Training thesis: Feasibility study of extracting water from near-Earth asteroids
MBRS_presentation
1. MODELING CONNECTIVITY AMONG
CORAL REEFS: QUANTITATIVE
PREDICTIONS OF LARVAL FISH
DISPERSAL PATTERNS
by
Pierluigi Pantalone
Supervisors: Dr. Barry Ruddick, Dr. Bruce Hatcher, Dr. Jinyu Sheng
(in collaboration with Windsor University – Dr. Peter Sale and his Lab)
3. The main goal is to estimate the time-averaged connectivity in the
MBRS
Time-averaged connectivity: probability of mean larval exchange
among discrete areas at given times [#larvae/Area*time]
4. Estimates of long-term connectivity are important for MPAs
planning and management
Russ, 2001.
5. More recent view…
recruitment variation
influenced by:
interaction of physical
transport mechanisms
and active larval
behavior
The conventional approach of
modelling fish larval
dispersal was dependent
on two key variables:
1. species-specific PLD
2. Knowledge of far-field
currents
6. Conclusions
• There is an increasing demand for
incorporation of biological behavior
into numerical models of larval
dispersal
9. TRACK
Random walk
K = 90 and 52 m2
/s
Reflective land condition
Absorbing boundaries
CANDIE
3D Ocean circulation model
Nested grid model applied to
MBRS
1. Outer model (19 km)
2. Middle model (6 km)
3. Inner model (2 km)
Forced by climatological surface
wind stress and heat flux (Da
Silva et al., 1994).
BIO-TRACK
S = 5 km radius
Vs = 13.5 cm/s
PLD = 15 days
Diurnal vertical
migration
10. Va = current speed = ? cm/s
Vs = swimming speed = 13.5 cm/s
After PLD = 15 days, swimming starts
Va = current speed = ? cm/s
Vs = swimming speed = 13.5 cm/s
11. Forecasting: larvae released at
South Water Cay.
Where do they go?
xt+1 = xtAij
A = transition probability matrix
1. Elements represent
probabilities (0 < aij < 1)
2. Conservative flow (∑aij = 1)
3. Absorbing boxes = particle
collectors (aii = 1)
Markov Property
xt+n = xtAn
mean circulation and k ≥ bi/Δt
are required
POPs
A = V-1
ΛV
Further reduction of the system
Define sink maps
12. •For both domains, RMSE and max|E| ↓
with k ↑
•max(|E|) are clustered
Where are the biggest errors ?
change
•Outliers > 0.08 for IM (k = 52 m2
/s) and
0.18 for OM (k = 90 m2
/s)
•Underestimation of the retention levels
due to presence of reef/islands reducing
particle diffusion
•For both OM and IM, overestimation
occurs for the (absorbing) boundary
boxes
Error vs Random Walk diffusivity, k
k =52 (m2/s)
k =90 (m2/s)
13. POPs
POPs = Principal
Oscillation Patterns
(Hasselman, 1988)
Eigenvectors – natural
modes of A
Eigenvalues – time-
scales/frequencies of A
VjA = lambdaj Vj
Multiple time-steps:
VjAn = lambdaJn Vj
Write on the figures Barry’s notes and group them
14. DTMC approach → xt-1 = xt(Aij)T
A = transposed transition probability matrix
1. Elements represent probabilities (0 < aij < 1)
2. Conservative flow (∑aij = 1)
3. Absorbing boxes = particle collectors (aii = 1)
Markov Property → xt-n = xt(AT
)n
mean circulation and k ≥ bi/Δt are required
POPs to reduce the system: AT
= VT
Λ(V-1
)T
Hindcasting: Larvae land on South Water Cay.
Where do they come from?
u → -u ⇒ A → AT (i.e. columns of A give hindcast)
Eigenvalues of AT are the same as for A
Eigenvectors are different (adjoint):
AT= VTlamda(V-1)TDefine source maps
15. DTMC approach → xt-1 = xt(Aij)T
A = transposed transition probability matrix
1. Elements represent probabilities (0 < aij < 1)
2. Conservative flow (∑aij = 1)
3. Absorbing boxes = particle collectors (aii = 1)
Markov Property → xt-n = xt(AT
)n
mean circulation and k ≥ bi/Δt are required
POPs to reduce the system: AT
= VT
Λ(V-1
)T
17. • Main (near-surface) particle transport
is in a South/South-West direction
• A large concentration of particles
from many reef boxes ends up into
Amatique bay (b13)
• pick 8 boxes and be consistent for
all the slides after…..
Sink map for physical connectivity (November)
18. Physical connectivity (November)
• Main (near-surface) particle transport is in a
South/South-West direction
• many boxes are a source for Amatique Bay (b13)
• lighthouse Reef Atoll (b11-b12) is well-connected
with Amatique Bay
•No particles are transported into Turneffe Islands (b7-
b8) and Lighthouse Reef atolls (b11-b12)
POPs
• E-folding time scale of the
eigenvalues (τ) < 20 days
• Virtually, all real modes (|θ| = 0)
19. Bio-physical connectivity
• Concentration of particles
ending up into Amatique bay
(b13) is reduced when swimming
behavior is added (up to .2)
• Decrease in long-distance
particle dispersal
• Increase in retention levels and
exchange among adjacent reef
boxes (up to .2)
POPs
•E-folding time scale (τ) of the
eigenvalues increases
• Phase of the eigenvalues
decreases (data not shown)
20. Bio-physical connectivity
• Concentration of particles ending
up into Amatique bay (b13) is further
reduced when vertical migration is
also added (up to .5)
• a larger concentration of larvae is
transported into the CC (b15)
• Further increase in exchange
levels occurs among adjacent reef
boxes as well as retention levels
POPs
•A further increase occurs in
the e-folding time scale (τ) of
the eigenvalues
22. • To achieve reliable
predictions for An
:
k ≥ L / ΔT
• Reef/island presence
reduces particle diffusion
increasing retention levels
for An.Problems in
predicting gyral circulation
• Better predictions for IM
due to the more
homogeneous sub-domain
discretization
23. • South/South-west particle
transport during November
• Amatique Bay and the lagoon
play an important role as sink
areas
• Turneffe Islands and
Lighthouse Reef atolls do not
receive particles from any of
the reef boxes
• In general, quick particle
flushing from the boxes (τ <
20 days)
24. • For horizontal swimming,
retention and exchange levels are
affected by up to |.2|.
• Adding also vertical migration,
retention and exchange between
the boxes are further affected (up
to |.5|)
• In general, larval behavior
increases the e-folding time (τ) of
the eigenvalues and decreases
their phase (θ)
26. Sensitivity analysis to k
•For both domains, RMSE
and max|E| ↓ with k ↑
•For (OM), max(|E|) increases
significantly at T=20 days for
k<90 m2
/s
•For the IM, max(|E|) are
more clustered
Where are the biggest errors ?
•Outliers > 0.08 for IM (k = 52 m2
/s) and
0.18 for OM (k = 90 m2
/s)
•For OM, underestimation of the retention
levels due to presence of reef/islands
reducing particle diffusion
•Boxes within the gyre show lower
retention and exchange levels. An
fails to
predict accurately gyral back-transport
•For both OM and IM, overestimation
occurs for the (absorbing) boundary
boxes
Editor's Notes
2 broad classes of goals for MPAs: (Gaines et al, 2003)
1.conservation of populations, habitats, and biodiversity
2.management of biological marine resources that are extracted from the sea (fisheries).
Effects inside reserves:
Lower fishing mortality (maybe even F=0)
Higher density of target species
Significantly higher mean size/age of target species.
Significantly higher biomass of target species.
Significantly higher production of propagules (eggs/larvae) of target species per unit area.
Fisheries effects:
Effects 1-4 result in net export of adult fishes.
Effects 1-5 result in net export of eggs/larvae.
