Ecological Modelling. 31 (1986) 145-174 145 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

POPULATION DYNAMICS O F ' RED TIDE' ORGANISMS IN EUTROPHICATED COASTAL WATERS - - NUMERICAL EXPERIMENT OF PHYTOPLANKTON BLOOM IN THE EAST SETO INLAND SEA, JAPAN

MICHIO KISHI

Ocean Research Institute, University of Tokyo, 1-15-1 Minamidai, Nakano, Tokyo 164 (Japan)

and SABURO IKEDA

Institute of Socio-Economic Planning, University of Tsukuba, Tsukuba, lbaraki 305 (Japan)

ABSTRACT

Ikeda, S. and Kishi, M., 1986. Population dynamics of 'red tide' organisms in eutrophicated coastal waters - - numerical experiment of phytoplankton bloom in the East Seto Inland Sea, Japan. Ecol. Modelling, 31: 145-174.

A system of simulation models on the outbreak of 'red tide', a large-scale phytoplankton bloom, is developed by identifying a model structure based on the marine ecological and hydrological conditions in the East Seto Inland Sea, Japan. The models consists of two parts: one is to determine hydraulic conditions of water movements in the sea, and the other is to calculate biological interactions among red tide organisms and nutrients under the diffusive and advective transportation associated with the calculated water movement.

The comparison between the results simulated by our models and the observed biological or physical data on 'red tide' has shown: (a) the amount of nutrients and oceanographic characteristics are basic factors influencing the rapid increase in phytoplankton population; (b) the alternate migration of both phyto- and zooplanktons in the vertical direction according to a light/dark cycle causes a dense phytoplankton population in the upper layer; and (c) the tidal current plus water movement induced by the wind has a great impact on phytoplankton dynamics.

INTRODUCTION

This paper is concerned with the identification of a model structure of phytoplankton dynamics associated with the outbreak of 'red tide' in coastal waters. 'Red tide' is a phenomenon often observed in summer in an eutrophicated sea area that has excessive inflows of nutrients. The sea water is colored red by an unusual increase in the phytoplankton population. Recent studies have shown that the oceanographic characteristics of coastal

0304-3800/86/$03.50 © 1986 Elsevier Science Publishers B.V.

146

saka

Fig. 1. Sketch of Seto Inland Sea.

waters also have strong influences on the generation mechanism of 'red tide' in such a semi-closed sea area as the Harima Sea located at the western part of the Seto Inland Sea (Iizuka, 1980; Yanagi, 1982; Okaichi, 1983; 1984). This sea is shallow (the average depth is about 30 m) and the water is not easily interchanged with that of the outer sea area. It is also surrounded by highly industrialized and urbanized regions including Osaka, Kobe and Harima. Consequently it has suffered from the inflow of high levels of nutrients and other pollutants from industrial and domestic drainage, as well as from the heavy sea traffic (see Fig. 1).

A large-scale Chattonella antiqua ' red tide' (a major species of phyto- plankton which blooms in summer and may cause damage to fisheries and recreational amenities) has appeared since the late 1960s. For example, in 1978, a number of the dense patches of the Chattonella antiqua blooms were observed over most of the northern Harima Sea and the highest cell number of the population amounted to 5840/ml on 28 July (Okaichi, 1983). It is now a common understanding among researchers on the 'red tide' problem

147

that the mechanism of a ' red tide' outbreak involves complicated interac- tions among biological specifics of the red tide organisms, local oceano- graphic characteristics, inflow of nutrients, climatic factors, and so on. To identify such a complicated model structure of ' red tide' in the Harima Sea, we use the systems approach by which we elaborate a marine ecological-hy- draulic system from a simple structure to a more complex one.

This paper consists of three sections. The first one is concerned with a simple structure of phytoplankton dynamics in one-dimensional space with the consideration of phytoplankton's vertical movement. The second one deals with a simple ecophysical structure of the two-dimensional model in view of wind-induced movement of sea water in order to evaluate the effect of upwelling on the primary production. The third is devoted to a more realistic structure of the three-dimensional model which has six ecological compartments in the tidal current plus the wind-induced water movement of two levels (layers): two kinds of 'phytoplanktons ' , 'zooplankton' , 'nitrogen' and 'phosphorus ' as nutrients for phytoplankton's growth, and 'detritus' as the dissolved organic matter in the sea water. By means of numerical experiments based on our three models, we will try to find out some specific combinations of the oceanographic and ecological factors that are supposed to cause a ' red tide' in the Harima Sea.

1. ONE-DIMENSIONAL MODEL

Model structure

The simple one-dimensional model is constructed to examine whether or not a vertical migration of both zooplankton and phytoplankton is essential to the formation of ' red tide'. In addition to the factors of nutrient-uptake for photosynthesis or physical accumulation for forming a plankton patch, the prey-preda tor interaction between phyto- and zooplankton plays an important role in terms of keeping a high growth rate in the phytoplankton population. It seems, therefore, to be critical to see the effect of interaction through the vertical migration of phyto- and zooplankton on the prey-pre- dator relationship.

~ Chattonella ~ Paracalanus parvus I (P) antlqUal/ I (Z) /

dP VmE dZ VmzP - p - Z

dt K + E dt K + P s sz

Fig. 2. Relationship of biological processes in the one-dimensional model.

148

The relationship of biological processes is illustrated in Fig. 2 in which Chattonella antiqua is a primary producer, P (this is a major species that causes 'red tide' in the Harima Sea). Paracalanus parous is a zooplankton, Z, as a representative species in this area, and PO4-P is a nutrient, E. The photosynthetic and grazing functions are approximated by the type of Michaelis-Menten relationship as follows (see Table 1):

dP VmE d~- - K s + ~ P (1.1)

d Z v=e d--t- = Ksz + ~ Z (1.2)

A simple nutrient uptake equation of Michaelis-Menten type is applied to our 'red tide' model. Nakamura and Watanabe (1983a) have shown that the N / P ratio of the minimum cell quota of Chattonella antiqua isolated from the water in the Seto Inland Sea is about 11.0 and that its nutrient uptake kinetics (N and P) is well described by the Michaelis-Menten equation under a nutrient starved condition which is often observed in summer in this area as shown in Fig. 3 (Nakamura and Watanabe, 1983b). The parameters of Michaelis-Menten curves are also experimentally ex- amined by our project team as displayed in Table 1 (principal investigator,

U

7 -C2

0.12 C}-

v

0~08

0.04 g -[

z 0

O

/~" • ." Measurement in the dark ~/~ Sol id l i n e ." Mich ea ll~-Menten curv E h- 1

(Ks -- 1.9 ~M, Vma x = 0.14 pmol per c e l l )

m l ! i u , m

2 4 6 8 10 Phosphate concentrat ion (~M P04)

Fig. 3. Phosphate uptake kinetics by Chattonella antiqua (source: Nakamura and Watanabe, 1983b).

149

TABLE 1

Biological parameters in the one-dimensional model and initial values of ecological compart- ments

V m maximum photosynthetic rate 2.0 day- 1

K~ half saturation constant 1.0 /~g at. PO 4-P 1 1 Vmz maximum grazing rate 1.5 ~tg C/~g-1 C copepoda day 1 Ksz half saturation constant in grazing 193.0 ~tg C 1-1 W vertical migration velocity 2.0 m h-1

Initial values E PO 4-P

upper layer 0.1 /~g at. P 1 1 lower layer 0.7 /~g at. P 1-1

P Chattonella antiqua 2.0 ~g Chl.a 1 1 Z Paracalanusparvus 15.0 /~g C 1-1

Professor T. Okaichi of Kagawa University, supported by the special re- search programs on environmental science, Ministry of Education, Japan 1982-1984).

I E __PI (a} [

!

I ,b, tk

Fig. 4. Vertical profiles of E, P and Z without vertical migrations: (a) initial states (6:00); (b) 9 h after initial states (15:00); (c) 81 h after initial states (15:00 on 4th day).

150

4O m

0 2000

(a)

0 2000 0 2000 ~g C 1-1

4o11 4oiie (c, m-" m : ~

Fig. 5. Vertical profiles of E, P and Z with vertical migrations: (a) initial states (6:00); (b) 9 h after initial states (15:00); (c) 33 h after initial states (15:00 next day).

Numerical results

Figure 4 shows vertical profiles of ecological compartments, E, P and Z in the case with no vertical migration either by phyto- or zooplankton. The population of Chattonella antiqua (indicated by P) first increases at the surface because of high light intensity (Fig. 4a). Then, the dense population moves to the point near the thermocline because of rich nutrients in the lower layer (Fig. 4b). However, after 57 h, zooplankton prevails at all layers because its grazing exceeds the rate of primary production through the phytoplankton's photosynthesis (Fig. 4c). The vertical profiles of compart- ments E, P and Z are shown in Fig. 5 in the case with migrations of both Chattonella antiqua and zooplankton. Chattonella antiqua moves upwards in daytime and sinks at night and zooplankton on the contrary moves upwards during the night and downwards in daytime with a speed of W. In this case, the population of Chattonella antiqua increases greatly at the surface causing an outbreak of 'red tide' (Fig. 5b). Chattonella antiqua is able to preserve its high growth rate till a depth of 11 m, because it has little chance to encounter zooplankton (Fig. 5c).

Discussion

These numerical results are quite easily understood if it is validated that the movement of Chattonella antiqua is directly opposed to that of zooplank- ton. However, this assumption is not yet solidly supported by the field study in this sea area. In the next section, let us take a vertical diffusion and upwelling of nutrients into the structure of the two-dimensional ecological-hydraulic model.

2. TWO-DIMENSIONAL MODEL

151

Model structure

This two-dimensional model is constructed to investigate how the wind- induced zonal circulation influences the occurrence of ' red tide'. Figure 6 shows a schematic view of the two-dimensional hydraulic model in terms of vertical profiles of temperature, salinity and nutrients. There is a thermo- cline at a depth of 20 m. When wind blows in parallel with the coast at a constant speed of 10 m / s as illustrated in Fig. 6, there is an upwelling stream of sea water in the left side of the coastal zone and a downstream in the right side.

The dynamics of the ecological compartments in this model are described by the terms of oceanographic transportation and biological interactions as shown in Fig. 7 (and also see Table 2):

a t = - u g - ; - w - ~ + ~ , ~ ~ + A , - ~

~3Z OZ OZ A O---- ( OZ / Ot - u-0-Tx - W-~z + x 0x T x

OE OE aE A ~ ( ~E ] at - U~x - WTz + ~' Ox ~x

oD_ oD OD+Ax¢? DI 0t UTx - w-~z dx \ dx ]

+ . , (E ) .~ ( , ) ,o

-g(P)z-,~? (2.1)

A °( zl + Z~z\-~z ] + g ( P ) Z - ~ Z (2.2)

A 0 - - ( ° E ) + ~0z - ~ - . , ( e ) . 2 ( / ) P

+aP (2.3)

[~D + Az-~z~ --~Z-z) + flZ (2.4)

where u, w horizontal and vertical current velocity, A x, A~ horizontal and

C)~/,.,~ S WIND

r~np,.H ,Sal--.-L IqArient---- L

,Thermoclino

Tornp.-L Sat.--H Nutrient.-.H

60 ~n

Fig. 6. Schematic view of the two-dimensional model.

152

Detritus I death egestion

z

? Photosynthes s , , . a I

~-"~" ~ chl. a razing extracellular release

120 .a

Fig. 7. Relationship of biological processes in the two-dimensional model.

vertical eddy diffusivity, and:

OmE

v l ( E ) - Ks + E

I( t) v2(I ) = I( t) exp 1.0 /opt

i ( t ) = {1"0 sin3( ~r ) ~ - t e x p ( - 0.01z)

0.0

(/opt = constant)

(daytime)

(night)

Rm{1 .O-exp[X(P*-P)]} (ifP>=P*) g(P) =

0.0 (if e __< P*)

in which P* is a threshold value for grazing. The model has no feedback loop from the detritus to other ecological

compartments. In the long run, this ecosystem will be composed entirely of detritus. However, since we are only concerned with the generation stage of the 'red tide' for the period of 2 or 3 days, it is sufficient to take such a simple model structure as shown in Fig. 7 for our numerical experiment.

Numerical results

Figure 8 shows initial and the calculated zonal distributions of phyto- plankton measured by chlorophyll-a (Chl.a) and nutrient PO4-P. Our calculation begins at 6:00 in the morning. Figure 8a (10:00 on the 1st day) displays the increased Chl.a near the thermocline where the nutrient is rich and light intensity is sufficient. At around 14:00 on the 1st day, the Chl.a increases rapidly near the coast up to the level of forming a "red tide' due to

1 5 3

(a)

4 . 8 4 . 9 ) ) . ':, ..... .~ ~

~I_A . , . . . . . . , . . . . . . . . . . . . . , . . , . . . . . . . . . - ~ v _ . . , - , ~ ' ~ J t ' t ¢

" 5 k m "

chl . a

POEP

• . -1 , ' ]5, ,~

" 5 km

chl . a

(b)

POcP

(c) " 5 k m ~ .....

i' ss,~ chLa

Fig. 8. Zonal distributions of PO4-P and Chl.a in the two-dimensional model: (a) 4 h after initial states (10:00); (b) 8 h after (14:00); (c) 32 h after (14:00 next day). (Units: mg at PO4-P m-3; mg Chl.a 1-1.)

the coastal upwelling induced by wind which carries nutrients from the bot tom to the surface (see Fig. 8b). In Fig. 8c (14:00 on the 2nd day), the increased phytoplankton near the coast is diffused during the night toward offshore; the Chl.a will again increase near the coast the next day because of newly upwelled water rich in nutrients. The biological parameters and the initial values of ecological compartments are listed in Table 2.

Discussion

The cycle of phytoplankton growth and decay can be explained in a quantitative way as described in Fig. 9. The terms of 'photosynthesis ' of primary production, 'grazing' of zooplankton and 'advection' of transporta- tion are shown in time axis in order to evaluate a material balance at the four specified points: 5 m depth at 3 km offshore, 5 m at 10 km, 15 m at 3 km, and 15 m at 10 km, respectively. The term of photosynthesis changes its

154

TABLE 2

Biological parameters in the two-dimensional model and ments

intial values of ecological compart-

V m maximum photosynthetic rate 1.0 K s half saturation constant 1.0 R m maximum grazing rate 0.5

ivlev constant 0.02 P* limiting constant in grazing 5.0 W~ vertical migration velocity 2.0 a , /3 mortality rates 0.2 C/Chl . a carbon/chlorophyll-a 30.0 C / P carbon/phosphorus 15.0

Initial values E PO 4-P

upper layer (z > 15 m) 4.5 ~g at. P 1-1 lower layer (z < 15 m) 0.0 # g at. P 1-1

P (Chattonella antiqua) 5.0 /~g Chl,a 1-1 Z (Paracalanusparvus) 15.0 /~g C 1-1

day- 1 /~g at. PO4-P 1-1 #g C # g - l C copepoda day -1 ~ g C 1 - 1 /~g Chl.a 1-1 m h - 1 day- l

/~g C ~g-1 Chl.a

value according to the cyclic change of light intensity at 5 m or 15 m depth near the coast and offshore. At the coastal point, the term of advection increases its negative value (transported to other regions) with the develop- ment of coastal upwelling and other water movement (Fig. 9a and c). On the other hand, at the offshore point of 15 m depth, the photosynthetic term has a smaller value because of low nutrients in the upper layer (Fig. 9b). The advection term has a positive value because of the supply from the lower layer through coastal upwelling on the 1st day (Fig. 9a and b). On the 2nd day, however, the advection term becomes negative (transported to other regions) due to the influence of surface offshore currents (Fig. 9a and c).

In this context, the existence of night may be important for the ap- pearance of 'red tide'. Figure 10 shows the time-dependent zonal distribu- tions of PO4-P and the Chl.a in the case without night. At first the Chl.a increases near the thermocline where the nutrient and light are sufficient as shown in Fig. 8. The steady sunshine provides phytoplankton with a sufficient photosynthesis capacity, in particular, at the place near the coast (where the upwelled nutrients exist) and the Chl.a increases like a 'red tide' (Fig. 10b and c). The experimental results by our model raise a question about the assumption that a vertial wind-induced upwelling along the coast is a major factor in the occurrence of plankton blooms. Namely, the diffusive transportation during the night carries dense phytoplankton out of the open sea area unless there is any vertical migration of plankton during the night. Thus both physical factors of phytoplankton movement and

10 "3

2-

I 0":

~ m

Photo

h

(a)

5 0

graz

10-3

1 0 "3

ph

.... " o

(c) acid:.-_-'"

Sm

I O0 ',.J

~gr~ (b)

- - io k ~---~

so p h ~ I oO

__ _< ~ . . . . .

( d )

1 5 5

Fig. 9. Time changes of each term in diffusion equation: solid line, photosynthesis; dotted line, advection; dashed line, grazing mortality. (Unit: mg C m -3 h-l . )

upwelling of sea water are essential to the development of a more realistic marine ecological model of 'red tides'.

3. THREE-DIMENSIONAL MODEL

Model structure

The three-dimensional model of two levels is constructed in order to simulate the 'red tide' observed on 26-28 July 1978 in Seto Inland Sea (see Fig. 11). This model consists of two parts: one is to determine the tidal or wind-induced currents which are numerically calculated by Navier-Stokes equations of fluid dynamics on tidal and wind forces in the Harima Sea, and the other is to calculate biological interactions among ecological compart- ments with diffusive and advective transportation in the current field of the

156

(a)

~, 35m

5 km

chl.a

PO4-P

' " " " ' ' / / 5 '

x 5 km

I

35m C hi . a

(b)

. . . . . 1-3 ) ,; ~-~ ~- ~ - q , ~ PO4-P

zl/l#/ll#1/I/I// ¢" ///#ll//I///Z;~¢ 6 ~ ~, ~ . . . . . z . ' F , ~', D . ~ / H ~ . . / !~2_ ' ~ ' Y I ' C ' L ' ~ ~ . . . . . . ~ " t . ' 7 " ~ - ~ . 5 ~ . ~ 1 ~ ,

"~ " D )1 -~ i,

. . . . . . . . . . . . . . , , . . . . . . . . . . . . . . . . . . . .-.,.4, . . . . . . . . . . . . . . . . . . . . .

5 km

I 35m ch [ .a

(c)

Fig. 10. Zonal distributions of PO4-P and Chl.a in the case without night: (a) 4 h after initial states (10:00); (b) 12 h after; (c) 24 h after.

Harima Sea. We divide the relevant area, Osaka Bay and Harima Sea, into 62 x 36 square meshes horizontally and into two layers vertically. The length of each mesh is 2.5 km and the mean depth of the upper layer is set at 10 m, which is an average depth of the stratification in summer in terms of temperature profile a n d / o r salinity difference. The depth of the lower layer is over 10 m.

First, let us describe a model of current movement of two layers. The direction of coordinate axes is shown in Fig. 12. Assuming that the move-

134"30' 135°00 ,

~ ~ , J u l y 26-28

" " c : Akashi

• ~ ~ . /

~ " ' - ~ / 7 ~O/Ocellslm'; " / / ' Shi - . ;:## . July 26-28 . . . .

5

157

34*45'

3403'0'

34015 '

Fig. 11. Schematic illustration of the observed red tides in July 1978 (Okaichi. 1982).

ment of water in the vertical direction is hydro-static, we integrate the Navier-Stokes equation on the plane in the vertical direction from z = 0 to H 1 in the upper layer and from //1 to H 2 in the lower layer, respectively as shown in Fig. 12. This leads to the following kinetic equations which consist of volume transport vector M k and N k, and velocity vector u k and vk, and other forcing terms (coriolis, viscosity, etc.) in each layer: - - upper layer

3-M1= __ ~-~-(Maul)_ ~---f(Mavl)+(uw) [ +fN, -p lg~x-½gAhl 3p' 3t ~x := -H, ~x

_ r ( ( u _ uz)~/ (ua _ uz)2 + ( v _ v,,_)2 + OaV2Wx l W l

+ A H ( 02M1 O2M 1 ] - - + (3.1) OX 2 Oy 2 ]

at - o')x -~y ( N l v l ) + ( - fMl-plg-~y -½gAhl Oy -H I

__.~i2(Ol__V2)ff(Ul__bl2)2q._(Ul__U.,..)2 + PaT~W~, i W I

[ ~2N 1 ~2N 1

+ AH 10x2 + - -Oy 2 (3.2)

158

. . . . . . . . . . . . . 7.":.-.-....:... . . . . . . . . . . . .

Z=~ Surface Z=O Mean level

of surface

Z=hB+n

Z=hB ..... ~ean level of

Interface interface

+~-H

Fig. 12. Direction of coordinate axes in the current field.

)ttOl~ Z~- H

- - lower layer OM 2 0

Ot - Ox ( M 2 u 2 ) - (M2vz)--(uw)lz=-.,+(UW)lz=-H2 o~ op2 Do, )~u, u2) 2 + (v, ,,~)~

_p,g_~x _½gAh2--~x -ghl--~x + y i2 (u l -u2 - -

( 02M2 02M2 ] (3.3)

- ~ ? u 2 ~ + v~ + A.I -L-~/+ -~y~ J ON2 0 0 (Nzv2) _(vw)lz=_H ' +(vw)l~=_. 2

- o,g~y - ½gAh2 - gh, 3p, Ap g(n + hB-- H) On Ox 02 3y

+ v ? ( u , - u~)v;(v , - o2) 2 + ( o , - o~) ~

( 32N2 02N2 1 (3.4) - r,~o~¢~ + v~ +A.~-ZS2 + - ~ y J

TABLE 3

Variables and symbols in equations (3.1)-(3.8)

159

Uk., V k, W k

P l , P2

Mk, Uk

g Ap Ah~ ya

f W Art

components in x-, y- and z-directions of the tidal current in the k th layer, respectively (k = 1, 2) water densities in the upper and lower layers, respectively a surface variation from the mean level an interface variation from the mean level h volume transports in the x- and y-directions (k = 1, 2), respectively, and defined by equations (3.7) and (3.8) acceleration of gravity difference of water densities between two layers vertical finite difference of k th layers (k = 1, 2) a friction coefficient between air and surface of the sea a friction coefficient between the sea water Of two layers a friction coefficient between the sea water and the sea bottom coriolis parameter (Wx, IVy), a vector of wind speed a coefficient of eddy viscosity in the horizontal direction

- - cont inui ty equat ion

0~' 0 0 ( N 1 + N2 ) oa t = _ ¢3--~-(M1 + M2) - ~ y

O~ ~}M2 ¢3N2

~t ~x ~y

where

(upper layer) (3.5)

(lower layer) (3.6)

M1 = - hB - n ) u l

M2= (hB + ~ - H ) u 2 (3.7)

Nl=( -ha-n)vl N 2 = (h a + ~ - H ) o 2 (3.8)

Variables and symbols in the above equat ions are listed in Table 3. As to the b o u n d a r y condi t ions on coastlines, we assume that the non-sl ip

condi t ion is applied to the coastlines along the shore, and as an open b o u n d a r y condi t ion on the open channels, we assume (see Table 4):

~ = ~'0 + A c o s ( w t - K ) ; ~ = 0 (3.9)

In addi t ion we have similar kinetic equat ions bo th for salinity and heat balance. Then, a finite difference scheme of explicit type is applied to equat ions (3.1)--(3.6) for numerical computa t ion .

Based on the current field calculated by the equat ions (3.1)-(3.9), let us

160

TABLE 4

Variables and symbols in equation (3.9)

~'o height of a mean surface of the upper layer at the boundary A magnitude of tidal current measured at the open boundary to angular velocity of tidal cycle K phase delay of tidal cycle n a normal vector at the interface of two layers

now build a model of ' red tide' which takes account of both physical and biological factors. So far, a number of mathematical simulation models have been developed for describing a coastal marine ecosystem associated with ' red tides' (Wroblewski and O'Brien, 1976; Steel and Henderson, 1977; Walsh, 1977; Ikeda and Yokoi, 1980; Kishi et al., 1981). These models are two-dimensional models either vertically or horizontally. Our previous dis- cussion made it clear that it is important to consider both the vertical migrations of plankton and the horizontal transportation of all compart- ments due to the water movement. Thus, we constructed the following three-dimensional ecological-physical model (see Table 5):

L B = 8 ( ( ) ) 0 8 IK 0B) oy w + w s B

19 / 8B ) 8 8B +-~y[Ky- - j - f y , +-~z ( K ~ - ~ z ) + S . (3.10)

Dynamics of each ecological compartment B in the above general equa- tion is illustrated in Fig. 13, phytoplanktons, Chattonella and Diatom uptake of dissolved inorganic nutrients, nitrogen and phosphorus. Zooplankton grazes both types of phytoplankton in proportion to their concentrations. The particulated detritus is produced by the mortality of plankton and egestion from zooplankton. It is decomposed into the dissolved inorganic

TABLE 5

Variables and symbols in equation (3.10)

U

V

w

w~

K x, Ky, K z Sa

a tidal current in the x-direction (cm s-1) a tidal current in the y-direction (cm S - 1 )

a tidal current in the z-direction (cm s -1) speed of vertical migration (up-and-down) of Chattonella under light/dark cycle (cm s- 1) coefficients of diffusion a function of biological interactions for compartment B

• t .

161

Fig. 13. Schematic view of the three-dimensional model.

nutrients by bacteria. The dissolved detritus is not directly considered because of the slow rate of variation in its concentration in the highly eutrophicated sea. Between layers, there is a material transportation due to both physical forces such as advection and diffusion and biological migra- tions. Besides these conditions, light intensity, water temperature, a daytime period and inflows of nutrients from major rivers are taken into considera- tion. Thus we have the following dynamic equations of S B in the ecological compartment B of equation (3.10):

Sp in= {p,,(I, T) L,(P, N ) - M , } P H 1

SpH2 "=" ( ~2(I , T) Lz(P, N) - M 2 }PH1

PH1 PH1 + PH2 gz (PH1, PH2)Z

(3.11) PH2

PH1 + PH2 gz (PH1, PH2)Z

(3.12)

162

Sz = { ez gz(PH1, PH2) - M 3 } Z

= [gz(PH1, PH2) { PH1 0PH1, P + PH2 0PH2, P So. PH1 + PH2

+ M 1 PH1 0pnl, e + M 2 PH2 0pn2, e -- ¢pDp

= [gz (PH 1 PH2) [ PH1 0PH1, N + PH2 0PH2, N ' / PH1 + PH2

+ M 1 PH1 0prn, N + M E PH2 0an2, N -- ~oD N

(3.13)

-- eyOz.P ) + g3Oz.p } Z

(3.14)

-- eyOz,N ) + M3Oz,N } Z

(3.15)

Sp= - /x , ( I , T) L,(P, N) PH1 0PH1.P--~2(1 , T) LE(P , N) PH2 0PH2, P

+(ey-- ez) gz(PH1, PH2) ZOz, P + ¢pDe + Op (3.16)

SN= - -~ , ( I , T) LI(P, N) PH1 0pro,N--#2(I , T) L2(P, N) PH2 0pH2, N

+(ey -- ez) gz(PH1, PH2) ZOz, N + ~0D N + ON (3.17)

where

I ( z )=I o exp( - kz)

{ Im~,Sin3[~r/DL/t] (daytime)

I ° = 0 (nighttime)

# i ( I , T ) = ]~i,max -T----exp/1 - - - i,opt

T

, Ah Jlayer L,opt I( Z ) )d z

/ ,opt

(3.18)

(3.19)

P N ) ( i = 1 2) L~=Min Kp,+ P' KN,+ N

gz(PH1, PH2) = gz, max( 1 -- exp[ •(-- PH1 - PH2)] )

Definitions of symbols and variables in these equations are listed in Table 6. Numerical values of ecological parameters and the initial values of each compartment used in this simulation are summarized in Tables 7 and 8.

(3.20)

(3.21)

Numerical results

The calculated tidal residual currents are shown in Fig. 14. There is a clockwise current in the northern part of the Harima Sea, and counterclock- wise currents in the southern part. They are in quite good accordance with the observed data concerning the constant flow in the upper layer of the sea as displayed in Fig. 15. Figure 16 illustrates the combined case of tidal and wind-induced residual current. The tidal boundary conditions at the Bisan Seto and the Kii Channel and other physical parameters are described in Tables 9 and 10.

TABLE 6

Variables and symbols in equations (3.11)-(3.21)

163

PH1 PH2

Z

Dp

DN

P N I

T gl(I, T), /x2(I, T)

LI(P, N), L2(P, N)

gz(PH1, PH2)

ey ez Mi, M2 M3 0pH1,P, 0PH2,P, 0Z,P

~PH1,N, 0PH2,N, OZ,N

Op

ON

concentration of Chattonella as measured by its carbon content concentration of diatoms as measured by its carbon content (/~g C 1-1 ) concentration of zooplankton as measured by its carbon content (/~g C 1-1) concentration of detritus as measured by its phosphorus content (gg P 1 - l ) concentration of detritus as measured by its nitrogen content (gg N 1-1) concentration of dissolved inorganic phosphorus (gg P 1-1) concentration of dissolved inorganic nitrogen (ttg N 1-1) light intensity at z, I (z) (ly day-1), as defined by equation (3.18), in which k is the extinction coefficient, and I 0, the light intensity at the surface, Io(t ) (ly day-l), as defined by (3.19), in which DL is a daytime period (s) water temperature (°C) saturated photosynthesis rates of Chattonella and diatoms, respectively (day-l), and defined by (3.20), in which /~i,m~, is the maximum photosynthesis rate of Chattonella or diatoms (day-1), /,.opt the optimum light intensity for photosynthesis (ly day -1), and T,.opt the optimum water temperature for photosynthesis (°C) growth limitations for Chattonella and diatoms for nutrients, and defined by (3.21), in which Kp,, KN, Michaelis-Menten's con- stant of Chattonella and diatoms for nutrients, Pi, Ni (#g C 1-1) grazing rate of zooplankton (day-i), and defined by (3.22), in which gz, max the maximum grazing rate of zooplankton (day-l), and h the ivlev constant in grazing curve assimilation efficiency of zooplankton gross growth efficiency of zooplankton mortality rate of Chattonella and diatoms (day-l) natural death rate of zooplankton (day -1 ) weight conversion rates from carbon to phosphorus with Chattonella, diatoms and zooplankton, respectively weight conversion rates from carbon to nitrogen with Chattonella, diatoms and zooplankton, respectively bacterial decomposition rate of detritus (day-1) influent concentration of dissolved inorganic phosphorus (/~g P 1-1) influent concentration of dissolved inorganic nitrogen (gg N 1-1)

ly, langley = 1 cal cm -2 = 41.868 kJ m -2.

As far as the d is t r ibut ional profi les of nu t r ien ts are concerned , the po r t i on of their high concen t ra t ion is located a round the loading poin ts of nu t r ien t s because of their diffusive na tu re (see Fig. 17 and Tab le 11). However , the

164

TABLE 7

Parameter values used in the three-dimensional model

Symbols Definitions Values

~l,max, ~2, rrmx KpI KN1 Kp2 KN2 0PH1,P, 0pH1,N

0pH2,P, 0pH2,N

/1,opt, I2,opt

Tl,opt, T2,opt

DL

k

gz, max

ey ez Oz,p O Z,N M1, M2 M3

U p, max UZ, max Kx, Kv K~

maximum photosynthesis rate half saturation constant

weight conversion rate of Chattonella

weight conversion rate of diatoms

2.0 10.0

108.8 12.8

108.6 1.58X10 -2 1.91 × 10-1 2.13×10 -2 1.81x10 -1

day - 1

# g P 1 - 1 /.tg N 1-1 p.g P 1-1 /.tg N 1-1

optimum light intensity for photosynthesis 150.0 ly d a y - 1

optimum water temperature for photosynthesis 25.0 (°C)

daytime period 0.5 maximum light intensity 600.0 ly day-1 extinction coefficient 1.28 × 10-1 m - I maximum grazing rate of zooplankton 2.0 d a y - 1 ivlev constant 2.0 x 10- 3 assimilation efficiency 0.7 gross growth efficiency 0.3 weight conversion rate of P in zooplankton 1.57 x 10-2 weight conversion rate of N in zooplankton 1.97 x 10-1 mortality rates of phytoplankton 0.1 day - 1 natural death rate of zooplankton 0.1 day-1 bacterial decomposition rate of detritus 3.5 x 10- 2 day - 1

(the bottom) 5.5 x 10- 5 d a y - maximum migration speed of Chattonella 3.5 x 10- 2 cm s - 1 maximum migration speed of zooplankton 2.1 x 10- 2 cm s - 1 diffusion coefficients 1.0 x 106 vertical diffusion coefficients 0.1

TABLE 8

Initial values used in the three-dimensional model

Symbols Definitions Values

P inorganic phosphorus 7.0/~g P cm -3 N inorganic nitrogen 65.0/tg N cm-3 PH1 Chattonella 60.0/xg C cm -3 PH2 diatoms 60.0 Fg C cm -3 Z zooplankton 3.5/~g C cm -3 D1, phosphorus in detritus 10.0/~g P cm -3

(the bottom) 6.5 mg P cm -2 D N nitrogen in detritus 120.0 #g N cm -3

(the bottom) 0.5 mg N cm -2

"(~oLI [1301.l.IOA) StOKe l

0~1 UOO/aloq (O) pu~ '~0,(~1 aO~OI (q) '.pu!ax OU ql!~ aO,~eI aoddn (e) :u! lenp!soa IePLL "*eI "~!~1

===================================== F:;~*~ :::~.*:= ~

-~:.;!ili!!!!;iiiiiii ,~)

h ~i'::::::::::::"='"'"'"'iiii~iii: :~": ~i i i! I: ::::: ::: :~~'~"-J ~-'~::: :{ "'"" "" '"'" "' ': ....... :':: : :';:'~" ":" :" :" '' ' " ~

~~;~5 !ii~ :A ??i .......... ~.;,:,/-'-"

":'^",t::: ",. ,,. (o)

.... " ......... i!iiiiiii

~~:?i?ii:i:i::i?i! ?:

j-. o,~

~9[

166

Fig. 15. Constant flow in the upper layer of the Harima Sea (Yanagi, 1982).

ho r i zon ta l d i s t r ibu t ion of Chattonella antiqua ( the m e a n value in 24 h on the 3rd d a y f r o m the init ial state) is qui te d i f fe ren t f r o m the d i s t r ibu t iona l

p a t t e r n of the nu t r i en t s as shown in Fig. 18. F igures 19a and 20a are the

d i s t r ibu t ions of Chattonella antiqua at the u p p e r layer w i thou t a n d wi th wind force, respect ively, and Figs. 19b a n d 20b are those at the lower layer , respect ively.

TABLE 9

Boundary conditions used in tidal current computations

Symbols Definitions Values

(Bisan Seto) ~0 height of a mean surface A amplitude of tidal current

from outside o~ angular velocity K phase angle

(Kii Channel) ~o height of a mean surface A amplitude of tidal current

from outside co angular velocity K phase angle

0.0 cm 89.0 cm

8.333 × 10 -3 degree s- 1 90.0 degree

0.0 cm 42.0

(Shikoku) 8.333 × 1 0 - 3 degree s -1

- 63.0 degree (Shikoku)

- 46.0 cm (Wakayama)

- 55.0 degree (Wakayama)

167

.... _., FI.FI ......

I ' U ~ ' : ' ~ _ . - . . . . "_5- D . ~ - - , , ~ 3 " ~ ' ~ \ . - , : - , I

t ' ' ~ . - . , . " - - - • , ~ ~. . , ~ , ~

N[NB D A T A ( l g T O . ' l . 2 q 1 lOOCt~IS

: : : ~ : : : :: :: : :: :: : ~ Y / / / / / . . / / / / / / X X / . x / / / / _ . ~ - ' ~ _

~ ~. i ! ! i ~ ~./Y//~////// - .

Fig. 16. Calculated tidal residual current in Harima-nada in the case with surface wind based on the data of meteorological stations on 24 July 1978.

In the case without wind, the dense population of Chattonella antiqua can be seen at the center of Harima Sea and Osaka Bay (Fig. 19a). In the case with wind, however, the densely populated area moves toward the east in the

168

T A B L E 10

Parameter values used in tidal current computa t ions

Symbols Defini t ions Values

7~ drag coefficient 1.3 x 1 0 - 3 yi 2 interlayer friction coefficient 1.3 x 10-3 72 bo t tom friction coefficient 2.6 x 1 0 - 3 Pa air densi ty 1.3 x 10 -3 f coriolis pa ramete r 8.3 x 10-5 A H eddy friction coefficient 1.0 x 10 + 5 K x, Ky eddy diffusion coefficients 1.0 × 10 + 5 K z vertical diffusion coefficient 5.0 X 1 0 - 2

g c m - 3

rad s - 1 c m 2 S -1 cm 2 s - 1 cm 2 s - 1

upper layer, because of wind-induced currents (Fig. 20a). In the lower layer, there are no dense patches of Chattonella antiqua due to the vertical migration of the phytoplankton (Figs. 19b and 20b). However, the phyto- plankton of other types such as diatoms has a more dense population than Chattonella antiqua at the northern part of the Harima Sea (Fig. 21). These results are in comparatively good agreement with the field observation of 26-28 July 1978 which detected a large-scale 'red tide' at the eastern part of Harima Sea as is schematically shown in Fig. 11 (Okaichi, 1982).

I 1

I

1

2

3

Harim Sea ~ Osaka ~y /

/

Fig. 17. Nutr ient loading points (Nos. 1-12).

TABLE 11

Nutrient loads (Nos. 1-12)

169

No. (t/day)

P N

1 1.3 17.2 2 2.1 27.8 3 1.5 19.8 4 1.2 13.0 5 2.0 24.4 6 7.0 62.7 7 3.4 62.7 8 2.1 31.4 9 0.9 10.7

10 0.1 1.1 11 1.4 18.0 12 0.7 10.0

Discussion

The calculated results shown here are the daily mean values on the 3rd day of the calculation following the uniform initial state. The numerical values of initial state displayed in Table 8 are assummed to be a kind of steady-state solution where the ecosystem has already reached some steady conditions. The additional nutrient inputs from rivers, winds or tides will change that steady-state into a different steady-state (see Figs. 17-21). To get a new steady-state solution in such a large area would take a very large computation interval, for example, at least more than 14 days in terms of stabilization of the computation. Hence it should be noted that the results shown here describe only some of the transient states after 3 days from the uniform state. Figure 22 illustrates a trend of phytoplankton concentrations at the point (30, 18, 1) located at the center of the Harima Sea for the period of four tidal cycles. For the analysis of 'red tide' outbreaks, it would be extremely important to have such good parameter values in the ecological- hydraulic structure that could stabilize a computation scheme of equations (3.1)-(3.8) within the blooming interval of several days.

CONCLUSION

The research project of 'Red Tides Outbreaks in Japanese Coastal Waters' started in 1979, headed by Professor T. Okaichi of Kagawa University. Since then, much effort has been made to obtain numerical values of biological parameters that are supposed to be associated with the generation mecha-

C~

(d)

l't

O

--k "1

. ..

.._:

i=

.1

H

Fig.

18.

Dis

trib

utio

n of

ino

rgan

ic P

(a,

lay

er 1

; b,

lay

er 2

) an

d in

orga

nic

N (

c, l

ayer

1;

d, l

ayer

2).

J

~J..

I-I QD

(b)

~II

IIII

o

~ 4I

~0

?2

8~

~g

14

.1

Fig.

19.

Dis

trib

utio

n of

Cha

ttone

lla w

itho

ut w

ind

(a,

laye

r 1;

b,

laye

r 2)

.

(b)

o 36

48

~o

72

e4

~

#glt

---.I

Fig.

20.

Dis

trib

utio

n of

Cha

ttone

lla w

ith

win

d (a

, la

yer

1; b

, la

yer

2).

:ig.

21.

Dis

trib

utio

n of

dia

tom

s (a

, la

yer

1; b

, la

yer

2).

173

I

° ............... 7 - - . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i i i . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . E . : . ,

. . " .

CD: ~-~ ~ z,,2,o~,.~ooeZZ~e e**,.Z 0.0. . . . . . .°°.i "/°7 Z °.a. 0.°o~z~,°~'oe~ZLoe,°0.E

* Chattonella antiqua 0 Diatom Point (30,18, l ) : upper layer 9. Total phosphorus I I I

1 2 3 tidal cycle

Fig. 22. Calculated trends of phytoplankton concentration at the center of the Harima Sea for

four tidal cycles.

nism of 'red tide' (Okaichi, 1982; 1984)• Using such values of biological parameters and physical conditions studied by other members of the project team, we constructed a system of simulation models.

The numerical experiments carried out by our three models have shown: (1) The amount of nutrients and oceanographic characteristics of the sea are

basic factors influencing the rapid increase in phytoplankton population• (2) The opposing migration of both phyto- and zooplankton in the vertical

direction according to a l ight/dark cycle causes a dense phytoplankton population in the upper layer•

(3) The tidal current plus the water movement induced by the wind has a great impact on phytoplankton dynamics.

However, we have not yet tested other cases where factors of inorganic or metallic matters such as vitamin B12 and ferrous matter from botton deposits are taken into the mechanism of a 'red tide' outbreak. Although it is widely accepted that those factors play an important part in the primary production, it is extremely difficult to establish a quantitative relationship between those factors and the growth-rate function• There have been few field studies on this problem except a couple of pioneer works (Nakamura and Watanabe 1983a; Hata and Nishijima, 1982)• Further work is necessary to establish the impacts of these uncertain factors on the generation mecha- nism of 'red tide', both by numerical experiments and field observations.

ACKNOWLEDGEMENT

This study is supported by the special research program on the Environ- mental Science funded by the Ministry of Education, Japan. We wish to express our sincere thanks to Professor Toshiyuki Hirano, University of

174

T o k y o for his gu idance in deve lop ing our mode l l i ng work, and also to Mr. H a j i m e N i s h i m u r a , g r a d u a t e s tudent , K y o t o Univers i ty , for his va luab le

ass i s tance in c o n d u c t i n g the c o m p u t e r s imula t ions . O u r g ra t i tude is also due to all m e m b e r s of the ' r e d t ide ' p r o b l e m pro jec t t e a m headed b y Pro fesso r

T o m o t o s h i Okaichi , K a g a w a Univers i ty .

REFERENCES

Hata, Y. and Nishijima, T., 1982. Distribution of aerobic heterotrophic bacteria and B group vitamins in Harima-Sea. In: T. Okaichi (Editor), Fundamental Studies on the Effects of Marine Environment on the Outbreaks of Red Tides. Res. Rep. Environ. Sci. B148-R14-8, Ministry of Education, Japan, pp. 109-119.

Iizuka, S., 1980. Red tide - - occurrence mechanism and control. In: Jpn. Soc. Fish. Ser. 34, Koseisha Koseikaku Publ., pp. 38-49 (in Japanese).

Ikeda, S. and Yokoi, T., 1980. Fish population dynamics under nutrient enrichment - - a case of the East Seto Inland Sea. Ecol. Modelling, 10: 141-165.

Kishi, M.J., Nakata, K. and Ishikawa, K., 1981. Sensitivity analysis of coastal marine ecosystems. J. Oceanogr. Soc. Jpn., 37: 120-134.

Nakamura, Y. and Watanabe, M., 1983a. Growth characteristics of Chattonella antiqua. J. Oceanogr. Soc. Jpn., 39: 110-114.

Nakamura, Y. and Watanabe, M., 1983b. Nitrate and phosphate uptake kinetics of Chat- tonella antiqua grown in light/dark cycles. J. Oceanogr. Soc. Jpn., 39: 167-170.

Okaichi, T. (Editor), 1982. Fundamental Studies on the Effect of Marine Environment on the Outbreaks of Red Tides. Res. Rep. Environ. Sci. B148-R14-8, Ministry of Education, Japan, 239 pp.

Okaichi, T., 1983. Marine environmental studies on outbreaks of red tides in neritic waters. J. Oceanogr. Soc. Jpn., 39: 267-275.

Okaichi, T. (Editor), 1985. Fundamental Studies on the Modeling of Ecophysical Environ- ment in Relation with Red Tides. Res. Rep. Environ. Sci. B264-R14-1, Ministry of Education, Japan, 190 pp.

Steel, J. and Henderson, E., 1977. Plankton patch in the North Sea. In: J. Steel (Editor), Fishery Mathematics. Academic Press, New York, NY, pp. 1-9.

Walsh, J., 1977. A biological sketchbook for an eastern boundary current. In: The Sea. Vol., Marine Modeling, Wiley-Interscience, New York, NY, pp. 923-968.

Wroblewski, J.S. and O'Brien, J.J., 1976. A spatial model of phytoplankton patchiness. Mar. Biol., 35: 357-394.

Yanagi, T., 1982. The ocean characteristics and their change in the Seto Inland Sea. Mer, 20: 170-177.