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New Numerical Model Study on a Tidal Flat System – Seasonal, Daily and Tidal Variations
Spill Science & Technology Bulletin, Vol. 6, No. 2, pp. 173±185, 2000 Ó 2000 Published by Elsevier Science Ltd. All rights reserved. Printed in Great Britain 1353-2561/00 $ - see front matter
PII: S1353-2561(00)00070-0
New Numerical Model Study on a Tidal Flat System ± Seasonal, Daily and Tidal Variations AKIO SOHMA *, TATSUAKI SATO , KISABURO NAKATAà Fuji Research Institute Corporation, Tokyo, Japan àTokai University, Shizuoka, Japan We developed a new numerical model to investigate the dynamics of tidal ¯at ecosystems and their role in water quality in terms of the carbon cycle. This model was applied to Isshiki, a natural tidal ¯at area, which is the largest in Mikawa Bay, Japan. This model dealt with variations of biochemical or physical interaction among dissolved oxygen and C± N±P species (comprised of carbon, nitrogen, and phosphorus elements) both on a short-time scale (<24 h) as well as over a long-time scale (seasonal variation). The model indicated that the time dependence on phytoplankton, NH4 ±N, NOx ±N, and PO4 ±P are more sensitive to daily environmental variation than to seasonal environmental variation. This means that the rotation speed of these materials in the tidal ¯at area is fast. Here, we de®ned the rotation speed as the ratio of total ¯uxes of substance to the mass of the substance. Phytoplankton with a high rotation speed in the tidal ¯at area means that the tidal ¯at has the potential to recover from rapidly increasing phytoplankton: red tide. The model also indicated that the peculiar feature of the tidal ¯at is the mineralization of organic material. The eect on a long term base, is that it prevents the accumulation of sediment, which results in controlling the increase of oxygen consumption in benthic system, which is the cause of oxygen depleted water. Ó 2000 Published by Elsevier Science Ltd. All rights reserved.
Introduction Much attention has been paid to the role and the eect of tidal ¯ats on the quality of sea water in tidal estuaries, especially those experiencing a rapid increase in the frequency of red tides and oxygen depleted water masses. Mikawa Bay is one of the most eutrophic estuaries in Japan. Ishida and Hara (1996), and Aoyama and Suzuki (1996) indicated that eutrophication is getting worse in Mikawa Bay, not only because of increasing nutrients (loads) from rivers, but also from a reduction in natural water puri®cation which results from loss of parts of the tidal ¯at area (wetlands). Suzuki and Matsukawa (1987) estimated the budget of nitrogen and dissolved oxygen of Isshiki, a natural tidal ¯at
*Corresponding author.
area, in Mikawa Bay and indicated that tidal ¯at system has become a storeroom of nutrients and a supply of dissolved oxygen, especially in summer, when eutrophication tends to be at its worst. Using a material budget model (Sasaki, 1989; Aoyama and Suzuki, 1996) estimated Isshiki's removable ability of total nitrogen and dissolved oxygen. A useful method to investigate the Isshiki tidal ¯at system, is to apply the numerical ecosystem model, which formulates dynamics of interaction among dissolved oxygen and C±N±P species (compositions formed out of carbon, nitrogen, and phosphorus elements). It is possible for models to simulate the dynamics of the circulation of carbon, nitrogen, and phosphorus elements in the system. Recently, numerical ecosystem models have been applied in several studies on oxygen depleted water masses and eutrophication, and are used as a tool of environmental assessment and management. Kremer 173
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and Nixon (1978) published a numerical coastal marine ecosystem model of Narragansett Bay, USA. This model emphasized carbon circulation in the pelagic system from the viewpoint of being plankton-based. It also described interactions among special compartments in the pelagic system and interactions across the boundaries of the system. In general, most numerical models for coastal marine ecosystem are composed of pelagic system and the benthic variables are given as boundary conditions. Thus, interactions between the benthic and pelagic systems cannot be analyzed. However, this may not matter very much since these model systems are viewed as being plankton-based. In tidal ¯at systems, the in¯uence of interaction between the benthic and pelagic system becomes important. Baretta and Ruardij (1988) and Barreta et al. (1996) produced a numerical model and applied it to Ems estuary, Holland, where the tidal ¯at systems are situated. Their model was constructed with pelagic, benthic, and epibenthic submodels and simulated the seasonal variations in the tidal ¯at systems. Nakata and Hata (1991, 1996) produced a tidal ¯at ecosystem model of Banzu, Tokyo Bay, Japan, focusing on nitrogen circulation. This model emphasized the benthic ecosystem. Suzuki et al. (1997) applied this model to Isshiki and estimated the removable ability of nitrogen in summer. In this paper, we report the new numerical ecosystem model produced for tidal ¯at systems and the new model study on the tidal ¯at system, Isshiki. One of the characteristic points of the new model is that it simulates the dynamics and periodical variation, which can be shown only over a short-time scale (<24 h). We also report the feature of the tidal ¯at's eect to the quality of the seawater, quantitatively.
Model Concepts and Construction Basic features of the model The model is composed of a benthic system (benthic submodel) and a pelagic system (pelagic submodel). Pelagic submodel treats the transport of water caused by tide. The model is described by partial dierential equations based on conservation of carbon mass. We included processes of diusion, physical advection, and biochemical reactions in these equations. In this model, there are compartments which means several C±N±P species. Compartments and biochemical reactions in this model are mainly composed from the viewpoint that emphasize primary productive processes both in pelagic and in benthic and early diagenetic processes. Biochemical reactions are formulated from temperature, intensity of daylight, concentration 174
of dissolved oxygen, and concentration of compartments (C±N±P species) at every time step of calculation. Even though temperature and intensity of daylight are taken as prescribed functions, which have several periodical variations, compartments (C±N±P species), dissolved oxygen, oxygen consumption from benthic system and thickness of oxygen layer in benthic system are calculated at every time step in this model. This structure means that the interactions of a compartment (a C±N±P species) with other compartments (other C±N±P species) and dissolved oxygen varies at every time step and these dynamics of interactions aect the time dependence of variation of the tidal ¯at system. One of the most characteristic aspects of the tidal ¯at system is the tidal submersion/emersion of the ¯ats, which makes the system more complicated. Besides this feature including the complexity of the physical processes, the coincidence of the daylight period and the submersion of the tidal ¯ats causes a shortening of the eective photosynthesis period for the phytobentos. For the phytobentos and phytoplankton in the tidal ¯at areas, depth variation of covered water caused by tide obviously makes a dierence, because the depth at tidal ¯at is very shallow. From these reasons, time scales of the dynamics period of photosynthesis ¯uxes become <24 h. And from the basic calculation, we conjecture that the amplitude of periodical ¯ux dynamics in 24 h ( short-time scale) has enough mass to in¯uence the dynamics of tidal ¯at's total system compared with other ¯uxes. To con®rm and estimate the in¯uence of the periodical variations over a short time, we must calculate the model with time-step <24 h. We also take into account the two dierences from emerged area to submerged area in a model, which are considered to aect the biochemical processes treated in this model directly. One is the dierence of oxygen supply to the benthic system. An emerged area has a more ready supply of oxygen than a submerged area. Another is the dierence in mud temperature, especially in summer. This phenomenon is important for biochemical reactions which depend on temperature.
Construction of boxes in the model When we apply this model to Isshiki tidal ¯at, the model is composed of two boxes and these boxes are connected one dimensionally in the plane direction. The two boxes represent the pelagic and benthic system. The benthic system has three layers in the vertical direction. The upper layer of benthic system consists Spill Science & Technology Bulletin 6(2)
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of an oxygen layer and a deoxidization layer. The second and third layers of the benthic system are deoxidization layers. The coordinates of the boundary point between oxygen layer and deoxidization layer is calculated at every time-step. The thickness of oxygen layer has an in¯uence on the several biochemical reactions (detritus mineralization, nitri®cation etc.) whose formulations are distinguished between oxygen layer and deoxidization layer. Box 1, shown on the right-hand side of Fig. 1, represents the area which can be emerged when the spring tide is at its lowest and can be submerged when the spring tide is at its highest. This box is composed of area 1: emerging area, and area 2: submerging area. The boundary of these areas varies along the water level caused by tide. Box 2, represents the area, which cannot be emerged and where the maximum depth, (depth from the sea surface to sea bottom) is 3 m when the spring tide is at its lowest. We also call box 2, area 3 (Figs. 2 & 3).
Formulation of geographical features (geographical function) To calculate the coordinates of the boundary between area 1 and 2, formulation of geographical feature is necessary. In this model, geographical feature is formulated by the function, water level n t vs square measure of submersion area Sw (n), where both values are zero when the water level is the lowest level of spring tide. We call this function as geographical function. n t is the periodical function and the period is 12 h 25 min. From this function, we can calculate several variables as ®gured in Table 1. Treatment of the time lag between daylight and tidal submersion/emersion The time lag (50 min) between the daily period (24 h) and twice the tidal period (24 h 50 min), the change of the daytime length in compliance with
Fig. 1 Diagram of a tidal ¯at ecosystem.
Fig. 2 Construction of boxes in the horizontal direction.
Fig. 3 Construction of boxes in the vertical direction. Spill Science & Technology Bulletin 6(2)
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AKIO SOHMA et al. Table 1 Information relevant to the geographical function n t n t Tn;
T 12 h 25 min : n
Sw n t
Sw n t : Sd n t Sw n t : Stot ÿ Sw n t Stot m2 : total of square measure of box 1 Sd n t m2 : square measure of emerged area Sw n t m2 : square measure of submerged area Z h t Vw n t Sw n t dh 0
Vw n t m3 : volume of submerged area depwat n t
Vw n t Sw n t
depwat n t cm: averaged depth of submerged area L1 L10
Sw n t Stot
L1: scale of submerged area in the direction of horizontal L10 : scale of box 1 in the direction of horizontal
season and the dierences of tide level between spring tide and neap tide vary the timing of the coincidence of daylight and submersion. To consider the variation of this timing in this model, we inputted the tide level and the time of sunrise for the season when the simulation began. Also we divided the running period of 24 h into separate time steps (e.g.: if a time step is to be 1 h, then the number of time separators is 24). By this, we can calculate the square measure of emersion area from the geographical function (Fig. 4) in each time separation. Compartments and ¯uxes in the model Circulation treated in one box of this model is shown in Fig. 5. Compartments, treating C±N±P
species in this model, are shown as boxes and the ¯uxes of biochemical reactions and transport processes are represented by arrows in Fig. 5. The concentration of each compartment, without seagrass and seaweed, is calculated at every time step. Changes in concentration of these compartments were caused by ¯uxes going in and out. Fluxes of biochemical reactions in one compartment are formulated with concentration of other compartments, temperature, intensity of light, and water-depth etc. at each timestep of calculation. Seagrass and seaweed were taken as prescribed seasonal periodical functions. Model equations for special Compartments In general, concentration changes of all compartments dependent on time are given in Table 2. The terms of these equations are: (1) advection from water transport caused by tides or rivers; (2) diusion from turbulent ¯ow of water; (3) advection from sediment deposition; (4) diusion from bioturbation and molecular motion; (5) biochemical reactions. Fluxes of (1) and (2) are horizontal, and ¯uxes of (3) and (4) are vertical. Compartments which exist only in the benthic system do not take into account the ¯uxes of (1) and (2). To describe changes of (4) in the model, the diffusive coecient for the benthic system is formulated by using a molecular diusion coecient dependent on temperature and concentration of suspension feeders and deposit feeders. Although the horizontal scale for the submerged part of box 1 varies every time, the diusive coecient in pelagic system is a function of the horizontal scale. Model equations for dissolved oxygen Concentration of dissolved oxygen in the pelagic system is determined from: (1) advection from water transport caused by the tide or river; (2) diusion from turbulent ¯ow of water; (3) total of oxygen consumption and production from both the pelagic system and the benthic system, which is calculated at each time-step. Processes of oxygen consumption and pro-
Fig. 4 Treatment of the time lag between daylight and tidal submersion/emersion. 176
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Fig. 5 Treatment of circulation in one box of the model.
duction can be calculated from biochemical reactions of compartment. In the benthic system, the oxygen layer and the deoxidization layer are de®ned (refer to Section: construction of boxes in the model). The way to solve the thickness of oxygen layer in benthic system is indicated in Table 3. The boundary between the oxygen layer and the deoxidization layer is calculated from (4) the concentration of dissolved oxygen in the pelagic system (5) total of oxygen consumption and production in the benthic system. (4) is the boundary condition of equation for the benthic system. In the emerged area, this boundary condition is based on the theory that there is a diusive boundary layer between air and water. To solve equation in benthic system, we chose and de®ned process (5) from process (3). Using this method, total mass of dissolved oxygen in the system was conserved. In the case that the total oxygen consumption in benthic system is less than the total production of oxygen in benthic system, the thickness of the oxygen layer, the solution of equation in benthic system, diverges to in®nity, and the model makes the thickness of oxygen layer equal to thickness in 1st layer. This also means that the thickness of 1st layer is the maximum thickness of oxygen layer. Spill Science & Technology Bulletin 6(2)
Calculation Boundary condition, prescribed function and initial value To run the model, we need to input initial values of compartments, several boundary conditions and prescribed functions. Tide level was taken from the component tides, M2, S2, O1, K1, results of the harmonic analysis of tide. Intensity of daylight is analyzed for two time scales. One is the variation within one day, daytime and nighttime, and the other is the seasonal variation. On the simulation, it is assumed that the variables which were taken as boundary conditions and prescribed functions except for the tide level and intensity of daylight, will not change for several years. These variables are taken from observed data averaged over the last ®ve years. In other words, the model is simulated for a standard year. So they are ®tted with f(t) shown below, which has the period of 1 yr. The number n must be less than the number of observations in a year. f t p0
X an sin nxt bn cos nxt: n
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AKIO SOHMA et al. Table 2 Model equations for special compartments (a) Equations for the compartments representing dissolved substances Pelagic system: 0th layer 0 1 Z X X o dep Cn o Cn o B oCn C o Ln ÿ @ u dz Cn A ÿ /Dz;n dep Dx dep Gn ÿ ot ox ox oz ox z0
dep
Benthic system: 1st layer X X oCn oCn /Dz;n G1;n ÿ L1;n ÿ /Dz;n / h1 oz oz z0 zz1
o Cn h1 / ot
Benthic system: 2nd layer X X o Cn h2 oCn oCn /Dz;n / L2;n G2;n ÿ ÿ /D / h2 z;n ot oz zz1 oz zz2 Benthic system: 3rd layer /
o Cn h3 ot
X X oCn oCn /Dz;n L3;n G3;n ÿ ÿ /Dz;n / h3 oz oz zz2 zz3
(b) Equations for the compartment representing particulate substances Pelagic system: 0th layer 0 1 Z X X o dep Pn o Pn o B oPn C o Ln W0;n ÿ W1;n ÿ /Dz;n depDx ÿ @ u dz Pn A dep Gn ÿ ot ox ox oz ox z0
dep
Benthic system: 1st layer X X o Pn h1 oPn oPn L1;n W1;n ÿ W2;n 1 ÿ / 1 ÿ /Dz;n ÿ 1 ÿ /D h1 1 ÿ / G1;n ÿ z;n ot oz z0 oz zz1 Benthic system: 2nd layer X X o Pn h2 oPn oPn 1 ÿ / 1 ÿ /Dz;n L2;n W2;n ÿ W3;n ÿ 1 ÿ /Dz;n h2 1 ÿ / G2;n ÿ ot oz zz1 oz zz2 Benthic system: 3rd layer 1 ÿ /
o Pn h3 ot
X X oPn oPn L3;n W3;n ÿ W4;n 1 ÿ /Dz;n ÿ 1 ÿ /Dz;n h3 1 ÿ / G3;n ÿ oz zz2 oz zz3
Cn lg=ml: concentration of nth compartment of dissolved substances Pn lg=cm3 D: concentration of nth compartment of particulate substances Dz;n cm2 =day: diusive coecient caused by bioturbation and molecular diusion Dx cm2 =day: diusive coecient caused by turbulent ¯ow of water dep cm: water depth u cm=h: velocity of water ¯ow P P Gn : total of the terms of increased biochemical reactions Ln : total of the terms of decreased biochemical reactions /: porosity Wk;n : advection caused by sedimentation
Initial values of compartments were taken from observed data collected in summer, 15±17 August 1997.
Biochemical parameters Equations for biochemical reactions include several biochemical parameters. We investigated a range of values for these parameters that have been observed 178
until now and set those parameters within that range. Values were given to the unknown parameters to validate the simulation. The results of the simulation in terms of the concentrations in the compartments and ¯uxes of the biochemical reactions that seemed unreasonable in comparison to the observed values indicated where the parameters needed tuning. Using this process, values for the unknown parameters were predicted from the results of the simulation. Spill Science & Technology Bulletin 6(2)
NEW NUMERICAL MODEL STUDY ON A TIDAL FLAT SYSTEM Table 3 Equations for dissolved oxygen Equation for concentration of dissolved oxygen (1) Equation in pelagic system 0 1 Z X X o dep DOn o DOn o B oDOn C o ÿ /Dz;n depD dep Gn ÿ Ln ÿ u dz DO @ A n x ot o x o x oz ox dep z0 (2) Equation in benthic system Changes of concentration of dissolved oxygen depending on time X o DO o2 DO X Dz Gbenthic ÿ Lbenthic ot o z2 Assumption 1:
o DO o z Z0
0
Assumption 2: DO Z0 0 Assumption 3: DO 0 DO0 From these assumptions, equation in benthic system can be solved below: P P r L LZ0 z DO0 , In oxygen layer DO 13 DO0 DO Z 2Dz Z 2 ÿ Dz Z DO0 , Z0 ÿ 2DP L X X Gbenthic ÿ Lbenthic photosynthesis of benthic algae ± excretion of benthic algae ± mineralization of detritus in oxygen layer ± nitrification in benthic system ± oxidation of oxygen demand materials Oxygen consumption and production are calculated from ¯uxes of biochemical reactions of compartments to use the chemical formulation which is indicated below 2ÿ CH2 Om NH3 nH3 PO4 m 2nO2 ! m CO2 n NOÿ 3 HPO4 m nH2 O n 2H Trace Element Energy
O:C (mass ratio of element) 32 m 2n=12m 2NH3 3O2 ! 2HNO2 2H2 O;
2HNO2 O2 ! 2HNO3
O:N (mass ratio of element) 32/7 DO mgO2 =l: concentration of dissolved oxygen 2 D P diusion coecient of dissolved oxygen Pz cm =day: Gbenthic ÿ Lbenthic : total of the oxygen consumption and production in benthic system
Time-step, time scale of parameters and length of layer We set the time-step of the calculation to 12 min and set the thickness of each layer as follows: 1st and 2nd layers at 1 cm, and layer 3 at 8 cm in the vertical.
Result and Discussion In this section, ®rst, we demonstrate the steadiness of the simulation, and show the periodical variation for three time scales, daily (24 h), tidal between spring tide and neap tide (15 days) and seasonal (1 yr). It is possible to explain the causes of variations in each compartment, but in this paper, we con®ne our argument to the variations of only several compartments. We discuss daytime scale variation, in detail. (Depending on the viewpoint, there are dierent explanations for the variability of compartments. The roots of variations of compartments cannot be de®ned in a correct meaning, because interactions between compartments and dynamics of compartments are not determined independently but in¯uences each other Spill Science & Technology Bulletin 6(2)
mutual in¯uences every time. Thus, the explanation which is indicated in this paper comes from one of the viewpoints.) Steadiness of result of simulation Periodical variation of compartments, more or less, reaches a steady state within 3 yr. On behalf of benthic and pelagic systems, variability in the concentration of phytoplankton and benthic algae are shown in Fig. 6, which indicates the state becoming steady. Discussion on variation in daily time scale (24 h) The simulation results for the submerged area in box 1, which focuses on the variation over a daily time-scale, from 1 August, 12:00 to 3 August, 0:00, summer, is shown in Figs. 7 & 8. In the following sections, we analyze the causes of variation for phytoplankton, organic carbon, and NOx in the pelagic system; benthic algae in the benthic system; and NH4 compartments in both pelagic and benthic systems. 179
AKIO SOHMA et al.
Fig. 6 Steadiness of compartments (plotting data is extracted results per day).
Fig. 7 Variation in the pelagic on a daily time scale (24 h) (values of the tide level and the intensity of light are relative values).
Phytoplankton in the pelagic system. The variation in phytoplankton mainly depends on production from photosynthesis, the input ¯ows from box 2, and feeding by suspension feeders. Phytoplankton biomass decreased through suspension feeding, but increased when the tide level rose through the water ¯ow input from box 2. The eect, increasing ¯ux of photosynthesis when the depth is shallow, cannot be omitted. Organic carbon in the pelagic system. The variation in organic carbon in pelagic system mainly depends on feeding by suspension feeders and the input ¯ows from box 2 and the river. The concentration of organic carbon roughly ¯uctuates with tide level. That is, feeding by suspension appears more conspicuously when the tide level is low than when the level is high. The minimum during night is sharper than the minimum during daytime. In other words, the decreasing rate of organic carbon at daytime becomes less than at 180
night, relatively. This is because phytoplankton during daytime is more active than at night and supplies the organic carbon from the process of excretion. The lower the water level becomes, the more the load from the river aects the concentration of organic carbon. This explains why the timing between the maximum and minimum of the carbon concentration becomes closer. NH4 in the pelagic system. The concentration of NH4 reaches a maximum at roughly the same time as the tide reaches its lowest level. This can be explained by the following; the eect of the load from river on the concentration of NH4 is more eective when the tide level is low: the water mass of submerged area in box 1 is less than when the tide level is high. In addition, during the night, decreasing eect coming from photosynthesis of phytoplankton does not exit, but during the day, decreasing eect to the concentration of NH4 becomes stronger. On the other hand, in the Spill Science & Technology Bulletin 6(2)
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Fig. 8 Variations in the benthic system on a daily time scale (24 h) (values of the tide level and the intensity of light are relative values).
benthic system, photosynthesis by benthic algae make a larger dierence to the concentration of NH4 in the benthic layer between daytime and nighttime. This phenomenon makes diusive ¯ux of NH4 from benthic system dierent between daytime and nighttime (detail written below). In general, under the situation that the tide level is low and the NH4 concentration in benthic system is high, the concentration of NH4 in pelagic system becomes high level. HNOx in the pelagic system. Comparing the variation in the concentrations of HNOx and NH4 , when the tide level is at its lowest during the day, HNOx reaches its maximum whereas NH4 is decreasing. This dierence can be traced to them being in dierent concentrations in the river nutrient load. The concentration of HNOx in river water is about eight times as much as the NH4 in August. This eect is stronger when the tide level is low, and makes a decreasing in¯uence caused by photosynthesis of phytoplankton to disappear. The cause of maximum when the tide level is lowest during night is the same as the case of NH4 . Dierences in the minimum value of the tide level between day and night means that Spill Science & Technology Bulletin 6(2)
the maximum value during the day is more than that it is at night. Dissolved oxygen. During the day, in particular, the dissolved oxygen concentration exceeds saturation point due to photosynthesis. Benthic algae. Photosynthesis by benthic algae is formulated by the half-saturated function. When the tide level is high, it is more dicult for daylight to reach the benthic system than when the tide level is low. Thus, the relationship between the tide level and daytime aects the variation of photosynthesis by benthic algae. Dissolved NH4 in the benthic system. Variation in dissolved NH4 over a daily period in the 1st layer results from the photosynthesis by benthic algae. Benthic algae uses NH4 in the ®rst layer in photosynthesis. Increasing ratio going up at the time of minimum point of tide level during night, is caused by decreasing the ¯ux to the pelagic system. Flux decreasing comes from the concentration of NH4 in pelagic system increasing. The in¯uence of NH4 from the river appeared more conspicuously when the tide level was 181
AKIO SOHMA et al.
low because the water volume in box 1 was smaller than when the tide level was high. Vibration whose time scale is about Dt is the phenomena caused by discrete quantity of time. The instantaneous ¯ux by photosynthesis is more compared to the pool of NH4 in the 1st layer in relative. Thus, NH4 in the 1st layer becomes scarce and this limits photosynthesis by benthic algae in the next calculating time t Dt. Other biochemical ¯uxes which produced NH4 , do not have obvious change during Dt. These are the explanations of vibration of Dt time scale. Using the concept of cell quarter, the instantaneous shortage of NH4 at 1st layer during daytime is taken during night in this model, and conserves the mass of elements. It is natural to think that in the real system, the NH4 takes the center of amplitude.
nutrient load from the river, the time lag between the tidal period and daylight period, and the mass of seaweed and seagrass. Circulation of nitrogen We demonstrated that the main ¯uxes of nitrogenous elements over 15 days of summer which was calculated from the results of the simulation of the model shown in Fig. 13. From this result, we can see one peculiar feature of the tidal ¯at is the mineralization of organic materials.
Conclusions and Remarks
Discussion on variation in time scale between spring and neap tide (15 days)
From the computational results of this model, we classify and arrange the role of the tidal ¯at area on coastal water quality into short-time and long-time scale.
Variation over a 15 day period in the compartments shown in Figs. 9 & 10 can largely be explained by the dierences in tidal levels between spring and neap tides.
Role of the tidal ¯at area seen from a short-time scale
Discussion on variation in seasonal time scale (1 yr) Variation over a 1 yr time-scale in the compartments shown in Figs. 11 & 12 can largely be explained by seasonal variation in temperature, intensity of light,
By looking at the time ¯uctuation of phytoplankton, NH4 ±N, NOx ±N, and PO4 ±P, we see that in tidal ¯at area, the amplitude of daily or 15 day periodical ¯uctuation is larger than that of seasonal. This means that the rotation speed of these compartments in the tidal ¯at area is fast. Here, we de®ned the rotation speed as the ratio of total ¯uxes of compartments to
Fig. 9 Variations in the pelagic system over a spring to neap tide scale (15 days) (values of the tide level and the intensity of light are relative values). 182
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Fig. 10 Variations in the benthic system over a spring to neap tide scale (15 days) (values of the tide level and the intensity of light are relative values).
Fig. 11 Variations in the pelagic system over a seasonal time scale (1 yr). Spill Science & Technology Bulletin 6(2)
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Fig. 12 Variations in benthic system over a seasonal time scale (1 yr).
Fig. 13 Main ¯uxes averaged for 15 days in summer based on nitrogen at Isshiki (submerged area: 6.07 km2 submerged/emerged area: 4.61 km2 ). 184
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the mass of compartments. When an impact such as red tide, namely, a sudden increase in phytoplankton occurs, a tidal ¯at with a large ¯ux able to remove that, improves the balance of the ecosystem in short time. Thus, the fast rotation speed of phytoplankton in the tidal ¯at suggests the possibility of retaining a sound ecological circulation. From a dierent perspective, if we were to lose tidal ¯ats, compartments where the rotation speed is high, there is a possibility of phytoplankton suddenly increasing, meaning that there is a possibility of a red tide to occur. Role of the tidal ¯at area seen from a long-time scale From the computational results of the model, the rotation speed of the organic material of sediment is slow. Therefore, time ¯uctuation for the organic material of sediment on a long-time scale becomes vital. From the material balance, the tidal ¯at is where organic substances become inorganic. The eect, on a long-term base, is that it prevents the accumulation of the organic material of sediment. AcknowledgementsÐWe thank Tervaki Suzuki and Tone Nakane for important advice about sampling and oering ®eld data and Jun Hirosaki and Yasuyuki Sekiguchi for useful discussions on producing the model. We also thank Asako Yanagihara and Linda Worland for critical review of the manuscript.
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References Aoyama, H., Suzuki, T., 1996. The quantitative evaluation about water puri®cation function on tidal ¯at in Mikawa Bay. Bulletin of the Aichi Fisheries Research Institute, vol. 3, pp. 17±41 (in Japanese). Baretta, J.W., Baretta-Bekker, J.G., Ruardij, P., 1996. EMS to ERSEM 18(3), 197±209. Baretta, J.W., Ruardij, P., 1988. Tidal Flat Estuaries. Simulation and Analysis of the Ems Estuary. Ecological studies 71. Springer, Berlin, p. 353. Hata, K., Nakata, 1996. Evaluation of near-shore benthic nitrogen cycle using benthic ecosystem model. J. Adv. Mar. Sci. Tech. Soci. 2 (2), 31±50. Ishida, M., Hara, T., 1996. Changes in water and eutrophication in Ise and Mikawa Bays. Bulletin of the Aichi ®sheries Research Institute No. 3, 29±41. Kremer, J.N., Nixon, S.W., 1978. A Coastal Marin Ecosystem, Ecological Studies, vol. 24. Springer, Berlin, Heidelberg, New York, p. 227. Nakata, K., Hata, K., 1991. Evaluation of Nutrient cycle in tidal falt. Journal of Japan Society on Water environment vol. 17, No. 3, 18±26. Sasaki, K., 1989. Material circulation in intertidal ¯at. Bulletin on Coastal Oceanography vol. 26, No. 2, 172±190. Suzuki, T., Aoyama, H., Hata, K., 1997. The quanti®cation of nitrogen cycle on tidal ¯at by ecosystem model. J. Adv. Mar. Sci. Tech. Soc. 3 (1), 63±80. Suzuki, T., Matsukawa, Y., 1987. Hydrographic and budget of dissolved total nitrogen and dissolved oxygen in the strati®ed season in Mikawa Bay, Japan. J. Oceanogr. Soc. Japan 43, 37±48.
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New Numerical Model Study on a Tidal Flat System ± Seasonal, Daily and Tidal Variations AKIO SOHMA *, TATSUAKI SATO , KISABURO NAKATAà Fuji Research Institute Corporation, Tokyo, Japan àTokai University, Shizuoka, Japan We developed a new numerical model to investigate the dynamics of tidal ¯at ecosystems and their role in water quality in terms of the carbon cycle. This model was applied to Isshiki, a natural tidal ¯at area, which is the largest in Mikawa Bay, Japan. This model dealt with variations of biochemical or physical interaction among dissolved oxygen and C± N±P species (comprised of carbon, nitrogen, and phosphorus elements) both on a short-time scale (<24 h) as well as over a long-time scale (seasonal variation). The model indicated that the time dependence on phytoplankton, NH4 ±N, NOx ±N, and PO4 ±P are more sensitive to daily environmental variation than to seasonal environmental variation. This means that the rotation speed of these materials in the tidal ¯at area is fast. Here, we de®ned the rotation speed as the ratio of total ¯uxes of substance to the mass of the substance. Phytoplankton with a high rotation speed in the tidal ¯at area means that the tidal ¯at has the potential to recover from rapidly increasing phytoplankton: red tide. The model also indicated that the peculiar feature of the tidal ¯at is the mineralization of organic material. The eect on a long term base, is that it prevents the accumulation of sediment, which results in controlling the increase of oxygen consumption in benthic system, which is the cause of oxygen depleted water. Ó 2000 Published by Elsevier Science Ltd. All rights reserved.
Introduction Much attention has been paid to the role and the eect of tidal ¯ats on the quality of sea water in tidal estuaries, especially those experiencing a rapid increase in the frequency of red tides and oxygen depleted water masses. Mikawa Bay is one of the most eutrophic estuaries in Japan. Ishida and Hara (1996), and Aoyama and Suzuki (1996) indicated that eutrophication is getting worse in Mikawa Bay, not only because of increasing nutrients (loads) from rivers, but also from a reduction in natural water puri®cation which results from loss of parts of the tidal ¯at area (wetlands). Suzuki and Matsukawa (1987) estimated the budget of nitrogen and dissolved oxygen of Isshiki, a natural tidal ¯at
*Corresponding author.
area, in Mikawa Bay and indicated that tidal ¯at system has become a storeroom of nutrients and a supply of dissolved oxygen, especially in summer, when eutrophication tends to be at its worst. Using a material budget model (Sasaki, 1989; Aoyama and Suzuki, 1996) estimated Isshiki's removable ability of total nitrogen and dissolved oxygen. A useful method to investigate the Isshiki tidal ¯at system, is to apply the numerical ecosystem model, which formulates dynamics of interaction among dissolved oxygen and C±N±P species (compositions formed out of carbon, nitrogen, and phosphorus elements). It is possible for models to simulate the dynamics of the circulation of carbon, nitrogen, and phosphorus elements in the system. Recently, numerical ecosystem models have been applied in several studies on oxygen depleted water masses and eutrophication, and are used as a tool of environmental assessment and management. Kremer 173
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and Nixon (1978) published a numerical coastal marine ecosystem model of Narragansett Bay, USA. This model emphasized carbon circulation in the pelagic system from the viewpoint of being plankton-based. It also described interactions among special compartments in the pelagic system and interactions across the boundaries of the system. In general, most numerical models for coastal marine ecosystem are composed of pelagic system and the benthic variables are given as boundary conditions. Thus, interactions between the benthic and pelagic systems cannot be analyzed. However, this may not matter very much since these model systems are viewed as being plankton-based. In tidal ¯at systems, the in¯uence of interaction between the benthic and pelagic system becomes important. Baretta and Ruardij (1988) and Barreta et al. (1996) produced a numerical model and applied it to Ems estuary, Holland, where the tidal ¯at systems are situated. Their model was constructed with pelagic, benthic, and epibenthic submodels and simulated the seasonal variations in the tidal ¯at systems. Nakata and Hata (1991, 1996) produced a tidal ¯at ecosystem model of Banzu, Tokyo Bay, Japan, focusing on nitrogen circulation. This model emphasized the benthic ecosystem. Suzuki et al. (1997) applied this model to Isshiki and estimated the removable ability of nitrogen in summer. In this paper, we report the new numerical ecosystem model produced for tidal ¯at systems and the new model study on the tidal ¯at system, Isshiki. One of the characteristic points of the new model is that it simulates the dynamics and periodical variation, which can be shown only over a short-time scale (<24 h). We also report the feature of the tidal ¯at's eect to the quality of the seawater, quantitatively.
Model Concepts and Construction Basic features of the model The model is composed of a benthic system (benthic submodel) and a pelagic system (pelagic submodel). Pelagic submodel treats the transport of water caused by tide. The model is described by partial dierential equations based on conservation of carbon mass. We included processes of diusion, physical advection, and biochemical reactions in these equations. In this model, there are compartments which means several C±N±P species. Compartments and biochemical reactions in this model are mainly composed from the viewpoint that emphasize primary productive processes both in pelagic and in benthic and early diagenetic processes. Biochemical reactions are formulated from temperature, intensity of daylight, concentration 174
of dissolved oxygen, and concentration of compartments (C±N±P species) at every time step of calculation. Even though temperature and intensity of daylight are taken as prescribed functions, which have several periodical variations, compartments (C±N±P species), dissolved oxygen, oxygen consumption from benthic system and thickness of oxygen layer in benthic system are calculated at every time step in this model. This structure means that the interactions of a compartment (a C±N±P species) with other compartments (other C±N±P species) and dissolved oxygen varies at every time step and these dynamics of interactions aect the time dependence of variation of the tidal ¯at system. One of the most characteristic aspects of the tidal ¯at system is the tidal submersion/emersion of the ¯ats, which makes the system more complicated. Besides this feature including the complexity of the physical processes, the coincidence of the daylight period and the submersion of the tidal ¯ats causes a shortening of the eective photosynthesis period for the phytobentos. For the phytobentos and phytoplankton in the tidal ¯at areas, depth variation of covered water caused by tide obviously makes a dierence, because the depth at tidal ¯at is very shallow. From these reasons, time scales of the dynamics period of photosynthesis ¯uxes become <24 h. And from the basic calculation, we conjecture that the amplitude of periodical ¯ux dynamics in 24 h ( short-time scale) has enough mass to in¯uence the dynamics of tidal ¯at's total system compared with other ¯uxes. To con®rm and estimate the in¯uence of the periodical variations over a short time, we must calculate the model with time-step <24 h. We also take into account the two dierences from emerged area to submerged area in a model, which are considered to aect the biochemical processes treated in this model directly. One is the dierence of oxygen supply to the benthic system. An emerged area has a more ready supply of oxygen than a submerged area. Another is the dierence in mud temperature, especially in summer. This phenomenon is important for biochemical reactions which depend on temperature.
Construction of boxes in the model When we apply this model to Isshiki tidal ¯at, the model is composed of two boxes and these boxes are connected one dimensionally in the plane direction. The two boxes represent the pelagic and benthic system. The benthic system has three layers in the vertical direction. The upper layer of benthic system consists Spill Science & Technology Bulletin 6(2)
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of an oxygen layer and a deoxidization layer. The second and third layers of the benthic system are deoxidization layers. The coordinates of the boundary point between oxygen layer and deoxidization layer is calculated at every time-step. The thickness of oxygen layer has an in¯uence on the several biochemical reactions (detritus mineralization, nitri®cation etc.) whose formulations are distinguished between oxygen layer and deoxidization layer. Box 1, shown on the right-hand side of Fig. 1, represents the area which can be emerged when the spring tide is at its lowest and can be submerged when the spring tide is at its highest. This box is composed of area 1: emerging area, and area 2: submerging area. The boundary of these areas varies along the water level caused by tide. Box 2, represents the area, which cannot be emerged and where the maximum depth, (depth from the sea surface to sea bottom) is 3 m when the spring tide is at its lowest. We also call box 2, area 3 (Figs. 2 & 3).
Formulation of geographical features (geographical function) To calculate the coordinates of the boundary between area 1 and 2, formulation of geographical feature is necessary. In this model, geographical feature is formulated by the function, water level n t vs square measure of submersion area Sw (n), where both values are zero when the water level is the lowest level of spring tide. We call this function as geographical function. n t is the periodical function and the period is 12 h 25 min. From this function, we can calculate several variables as ®gured in Table 1. Treatment of the time lag between daylight and tidal submersion/emersion The time lag (50 min) between the daily period (24 h) and twice the tidal period (24 h 50 min), the change of the daytime length in compliance with
Fig. 1 Diagram of a tidal ¯at ecosystem.
Fig. 2 Construction of boxes in the horizontal direction.
Fig. 3 Construction of boxes in the vertical direction. Spill Science & Technology Bulletin 6(2)
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AKIO SOHMA et al. Table 1 Information relevant to the geographical function n t n t Tn;
T 12 h 25 min : n
Sw n t
Sw n t : Sd n t Sw n t : Stot ÿ Sw n t Stot m2 : total of square measure of box 1 Sd n t m2 : square measure of emerged area Sw n t m2 : square measure of submerged area Z h t Vw n t Sw n t dh 0
Vw n t m3 : volume of submerged area depwat n t
Vw n t Sw n t
depwat n t cm: averaged depth of submerged area L1 L10
Sw n t Stot
L1: scale of submerged area in the direction of horizontal L10 : scale of box 1 in the direction of horizontal
season and the dierences of tide level between spring tide and neap tide vary the timing of the coincidence of daylight and submersion. To consider the variation of this timing in this model, we inputted the tide level and the time of sunrise for the season when the simulation began. Also we divided the running period of 24 h into separate time steps (e.g.: if a time step is to be 1 h, then the number of time separators is 24). By this, we can calculate the square measure of emersion area from the geographical function (Fig. 4) in each time separation. Compartments and ¯uxes in the model Circulation treated in one box of this model is shown in Fig. 5. Compartments, treating C±N±P
species in this model, are shown as boxes and the ¯uxes of biochemical reactions and transport processes are represented by arrows in Fig. 5. The concentration of each compartment, without seagrass and seaweed, is calculated at every time step. Changes in concentration of these compartments were caused by ¯uxes going in and out. Fluxes of biochemical reactions in one compartment are formulated with concentration of other compartments, temperature, intensity of light, and water-depth etc. at each timestep of calculation. Seagrass and seaweed were taken as prescribed seasonal periodical functions. Model equations for special Compartments In general, concentration changes of all compartments dependent on time are given in Table 2. The terms of these equations are: (1) advection from water transport caused by tides or rivers; (2) diusion from turbulent ¯ow of water; (3) advection from sediment deposition; (4) diusion from bioturbation and molecular motion; (5) biochemical reactions. Fluxes of (1) and (2) are horizontal, and ¯uxes of (3) and (4) are vertical. Compartments which exist only in the benthic system do not take into account the ¯uxes of (1) and (2). To describe changes of (4) in the model, the diffusive coecient for the benthic system is formulated by using a molecular diusion coecient dependent on temperature and concentration of suspension feeders and deposit feeders. Although the horizontal scale for the submerged part of box 1 varies every time, the diusive coecient in pelagic system is a function of the horizontal scale. Model equations for dissolved oxygen Concentration of dissolved oxygen in the pelagic system is determined from: (1) advection from water transport caused by the tide or river; (2) diusion from turbulent ¯ow of water; (3) total of oxygen consumption and production from both the pelagic system and the benthic system, which is calculated at each time-step. Processes of oxygen consumption and pro-
Fig. 4 Treatment of the time lag between daylight and tidal submersion/emersion. 176
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Fig. 5 Treatment of circulation in one box of the model.
duction can be calculated from biochemical reactions of compartment. In the benthic system, the oxygen layer and the deoxidization layer are de®ned (refer to Section: construction of boxes in the model). The way to solve the thickness of oxygen layer in benthic system is indicated in Table 3. The boundary between the oxygen layer and the deoxidization layer is calculated from (4) the concentration of dissolved oxygen in the pelagic system (5) total of oxygen consumption and production in the benthic system. (4) is the boundary condition of equation for the benthic system. In the emerged area, this boundary condition is based on the theory that there is a diusive boundary layer between air and water. To solve equation in benthic system, we chose and de®ned process (5) from process (3). Using this method, total mass of dissolved oxygen in the system was conserved. In the case that the total oxygen consumption in benthic system is less than the total production of oxygen in benthic system, the thickness of the oxygen layer, the solution of equation in benthic system, diverges to in®nity, and the model makes the thickness of oxygen layer equal to thickness in 1st layer. This also means that the thickness of 1st layer is the maximum thickness of oxygen layer. Spill Science & Technology Bulletin 6(2)
Calculation Boundary condition, prescribed function and initial value To run the model, we need to input initial values of compartments, several boundary conditions and prescribed functions. Tide level was taken from the component tides, M2, S2, O1, K1, results of the harmonic analysis of tide. Intensity of daylight is analyzed for two time scales. One is the variation within one day, daytime and nighttime, and the other is the seasonal variation. On the simulation, it is assumed that the variables which were taken as boundary conditions and prescribed functions except for the tide level and intensity of daylight, will not change for several years. These variables are taken from observed data averaged over the last ®ve years. In other words, the model is simulated for a standard year. So they are ®tted with f(t) shown below, which has the period of 1 yr. The number n must be less than the number of observations in a year. f t p0
X an sin nxt bn cos nxt: n
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AKIO SOHMA et al. Table 2 Model equations for special compartments (a) Equations for the compartments representing dissolved substances Pelagic system: 0th layer 0 1 Z X X o dep Cn o Cn o B oCn C o Ln ÿ @ u dz Cn A ÿ /Dz;n dep Dx dep Gn ÿ ot ox ox oz ox z0
dep
Benthic system: 1st layer X X oCn oCn /Dz;n G1;n ÿ L1;n ÿ /Dz;n / h1 oz oz z0 zz1
o Cn h1 / ot
Benthic system: 2nd layer X X o Cn h2 oCn oCn /Dz;n / L2;n G2;n ÿ ÿ /D / h2 z;n ot oz zz1 oz zz2 Benthic system: 3rd layer /
o Cn h3 ot
X X oCn oCn /Dz;n L3;n G3;n ÿ ÿ /Dz;n / h3 oz oz zz2 zz3
(b) Equations for the compartment representing particulate substances Pelagic system: 0th layer 0 1 Z X X o dep Pn o Pn o B oPn C o Ln W0;n ÿ W1;n ÿ /Dz;n depDx ÿ @ u dz Pn A dep Gn ÿ ot ox ox oz ox z0
dep
Benthic system: 1st layer X X o Pn h1 oPn oPn L1;n W1;n ÿ W2;n 1 ÿ / 1 ÿ /Dz;n ÿ 1 ÿ /D h1 1 ÿ / G1;n ÿ z;n ot oz z0 oz zz1 Benthic system: 2nd layer X X o Pn h2 oPn oPn 1 ÿ / 1 ÿ /Dz;n L2;n W2;n ÿ W3;n ÿ 1 ÿ /Dz;n h2 1 ÿ / G2;n ÿ ot oz zz1 oz zz2 Benthic system: 3rd layer 1 ÿ /
o Pn h3 ot
X X oPn oPn L3;n W3;n ÿ W4;n 1 ÿ /Dz;n ÿ 1 ÿ /Dz;n h3 1 ÿ / G3;n ÿ oz zz2 oz zz3
Cn lg=ml: concentration of nth compartment of dissolved substances Pn lg=cm3 D: concentration of nth compartment of particulate substances Dz;n cm2 =day: diusive coecient caused by bioturbation and molecular diusion Dx cm2 =day: diusive coecient caused by turbulent ¯ow of water dep cm: water depth u cm=h: velocity of water ¯ow P P Gn : total of the terms of increased biochemical reactions Ln : total of the terms of decreased biochemical reactions /: porosity Wk;n : advection caused by sedimentation
Initial values of compartments were taken from observed data collected in summer, 15±17 August 1997.
Biochemical parameters Equations for biochemical reactions include several biochemical parameters. We investigated a range of values for these parameters that have been observed 178
until now and set those parameters within that range. Values were given to the unknown parameters to validate the simulation. The results of the simulation in terms of the concentrations in the compartments and ¯uxes of the biochemical reactions that seemed unreasonable in comparison to the observed values indicated where the parameters needed tuning. Using this process, values for the unknown parameters were predicted from the results of the simulation. Spill Science & Technology Bulletin 6(2)
NEW NUMERICAL MODEL STUDY ON A TIDAL FLAT SYSTEM Table 3 Equations for dissolved oxygen Equation for concentration of dissolved oxygen (1) Equation in pelagic system 0 1 Z X X o dep DOn o DOn o B oDOn C o ÿ /Dz;n depD dep Gn ÿ Ln ÿ u dz DO @ A n x ot o x o x oz ox dep z0 (2) Equation in benthic system Changes of concentration of dissolved oxygen depending on time X o DO o2 DO X Dz Gbenthic ÿ Lbenthic ot o z2 Assumption 1:
o DO o z Z0
0
Assumption 2: DO Z0 0 Assumption 3: DO 0 DO0 From these assumptions, equation in benthic system can be solved below: P P r L LZ0 z DO0 , In oxygen layer DO 13 DO0 DO Z 2Dz Z 2 ÿ Dz Z DO0 , Z0 ÿ 2DP L X X Gbenthic ÿ Lbenthic photosynthesis of benthic algae ± excretion of benthic algae ± mineralization of detritus in oxygen layer ± nitrification in benthic system ± oxidation of oxygen demand materials Oxygen consumption and production are calculated from ¯uxes of biochemical reactions of compartments to use the chemical formulation which is indicated below 2ÿ CH2 Om NH3 nH3 PO4 m 2nO2 ! m CO2 n NOÿ 3 HPO4 m nH2 O n 2H Trace Element Energy
O:C (mass ratio of element) 32 m 2n=12m 2NH3 3O2 ! 2HNO2 2H2 O;
2HNO2 O2 ! 2HNO3
O:N (mass ratio of element) 32/7 DO mgO2 =l: concentration of dissolved oxygen 2 D P diusion coecient of dissolved oxygen Pz cm =day: Gbenthic ÿ Lbenthic : total of the oxygen consumption and production in benthic system
Time-step, time scale of parameters and length of layer We set the time-step of the calculation to 12 min and set the thickness of each layer as follows: 1st and 2nd layers at 1 cm, and layer 3 at 8 cm in the vertical.
Result and Discussion In this section, ®rst, we demonstrate the steadiness of the simulation, and show the periodical variation for three time scales, daily (24 h), tidal between spring tide and neap tide (15 days) and seasonal (1 yr). It is possible to explain the causes of variations in each compartment, but in this paper, we con®ne our argument to the variations of only several compartments. We discuss daytime scale variation, in detail. (Depending on the viewpoint, there are dierent explanations for the variability of compartments. The roots of variations of compartments cannot be de®ned in a correct meaning, because interactions between compartments and dynamics of compartments are not determined independently but in¯uences each other Spill Science & Technology Bulletin 6(2)
mutual in¯uences every time. Thus, the explanation which is indicated in this paper comes from one of the viewpoints.) Steadiness of result of simulation Periodical variation of compartments, more or less, reaches a steady state within 3 yr. On behalf of benthic and pelagic systems, variability in the concentration of phytoplankton and benthic algae are shown in Fig. 6, which indicates the state becoming steady. Discussion on variation in daily time scale (24 h) The simulation results for the submerged area in box 1, which focuses on the variation over a daily time-scale, from 1 August, 12:00 to 3 August, 0:00, summer, is shown in Figs. 7 & 8. In the following sections, we analyze the causes of variation for phytoplankton, organic carbon, and NOx in the pelagic system; benthic algae in the benthic system; and NH4 compartments in both pelagic and benthic systems. 179
AKIO SOHMA et al.
Fig. 6 Steadiness of compartments (plotting data is extracted results per day).
Fig. 7 Variation in the pelagic on a daily time scale (24 h) (values of the tide level and the intensity of light are relative values).
Phytoplankton in the pelagic system. The variation in phytoplankton mainly depends on production from photosynthesis, the input ¯ows from box 2, and feeding by suspension feeders. Phytoplankton biomass decreased through suspension feeding, but increased when the tide level rose through the water ¯ow input from box 2. The eect, increasing ¯ux of photosynthesis when the depth is shallow, cannot be omitted. Organic carbon in the pelagic system. The variation in organic carbon in pelagic system mainly depends on feeding by suspension feeders and the input ¯ows from box 2 and the river. The concentration of organic carbon roughly ¯uctuates with tide level. That is, feeding by suspension appears more conspicuously when the tide level is low than when the level is high. The minimum during night is sharper than the minimum during daytime. In other words, the decreasing rate of organic carbon at daytime becomes less than at 180
night, relatively. This is because phytoplankton during daytime is more active than at night and supplies the organic carbon from the process of excretion. The lower the water level becomes, the more the load from the river aects the concentration of organic carbon. This explains why the timing between the maximum and minimum of the carbon concentration becomes closer. NH4 in the pelagic system. The concentration of NH4 reaches a maximum at roughly the same time as the tide reaches its lowest level. This can be explained by the following; the eect of the load from river on the concentration of NH4 is more eective when the tide level is low: the water mass of submerged area in box 1 is less than when the tide level is high. In addition, during the night, decreasing eect coming from photosynthesis of phytoplankton does not exit, but during the day, decreasing eect to the concentration of NH4 becomes stronger. On the other hand, in the Spill Science & Technology Bulletin 6(2)
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Fig. 8 Variations in the benthic system on a daily time scale (24 h) (values of the tide level and the intensity of light are relative values).
benthic system, photosynthesis by benthic algae make a larger dierence to the concentration of NH4 in the benthic layer between daytime and nighttime. This phenomenon makes diusive ¯ux of NH4 from benthic system dierent between daytime and nighttime (detail written below). In general, under the situation that the tide level is low and the NH4 concentration in benthic system is high, the concentration of NH4 in pelagic system becomes high level. HNOx in the pelagic system. Comparing the variation in the concentrations of HNOx and NH4 , when the tide level is at its lowest during the day, HNOx reaches its maximum whereas NH4 is decreasing. This dierence can be traced to them being in dierent concentrations in the river nutrient load. The concentration of HNOx in river water is about eight times as much as the NH4 in August. This eect is stronger when the tide level is low, and makes a decreasing in¯uence caused by photosynthesis of phytoplankton to disappear. The cause of maximum when the tide level is lowest during night is the same as the case of NH4 . Dierences in the minimum value of the tide level between day and night means that Spill Science & Technology Bulletin 6(2)
the maximum value during the day is more than that it is at night. Dissolved oxygen. During the day, in particular, the dissolved oxygen concentration exceeds saturation point due to photosynthesis. Benthic algae. Photosynthesis by benthic algae is formulated by the half-saturated function. When the tide level is high, it is more dicult for daylight to reach the benthic system than when the tide level is low. Thus, the relationship between the tide level and daytime aects the variation of photosynthesis by benthic algae. Dissolved NH4 in the benthic system. Variation in dissolved NH4 over a daily period in the 1st layer results from the photosynthesis by benthic algae. Benthic algae uses NH4 in the ®rst layer in photosynthesis. Increasing ratio going up at the time of minimum point of tide level during night, is caused by decreasing the ¯ux to the pelagic system. Flux decreasing comes from the concentration of NH4 in pelagic system increasing. The in¯uence of NH4 from the river appeared more conspicuously when the tide level was 181
AKIO SOHMA et al.
low because the water volume in box 1 was smaller than when the tide level was high. Vibration whose time scale is about Dt is the phenomena caused by discrete quantity of time. The instantaneous ¯ux by photosynthesis is more compared to the pool of NH4 in the 1st layer in relative. Thus, NH4 in the 1st layer becomes scarce and this limits photosynthesis by benthic algae in the next calculating time t Dt. Other biochemical ¯uxes which produced NH4 , do not have obvious change during Dt. These are the explanations of vibration of Dt time scale. Using the concept of cell quarter, the instantaneous shortage of NH4 at 1st layer during daytime is taken during night in this model, and conserves the mass of elements. It is natural to think that in the real system, the NH4 takes the center of amplitude.
nutrient load from the river, the time lag between the tidal period and daylight period, and the mass of seaweed and seagrass. Circulation of nitrogen We demonstrated that the main ¯uxes of nitrogenous elements over 15 days of summer which was calculated from the results of the simulation of the model shown in Fig. 13. From this result, we can see one peculiar feature of the tidal ¯at is the mineralization of organic materials.
Conclusions and Remarks
Discussion on variation in time scale between spring and neap tide (15 days)
From the computational results of this model, we classify and arrange the role of the tidal ¯at area on coastal water quality into short-time and long-time scale.
Variation over a 15 day period in the compartments shown in Figs. 9 & 10 can largely be explained by the dierences in tidal levels between spring and neap tides.
Role of the tidal ¯at area seen from a short-time scale
Discussion on variation in seasonal time scale (1 yr) Variation over a 1 yr time-scale in the compartments shown in Figs. 11 & 12 can largely be explained by seasonal variation in temperature, intensity of light,
By looking at the time ¯uctuation of phytoplankton, NH4 ±N, NOx ±N, and PO4 ±P, we see that in tidal ¯at area, the amplitude of daily or 15 day periodical ¯uctuation is larger than that of seasonal. This means that the rotation speed of these compartments in the tidal ¯at area is fast. Here, we de®ned the rotation speed as the ratio of total ¯uxes of compartments to
Fig. 9 Variations in the pelagic system over a spring to neap tide scale (15 days) (values of the tide level and the intensity of light are relative values). 182
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Fig. 10 Variations in the benthic system over a spring to neap tide scale (15 days) (values of the tide level and the intensity of light are relative values).
Fig. 11 Variations in the pelagic system over a seasonal time scale (1 yr). Spill Science & Technology Bulletin 6(2)
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Fig. 12 Variations in benthic system over a seasonal time scale (1 yr).
Fig. 13 Main ¯uxes averaged for 15 days in summer based on nitrogen at Isshiki (submerged area: 6.07 km2 submerged/emerged area: 4.61 km2 ). 184
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the mass of compartments. When an impact such as red tide, namely, a sudden increase in phytoplankton occurs, a tidal ¯at with a large ¯ux able to remove that, improves the balance of the ecosystem in short time. Thus, the fast rotation speed of phytoplankton in the tidal ¯at suggests the possibility of retaining a sound ecological circulation. From a dierent perspective, if we were to lose tidal ¯ats, compartments where the rotation speed is high, there is a possibility of phytoplankton suddenly increasing, meaning that there is a possibility of a red tide to occur. Role of the tidal ¯at area seen from a long-time scale From the computational results of the model, the rotation speed of the organic material of sediment is slow. Therefore, time ¯uctuation for the organic material of sediment on a long-time scale becomes vital. From the material balance, the tidal ¯at is where organic substances become inorganic. The eect, on a long-term base, is that it prevents the accumulation of the organic material of sediment. AcknowledgementsÐWe thank Tervaki Suzuki and Tone Nakane for important advice about sampling and oering ®eld data and Jun Hirosaki and Yasuyuki Sekiguchi for useful discussions on producing the model. We also thank Asako Yanagihara and Linda Worland for critical review of the manuscript.
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References Aoyama, H., Suzuki, T., 1996. The quantitative evaluation about water puri®cation function on tidal ¯at in Mikawa Bay. Bulletin of the Aichi Fisheries Research Institute, vol. 3, pp. 17±41 (in Japanese). Baretta, J.W., Baretta-Bekker, J.G., Ruardij, P., 1996. EMS to ERSEM 18(3), 197±209. Baretta, J.W., Ruardij, P., 1988. Tidal Flat Estuaries. Simulation and Analysis of the Ems Estuary. Ecological studies 71. Springer, Berlin, p. 353. Hata, K., Nakata, 1996. Evaluation of near-shore benthic nitrogen cycle using benthic ecosystem model. J. Adv. Mar. Sci. Tech. Soci. 2 (2), 31±50. Ishida, M., Hara, T., 1996. Changes in water and eutrophication in Ise and Mikawa Bays. Bulletin of the Aichi ®sheries Research Institute No. 3, 29±41. Kremer, J.N., Nixon, S.W., 1978. A Coastal Marin Ecosystem, Ecological Studies, vol. 24. Springer, Berlin, Heidelberg, New York, p. 227. Nakata, K., Hata, K., 1991. Evaluation of Nutrient cycle in tidal falt. Journal of Japan Society on Water environment vol. 17, No. 3, 18±26. Sasaki, K., 1989. Material circulation in intertidal ¯at. Bulletin on Coastal Oceanography vol. 26, No. 2, 172±190. Suzuki, T., Aoyama, H., Hata, K., 1997. The quanti®cation of nitrogen cycle on tidal ¯at by ecosystem model. J. Adv. Mar. Sci. Tech. Soc. 3 (1), 63±80. Suzuki, T., Matsukawa, Y., 1987. Hydrographic and budget of dissolved total nitrogen and dissolved oxygen in the strati®ed season in Mikawa Bay, Japan. J. Oceanogr. Soc. Japan 43, 37±48.
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