1. Connectivity in SoCal Bight UCLA-UCSB Telecon 1/14/08

2. Lagrangian Particle Tracking Used 6-hourly mean flow fields from 1996 thru 1999 (Thanks, Charles!) 1-hour time stepping for particle tracking Output particle data every 6 hours Used UCLA particle tracking code Released within 10 km from coast Every 1 km, every 6 hours (32,748 particles / day) Depth is fixed at 5 m below top surface

3. Single-day, Single-point Release (30-day trajectories) Release location Red dots = location 30 days later Release = Jan 1, 1996Release = Jan 1, 1997 Release = Jan 1, 1998Release = Jan 1, 1999 Particles released on the same date from the same location show different dispersal patterns every year

4. Single-day, Single-point Release (30-day trajectories) Release location Release = Jan 1, 1996Release = Jan 16, 1996 Release = Jan 31, 1996Release = Feb 15, 1999 Red dots = location 30 days later 2 weeks of difference in release timing can result in very different dispersal patterns

5. Single-day, Single-Point Release (30-day trajectories) Release location Palos VerdesNear San Diego Dispersal patterns depend on release locations

6. Points Dispersal patterns show strong intra- & inter-annual variability (turbulent dispersion) Particles released at the same location on the same day shows different patterns every year 15 days of difference in release timing can lead to different dispersal patterns Dispersal patterns depend on release location Trajectories show chaotic eddying motions, very different from a simple diffusion process We need statistical description

7. Comparison with Drifter Data (Not done yet. Hopefully done by Monday)

8. Lagrangian (Transition) PDF Probability density of Lagrangian particle location after time interval tau from release Estimate using all particles (1996-1999) First, we neglect inter- & intra-annual variability Pretend as if they were statistically stationary processes (i.e., independent of t 0 ) and assume ergodicity... Particle release location & date Particle location after time interval tau

9. Lagrangian (Transition) PDF x 0 = San Nicholas Island Release location tau = 1 daytau = 10 days tau = 20 daystau = 30 days (Bin size: 5 km radius in space; 1 day in time) Spread out in 20-30 days; more isotropic

10. Lagrangian (Transition) PDF x 0 = Near San Diego (Oceanside) Release location tau = 1 daytau = 10 days tau = 20 daystau = 30 days (Bin size: 5 km radius in space; 1 day in time) Strong directionality (pole-ward transport)

11. From 9 Different Sites Release location tau = 30 days more isotropic spread eddy retention pole-ward transport Strong release-position dependence

12. Connectivity Matrix Lagrangian PDF in a matrix form Or, we can average Lagrangian PDF over some time interval (larval fish dispersal case) (We can do weighted-mean, too)

13. Site Locations & Connectivity Mainland N. Islands S. Islands Mainland N. Islands S. Islands Pole-ward transport & eddy retention show up in connectivity

14. As a Function of Evaluation Time tau = 30 daystau = 35 daystau = 40 daystau = 45 days tau = 20 -- 40 daystau = 24 -- 48 daystau = 28 -- 56 daystau = 32 -- 64 days Spatial structures in connectivity fade away as tau increases (well mixed) Time averaging does not change connectivity

15. Source & Destination Strength Summation of connectivity matrix over i or j (Would be useful for MPA design)

16. Source & Destination Strength tau = 30 days tau = 40 days Strongest Destination at Chinese Harbor Match well with observation (not shown here) Strongest Destination at Chinese Harbor Match well with observation (not shown here)

17. Summary Lagrangian particle can reach entire Bight in 30 days Dispersal patterns show release-position dependence Strong directionality along mainland More isotropic from Islands Eddy retention in Channel & near San Clemente Island After spreading out in entire Bight, spatial patterns in Lagrangian PDF gradually fade away Particles either go out of domain or go any places in Bight (well mixed)

18. Summary Connectivity shows spatial patterns, reflecting pole- ward transport along mainland & eddy retention But, spatial patterns fade away in time (~ 60 days) As particles from various sources become well mixed Almost all sites can be connected in 30 days Source & destination strength patterns: Strong source: mainland (SD ~ SB) Strong destination: Santa Cruz, E. Anacappa, E. San Nicolas, North mainland (Palos Verdes ~ SB) Strongest destination: Chinese Harbor (self retention + transport from mainland)

19. Inter-annual Variability Compute Lagrangian PDF using particles released in a particular year instead of using all years 1) 1996, 2) 1997, 3) 1998, or 4) 1998 Let’s see PDF shows inter-annual variability

20. Lagrangian (Transition) PDF x 0 = Near San Diego (Oceanside), tau = 30 days Release location Alongshore transport disappears in 1999 (La Nina); very strong in 1997 (El Nino) Important for species invasion from Mexico Alongshore transport disappears in 1999 (La Nina); very strong in 1997 (El Nino) Important for species invasion from Mexico

21. Lagrangian (Transition) PDF x 0 = north shore of Santa Cruz Island, tau = 30 days Release location Eddy retention does not occur every year Important for species retention Eddy retention does not occur every year Important for species retention

22. Destination Strength tau = 30 days

23. Source Strength tau = 30 days

24. Summary Lagrangian PDF shows strong inter-annual variability Northward transport is strongest in 1997 (El Nino), while it disappears in 1999 (La Nina). Eddy retention does not appear every year These will mean a lot to population ecology Source & destination strength changes accordingly

25. Seasonal Variability Compute Lagrangian PDF using particles released in a particular season 1) Winter of 1996-1999, 2) Spring of 1996-1999, 3) Summer of 1996-1999, and 4) Autumn of 1996-1999 Seasonal variations are expected

26. Lagrangian (Transition) PDF x 0 = Near San Diego (Oceanside), tau = 30 days Release location Pole-ward transport disappears spring & summer when equator-ward wind is strong

27. Lagrangian (Transition) PDF x 0 = north shore of Santa Cruz Island, tau = 30 days Release location Eddy retention is weakened in spring & summer when equator-ward wind is strong

28. Lagrangian (Transition) PDF x 0 = Palos Verdes Peninsula, tau = 30 days Release location Palos Verdes shows self retention in summer possibly due to wind sheltering

29. Inter-annual & Seasonal Variability in Connectivity tau = 30 days Seasonal variability is stronger than inter-annual variability (as expected) Self retention at many sites Self retention at limited sites Pole-ward transport

30. Source Strength tau = 30 days

31. Destination Strength tau = 30 days

32. Summary Lagrangian PDF shows strong inter-seasonal variability (as expected) Pole-ward transport along the mainland appears fall & winter; gone in spring & summer Eddy retention in Channel appears fall & winter Depending on strength of equator-ward wind Seasonal patterns in connectivity are: Winter: strong self retention at many sites Spring & summer: strong self retention at limited places Fall: strong pole-ward transport

33. Applications (to be done) We need several applications here Ex. 1. Dispersal of fish larvae Ex. 2. Spread of pollutants Given distributions of materials at x 0 and t 0, concentrations of materials after tau are given by This can be larval production, oil spill distributions & etc If molecular diffusion & chemical reactions are negligible, though