Applying ETKF in Stochastic Bioeconomic Model

Applying ETKF in Stochastic

Bioeconomic Model

The Barents Sea Cod, Capelin, and Herring

eVITA-EnKF meeting, May 2010

Sameh Gharib, [email protected]


The Study Area

• North East Arctic (Area I and IIa)

• Source of data is ICES Data sets.

ICES: International Council for the Exploration of the Sea.

http://www.ices.dk/

2/1521.05.2010 Sameh Gharib, [email protected]


Fishery Industry

Fish stock and Harvest for Cod, Capelin, and Herring


1. Find optimal TACs from the management model according to

the present stock sizes.

2. Set optimal TACs into the simulation model.

3. Simulate next year stock sizes in accordance with the TACs.

4. Start again from point 1 with new stock sizes as starting point.


Working Plan

• Two bioeconomic models:

– Single species (1D model : NEAC)

– Multispecies (3D model: Cod, Capelin and Herring)

• Two techniques:

– VAM (used for 1D model).

– ETKF (1D stochastic model, Multispecies Model)

– EnKS.

• Working Papers:

– Paper 1: A comparison between the VAM and EnKF in 1D bioeconomic models.

– Paper 2: Applying ETKF for stochastic biomass models.

– Paper 3: EnKS for 3D multispecies model.



The population dynamics are described by:

…….. (1)

where x is the biomass and y is the harvest.

The logistic growth function f takes the form:

..…… (2)

where r is the intrinsic growth rate and K is the carrying capacity.

Let p be the unit price of fish and c be a proportionality constant,

then the average net revenue is given by:

……… (3)

the relationship between the rate of change of fish biomass, y, and the function

is given by:

……….(4)

where is an adjustment parameter, and therefore,

we get the system of equations:

……… (5)

where the term is the annual total profit (total revenues - total costs).

yxfdtdx )(/

)/1()( Kxrxxf

yxcpyx )/(),(

/ ( , )dy dt y x y

)/(/

)/1(/

xcpydtdy

yKxxrdtdx

),( yx

)/( xcpy

1-D Bioeconomic Model (Cod) – logistic model



ETKF Results for 1D model – logistic model

Cod Stock (x)

Growth rate (r)

Cod Harvest (h)

Carrying Capacity (K)


1-D Bioeconomic Model (Cod) – Stochastic model



ETKF Results for 1D model – Stochastic model

Cod Stock (x=0.1242 e+6)

Growth rate (r=0.2487)

Cod Harvest (h=0.04903 e+6)

(K=1.187 e+6)

Eps = 0.1149

0

21( ) 0.092812

eVITA-EnKF meeting, May 2010 9/1521.05.2010 Sameh Gharib, [email protected]

The Multispecies Model (3-D)

C:/BMAME Project/BMAME concept2.pdf


Observations: The 3 species distribution



Herring Data



Discussion: Results for 3D model



Discussion: Results for 3D model



Oral Communications:

• Data Assimilation Techniques and Inverse Methods, NHH Annual meeting ,

10-12 March 2010, Geilo, Norway.

• Applying Data Assimilation in Bioeconomics Management: A case study of North

East Arctic Cod Stock, Invited talk at ”The First meeting of BMAME Project”

4 March 2010, NHH, Bergen, Norway.



End of Part I



3-D model

Stock biomasses are given by the vector x = [x1, x2, x3] and harvest by u = [u1, u2, u3], where the

indexes 1, 2 and 3 represent Capelin, Cod and Herring respectively. The growth functions are:

Notice that the growth of herring is somewhat different from that of capelin and cod. Whereas r1

and r2 represent intrinsic growth-rate of respectively capelin and herring, the interpretation of ˜r3 is

more moot, as it also represents positive inflow of biomass when the stock-size is zero. In fact

This reflects the positive inflow of herring from the Norwegian Sea to the Barents Sea, which in this

model only depends on year class 1-3.


For Capelin, Cod and Herring :

Applying ETKF in Stochastic Bioeconomic Model

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