**1. Introduction**

Water tensions are particularly acute in arid regions globally due to the infrequency and short periods of rainfall. The urbanization process of expanding populations has exacerbated water scarcity

in these areas, which are generally underdeveloped and lack hydrological gauging stations [1–3]. The quantity and quality of water resources in arid ungauged regions remain crucial issues of common concern to international communities [4].

In arid ungauged regions, most water resources are in the form of surface runo ff, largely accounted for by ephemeral rivers, especially in upstream mountainous water systems [5]. As one of the least-known aquatic ecosystems, ephemeral rivers are not only crucial as an essential water supply, but also support vegetation and other biota living nearby [6]. The structure, productivity, and spatial distribution of biotic communities in semi-arid and arid regions are strongly a ffected by ephemeral water flows [7,8]. There is thus an urgen<sup>t</sup> need to monitor the discharge of ephemeral rivers, especially in upstream watersheds. Moreover, the shortage of available data for traditional hydrological research methods severely impedes the study of ephemeral rivers and related ecological-hydrological processes in arid regions, which further limits the rational exploitation and managemen<sup>t</sup> of water resources.

Hydrological models have long been used to demonstrate hydrological processes and to estimate the discharge of ephemeral rivers [9], such as the lump model [10] and the Soil and Water Assessment Tool (SWAT) model [11]. However, the time-consuming processing of hydrological models requires a grea<sup>t</sup> deal of observation data and regional parameterization. Furthermore, results of hydrological models vary significantly because of highly unpredictable flow patterns, complex interactions with and among anthropogenic pressures, and lack of information on the physiographic and environmental conditions of many catchments [11,12]. Satellite remote sensing has been widely applied to extract river hydraulic variables in the calculation of peak discharge because of its low cost and high sequence characteristics [13–15], and most studies have estimated discharge by constructing the relationship between channel geometry and discharge [16–18]. Nevertheless, the extremely high variability of ephemeral river runo ff at di fferent spatial and temporal scales has made it hard to estimate the discharge of ephemeral rivers with the abovementioned methods [19]. Specifically, when the river is too narrow or the river only flows for a few days, it is di fficult to determine the water level and water surface area, and furthermore, to extract hydraulic variables with coarse remotely sensed data. Additionally, the peak discharge of ephemeral rivers has commonly been calculated by indirect means, such as the slope-area method [20]. The continuous slope-area method for gaging volumetric discharge has been tested in various ephemeral channels [21,22], while the method is still hard to implement in arid ungauged regions where access is limited.

In recent years, the rapid development of unmanned aerial vehicle (UAV) techniques has made it possible to obtain terrain information at centimeter-level precision [23–25]. These advances help to determine the hydraulic geometry accurately [26], and thus to identify riverbed change and sediment movement in a river channel, especially of ephemeral rivers in arid ungauged regions. With the help of UAV data, the study of riverbed sediment could provide a new perspective to estimate flood peak discharge [27]. The most commonly used approach defining the critical hydrodynamic conditions of sediment transport is still regarded as the Shields approach [28]. In subsequent studies, the threshold of the initiation of sediment transport was expressed by either the bed shear stress or the average flow rate, and numerous equations have been published based on simplified assumptions, laboratory data, and field measurements [29–31]. Among the equations, the power law and Prandt–von Karman velocity distribution are widely employed to estimate the critical velocities of sediment transport in open-channel flow, separately representing the logarithmic and exponential velocity distribution. Therefore, it is worth exploring the performance of UAVs in estimating the flood peak discharge of ephemeral rivers, with the logarithmic or the exponential velocity distribution equations applied.

The present paper uses high-resolution UAV data identifying stone movements to explore a fast and convenient method of calculating the flood peak discharge of ephemeral rivers in ungauged arid regions. The research objectives of the study are (1) to identify the movement of stones in the channel of the ephemeral river and to calculate the critical initial velocities of moving stones using high-resolution UAV data, (2) to obtain the flood peak discharge of the ephemeral river, and (3) to compare the performance of the logarithmic and the exponential velocity distribution methods. The proposed method of estimating the flood peak discharge of ephemeral rivers is presented to address the conflict between the shortage of hydrological gauge data and the data needs for research and managemen<sup>t</sup> of ephemeral rivers.
