A New and Simpliﬁed Approach for Estimating the Daily River Discharge of the Tibetan Plateau Using Satellite Precipitation: An Initial Study on the Upper Brahmaputra River

: Collecting in situ observations from remote, high mountain rivers presents major challenges, yetreal-time, hightemporal resolution (e.g., daily)dischargedata are criticalfor ﬂoodhazardmitigation and river management. In this study, we propose a method for estimating daily river discharge (RD) based on free, operational remote sensing precipitation data (Tropical Rainfall Measuring Mission (TRMM), since 2001). In this method, an exponential ﬁlter was implemented to produce a new precipitation time series from daily basin-averaged precipitation data to model the time lag of precipitation in supplying RD, and a linear-regression relationship was constructed between the ﬁltered precipitation time series and observed discharge records. Because of di ﬀ erent time lags in the wet season (rainfall-dominant) and dry season (snowfall-dominant), the precipitation data were processed in a segmented way (from June to October and from November to May). The method was evaluated at two hydrological gauging stations in the Upper Brahmaputra (UB) river basin, where Nash–Sutcli ﬀ e E ﬃ ciency (NSE) coe ﬃ cients for Nuxia ( > 0.85) and Yangcun ( > 0.80) indicate good performance. By using the degree-day method to estimate the snowmelt and acquire the time series of new active precipitation (rainfall plus snowmelt) in the target basins, the discharge estimations were improved (NSE > 0.9 for Nuxia) compared to the original data. This makes the method applicable for most rivers on the Tibetan Plateau, which are fed mainly by precipitation (including snowfall) and are subject to limited human interference. The method also performs well for reanalysis precipitation data (Chinese Meteorological Forcing Dataset (CMFD), 1980–2000). The real-time or historical discharges can be derived from satellite precipitation data (or reanalysis data for earlier historical years) by using our method.


Introduction
River discharge (RD) data are indispensable for water resources management and flood prediction, and are also important for climate change studies and hydrological modeling [1][2][3]. RD data are the data that were used and the method that was developed in the study. Section 4 presents the discharge estimates and performance of the method. Section 5 discusses the impact factors for the method and concludes the utilities of the method.

Study Regions
The UB river basin is located in the south of the Tibet Plateau (TP) (Figure 1) and covers an area of around 241,000 km 2 . The river basin is in the upstream region of the Brahmaputra River, a trans-boundary river that flows through China, India, and Bangladesh. With an average elevation of 4000 m above sea level, the Upper Brahmaputra river is the world's highest river. The TP is one of the most sensitive regions to climate change [33], and understanding changes in river discharge on the TP is important for climate change studies; however, the region's remoteness, high altitude, and harsh weather conditions make field observations difficult and expensive. The width for the UB river ranges from <100 m in winter to nearly 500 m in summer. The rainy season is June to September (the Indian monsoon season), which accounts for 60-80% of the annual precipitation [34]. Two gauging stations (Nuxia and Yangcun) were used to validate our approach in the study area ( Figure 1). Both catchments above the two stations are fed mainly by precipitation (rain and snow), as glaciers occupy only a small proportion (Table 1). In a preceding study, which simulated the discharge with a variable infiltration capacity (VIC) model [35], the contribution of glacier melt to RD was about 10% in the basin. The width for the UB river ranges from <100 m in winter to nearly 500 m in summer. The rainy season is June to September (the Indian monsoon season), which accounts for 60-80% of the annual precipitation [34]. Two gauging stations (Nuxia and Yangcun) were used to validate our approach in the study area ( Figure 1). Both catchments above the two stations are fed mainly by precipitation (rain and snow), as glaciers occupy only a small proportion (Table 1). In a preceding study, which simulated the discharge with a variable infiltration capacity (VIC) model [35], the contribution of glacier melt to RD was about 10% in the basin.

Datasets
Two types of operational precipitation data were used to test our method: satellite precipitation data and reanalysis precipitation data. The satellite precipitation data were acquired from the Tropical Rainfall Measuring Mission (TRMM) Multi-Satellite Precipitation Analysis (TMPA) and the reanalysis precipitation data were from the Chinese Meteorological Forcing Dataset (CMFD). These are among the most popular satellite precipitation products and they have been applied and evaluated in other basins [36][37][38][39].
The TRMM satellite is a rain-monitoring meteorological satellite that was jointly launched by the American National Aeronautics and Space Administration (NASA) and the Japanese National Space Development Agency (NASDA) in 1997 [40]. The TRMM_3B42_Daily dataset, a quasi-global (50 • S-50 • N, 180 • E-180 • W), three-level precipitation product of TRMM satellites, was used in this study. It is a fusion of data from TMI (microwave imager), SSMI (special microwave imaging sensor), AMSR (enhanced microwave scanning radiometer), AMSU (advanced microwave), and thermal infrared sensors. This dataset contained 0.25 • × 0.25 • daily precipitation accumulation data generated from the research-quality 3-hourly TMPA precipitation data [41]. A total of 6328 files (from 1 January 2001 to 29 April 2018) were used in this study.
The China Meteorological Forcing Dataset (CMFD) is a near-surface meteorological and environmental reanalysis dataset developed by the Institute of Tibetan Plateau Research at the Chinese Academy of Science [42]. The dataset is based on the Princeton reanalysis data, GEWEX-SRB, GLDAS, and TRMM precipitation data, combined with meteorological data from the China Meteorological Administration. Its resolution is 0.1 • . In this study, the daily precipitation product for the period 1979-2018 is used, including 15,460 files (from 1 January 1979 to 29 April 2018). The daily precipitation data were computed from the 3 h precipitation data.
In the process of snowmelt estimation, the daily temperature data used for differentiating rain and snow as well as the calculation of snowmelt were also from CMFD. Daily temperature (from 1 January 1979 to 29 April 2018) was used to split rainfall and snowfall, as well as to calculate daily snowmelt based on a degree-day model. The extracted rainfall and snowfall data between 1 January 2001 and 31 December 2010 were used to compute the multi-year monthly mean precipitation of rain and snow.
Observed discharge data included daily data and monthly data. Daily data were available for Nuxia station (2001 to 2018) and Yangcun station (2003 to 2015). As daily data were not available before 2000, we used monthly data to evaluate historically simulated discharge. All the discharge data were processed into the normalized form.

Basin-Averaged Precipitation
Our method attempted to estimate daily discharge by constructing a statistical relationship between operational precipitation data and observed discharge. The basin-averaged precipitation over the study catchment was computed and used as the input of the method. The average precipitation data for the two catchments ( Figure 1) were obtained by clipping and statistical analysis. To compute the average precipitation over the basin, we resampled the original data into uniform grids (5 × 5 km).

Exponential Filter
The exponential filter was used to model the time lag of the precipitation supply for the RD. There was an obvious delay in the peak discharge relative to the basin-averaged precipitation peak (Figure 2), resulting in poor correlation between the original average precipitation and observed discharge. The discharge often has a time lag relative to the supplements of both rainfall and snowfall because of the storage in a river system, while the time length is different. Physically, the discharge is correlated to the total precipitation over several days before the discharge observation time. Moreover, precipitation closer to the observation time has a greater contribution to the measured discharge. Therefore, an exponential filter [43,44] was applied to process the average precipitation data time series, which was continually calculated as a weighted average of recent precipitation data by giving less weight to older data. A new time series of precipitation data were acquired through the exponential filter. This filter uses a single tuning parameter named the characteristic time T. The correlation coefficient between filtered precipitation and observed discharge changes when T changes. When the correlation coefficient reaches the maximum, the value of T is defined as T peak . The new time series of precipitation was calculated by using the exponential filter and setting T as T peak . measured discharge. Therefore, an exponential filter [43,44] was applied to process the average precipitation data time series, which was continually calculated as a weighted average of recent precipitation data by giving less weight to older data. A new time series of precipitation data were acquired through the exponential filter. This filter uses a single tuning parameter named the characteristic time T. The correlation coefficient between filtered precipitation and observed discharge changes when T changes. When the correlation coefficient reaches the maximum, the value of T is defined as Tpeak. The new time series of precipitation was calculated by using the exponential filter and setting T as Tpeak.
The exponential filter uses a recursive formula [43]: where is the average precipitation at time and * is the respective filtered value at the previous time . T is the characteristic time and K ranges between 0 and 1. To initialize the filter, and * were set to 1 and (the precipitation for the first day in the records), respectively. Basin-averaged precipitation (P) and normalized observed discharge (Q_obs) at the area upstream of Nuxia hydrological station (hereafter the Nuxia basin). Note that the discharge observations used in this study have been normalized using Equation (8) to comply with the policy of the data provider. The precipitation data are from the Tropical Rainfall Measuring Mission (TRMM) dataset.

Linear Least-Squares Regression
After the value of Tpeak was determined and the corresponding filtered basin-averaged precipitation was obtained, a linear least-squares regression model was constructed with the filtered average precipitation as the independent variable and observed discharge as the dependent variable. Discharge for the times without observations was then estimated using the linear regression model. The filtering and linear regression (FLR) method is summarized in a flow chart ( Figure 3). The exponential filter uses a recursive formula [43]: where P t n+1 is the average precipitation at time t n+1 and P * t n is the respective filtered value at the previous time t n . T is the characteristic time and K ranges between 0 and 1. To initialize the filter, K t 1 and P * t 1 were set to 1 and P t 1 (the precipitation for the first day in the records), respectively.

Linear Least-Squares Regression
After the value of T peak was determined and the corresponding filtered basin-averaged precipitation was obtained, a linear least-squares regression model was constructed with the filtered average precipitation as the independent variable and observed discharge as the dependent variable. Discharge for the times without observations was then estimated using the linear regression model. The filtering and linear regression (FLR) method is summarized in a flow chart ( Figure 3). Remote Sens. 2020, 12, x FOR PEER REVIEW 6 of 20

Segmented Processing of Precipitation Data
Due to the high elevation of the UB river basin above sea level, both rainfall and snowfall are supplies for the discharge. In the wet season, rainfall is the dominant supply, while snowmelt is more important in the dry season. To distinguish the wet season and dry season, the multi-year monthly mean basin-averaged rainfall and snowfall were calculated by applying a relationship between air temperature and precipitation type constructed by Ding et al. [45]. The study of Ding et al. presented the function relationship of proportions of precipitation types with surface elevation and temperature. The multi-year mean monthly precipitation of rain and snow is presented in Figure 4. It shows that the precipitation over the UB river basin is mainly rainfall from June to August. In September and October, although there is less rainfall than snowfall, it is still the dominant supply for the RD, considering the time lag of the confluence. Additionally, the snowfall over the two months melts quickly due to the warm temperature. Therefore, the wet season includes summer and autumn, while the dry season includes winter and spring for the UB river basin. Therefore, basin-averaged precipitation from June to October (wet season) and precipitation data from November to the next May (dry season) are processed separately ( Figure 3).
Considering the different dominant types of precipitation in wet seasons and dry seasons, the segmented method was used to deal with the basin-averaged precipitation instead of the year-round method. Discharge often has different time lags relative to the supplements of both rainfall and snowfall, so the wet season (rainfall dominant, warm) and dry season (snow dominant, cold) are separated for estimation ( Figure 3). In the segmented method, all the processes are doubled and Tpeak has two values. The two values of Tpeak are acquired by recognizing the max correlation coefficients in two periods (the wet season and dry season, respectively).

Segmented Processing of Precipitation Data
Due to the high elevation of the UB river basin above sea level, both rainfall and snowfall are supplies for the discharge. In the wet season, rainfall is the dominant supply, while snowmelt is more important in the dry season. To distinguish the wet season and dry season, the multi-year monthly mean basin-averaged rainfall and snowfall were calculated by applying a relationship between air temperature and precipitation type constructed by Ding et al. [45]. The study of Ding et al. presented the function relationship of proportions of precipitation types with surface elevation and temperature. The multi-year mean monthly precipitation of rain and snow is presented in Figure 4. It shows that the precipitation over the UB river basin is mainly rainfall from June to August. In September and October, although there is less rainfall than snowfall, it is still the dominant supply for the RD, considering the time lag of the confluence. Additionally, the snowfall over the two months melts quickly due to the warm temperature. Therefore, the wet season includes summer and autumn, while the dry season includes winter and spring for the UB river basin. Therefore, basin-averaged precipitation from June to October (wet season) and precipitation data from November to the next May (dry season) are processed separately (Figure 3).
Considering the different dominant types of precipitation in wet seasons and dry seasons, the segmented method was used to deal with the basin-averaged precipitation instead of the year-round method. Discharge often has different time lags relative to the supplements of both rainfall and snowfall, so the wet season (rainfall dominant, warm) and dry season (snow dominant, cold) are separated for estimation ( Figure 3). In the segmented method, all the processes are doubled and T peak has two values. The two values of T peak are acquired by recognizing the max correlation coefficients in two periods (the wet season and dry season, respectively).

Calculation of Snowmelt
Differing from rainfall, the contribution of snowfall to discharge is more complex. It includes the accumulation and melting of snow. To explicitly study the impact of snow melting on discharge estimation by using the FLR, we used the degree-day method (DDM) [46] to simply estimate the snow melt. After using the DDM to calculate the snowmelt, the summation of daily snowmelt and rainfall produced a new basin-averaged total liquid water (hereafter the active precipitation, Pa) received by the target basin. The time series of active precipitation at each grid cell (5 × 5 km) in this study can be computed through the following procedures: (1) Separate the rainfall (Pr) and snowfall (Ps) from the daily precipitation data by using the method provided by Ding et al. [45]; (2) Calculate the potential snowmelt capacity (SMc) by using the DDM; (3) If SMc > Ps, the actual snowmelt (SMa) is equal to the snowfall (that is SMa = Ps); otherwise SMa = SMc, and the value of Ps minus SMc is added to the Ps of the next day; (4) The daily active precipitation Pa is equal to the summation of Pr and SMa (Pa = Pr + SMa).
After calculating the Pa for all the grid cells in the target basin, then the basin-averaged Pa can be obtained. The new basin-averaged active precipitation Pa is then processed by using the FLR method and the estimation of RD is compared with the result from the original precipitation data to assess the impacts of snowfall and snow melting on the discharge estimation.
The equations to compute the potential snowmelt capacity are listed as follows: where DDF (mm/d/°C) is the degree-day factor and PDD (°C) is the positive degrees in a day. DDF is an empirical parameter. The DDF used in the study is obtained by the method provide by Liu and Zhang [47], who developed an algorithm to spatially estimate the positive DDFs based on available observed DDFs. The spatial distribution of DDFs in the Yarlung Zangbo River Basin were presented in the paper. Here, is the daily temperature and is a logical variable ( = 1.0 when 0; = 0.0 when 0).

Calculation of Snowmelt
Differing from rainfall, the contribution of snowfall to discharge is more complex. It includes the accumulation and melting of snow. To explicitly study the impact of snow melting on discharge estimation by using the FLR, we used the degree-day method (DDM) [46] to simply estimate the snow melt. After using the DDM to calculate the snowmelt, the summation of daily snowmelt and rainfall produced a new basin-averaged total liquid water (hereafter the active precipitation, Pa) received by the target basin. The time series of active precipitation at each grid cell (5 × 5 km) in this study can be computed through the following procedures: (1) Separate the rainfall (Pr) and snowfall (Ps) from the daily precipitation data by using the method provided by Ding et al. [45]; (2) Calculate the potential snowmelt capacity (SMc) by using the DDM; (3) If SMc > Ps, the actual snowmelt (SMa) is equal to the snowfall (that is SMa = Ps); otherwise SMa = SMc, and the value of Ps minus SMc is added to the Ps of the next day; (4) The daily active precipitation Pa is equal to the summation of Pr and SMa (Pa = Pr + SMa).
After calculating the Pa for all the grid cells in the target basin, then the basin-averaged Pa can be obtained. The new basin-averaged active precipitation Pa is then processed by using the FLR method and the estimation of RD is compared with the result from the original precipitation data to assess the impacts of snowfall and snow melting on the discharge estimation.
The equations to compute the potential snowmelt capacity are listed as follows: where DDF (mm/d/ • C) is the degree-day factor and PDD ( • C) is the positive degrees in a day. DDF is an empirical parameter. The DDF used in the study is obtained by the method provide by Liu and Zhang [47], who developed an algorithm to spatially estimate the positive DDFs based on available observed DDFs. The spatial distribution of DDFs in the Yarlung Zangbo River Basin were presented in the paper. Here, T t is the daily temperature and H t is a logical variable (H t = 1.0 when T t ≥ 0; H t = 0.0 when T t < 0).

Performance Evaluation
The accuracy of the discharge estimates was determined by using different performance measures, such as the Nash-Sutcliffe efficiency coefficient (NSE) [48], the root mean square error (RMSE), and the BIAS, which are defined as follows: where Q obs i , Q obs , and Q est i are the observed discharge, mean observed discharge, and estimated discharge at a given time from paired observations and estimates. NSE ranges from −∞ to 1, where 1 is the perfect match between the estimates and observations. RMSE ranges from 0 to +∞, where 0 is the perfect match between the estimates and observations. BIAS ranges from −∞ to +∞, where 0 indicates no BIAS.
To ensure the confidentiality of the in situ data, all discharge observation data were normalized as follows: where Q NOR is the normalized discharge, Q is the discharge before normalization (including both discharge estimates and observations), and A and B are both constants (0 < A < Q MIN and B > Q MAX ). Q MIN and Q MAX are the minimum and the maximum gauged discharge for a given gauging station in the study period, respectively.

Sensitivity Analysis of FLR
To assess how the time series length of training data impact the estimated discharge, results based on training data time series lengths of one year, five years, and ten years were compared (see Table 2). Eight groups of single-year training data (from 2003 to 2010) were trained and six groups of five-year training data were trained.

Results of Filtration
The results of filtration are affected by the characteristic time length T. Here, T was selected by comparing the correlation coefficients between the observed discharge and the filtered average precipitation for values of T ranging from 1 to 100. For each precipitation dataset (wet season or dry season), the correlation coefficients show a unimodal distribution (Figure 5a). The values of T corresponding to the peak correlation coefficient (T peak ) at Nuxia station during 2001-2010 were 23 for the rainy season and 42 for the dry season. The different values of T for the wet season and dry season are because of the different time lags of rainfall and snowfall in supplying RD. The time lag of rainfall supply is about twenty days, while the time lag of snowfall supply is about 1.5 months. The filtered average precipitation data stream was calculated using Equations (1) and (2) by setting T equal to T peak for the segmented (rainy season and dry season) method (Figure 5b). This shows that the filtered precipitation lags according to the primal precipitation.

Results of Filtration
The results of filtration are affected by the characteristic time length T. Here, T was selected by comparing the correlation coefficients between the observed discharge and the filtered average precipitation for values of T ranging from 1 to 100. For each precipitation dataset (wet season or dry season), the correlation coefficients show a unimodal distribution (Figure 5a). The values of T corresponding to the peak correlation coefficient (Tpeak) at Nuxia station during 2001-2010 were 23 for the rainy season and 42 for the dry season. The different values of T for the wet season and dry season are because of the different time lags of rainfall and snowfall in supplying RD. The time lag of rainfall supply is about twenty days, while the time lag of snowfall supply is about 1.5 months. The filtered average precipitation data stream was calculated using Equations (1) and (2) by setting T equal to Tpeak for the segmented (rainy season and dry season) method (Figure 5b). This shows that the filtered precipitation lags according to the primal precipitation.

Performance of FLR in Discharge Estimation
Two linear-regression models were established based on linear regression, using the data from 2001 to 2010 as training data. One was for the wet season data (Figure 6a) and the other for the dry season data (Figure 6b). parameters were different when the TRMM and CMFD data were processed. The NS coefficients exceeded 0.85 in training and validation, and the bias for the two estimates was under 5% in training and about 10% in validation; these results demonstrate that the FLR is reliable in simulating daily discharge using satellite precipitation data.
FLR was then applied at another hydrological station (Yangcun), with estimates based on satellite and reanalysis precipitation datasets both yielding good results (Figure 8). Therefore, the FLR method is applicable to different locations and with different precipitation data.
Comparing the estimations from TRMM and CMFD precipitation data, both the results at Nuxia station and Yangcun station prove that the CMFD achieves better performance (Figures 7  and 8). This owes to the fact that CMFD is reanalysis data, which have combined various satellite precipitation data with more comprehensive local meteorological observations. Therefore, the accuracy of CMFD is supposed to be higher than the TRMM precipitation data.  Based on the FLR method, two estimated discharge time series were calculated from 2001 to 2018. The FLR showed satisfactory performance with both segmented TRMM and CMFD precipitation data for Nuxia basin (Figure 7). The FLR were calibrated respectively and the parameters were different when the TRMM and CMFD data were processed. The NS coefficients exceeded 0.85 in training and validation, and the bias for the two estimates was under 5% in training and about 10% in validation; these results demonstrate that the FLR is reliable in simulating daily discharge using satellite precipitation data.
FLR was then applied at another hydrological station (Yangcun), with estimates based on satellite and reanalysis precipitation datasets both yielding good results (Figure 8). Therefore, the FLR method is applicable to different locations and with different precipitation data.

How the Time Length of Training Data Series Influence FLR
The highest NS coefficients for the training data and validation data were achieved in the single-year training group, however these were not in the same year (Table 2). Generally, high accuracy in both training and validation was difficult to achieve simultaneously. Almost all NS coefficients for the single-year training data exceeded 0.9; however, their respective NS coefficients Comparing the estimations from TRMM and CMFD precipitation data, both the results at Nuxia station and Yangcun station prove that the CMFD achieves better performance (Figures 7 and 8). This owes to the fact that CMFD is reanalysis data, which have combined various satellite precipitation data with more comprehensive local meteorological observations. Therefore, the accuracy of CMFD is supposed to be higher than the TRMM precipitation data.

How the Time Length of Training Data Series Influence FLR
The highest NS coefficients for the training data and validation data were achieved in the single-year training group, however these were not in the same year (Table 2). Generally, high accuracy in both training and validation was difficult to achieve simultaneously. Almost all NS coefficients for the single-year training data exceeded 0.9; however, their respective NS coefficients in the validation were mostly smaller than those for the multiple-year training ( Table 2). For single-year training, the differences in accuracies among different years and between training and validation were more obvious than those for multiple-year training. This means that uncertainties associated with the selected single-year training data are larger than those associated with multiple-year training data.
Average NS coefficient and average RMSE were calculated for all single-year training and five-year training data. As the training time increased, the average NS coefficient decreased and the average RMSE increased for the training data ( Figure 9). Meanwhile, the average NS coefficient increased and the average RMSE decreased for the validation data. Increasing training time could reduce the gap between the accuracies of the training data and validation data, thereby maintaining both at relatively high levels simultaneously.
Remote Sens. 2020, 12, x FOR PEER REVIEW 13 of 20 Figure 9. Variations in NSE and RMSE for daily discharge estimates at Nuxia station with changing duration of the precipitation training data time series. The Y axis is the average NSE or RMSE of daily discharge estimates for all combinations using the same duration of training data (see Table 2). The precipitation data are from the TRMM dataset.

Estimates of Historical Discharge Using Segmented CMFD Precipitation Data
The daily historical discharges  at Nuxia and Yangcun stations were estimated using CMFD precipitation data based on the FLR (Figure 10a,b). Providing that the historical daily discharge (before 2000) was not available, monthly discharge estimates generated from daily discharge estimates were evaluated using the monthly discharge observations (Figure 10c,d). NS coefficients exceeded 0.8 for the monthly validation data (Figure 11), demonstrating that the FLR is useful for simulating discharge using historical satellite precipitation data. Figure 9. Variations in NSE and RMSE for daily discharge estimates at Nuxia station with changing duration of the precipitation training data time series. The Y axis is the average NSE or RMSE of daily discharge estimates for all combinations using the same duration of training data (see Table 2). The precipitation data are from the TRMM dataset.

Estimates of Historical Discharge Using Segmented CMFD Precipitation Data
The daily historical discharges  at Nuxia and Yangcun stations were estimated using CMFD precipitation data based on the FLR (Figure 10a,b). Providing that the historical daily discharge (before 2000) was not available, monthly discharge estimates generated from daily discharge estimates were evaluated using the monthly discharge observations (Figure 10c,d). NS coefficients exceeded 0.8 for the monthly validation data (Figure 11), demonstrating that the FLR is useful for simulating discharge using historical satellite precipitation data.
Remote Sens. 2020, 12, x FOR PEER REVIEW 14 of 20 Figure 10. The normalized daily discharge estimates from the segmented CMFD precipitation upstream of Nuxia (a) and Yangcun (b). Additionally included is a comparison between observations and estimates of normalized monthly streamflow (based on the segmented CMFD precipitation) upstream of Nuxia (c) and Yangcun (d).  Figure 11. The average daily precipitation data before (Pb, including snowfall and rainfall) and after (Pa, including snowmelt and rainfall), considering the process of snow melting by using the degree-day model (a) and the multi-year monthly mean value of (Pa-Pb) (b).

Factors Impacting the Estimation Accuracy
As the discharge is estimated by using the precipitation data, the quality of the original data is one of the factors that influence the estimation accuracy. Usually, the quality of the precipitation data is evaluated by using the meteorological station observations as reference data. Here, we use the correlation coefficient between the filtered basin-averaged precipitation and the observed RD to evaluate the quality of precipitation. If the precipitation data are qualified well for estimating RD, the max correlation coefficient between filtered basin-averaged precipitation and observed discharge is suggested to be larger than 0.85. When the max correlation coefficient is very low, this means that the quality of precipitation data is bad or a more complicated relationship between rainfall and runoff characterizes the watershed.
The input of the FLR method is the basin-averaged precipitation, because the average precipitation is an index that can represent the whole basin. The spatial variation of precipitation is not considered.

The Impact of Snow Melting on the Discharge Estimation
To figure out how the daily temperature impacts the snow melting and then influences the river discharge, we used the DDM and daily temperature data from CMFD to compute daily snowmelt and produced a new time series of active precipitation data (Pa) by adding daily snowmelt to daily rainfall. The comparison between the new active precipitation (Pa) and the original TRMM precipitation (Pb) data shows that Pb including rainfall and snowfall is obviously greater than Pa (sum of rainfall and snowmelt) in the dry season (Figure 11a). In one year, the snow accumulation lasts from the October to the next March and the snowmelt is concentrated between April and July (Figure 11b). This is consistent with the field observation. Figure 11. The average daily precipitation data before (Pb, including snowfall and rainfall) and after (Pa, including snowmelt and rainfall), considering the process of snow melting by using the degree-day model (a) and the multi-year monthly mean value of (Pa-Pb) (b).

Factors Impacting the Estimation Accuracy
As the discharge is estimated by using the precipitation data, the quality of the original data is one of the factors that influence the estimation accuracy. Usually, the quality of the precipitation data is evaluated by using the meteorological station observations as reference data. Here, we use the correlation coefficient between the filtered basin-averaged precipitation and the observed RD to evaluate the quality of precipitation. If the precipitation data are qualified well for estimating RD, the max correlation coefficient between filtered basin-averaged precipitation and observed discharge is suggested to be larger than 0.85. When the max correlation coefficient is very low, this means that the quality of precipitation data is bad or a more complicated relationship between rainfall and runoff characterizes the watershed.
The input of the FLR method is the basin-averaged precipitation, because the average precipitation is an index that can represent the whole basin. The spatial variation of precipitation is not considered.

The Impact of Snow Melting on the Discharge Estimation
To figure out how the daily temperature impacts the snow melting and then influences the river discharge, we used the DDM and daily temperature data from CMFD to compute daily snowmelt and produced a new time series of active precipitation data (Pa) by adding daily snowmelt to daily rainfall. The comparison between the new active precipitation (Pa) and the original TRMM precipitation (Pb) data shows that Pb including rainfall and snowfall is obviously greater than Pa (sum of rainfall and snowmelt) in the dry season (Figure 11a). In one year, the snow accumulation lasts from the October to the next March and the snowmelt is concentrated between April and July (Figure 11b). This is consistent with the field observation.
The FLR method is used for the newly produced precipitation data stream. The estimations derived from the new precipitation data stream are better than the results from the original precipitation data. The NSE increases and the BIAS decreases according to the performance of the original precipitation data under the consideration of the snow melting process (Figures 7 and 12). It is concluded that calculating snowmelt by using the DDM can improve the estimations from operative precipitation data, as well as by using the FLR method.
Remote Sens. 2020, 12, x FOR PEER REVIEW 16 of 20 The FLR method is used for the newly produced precipitation data stream. The estimations derived from the new precipitation data stream are better than the results from the original precipitation data. The NSE increases and the BIAS decreases according to the performance of the original precipitation data under the consideration of the snow melting process (Figures 7 and 12). It is concluded that calculating snowmelt by using the DDM can improve the estimations from operative precipitation data, as well as by using the FLR method. Figure 12. Normalized daily discharge estimates using the segmented TRMM precipitation data (a) and CMFD precipitation data for Nuxia basin (b) after the snow melting was considered.

Discussion and Conclusions
In this study, we developed a method combining an exponential filter and linear regression models to simulate river discharge using operational and gridded precipitation data. The exponential filter can simulate the time lag of rainfall and snowfall in supplying the RD. The UB river basin was selected as the study area. The basin is predominantly supplied by rainfall in the wet season and fed by snow in the dry season. Therefore, the method deals with the precipitation data in a segmented way (dry season and wet season). The method performs well for different locations (Nuxia and Yangcun in the UB river basin) and for different precipitation data (TRMM and CMFD). It was used to estimate real-time river discharge with the real-time satellite precipitation data (e.g., TRMM). It was also used to establish long time-series of historical discharge in remote regions of the TP, yielding good performance, as shown above. All the estimates yielded an NS coefficient greater than 0.8, which is suitable for most applications.
The accuracy of the precipitation data is one of the factors impacting the quality of RD estimates based on this method. To test if the precipitation is qualified for estimating RD by using FLR, the correlation coefficient between the filtered basin-averaged precipitation and observed discharge can Figure 12. Normalized daily discharge estimates using the segmented TRMM precipitation data (a) and CMFD precipitation data for Nuxia basin (b) after the snow melting was considered.

Discussion and Conclusions
In this study, we developed a method combining an exponential filter and linear regression models to simulate river discharge using operational and gridded precipitation data. The exponential filter can simulate the time lag of rainfall and snowfall in supplying the RD. The UB river basin was selected as the study area. The basin is predominantly supplied by rainfall in the wet season and fed by snow in the dry season. Therefore, the method deals with the precipitation data in a segmented way (dry season and wet season). The method performs well for different locations (Nuxia and Yangcun in the UB river basin) and for different precipitation data (TRMM and CMFD). It was used to estimate recent river discharge since 2001 with the satellite precipitation data (e.g., TRMM). It was also used to establish long time-series of historical discharge in remote regions of the TP, yielding good performance, as shown above. All the estimates yielded an NS coefficient greater than 0.8, which is suitable for most applications.
The accuracy of the precipitation data is one of the factors impacting the quality of RD estimates based on this method. To test if the precipitation is qualified for estimating RD by using FLR, the correlation coefficient between the filtered basin-averaged precipitation and observed discharge can be a useful index. A correlation coefficient >0.85 is suggested. As the quality of satellite precipitation retrievals gradually improves, the corresponding estimates will become more reliable.
The FLR method is used to estimate RD based on the regression model constructed from free operational grid precipitation datasets (satellite and reanalysis). This method can be used to estimate historical discharges based on reanalysis precipitation, real-time discharge based on satellite observing precipitation, as well as to supplement the missing data due to interrupted observations. Differing from traditional methods for short-term storm events [49][50][51], the FLR method (applicable to long-term time series) is suitable for different kinds of basins, as long as they are mainly fed by precipitation and there is a linear relationship between filter basin-averaged precipitation and runoff. For the basins where precipitation is not the main water source for the RD (such as glacier-melt-fed basin), FLR is not an ideal choice for RD estimation. If the RD management is adjusted artificially, the accuracy of FLR will be affected.
The advantage of our method is that it is straight forward and easily applied to different sized rivers where precipitation is the main water source for the river. Although the method was demonstrated and validated for discharge estimates in mountainous river basins, it can be extended to other river basins where the impact of human activities on discharge is limited. The satellite precipitation data can provide daily estimates, in contrast to many other remote sensing datasets, which are affected by missing data due to cloud cover. This is very important for remote regions where observations are hard to obtain and for basins where the observations are interrupted by economic or political factors. The method can also be used for new gauging stations where the historical observations are absent. The method also has its limitations, since it relies on a certain period of available discharge observations to develop the linear regression model, and thus is not suitable for ungauged basins.
The cryosphere is widespread on the Tibetan Plateau, and thus snowmelt and glacier melt are also important supplies for the river discharge. Traditional fitting methods that construct rating curves between basin-wide rainfall and basin outlet river discharges are not applicable for most rivers on the TP. The rivers on the TP are mostly fed by both snowmelt and rainfall (as well as glacier melt in some glaciated head water regions). In this study, we used the degree-day method to calculate the snowmelt and improved the discharge estimations, which were derived from original precipitation data. This improvement makes the FLR method applicable to most rivers on the Tibetan Plateau.