1. Established
2. To be explored
3. * Note (lines icon) : specify if somebody did a study using that tool (add Github link to code if available) * Comment (bubble icon) : papers which use this technique
4. How to get a representative set of Lagrangian particle trajectories?
5. Which Lagrangian statistics to use?
5.1. Single-particle statistics
5.1.1. Lagrangian velocity
5.1.1.1. Lagrangian velocity autocovariance/autocorrelation
5.1.1.1.1. Lagrangian integral time and space scale
5.1.2. (cumulative/along-track) distance
5.1.3. Displacement (final - initial position), its magnitude is also called absolute distance
5.1.4. Absolute (eddy) dispersion = mean squared (residual) displacement (eddy: Lagrangain mean displacement subtracted, i.e. removing mean advective part)
5.1.4.1. Absolute (eddy) diffusivity = half growth rate of absolute (eddy) dispersion
5.1.5. Trajectory spin (loopers/non-loopers)
5.1.6. straightness index (magnitude of net displacement divided by cumulative distance)
5.2. Particle-pair statistics
5.2.1. Separation or relative distance (distance of a particle pair at any point in time)
5.2.2. Cumulative separation distance
5.2.3. Relative dispersion = mean squared separation distance
5.2.3.1. Relative diffusivity = half growth rate of relative dispersion
5.2.4. Lagrangian velocity covariance/correlation
5.3. Particle-group statistics
5.3.1. mediod ("most representative trajectory")
5.4. Spatial maps of particle distributions
5.4.1. Raw particle distributions
5.4.2. 2D histograms
5.4.2.1. Squared grid
5.4.2.2. Hexagonal grid
5.4.3. Gaussian Kernel Density Estimation
5.5. Lagrangian Connectivity
5.5.1. connectivity timescales
5.5.1.1. transit time (between location A and B)
5.5.1.2. exposure time
5.5.1.3. residence time
5.5.2. connectivity pathways
5.5.2.1. transition matrices
5.5.2.2. time-cumulative 2D histograms
5.6. Lagrangian Coherent Structures
5.6.1. Lyapunov Exponents
5.6.1.1. Finite Size Lyapunov Exponents (FSLE)
5.6.1.1.1. Lagrangian Anisotropy Index
5.6.1.1.2. FSLE spectra
5.6.1.2. Finite Time Lyapunov Exponents (FTLE)
5.6.2. Lagrangian Averaged Vorticity Deviation
5.6.3. Finite Time Coherent Sets
5.7. Clustering methods
5.7.1. Infomap
5.7.2. Spectral clustering
5.7.3. Hierarchical clustering
5.7.4. OPTICS
5.8. Energy spectra
5.8.1. Rotary spectra
5.8.2. Structure functions (related to Energy spectrum / Lagrangian spectra)