1

Data assimilation in APECOSM-E

Sibylle Dueri, Olivier Maury

Tropical tuna exploitation in the Indian Ocean

From IOTC – Report 2009

Targeted tuna species

Skipjack (SKJ) Yellowfin (YFT) Bigeye (BET)

Catchtons/year 1983 2009

SKJ 70 000 400 000

YFT 60 000 300 000

BET 40 000 120 000

Industrial fisheries start in 1983, rapid increaseIndustrial fisheries start in 1983, rapid increase

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From IOTC – Report 2009

Main fishing gears: purse seine, bait boat, gillnet and long line

Skipjack tuna fishery: spatial distribution

3

4

Fishing gears• Purse seiners (French, Spanish and other)• Maldivian Baitboat

Data• Monthly catch 1x1 degree grid• Monthly size frequency 5x5 degree grid• Monthly fishing effort 1x1 degree grid

Skipjack fishery: available data

From IOTC – Report 2009

APECOSM-E

• Dynamic, deterministic spatially explicit and size structured model• Single species of top predator (i.e. skipjack tuna)• Devoted to parameter estimation• State variable Tuna biomass f(x,y,z,t,V)• Partial differential equation, discretized and solved numerically• 48 parameters: 19 related to fisheries, 8 energetic (DEB), 21 ecological parameters

5

•1º x 1º horizontal grid of the Indian Ocean (4230 cellules)

• 20 vertical layers, 10 m interval in the first 150m and max depth of 500m

• 83 size classes, from 1mm to 1m

• 1 day time step

Discretisation

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7

APECOSM-E – Model Structure

Fishing mortality• 4 fleets : French, Spanish and other (Seychelles, Ile Maurice, NEI) purse seiners and Maldivian Bait boat

szsskkk zzklwlktaptzyxef

exp1

1

exp1

1exp,,,

• Fish size and fishing depth selectivity functions

• Fishing power pk multiplies by an exponential function representing the increase in fishing efficiency due to technological development

• Monthly value of spatial effort ek is applied on simulated biomass

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Observed catches vs distribution of simulated biomass

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Vertical transect of biomass distribution along theEquator

Observed catchVertical transect along the Equator

Total biomass

Exploitable biomass + observed catch

Mars 1993

Data assimilation

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3 Steps

• Identifiability of the model parameters (Hessian Matrix)• Parameter estimation• Sensitivity analysis of non-estimated parameters

Cost function combines

1) –log likelihood of catches JCAPT(K)

2) –log likelihood of size frequencies JFDT(K)

3) –log likelihood of parameters JPAR(K)

• Minimization algorithm requires the derivation of the code automatic differentiation tool (TAPENADE-Inria)

• Derives the exact gradient of the cost function with respect to model parameters

Data assimilation over 10 year period: 84-93

Optimization of fishery related parameters: fishing power, size and depth selectivity, …

11Iterations

Data assimilation: convergence

1984 1986 1988 1990 1992 1994 1996 1998 2000 20020

5000

10000

15000PS France

1984 1986 1988 1990 1992 1994 1996 1998 2000 20020

1

2x 10

4 PS Spain

1984 1986 1988 1990 1992 1994 1996 1998 2000 20020

5000

10000

15000Ps World

1984 1986 1988 1990 1992 1994 1996 1998 2000 20020

5000

10000

15000BB Maldives

Overall catch: simulated vs observed

12Temporal window used for optimisation

Skipjack tuna fisheries: fishing strategy

Peaks of catches occurring in association with Fish Aggregation Devices (FADs) are difficult to represent

Associative behavior of fishesIncrease the catchability?

Ecological trap? (Marsac et al. 2000, Hallier and Gaetner 2008)

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1984 1986 1988 1990 1992 1994 1996 1998 2000 20020

2000

4000

6000PS France

1984 1986 1988 1990 1992 1994 1996 1998 2000 20020

5000

10000PS Spain

1984 1986 1988 1990 1992 1994 1996 1998 2000 20020

2000

4000

6000PS World

Free-school catch

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20 40 60 800

0.02

0.04

0.06

0.08PS France

20 40 60 800

0.05

0.1PS Spain

20 40 60 800

0.02

0.04

0.06

0.08

length [cm]

PS Word

20 40 60 800

0.02

0.04

0.06

0.08

length [cm]

BB MDV

Observed

Simulated

Size frequencies

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Bimodal distribution

1984 1986 1988 1990 1992 1994 1996 1998 200040

50

60

70

Year

leng

th [

cm]

PS France

1984 1986 1988 1990 1992 1994 1996 1998 200040

50

60

70

Year

leng

th [

cm]

PS Spain

1984 1986 1988 1990 1992 1994 1996 1998 200040

50

60

70

Year

leng

th [

cm]

PS World

1984 1986 1988 1990 1992 1994 1996 1998 200040

50

60

70

Year

leng

th [

cm]

BB MDV

Size frequencies: temporal dynamics

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mean

Sensitivity analysis

Ecological parameters DEB Param.

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Based on the evaluation of the gradient of the cost function

The gradient represents the variation of the cost function for a change in parameters

Local sensitivity, changes in time

3 x 6 year periods

1984-19891990-19951996-2001