Methodology for Joint Use of Eulerian and Lagrangian Measurements in Order to Estimate Horizontal Diffusion Coefficients in Coastal Zones
VHF Doppler radars have been used by LSEET for the measurements of Eulerian superficial currents in coastal zones (between 1 to 30 km from the shore). For radar frequencies close to 50 MHz, the velocity measured is integrated over a depth of 25 cm, over an area of a few hundred square metres, and for times of one to ten minutes. The accuracy of the velocity measurements is better than 5 cm/s. The radars are set up on the sea-shore and their maximum range, depending upon sea-state, is 20 to 30 km. Two radars are needed to obtain a mapping of current vectors. These measurements don't account for velocity fluctuations at scales less than the mesh size, which are generally described by a diffusion coefficient (K[inf]h). On the other hand, Lagrangian measurements can be made by tracking surface drifters. The same VHF radars can be used for such tracking by using radio beacons placed on the drifters. This paper proposes a method for using both the Eulerian velocity field (usual product of VHF radars) and the Lagrangian trajectories of several drifters in order to estimate the horizontal diffusion coefficient. This method consists of comparing the statistical characteristics of the observed drifters distribution with those obtained by numerical simulations based on a random walk method. Numerical experiments concerning the influence of the accuracy and the spatial resolution of current measurements and the effect of the number of drifters on the accuracy of dispersion estimate have been carried out. In the particular case of a river plume with an outflow of the order of 1000 m3/s, we have shown that the accuracy of the horizontal diffusion coefficient estimation is of the order of 35 % for the realistic number of 5 drifters, with a spatial resolution of 500 x 500 m2. The system (radars and drifters) provides a powerful tool for a dynamic diagnosis in the coastal zone, and should be of interest for the study of discharges or the evolution of waterborne pollutants.