## 2 Materials and Methods
### Flow Field Hydrodynamics  
In addition to fish position estimates using sonar, our aim was to compare these estimates with in situ measurements of the flow field. This required the development and testing of a new device and method for turbulent flow measurements needed for in situ studies of down-stream migration. To achieve this, we developed a new pressure-based field probe for flow turbulence measurement (\"Differential Pressure Box\"; DBox). The device is based on the Fechheimer Pitot concept [45], which the authors have successfully developed and tested extensively for underwater vehicles [46; 47]. It was designed and implemented for application in rivers with highly turbulent flows ranging from 0 to 3 m/s, and calibrated using in situ ADCP measurements [48]. The combination of spatially explicit, time-averaged flow velocities recovered from ADCP in conjunction with the DBox differential pressure turbulence measurements thus form a spatially resolved, dynamic picture of the complex flow field experienced by fish in front of hydropower intakes. Estimation of the time-averaged flow velocity as well as its fluctuations caused by turbulence are achieved using the optimized, Fechheimer arrangement of the pressure sensors; the differential pressure is measured at the nose at the stagnation point where velocity goes to zero, and kinetic energy is transferred into pressure. In addition, two pressure ports are located at 35\({}^{\circ}\) to the left and right of the stagnation point, which correspond to the locations of local hydrostatic pressure on a cylindrical surface (Figure 6a). The relationship (Equation (1)) between the pressure difference (\(\Delta\)P) for both sides of the prototype (\(\Delta\)P\({}_{1}\) and \(\Delta\)P\({}_{2}\)) and the time-averaged flow velocity (V) is defined by the Pitot equation for 0\({}^{\circ}\) of angle of attack, where \(\Delta\)P\({}_{1}\) = \(\Delta\)P\({}_{2}\). Note that with two transducers the equation can be applied including angular deviations of up to 45\({}^{\circ}\):  
\[V=\sqrt[4]{a\left(\Delta\text{P}_{1}^{2}\ +\Delta\text{P}_{2}^{2}\right)} \tag{1}\]  
where \(a\) is an empirical coefficient to be fitted according to the prototype geometry and chosen sensors. The calculation of the flow-induced turbulence was performed using the dynamic pressure coefficient, \(K_{pv}\). The coefficient is defined as the dynamic pressure coefficient, calculated using the standard deviation of the pressure fluctuations [49]. The \(K_{pv}\) describes the flow turbulence at the measurement location as the ratio between the fluctuating pressure field as experienced by the sensor body, scaled against the average velocity magnitude at each measurement point:  
\[K_{pv}=\ \frac{\sqrt{\sum\left[\Delta\mathrm{P}(t)-\overline{\Delta\mathrm{P}} \right]^{2}}}{\frac{1}{2}\rho\overline{v}^{2}} \tag{2}\]  
where \(\Delta\mathrm{P}\) is the data recorded at each time, \(t\) of the differential pressure sensor (P\({}_{1}\) or P\({}_{2}\)), \(\overline{\Delta\mathrm{P}}\) the time-averaged differential pressure calculated over a single point measurement, \(\rho\) is the density of water (here taken as a constant value of 1000 kg/m\({}^{3}\)) and \(\overline{v}^{2}\) is the square of the time-averaged bulk flow velocity at the measurement location. This approach to assess the local flow turbulence follows the use of \(K_{pv}\) in a comprehensive study on the 3D hydrodynamics of a trash rack, with different bar element angles to assess the turbulence in the local flow [50]. Here we adopt the same formulation to assess the relationship between the differential pressure fluctuations and time-averaged velocities, which were obtained using the DBox at selected measuring points. Measurements were recorded at 5 m intervals across the channel and at three depth ranges (0.5-1, 1.5-2.0 and 2.0-2.5 m). Afterwards, the measurements were compared to the spatial map of the velocity field measured by the ADCP. Measurements were taken at each location by mounting the DBox on the large debris removal arm (Figure 6c).