A Vector Geometry Based Eddy Detection Algorithm Eulerian
A Vector Geometry Based Eddy Detection Algorithm: Eulerian Data Developers: Francesco Nencioli Changming Dong
Outline: • Existing algorithms • A new method for eddy detection • Algorithm validation and limitations
Background Existing Eddy Detection Algorithms 1. Relative Vorticity (Mc. Williams, 1990) 2. Okubo-Weiss Parameter Method 3. 2 -D Wavelet Method (Doglioli et al. , 2007) 4. Winding Angle Method (Sandarjoen et al. , 2000; Chaigneau et al. , 2008) 5. Local Extremes (Chelton et al, 2011) (Okubo, 1970; Weiss, 1991
Background 1. Relative Vorticity Method Numerical simulation of decaying 2 D turbulence Rotation dominates Closed contour of ξ (Mc. Williams, 1990)
Background 2. Okubo-Weiss Parameter Method Okubo-Weiss parameter: (computed from velocity field) Deformation (shear and strain) Rotation (vorticity) Mesoscale eddy Rotation dominates W<0 (Calil et al. , 2008) Limits: • Noisy O-W parameter field • Threshold value
Background 3. 2 -D Wavelet Method Based on the vorticity field: • 2 -D Wavelet Analysis on vorticity field • Smoother field reconstructed using basis with larger coefficients • Where vorticity 0 => eddies • Smoother field than OW (more accurate) Limits: • Filaments detected (Doglioli et al. , 2007)
Background 4. Winding Angle Method • Instantaneous streamlines rotates around an eddy Winding Angle (αw) of a streamline: (Sandarjoen et al. , 2000) • Streamlines with αw > abs(2π) delimit an eddy: Very accurate!!! Limits: • Computationally demanding (Sandarjoen et al. , 2000)
Background 5. Local Extremes • Developed by Chelton et al (2011) • Applied to the altimeter-measured SSHA data • Its application is subject to the noise level
New Algorithm Case of Study: High Resolution Numerical Simulation of the SCB • ROMS • 1 Km Resolution • 356 x 287 grid pts • 9 years
New Algorithm Okubo-Weiss in the SCB • Not all eddies with high negative W • Not all high negative W are eddies
New Algorithm Assumptions for the New Algorithm • Eddies detected from the characteristics of the velocity field Eddy Velocity field characteristics: • Rotatory pattern • Minimum velocity at the center • Tangential velocities increase radially From this characteristics derived 4 constraints to detect eddies
New Algorithm The 4 Constraints 1. From West to East, V reverses in sign across the eddy center and increase in magnitude away from it 2. From South to North, U changes in sign across the eddy center and increase in magnitude away from it (sense of rotation has to be the same as for V) 3. Velocity magnitude minimum at the center 4. Velocity vectors around the center must gradually rotate with same sense of rotation Eddy centers where all the constraints are satisfied!!!! NOTE: These constraints need two parameters to be defined (flexibility!!!)
New Algorithm Example: Day 51
New Algorithm Constraint 1: Latitudinal (EW) section of V First parameter a • Points where V reverses in sign • V has to increase radially NOTE: sense of rotation can be already determined
New Algorithm Constraint 2: Longitudinal (NS) section of U Applied only to the points that satisfy constraint 1: • U has to increase radially First parameter a • U has to have the same sense of rotation as V
New Algorithm Constraint 3: Minimum of Velocity Second parameter b Applied only to the points that satisfy constraint 1 and 2: • Local minimum of velocity at the center
New Algorithm Why Constraint 4? • Eddies centers already detected after constraint 3, however…
New Algorithm Constraint 4: Vector rotation around the center Parameter (a-1) Applied to the vectors (a-1) points from the estimated center of the eddy: • Velocity vectors have to rotate in the same direction • Rotation has to be gradual
New Algorithm Constraint 4: Vector rotation around the center • Consecutive vectors no more than one quadrant apart • Eddy • Meander • Shear region
New Algorithm Eddy Boundaries • Streamfunction integrated in the domain NOTE: assumption of weak divergence!! • Largest closed contour around the center • Velocity magnitude has to decrease across it
New Algorithm Eddy Boundaries • Comparison with other methods: Streamfunction Streamlines OW Similar shapes, different sizes; not universal definition!!!
New Algorithm Map from day 51
Validation and Limits Validation Algorithm detection tested against manual detection for 10 randomly selected days
Validation and Limits Validation Tested for different values of pramters a and b: • Best performance for a = 4 and b = 3 • SDR ~ 92. 9% • EDR ~ 2. 9 %
Validation and Limits HF Radar surface velocities Algorithm can be applied to any velocity field • SB Channel • Daily average • 2 km resolution • Good results • Less performant for smaller eddy • Resolution implications
Validation and Limits Eddy Tracking Similar to what already proposed • Eddy tracks are updated comparing successive time steps
Eddy Statistics Examples
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