Low Altitude Unmanned Aerial Vehicles (UAVs) and Satellite Remote Sensing Are Used to Calculated River Discharge Attenuation Coe ﬃ cients of Ungauged Catchments in Arid Desert

: The arid desert ecosystem is very fragile, and the change of its river discharge has a direct impact on irrigation and natural environment. River discharge attenuation coe ﬃ cients is a key index to reveal the stability of desert river ecosystem. However, due to the harsh conditions in desert areas, it is di ﬃ cult to establish a hydrological station to obtain data and calculate the attenuation coe ﬃ cients, so it is urgent to develop new methods to master the attenuation coe ﬃ cients of rivers. In this study, Taklamakan desert river was selected as the research area, and the river discharge of the desert river were estimated by combining low-altitude UAV and satellite remote sensing technology, so as to calculate the attenuation status of the river in its natural state. Combined with satellite remote sensing, the surface runo ﬀ in the desert reaches of the Hotan River from 1993 to 2017 were estimated. The results showed that the base of runo ﬀ attenuation in the lower reaches of the Hotan River is 40%. Coupled UAV and satellite remote sensing technology can provide technical support for the study of surface runo ﬀ in desert rivers within ungauged basins. Using UAV and satellite remote sensing can monitor surface runo ﬀ e ﬀ ectively providing important reference for river discharge monitoring in ungauged catchments.


Introduction
The flow of arid desert river affects the stability of regional ecosystem and plays a vital role in maintaining the biodiversity and ecosystem integrity of the river [1][2][3]. Therefore, the availability of river discharges in ungauged catchments of arid desert is of great concern [4,5]. In recent years, the study of desert rivers has attracted the attention of many scholars [4,6], but in the past, there were more attention to the quaternary geology, paleoenvironment and fluvial geomorphologic evolution [7,8], and there is a lack of quantitative expression of river discharge [6]. There is a great obstacle to the study of surface runoff in ungauged catchments of arid desert, and it is difficult to meet the demand of hydrological monitoring data for current global change research.

Study Area
The Taklamakan Desert, located in the middle latitudes of Eurasia in the Northern Hemisphere, is famous for its extremely dry climate and the second largest mobile desert in the world. It also serves as an indicator of global climate change [3,51]. The Taklamakan Desert exhibits unique patterns in its material energy and water circulation. Its material and energy transport are important influences on the circulation of the atmosphere in Central Asia [52,53]. At present, the ecological environment, fluvial resources, and hydrological characteristics of the Taklamakan Desert have attracted global attention [54,55]. In the Taklamakan Desert, the main aquatic systems are the Hotan, Yerqiang, Weigan, and Aksu river systems, as well as the Bosten lake system. Among them, Hotan River Basin is adjacent to Yerqiang River Basin, as shown in Figure 1. The Hotan River spans from Mount Muztagh Ata at an altitude of 6638 m in the northern Tibetan Plateau to the Tarim Basin, crossing the Taklamakan Desert into the Tarim Basin after~500 km; it is currently the only river that ranges throughout the renowned desert [56]. The Yerqiang river is located in the west of Taklamakan Desert and has similar geographical environment and climatic conditions with Hotan river. arid scarcity areas, which can reflect the change of discharge in different periods. Therefore, for such unmeasured rivers, low-altitude UAV data was carefully combined with satellite remote sensing data to estimate the river discharge, and to further estimate the attenuation coefficients of the river in its natural state. The objectives of this study were to: (1) acquire the digital surface model (DSM) data of river sections from UAV, with which the shapes of river sections were determined, (2) calculate the river discharge by UAV and satellite remote sensing, and (3) obtain the attenuation coefficients of desert rivers. Finally, the attenuation pattern of surface runoff in desert rivers in this extremely arid climate was revealed, providing insights into the effects of global climate change in this region for hydrological monitoring.

Study Area
The Taklamakan Desert, located in the middle latitudes of Eurasia in the Northern Hemisphere, is famous for its extremely dry climate and the second largest mobile desert in the world. It also serves as an indicator of global climate change [3,51]. The Taklamakan Desert exhibits unique patterns in its material energy and water circulation. Its material and energy transport are important influences on the circulation of the atmosphere in Central Asia [52][53]. At present, the ecological environment, fluvial resources, and hydrological characteristics of the Taklamakan Desert have attracted global attention [54][55]. In the Taklamakan Desert, the main aquatic systems are the Hotan, Yerqiang, Weigan, and Aksu river systems, as well as the Bosten lake system. Among them, Hotan River Basin is adjacent to Yerqiang River Basin, as shown in Figure 1. The Hotan River spans from Mount Muztagh Ata at an altitude of 6638 m in the northern Tibetan Plateau to the Tarim Basin, crossing the Taklamakan Desert into the Tarim Basin after ~500 km; it is currently the only river that ranges throughout the renowned desert [56]. The Yerqiang river is located in the west of Taklamakan Desert and has similar geographical environment and climatic conditions with Hotan river.
Along the banks of the river are Populus euphratica forests, Tamarix sp., licorice, Alhagi sp., and a few reeds. The variation of desert river discharge is very important to the diversity of coastal ecosystem and the utilization of downstream water resources. However, due to the lack of hydrological observation data along the way, runoff and the patterns thereof remain poorly controlled. Therefore, Yerqiang River Basin and Hotan River Basin are selected as research areas to estimate the river discharge of desert rivers and discuss the attenuation coefficients of desert rivers, so as to provide reference for the utilization of desert rivers.  Along the banks of the river are Populus euphratica forests, Tamarix sp., licorice, Alhagi sp., and a few reeds. The variation of desert river discharge is very important to the diversity of coastal ecosystem and the utilization of downstream water resources. However, due to the lack of hydrological observation data along the way, runoff and the patterns thereof remain poorly controlled. Therefore, Yerqiang River Basin and Hotan River Basin are selected as research areas to estimate the river discharge of desert rivers and discuss the attenuation coefficients of desert rivers, so as to provide reference for the utilization of desert rivers.

Estimated River Discharge
Flow velocity Equations from local-scale models can be parameterized with specific catchment values. However, flow velocities have to be modelled enough to derive the required parameters from data available for the study region and sophisticated enough to deliver realistic flow velocity values for a large variety of environmental conditions. The Manning Equation was proposed in accordance with 200 experimental data [57], reflecting the relationship between water flow and a river bed, as well as internal factors of a river bed [58,59]. Current research mainly focuses on the hydrologic characteristics of uniform flow and the Manning coefficient, which simplifies non-uniform flow to a uniform flow state [32]. The approximate flow state is considered uniform in a traditional open channel with no vegetation on a large scale. In this case, the Manning Equation can be used to directly quantify the relationship between the Manning coefficient, velocity and water depth. In a few global scale models, the Manning-Strickler Equation has been applied to simulate variable river flow velocities [31,60], which led to enhanced representations of flow velocities [31] and discharge [60]. The Manning-Strickler Equation for calculating river discharge is: where n is the field roughness value. A is the area of the cross-section, m 2 . and P is the wet perimeter. S is the hydraulic slop. In general, the relationship between river width and discharge varies between different cross sections, which prompts the question of how the relationship between width and flow changes with narrow rivers and wide and shallow rivers in arid data-poor areas. According to the field investigation, the Taklamakan Desert river can be mainly categorized into trapezoidal section ( Figure 2).
Water 2020, 12, x FOR PEER REVIEW 4 of 18

Estimated River Discharge
Flow velocity Equations from local-scale models can be parameterized with specific catchment values. However, flow velocities have to be modelled enough to derive the required parameters from data available for the study region and sophisticated enough to deliver realistic flow velocity values for a large variety of environmental conditions. The Manning Equation was proposed in accordance with 200 experimental data [57], reflecting the relationship between water flow and a river bed, as well as internal factors of a river bed [58][59]. Current research mainly focuses on the hydrologic characteristics of uniform flow and the Manning coefficient, which simplifies non-uniform flow to a uniform flow state [32]. The approximate flow state is considered uniform in a traditional open channel with no vegetation on a large scale. In this case, the Manning Equation can be used to directly quantify the relationship between the Manning coefficient, velocity and water depth. In a few global scale models, the Manning-Strickler Equation has been applied to simulate variable river flow velocities [31,60], which led to enhanced representations of flow velocities [31] and discharge [60]. The Manning-Strickler Equation for calculating river discharge is: where n is the field roughness value. A is the area of the cross-section, m 2 . and P is the wet perimeter. S is the hydraulic slop. In general, the relationship between river width and discharge varies between different cross sections, which prompts the question of how the relationship between width and flow changes with narrow rivers and wide and shallow rivers in arid data-poor areas. According to the field investigation, the Taklamakan Desert river can be mainly categorized into trapezoidal section ( Figure 2). where, W is the width of the water surface; D the depth of the water; α and θ are the angles of the river bank. According to Huang [61], the river discharge of trapezoidal section can be estimated by using altimetry satellite and optical image. However, in a data-poor area, it is difficult to obtain effective water depth data from medium-sized and small, wide and shallow rivers because the depth extraction error is large from a lack of verification points and poor data quality from satellite altimetry. Therefore, satellite altimetry is not suitable for wide and shallow rivers in the arid and data-poor areas in northwestern China. According to Huang [61], the roughness coefficient (n) and slope (S) are considered as constants to avoid using them as dynamic variables. Based on this hypothesis and the characteristics of rivers in arid areas, this study determined coefficient c and water depth index (f) to describe the relationship between water depth and river discharge using the method proposed by Huang [61] combined with energy Equations (2)-(4) [62]. On this basis, the water depth D [61] was replaced by the water depth (d) in Equation (3), i.e., Equation (5). Finally, for different river sections, river parameters were obtained based on low-altitude UAV images, which were then converted into Equations dependent on different satellite source variables as input data to obtain the river discharge estimation method of this study Equation (6). According to Huang [61], the river discharge of trapezoidal section can be estimated by using altimetry satellite and optical image. However, in a data-poor area, it is difficult to obtain effective water depth data from medium-sized and small, wide and shallow rivers because the depth extraction error is large from a lack of verification points and poor data quality from satellite altimetry. Therefore, satellite altimetry is not suitable for wide and shallow rivers in the arid and data-poor areas in northwestern China. According to Huang [61], the roughness coefficient (n) and slope (S) are considered as constants to avoid using them as dynamic variables. Based on this hypothesis and the characteristics of rivers in arid areas, this study determined coefficient c and water depth index (f) to describe the relationship between water depth and river discharge using the method proposed by Huang [61] combined with energy Equations (2)-(4) [62]. On this basis, the water depth D [61] was replaced by the water depth (d) in Equation (3), i.e., Equation (5). Finally, for different river sections, river parameters were obtained based on low-altitude UAV images, which were then converted into Equations dependent on different satellite source variables as input data to obtain the river discharge estimation method of this study Equation (6).
where, Q is flow rate, a, c, f is coefficient, and W is river width. According to the field measured flow, the unknown parameter a is optimized. The specific calculation method of parameter can be referred to Huang [61]. Given that discharge is related to river width, cross-section, and water depth, understanding these basic hydraulic variables is a priority for discharge estimation.

Validating the River Section Shape by UAV
Small consumer UAV has the advantages of being easy to use, low cost, high efficiency and flexible flight [63,64]. At present, research showed that the precision of terrain measurement based on UAV can reach centimeters [65]. In this study, an UAV was employed to acquire high-resolution stereoscopic images, which were used to obtain high-resolution topographic data. The measurement setup consisted of an UAV DJI Phantom 4 Professional including a Cardan suspension and an action-camera FC300X_3.6_4000x3000 edition. Stereoscopic images were processed by the rapid and automatic professional processing software Pix4Dmapper (https://pix4d.com/). Pix4Dmapper not only supports UAV data, but also supports aerial photography, oblique photography, and close-range photogrammetry. In this study, we conducted flight missions using the DJI Phantom 4 Professional UAV. The flight was controlled by the intelligent flight control software Pix4D capture, with a flying hnine of 150 m. The photo overlap is set to be 70% to ensure the subsequent generation of stereoscopic image pairs, and obtain 1054 high-resolution photos of UAV. Generally, image treatment includes data importing, initial processing, three-dimensional triangulation processing, digital orthophoto map (DOM) generation, and DSM generation [66,67]. Preparation of the aerial flights and image processing corresponded to the scheme in Figure 3.
Due to the lack of data in the desert area of Hotan River Basin, the Kaqun hydrologic station of Yerqiang river in similar basins was selected as the experimental area to discuss the applicability of Equation (6) in estimating the river discharge of medium and small wide shallow rivers in the desert area without data. UAV was used to obtain the above-ground terrain information in order to verify the shape of river section. In this research, the measured data of Total Station were used to verify the results, which included 22 ground control points. The verification method used the relative root-mean-square error (RMSE) to evaluate the accuracy of UAV data [68]. Among them, the underwater terrain was difficult to obtain through the UAV, so the underwater terrain of this section was measured manually with a water gauge, as shown in Figure 4.
Professional UAV. The flight was controlled by the intelligent flight control software Pix4D capture, with a flying hnine of 150 m. The photo overlap is set to be 70% to ensure the subsequent generation of stereoscopic image pairs, and obtain 1054 high-resolution photos of UAV. Generally, image treatment includes data importing, initial processing, three-dimensional triangulation processing, digital orthophoto map (DOM) generation, and DSM generation [66][67]. Preparation of the aerial flights and image processing corresponded to the scheme in Figure 3.  Due to the lack of data in the desert area of Hotan River Basin, the Kaqun hydrologic station of Yerqiang river in similar basins was selected as the experimental area to discuss the applicability of Equation (6) in estimating the river discharge of medium and small wide shallow rivers in the desert area without data. UAV was used to obtain the above-ground terrain information in order to verify the shape of river section. In this research, the measured data of Total Station were used to verify the results, which included 22 ground control points. The verification method used the relative rootmean-square error (RMSE) to evaluate the accuracy of UAV data [68]. Among them, the underwater terrain was difficult to obtain through the UAV, so the underwater terrain of this section was measured manually with a water gauge, as shown in Figure 4. The elevation of the same point as Ground Control Points (GCPs) were obtained by UAV, and the RMSE was calculated. The results showed that the RMSE error between the UAV data and the topographic measurement data above the river section measured on site was 5.65 cm. It can be seen that the accuracy of river section data obtained by UAV has reached the centimeter level, so we think it is completely feasible to obtain the river section shape by UAV and estimate the river discharge in ungauged catchments area.

Validating Water Surface Areas by UAV
We used the modified normalized difference water index (MNDWI, see Equation (7)) to extract the width of water surface using Sentnel-2 data (https://scihub.copernicus.eu/). Then the UAV images were used to verify river width ( Figure 5) [69]. The elevation of the same point as Ground Control Points (GCPs) were obtained by UAV, and the RMSE was calculated. The results showed that the RMSE error between the UAV data and the topographic measurement data above the river section measured on site was 5.65 cm. It can be seen that the accuracy of river section data obtained by UAV has reached the centimeter level, so we think it is completely feasible to obtain the river section shape by UAV and estimate the river discharge in ungauged catchments area.

Validating Water Surface Areas by UAV
We used the modified normalized difference water index (MNDWI, see Equation (7)) to extract the width of water surface using Sentnel-2 data (https://scihub.copernicus.eu/). Then the UAV images were used to verify river width ( Figure 5) [69].
where Green and MIR are the surface reflectance of the green band and middle-infrared band, respectively. Then, we used the maximum between-class variance method [70] to determine the thresholds of binarization for MNDWI.

Performance Metrics
In this study, we selected the root-mean-square error (RMSE) and the Nash-Sutcliffe efficiency coefficient (NSE) [68] to evaluate the discharge estimation performance. The RMSE is used to quantify the deviations of the estimates from the observations. The NSE varies from to 1, and 1 indicates the optimal status where the simulated discharge equals the in situ measurements.
In Kaqun station, the shape of the river sections was obtained by UAV and underwater topography measurement, as shown in Figure 4.
Firstly, the measured average water depth, average velocity and average width data of this hydrologic station from 1998 to 2018 were used to determine the regression coefficient c and water depth index f based on Equation (2)-(4). DSM data were used to obtain the difference between upstream and downstream water levels in river sections. The difference was then divided by the distance between the two points and the ratio, i.e., hydraulic slop, was 0.0019. The coefficient n is empirically derived, which is dependent on many factors, including surface roughness and sinuosity [71]. According to the long-term observation of local hydrographic bureau, the roughness coefficient n is determined to be 0.048. Combined with the field measurement of the side slope of the river section, the obtained data are finally put into Equation (6) as input data. As the Yerqiang river is a seasonal river, we selected hydrographic station data during the summer abundant water period of 2008-2018 (May to September) as the verification data. On this basis, the river discharge was calculated through water surface width of the river section in different periods (Table 1), and verified by comparing with monthly average discharge data of the hydrographic station ( Figure 6).

Performance Metrics
In this study, we selected the root-mean-square error (RMSE) and the Nash-Sutcliffe efficiency coefficient (NSE) [68] to evaluate the discharge estimation performance. The RMSE is used to quantify the deviations of the estimates from the observations. The NSE varies from to 1, and 1 indicates the optimal status where the simulated discharge equals the in situ measurements.
In Kaqun station, the shape of the river sections was obtained by UAV and underwater topography measurement, as shown in Figure 4.
Firstly, the measured average water depth, average velocity and average width data of this hydrologic station from 1998 to 2018 were used to determine the regression coefficient c and water depth index f based on Equations (2)-(4). DSM data were used to obtain the difference between upstream and downstream water levels in river sections. The difference was then divided by the distance between the two points and the ratio, i.e., hydraulic slop, was 0.0019. The coefficient n is empirically derived, which is dependent on many factors, including surface roughness and sinuosity [71]. According to the long-term observation of local hydrographic bureau, the roughness coefficient n is determined to be 0.048. Combined with the field measurement of the side slope of the river section, the obtained data are finally put into Equation (6) as input data. As the Yerqiang river is a seasonal river, we selected hydrographic station data during the summer abundant water period of 2008-2018 (May to September) as the verification data. On this basis, the river discharge was calculated through water surface width of the river section in different periods (Table 1), and verified by comparing with monthly average discharge data of the hydrographic station ( Figure 6).   Finally, error analysis was conducted on the calculated results, and the RMSE and NSE evaluation results were shown in Table 2. It can be seen that Equation (6) can be used to better estimate the discharge of wide and shallow rivers, indicating that this method is applicable to the estimation of medium and small wide shallow rivers rivers.

Estimated Environmental Flow
On the basis of verifying the applicability of Equation (6), this method is adopted to estimate the river discharge of P1 and P2 monitored sections of the desert reach during dry season in similar basins of Hotan river, where there is a no data area. P1 and P2 sections are 100 km apart, accounting for about 1/5 of the total length of the desert river section. The attenuation coefficient within 100 km of the desert river was discussed to provide a basis for the ecological environment protection of the desert river. Combined with the methods outlined in Sections 3.1 and 3.2, the shapes of the monitored sections were first established, and then the river discharge at P1 and P2 was estimated. Finally, the difference in the river discharge between the two monitored sections was calculated, as shown in Figure 6. River discharge estimation using Equation (8) in combination with satellite-derived river widths.
Finally, error analysis was conducted on the calculated results, and the RMSE and NSE evaluation results were shown in Table 2. It can be seen that Equation (6) can be used to better estimate the discharge of wide and shallow rivers, indicating that this method is applicable to the estimation of medium and small wide shallow rivers rivers.

Estimated Environmental Flow
On the basis of verifying the applicability of Equation (6), this method is adopted to estimate the river discharge of P1 and P2 monitored sections of the desert reach during dry season in similar basins of Hotan river, where there is a no data area. P1 and P2 sections are 100 km apart, accounting for about 1/5 of the total length of the desert river section. The attenuation coefficient within 100 km of the desert river was discussed to provide a basis for the ecological environment protection of the desert river. Combined with the methods outlined in Sections 3.1 and 3.2, the shapes of the monitored sections were first established, and then the river discharge at P1 and P2 was estimated. Finally, the difference in the river discharge between the two monitored sections was calculated, as shown in Equation (8). The minimum attenuation coefficients of the Hotan River within 100 km was obtained during the dry season.
where AC is the attenuation coefficients, Q P1 is the river discharge at point P1, and Q P2 is the river discharge at point P2.
On the bases of the relationships described in Equations (6), combined with high-resolution satellite remote sensing images, the river discharge of Hotan Rivers sections in different periods were estimated, and the changes in the attenuation coefficients during the dry season were then analyzed. In this study, the attenuation coefficients were calculated by using the minimum river discharge during the dry season. The lowest attenuation coefficients within 100 km of the Hotan River under the condition of extreme drought during the dry season was analyzed.

UAV Data
Nine flight missions in Hotan River in the Taklamakan Desert were conducted using the DJI Phantom 4 Professional UAV during the period from 1 December to 2 December of 2017. The flight was controlled by the intelligent flight control software Pix4Dcapture, and the photo overlap was set to 70% to ensure the subsequent generation of stereoscopic image pairs. There were 7 flights in P1 sample area and 2 flights in the P2 sample area, in which the flight height was 160 m and each flight number was 5. A total of 795 photos were obtained from the P1 sample area, and 505 photos were taken from the P2 sample area. The Pix4Dmapper software was then used to extract the modern point cloud and DSM of P1 and P2 (Figure 7). The obtained DOM and DSM data spaces are referred to as WGS1993/UTM zone 48N.  (8) where AC is the attenuation coefficients, QP1 is the river discharge at point P1, and QP2 is the river discharge at point P2.
On the bases of the relationships described in Equations (6), combined with high-resolution satellite remote sensing images, the river discharge of Hotan Rivers sections in different periods were estimated, and the changes in the attenuation coefficients during the dry season were then analyzed. In this study, the attenuation coefficients were calculated by using the minimum river discharge during the dry season. The lowest attenuation coefficients within 100 km of the Hotan River under the condition of extreme drought during the dry season was analyzed.

UAV Data
Nine flight missions in Hotan River in the Taklamakan Desert were conducted using the DJI Phantom 4 Professional UAV during the period from 1 December to 2 December of 2017. The flight was controlled by the intelligent flight control software Pix4Dcapture, and the photo overlap was set to 70% to ensure the subsequent generation of stereoscopic image pairs. There were 7 flights in P1 sample area and 2 flights in the P2 sample area, in which the flight height was 160 m and each flight number was 5. A total of 795 photos were obtained from the P1 sample area, and 505 photos were taken from the P2 sample area. The Pix4Dmapper software was then used to extract the modern point cloud and DSM of P1 and P2 (Figure 7). The obtained DOM and DSM data spaces are referred to as WGS1993/UTM zone 48N.

Remote Sensing Data
In this study, Landsat images data were used for detecting changes in water surface area of the Hotan River in the study area. The details are shown in Table 3.

Remote Sensing Data
In this study, Landsat images data were used for detecting changes in water surface area of the Hotan River in the study area. The details are shown in Table 3.

Ground-Based Data
At the monitoring stations (P1 and P2), water depth was concurrently measured by using a measuring tape. At the same time, the edge slope (horizontal Angle α, θ) of the river section was measured using a level. In addition to field measured data, monthly average runoff data were collected from the Hotan River from 1964 to 2008. According to the research of Wang [72], monthly average runoff was divided into annual groups. Among them, the upstream river inflow, which was greater than 5 billion m 3 , was in the group of abundant water, the upstream river inflow, which ranged between 4 billion m 3 and 5 billion m 3 , was in the group of horizontal water, and the upstream river inflow, which was less than 4 billion m 3 , was in the group of dry water.

Acquired Features of River Cross Sections Via UAV Imagery
From the high-resolution UAV images, it can be seen that the river runs through the desert, and that the river is winding and branching, as shown in Figure 8. Combined with such images, it can be seen from the monitoring sections P1 and P2 that the river runs through the desert with relatively small fluctuations in surface area, but the river meanders and is more bifurcated. The river, in these sections, has a large amplitude in the desert, and the direction of the local area changes greatly. However, the position of the river bed has changed slightly over the years, and the river bed and the rocks on both banks are composed of silty sand.
Since the Hotan River is a seasonal river, no water flows through it during the dry season, and the river bed is exposed to the surface. The data obtained during this period can then be regarded as a water-free section. However, in the study area, the internal part of the channel is not completely free of water. Therefore, to determine a more accurate shape of the section, water depth measurements were acquired for large sections that had water. Finally, DSM data were combined with the water depth data to determine the river section morphology during the dry season. The shapes of these sections of the river are shown in Figure 9.
that the river is winding and branching, as shown in Figure 8. Combined with such images, it can be seen from the monitoring sections P1 and P2 that the river runs through the desert with relatively small fluctuations in surface area, but the river meanders and is more bifurcated. The river, in these sections, has a large amplitude in the desert, and the direction of the local area changes greatly. However, the position of the river bed has changed slightly over the years, and the river bed and the rocks on both banks are composed of silty sand. Since the Hotan River is a seasonal river, no water flows through it during the dry season, and the river bed is exposed to the surface. The data obtained during this period can then be regarded as a water-free section. However, in the study area, the internal part of the channel is not completely free of water. Therefore, to determine a more accurate shape of the section, water depth measurements were acquired for large sections that had water. Finally, DSM data were combined with the water depth data to determine the river section morphology during the dry season. The shapes of these sections of the river are shown in Figure 9.

Calculated Attenuation Coefficient in the Desert Reaches of the Hotan River
River section DSM data were obtained using high-precision images of a low-altitude UAV. Then, the hydraulic slope of each river section was calculated. Based on Equation (2)-(4), the section data of the upper reaches of Hotan river were used to determine coefficient c and water depth index f. Finally, the average water depth index f was 0.36, and the value of coefficient c was 1.07. The value of river roughness coefficient n is provided by experts of hydrology bureau, and the value is 0.035. Combined with the field measurement of the river section of the edge slope, the obtained data as

Calculated Attenuation Coefficient in the Desert Reaches of the Hotan River
River section DSM data were obtained using high-precision images of a low-altitude UAV. Then, the hydraulic slope of each river section was calculated. Based on Equations (2)-(4), the section data of the upper reaches of Hotan river were used to determine coefficient c and water depth index f. Finally, the average water depth index f was 0.36, and the value of coefficient c was 1.07. The value of river roughness coefficient n is provided by experts of hydrology bureau, and the value is 0.035. Combined with the field measurement of the river section of the edge slope, the obtained data as input data. On this basis, the river discharge of each river section was estimated through Equation (6), as shown in Table 4. Among them, the river width in 2017 were extracted from the UAV images. Table 4. Estimated river discharge based on historical images.

River-Course Cross-Sections
Hydraulic Slope (%) Q (m 3  In order to further analyze the water consumption situation after 100 km in the area of the desert reaches of the Hotan River for which there are no data, the river discharge of monitoring points P1 and P2 were counted from 1993 to 2017, and the results are shown in Table 5. Table 5. Attenuation in the desert reaches of the Hotan River. According to the comparative analyses shown in Table 4, a loss of 0.48 m 3 /s occurred within 100 km of the desert reaches of the Hotan River in 1993, and the loss percentage was 41.74%. In 1997, a loss of 4.81 m 3 /s occurred within 100 km of the desert reaches of the Hotan River, and the loss percentage was 44.29%. In 2010, 5.69 m 3 /s was lost within 100 km of the desert reaches of the Hotan River, and the loss percentage was 39.51%. In 2017, 0.989 m 3 /s was lost within 100 km of the desert reaches of the Hotan River; the loss percentage was 42.89%. In general, the attenuation rate of the desert reaches of the Hotan River was <45%, and the attenuation coefficient tended to be consistent at approximately 40%.

Parametric Sensitivity Analysis
According to Equation (6), the river discharge of hydrologic section in Kaqun were estimated. Coefficients a, c and f were key parameters in the flow estimation process. The relation between coefficient c and depth index f were obtained by calibration of the measured data of the hydrological station. Therefore, we only discussed the influence of coefficient a on the estimation results. Sichangi [73] research shows that for the trapezoidal section, coefficient a is shown in Equation (9). When river width >> depth, coefficient a can be approximately equal to S 1/2 /n, as shown in Equation (10).
where, S is hydraulic slope, n is roughness coefficient, W is water surface width, θ is edge slope, and D is average water depth. The width and depth of the channel were obtained every 0.5 m so as to establish the width-depth relationship of the channel. Finally, the coefficient D of this study was obtained by measuring the width of the river. The section of Kaqun hydrographic station was used as the experimental area to conduct a comparative study on the influence of the above two calculation methods of coefficient a on the estimation results, and the results were verified with the monthly average discharge data. The results were shown in Figure 10. On this basis, error analysis was conducted on the value results of different coefficients a, and the results were shown in Table 6.
Water 2020, 12, x FOR PEER REVIEW 13 of 18 establish the width-depth relationship of the channel. Finally, the coefficient D of this study was obtained by measuring the width of the river. The section of Kaqun hydrographic station was used as the experimental area to conduct a comparative study on the influence of the above two calculation methods of coefficient a on the estimation results, and the results were verified with the monthly average discharge data. The results were shown in Figure 10. On this basis, error analysis was conducted on the value results of different coefficients a, and the results were shown in Table 6.

River-Course Cross-Sections RMSE (±m 3 /s) NSE (±)
Equation (9) 2.91 0.00 Equation (10) 12.77 0.01 The results showed that the coefficient a was approximately S 1/2 /n in Equation (10) for the section of Kaqun hydrologic station, and the estimated flow error were large. It is better to estimate the precision measured section of hydraulic slope obtained by combining low-altitude UAV with measured edge slope. Therefore, it is necessary to determine the calculation method of coefficient a according to the width-depth ratio of the river. When river width >> water depth, Equation (10) can be used to calculate a, while Equation (9) should be used for general wide and shallow rivers.

Uncertainty Evaluation
The river width of P1 and P2 sections of Hotan river in 1993, 1999 and 2010 were extracted by remote sensing images and compared with the river section width extracted by UAV images for verification. Errors caused by river width extracted from remote sensing images are evaluated by using RMSE. The uncertain results of discharge estimates associated with river width were shown in Table 7. According to the river discharge estimation results of P1 and P2 sections of Hotan river in Section

River-Course Cross-Sections RMSE (±m 3 /s) NSE (±)
Equation (9) 2.91 0.00 Equation (10) 12.77 0.01 The results showed that the coefficient a was approximately S 1/2 /n in Equation (10) for the section of Kaqun hydrologic station, and the estimated flow error were large. It is better to estimate the precision measured section of hydraulic slope obtained by combining low-altitude UAV with measured edge slope. Therefore, it is necessary to determine the calculation method of coefficient a according to the width-depth ratio of the river. When river width >> water depth, Equation (10) can be used to calculate a, while Equation (9) should be used for general wide and shallow rivers.

Uncertainty Evaluation
The river width of P1 and P2 sections of Hotan river in 1993, 1999 and 2010 were extracted by remote sensing images and compared with the river section width extracted by UAV images for verification. Errors caused by river width extracted from remote sensing images are evaluated by using RMSE. The uncertain results of discharge estimates associated with river width were shown in Table 7. According to the river discharge estimation results of P1 and P2 sections of Hotan river in Section 5.2, the flow in dry season 2010 > 1999 > 1993. Combined with the error evaluation results, the measurement error of width in the years with low river discharge was larger, that was, the estimation error in 1993 was larger than that in other years. Moreover, the estimation error of upstream P1 section was smaller than that of downstream P2 section, which further indicated that with the decrease of river discharge, the error of width extraction increases, affecting the estimation accuracy.

The Attenuation Coefficients Are Compared with the Theoretical Results During the Dry Season
Generally, dry water flow is the type of runoff that can exist year-round in the course of a river, and it is the minimum water flow that can be maintained during the dry season [74]. In this study, the wetted perimeter method in hydraulics was used to further analyze and calculate the attenuation coefficients of Hotan River surface runoff, which has commonly been used in the estimation of dry water flow [75]. The wetted perimeter method is generally applicable to wide, shallow channels and paraboloid channels. Therefore, it is suitable for wide shallow river in the desert reaches of the Hotan River. It is relevant to note that Leopold and Maddock's analysis of the at-a-station hydraulic geometry found that the general relationship between channel width (closely related to the wetted perimeter) and discharge was a power function in the form of Equation (11) [62]: where P w is the wetted perimeter in meters and Q is the river discharge (m 3 /s). In general, the inflection point of the wetted perimeter change curve is found in the curve of wetted perimeter and river discharge. The river discharge value of this inflection point is regarded as the critical flow value of the flow in the river channel during the dry season [76].
In this study, sample points were selected at intervals of 0.5 m between the monitoring sections P1 and P2 in the desert reaches of the Hotan River using high-resolution images obtained from 1 December 2017 to 2 December 2017, where P1 included 50 sample points and P2 included 48 sample points. The river discharge and wetted perimeter of sample points P1 and P2 in the same period were calculated. Finally, the relationship between surface runoff and the wetted perimeter were calculated according to Equation (11). The results are shown in Figure 11.
Water 2020, 12, x FOR PEER REVIEW 14 of 18 measurement error of width in the years with low river discharge was larger, that was, the estimation error in 1993 was larger than that in other years. Moreover, the estimation error of upstream P1 section was smaller than that of downstream P2 section, which further indicated that with the decrease of river discharge, the error of width extraction increases, affecting the estimation accuracy.

The Attenuation Coefficients Are Compared with the Theoretical Results During the Dry Season
Generally, dry water flow is the type of runoff that can exist year-round in the course of a river, and it is the minimum water flow that can be maintained during the dry season [74]. In this study, the wetted perimeter method in hydraulics was used to further analyze and calculate the attenuation coefficients of Hotan River surface runoff, which has commonly been used in the estimation of dry water flow [75]. The wetted perimeter method is generally applicable to wide, shallow channels and paraboloid channels. Therefore, it is suitable for wide shallow river in the desert reaches of the Hotan River. It is relevant to note that Leopold and Maddock's analysis of the at-a-station hydraulic geometry found that the general relationship between channel width (closely related to the wetted perimeter) and discharge was a power function in the form of Equation (11) [62]: b w Q P = (11) where Pw is the wetted perimeter in meters and Q is the river discharge (m 3 /s). In general, the inflection point of the wetted perimeter change curve is found in the curve of wetted perimeter and river discharge. The river discharge value of this inflection point is regarded as the critical flow value of the flow in the river channel during the dry season [76].
In this study, sample points were selected at intervals of 0.5 m between the monitoring sections P1 and P2 in the desert reaches of the Hotan River using high-resolution images obtained from 1 December 2017 to 2 December 2017, where P1 included 50 sample points and P2 included 48 sample points. The river discharge and wetted perimeter of sample points P1 and P2 in the same period were calculated. Finally, the relationship between surface runoff and the wetted perimeter were calculated according to Equation (11). The results are shown in Figure 11. The results showed that the critical flow rate of sections P1 and P2 in the same period of dry water were 1.21 m 3 /s and 0.73 m 3 /s, respectively. On this basis, a critical flow difference of 0.48 m 3 /s between sections P1 and P2 was calculated. At this point, the critical flow between the two sections decreases to 39.67%, and the results also tended to be 40%. The surface runoff satisfies the critical flow, and the attenuation coefficients of Hotan River natural channel is about 40%. P1 P2 Figure 11. Relationships between the wetted perimeter and river discharge.
The results showed that the critical flow rate of sections P1 and P2 in the same period of dry water were 1.21 m 3 /s and 0.73 m 3 /s, respectively. On this basis, a critical flow difference of 0.48 m 3 /s between sections P1 and P2 was calculated. At this point, the critical flow between the two sections decreases to 39.67%, and the results also tended to be 40%. The surface runoff satisfies the critical flow, and the attenuation coefficients of Hotan River natural channel is about 40%.
At the same time, these results were generally consistent with the calculated results of Huang [77]. They used 3 hydrological stations, 2 drainage channels, and connected the two tributaries as nodes to divide the river into 5 sub-sections, and then used a water-balance model to simulate Hotan River runoff. The results showed that the loss of surface runoff in the desert reaches of the Hotan River was 45.44%. These results were further supports the reliability of the calculated results of the attenuation coefficients in this study.

Conclusions
As an important source of water in the arid inland areas of northwest China, rivers play an important role in maintaining the integrity of river ecosystems. This study coupled UAV high-resolution images and remote sensing images, combined with the ground-based experimental data, to analyze the lowest attenuation coefficients of the Hotan River within 100 km in the case of an extreme drought season. The results revealed that:

1.
Through Equation (6), the combination of low-altitude UAV remote sensing and high-altitude remote sensing can well realize the estimation of medium and small wide shallow rivers flow in arid areas.

2.
Combined with satellite remote sensing images, the river discharge of the lower reaches of the Hotan River from 1993 to 2017 was estimated. Attenuation losses of surface runoff during this time were 0.51 m 3 /s, 4.55 m 3 /s, 5.69 m 3 /s, and 0.99 m 3 /s, respectively. 3.
By calculating the attenuation coefficients from 1993 to 2017, the results showed that the attenuation coefficients of each year were 44.34%, 41.74%, 39.51%, and 42.89%, respectively. Therefore, the attenuation coefficients of the Hotan River appears to be stable at 40%.
Overall, the usage of UAVs to acquire channel parameters in this study provided a novel prospect for rapid river discharge assessments. With low-altitude UAV technologies, changes in the water conditions of monitoring sections and the lack of stations can be obtained according to the inversion flow results of a multi-phase UAV. Based on low-altitude remote sensing and satellite remote sensing, the attenuation coefficients of the Hotan River was deduced, and this provided abundant hydrological data for the desert in which there are few stations. Furthermore, the methods employed in this study can effectively promote research progress into basin river discharge and provide an important reference for global river discharge monitoring.