## 3 Materials and Methods
### Modified ISSDOTv2 Method  
In rivers with bedforms, dune tracking is considered an effective way for estimating bedload transport. In this case, successive surveys were performed along a longitudinal bathymetric profile and, based on sediment and bedform characteristics, unit bedload was calculated [5; 12; 35; 36]. The integrated section surface difference over time method (ISSDOTv2) uses the scour volumes computed from the difference plots of time-sequenced bathymetric data to estimate bedload transport [14; 15; 37]. This method is represented by Equation (9), which is mathematically equivalent and dimensionally homogeneous to Equation (10), developed by [PERSON] et al. [38]. The main advantage of the ISSDOTv2 method is that Equation (9) is applied over a longitudinal profile, while Equation (10) requires averaged wave heights and velocities. \[q_{b,\text{ISSDOTv2}}=\frac{(1-p)\times\rho_{s}\times V}{1.82\times\Delta t_{ bat}\times N_{d}} \tag{9}\]  
\[q_{b}=\frac{(1-p)\times v_{d}\times H_{d}\times\rho_{s}}{2} \tag{10}\]  
where \(q_{b,\text{ISSDOTv2}}\) is the bed-material load moving in the sand wave computed by the ISSDOTv2 method (in kg/s); \(\rho_{s}\) is the density of sand (=2650 kg/m\({}^{3}\)); \(p\) is the porosity of sand (adopted as 0.4); 1.82 is a constant that accounts for the nontriangular shape of dunes; \(N_{d}\) is the number of dunes along the longitudinal profile; \(V\) is the scoured volume (m\({}^{3}\)) during the time interval \(\Delta t_{bat}\) between the bathymetric surveys (s); \(v_{d}\) is the dune speed (celerity, in m/s); and \(H_{d}\) is the dune height (m). The condition for applying the methodology is that the scoured volumes are equal to (or very close to) the depositional volumes. In rivers, unlike laboratory experiments, this condition is rarely observed, since flow is unsteady and the interaction between turbulence and high shear stresses results in the suspension of bed-material. Some of these suspended sediment particles might travel downstream and deposit on a different dune from which they originated, thus, adding depositional volume to another dune. [PERSON] et al. [37] recommend scour-deposition ratios between 0.8 and 1.2 (20% variation); otherwise, the profile is considered unsuitable for the method. Furthermore, a systemic bias inherent in the methodology underestimates the bedload rates. This error is related to the dune celerity and to the time interval between the surveys. In the process of subtracting longitudinal bathymetric profiles, some scour volumes are not computed (triangles C and D in Figure 5). The larger the time interval and the dune celerity, the greater the not computed volumes and the lower the calculated bedload. [PERSON] et al. [15] proposed a procedure to correct this systemic bias, represented by Equation (11), allowing the application of the ISSDOTv2 method with large time intervals. \[q_{b,\text{ISSDOTv2,corr}}=q_{b,\text{ISSDOTv2}}+\frac{v_{d}^{2}\times\Delta t_ {bat}\times H_{d}}{2\times\lambda} \tag{11}\]  
where \(q_{b,\text{ISSDOTv2,corr}}\) is the corrected dune transport rate (kg/s); and \(\lambda\) is the dune wavelength (m). Originally, the ISSDOTv2 method was developed to be applied over longitudinal bathymetric profiles surveyed with multibeam echosounders. The higher spatial resolution of the depth points measured with multibeam yields high accuracy in the interpolated digital elevation models (DEMs), thus, improving the quality of bedload estimates. In the present study, the lower resolution resulting from the ADCP survey (using only 5 beams) increases the uncertainties in the DEMs' construction and in the subsequent profiles' extraction. This modified approach, regarding the difference in bathymetric data collection and its spatial resolution, motivated the authors to test a modified ISSDOTv2 method, hereafter called mISSDOTv2. The mISSDOTv2 method was applied in the central region of the study area (Figure 6), in a reach approximately 300 m long and with 85 longitudinal profiles spaced approximately 1.15 m apart.