ellebo lake (Version: 0)

ECOBAS Documentation (ECOBAS_MIF 3.1) ¹

1 Structure
2 AGG: ellebo lake (Version: 0)
    2.1 Structure of the aggregate
        2.1.1 Declaration of variables
        2.1.2 Components
        2.1.3 Connections
    2.2 Description of Specification
    2.3 List of figures
3 SPEC: zooplankton (Version: 0)
    3.1 Declaration of Quantities
4 SPEC: phytoplankton (Version: 0)
    4.1 Declaration of Quantities
5 SPEC: fish (Version: 0)
    5.1 Declaration of Quantities
6 MATH: zooplankton (Version: 1)
    6.1 Declaration of Variables
    6.2 Equation(s)
        6.2.1 Initial state of the system     (t = = 0) :
        6.2.2 dynamics of zooplankton biomass Equationblock(1)
        6.2.3 grazing Equationblock(2)
    6.3 Description of MATH module
7 MATH: phytoplankton (Version: 0)
    7.1 Declaration of Variables
    7.2 Equation(s)
        7.2.1 Initial state of the system     (t = = 0) :
        7.2.2 dynamics of phytoplankton Equationblock(1)
        7.2.3 growth Equationblock(1)
    7.3 Description of MATH module
8 MATH: fish (Version: 1)
    8.1 Declaration of Variables
    8.2 Equation(s)
        8.2.1 Initial state of the system     (t = = 0) :
        8.2.2 fish Equationblock(1)
9 Domain: ELLOBO
    9.1 Classification of Domain
        9.1.1 Description of Domain

1 Structure

                               AGG:elle
                                  |
   _______________________________|________________________________
   |                    |                    |                    |
DOM:ELLO            SPEC:zoop            SPEC:phyt            SPEC:fish
                        |                    |                    |
                   _____|______         _____|______         _____|______
                   |          |         |          |         |          |
                DOM:ELLO  MATH:zoop  DOM:ELLO  MATH:phyt  DOM:ELLO  MATH:fish

2 AGG: ellebo lake (Version: 0)

Domain identifier: ELLOBO (see section: 9)
Author: Angelini,Ronaldo
Documented by: Benz,Joachim
Model (Origin of this mathematical formulation):

ELLOBO; A model for the plankton system of the Broa reservoir, Sao Carlos, Brazil
References: [Ang00]
Keywords: undefined

2.1 Structure of the aggregate

2.1.1 Declaration of variables

acronym	description

INPUT:
temperature	temperature (of water)

2.1.2 Components

Name of module		Type of module

zooplankton (version: 0)		DYNAMIC
phytoplankton (version: 0)		DYNAMIC
fish (version: 0)		DYNAMIC

2.1.3 Connections

`source` `module`:variable	= >	`sink` `module`:variable

`phytoplankton_0` : PHYT	= >	`zooplankton_0`:PHYT
`zooplankton_0` : GRAZZ	= >	`phytoplankton_0`:GRAZZ
`zooplankton_0` : ZOO	= >	`fish_0`:Z
`fish_0` : pred	= >	`zooplankton_0`:PRED
`INPUT` : temperature	= >	`phytoplankton_0`:temperature
`INPUT` : temperature	= >	`zooplankton_0`:TEMPERATURE

2.2 Description of Specification

Template Content

2.3 List of figures

Figure(1): ellebo_lake_0_s.eps

3 SPEC: zooplankton (Version: 0)

Instance of MATH module: zooplankton (Version: 1)
Domain identifier: ELLOBO (see section: 9)
Author: Petrere,Miguel
Author: Angelini,Ronaldo
Documented by: Noeding,Dirk
Model (Origin of this mathematical formulation):

ELLOBO; A model for the plankton system of the Broa reservoir, Sao Carlos, Brazil
References: [Ang00]
Keywords: biomass

3.1 Declaration of Quantities

acronym	unit	meaning	method	value	range	indomain
t	d				0:365
ZOO₀	mug/l	concentration		0.1
k_phyt	l/mug	-		1.0
ZOO_up	mug/l	-		3.3
ZOO_low	mug/l	-		0.8
M_zoo	1/d	-		0.3
TEMPERATURE_max	C	-		27.1
C_k	mug/l	-		3.3
K_z	1/d	-		0.5
PRED	mug/(l*d)	-
TEMPERATURE	C	-		23
PHYT	mug/l	biomass		4.0
ZOO	mug/l	biomass
PHYT_av	unitless	-
GRAZZ	mug/(l*d)	-
M_yz	1/d	-
LOSS	mug/(l*d)	-

4 SPEC: phytoplankton (Version: 0)

Instance of MATH module: phytoplankton (Version: 0)
Domain identifier: ELLOBO (see section: 9)
Author: Angelini,Ronaldo
Documented by: Noeding,Dirk
Model (Origin of this mathematical formulation):

ELLOBO; A model for the plankton system of the Broa reservoir, Sao Carlos, Brazil
References: [Ang00]
Keywords: nitrogen, Phytoplankton, grazing, light, phosphor

4.1 Declaration of Quantities

acronym	unit	meaning	method	value	range	indomain
t	d
PHYT₀	mug/l	concentration		1.0
K_c	1/d	-		0.2
K_sr	mumol	-		140
K_pd	mug/l	-		1.1
K_nt	mug/l	-		0.5
G_phyt	mug/l/d	-		0.5
GRAZZ	mug/l/d	-		0.0
solarradiation	mumol	-
nitrate	mug/l	-
phosphorus	mug/l	-
temperature	C	-		23
PHYT	mug/l	-
GROWTH	mug/l/d	-
LOSS	mug/l/d	-
G_max	mug/l/d	-
MM_sr	unitless	-
MM_nt	unitless	-
MM_pd	unitless	-

5 SPEC: fish (Version: 0)

Instance of MATH module: fish (Version: 1)
Domain identifier: ELLOBO (see section: 9)
Documented by: Noeding,Dirk
Model (Origin of this mathematical formulation):

ELLOBO; A model for the plankton system of the Broa reservoir, Sao Carlos, Brazil
References: [Ang00]
Keywords: biomass, Astyanax fasciatus, predation

5.1 Declaration of Quantities

acronym	unit	meaning	method	value	range	indomain
t	d
K_l	1/d	-		0.5
K_p	1/d	-		0.24
Z	mug/l	-
F	mug/l	-
pred	mug/(l*d)	-
loss	mug/(l*d)	-

6 MATH: zooplankton (Version: 1)

Author: Petrere,Miguel
Author: Angelini,Ronaldo
Documented by: Noeding,Dirk
Model (Origin of this mathematical formulation):

ELLOBO; A model for the plankton system of the Broa reservoir, Sao Carlos, Brazil
References: [Ang00] [Joe83]
Keywords: biomass, population dynamics, zooplankton
Simtype: DYNAMIC

6.1 Declaration of Variables

acronym	type*	description	time scale	time agg.	intime/state type

DEPENDENT:
PHYT_av	FM	availability of phytoplankton for grazing		none
GRAZZ	FM	predation of zooplankton on phytoplankton		none
M_yz	FM	temperatur dependent growth rate of zooplankton		none
LOSS	FM	respiration and mortality of zooplankton		none

STATE:
ZOO	FM	biomass of zooplankton		none	CONTINUOUS

INPUT:
PRED	FM	feeding by fish		none
TEMPERATURE	FM	temperature of water		none
PHYT	FM	biomass of phytoplankton		none

CONSTANT:
ZOO₀	FM	inital value of zooplankton biomass		none
k_phyt	FM	constant used for phytoplankton availability		none
ZOO_up	FM	upper limit of random mumber RANZOO		none
ZOO_low	FM	lower limit of random number RANZOO		none
M_zoo	FM	is the calibrated value for growth rate		none
TEMPERATURE_max	FM	maximale temperature at Broa reservoir		none
C_k	FM	carring capacity for zooplankton		none
K_z	FM	respiration and mortality per day		none

TIME:
t		time

6.2 Equation(s)

6.2.1 Initial state of the system (t = = 0) :

Bound: ZOO =

ZOO₀

(1)

6.2.2 dynamics of zooplankton biomass Equationblock(1)

dZOO

GRAZZ-LOSS-PRED

(2)

LOSS =

ZOO ·K_z

(3)

6.2.3 grazing Equationblock(2)

GRAZZ =

M_yz ·PHYT_av ·(1-

ZOO

C_k

) ·RUNIFORM(ZOO_low,ZOO_up)

(4)

M_yz =

M_zoo ·0.98^{TEMPERATURE-TEMPERATURE_max}

(5)

PHYT_av =

k_phyt ·PHYT

(6)

6.3 Description of MATH module

Zooplankton in Broa reservoir is represented by Cladocera (13.8%), Copepod (81%) and Rotifers (5.4%). The dynamics of zooplankton is determined by 3 terms:

grazing of phytoplankton (GRAZZ)
respiration and mortality (LOSS) and
feeding of zooplankton by fish (PRED)

Grazing is formulated according ODUM 1972(see: [Joe83], page83). The dependence of amount of zooplankton is formulated here by introducing a uniform distributed random variable.

7 MATH: phytoplankton (Version: 0)

Author: Angelini,Ronaldo
Author: Petrere,Miguel
Documented by: Noeding,Dirk
Model (Origin of this mathematical formulation):

ELLOBO; A model for the plankton system of the Broa reservoir, Sao Carlos, Brazil
Keywords: Phytoplankton, biomass dynamic
Simtype: DYNAMIC

7.1 Declaration of Variables

acronym	type*	description	time scale	time agg.	intime/state type

DEPENDENT:
GROWTH	FM	growth rate of phytoplankton		none
LOSS	FM	respiration and mortality of phytoplankton		none
G_max	FM	Rate coefficient of temperature		none
MM_sr	FM	light		none
MM_nt	FM	nitrogen		none
MM_pd	FM	phosphor		none

STATE:
PHYT	FM	Phytoplankton		none	CONTINUOUS

INPUT:
GRAZZ	FM	predation of zooplankton on phytoplankton		none
solarradiation	FM	light		none
nitrate	FM	nitrogen		none
phosphorus	FM	phosphor		none
temperature	FM	temperature		none

CONSTANT:
PHYT₀	FM	inital biomass of phytoplankton		none
K_c	FM	parameter of temperature function		none
K_sr	FM	half saturation of solarradiation		none
K_pd	FM	half saturation of phosphorous		none
K_nt	FM	half saturation of nitrogen function		none
G_phyt	FM	value is adjusted for the maximum growth rate		none

TIME:
t		time

7.2 Equation(s)

7.2.1 Initial state of the system (t = = 0) :

Bound: PHYT =

PHYT₀

(7)

7.2.2 dynamics of phytoplankton Equationblock(1)

dPHYT

GROWTH-LOSS-GRAZZ

(8)

LOSS =

PHYT ·0.5

(9)

7.2.3 growth Equationblock(1)

GROWTH =

G_max ·MM_sr ·MM_pd ·MM_nt

(10)

G_max =

G_phyt ·e^{K_c ·temperature}

(11)

MM_sr =

solarradiation

K_sr+solarradiation

(12)

MM_pd =

phosphorus

K_pd+phosphorus

(13)

MM_nt =

nitrate

K_nt+nitrate

(14)

7.3 Description of MATH module

Phytoplankton is a collection of several species of algae. For growing we consider input of the nutrients nitrate and phosphor , temperature and light(solar radiation). LOSS describes the loss by respiration and mortality of phytoplankton. GRAZZ is the predation of zooplankton on phytoplankton.

8 MATH: fish (Version: 1)

Author: Angelini,Ronaldo
Documented by: Noeding,Dirk
Model (Origin of this mathematical formulation):

ELLOBO; A model for the plankton system of the Broa reservoir, Sao Carlos, Brazil
References: [Ang00]
Keywords: predation, fish
Simtype: DYNAMIC

8.1 Declaration of Variables

acronym	type*	description	time scale	time agg.	intime/state type

DEPENDENT:
pred	FM	zooplankton biomass and predation rate		none
loss	FM	keep alive rate and mortality of fish		none

STATE:
F	FM	population of fishs		none	CONTINUOUS

INPUT:
Z	FM	calculated zooplankton biomass		none

CONSTANT:
K_l	FM	calculated fish mortality and keep alive rate per day		none
K_p	FM	calculated zooplankton predation rate per day		none

TIME:
t		time

8.2 Equation(s)

8.2.1 Initial state of the system (t = = 0) :

Bound: F =

(15)

8.2.2 fish Equationblock(1)

pred-loss

(16)

pred =

Z ·K_p

(17)

loss =

F ·K_l

(18)

9 Domain: ELLOBO

9.1 Classification of Domain

Soil classification (FAO): any

Soil texture (US-Soil classification): any

Climate classification (Walther/Lieth): II tropical and subtropical area

swr dominant winter rain

Type of ecosystem (Ellenberg): Oligotrophic_Lakes

Mesotrophic_Lakes

Biological classification: Fish Astyanay fasciats

Phytoplankton serveral species

Zooplankton Argyrodiaptomus furcatus

Cladocera

Rotifers

9.1.1 Description of Domain

mean depth 3.0m

References

[Ang00]: Ronaldo Angelini. A model for the plankton system of the broa reservoir sao carlos, brazil. Ecological Modelling, 126:131-137, 2000.
[Joe83]: S.E. Joergensen. Application of Ecological Modelling in Environmental Management, volume Part A. Elsevier Scientific Publishing Company, 1983.

Footnotes:

¹Database: /eco6/benz/_ecobas/db/dbb/

Soil classification (FAO):	any
Soil texture (US-Soil classification):	any
Climate classification (Walther/Lieth):	II tropical and subtropical area
	swr dominant winter rain
Type of ecosystem (Ellenberg):	Oligotrophic_Lakes
	Mesotrophic_Lakes
Biological classification:	Fish Astyanay fasciats
	Phytoplankton serveral species
	Zooplankton Argyrodiaptomus furcatus
	Cladocera
	Rotifers