Transcript SiegelKGG_021504 - icess - University of California, Santa

Lagrangian Descriptions of
Marine Larval Dispersion
David A. Siegel
Brian P. Kinlan
Brian Gaylord
Steven D. Gaines
Institute for Computational Earth System Science &
Marine Science Institute
University of California, Santa Barbara
Talk Outline
• Develop a Lagrangian model for larval
dispersal driven by ocean circulations
• Use this to construct a dispersal kernel &
compare with current understandings
• Assess role of time on recruitment patterns
for nearshore communities
Life History of Nearshore Organisms
Coastal flows are highly variable...
Libe Washburn [UCSB]
and in a Lagrangian frame…
Ed Dever & Clint Winant [SIO]
Larval Transport
• Planktonic larvae are planktonic  follow currents
• Determinants of larval transport are …
– Time in the plankton
• Duration of pre-competency & settlement time scales
– Coastal circulation characteristics
• Mean & time varying velocity field
– Larval behavior [during latter development stages]
• Changing depth distribution & possible settlement cues
Larval Transport
• Planktonic larvae are planktonic  follow currents
• Determinants of larval transport are …
– Time in the plankton
• Duration of pre-competency & settlement time scales
– Coastal circulation characteristics
• Mean & time varying velocity field
– Larval behavior [during latter development stages]
• Changing depth distribution & possible settlement cues
Dispersal vs. Time in Plankton
Genetic Dispersal Scale
(km)
r2 = 0.802, p<0.001
n=32
Planktonic Larval Duration (days)
From Siegel et al. 2003 (MEPS 260:83-96)
Modeling Larval Transport
• Provide a metric for source-to-destination
exchanges among nearshore populations
• Incorporate important oceanographic & organism
life history characteristics
• Constrain using easily obtained observations
• Useful for modeling spatial population dynamics
Siegel et al. [2003; MEPS 260: 83-96]
Dispersal Kernels
• Dispersal kernels define settling probability as
function of distance for a given time scale
• Units are [settlers / km / total settlers]
•



K(x)dx  1
K(x)
X=0
Distance alongshore [km]
Modeling of Dispersal Kernels
• Model trajectories of many individual larvae
• Correlated random walk -> Markov chain
• Based on realistic velocity statistics
– Simple ocean with constant circulation statistics
– “CODE-like” scenario following Davis (1985)
• Ensemble averaging location of “settled larvae”
provides the dispersion kernel
Example Trajectories
PLD = 0 to 5 days
6 to 8 weeks
Flow Statistics:
U = 5 cm/s, su = 15 cm/s & tL = f(y) (0.5 to 3 d)
Dispersion Kernels
U = 5 ustd = 15 To = 0 Tf = 5
U = 5 ustd = 15 To = 42 Tf = 56
250
100
200
total settlers= 1024 total part = 5000
total settlers= 1366 total part = 5000
90
150
100
50
80
70
60
50
40
30
20
10
0
-150
-100
-50
0
50
100
alongcoast (km) (a,b,c = 205.2 5.6392 18.974)
PLD = 0 to 5 days
150
0
-600
-400
-200
0
200
400
600
800
alongcoast (km) (a,b,c = 84.815 200.39 216.62)
6 to 8 weeks
• K(x) defines along shore settling probability distribution
• 5000 trajectories are summed to determine K(x)
1000
Kernel Modeling Results
A Gaussian form for K(x) holds for nearly all
flow/settling protocols:
 (x  x d ) 2
[
$
 K o exp
K(x)
2
s
2 d
]
Mean currents regulate offset (xd)
RMS flow drives spread (sd) & amplitude (Ko)
Kernel Modeling Results
sd = f(TMsu2)
xd = f(TMU)
“offset”
Ko = f(1/(TMsu))
“amplitude”
“spread”
Dd = f(TMU+TMσu)
“dispersion
scale”
Modeled Dispersion Scale, Dd (km)
Model Validation?
Genetic Dispersion Scale (km)
Conclusions & Possibilities
• Simulations of Lagrangian particle dispersion are
consistent with biological larval dispersal metrics
• Scaling collapses model results well & is
consistent with classical diffusion theory
• Useful for spatial population dynamic modeling
• Dispersal kernels can be easily configured for
arbitrary environments  K(x,y,t)
Implied Issue of Time...
• Idealized kernels calculated use many
individual particle trajectories (N=5000)
• Represents ensemble mean conditions
• The implied time to construct this mean
estimate is ~20 years!!
– Assumes larval releases are daily & a
decorrelation time scale of 3 days
Time, continued...
• An actual recruitment pulse may be a small
sampling of the kernel (N = 10?, or less!!)
– (300 releases / year) * (10% survival) / (3 day tL)
• Example - intermediate disperser (N = 100)
U = 5 Ustd = 15 To = 14 Tf = 21
1.8
total settlers= 13 total part = 100
• A discrete K(x) suggests
that connections among
sites are stochastic &
intermittent
2
N=5000
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
-100
-50
0
50
100
150
alongcoast (km)
200
250
300
350
Invertebrate Settlement Time Series – Ellwood, CA
Ellwood Invert Setttlment Time Series
70
60
Mytilus
Clams (excl razor & HIAARC)
any marine snail (excl. veligers, limp)
Limpet species
Snail veliger
any seastar
Hiatella arctica
# settlers/deployment
50
40
30
20
10
0
160
180
200
220
240
JD 2001
260
280
300
320
Data Courtesy - PISCO [UCSB]
Interpreting Settlement Time Series
• Stochastic, quasi-random time series
• No correlation of settling among species
• Few settlement events for each species
• Events are short
Ellwood Invert Setttlment Time Series
70
60
(2 days)
Mytilus
Clams (excl razor & HIAARC)
any marine snail (excl. veligers, limp)
Limpet species
Snail veliger
any seastar
Hiatella arctica
# settlers/deployment
50
40
30
20
10
0
160
180
200
220
240
JD 2001
260
280
300
320
A Stirred, Not Mixed Ocean!
• Short-time larval transport is driven by
coastal stirring rather than mixing
• Quasi-random sampling of K(x) leads to
stochasticity in settlement time series
• Larval dispersal needs to be modeled
using discrete (or “spiky”) kernels
Implications of Stirring
• Makes observations/assessments difficult
Hard to relate larval sources to settlement
Local stock-recruitment relationships will be noisy
• Limits applicability of smooth dispersal kernels
Evolution/genetics/biogeography?
Probably
Annual management of a fishery?
No!!
Flow, Fish and Fishing
Dave Siegel, Chris Costello, Steve Gaines,
Bruce Kendall & Bob Warner [UCSB]
Ray Hilborn [UW]
Steve Polasky [UMn]
Kraig Winters [SIO/UCSD]
A Biocomplexity in the Environment Project
The Flow, Fish & Fishing Idea
• Larval transport is stochastic driven by stirring
• Fish stocks, yields & their assessment are
directly affected by this stochastic signal
• Management must account for this uncertainty
• The key is assessing the flows & values of
information in this complex dynamical system
Flow, Fish & Fishing…
Summary
• Lagrangian estimation of larval dispersal kernels
– Physical oceanography & organism life history
– General applicability  challenge to oceanographers
• Kernels provide many insights
– Larval transport is stochastic
– Both local & non-local transports are important
– Leads to uncertainty in stock-recruitment relationships
Thank You!!
Where do drifter beach?
CCS Drifter Beachings from inshore stations
o = release site & + = beaching
Data from Ed Dever & Clint Winant (SIO)
Drifter Model Validation??
PLD = 2 d
U = 15 cm/s
su = 15 cm/s
PLD = 7 d
U = 5 cm/s
su = 15 cm/s
Dispersion Modeling
• Choose a velocity field
Mean flow - U = 0, 5 & 10 cm/s & V = 0
RMS fluctuation - su = 5, 10, 15 & 20 cm/s
Alternatives - CODE (Davis, 1985)
t varies from 0.5 to 3 d from on- to off-shore
• Choose a Planktonic Larval Duration (PLD)
Many macroalgae
Some inverts & fish
Many others
0 to 5 days
2 to 3 weeks
1 to 3 months
Mathematically ...
x
x
t
i
t
i
t 1
i
t c h
i
 x  t u  U
t
i
x it 1  x it  t u it  U
x  location of particle i at time t
x it x  location of particle i at time t
u fluctuating x - velocity of particle i
U i mean x - velocity
t time step
Repeat for y - direction
u it fluctuating x - velocity of particle i
U i mean x - velocity
t time step
Repeat for y - direction
Modeling Fluctuating Velocity
u
t 1
i
t
su
 u
t
i
1
t
t I
F
G
HtJ
K
u it 1  u it 1 
t
 RN
RN
2 t
t
su
2 t
t
su
Lagrangian autocorrelation time scale
Root mean squared x  velocity
RN Normal random deviate
t
su
Lagrangian autocorrelation time scale
Root mean squared x  velocity
RN Normal random deviate
Here, spatial homogeneity in velocity statistics is assumed
Example F3 Questions
What sets the scales of fish stocks & harvest?
larval settlement, habitat, natural & fishing mortality, fluid
stirring scales, adult migration, regulation, bathymetry, ??
Given the sources of uncertainty, how can we
best manage resources?
What are optimal instruments?
What is the value of information?
How do fishermen adapt & learn?
A Lagrangian View
34.5
34.4
Latitude (oN)
34.3
34.2
34.1
34
33.9
33.8
-120.6
-120.4
-120.2
-120
-119.8
Longitude (oE)
-119.6
-119.4
-119.2
?
≈
Drifter tracks from E. Dever & C. Winant - CCS/SIO
Stock / Recruitment in Rockfish
Bocaccio (MacCall et al. 1999)
40,000
30,000
20,000
10,000
Pacific whiting (Dorn et al. 1999)
0
0
2,000
4,000
6,000
8,000
10,000
14
12,000
Spawning Output
12
Recruits (x 1000)
Recruits (x 1000)
50,000
10
8
6
4
2
0
Steve Ralston [NMFS]
0.0
0.5
1.0
1.5
2.0
Female Spawning Biomass
2.5
3.0
Extreme Variation in Dispersal
n=90
Average Alongshore Dispersal Distance (Genetic Estimates)
Kinlan & Gaines (2003) Ecology 84(8):2007-2020
Dispersal Differs Among
Taxonomic Groups
Kinlan & Gaines (2003) Ecology 84(8):2007-2020
Crossshore velcoity (cm/s) Alongshore velcoity (cm/s)
Inhomogeneous case –
‘CODE-like’ flow
Distance Offshore (km)
Davis, 1985