Transcript web2.sca.uqam.ca

Modelling to address aquaculture issues
David Greenberg
DFO Bedford Institute of Oceanography
Southern Grand Manan
2000
7 farms within 3 BMAs; ~1.79M fish
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odd year-classes (black); even yearclasses (white)
2003
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5 new odd year-class farms authorised
(hatched);
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total of 12 farms ~3.69M fish
Concerns that the fish health
management strategy may be
ineffective due to uncertainties in
the knowledge concerning:
water exchange between sites
effectiveness of the existing BMA
boundaries
•
•
Simple Approach: 5 km radius “buffer”
zones
Site 303’s Buffer Zone or
Zone of Influence encompasses
7 sites - 0 in BMA 19
4 in BMA 20
3 in BMA 21
Determined each farm’s buffer zone
overlap
• with other farms
• with other buffer zones
• Used GIS software (MapInfo)
•
Model-derived particle tracks over 1 tidal cycle i.e. tidal excursions
Particle release grid
5 km radius ZPI
Particle trajectories
Farm sites
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Released 36 “drogues” evenly spaced on a 200 m  200 m grid centred on each farm site
Drogues released from each point at 1 hour intervals for 12 hours
Each drogue followed for at least one tidal cycle (12.42 h)
Tidal excursion estimated as area covered by all drogue tracks during 1 tidal cycle
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Excursion not a circle and covers less area than circle
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Model-derived tidal excursions for all fish farms (1 tidal cycle)
Applications – WebDrogue, Aquaculture parasites and disease, SAR, IBMs, dead whales ...
- may mimic concentration applications – sediment, oils spills
Use and derive statistical properties
Fourth order Runge-Kutta with 5th order correction
We assume we have the fields we need – Z, U, V, T, S …,
- can be extremely complex
Some Issues
 Random numbers
 Interpolation
- time and space
 Non convergent fields
 How many particles
 Under sampling
DFO Website
Application of a nested-grid ocean circulation model to Lunenburg Bay of Nova Scotia:
Verification against observations Li Zhai, Jinyu Sheng and Richard J. Greatbatch, J. Geophys.
Res., 113, C02024, doi:10.1029/2007JC004230
Lagrangian Stochastic Modeling in Coastal Oceanography, DAVID BRICKMAN AND P. C.
SMITH, J. Atmos. Ocean. Tech., 19:83-99, 2002.
Under-sampling:
Inhomogeneous diffusion:
Per-step displacement
A hierarchy of Lagrangian Stochastic Models: AR0, AR1, AR2 (... ARn)
AR0 Uncorrelated random walk and simple diffusion
=
= 0
AR1 Autocorrelated Velocity
= 0
AR1
AR2 Autocorrelated acceleration
AR0
,
≠ 0
Lagrangian Dispersion in Sheared Flow, D.R. Lynch and K.W. Smith,
Contin. Shelf Res.,30:2092-2105, 2010.
Keith R. Thompson, Michael Dowd, Yingshuo Shen, David A. Greenberg, Probabilistic
characterization of tidal mixing in a coastal embayment: a Markov Chain approach,
Continental Shelf Research 22 (2002) 1603–1614
Probability a particle stays in the region in
which it was released as a function of time.
Probability that a particle moves from Ri to
Rj in k tidal cycles or less.
Susan Haigh, St. Andrews Biological Station FVCOM
See:
Suh, Seung-Won, A hybrid approach to particle tracking and Eulerian–Lagrangian models in the
simulation of coastal dispersion, Environmental Modelling & Software 21 (2006) 234–242
David I. Graham, Rana A. Moyeed, Powder Technology 125 (2002) 179– 186
How many particles for my Lagrangian simulations?
‘What is a “statistically significant” sample of particles to determine particle statistics
such as concentrations, fluxes, dispersivities or root mean square velocities?
Different samples of the same number of (physically identical) particles will
produce different results.
“This means that Lagrangian modellers are experimentalists rather than
theoreticians.”
Findings
1. In order to characterize the variability of computed results, computations must be repeated
(>1 times);
2. The variability depends on the quantity in question as well as the location in the flow;
3. For any given point and for a given quantity, the standard deviation s of the quantity is
initially low and then increases, but eventually decreases like sqrt(number of points)
...
Continued
David I. Graham, Rana A. Moyeed, Powder Technology 125 (2002) 179– 186
How many particles for my Lagrangian simulations?
Method
1. Select a region of interest in the flow.
2. Decide the levels of precision required for each quantity.
3. Decide on the number of repetitions (Nr) required (50 appears reasonable, but the larger, the
better subject to storage constraints—remember that the variability is determined by the product
of the number of particles Np with the number of repetitions Nr);
4. Perform repeated calculations with ‘small’ numbers of particles (100, 200, 500, 1000, 2000. . .
), calculate variability, and ensure that the largest numbers of
particles used are sufficient for the variability to be proportional to sqrt(Np).
5. Using the results from part 4, extrapolate down to the required level of accuracy (i.e.,
determine the number of particles No that would ensure variability within the prescribed limits).
6. Perform Nr calculations with No particles, determine means and confidence limits (error
bars), and display results.
Parting shots
Simulating particles in model fields
may not be simple
“This means that Lagrangian modellers are
experimentalists rather than theoreticians.”
Graham and Moyeed (2002)
Particles in Motion
Pathways in the Coastal
Ocean
Daniel R. Lynch
Dartmouth College, Hanover, NH, USA
David A. Greenberg
Fisheries and Oceans, Bedford Institute of Oceanography, NS, Canada
Ata Bilgili
Istanbul Technical University, Istanbul, Turkey