eulerian movement models example grid point model: an advection-diffusion-reaction model for the...
DESCRIPTION
Diffusion terms Advection terms Grid points Continuous form: Discrete form: Reaction termParametersAlternating direction, implicit time stepsTRANSCRIPT
Eulerian Movement Models
• Example grid point model:An advection-diffusion-reaction model for the estimation of fish movement parameters from tagging data, with application to skipjack tuna (Katsuwonus pelamis). Sibert, J, J. Hampton, D. Fournier, and P. Bills (1999). CJFAS. 56: 925-938
• Example grid line (block transfer) model:Modeling effects of FADs and islands on movement of skipjack tuna (Katsuwonus pelamis): estimating parameters from tagging data. Kleiber, P. and J. Hampton. 1994. CJFAS. 51:2642-2653.
Estimating Skipjack Movement Parameters
The Data: ~90k releases and ~5k recaptures by pole-and-line and purse seine fishing fleets
Grid point model
The Universe:
Diffusion terms Advection terms
Grid points
Continuous form:
Discrete form:
Reaction term Parameters Alternating direction, implicit time steps
Movement parameter estimates
Observation model Poisson likelihood
Model Performance
Solomon Islands
Modeling effects of FADs and Islands on Skipjack Movement
• Many FADs
• Two fleets
• 7730 tag releases
• 914 returns
• 1/2 degree square grid
Grid line model
1, jiN
jiN ,1
1, jiN
jiN ,1
jiN ,
1, jim
jim ,
jim ,
jim ,1
jim ,
1, jim
jim ,1
jim ,
Movement by block transfer
transfer coefficients:
FAD effect
FAD
fact
or
no. FADs
Island effects
ba
Model Parameters
ADI -- Alternating Direction, Implicit time steps
Index time differently in alternating steps
step A: step B:
Example: step A (NS implicit). Collect ) terms on the left(i.e.i-1,j
i,j
i+1,j
add neighboring equations and arrange
ADI -- alternating direction, implicit time steps
i-1,j
i,j
i+1,j
makes tri-diagonal system
ADI -- alternating direction, implicit time steps
i-1,j
i,j
i+1,j
Objective function
Two alternatives:
• tag release sets combined
single model run includes all sets
Poisson likelihood
• individual tag release sets
separate model run for each set
Multinomial likelihood
Model Performance
Months at large Months at large
Ret
urns
per
mon
th
Mea
n di
stan
ce (n
m)
Return rate Mean distance moved
Results
• D = 3.2 nm2/mo
• FF = 0.36
• M = 0.15 mo-1
≈ 10 nm
radius of FAD actionparameter estimates
0.49
1.3 FADs
Diffusion bias