1. MODELING OF LARVAL DISPERSAL IN CALIFORNIA CURRENT Satoshi Mitarai 06/26/05

2. GOAL Assess larval dispersal scales in California Current using idealized simulations –Strong / weak upwelling cases Develop simple modeling to establish source-destination relationships in California Current –Idealized simulations are too expensive

3. WHAT’S NEW? Numerical resolution is now 2 km More realizations Weak upwelling case is added Larval dispersal scales are quantified A new model for connectivity matrix of larval dispersal is proposed

4. TEMPERATURE FIELD (TOP VIEW) Strong upwellingWeak upwelling Summer Winter

5. MEAN TEMPERATURE FIELD (SUMMER) Simulation CalCOFI Shows reasonable agreement with CalCOFI data (Averaged over 6 realizations)

6. MEAN TEMPERATURE FIELD (WINTER) Simulation CalCOFI Shows a good agreement with CalCOFI data (Averaged over 6 realizations)

7. LARVAL DISPERSAL ON COASTAL CIRCULATION SummerWinter Transported by coastal circulation processes

8. LAGRANGIAN STATISTICS Data Set Time scale Zonal / Merid Length Scale Zonal / Merid Diffusivity Zonal / Merid Summer Simulations 3.7 / 3.731 / 353.1 / 4.1 Winter Simulations 6.9 / 5.729 / 291.6 / 1.8 Swenson et al (2001) 2.9 / 3.532 / 384.3 / 4.5 Poulain et al (1998) 4.2 / 4.640 / 483.4 / 4.3 Simulations: 6 realizations, 6000 particles Swenson et al (2001): late spring to early fall, 1985-1990, 124 drifters, 18N-40N Poulain et al (1998): early spring to late fall, 1985-1986, 29 drifters, 18N-36N

9. LAGRANGIAN STATISTICS Data Set Time scale Zonal / Merid Length Scale Zonal / Merid Diffusivity Zonal / Merid Summer Simulations 3.7 / 3.731 / 353.1 / 4.1 Winter Simulations 6.9 / 5.729 / 291.6 / 1.8 Swenson et al (2001) 2.9 / 3.532 / 384.3 / 4.5 Poulain et al (1998) 4.2 / 4.640 / 483.4 / 4.3 Summer simulations show a good agreement with summer drifter data Winter simulations show less correlation in time & diffusivity

10. LARVAL DISPERSAL & SETTLEMENT Summer Winter Settlement = 7.8 %Settlement = 21.8 %

11. ONLY SETTLERS SummerWinter Q: How far do they travel?

12. ALONGSHORE TRAVEL DISTANCE OF SETTLERS SummerWinter Gaussian fitting Less alongshore travel distance in winter (Obtained from 6 realizations)

13. CROSS-SHORE TRAVEL DISTANCE OF SETTLERS Lognormal fitting SummerWinter Less offshore travel distance in winter (Obtained from 6 realizations)

14. ARRIVAL DIAGRAM Summer Winter Larval arrival “packets” have some time & length scales

15. SCALING OF ARRIVAL TIME Summer 1. Pick one destination compute correlated time scale from auto-correlation function of # of setters 2. Repeat 1 for all destinations 3. Make PDF of the obtained time scale

16. ARRIVAL TIME SCALE Lognormal fitting SummerWinter Longer arrival time in winter (Obtained from 6 realizations)

17. SCALING OF ARRIVAL LENGTH Summer 1. Pick one day and compute correlated length scale from auto-correlation function of # of settlers 2. Repeat 1 for 90 to 130 days 3. Make PDF of the obtained length scale

18. ARRIVAL LENGTH SCALE Lognormal fitting SummerWinter Longer arrival length in winter (Obtained from 6 realizations)

19. CONNECTIVITY MATRIX Summer Winter “Hot spots” exist for some destinations

20. SCALING OF “HOT SPOT” Summer 1. Pick one destination & compute correlated length scale 2. Repeat 1 for all destinations 3. Make PDF of the correlated length scale

21. “HOT SPOT” SCALE Lognormal fitting SummerWinter “Hot spot” scales are comparable (Obtained from 6 realizations)

22. SUMMARY & SOME IMPLICATION Season Settle. Rate (%) Alongshore Distance (km) Cross-shore Distance (km) Arrival Time (days) Arrival Length (km) “Hot Spot” Scale (km) Summer7.8 122.4 ± 103.5 47.2 ± 26.9 (107.9@99%) 15.0 ± 3.1 (22.0@99%) 43.3 ± 21.5 (82.4@99%) 48.8 ± 10.5 (69.5@99%) Winter21.8 79.9 ± 92.4 32.8 ± 13.1 (74.7@99%) 21.8 ± 4.8 (30.9@99%) 64.3 ± 19.7 (92.4@99%) 53.3± 15.3 (88.5@99%) MPA’s < 207.0 km will have 30% or more of “spill” (summer) MPA’s < 82.4 km will share settlers with their neighbors (summer) MPA’s > 69.5 km may completely cover a “hot spot,” and stop larval supply to a destination (summer)

23. CONNECTIVITY MATRIX MODEL Diffusion model Spiky kernel model Not account for heterogeneityNot account for structures

24. LET US PROPOSE A NEW MODEL Idea: larval dispersal & settlement are not point-to-point process (spiky kernel model), but with some scales –When settlement is observed at a destination, its neighbors also observe settlers, and its source is not a point, but “hot spots” There are two steps

25. Produce “settlement patches” –Each represents a pulse of settlement from a given source to a given destination –Not point to point, but with some width –Size = (arrival length) x (hot spot scale) –Number = (larval release duration) / (mean arrival time) x (# of destinations) A NEW PROPOSED MODEL (1) 43.3 ± 21.5 km Arrival length Hot spot scale 48.8 ± 10.5 km Number of patches = 384

26. A NEW PROPOSED MODEL (2) Destination (km) Source (km) Connectivity Matrix Place the “patches” on connectivity matrix –Randomly based on alongshore travel PDF Settlement “patches”

27. MODEL PREDICTIONS SummerWinter Looks great to me! What do you think?

28. MATLAB CODE % Set up parameters N = 6*64 ; % # of settlement patches kernel.Domain = 256 ; % Domain size (km) kernel.Resol = 2 ; % Resolution (km) Along.AVG = 122.4 ; % Alongshore travel mean (km) Along.STD = 103.5 ; % Alongshore travel STD (km) Arrival.AVG = 43.3 ; % Arrival length mean (km) Arrival.STD = 31.5 ; % Arrival length STD (km) HotSpot.AVG = 48.8 ; % Hot spot mean (km) HotSpot.STD = 10.5 ; % Hot spot STD (km) % Determine hot spot scale tmp.STD = sqrt(log((HotSpot.STD^2)/(HotSpot.AVG^2)+1)); tmp.AVG = log( HotSpot.AVG ) - 0.5*(tmp.STD^2); HotSpot.Width = exp( tmp.AVG + tmp.STD*randn(1,N) ); % Determine arrival length tmp.STD = sqrt(log((Arrival.STD^2)/(Arrival.AVG^2)+1)); tmp.AVG = log( Arrival.AVG ) - 0.5*(tmp.STD^2); Arrival.Width = exp( tmp.AVG + tmp.STD*randn(1,N) ); % Determine locations of settlement patch Along.Travel = Along.AVG + randn(1,N)*Along.STD ; Position.Dest = rand(1,N)*256 ; Position.Source = Position.Dest + Along.Travel ; % Construct connectivity matrix kernel.Source = -L : kernel.Resol : 2*L ; kernel.Dest = 0 : kernel.Resol : L ; kernel.Source = … ( kernel.Source(1:end-1) + kernel.Source(2:end) ) / 2 ; kernel.Dest = … ( kernel.Dest(1:end-1) + kernel.Dest(2:end) ) / 2 ; kernel.Matrix = … zeros( length(kernel.Source), length(kernel.Dest) ); for n = 1 : N tmp.Matrix = zeros(size(kernel.Matrix)); ii = Position.Source(n) - HotSpot.Width(n)/2 :… Position.Source(n) + HotSpot.Width(n)/2; jj = Position.Dest(n) - Arrival.Width(n)/2 :… Position.Dest(n) + Arrival.Width(n)/2; ii = round((ii-kernel.Source(1))/kernel.Resol) ; jj = round((jj-kernel.Dest(1) ) /kernel.Resol) ; ii( find( ii<1 | size(kernel.Matrix,1)<ii ) ) = [] ; jj( find( jj<1 | size(kernel.Matrix,2)<jj ) ) = [] ; tmp.Matrix(ii,jj) = 1 ; kernel.Matrix = kernel.Matrix + tmp.Matrix ; end It is short. Please use it in F 3 model!

29. CONCLUSION Larval dispersal scales in California Current (CC) are assessed –Such info will be useful in designing MPA’s A new simple modeling to establish larval dispersal in CC is proposed –Given larval dispersal scales, model yields excellent predictions of connectivity matrix

30. NEXT STEPS Investigate effect of larval behavior –Preliminary study has been already done Investigate effect of coastal topography Use proposed model in F 3 model