Application of SWAT in Hydrological Simulation of Complex Mountainous River Basin (Part I: Model Development)

: The soil and water assessment tool (SWAT) hydrological model has been used extensively by the scientiﬁc community to simulate varying hydro-climatic conditions and geo-physical environment. This study used SWAT to characterize the rainfall-runoff behaviour of a complex mountainous basin, the Budhigandaki River Basin (BRB), in central Nepal. The speciﬁc objectives of this research were to: (i) assess the applicability of SWAT model in data scarce and complex mountainous river basin using well-established performance indicators; and (ii) generate spatially distributed ﬂows and evaluate the water balance at the sub-basin level. The BRB was discretised into 16 sub-basins and 344 hydrological response units (HRUs) and calibration and validation was carried out at Arughat using daily ﬂow data of 20 years and 10 years, respectively. Moreover, this study carried out additional validation at three supplementary points at which the study team collected primary river ﬂow data. Four statistical indicators: Nash–Sutcliffe efﬁciency (NSE), percent bias (PBIAS), ratio of the root mean square error to the standard deviation of measured data (RSR) and Kling Gupta efﬁciency (KGE) have been used for the model evaluation. Calibration and validation results rank the model performance as “very good”. This study estimated the mean annual ﬂow at BRB outlet to be 240 m 3 /s and annual precipitation 1528 mm with distinct seasonal variability. Snowmelt contributes 20% of the total ﬂow at the basin outlet during the pre-monsoon and 8% in the post monsoon period. The 90%, 40% and 10% exceedance ﬂows were calculated to be 39, 126 and 453 m 3 /s respectively. This study provides additional evidence to the SWAT diaspora of its applicability to simulate the rainfall-runoff characteristics of such a complex mountainous catchment. The ﬁndings will be useful for hydrologists and planners in general to utilize the available water rationally in the times to come and particularly, to harness the hydroelectric potential of the basin.


Introduction
Complex interactions between the atmospheric system and the underlying topography determine river discharge. It is a part of rainfall that appears in a stream and represents the total response of a basin. Surface flow, subsurface flow, base flow and precipitation that directly falls on the stream constitutes the total discharge in the river [1,2]. Time series of flow data is one of the most important requirements for planning, operation and control of all water resources projects [3][4][5]. However, measured flow data are not available in most of the cases in such project sites [5]. It is because of the lack of sufficient flow gauging stations in most river basins. The situation is more severe in mountainous basins [6] because of the inaccessibility of most of these sites for local observations. It is the reason why water budget analyses in such basins are not as easy as in other gauged basins [7,8]. However, most of the large rivers (e.g., the Ganga, the Indus, the Sutlej, the Brahmaputra, the Mekong, the Yellow) in the world originate from the mountains and are perennial in nature as they are constantly fed by snow and glaciers. Mountain basins might have, thus, been considered as the water towers of the world [7,9].
The characteristics of the river basins are usually controlled by the geo-physical environment and hydro-climatic conditions [10]. In central Himalaya, high relief with steep topography along with tectonic activities, climate-driven erosional process and high sediment yield, among many other factors, make the basins complex [11]. Precipitation in Nepalese mountainous river basins, including the Budhigandaki River Basin (BRB), are mostly influenced by orography, aspect and physiography, with more amount of precipitation in the windward side than in leeward side [12][13][14][15][16][17][18]. The challenge is further exacerbated due to limited data availability in these regions because of difficult access.
To address the challenge of non-availability of observed data at local level for water resources planning and utilization in the river basin, hydrologic simulation method has been widely used in recent years [19][20][21][22][23]. Simulation models provide excellent platforms for evaluating various options for water resources as well as environmental planning [24,25]. In hydrological simulation, a hydrologic model which is a simplified software representation of the hydrological process within a basin boundary, is used to generate the flow at required locations of the river basin.
The SWAT model [30,31] has been chosen among many hydrological models for this study. Several studies have been carried out to assess the water availability and impacts of climate change; land use and land cover changes around the world using SWAT model [21,[32][33][34]. Studies in the Nile Basin by Griensven et al. [35], Itapemirim River basin (Brazil) by Fukunaga et al. [36], Ganga Basin by Anand et al. [37], and Mekong Basin by Tang et al. [38] are some of them. Details on the use of SWAT for various purposes can be found in [39]. Shrestha et al. [40] has evaluated the hydrological responses of SWAT models for 11 basins in two contrasting climatic regions (Himalayan and Tropical) of Asia. Their result reveals that SWAT is a suitable tool for modelling hydrological responses in both regions including four snow-fed basins of Nepal. SWAT model has successfully been used in other Nepalese catchments too; Koshi [27,41] Narayani [42], West Rapti [43] and Karnali [25,[44][45][46]. There are a number of similar studies that used SWAT model in other river basins of Nepal to assess the river hydrology and the impact of climate change [47] in Kaligandaki basin; [48,49] in Bagmati basin; [50] in Karnali basin; [51] in Tamor basin, and [52] in Koshi basin. SWAT being a freely available public domain hydrological model capable of simulating complex hydrological processes might have made it popular for hydrological simulation around the world.
The Budhigandaki River Basin (BRB) was selected for this study. Altitudinal variation in precipitation pattern is remarkable in this basin [53][54][55] including Tibet. Furthermore, precipitation is quite high (>75% of the total) during the monsoon season (June-September) as compared to other months of the year [56,57]. The main objective of this study is to apply SWAT model to simulate the river hydrology of BRB. The specific objectives are to: (i) assess the applicability of SWAT model in data scarce and complex mountainous river basin using well-established performance indicators; and (ii) generate spatially distributed flows and evaluate the water balance at the sub-basin level. Further, the model was used to assess the impact of climate change in the hydrology of the basin (Part II-accompanied paper).

Study Area
The BRB is a transboundary river basin of which about one-fourth of the basin area lies in Tibetan plateau of People's Republic of China and the remaining part lies in Federal Democratic Republic of Nepal ( Figure 1). The basin area at the confluence of Trishuli River is 4988 km 2 , with an average elevation of 3723 masl (range: 315 m-8163 m). Physiographically, the basin falls in the Middle Mountains and the Himalayas. It is noted here that Mount Manaslu, the eighth highest peak in the world, is situated in this basin [58]. Long-term annual rainfall of the BRB is 1495 mm with an extremely high spatial variability within the basin. Rainfall intensities vary throughout the basin with maximum intensity occurring on the south facing slopes of the mountains. The station Arughat receives an annual precipitation of greater than 2500 mm while the Tibetan part of the basin receives less than 700 mm [57,59]. The mean annual flow of the Budhigandaki river near the Budhigandaki Hydroelectric Project (BGHEP) dam site is estimated at 222 m 3 /s [53]. The temperature varies from −2.0 • C in winter to 33.0 • C in summer in the study basin [60]. model was used to assess the impact of climate change in the hydrology of the basin (Part II-accompanied paper).

Study Area
The BRB is a transboundary river basin of which about one-fourth of the basin area lies in Tibetan plateau of People's Republic of China and the remaining part lies in Federal Democratic Republic of Nepal ( Figure 1). The basin area at the confluence of Trishuli River is 4988 km 2 , with an average elevation of 3723 masl (range: 315 m-8163 m). Physiographically, the basin falls in the Middle Mountains and the Himalayas. It is noted here that Mount Manaslu, the eighth highest peak in the world, is situated in this basin [58]. Longterm annual rainfall of the BRB is 1495 mm with an extremely high spatial variability within the basin. Rainfall intensities vary throughout the basin with maximum intensity occurring on the south facing slopes of the mountains. The station Arughat receives an annual precipitation of greater than 2500 mm while the Tibetan part of the basin receives less than 700 mm [57,59]. The mean annual flow of the Budhigandaki river near the Budhigandaki Hydroelectric Project (BGHEP) dam site is estimated at 222 m 3 /s [53]. The temperature varies from −2.0 °C in winter to 33.0 °C in summer in the study basin [60].

Data Used
The hydro-meteorological data that has been used for the SWAT model in this study are precipitation, minimum and maximum air temperature. Besides, Digital Elevation Model (DEM), land use and soil map data are the spatial data required (Table 1).

Data Used
The hydro-meteorological data that has been used for the SWAT model in this study are precipitation, minimum and maximum air temperature. Besides, Digital Elevation Model (DEM), land use and soil map data are the spatial data required (Table 1). Meteorological data from eight stations in and around the study basin (1981-2015) were used as input to the model ( Figure 1). Two stations have both observed precipitation and temperature data while the remaining six stations have only precipitation data. Gridded data of precipitation and temperature for the Tibet part of the basin was also used in the study. Quality checking of the data was done through various methods: homogeneity test, outliers checking, inter parameter consistency checking, spatial checking and double mass curve analysis. The average areal precipitation over the catchment was calculated by the Thiessen polygon method [67] using geographic information system (GIS).

Flow Data
Long term daily flow data  of Budhigandaki river at Arughat gauging station has been used for calibration and validation of the model. Similarly, short term flow data available at the damsite of the proposed Budhigandaki Storage Hydropower Project (2013-2014) lying downstream of the Arughat station and headwork sites of two proposed run of the river hydropower projects, viz., Budhigandaki KA and KHA (2009) lying upstream of Arughat ( Figure 1) were also used for additional validation of the model.

SWAT Model
The Soil Water Assessment Tool (SWAT model) is a continuous-time, semi-distributed, process-based river basin simulation model operating on a daily or sub-daily time steps [68][69][70]. The basin is partitioned into a number of subbasins. Each sub-basin is further discretised into a number of hydrologic response units (HRUs), which are unique combinations of soil-landuse-slope exceeding a certain user defined threshold. Processes are simulated at HRU level and aggregated for each sub-basin, which are then routed through the river system using the variable storage or Muskingum method. SWAT facilitates an assortment of parameters defined at HRU, subbasin or basin level. The SWAT model simulates the various hydrological processes occurring in the river basin based on water balance within the basin as given by Equation (1).
where SWt is the final soil water content (mm), SW0 is the initial soil water content (mm), t is the time in days, Rday is the amount of precipitation on day i (mm), Qsurf is the amount of surface runoff on day i (mm), Ea is the amount of evapotranspiration on day i (mm), Wseep is the amount of water entering the vadose zone from soil profile on day i (mm), Qgw is the amount of return flow on day i (mm). SWAT uses the climate data from the station nearest to the centroid of each sub-basin. A given precipitation is classified as solid (snow) and liquid (rainfall) based on a user-

SWAT Model
The Soil Water Assessment Tool (SWAT model) is a continuous-time, semi-distributed, process-based river basin simulation model operating on a daily or sub-daily time steps [68][69][70]. The basin is partitioned into a number of subbasins. Each sub-basin is further discretised into a number of hydrologic response units (HRUs), which are unique combinations of soil-landuse-slope exceeding a certain user defined threshold. Processes are simulated at HRU level and aggregated for each sub-basin, which are then routed through the river system using the variable storage or Muskingum method. SWAT facilitates an assortment of parameters defined at HRU, subbasin or basin level. The SWAT model simulates the various hydrological processes occurring in the river basin based on water balance within the basin as given by Equation (1).
where SW t is the final soil water content (mm), SW 0 is the initial soil water content (mm), t is the time in days, R day is the amount of precipitation on day i (mm), Q surf is the amount of surface runoff on day i (mm), E a is the amount of evapotranspiration on day i (mm), W seep is the amount of water entering the vadose zone from soil profile on day i (mm), Q gw is the amount of return flow on day i (mm). SWAT uses the climate data from the station nearest to the centroid of each subbasin. A given precipitation is classified as solid (snow) and liquid (rainfall) based on a user-defined threshold value of mean air temperature. Snow melts when the maximum temperature on a given day exceeds the user defined threshold level. In snow covered areas, a fraction of the estimated daily potential evapotranspiration occurs by sublimation. Evaporation from soils and plants is computed separately by the model. Details of the SWAT model can be found in [30,70,71].

Model Setup and Simulation
The BRB was divided into 16 sub-basins and five slope classes (0-30, 30-50, 50-70, 70-90 and >90 percent). A threshold value of 10% each for land use and land cover, soil ( Figure 2) and slopes were used to divide the subbasin into unique 344 HRUs. Further, to account for orographic effects, we generated 500 m range elevation band in each sub basin. The methodological framework for model setup and simulation is given in Figure 3. defined threshold value of mean air temperature. Snow melts when the maximum temperature on a given day exceeds the user defined threshold level. In snow covered areas, a fraction of the estimated daily potential evapotranspiration occurs by sublimation. Evaporation from soils and plants is computed separately by the model. Details of the SWAT model can be found in [30,70,71].

Model Setup and Simulation
The BRB was divided into 16 sub-basins and five slope classes (0-30, 30-50, 50-70, 70-90 and >90 percent). A threshold value of 10% each for land use and land cover, soil ( Figure 2) and slopes were used to divide the subbasin into unique 344 HRUs. Further, to account for orographic effects, we generated 500 m range elevation band in each sub basin. The methodological framework for model setup and simulation is given in Figure 3.  [1981][1982] was excluded from the analysis. The model was calibrated using 20 years (two-thirds) of the study period (1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002) and validated using the remaining one-third i.e., 10 years (2003-2012). Based on the modeling experience in Nepalese basins and judgement of the study team, manual method was used for calibrating the model. Surface runoff was estimated by the SCS curve number (SCS-CN) [75] method. The potential evapotranspiration was computed using Hargreaves method [76]. The computed runoff from each sub-basin was routed through the river network to the main basin outlet by using variable storage method.

Performance Evaluation Criteria
Moriasi et al. [77] has discussed various graphical and statistical model evaluation techniques. Among them, three well-established statistical indicators: Nash-Sutcliffe efficiency (NSE), percent bias (PBIAS), and ratio of the root mean square error to the standard deviation of measured data (RSR) were used in this study for model evaluation [ [19,[72][73][74] of relatively better data before 2013, observed flow data of Arughat station from 1981-2012 were used in the study. A warm up period (to stabilize the model initially) of 2 years (1981-1982) was excluded from the analysis. The model was calibrated using 20 years (two-thirds) of the study period (1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002) and validated using the remaining one-third i.e., 10 years (2003-2012). Based on the modeling experience in Nepalese basins and judgement of the study team, manual method was used for calibrating the model. Surface runoff was estimated by the SCS curve number (SCS-CN) [75] method. The potential evapotranspiration was computed using Hargreaves method [76]. The computed runoff from each sub-basin was routed through the river network to the main basin outlet by using variable storage method.

Performance Evaluation Criteria
Moriasi et al. [77] has discussed various graphical and statistical model evaluation techniques. Among them, three well-established statistical indicators: Nash-Sutcliffe efficiency (NSE), percent bias (PBIAS), and ratio of the root mean square error to the standard deviation of measured data (RSR) were used in this study for model evaluation [69,77,78].
In addition to these three, Kling Gupta efficiency (KGE) prescribed by [79][80][81][82] has also been used for the purpose of evaluation.
Nash-Sutcliffe efficiency (NSE) is a normalized statistic that determines the relative magnitude of the residual variance ("noise") compared to the measured data variance ("information"). NSE indicates how well the plot of observed versus simulated data fits the 1:1 line [83]. NSE is computed using Equation (2): where, Q 0i and Q ei are respectively observed and estimated discharge of day i, Q 0 is the mean of the observed discharges. The optimum value is 1.0, with higher value indicating better model performance. Percent bias (PBIAS) measures the average tendency of the simulated data to be larger or smaller than their observed counterparts. The optimal value of PBIAS is 0.0, with lowmagnitude values indicating accurate model simulation. Positive values indicate model underestimation bias, and negative values indicate model overestimation bias [77]. PBIAS is, generally, expressed in percentage and is calculated using Equation (3).
where V o and V e are respectively the observed and simulated volumes of water for day i. The root mean square error (RMSE) and the standard deviation of observed flow (σ o ) can be expressed as a ratio (RSR). It is commonly accepted that the lower the RMSE the better the model performance. RSR varies from the optimal value of 0, which indicates zero residual variation and therefore perfect model simulation, to a large positive value that indicates poorer model performance [77]. RSR is calculated using Equation (4).
The Kling-Gupta efficiency (KGE) that incorporates correlation, variability bias and mean bias [80] is increasingly used for model calibration and evaluation. It is expressed using Equation (5).
where, r is the correlation coefficient between the observed and simulated flows, σ o and σ e are standard deviations of observed and simulated flows respectively.

Observed Rainfall-Runoff Characteristics
Long term monthly average precipitation and observed flow (1983-2012) based on Department of Hydrology and Meteorology (DHM) at Arughat gauging station is depicted in Figure 4. The figure shows that the flow closely follows the precipitation pattern of the basin. Long term annual basin precipitation has been calculated as 1301 mm (maximum 278 mm in July and minimum 11 mm in November). Similarly, the long-term average and standard deviation of the monthly flows are 163 m 3 /s and 156 m 3 /s, respectively.

SWAT Model Performance
The SWAT model was calibrated and validated manually for a simulation period of 30 years (1983-2012). The 15 most sensitive parameters were selected for calibration. The final adopted values of the parameters (in alphabetical order) are shown in Table 2. It can be seen that two different sets of parameters directly influence the surface runoff (CN2 and OV_N) and lateral flow (LAT_TIME and SURLAG) whereas five parameters (AL-PHA_BF, GWDELAY, GWQMIN, SOL_AWC and SOL_Z) impact the baseflow from the basin. It is interesting to note that there are six snow related parameters (snowfall temperature (SFTMP), snowmelt temperature (SMTMP), snow cover (SNOCOVMX), degree-day factors (SMFMX, SMFMN) and temperature lapse rate (TLAPS)) which are used to calculate the snow component of the total flow. Thus, it is seen that the basin demonstrates a high degree of complexity among the different interacting components of the hydrological cycle. Simulated and observed hydrographs for the calibration and the validation periods at Arughat on daily and monthly time steps are shown in Figure 5

SWAT Model Performance
The SWAT model was calibrated and validated manually for a simulation period of 30 years (1983-2012). The 15 most sensitive parameters were selected for calibration. The final adopted values of the parameters (in alphabetical order) are shown in Table 2. It can be seen that two different sets of parameters directly influence the surface runoff (CN2 and OV_N) and lateral flow (LAT_TIME and SURLAG) whereas five parameters (ALPHA_BF, GWDELAY, GWQMIN, SOL_AWC and SOL_Z) impact the baseflow from the basin. It is interesting to note that there are six snow related parameters (snowfall temperature (SFTMP), snowmelt temperature (SMTMP), snow cover (SNOCOVMX), degree-day factors (SMFMX, SMFMN) and temperature lapse rate (TLAPS)) which are used to calculate the snow component of the total flow. Thus, it is seen that the basin demonstrates a high degree of complexity among the different interacting components of the hydrological cycle. Simulated and observed hydrographs for the calibration and the validation periods at Arughat on daily and monthly time steps are shown in Figure 5. The mean and standard deviation of the observed (and simulated) flows are 168 (170) m 3 /s and 167 (168) m 3 /s, respectively for the calibration period and 154 (181) m 3 /s and 163 (180) m 3 /s, respectively for the validation period (Table 3). It can be seen from Figure 5 that the model simulates the flow pattern very well and the hydrographs are in good agreement with the rainfall pattern at daily and monthly timescales even for this length of time (20 years for calibration and 10 years for validation). It is also evident from the scatter plots of simulated vs. observed daily flows of these periods (Figure 6a,b). The difference in cumulative volume between the simulated and observed flow is very small for the calibration period (Figure 6c), however, the model has over-estimated the flow in the validation period (Figure 6d).
The NSE, PBIAS, RSR and KGE values for the calibration period are, respectively, 0.78, −1.46%, 0.47 and 0.89. Similarly, for the validation period, the values of NSE, PBIAS, RSR and KGE are 0.81, −17.1%, 0.44 and 0.79, respectively (Table 3). Based on the criteria prescribed by [77,80], all these indices fall in the 'very good' category except PBIAS in the validation period ('satisfactory' range). The graphical comparison (Figures 4-6) and the performance rating (Table 3) show that the SWAT model is well calibrated and validated for the BRB at Arughat.
The monthly flows, both observed and simulated, for the period 1983-2012 are depicted in Figure 5b. The model performance parameters for monthly flows are 0.88 (NSE), −6.5% (PBIAS), 0.35 (RSR) and 0.91 (KGE). The graph and the performance statistics show that the calibrated SWAT model is capable of simulating the monthly flows well which is required for water availability studies in the BRB.

Additional Validation of SWAT at Supplementary Stations
Previous studies, e.g., [25,85] have used multi-site approach to calibrate the SWAT model. In the current study, the model is calibrated at a single point and validated at three supplementary points upstream and downstream of Arughat: (i) intake site of Budhigandaki KA (BG KA), (ii) intake site of Budhigandaki KHA (BG KHA) and (iii) 1200 MW Budhigandaki Hydroelectric Project (BGHEP) dam site (see Figure 1). It is to be noted that the study team carried out rigorous discharge measurements and prepared rating curves at these three locations during 2009-2010 (BG KA and BG KHA) and 2013-2014 (BGHEP damsite) which has been used for the additional validation. The results of the validation  (Table 3). Based on the criteria prescribed by [77,80], all these indices fall in the 'very good' category except PBIAS in the validation period ('satisfactory' range). The graphical comparison (Figures 4-6) and the performance rating (Table 3) show that the SWAT model is well calibrated and validated for the BRB at Arughat.
The monthly flows, both observed and simulated, for the period 1983-2012 are depicted in Figure 5b. The model performance parameters for monthly flows are 0.88 (NSE), −6.5% (PBIAS), 0.35 (RSR) and 0.91 (KGE). The graph and the performance statistics show that the calibrated SWAT model is capable of simulating the monthly flows well which is required for water availability studies in the BRB.

Additional Validation of SWAT at Supplementary Stations
Previous studies, e.g., [25,85] have used multi-site approach to calibrate the SWAT model. In the current study, the model is calibrated at a single point and validated at three supplementary points upstream and downstream of Arughat: (i) intake site of Budhigandaki KA (BG KA), (ii) intake site of Budhigandaki KHA (BG KHA) and (iii) 1200 MW Budhigandaki Hydroelectric Project (BGHEP) dam site (see Figure 1). It is to be noted that the study team carried out rigorous discharge measurements and prepared rating curves at these three locations As per the rating criteria by [77,80], the model performance is "very good" at the BGHEP dam site, "good" at BG KA and "satisfactory" at BG KHA. This independent validation at supplementary sites reveals that the calibrated model at Arughat can simulate the flow well for the Budhigandaki Basin up to the Trishuli confluence, although the performance is better in the downstream reach compared to the upstream reach. 0.58, 21% and 0.59 and 0.58, 0.65, 13% and 0.54 for BG KHA, respectively. Similarly, their respective values for the BGHEP damsite are 0.91, 0.31, 7.88% and 0.81. As per the rating criteria by [77,80], the model performance is "very good" at the BGHEP dam site, "good" at BG KA and "satisfactory" at BG KHA. This independent validation at supplementary sites reveals that the calibrated model at Arughat can simulate the flow well for the Budhigandaki Basin up to the Trishuli confluence, although the performance is better in the downstream reach compared to the upstream reach.

Flow Duration Curve
The flow-duration curve (FDC) is a probability discharge curve that shows the percentage of time in which a particular flow is equaled or exceeded [1]. FDC was prepared from the observed as well as simulated daily flow data at Arughat (Figure 8a). From the figure, it can be seen that the magnitude of the observed flows at 10%, 40% and 90% exceedance probabilities are 431, 118 and 29 m 3 /s respectively. Similarly, the exceedance probabilities are respectively 453, 126 and 39 m 3 /s for simulated flows. This indicates that the fractional difference between the corresponding values of the two flow-series are 5%, 7%, and 33%, respectively. The relationship between the simulated and observed values at 10 percentile exceedance intervals are plotted in Figure 8b. A very good linear correlation is found between these two series as indicated by the R 2 value of 0.998.

Flow Duration Curve
The flow-duration curve (FDC) is a probability discharge curve that shows the percentage of time in which a particular flow is equaled or exceeded [1]. FDC was prepared from the observed as well as simulated daily flow data at Arughat (Figure 8a). From the figure, it can be seen that the magnitude of the observed flows at 10%, 40% and 90% exceedance probabilities are 431, 118 and 29 m 3 /s respectively. Similarly, the exceedance probabilities are respectively 453, 126 and 39 m 3 /s for simulated flows. This indicates that the fractional difference between the corresponding values of the two flow-series are 5%, 7%, and 33%, respectively. The relationship between the simulated and observed values at 10 percentile exceedance intervals are plotted in Figure 8b. A very good linear correlation is found between these two series as indicated by the R 2 value of 0.998. Water 2021, 13, x FOR PEER REVIEW 12 of 19

Water Balance of the Budhigandaki Basin
Monthly water balance of the BRB is shown in Figure 9. The figure depicts the distribution of water balance components, namely, precipitation (P), actual evapotranspiration (AET) and the net water yield (WY) of the study basin. The WY refers to the total flow coming as surface runoff, lateral flow, and groundwater flow minus transmission losses and pond abstractions [30]. Change in storage is defined as ∆Storage = −[(Precipitation (P) − Net Water Yield (WY) − Evapotranspiration (ET)]. It implies that if P > (WY + ET), the excess water infiltrates and is stored, as soil moisture and GW storages, of the basin. On the other hand, if (WY + ET) > P, the water deficit is met by soil and GW storages of the basin. For example, in January, some water is released from the basin to meet the WY and ET while it is stored in the soil and GW storage in July. It is noted here that ∆storage accounts for model errors too. It can be seen from the results that precipitation across the SWAT sub-basins varies from less than 700 mm (leeward side of northern Trans-Himalayan region) to above 2500 mm (foothills of the Himalayas). The average annual precipitation over the entire basin is 1528 mm. Here precipitation has been taken as the sum of annual rainfall and snowmelt (318 mm). The percentage of precipitation falling in premonsoon, monsoon, post monsoon and winter are respectively 16%, 74%, 4% and 6% of the total annual value. The average annual AET over the basin is 402 mm while WY is 1010 mm. The WY is about 56% during monsoon (June-September) while it is only 28% and 9% in pre-monsoon (March-May) and post-monsoon (October and November) seasons, respectively. It is only 7% of the total annual volume for the winter season (December-February). Delta storage for the entire simulation period has been calculated to be around 8%.

Water Balance of the Budhigandaki Basin
Monthly water balance of the BRB is shown in Figure 9. The figure depicts the distribution of water balance components, namely, precipitation (P), actual evapotranspiration (AET) and the net water yield (WY) of the study basin. The WY refers to the total flow coming as surface runoff, lateral flow, and groundwater flow minus transmission losses and pond abstractions [30]. Change in storage is defined as ∆Storage = −[(Precipitation (P) − Net Water Yield (WY) − Evapotranspiration (ET)]. It implies that if P > (WY + ET), the excess water infiltrates and is stored, as soil moisture and GW storages, of the basin. On the other hand, if (WY + ET) > P, the water deficit is met by soil and GW storages of the basin. For example, in January, some water is released from the basin to meet the WY and ET while it is stored in the soil and GW storage in July. It is noted here that ∆storage accounts for model errors too. It can be seen from the results that precipitation across the SWAT sub-basins varies from less than 700 mm (leeward side of northern Trans-Himalayan region) to above 2500 mm (foothills of the Himalayas). The average annual precipitation over the entire basin is 1528 mm. Here precipitation has been taken as the sum of annual rainfall and snowmelt (318 mm). The percentage of precipitation falling in pre-monsoon, monsoon, post monsoon and winter are respectively 16%, 74%, 4% and 6% of the total annual value. The average annual AET over the basin is 402 mm while WY is 1010 mm. The WY is about 56% during monsoon (June-September) while it is only 28% and 9% in pre-monsoon (March-May) and post-monsoon (October and November) seasons, respectively. It is only 7% of the total annual volume for the winter season (December-February). Delta storage for the entire simulation period has been calculated to be around 8%.

Discussion
In the BRB, the monsoon season (June-September) contributes approximately 74% of the total annual flow while the flow during the other eight months is only 26%. The highest flow occurs in August (23% of the total annual flow) while the lowest flow occurs in February (1.5%). The fractional difference between these two months was calculated to be more than 15, showing high runoff variability in the study basin. This value is comparable with other large and medium size basins of Nepal, for example, West Seti, Karnali, Trishuli, Narayani, Dudhkoshi and Sapta Koshi. The fractional differences of these basins range from 13 (West Seti at Gopighat and Sapta Koshi at Chatara) to 18 (Dudhkoshi at Rabuwa); flow contribution in monsoon season ranges from 72% to 77%, respectively. Furthermore, the low flow contribution is relatively higher in Karnali, West Seti and Saptakoshi (approximately 2%) while this is less than 1.5% in Dudhkoshi. It is interesting to note that low flow contribution is higher in the basins with a significant drainage area of Tibet and lying in the western part of Nepal.

Discussion
In the BRB, the monsoon season (June-September) contributes approximately 74% of the total annual flow while the flow during the other eight months is only 26%. The highest flow occurs in August (23% of the total annual flow) while the lowest flow occurs in February (1.5%). The fractional difference between these two months was calculated to be more than 15, showing high runoff variability in the study basin. This value is comparable with other large and medium size basins of Nepal, for example, West Seti, Karnali, Trishuli, Narayani, Dudhkoshi and Sapta Koshi. The fractional differences of these basins range from 13 (West Seti at Gopighat and Sapta Koshi at Chatara) to 18 (Dudhkoshi at Rabuwa); flow contribution in monsoon season ranges from 72% to 77%, respectively. Furthermore, the low flow contribution is relatively higher in Karnali, West Seti and Saptakoshi (approximately 2%) while this is less than 1.5% in Dudhkoshi. It is interesting to note that low flow contribution is higher in the basins with a significant drainage area of Tibet and lying in the western part of Nepal.
The SWAT model was calibrated using 20 years (two-thirds) of the study period (1983)(1984)(1985)(1986)(1987)(1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998)(1999)(2000)(2001)(2002) and validated using the remaining one-third 10 years (2003-2012) which is comparable with the time period taken by [24]. The performance indices of this study are found better or comparable to similar studies carried out in other Nepalese basins.  [25,40,45,47,51,[85][86][87]. Similarly, NSE (and PBIAS) values of Gilgelabay basin of Ethiopia, Gurupura basin of India and Tizinafu basin of Western China were found to be respectively 0.69 (+4.8%), 0.83 (+17.5%) and 0.71 (+5.79%) for calibration period while these values for validation period were 0.68 (+4.9%), 0.85 (−3.9%) and 0.64 (−18.0%), respectively [88][89][90]. Moreover, [42] used SWAT model to simulate five glacierized mountain river basins of the world that includes the Narayani (Nepal), Vakhsh (Central Asia), Rhone (Switzerland), Mendoza (Central Andes, Argentina), and Chile (Central Dry Andes, Chile). The magnitudes of the statistical indicators of NSE, RSR and PBIAS of our study are comparable with this study. Even though the model has simulated the flow very well in general, it has underestimated the high flow in some cases (e.g., 1992, 1993, 1999, 2000) while overestimated in some other cases (e.g., 1986, 2008) ( Figure 5). The hydrographs in Figure 7a,b show the extended validation results which are based on the primary data collected at BG KA and BG KHA intake sites by the study team during 2009-2010. Figure 7c shows the simulated and observed hydrographs at BGHEP damsite for the year 2013-2014. The reference hydrological station (Arughat) is a few kilometers downstream and upstream from these points. It is to be noted here that the time of simulation for the Figure 7a Figure 7c follows the precipitation pattern and as a result, the simulated hydrograph can be considered to be reasonable, although underestimated from the observed data. It is worth mentioning here that a longer simulation and observation period would add more confidence in the model performance at these locations. There are various factors that cause the difference in the observed and simulated flows that can be grouped into observation errors and model errors. Observation errors are attributed to (i) error in precipitation (human error while reading precipitation and instrumental error); (ii) inadequate rain-gauge stations to capture the spatial variation of precipitation including windward/leeward effect; (iii) error in water level reading; (iv) use of extrapolated stage-discharge relationship while calculating higher and lower flows; and (v) possible combinations of above [61,73,[91][92][93][94]. In addition to observation errors discussed above, inherent limitations of SWAT flow calculation modules also affect simulated flows. Similarly, resolution of the DEM, land use and land cover, and soil types are only approximations of the real system. The differences between the observed and simulated flows at short timespans are found to be more compared to the long-term values. Despite these differences, the long-term values of the simulated and observed flows and their statistics are highly comparable.
In a water resources project, FDC is a useful tool to know the dependable flow while planning and designing engineering structures. For the BRB, the fractional difference between the simulated and observed low flows is seen to be high. However, the difference in the absolute values of the flows is considerably less compared to the high flows. Twentyeight percent of the Budhigandaki River Basin is covered with snow and less than one percent (315 km 2 ) is covered with glaciers. In the upper subbasins, the contribution of the glacier melt might affect the total runoff to some extent [95][96][97][98] whereas our area of interest lies in the lower part of BRB near Arughat (elevation 540 masl), where the contribution of glacier melt is insignificant in the total runoff. Past studies have modeled glacier melt in high altitude catchments above 3000 masl (for e.g., [95,97]) in which the calibration stations are also located in high elevations (Langtang at 3670 masl; catchment area 353 km 2 ). Furthermore, from these studies it can be seen that the annual runoff quantified at the reference stations is around 9 m 3 /s while it is about 160 m 3 /s at Arughat. Thus, even a small contribution from glacier melt will have a huge impact on the high elevation stations while it will be less considerable at stations lying in lower elevations. There is some contribution of snowmelt flow during the pre-monsoon period whereas the base flow contribution is more in post monsoon period. It is to be noted that the precipitation contributes to net storage from May to September (wet period) and the storage depletes during most of the dry period from October to April. This causes the percentage of precipitation contribution to net water yield to be smaller during the monsoon period than the other three periods.

Conclusions
This study discretized the BRB into 16 sub-basins and 344 HRUs and developed a hydrological model in SWAT to characterize spatial and temporal distribution of water availability. Calibration and validation of the model was carried out at Arughat using daily flow data of 20 years and 10 years respectively. Even in such a long duration, the model performed well and was ranked "very good". In addition to the conventional method of validation at the calibration station, this study further carried out validation at three supplementary points (two upstream and one downstream) at which the study team collected primary river flow data and prepared rating curves. Results of the supplementary validation further added confidence to the model performance.
This study estimated the mean annual flow at BRB outlet to be 240 m 3 /s with annual precipitation 1528 mm and AET approximately 26% of the precipitation. However, distinct seasonal variability is noted in the basin with precipitation varying from 67 mm (postmonsoon) to 1122 mm (monsoon), AET from 28 mm (winter) to 225 mm (monsoon), and WY from 92 mm (winter) to 670 mm (monsoon). The monsoon season contribution is 73%, 56%, and 66% in the average annual precipitation, AET, and WY, respectively in the BRB. Snowmelt contributes 20% of the total flow at the basin outlet during the pre-monsoon period and 8% in the post monsoon period. The magnitude of the simulated flows at 10%, 40% and 90% exceedance probabilities are 453, 126 and 39 m 3 /s respectively indicating high energy generation potential.
This study provides additional evidence to the SWAT diaspora of its applicability to simulate the rainfall-runoff characteristics of complex mountainous basin. Furthermore, the spatial and temporal variability in the available water of the BRB was estimated. The findings will be useful for hydrologists and planners in general to utilize the available water rationally in the times to come and particularly, to harness the hydroelectric potential of the basin.