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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i

Approach

Approach

Approach

Approach

Logit Transformation

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0.0010.003

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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

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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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Amplitude ()

Balanus glandula

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ude

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Amplitude ()

Chthamalus spp.

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ude

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Myt (74%) Bal (85%) Cht (69%)

45%; ns87%; ***

Balanus predicted from Mytilus Chthamalus predicted from Mytilus

Mytilus spp.

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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

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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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ield

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/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

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Fra

ctio

n of

Kel

p H

abita

t in

MP

As

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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)

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vera

ge

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p C

ano

py

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ma

ss (

US

to

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Change in Canopy Area Over Time: All So Cal Islands

Change in Canopy Area Over Time: CINMS vs. Other Islands

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lp C

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as

s (

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)

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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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Kelp Biomass at Islands

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Kel

p C

anop

y B

iom

ass

(US

Ton

s)

Kelp Biomass – CINMS Region

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Kel

p C

an

opy

Bio

ma

ss (

US

To

ns)

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Date of Survey

Kel

p C

an

opy

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ma

ss (

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To

ns)

CINMS Region

Other Islands

Patterns Different from MainlandPatterns Different from Mainland

EN

SO

In

de

x -

(SO

I)

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Date of Survey

Kelp

Ca

nop

y B

iom

ass (

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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

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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