1. SPACE / TIME SCALS OF LARVAL SETTLEMENT AND ITS MODELING Satoshi Mitarai Oct. 18, 2005

2. GOAL Assess larval dispersal scales in California Current using idealized simulations –Strong / weak upwelling cases Develop a 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 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 Let us compute space / time scales…

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

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

14. ARRIVAL DIAGRAM Summer Larval arrival “packets” are observed 15 days 21 days 43 km 64 km Using variogram … Winter

15. CONNECTIVITY MATRIX Summer Winter “Hot spots” exist for some destinations 48 km 53 km

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

17. A NEW MODEL FOR HABITAT CONNECTIVITY Idea: model settlement events as a summation of settlement packets –Proposed model is in between diffusion model and spiky kernel model –Spiky kernel model + spatial scale

18. Determine # of settlement packets N = (T/t) (L/l) f (D/l) A NEW MODEL: STEP 1 T: Larval release duration t: Lagrangian correlation time L: Domain size l: Rossby radius (or eddy size) f: survivability D: standard deviation of dispersal kernel

19. Determine the source locations of a packet of settlers randomly Determine their travel distance randomly based on dispersal kernel A NEW MODEL: STEP 2

20. 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”

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

22. 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!

23. 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

24. 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