Using the Mathermatical Models to Study the Marine Ecosystem of Binh THuan - Ninh Thuan Sea Area and...

VNU.

JOURNAL

USING

OF

SCIENCE,

THE

MARINE
SEA

Nat

Sci, t XVII, n92 - 2001

MATHEMATICAL

ECOSYSTEM
AREA

AND

OF

TAM

MODELS

BINH

STUDY

THUAN-NINH

GIANG-CAU
Doan

TO
HAI

THE

THUAN

LAGOON

Bo

Faculty of Hydro Meteorology and Oceanography
College of Natural Sciences,

Abstract:

The marine

Vietnam National

Unive

Hanoi

stem model has been established on the basis mathemat-

ical simulation for the material transformation through compounds
The phosphor cycle is chosen as an example for eco-hydrodynamic

of the system.
model. In the

cycle, phosphorus element is transformed through five compounds (Phytoplankton,
Zooplankton, Detritus, Dissolved Organic and Inorganic phosphorus) by different
bio-chemical processes.

The

eco-hydrodynamic

model

has

been

established

on the

basis turbulent diffuse model in combination with the material transformation model
(as phosphor cycle model).

The general model is analyzed into simple models,

are applied to the sea area of Binh
Hai lagoon of Thua

Thuan-Ninh

Thien-Hue province.

which

Thuan province and Tam Giang-Cau

The obtained results are very important to

study the biological and ecological characteristics of marine plankton communities,
to simulate and predict the variation of living and non-living compounds, especially,
to monitor

the marine

environment

and ecosystem.

1. Introduction
Recently, mathematical models and numerical methods have been widely used for

researching the marine ecosystems. One of those is to solve the Eco-hydrodynamic prob-

lems that have been established on the basis of combination between diffusion model and
the model of material transformation in the marine ecosystem. The results coming from
the application of the model allow us to look totally and optically at the development
tendency

of the system

under the influence of the marine

thermo-hydrodynamic

condi-

tions. The results also allow us to determine the basic and general relationship in the
marine ecosystem, to predict the variation of living and non-living compounds in the sea,

especially to monitor marine environment and ecosystem.
In this paper, some kinds of marine ecological model and Eco-hydrodynamic model
are introduced. The applications of these models to Binh Thuan-Ninh Thuan sea area
Giang-Cau

Hai lagoon

in order to study characteristics and variation of com-

N

and Tam

8

Doan

Bo

pounds of marine ecosystem, especially primary productivity and in order to study the
ecological effects of physical, environmental conditions show that the good results have

been obtained.
2.

Equations

of the models

Marine

Ecological Model

The marine ecological model has been established on the basis of mathematical simulation for the material transformation through the compounds of the marine ecosystem,

in which the living compounds are only limited by phytoplankton and zooplankton. In this
study, the phosphorus transformation cycle is chosen as an experiment for application of
the Eco-hydrodynamic model. In the cycle, the phosphorus (an essential element for life)
is transformed

five compounds

through

C{i

processes

bio-chemical

= 1...5) by different

K;(j = 0...7), fig. 1 [1]. The cycles for transformation of other elements are considered in

the same way. Combining the cycles to each other, we have the general model for material
transformation in the marine ecosystem.

Legend:

Cy,

Cy

Cs — Biomass

Cy

Cay

Phytoplankton, — Zooplankton
concentration

of Detritus,

Organic and Inorganic
respectively,
Ka

Ky,

Ky

-

Own

of

and

Dissolved

Phosphorus,
speeds

of

respiration,
photosvnthesis
and
natural

death
of — Phytoplankton
population, respectively.

Ky Ky Ks - Own speed of water

filtering,

death

of

respectively,

respiration

and

natural

Zooplankton — population,

Ko, Ky ~ Own speed of decomposition

Phosphorus (C4)
«
~

Inorg. Diss.

Phosphorus (C5)
Fig.
is following:

model

mineralization

of — organic

by,

b3 - Coefficient

of selecting

compounds, respectively.

bs

Phytoplankton and Detritus as natural

food by Zooplankton,

lạ(b5) |

1: Schema of phosphorus

Mathematical

and

by. bs, be b> ~ Ratio of transformation
into different material kinds.

bs

Hae of Phosphorus in organic

compounds

transformation cycle in marine ecos;

to simulate dynamic

of material

dC; /dt = Rys(i = 1...n)

transformation

em
in the c

(1)


Using
where

the mathematical
C,

is the

biomass

models

to study

(or concentration)

the marine

ecosystem...

of it? compound;

variation of biomass (or concentration) of i” compound.
cycle, the mathematical model is following:

R,

- the

9
total

speed

of

For phosphorus transformation

dC, /dt = Ry = (Ky — Ko — Ka — b K2C2)Cy
dCy/dt = Re{(byCy

+ b3C3)b2
Kg — Ky — Ks|Cz

dCy/dt ~ Ry = KyCy + KxCo + (bxCy + bgCs)(1 — bp)bg oC
dC, /dt = Rg

= (byCy

+ b3C3)(1

— b2)(1 — bg )bg K2C2

— b3 K2C2C3 — KeCa

+ bsbg K3Ce2 + bobs KeC3+

+ brbg KoCy — KrCy
dCs/dt — Rs = K7C4

+ (1 = bs)bgh3C2

+ (1 — bg )bg K6C3

+ (1 — b7)bgKoCy

— bg Ki Cy

‘The speeds of A); depends on environmental conditions, they can be

-

using some empirical formulae, as follows [4, 5, 6]:

2

Ko(1/day) = PoE xp|Qo(T — 20) — Uo.Ln(MP)|
WW (1/day) = Ky max-min|A, B,C, D|

i

Pi

W2(m* /ing.day)

0

if S=0

Kemax-5(2— $/5))/51

if

0
if

S;
1ƒ

S > S2

max

Kamax/[1

+ Pa(S ~ S2)]

Ks(1/day) = Py.ExplQs(T — 20) — Us.Ln(MZ)|
Kas(1/day) = Pas.exp(Qas.T —Uss.7)
No7(1/day) = Po.7 Exp(Qo71)
where:

Ky max(1/day) = Exp(QiT' — U;)

"“Ắ=....

e

N=

rao!

ĐỘC

No

SIO

3,720: ) 8 ~ PTO," ~ NaN? * Bie tSiOD

NHị + NÓ; + NÓ¿

8=Œ\+Ca

Nam =4

X.Exp|0,08(Tinin — 7)
Ä

if TeTnu
if Thìn ST! STmex

X.Erp|0,08ŒT — Tiax)| — Qa(T — Thấy)

if

X = 0,000682F'xp|-U2.Ln(MZ)|
In the empirical formulae:
- the minimal and maximal

of zooplankton

ically

T(°C) is the environmental temperature; Tinin, Tmax (°C)

temperature

in the optimal

population, respectively; Q,Q«

active radiation

and

T > Tinax

temperature

interval for growth

(cal/em?/min) - energy of photosynthet-

half-saturation coefficient

of light

intensity,

respectively;

€ -


10

Doan

base of natural

logarithm;

Bo

PO4, NH,, NO2,
NOs, SiOs(mgP, N, Si/m*) - concentration
nitrite, nitrat and silicon, respectively (here, PO4 is compound

of phosphate, ammonium,

C5); Px, Nx, Si * (mgP,N,Si/m’)- half-saturation coefficient for the salts of phosphor,

nitrogen and silicon, respectively; $;,S2 (mg)- optimal interval of food concentration of
zooplankton; Mp, Mz - the mean size of phytoplankton cell and zooplankton individual,
respectively; Py, QK,UK(k = 0...7) - experimental coefficients.

Eco-hydrodynamic

model

By adding the functions F, of system (2) into the equations of diffusion model, the

general model to simulate for time and space variation of compounds under the influence
of thermo-hydrodynamic

processes can be obtained, as follows:

Tên

aC,
+V loi

tí

Oy

OC

và (AE
3

(3)

8 2 (atémY sn
0

Oc;

ằ

where U,V, W

are the components of velocity of current in the x,y,z directions, respectively; W, - the sedimentation velocity ofi"th compound (W, = 0 for dissolved compounds);
Axi, Azi - the horizontal and vertical turbulent diffusion coefficients of it” compound. The
boundary and initial conditions are chosen suitable with the normal diffusion model.

ion of current, diffusion coeflicients, water
intensity of photosynthetically active radiation at the water surface, con-

‘The input

temperature,

values are velocity and dire

centration of PO4, N H4, NO2, NO3, SiO3... depending on the objective of study and the
source data, the model can be simplified for some certain cases of study.

3. Some

study

Dynamic

results
model for material transformation

in the phosphorus

cycle

The model (2) with initial conditions C; = C? at t = fo is solved by Runge-Kutta
method.

The solutions are the time variations of biomass

(or concentration)

of the com-

pounds in the phosphorus cycle. The biological productivity of plankton community and
the ecological effects of autotrophic and first heterotrophic hierarchy are also calculated
from the model.
The mentioned model is named PMOD and has been applied to the sea area of
Binh Thuan-Ninh

Thuan

province in order to study the annual

of phosphorus cycle [1]. The results are depicted in figure 2.

variations of compounds


Using

the mathematical

SO)

models

to study

the marine

ecosystem...

11

——Phytoplankton (10 mg/m3)

—o— Zooplankton (mg/m3)
——— Detritus (.100 mg/m3)

40 +

—x— Organic Phosphorus (mgP/m3)
—#— Inorganic Phosphorus (mgP/m3)

30
20

Or

1

2
Fig.

3

4

5

6

7

8

9

10

11

Month

2: The annual variation of compounds of phosphorus cycle

at the sea area of Binh Thuan-Ninh Thuan province (results estimated by PMOD)
The

Model

of competition

in marine

plankton

communities

Separating

first two

equations of the system (2), we have model of competition in marine plankton communities (the model is called PLAMOD). The model is, the same as the model of ” prey-predator”

relationship of Voltera.
ton as "prey”.

In the model, the concentration of detritus (C's) is determined through the

value of BOD or COD.
Thua

Where, zooplankton is considered as ” predator” and phytoplank-

Thien-Hue

The PLAMOD

has been applied to Tam Giang-Cau Hai lagoon,

province in order to study

cal productivity of plankton community [3].

the daily variations of biomass and biologi-

The input

environmental data at 24-hours continuous stations.

values of the PLAMOD

The results are depicted in figure 3.

30
20
10
0

+

-10

= = Biomass (100 mg-wet/m3)
Rough Primary Productivity (mgC/m3/hour)
oO Pure Primary Productyvity (mgC/m3/hour)
--*--

Temperature

(oC)

Inorganic Phosphorus (mgP/m3)

Fig. 3: Daily variation of biomass and primary productivity
of phytoplankton at Thuan An Stations (Tam Giang-Cau Hai lagoon)
in October

are the

1995 (results estimated by PLAMOD)


12

Doan
Two-dimensions

model for distribution

of the compounds

Bo

in phosphorus

cycle
Integrate equation (3) in the vertical direction from free surface to depth D and
consider the steady state, diffusion coefficient is constant, to have the two-dimension steady

model,

This model is named P2DMOD,

9C;
V ,8G:
9 Ox TU
Oy
The

boundary

%C,

=A

conditions

as follows:

used

„0Ý 1 ĐỤC,
D

_ 3C,
Oy?

in this model

are:

aC;

+ Ri

(4)

ae

+ b(0C;/OL)

with

= land b
0 if at the solid boundary, a = 0 and b
1 if at the open boundary, L
is the unit vector normal to the open boundary, Cy is the given value of C; at the solid
boundary,

In the case of having no values Cf we can use the condition OC, /On

0 (nis

the unit vector normal to the solid boundary).
The P2DMOD can be reduced to solve the competition problem in the plankton
community. In this case, system (4) includes 2 equations, one for phytoplankton, another

The model has also
been applied for Binh Thuan-Ninh Thuan sea area in order to estimate ecological role of
for zooplankton,

R;

and

Ry are first two equation

from system

(2).

upwelling in the primary production process [2]. The input data got from investigation in

upwelling sea area in 8/1992.

|[BIOMASS

Figure 4 shows the results.

OF aac

x0

(mg-weUm3)

{

A

| Phan Thieta

-

joe

1075

1080

~706

1085

300,

|
1

|
`

1090

eee
Tuy Ph

"Phan Thiets,/~)

1095

BY

wy

|

110

1080

1000

1085

sary

pry
1090

Phan Rang gˆÝ
Ca Na!
Tuy Phong /
Phan Ri > "66

L2

105

1080

500

ae

+ Phụ Quy

1085

⁄

|

1100

4: Distribution of biomass of phytoplankton

Let

1075

1080

`

30

1090

Phan Rang

eae,

if

|

NĨ

1095

|

1100

\;

Tuy Phong

1) Phan Thiet,

1000
1095

bo

Cim2. day)

D

sa

„í

PRODUCTIVITY

(mg

`

f

FY SECONDARY

CaNas

1500/2000

fp

B

Phan Thieta

Phan Rang“

Cc

OF ZOOPL, ANKTONS

(mg-wet/m3)

re

(Phu Quy.

(mg-C/m2.day)

Fig.

1

|

500

“PRIMARY PRODUCTIVITY

1075

J

Phan Reng
CaNas
Tuy Phong
Phan Rif

vi BIOMASS

\

|

wis

CaNa!.-

1085

(A), of zooplankton

5

“ˆ ”

7 / ey
‘i

Ae

“7°40

|

Nero
~ 4030

1095

1100

(B) in the surface layer

and total of primary productivity (C), of secondary productivity of zooplankton (D) in Im?

water column of the photosynthetically layer in Binh Thuan-Ninh Thuan sea area
in Aug, 1992 (results estimated by P2DMOD)


Using

the mathematical
One-dimension

models

to study

the marine

ecosystem...

13

model for vertical distribution of the compounds

in cycle

The governing equations:

yo

sự

(w +u)ŠtOz

s2 (25 Oz ‘) t Ry

values Co,

(5)

Oz

Boundary condition:
- At the free surface (z = 0),C, = Cio
given

"

(Cio

is the given

values).

If there are no

.¡(0Œ,/8z) — WiC, = 0.

the balance condition is applied:

- At the level 2 = D (D is under boundary of photosynthesis layer):
the given

values Cjp,

the equation

will be taken as C’, — Cp;

that the vertical gradients of compounds
deep-water

area,

where

the

light

can

are zero (OC',/0z =

not

reach,

the biomass

if there are

if there are not, we assume

0).
can

If D is bottom
be taken

in the

to be

zero

(Cy = Cy = 0).
‘This model is called PIDMOD.
Thuan-Ninh Thuan

sea are shown

The results of application of this model for Binh

in figure 5.

mựụC/m /day
0

40

80

+

120

58

ð& 8

0

-100
Fig. 5:

Vertical profile of primary productivity of phytoplankton at Binh ‘ThuanNinh Thuan

sea area in Aug.

1992 results estimated by PIDMOD)

4. Conclusion
The

Eco-hydrodynamic

fusion model

in combination

model

has been established on the basis of turbulent dif-

with the phosphorus

transformation model.

Four simplified

forms of the model were also given, as follows: the model for material transformation in
the phosphorus cycle (PMOD), the model of competition in marine plankton communities
(PLAMOD), the two-dimensions model (P2D MOD) and one-dimension model (PIDMOD)
for distribution of the compounds

in phosphorus cycle.

The models were applied to the sea area of Binh Thuan-Ninh

Tam Giang-Cau Hai lagoon of Thua Thien-Hue province.
important

for studying

the biological

and ecological

Thuan province and

The received results are very

characteristics of marine

plankton


14

Doan

Bo

communities and also for simulating and predicting the variation of living and non-living
compounds,

especially, for monitoring the marine environment

and ecosystem.

We thank the Foundational Research Program 1998-2000 for financial assistance to
carry out this research,

Department
Hanoi.

We also wish to acknowledge

the helpful comments of Scientists of

of Oceanography, College of Natural Sciences, Vietnam National University,

REFERENCES
. Đoàn Bộ. Tính tốn biến đổi năm khối lượng sinh vật nổi bằng mơ hình chu trình

phốtpho trong hệ sinh thái vùng biển Thuận

Hải, Tạp chí Sinh học, Hà Nội, T15,

No3(1993), tr. 7-20.

Đồn Bộ. Mơ hình tốn học về sự phân bố sinh vật nổi và năng suất sinh học sơ
cấp vùng nước trồi thềm lục địa Nam Trung bộ, Tạp chí Sinh học, Hà Nội, T.19,
No4(1997), tr. 35-42.

. Đồn Bộ. Nghiên cứu năng suất sinh học quần xã plankton vùng đầm pha Tam
Giang-Cầu Hai bằng phương pháp mơ hình tốn, Tạp chí Khoa học, Dại học Quốc
gia Hà Nội, Tuyển

tập các cơng trình hội nghị khoa học Trường, Đại học Khoa học

Tự nhiên, ngành Khí tượng-Thuỷ văn và Hải dương học, 4-1998, tr. 1-7.
Jinghui Guo, Karina Yew Hoong Gin, Hin Fatt Cheong.
A Size-based

Model

of Plankton Dynamics in Sub-tropical Ocean Waters, Proceeding of Conference:
Oceanology International 1997 Pacific Rim, Vol. 1: Extending the Reach of Ocean
Technologies, Singapore

1997, pp. 45-56.

. J. Kishi, Nakata, Ishikawa.
Sensitivity analysis of a coastal marine ecosystem,
Journal of the Oceanographic Society of Japan, Vol. 37(1981), pp. 120-134.
‘Takashi

Asaeda,

Truong

Van

Bon.

Modeling

the effects of macrophytes

blooming in eutrophic shallow lake, Ecological Modeling,

on alga

No 104(1997), pp.

261-

287.

II, n°2- 2001
SU DUNG MO HINH TOAN TRONG NGHIEN CUU HE SINH THAI

VUNG BIỂN BÌNH THUẬN-NINH THUẬN VÀ DAM PHA TAM GIANG-CAU HAI
Doan Bo
Khoa Khí tượng Thuỷ văn &_ Hải dương hoc
Đại học Khoa học Tự nhiên - Đại học Quốc gia Hà Nội
Mơ

hình sinh thái biển được

xảy dựng

trên cơ sở mơ phỏng

tốn

học q trình

chuyển hố vật chất qua các hợp phần của hệ. oO đây, chu trình chuyển hod phosphor
đã được xây dựng làm thí nghiệm cho việc triển khai bài tốn sinh thái-thuỷ động lực.

“Trong chu trình, nguyên tố phosphor được chuyển hoá qua 5 hợp phần (thực vật nổi,


Using

the mathematical

models

to study

the marine

ecosystem...

15

động vật nói, chất vấn, phosphor hữu cơ và võ cơ hồ tan) nhờ các q trình sinh hố

khác nhan, Mơ hình sinh thái thuỷ động lực được xây dựng trên cơ sở kết hợp mỏ hình

chu trinh chuy
vat chất (ở đảy là chủ trình phosphor) với mơ hình khuếch tán rối,
nó cho phép đánh giá ảnh hưởng của các điều kiện vật lý môi trường tới chiều hướng.
phát

triển của hệ sinh thái
vùng biển nghiên cứu.
Mo hình chung được phần tích thành các mỏ hình giản đơn

và các mơ hình giản

đơn này đã được triển khai tại vùng biển Bình Thuận-Ninh Thuận và vùng đầm phá
‘Tam € ang-Cầu Hai (mơ hình động lực
r chuyển hố vật chất trong chu trinh phosphor,
mỏ hình anh tranh trong quần xã plankton biển, mơ hình 2 chiều ngang, 1 chiều thẳng
đứng phản bố các

hợp phần của chu trình phosphor và năng suất sinh học plankton).

Các

kết quả nhận được rất có ý nghĩa trong việc nghiên cứu định lượng các đặc trưng sinh
học, sinh thái học quần xã plankton biển, tính tốn và dự báo biến động các hợp phần
vỏ sinh, hữu sinh, đặc biệt trong việc

kết quả nà,

kiểm sốt mơi trường và hệ sinh thái biển.

cũng mở ra triển vọng sử dụng

trong nghiên cứu hệ

sinh thái

ác mơ hình tốn

vùng biển nhiệt đới

et Nam.

và các phương

Những
pháp số