spatio-temporal stochastic simulation of connectivity matrices from lagrangian ocean models
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Spatio-temporal Stochastic Simulation of Connectivity Matrices
from Lagrangian Ocean Models
The Raw Material: Time series of simulated daily Kij Matrices
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Approach
Approach
Approach
Approach
Logit Transformation
-6 -5.5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5
0.0010.003
0.01 0.02
0.05 0.10
0.25
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0.75
0.90 0.95
0.98 0.99
0.9970.999
Data
Pro
ba
bilit
y
Normal Probability Plot
Remove Temporal Trend
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-4.8
-4.6
-4.4
-4.2
-4
day
logi
t(K
ij)
Remove Spatial Trend
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Residuals
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h (lag distance, km)
h (lag distance, km)
h (lag distance, days)
VARIOGRAMS ON PRESENCE/ABSENCE OF SETTLEMENT (INDICATOR VARIABLE, 0/1)
Along-Rows
(t, i, i)(t, i, i+h)correlation of settlement at adjacent
destinations from same source
Time
(t,i,j)(t+h,i,j)correlation of settlement at time t
in patch (i,j) with settlement at time t+h in same patch
Down-Columns
(t, j, j)(t, j+h, j)correlation of settlement from adjacent
sources to the same destination
γ(h)
γ(h)
γ(h)
h (lag distance, km)
h (lag distance, km)
h (lag distance, days)
VARIOGRAMS ON MAGNITUDE OF SETTLEMENT AT NON-ZERO LOCATIONS
Along-Rows
(t, i, i)(t, i, i+h)correlation of settlement at adjacent
destinations from same source
Time
(t,i,j)(t+h,i,j)correlation of settlement at time t
in patch (i,j) with settlement at time t+h in same patch
Down-Columns
(t, j, j)(t, j+h, j)correlation of settlement from adjacent
sources to the same destination
SGEMS
• ….4D simulation…yay
Predicting Alongshore Patterns from Coastal Topgraphy
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‘Coastal Anomaly’
Broitman and Kinlan 2006 MEPS, In press
Smoothing Scale=1000 km
COASTAL STRUCTURE
Smoothing Scale=50 km
COASTAL STRUCTURE
-10 -5 0 5 10Residual from smoothed coast (km)
Smoothing Scale = 10 km
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5000D
ista
nce
alo
ng
coas
t (k
m)
Residual from smoothed coast (km)
Smoothing Scale = 150 km
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West Coast NA
Longitude
Lat
itu
de
S.Africa WNAChile
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xcorr: Urchin GSI vs. Topographic Index
smoothing scale for topographic index (km)
corr
ela
tion
co
eff.
What scale of coastal features matter to the What scale of coastal features matter to the process you’re interested in?process you’re interested in?
Correlation between variable of interest and topographic index at each smoothing scale
myt
bal
cht
Smoothing scale (km) for topo index
Corr
elati
on c
oeffi
cien
t
myt
bal
cht
alongshore lag (km) (negative lags are poleward)
Corr
elati
on c
oeffi
cien
t
myt
bal
cht
The “Topographic Response Function”
Correlation coefficient
Alongshore Lag (km) – positive lags poleward – sorry!
Smoo
thin
g sc
ale
(km
) for
topo
inde
x
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alon
gsho
re la
g (k
m)
Amplitude ()
Mytilus spp.
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Filter length (km)
PC
am
plit
ude
PC1PC2PC3
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alon
gsho
re la
g (k
m)
Amplitude ()
Balanus glandula
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Filter length (km)
PC
am
plit
ude
PC1PC2PC3
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alon
gsho
re la
g (k
m)
Amplitude ()
Chthamalus spp.
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Filter length (km)
PC
am
plit
ude
PC1PC2PC3
Myt (74%) Bal (85%) Cht (69%)
45%; ns87%; ***
Balanus predicted from Mytilus Chthamalus predicted from Mytilus
Mytilus spp.
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Balanus
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Chthamalus
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√√ Settlement Rate (indiv/day)
Coa
stal
Coo
rdin
ate
(km
)REGION: Chile; ZONE: ALL; RESPONSE: PeruRecTx
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Longitude (degrees)
coastline
regressing PeruRecTx and topographyVar Explained = 0.687003Model significance = 0.436829
2.9442 + -0.0014604 * COAST + -0.0024253 * Topo(521,-238) + 0.0067157 * Topo(753,15) + 0.023021 * Topo(58,156) + 0.011621 * Topo(521,-187) + 0.0054632 * Topo(753,-186) + -0.0095863 * Topo(58,103)
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√√Settlement Rate (indiv/day)
Coa
stal
Coo
rdin
ate
(km
)REGION: Chile; ZONE: ALL; RESPONSE: SemiRecTx
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Longitude (degrees)
coastline
regressing SemiRecTx and topographyVar Explained = 0.795611Model significance = 0.229436
-0.039258 + 0.00030025 * COAST + 0.024883 * Topo(522,-224) + -0.024115 * Topo(837,-217) + -0.020776 * Topo(62,-233) + -0.015662 * Topo(522,-65) + 0.013502 * Topo(837,-114) + -0.039298 * Topo(62,235)
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Settlement Rate (indiv/day)
Coa
stal
Coo
rdin
ate
(km
)REGION: Chile; ZONE: ALL; RESPONSE: JhelRecTx
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Longitude (degrees)
coastline regressing JhelRecTx and topographyVar Explained = 0.914106Model significance = 0.0501796
-0.055945 + 0.00044229 * COAST + 0.0040024 * Topo(519,-237) + -0.0026306 * Topo(253,22) + -0.079962 * Topo(44,102) + -0.0096198 * Topo(519,196) + -0.043207 * Topo(253,-187) + 0.079086 * Topo(44,-175)
A Global, Daily, Sub-Kilometer-Scale Index of Wind-Driven Dynamics in
Nearshore Ecosystems
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curl
of
2D
win
d ve
loci
ty f
ield
(m
/s)
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JPL Model Nowcast – 1km wind field
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wind stress curlwestward wind stressequatorward wind stressoffshore windstress
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topo(s=500km)topo(s=200km)topo(s=50km)
Kelp Dynamics at the California Channel Islands
Responses to Ocean Climate, Trophic Structure, and Management
Overall Protection of Kelp Habitats
Based on 1989-2003 Kelp Map Based on 2004-2005 Kelp MapArea of Kelp in MPA’s in 2004-2005 versus 1989-2003 Baseline
0
0.05
0.1
Fra
ctio
n of
Kel
p H
abita
t in
MP
As
11.0%
5.56 km2
of50.50 km2
13.6%
5.56 km2
of 40.92 km2
11.8%
4.82 km2
of40.92 km2
Kelp Canopy at San Miguel Island
Kelp Canopy at Santa Rosa Island
Kelp Canopy at Santa Cruz Island
Kelp Canopy at Anacapa Island
Kelp Canopy at Santa Barbara Island
For Comparison: San Nicolas Island
For Comparison: Campus Point (Mainland)
Before (1989-2002) Before (1999-2002) After (2003-2006)
0
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vera
ge
Kel
p C
ano
py
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ma
ss (
US
to
ns)
Change in Canopy Area Over Time: All So Cal Islands
Change in Canopy Area Over Time: CINMS vs. Other Islands
Before (1989-2002) Before (1999-2002) After (2003-2006)
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Av
era
ge
Ke
lp C
an
op
y B
iom
as
s (
US
to
ns
)
Before (1989-2002) Before (1999-2002) After (2003-2006)
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CINMS San Nicolas, Clemente, Catalina
Kelp Biomass at Islands
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005San Clemente(S)San Clemente(W)San Clemente(N)San Clemente(E)
Santa CatalinaSanta Barbara
San Nicolas(107A)San Nicolas(107B Foul)
San Nicolas(108A Rockpile)San Nicolas(108B Westend)San Nicolas(108C Barrack)
AnacapaSanta Cruz(N)Santa Cruz(W)Santa Cruz(N)
Santa Rosa(SE)Santa Rosa(SW)Santa Rosa(NW)Santa Rosa(NE)
San Miguel(S)San Miguel(N)
1960 1965 1970 1975 1980 1985 1990 1995 2000 200510
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102
103
Kelp Biomass at Islands
1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 20070
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Date of Survey
Kel
p C
anop
y B
iom
ass
(US
Ton
s)
Kelp Biomass – CINMS Region
1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 20070
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1000
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Date of Survey
Kel
p C
an
opy
Bio
ma
ss (
US
To
ns)
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Date of Survey
Kel
p C
an
opy
Bio
ma
ss (
US
To
ns)
CINMS Region
Other Islands
Patterns Different from MainlandPatterns Different from Mainland
EN
SO
In
de
x -
(SO
I)
1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 20070
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Date of Survey
Kelp
Ca
nop
y B
iom
ass (
US
To
ns) Islands
Mainland
CINMS Region
MBNMS Region
(1985-2001)
Figure 4
Kelp
fore
st s
tate
De-forested state
From Behrens and Lafferty 2004; based on 1985-2001 data from Kelp Forest Monitoring Project
Indirect Effects of Fishing on Kelp Forests?
Interesting Pattern at Anacapa Island
1989 1999 2002 2003 2004 2005 20060
0.1
0.2
0.3
0.4
0.5
0.6
0.7
ReserveMCAOutside
MCA established
F^3 Needs?
1960 1965 1970 1975 1980 1985 1990 1995 2000 2005San Clemente(S)San Clemente(W)San Clemente(N)San Clemente(E)
Santa CatalinaSanta Barbara
San Nicolas(107A)San Nicolas(107B Foul)
San Nicolas(108A Rockpile)San Nicolas(108B Westend)San Nicolas(108C Barrack)
AnacapaSanta Cruz(N)Santa Cruz(W)Santa Cruz(N)
Santa Rosa(SE)Santa Rosa(SW)Santa Rosa(NW)Santa Rosa(NE)
San Miguel(S)San Miguel(N)
1960 1965 1970 1975 1980 1985 1990 1995 2000 200510
0
101
102
103