Taplejung, which is 1732 m above sea level (a.s.l.) is used as input data set for Tamor River basin, together with the hydrological station at Majhitar at an elevation of 533 m a.s.l. Likewise, data from the Khudi Bazar (823 m a.s.l.) and Chame (2680 m a.s.l.) climatological stations are used to derive temperature lapse rate and precipitation gradient in the MRB. Similarly, the Timure (1900 m a.s.l.) and Kyangjing (3862 m a.s.l.) climatological station datasets are used to derive temperature lapse rate and precipitation gradient in Trishuli River basin.
For the geo-spatial dataset, the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) global digital elevation model version 2, with 30 m spatial resolution, available from the United States Geological Survey 1 , is used for the grid elevation information. GlobeLand30 with 30-m resolution 2 is used for land cover. Ten different land cover classes from the GlobeLand 30 dataset are merged with similar topology character and surface runoff behavior to create six land classes for similar ranges of rainfall runoff coefficient, as shown in Table 2. In this study, land use type is classified into six classes (land use types 1, 2, 3, 4, debris-covered glacier and clean glacier ice). The shape files from the International Centre for Integrated Mountain Development Glaciers Inventory (2010) are used for clean and debris-covered glacier information. The land use types and hypsometry of all three river basins are shown in Figure 2.

Hydrologic Simulation Experiment Design
The performance of GDM is first calibrated in all three river basins by comparing the simulated discharge with the respective observed discharge from 2000in Tamor River basin, 2007in Trishuli River basin and 2004 in Marsyangdi River basin at respective hydrological stations of the basins. The melt module parameters, such as degree-day factors for snow and ice melt, are based on field observations in the Nepal Himalayas carried out by Kayastha et al. (2000) and Kayastha et al. (2003). The degree-day factor for ice melt under a debris layer is assumed to be around half than that of clean ice, based on the field observation on Khumbu and Lirung Glaciers in the Nepal Himalayas.

Performance Indices
To assess the model's performance efficiency, we compared the daily time-series observed and simulated discharges. The Nash-Sutcliffe efficiency (NSE) index (Nash and Sutcliffe, 1970) is used to assess the model's simulated discharge against the observed discharge, as shown in equation 8.  Numbers without parenthesis in land use type denote area in% and numbers in parentheses denote area in km 2 . where n is the number of days, Q obs is the daily observed discharge, Q sim is the daily simulated discharge, and Q avg is the average observed discharge.
Similarly, volume differences are used to determine the model's accuracy and calculated by using the following equation: where V R and V' R are the measured and the simulated discharge, respectively.
A prediction from such a model is associate with a certain degree of uncertainty due to errors during the calibration of parameters, the design of the model and measurements of input data. In this study we assume that the model has higher degree of accuracy and certainty if the NSE index higher than 0.7 and volume difference up to ± 10%.

Glacier Melting Based on Satellite Observation
We used radar observations from ASCAT, on EUMETSAT satellites MetOp-A and -B, to detect glacier melting in mountain basins at a daily time-step (Steiner and McDonald, 2018). The ASCAT Scatterometer is a six-beam radar instrument that measures normalized backscatter at microwave frequencies (C-band, 5.255 GHz) with vertically polarized antennae. These observations are not sensitive to clouds and provide a temporally dense time-series of surface observations. The full-resolution ASCAT swath is normalized to an incident viewing angle of 40 • and spatially enhanced using the Scatterometer image reconstruction algorithm (SIR) (Early and Long, 2001). The ASCAT normalized SIR backscatter observations have an effective spatial resolution between 15 and 20 km and are gridded to 4.45 km (Lindsey and Long, 2012).
In glaciated high mountain landscapes, radar backscatter signatures are dominated by scattering from deep snow and firn (Drinkwater et al., 2001). Snowfields in the accumulation zone of mountain glaciers are distinguishable in imaging radar mapping by large-magnitude backscatter caused by volume scattering from subsurface structures (Rignot, 1995). During melting conditions, volume scattering at microwave frequencies is greatly reduced because of increased absorptivity caused by wet snow and ice (Nghiem et al., 2001). Associated time-series changes in backscatter are abrupt as melt onset occurs and lead to discontinuous step-changes in the backscatter time-series that can be detected numerically (Steiner and Tedesco, 2014). We determined the timing of glacier melting events from these radar signatures over the entire Himalayas, from 2007 to 2018, similar to Steiner and Tedesco (2014), using a multiscale analysis to detect negative (melting) and positive (refreeze) changes in backscatter (Mallat, 1999). To isolate glacier-dominated backscatter we apply a criterion to ensure that the frozen season is separable from periods of melting, as detected using wavelet classification. To identify melting conditions, the associated backscatter must be separated from the frozen state backscatter by at least two standard deviation (σ) of the frozen season backscatter variability. These data are stored at the National Snow and Ice Data Center, as part of the ASCAT freeze/thaw and glacier-melt product (ASCAT FTGM) (Steiner and McDonald, 2018). We spatially harmonized the ASCAT FTGM product with output from the GDM model using nearest-neighbor interpolation.

Model Calibration
The positive degree-day factors, snow and rain coefficients, and recession coefficient are the main calibrating parameters of the GDM. The model is calibrated with different positive degree-day factors, and a set of degree-day factors is adopted for different months, within the range of estimated degree-day factors on different glaciers of the Nepal Himalayas. Two sets of degreeday factors for snowmelt and icemelt; lower degree-day factors at altitudes lower than 5000 m and higher degree-day factors at higher than 5000 m altitudes are used. Again higher degree-day factors are used in non-monsoon months and lower degreeday factors are used in monsoon months; June to September. Similarly, the model is also calibrated with snowmelt and rain runoff coefficients and recession coefficients. Snowmelt and rain runoff coefficients are also used higher in monsoon months (from 0.4 to 0.9). All the calibrated parameters and coefficients used in the study are listed in Table 3. The degree-day factors, snow and rain runoff coefficients, recession coefficients, and other input parameters used in the 5-year calibration period were fixed and used for flow simulations for the whole period in all river basins.

Parameters
Tamor River basin Trishuli River basin Marsyangdi River basin   Daily simulated discharge is compared with the observed hydrographs of all three river basins Tamor, Trishuli and Marsyangdi River basins as shown in Figure 3. Both high and low simulated discharge were consistent with the observed discharge in the river basins, except in few cases. The model also caught pre-monsoon low flows reasonably accurately. The model could not catch few peaks in the graphs, which may be due to underestimation of the precipitation at high altitudes. Barry (2012) and Baral et al. (2014) reported that the precipitation gradient in the mountainous environment is considered to vary vertically and horizontally. The high Himalayan region, with complex topography within the basin, also affects the spatial and temporal distribution of precipitation, which might be a constraint on representing the precipitation pattern or distribution. In this study, climatological stations within each respective basin were used to derive the precipitation gradient and distribution. Even with such limitations, the model simulated the daily discharge with good NSE values and within 10% of the actual volume, in spite of limited input data ( Table 4).

Contributions of Snowmelt, Icemelt, Rainfall, and Baseflow
Glacio-hydrological Degree-day Model also estimates the contributions of snowmelt, icemelt, rainfall, and baseflow to river flows. Figure 4 and Table 4 show the mean annual contributions of snowmelt, icemelt (clean and debris-covered), rainfall, and baseflow for in all three river basins of this study. The contribution of snowmelt ranges from 7.8% in the Marsyangdi River basin to 13.93% in the Trishuli River basin. The contribution of icemelt in river flow ranges from 6.6% in the Tamor River basin to 12.88% in the Marsyangdi River basin. Rainfall contribution to river flow is 29.9% in Trishuli River basin and 39.04% in the Tamor River basin, and baseflow varies from 41.35% in Marsyangdi River basin to 45.44% in the Trishuli River basin. This range of contributions to river flow is consistent with the area covered by glaciers and the climatological condition of the river basins.

Comparison of Snow and Icemelt From GDM and ASCAT Product
Icemelt derived from GDM is compared with the ASCAT FTGM dataset to investigate the differences in melt extent and duration.
With this comparison we also evaluate the utility of the ASCAT satellite record in providing observations that can be used to inform, complement, or validate hydrological modeling. Table 5 summarizes some spatial and temporal statistics of observed icemelt during 2007-2010. For all basins ASCAT detects melting extent at substantially higher elevations and over larger areas, on average, than GDM, with exception of the Trishuli River basin. We find that the melt duration detected by ASCAT is longer than the melt duration estimated using GDM. This is especially true in the Trishuli River basin and Tamor River basin where ASCAT-observed melting is 20 and 26% longer, respectively, than modeling suggests. There is also a lesser degree of spatial variability in the duration of melting observed by ASCAT. The longer melting duration observed by ASCAT is largely related to melt persisting later into the season, as ASCAT observes Marsyangdi River basin as having later icemelt start than does GDM whereas Tamor River basin has earlier icemelt starts than GDM. Summations of annual glacier melt duration derived after running the GDM by increasing and decreasing one σ of the air temperature and precipitation over the Tamor, Trishuli and Marsyangdi River basins compared with the ASCAT observation are shown for water-year 2007 in Figure 5.
For the Marsyangdi River basin, the ASCAT FTGM product ( Figure 5A) covers a larger area than the GDM at -1σ ( Figure 5B) as well as that of +1σ ( Figure 5C). Compared to the GDM, the ASCAT product shows less spatial variability at the 4.5 km grid-size. Larger melt extents observed by ASCAT are a result of apparent spatial continuity in surface melt introduced by ASCAT spatial resolution limitations over discontinuous glacier land-cover as well as ASCAT observations of icemelt at higher elevations. There is little variability in melt duration with elevation. For the Trishuli River basin, the ASCAT FTGM dataset shows melting over a lesser area (Figure 5D) than the GDM at −1σ ( Figure 5E) as well as +1σ (Figure 5F). Similar to the Marsyangdi River basin, ASCAT FTGM shows melting at higher elevations with little variability in melt duration compared to the GDM. In the Trishuli the ASCAT product does not detect melting over areas where GDM predicts a majority of the melting, at elevations below 5000 m a.s.l. Over the Tamor River basin, the ASCAT FTGM product ( Figure 5G) and the GDM maximum ice melting extents are within the −1σ ( Figure 5H) and +1σ (Figure 5I) of GDM extents and the satellite observes melting at higher elevations. In the Tamor River basin, both estimates found a similar degree of spatial heterogeneity with a less pronounced elevational gradient from the ASCAT FTGM product. This ±1σ analysis is done to check the elevation dependent of ASCAT melt. Even with +1σ temperatures we are seeing more melting at higher elevations with the ASCAT product. This is due to radiation-driven melting at high elevations. Most of the meltwater will be refrozen in-place, therefore not contributing to runoff. This makes sense as refrozen ice structures are though to drive the radar brightness especially at C-Band. This indicates that ASCAT (C-Band, VV-pol) is not the ideal type of radar to look at hydrological modeling for river flow. There are some places where it will overlap with temperature driven melting but the signal will be dominated by accumulation zone melting.
A comparison of glacier melt with elevation from modeling and radar observations during 2007-2010 finds clear and systematic differences in distribution in the melting magnitude, i.e., melt area over time, with elevation ( Figure 6). For the Marsyangdi River basin ( Figure 6A) glacier melting has similar magnitude below 5000 m a.s.l. Over 5000 m a.s.l. we find ASCAT observes substantially larger glacier melting occurrences persisting to very high elevations, greater than 6500 m a.s.l. For the Trishuli ( Figure 6B) and Tamor River basins ( Figure 6C) we find melting distributions with elevations to be translated, relative to the GDM, toward higher elevations with 5000 m a.s.l. being the elevation where these distributions find similar magnitudes of melting.

DISCUSSION
Using remote sensing datasets to understand processes more accurately in the data-scarce HMA region may support both science and water resource management. We used C-band radar backscatter observations from ASCAT, spatially enhanced and posted to a 4.5 km grid, to examine glacier melting in mountain basins at a daily time-step, and compared that with GDM results. A comparison of the extent of glacier melting in the Tamor, R Marsyangdi and Trishuli River basins indicates systematic differences in GDM estimates and ASCAT observations of melting. ASCAT generally observes melting over longer durations, at higher elevations, and with less spatial variability than GDM predicts.
C-band radar backscatter such as that provided by ASCAT is especially sensitive to melting over snow-fields and glacier firn as occurs over percolation zones (König et al., 2002) because these areas exhibit a strong volume scattering contribution to the radar signature from the complex snow and ice stratigraphy (e.g., Parry et al., 2007). This sensitivity to dry firn gives rise to C-band radar backscatter sensitivity to small changes in the amount of liquid water contained in the upper 1 m of glacier firn even when buried under refrozen snow (Bevan et al., 2018). The persistence of buried liquid water under frozen snow while frozen surface temperatures persist will lengthen the melting season observed by radar. Models that do not account for 2D surface energy balance affecting snow and firn may not account this phenomenon.
Accumulation zone melt-area is likely overestimated by ASCAT because of the coarse spatial resolution of the sensor. The complex terrain of and surrounding mountain glaciers also limits determining the source of the melt signal using coarse resolution remote sensing datasets. It is likely that the subpixel glacier fraction within the ASCAT footprint has a large influence on the radar backscatter response to melt events. The Marsyangdi and Tamor River basins have ASCAT melting areas greater than that predicted by the GDM; here ASCAT is likely attributing melting over areas where glaciers are regularly distributed over mountainous terrain. In the Trishuli River basin, where glaciers are not spatially dense, we find ASCAT observing less melt area than GDM.
Since the ASCAT response to melt onset is strong over much of the glacier accumulation zone, it likely indicates that melting does occur over glaciated areas even though modeling predicts frozen conditions. Accounting for variability in GDM melting ( Figure 5) we find that ASCAT observes melting at elevations exceeding that modeled by GDM. Melting driven by shortwave radiation is likely to occur these high elevations in the HMA although surface temperatures are below zero (Litt et al., 2019). With this reason the onset date of ASCAT melting is 31 days earlier and end date of melting is 44 days delayed in Tamor River basin. Very few days are differ in other two river basins; Trishuli and Marsyangdi River basins. It has been demonstrated that much of the water generated from melting over snow and firn is frozen in place and does not contribute to run-off (Meyer and Ian Hewitt, 2017).
Observations of barren landscape and glacier surfaces in the ablation zone are expected to have a lower radar return at C-band frequencies (e.g., König et al., 2002). Without fully polarimetric observations, appreciable signal change with surface melting can be difficult to detect. ASCAT is likely underestimating melting over areas large at elevations below 5000 m a.s.l. because of this limited sensitivity. However, at the basin scale, the ASCAT FTGM dataset and the GDM model results show agreement in seasonal timing of melt onset and freeze-up. It is likely that pronounced variability in slope-aspect effects on the radar backscatter signatures is introduced in the resolution enhancement technique applied to the ASCAT native resolution data thereby affecting observation consistency in complex terrain. Use of high resolution datasets such as provided by Synthetic Aperture Radar may improve characterization of spatial extent and variability and in identifying location of glacier melt.
The contribution of icemelt in river flow estimated by the GDM is comparable to the results obtained by earlier studies. Racoviteanu et al. (2013) used a simple elevation-dependent ice ablation model based on glacier areas from ASTER and IKONOS remote-sensing data combined with hypsometry from the Shuttle Radar Topography Mission to estimate icemelt contribution at 9.5%, which is close to our result of 10.73%, at Betrawati. Using the HBV light model, Bhattarai et al. (2018) found that the contribution of snow and icemelt in river flow was from 27.5 to 33.7% at the Betrawati hydrological station in the Trishuli River basin from 1995 to 2005. When we added snowmelt and icemelt percentages in the river flow at the same station, it was 24.66%, which is also very near to their results. Panday et al. (2013) used the snowmelt runoff model and found that the average contribution of snowmelt in flow in the Tamor River basin at the Majhitar hydrological station from 2002-2006 was 29.7 ± 2.9% (including 4.2 ± 0.9% from snowfall that promptly melts), whereas 70.3 ± 2.6% is attributed to contributions from rainfall. However, the present study using the GDM from 2002 to 2006 showed 9.64% snowmelt and 5.86% icemelt. Such a difference in snowmelt and icemelt may be due to the fact that GDM separately calculates the snowmelt, icemelt, rainfall and baseflow components of river flows rather than considering just two components as the snowmelt runoff model does.

CONCLUSION
The GDM has been successfully used in three glacierized river basins, Tamor, Trishuli and Marsyangdi in Nepal. The calculated discharges from GDM match the observed discharges from the respective rivers: NSE ranges from 0.69 to 0.81 and volume difference from −7.51% to 4.64%. The maximum snowmelt contribution in river flow is 13.93% in Trishuli River and the minimum 7.8% in Marsyangdi River basin; maximum icemelt contribution is 12.88% in Marsyangdi River basin and the minimum 6.6% in Tamor River basin. The maximum and minimum icemelt contribution in Marsyangdi and Tamor River basin, respectively, is consistent with the maximum and minimum permanent ice cover area in those basins. Similarly, the highest rainfall contribution in river flow is found in Tamor (39.04%) and the lowest in Trishuli (29.9%), and the highest baseflow contribution is in Trishuli River basin (45.44%) and the lowest in Marsyangdi River basin (41.35%). The higher contribution of rainfall in Tamor and Marsyangdi River basins is also consistent with the higher precipitation areas within Nepal. Usually, precipitation is higher in east Nepal and Pokhara area near Marsyangdi River basin. About 62% of Trishuli River basin lies in Tibet, China, in a very low precipitation area, and so rainfall contribution is comparatively lower than in the other two basins.
Comparisons between the GDM icemelt and ASCAT FTGM observations find disparities between the spatial extent areas where ASCAT is sensitive to melting and where GDM is predicting melt. Generally, the ASCAT product is more sensitive to melting over ice-fields in the accumulation zone and less sensitive to melting occurring over barren landscape areas and glacier surfaces in the ablation zone. This difference in sensitivity can lead to spatial mismatch between the GDM model and radar estimates of melting area. Glaciers that are spatially dense, like the Tamor River basin, create better agreement. The timings of glacier-melt in the ASCAT FTGM product match increment predictions from GDM.
High Mountain Asia Program. Argonne National Laboratory's work was supported under interagency agreement, through United States Department of Energy contract DE-AC02-06CH11357. The City College of New York was supported by NASA Award Number NNX16AQ83. Kathmandu University worked as an international collaborator on the NASA project on a no-exchange-offunds basis.