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,…