Estimate the wind direction for the four cases: extracted radon profile of the WDH and Gaussian fit (red dashed line) whose maximum (red dot-dashed line) shows the estimated preferential direction (left), and contour plot of the WDH showing the fitted wind direction (red cross) with the described procedure (right). From top to bottom: Case 1 (from AO simulations including only the fitting and servolag errors), case 2 (adding NCPA), case 3 (adding LOR and LWE), and case 4 (51 Eri on-sky data). Except for case 1, a filtering fraction of 15% has been used to isolate the WDH. For the first three cases we simulated, the green line shows the simulated wind direction (125 degrees).