Schematic diagram for the calculation of the index Dir. Dir is defined as the inner product of the unit vector indicating the direction from the AR to each sampling statio (r→) and the velocity vecto (U→) . By assuming r→ = (0, 1) for the northern stations, (0, -1) for the southern stations, (1, 0) for the eastern stations, and (-1,0) for the western stations, Dir is expressed more specifically as sin (θ) (northern), -sin (θ) (southern), cos (θ) (eastern), and -cos (θ) (western). The value of Dir ranges from -1.0 to 1.0, where the negative (blue color) and positive (red color) values respectively indicate upstream and downstream directions from the AR.