Scaling of Larval Scaling of Larval Transport in the Transport in the Coastal OceanCoastal Ocean
Satoshi Mitarai, Dave Siegel, Kraig Satoshi Mitarai, Dave Siegel, Kraig WintersWinters
Postdoctoral ResearcherPostdoctoral ResearcherUniversity of California, Santa BarbaraUniversity of California, Santa Barbara
BACKGROUNDBACKGROUND
Quantitative description of larval Quantitative description of larval transport is important in marine transport is important in marine ecologyecology• e.g., marine population dynamics, fishery e.g., marine population dynamics, fishery
stock management, design of MPA’sstock management, design of MPA’s For many important applications, For many important applications,
eddy-diffusion model (or dispersal eddy-diffusion model (or dispersal kernel) has been usedkernel) has been used
F3 idea: eddy-diffusion modeling F3 idea: eddy-diffusion modeling approach is not appropriateapproach is not appropriate
EDDY DIFFUSION EDDY DIFFUSION MODELSMODELS
Describe probability distribution of larval source Describe probability distribution of larval source locations (or destination locations)locations (or destination locations)• Often called dispersal kernelOften called dispersal kernel
Not larval transport for a single season (or year)Not larval transport for a single season (or year)
Steneck (2006)
Dispersal Kernel
Larval source # o
f su
ccess
ful re
cruit
s
SIEGEL ET AL (2003)SIEGEL ET AL (2003) Larval transport for a single season should Larval transport for a single season should
be described somehow in a stochastic way be described somehow in a stochastic way based on dispersal kernelbased on dispersal kernel
F3 STOCK/HARVEST F3 STOCK/HARVEST MODELMODEL
'))(1( ','1 dxRKPHAMA n
xnxx
nx
nx
nx
nx
# of adults harvested
# of adults at x in year n+1
# of recruits to x from everywhere
# of survivors at x in year n
Natural mortality
x’ x
nxR
nxxK ',
Fraction of settlers successfully recruit at
x nxP '
Fraction of larvae settling at x
# of larvae produced at
x’
Stochasticity in larval transport will lead to unavoidable Stochasticity in larval transport will lead to unavoidable uncertainty in recruitment patternsuncertainty in recruitment patterns
Connectivity matrix
COASTAL OCEAN IS COASTAL OCEAN IS TURBULENTTURBULENT
Falkland Islands
MODIS - NASA
Characteristics of turbulence is coherent structures (eddies)
SURFACE DRIFTERS SURFACE DRIFTERS AROUND EDDIESAROUND EDDIES
Ohlmann et al, JGR (2001)
Cold eddies Warm eddies
Drifters are advected by currents around eddies
LARVAL TRANSPORT LARVAL TRANSPORT AROUND EDDIESAROUND EDDIES
Nishimoto & Washburn (2002)
Red bars = juvenile fish abundance
High juvenile fish abundance near the center of the eddy
IDEAIDEA
Turbulent eddy motions set Turbulent eddy motions set stochasticity in larval transportstochasticity in larval transport
Temporal & spatial patterns in larval Temporal & spatial patterns in larval transport should be related with eddy transport should be related with eddy motionsmotions• e.g., eddy size, eddy turn-over time, …e.g., eddy size, eddy turn-over time, …
GOALSGOALS
Scale temporal & spatial patterns Scale temporal & spatial patterns induced by eddies in larval transportinduced by eddies in larval transport• As a function of upwelling condition, PLD As a function of upwelling condition, PLD
& larval behavior& larval behavior Propose simple scaling tool that Propose simple scaling tool that
describes larval transport describes larval transport (connectivity matrix) for a single (connectivity matrix) for a single season season • Along with eddy-diffusion model Along with eddy-diffusion model
COASTAL CIRCULATION COASTAL CIRCULATION SIMULATIONSSIMULATIONS
Modeled after circulation processes in Central Modeled after circulation processes in Central California under strong & weak upwelling California under strong & weak upwelling
Strong Upwelling Weak Upwelling
SIMULATION SETUPSIMULATION SETUP
Top View
Alongshore pressure gradient obtained from observation data
Stochastic wind stressestimated from observation data
Side View
Periodic
Periodic
Wal
l
Ope
n Poleward
ADDING LARVAEADDING LARVAE
Released daily for 90 d, uniformly distributed Released daily for 90 d, uniformly distributed in nearshore waters at near top surfacein nearshore waters at near top surface• Nearshore = within 10 km from coastNearshore = within 10 km from coast
Larvae settle when found in nearshore Larvae settle when found in nearshore during competency time windowduring competency time window• Competency = 10-20, 20-40, 30-60, 40-80 dCompetency = 10-20, 20-40, 30-60, 40-80 d
Two types of larval behaviorTwo types of larval behavior• Surface-following Surface-following • Vertically-migrating (shift 30 m 5 d after release)Vertically-migrating (shift 30 m 5 d after release)
LARVAL TRANSPORT & LARVAL TRANSPORT & SETTLEMENTSETTLEMENT
Red dots = settling larvae
Strong Upwelling Weak Upwelling
DISPERSAL & KERNELDISPERSAL & KERNEL
MEAN ADVECTION & MEAN ADVECTION & DISPERSAL DISPERSAL
Strongly depend on Strongly depend on upwelling upwelling condition, PLD & condition, PLD & behaviorbehavior
Dispersal is not Dispersal is not sensitive to sensitive to behavior, thoughbehavior, though
Surface following larvae (solid lines)Migrating larvae (dashed lines)
28 realizations of simulations used
SETTLEMENT RATE & SETTLEMENT RATE & VARIATIONVARIATION
Strongly depend on Strongly depend on upwelling upwelling condition, PLD & condition, PLD & behaviorbehavior
Variation is not Variation is not sensitive to sensitive to behavior, thoughbehavior, though
Surface following larvae (solid lines)Migrating larvae (dashed lines)
28 realizations of simulations used
DISPERSAL KERNELDISPERSAL KERNEL
In all cases, substantial portion of larvae are retained In all cases, substantial portion of larvae are retained in natal area in natal area
SETTLEMENT TIME SETTLEMENT TIME SERIESSERIES
& CONNECTIVITY& CONNECTIVITY
Only a few settlement pulses are observed, leading to Only a few settlement pulses are observed, leading to heterogeneous connectivityheterogeneous connectivity
TIME & LENGTH OF TIME & LENGTH OF SETTLEMENT PULSESSETTLEMENT PULSESArrival Scales Departure scales
Rather consistent regardless upwelling, PLD or behaviorRather consistent regardless upwelling, PLD or behavior
~ eddy turn-over time(a few weeks)
~ eddy turn-over time(a few weeks)
~ eddy size (40 to 60 km)
CONNECTIVITY IS CONNECTIVITY IS STOCHASTICSTOCHASTIC
PACKET MODELPACKET MODEL
Idea: portrays settlement processes in terms Idea: portrays settlement processes in terms of N statistically-independent, equally-sized of N statistically-independent, equally-sized (eddy size) packets of individual larvae(eddy size) packets of individual larvae
N = (L/l) (T/t) fN = (L/l) (T/t) fL = domain size = 256 kmL = domain size = 256 km
l = eddy size ~ 50 kml = eddy size ~ 50 km
T = observation time = 90 d + mean PLDT = observation time = 90 d + mean PLD
t = eddy turn-over time ~ 2 weekst = eddy turn-over time ~ 2 weeks
f = packet survivability ~ 0.5f = packet survivability ~ 0.5
Source of each packet is determined Source of each packet is determined randomly based on dispersal kernel (random randomly based on dispersal kernel (random sampling)sampling)
PACKET MODEL VS PACKET MODEL VS SIMULATIONSSIMULATIONS
Shows a good Shows a good agreement with agreement with simulation datasimulation data
As observation As observation time increases, time increases, heterogeneity is heterogeneity is smoothed outsmoothed out
MORE EVALUATIONMORE EVALUATIONStochasticity in larval transport e-folding time scale
Shows a reasonable quantitative agreementShows a reasonable quantitative agreement
CONCLUSIONS (1/2)CONCLUSIONS (1/2)
Simulation results suggestSimulation results suggest• Larvae are accumulated & delivered by Larvae are accumulated & delivered by
eddies, leading to high variation in eddies, leading to high variation in settlement patternssettlement patterns
• Temporal & spatial scales are rather Temporal & spatial scales are rather consistent regardless upwelling, PLD or consistent regardless upwelling, PLD or behavior, reflecting eddy motionsbehavior, reflecting eddy motions
CONCLUSIONS (2/2)CONCLUSIONS (2/2)
Propose simple scaling tool that Propose simple scaling tool that describes larval transport for a single describes larval transport for a single season based upon dispersal kernel season based upon dispersal kernel • Without performing expensive numerical Without performing expensive numerical
simulations of coastal circulation simulations of coastal circulation processesprocesses
• Handy tool to be used in applications in Handy tool to be used in applications in marine ecologymarine ecology
MORE CONNECTIVITY,…MORE CONNECTIVITY,…