Modelling to address aquaculture issuesModelling to address aquaculture issues

David Greenberg David Greenberg

DFO Bedford Institute of OceanographyDFO Bedford Institute of Oceanography

Contact: david.greenberg@dfo-mpo.gc.caContact: david.greenberg@dfo-mpo.gc.ca

2000 7 farms within 3 BMAs; ~1.79M fish odd year-classes (black); even year-

classes (white)2003 5 new odd year-class farms authorised

(hatched); total of 12 farms ~3.69M fish

Southern Grand Manan

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

• Determined each farm’s buffer zone overlap

• with other farms • with other buffer zones

• Used GIS software (MapInfo)

Site 303’s Buffer Zone or Zone of Influence encompasses7 sites - 0 in BMA 19

4 in BMA 203 in BMA 21

Model-derived particle tracks over 1 tidal cycle i.e. tidal excursions

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 Excursion not a circle and covers less area than circle

Particle release grid

Particle trajectories

5 km radius ZPI

Farm sites

Model-derived tidal excursions for all fish farms (1 tidal cycle)

Some Issues Random numbers Interpolation- time and space Non convergent fields How many particles Under sampling

We assume we have the fields we need – Z, U, V, T, S …, - can be extremely complex

Applications – WebDrogue, Aquaculture parasites and disease, SAR, IBMs, dead whales ... - may mimic concentration applications – sediment, oils spillsUse and derive statistical propertiesFourth order Runge-Kutta with 5th order correction

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

DFO Website

Lagrangian Stochastic Modeling in Coastal Oceanography, DAVID BRICKMAN Lagrangian Stochastic Modeling in Coastal Oceanography, DAVID BRICKMAN AND P. C. SMITH, AND P. C. SMITH, J. Atmos. Ocean. Tech.J. Atmos. Ocean. Tech., 19:83-99, 2002., 19:83-99, 2002.

Under-sampling:

Inhomogeneous diffusion:

Per-step displacement

A hierarchy of Lagrangian Stochastic Models: AR0, AR1, AR2 (... ARn)

AR1 = 0

= = 0

AR0 , ≠ 0

AR2 Autocorrelated acceleration

AR1 Autocorrelated Velocity

AR0 Uncorrelated random walk and simple diffusion

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 that a particle moves from Ri to Rj in k tidal cycles or less.

Probability a particle stays in the region in which it was released as a function of time.

SeeSee: 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

Susan Haigh, Susan Haigh, St. Andrews Biological Station FVCOM

David I. Graham, Rana A. Moyeed, Powder Technology 125 (2002) 179– 186

How many particles for my Lagrangian simulations?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 willproduce 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)...

ContinuedDavid I. Graham, Rana A. Moyeed, Powder Technology 125 (2002) 179–

186

How many particles for my Lagrangian simulations?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 ofparticles 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.

Simulating particles in model fields Simulating particles in model fields may not be simplemay not be simple

““This means that Lagrangian modellers are This means that Lagrangian modellers are experimentalists rather than theoreticians.”experimentalists rather than theoreticians.”

Graham and Moyeed (2002)

Parting shotsParting shots

Daniel R. LynchDartmouth College, Hanover, NH, USA David A. Greenberg

Fisheries and Oceans, Bedford Institute of Oceanography, NS, CanadaAta Bilgili

Istanbul Technical University, Istanbul, Turkey

Particles in MotionPathways in the Coastal

Ocean