Field conditions summary

The data on the currents field were obtained from a downward-looking Acoustic Doppler Current Profiler (ADCP) (Workhorse Sentinel 600 kHz model, RD Instruments, Inc.) deployed through a small boat for a few minutes before the start of the AUV mission. One vertical profile of horizontal current components was provided with measurements at 0.5 m vertical increments between 1.55 and 14.05 m depth.

The motion of the surface waters, down to a depth of about 8.55 m, was generally to the South; the deeper currents moved generally between SE-SSE, with average direction 176.14° over the whole water column. The predominant current direction was then to the south, almost perpendicular to the diffuser axis. Current speeds were generally between 0.1-0.25 m/s over the whole water column, with the average being about 0.132 m/s. Information on density stratification at the same location was also obtained with an OCEANSEVEN 316 multi-sensor (manufactured by IDRONAUT-Italy) to run RSB model. A similar profile was acquired by Isurus AUV close to Point 1 during its ascending trajectory from 12 m depth to the surface, at the end of the mission. Fig. 6 shows vertical temperature, salinity and density measurements averaged into 2-s bins.

35.64 35.65 35.66 35.67 35.68 35.69 35.7 Salinity (psu)

Temperature (°C)

35.64 35.65 35.66 35.67 35.68 35.69 35.7 Salinity (psu)

Temperature (°C)

Fig. 6. Vertical STD profiles measured by Isurus near the diffuser.

The water column was weakly stratified due to both low temperature and salinity variations in the vicinity of the diffuser.

The temperature difference between the surface and the bottom was about 1.5°C, with most of the difference occurring in a thermocline that extended from ~2 m to 10 m. The salinity profile showed some variability extending over the whole water column, with the difference between the bottom and the surface being about 0.07 psu.

The total difference in density over the water column was about 0.48 CT-units, with the change with depth being approximately linear.

The buoyancy frequency from the discharge depth to the surface was then

V Pa dz where g = 9.8 is the acceleration due to gravity, p = 1026.99 is the seawater density at the port depth, and dp / dz = 0.48 /15 is the vertical density gradient. The discharge depth during the AUV mission was about 15 m. The Froude number F, based upon the current speed and one of the most important parameters governing the dynamics of the diffuser flow in the near-field, was equal to (Roberts et al., 1989)

b where u = 0.132 is the current speed, and b is the buoyancy flux per unit length of the diffuser equal to g (Ap/pa )Q/L, where Ap = 31.47 is the density difference between the seawater and wastewater at the port level, Q = 0.61 the volume flow rate of wastewater, and L = 98.2 the diffuser length.

3. Results and discussion

3.1 Plume spatial characterization 3.1.1 Data processing

In order to map effectively the dispersion of the effluent using the AUV data, three main steps were followed.

In the first step, after a global analysis of the collected data (where, for example, errors due to sensor malfunctions were detected), an estimate of the appropriate trajectory described by the vehicle for the spatial location of the collected oceanographic data was produced. The uncertainty of the horizontal position estimate was less than 5 m. The uncertainty of the vertical position estimate was even less, due to the high precision complementary measurements of the eco-sounder. Then CTD and navigation data were merged onto a common time base using linear interpolation. Positioning data were rotated about -3.86° so that North-South/East-West lines were aligned with x - y axis.

In the second step, using the polynomials developed by Millero et al. (1980), in situ conductivity, temperature and pressure were used to compute salinity. Then, density was estimated by using this computed salinity and the measured temperature and pressure. Finally, the last step was to plot the desired variables onto x - y, x - z, and y - z $ grids using the Least Squares Collocation Method (LSCM) technique (see details in Zhang et al.

(2001) and Ramos (2005)). The LSCM has been used for numerous applications, namely the numerical solution of differential equations such as the Navier-Stokes equations and hyperbolic problems, including the shallow water equations, to interpolate gravity at any given location using only measurements at some discrete locations, etc. To apply Least-Squares Collocation Method, we first chose a finite set of N = 396

collocation points fa} ^ ^ = {{-90 : 20 : 110},{-120 : 20 : -20},{2 : 2 : 12}} in the measurements domain Q = [-98,118] x [-125,3] x [1,13].

Fig. 7. Plan view of the AUV plume tracking survey and collocation points.

Fig. 7. Plan view of the AUV plume tracking survey and collocation points.

Then an approximation of the desired variable (in this case, salinity, temperature and density, denoted by P) between measured and collocation points in the form was assumed

where p is the measurement at point Xt, with n = 16075 observations, Pj represents the approximated measurement at collocation point Xj, and W ^ is an elementary function usually built in such a way that it takes a certain value if Xi is in the influence domain of point Xj, the region , and vanishes outside the region surrounding the point Xj. W is a n by N matrix ( n > N ) where the column vector j represents the magnitudes of the approximated measurement of collocation point Xj with respect to each observation i, and where the row vector i represents the magnitudes of the approximated measurements of each collocation point Xj with respect to observation point Xi . The choice for the elementary function Wij was the following raised cosine function

where d is a normalized distance given by d(X,,Xy) = ||X, - Xy|

being nrm = 2.45, Xt =(xt,yi,zt), Xj = (xj,y ■,z,), and Ax = 20, Ay = 20 and Az = 2 the cell grid distances, respectively, in x , y and z axis, between consecutive collocation points. If X is in the influence domain of point X j, the value Wj is as large as less distanced are the points Xt and Xj, being a unit value when Xj = Xt (and null for all the other collocation points).

Since the magnitudes are constants, Equation (3) is an overdetermined linear system of equations (n equations with N unknowns) that can be solved using least squares method, by one of the several mathematical packages such as Matlab, the one used in this case. The least squares functional is defined by summing the squares of the residuals evaluated for each point Xi

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