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Some difficulties in modelling chlorophyll a evolution in a high rate algal pond ecosystem
E[OLOGItflL mODELLlil6 ELSEVIER
Ecological Modelling 78 (1995) 25-36
Some difficulties in modelling chlorophyll a evolution in a high rate algal pond ecosystem Fabrice Mespl6 a,,, Claude Casellas a, Marc Troussellier b, Jean Bontoux
a
a Ddpartement Sciences de l'Environnement et Santd Publique, URA CNRS 1355, Facultd de Pharmacie, Avenue C. Flahault, F-34060, Montpellier, France b Laboratoire d'Hydrobiologie Marine et Continentale, URA CNRS 1355, Universitd Montpellier lI, F-34095, Montpellier, France
Received 30 January 1993; accepted 1 February 1994
Abstract The High Rate Algal Pond (HRAP) is an efficient treatment for controlling wastewater pollution by reducing the organic matter and the inorganic nutrient content. Deterministic modelling of temporal evolution of algae could provide a rational basis for pond management. An experimental H R A P was set up in M~ze (France) and sampled weekly over 24 months. Models simulating the evolution of chlorophyll a concentration and nutrients (N and P) were constructed using Stella II software. The seasonal pattern of chlorophyll a concentrations results from the annual cycle of solar irradiance and temperature, whereas shorter trends (1 to 4 weeks) are dependent on the evolution of zooplankton groups. The first difficulty is to determine the functional relationships of the phytoplankton and zooplankton groups. In the model the evolution of the phytoplankton taxa is considered to be dependent on (i) inherent parameters of phytoplankton taxa (mortality rate, growth rate, saturating light intensity, etc.) and on (ii) parameters of zooplankton taxa (filtration rate, size selectivity, etc.). To take all these taxa as state variables, and all the associated parameters, into account is impossible: to solve such a problem, we forced the evolution of the biomass of the phytoplankton and zooplankton taxa. This approach improves the agreement between the simulated and observed chlorophyll a concentration values. The second difficulty concerns the determinism of appearance of the phytoplankton and zooplankton taxa used in the model: up to now we are only able to force these appearances. Thus, even in quite simple ecosystems, using deterministic modelling as a predictive tool requires a full understanding of the exact biological succession and interaction processes. Keywords: Algae; Chlorophyll; Pond
1. Introduction
* Corresponding author. Present address: Laboratoire d'Hydrobiologie Marine et Continentale, URA CNRS 1355, Universit6 Montpellier II, Place E. Bataillon, F-34095, Montpellier Cedex 05, France.
H i g h R a t e A l g a l P o n d ( H R A P ) is an efficient t r e a t m e n t system for c o n t r o l l i n g w a s t e w a t e r pollution t h r o u g h o p t i m i z a t i o n of algal g r o w t h (Picot et al., 1991). T h e p e r f o r m a n c e o f high r a t e p o n d s
0304-3800/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0304-3800(94)00115-X
26
F. Mespld et aL / Ecological Modelling 78 (1995) 25-36
(HRAPs) depends mainly on the climatic conditions of the pond's location because the major factors affecting the pond's performance, on a seasonal scale, are solar irradiance and water temperature (Goldman, 1979). To optimize the performance of this low-cost and simple-technology wastewater treatment system, one needs a quantitative understanding of the relationships between these keys parameters and the growth of the algae. Computer modelling provides a valuable tool to explore the factors controlling this relationship and to provide information on the design and operation of the ponds. Models simulating the different parts of a HRAP's ecosystem have already been developed. Fallowfield and Martin (1988) and Martin and Fallowfield (1989) described a model to predict the evolution of algal productivity (as dry matter) over the year. Buhr and Miller (1983) presented a model of algae and bacterial growth on a day scale. However, there is still a need for a model simulating the weekly evolution of the phytoplankton compartment over the year. This frequency is adequate to describe phytoplankton dynamics in the ponds (Harris, 1980).
2. Materials and methods
.q
12, m
waTwate~ ~
°'~
I paddle wheel depth = 0.35 m
Fig. 1. Schematic view of a H R A P (~ flow speed).
from the village of M~ze (8500 inhabitants in winter and 20000 in summer), which was screened, grit and oil removed, and treated in an open unmixed primary settling tank with an 8-day retention time.
2.2. Model calibration data The sampling program lasted two years, from February 1988 to February 1990. Measurements of the inflow from the primary pond and in the HRAP were made at the same frequency. Water
INPUT ~
S~aolar r a d i ~
-- -- - R ~ e n c e f i m ~ - -
~
-- -{
.--
2.1. High rate algal ponds Two experimental HRAPs were operated at M6ze in southern France (03°35'E, 43°25'N) where a facultative pond treatment existed since 1980. The experimental ponds are 12 m by 4 m with a volume of 16.8 m 3 at 0.35 m depth with a central baffle. A circulation flow of 15 cm s -1 was maintained with a six-bladed paddle wheel mounted transversely across one channel (Fig. 1). Pond A was run at a seasonally variable retention time calculated using Oswald's (1988) empirical formula, and pond B was run at a fixed retention time of 8 days; pond B is used as a reference to determine the influence of a variable retention time (pond A) on the ecosystem and on the outflow water quality. The inflow for the ponds was sewage water
[
I - - ' 1 : State variables
~
/
p
: Forcing variables
J
I~
O
: Sink
Fig. 2. Conceptual model of chlorophyll a evolution in a HRAP. The so-called "model without grazing process" does not take into account grazing and defecation processes and the "model with grazing process" takes all processes into account.
F. Mespld et al. / Ecological Modelling 78 (1995) 25-36
temperature and chlorophyll a (French standard A F N O R T 90-117) were measured weekly. Phytoplankton and zooplankton populations, and their biomass, were determined weekly. Daily light intensity was obtained from the FrEjorgues meteorological station 35 km away.
27
2.3. Modelling A conceptual model (Fig. 2) was first developed based on knowledge of algal evolution in a eutrophic ecosystem (Richmond, 1986). The model was constructed using the simulation pro-
Table 1 Model parameters, definitions, values and sources for H R A P chlorophyll a model Symbol
Name
Values/Units
Source
total phytoplankton in pond TSS minus P total suspended solids in pond
mg chlorophyll a mg dry weight mg dry weight
pond data TSS - P pond data
Ly d a y - t oC pond A: 2 to 12 days pond B: 8 days
meteorological station pond data pond data
State variables P DET TSS
Forcing functions t~
photoperiod
Forcing variables It T 0
solar radiation water temperature residence time
Phyto structure
phytoplankton structure total biomass of i in the pond (i = cladocerans, rotifers or copepods) TSS concentration in primary pond P concentration in primary pond D E T concentration in primary pond
Zi [TSS]pp [P]pp [DET]pp
mg fresh weight
pond data pond data
mg dry weight 1- i mg chlorophyll a l mg dry weight 1- 1
primary pond data primary pond data primary pond data
1 day -1 16800 1 3 day- 1 Ly d a y - 1
pond data calibration
Parameters and coefficients Q V Gpmax Ia Ke Ks Kc h D FRZimax
flow rate ( = V/O) water volume in the pond phytoplankton maximal growth rate m e a n solar irradiance during the photoperiod ( = It/4~) total extinction coefficient specific extinction coefficient of TSS minus P specific extinction coefficient of chlorophyll a water depth mortality rate m a x i m u m filtration rate of i (i = cladocerans, rotifers or copepods)
CI
chlorophyll a/dry weight ratio
C2
dry w e i g h t / f r e s h weight ratio for zooplankton d e f e c a t e d / i n g e s t e d ratio mineralization rate threshold u n d e r which filtration rate is independent from food concentration
r R [F]0
m-1 0.05 m - 1 (rag dry weight l - i ) - i 0.016 m e mg - I chlorophyll a 0.35 m 0.15 d a y - 1 1day- i mg- 1 fresh weight zooplankton FRZcladma x = 0.12 FRZRotmax = 0.005 FRZcoomax = 0.12 70 mg dry weight mg i chlorophyll a 0.13 0.3 0.005 day 1 2 mg dry weight 1- t
pond data Richmond, 1986 pond data Sciandra, 1986
T h o m a n n and Mueller, 1986 calibration T h o m a n n and Mueller, 1986 Dauta, 1982
Bougis, 1974 Sciandra, 1986 Sciandra, 1986 Stra~kraba and Gnauck, 1985
F, Mesplget al. / EcologicalModelling 78 (1995)25-36
28
gram STELLA II © (High Performance Systems, Inc.) on an Apple Macintosh S E / 3 0 microcomputer. Simulations used a second-order R u n g e Kutta technique and an integration interval of 1 day. The model with grazing was calibrated with pond A 1988 and 1989 data, and run on pond B. Then the same model without grazing was run on pond A and B. The model parameters, definitions, values and their sources are given in Table 1.
V/O), where V is the volume of the pond and 0 is the residence time; then Input X = [ X ]ppV/O. For the same state variable X, the total output of X via the outflow from the H R A P is: Output X = X/O, where X is the total quantity of a state variable.
3.2. Phytoplankton submodel 3. Results
3.1. Hydrology submodel The hydrology submodel depicts inflow and outflow of wastewater in the pond, with a retention time (0) varying from 2 to 12 days for pond A and constant (8 days) for pond B (Fig. 3). The H R A P is assumed to be homogeneous and not vertically stratified, as confirmed by tracer experiments using chemical (El Halouani, 1990) and bacterial markers (Bahlaoui, 1990). We do not take into account sedimentation because the low depth and the continuous mixing prevent sludge accumulation (Fallowfield and Garrett, 1985). Considering a state variable X, the total input of X via the inflow from the primary treatment tank, is: Input X = [ X ] p p . Q , where [X]pp is the concentration of the state variable in the inflow, Q is the flow rate (Q =
We have chosen to represent the phytoplankton compartment by chlorophyll a which is an integral variable, simple to measure. Knowing the concentration of chlorophyll a in the primary pond ([P]pp) and the residence time (0), we can determine the phytoplankton input and output per day (see Section 3.1): Input P = [P]ppV/O, Output P = P/O.
Growth As the H R A P is continuously supplied with sewage water, phosphates and nitrates are never rate limiting; the mean pond N-NH 4 concentration of 9 mg 1-1 (range 0 . 0 3 - > 30 mg 1-1) remains well above the half-saturation constant of 15 ~ g 1-1 for N-NH 4 (Thomann and Mueller, 1986). Mean P-PO 4 concentrations of 4.6 mg 1-1 (range 0 . 4 5 - > 8 mg l - t ) also greatly exceed the half-saturation constant of 2.5 /zg l -x (Thomann and Mueller, 1986). We therefore only consider light energy and temperature as controlling growth:
Gp=Gpmax[f(lt)] [ f ( T ) l , 14.
Gp being the instantaneous growth rate, Gpmax the maximal growth rate, f ( I t) and f ( T ) the
12 1o .....
influence of solar radiation and temperature, respectively.
.....
Influence of solar radiation Spring S u m m e r Fall 1988
Winter
Spring S u m m e r 1989
Fall
Fig. 3. Residence time (0) in ponds A (solid line) and B (dashed line).
B e e r - L a m b e r t ' s law describes the light I at a depth h, in a light-absorbing medium (Kirk, 1983): I = Io exp(-Keh),
F. Mespldet al. / Ecological Modelling 78 (1995)25-36 where I 0 is the surface irradiance and K e the overall extinction coefficient. This law has been experimentally verified for dense algal cultures (Oswald et al., 1953). Several authors (Steele, 1962; Fee, 1969; Bannister, 1974) have shown that, at a constant temperature, as the irradiance increases, photosynthesis increases to a maximum. Further increase in irradiance tends to result in a decrease in photosynthesis due to photoinhibition. The response of photosynthesis to irradiance is modelled by Steele's (1962) equation, which takes into account the effects of photoinhibition at high light intensities. All irradiances are expressed in Langleys.
g( I ) = Gpmax( I / I s ) exp(1 - I / I s ) , where g ( I ) is the growth rate at irradiance 1 and I s is the saturating light intensity. The model combines B e e r - L a m b e r t ' s and Steele's equations to calculate the daily production rate, using the simplification of Di Toro et al. (1971) about the incident irradiance I0: during the photoperiod I 0 = I a = It/4, and outside the photoperiod I 0 = 0, with I a the mean solar irradiance during the photoperiod, I t the total daily irradiance and 4' the photoperiod in a day. Over the day, for a water depth h (see Di Toro et al., 1971): f ( I t ) = 2.718 4'[exp(--o/1)
--
exp(ao)]/(Keh),
where
Ol1
=
( I./Is) exp(-Keh )
and
c% = l a / I s. The extinction coefficient ( K e) equals: K e = K w + Ks([TSS ] - [ P ] C 1 ) + K c [ P ] , where K w is the extinction coefficient of pure water, K S is the specific extinction coefficient of the total suspended solids minus phytoplankton, expressed in dry weight ( [ T S S ] - [ P ] C 1 ) , K c is the specific extinction coefficient of chlorophyll a, and [P] is the concentration of chlorophyll a. In such ponds - containing wastewater - there
29
is no significant influence of the pure water coefficient of extinction (Kw) on K~. At the latitude of M6ze, we have simulated the evolution of the photoperiod & as: 4, = 12.6 - 3.97 cos[2~-(t + 3 9 ) / 3 6 5 ] / 2 4 , where t is days from 1 January.
Influence of temperature The effect of temperature ( f ( T ) ) o n G p m a x is approximated (Thomann and Mueller, 1986) by: f ( T ) = 1.066 (r-z°), where T is the temperature in °C.
Death Death rate (D) is considered constant over the year. Grazing This process is taken into account only in the model incorporating the grazing process. Modelling the grazing process requires us to focus, firstly, on zooplankton and phytoplankton community structures and secondly on the interactions between these two compartments. The zooplankton compartment cannot be considered as a black box because the structure of the zooplankton community is highly complex and is constantly changing. The study made by Canovas (1991) has shown that this compartment is divided into 5 taxa: Cladocerans, Ostracods, Rotifers, Copepods and Ciliates. As Ostracod biomass is less than 6% of the total zooplankton biomass and Ciliate biomass is less than 10% (Canovas, 1991), these two taxa are neglected in the model. Each taxon possesses different parameters associated with the grazing process (Peters and Downing, 1984; Thomann and Mueller, 1986). Fig. 4 shows the explosive evolution of these groups, which appear difficult to simulate. Indeed, this is why the evolution of each of the zooplankton groups is forced by the variables Zi, representing respective biomass. With regard to the phytoplankton, the chlorophyll a variable is too integral to be able to simulate the grazing process. Moreover, as the zooplankton groups graze different sizes of phytoplankton cells, we have to take into account the size structure of the
F. Mespl~ et al. / Ecological Modelling 78 (1995) 25-36
30
-
-
Cladocerans
----a-- Rotifers
Copepods
1000. pond A o~
~,~, 400
~g
260 o
~,
1750
pond B
E ~ 1500 O.E .~
looo
~
750 250 Spring Summer Fall 1988
Winter Spring Summer Fall 1989
Fig. 4. Evolution of the zooplankton biomass in ponds A and B.
phytoplankton population and its temporal evolution in the model. Unfortunately, it is impossible to calibrate a model taking into account ten phytoplankton taxa as state variables, because the number of associated parameters (growth rate, death rate, saturating light intensity, temperature optimum, etc.) to determine accurately is too large. As with the zooplankton, a forcing variable is used; this is "Phyto structure", which represents the daily taxonomic composition of the phytoplankton population as a percentage of the total biomass (Fig. 5). Only the total mass of chlorophyll a is computed, and then distributed in each taxon in proportion to their biomass. The taxa observed in the ponds during sampling are: Ankistrodesmus, Astasia, Dictyosphora,
Chlorella, Chloridella, Chloromonas, Coelastrum, Diatoms, Euglena, Golenkinia, Kirchneriella, Micractinium, Microcystis, Oocystis, Pediastrurn and Scenedesmus. Taxa that appeared less than 7 times during the two-year sampling period, with a relative biomass of less than 10% are neglected; these taxa are: Dictyosphora, Chloridella, Coelastrum, Golenkinia and Micractinium in pond A, and Astasia, Dictyosphora, Chloridella, Codastrum, Golenkinia, Kirchneriella, Micractinium and Oocystis in pond B.
The third point to take into account is the interaction between phytoplankton and zooplankton. The phytoplankton groups do not react similarly to different zooplankton groups, mainly because of cell sizes. This information has also to be considered by the model, and can be presented as a table, in which the columns are the zooplankton groups, the rows the phytoplankton taxa, and the cells the potential connections between the prey and the grazer (Table 2). Let us consider a group of zooplankton i, represented by its biomass, Z i ( i - Cladocerans, Rotifers or Copepods). The mass of chlorophyll a grazed by this zooplankton group, for a time step dt, is equivalent to: Graz Z i = [ P ] i F R Z i Z i f ( T ) , where [P]i is the chlorophyll a concentration edible by one of the three groups of zooplankton, FRZi is the filtration rate per day, Z i is the total biomass of one of three groups of zooplankton, and f ( T ) is the influence of temperature.
[ ] Microcvstis
[ ] Pediastrum
k~ Astasia
[ ] Ankistrodesmus [ ] Chlorella
[ ] $¢¢nedesmus
[ ] Diatoms
[ ] Euglena
•
i 100%
0 100%'
[ ] Kirchneriena
[ ] Oocystis
Chloromonas
.....
iiiiiiiii i i i i|I l ii l l l l | l | l l ,
"~ 0 50o/=
0"/, Spring Summer Fall Winter Spring Summer Fall 1988 1989
Fig. 5. Taxonomicstructures of phytoplanktoncommunitiesin ponds A and B, expressed in relative biomass.
F. Mespld et al. ~Ecological Modelling 78 (1995) 25-36
31
Table 2 "Edible" (Y) and "inedible" (n) algal taxa to zooplankton taxa, relating to their diameter (@) Cladocerans "edible" algal sizea: 3-20/xm
Copepods "edible" algal sizea: 10-50/xm
Rotifers "edible" algal sizea: < 20/~m
y
y
Y
y
y
Y
y
y
Y
y
y
Y
n (because of hard cell walls)
Y
Y
n
Y
n
y
n
n
n (because of gelatinous sheath)
Y
(calibration) Y
y
y
Y
n
n
n
n
Y
n
Ankistrodesmus (@ = 6.8 _ 1.2 tzm b)
Astasia (@ = 15.8 _+ 2.5 Ixm b)
Chlorella (@ = 5.1 ± 0.3 tzm b)
Chloromonas (@ = 18.3 _+ 4.4/xm b)
Diatoms ( 0 = 13.2 _+ 2 . 4 / z m b)
Euglena (@ = 29.8 ± 3.4/~m b)
tO'rchneriella (@ = 6.2 _4- 1.5/Lm
b)
Microcystis (@ = 13.2 _+ 2.4 ~ m b)
Oocystis (@ = 17.6 _+ 4 . 2 / x m b)
Pediastrum ( 0 = 54.2 + 2.1 ~ m b)
Scenedesmus ( ~ = 22.6 ± 4.2 tzm b)
a Sterner, 1989; b Zulkifli, 1992.
Under a certain concentration of food ([F]0), the filtration rate is independent from the food concentration and equal to FRZima~; above this level, the filtration rate decreases (Stra~kraba and Gnauck, 1985). F R Z / = FRZirnax, if
ature effect with the same function as for phytoplankton growth: f ( T ) = 1.066 (T-2°). Finally, we may write the instantaneous variation of phytoplankton, represented by chlorophyll a, as:
[F]~<[F]0;
F R Z i = exp(FRZim~[F]o/In[F]),
d P / d t = Input P - Output P + Growth - Death -
if [ F ] > [F]0. Food concentration ([F]) is the sum of phytoplankton concentration and detritus concentration (see below). The temperature effect on grazing varies from one species to another (Di Toro et al., 1971) and it is difficult to simulate the effect while the zooplankton groups are not divided into species. As a first approximation we simulate the temper-
=
Grazing
[P]ppV/O
-
P/O + PGpmax[2.718~b[exp((--Ia/Is)
-
exp(-K~h))
-
e x p ( I J l s ) ] / ( K¢h)] 1.066 (v- 2°)
- DP - Y~[P]iFRZiZi1.066 (T-2°).
F. Mesplg et al. / Ecological Modelling 78 (1995) 25-36
32
3.3. Detritus submodel The state variable D E T regroups the detritus of the model, i.e. phytoplankton necromass and faecal pellets. Knowing the concentration of chlorophyll a and total suspended solids in the inflow, we are able, by difference, to calculate the detritus concentration [DET]pp. The detritus input and output per day are: Input D E T = [DET]opV/O, Output D E T = D E T / 0 . This compartment is supplied by the flow "phytoplankton death" (expressed in chlorophyll a per day) converted to dry weight using the chlorophyll a/dry weight ratio, C 1. This ratio is constant when the algal cells are not deprived of nutrients (Dauta, 1983). The zooplankton also graze this compartment. The grazing process is represented by the same equation as phytoplankton grazing. When zooplankton graze phytoplankton and detritus, faecal pellets add to this state variable. One can consider that the input of these faecal pellets is a fraction, r, of the grazed matter. Considering phytoplankton, this fraction is computed in chlorophyll a and then converted to dry weight with C 1 ratio. The organic matter in this compartment is mineralized at a rate R, related only to temperature by f ( T ) . The instantaneous variation of D E T is therefore: d D E T / d t = Input D E T - Output D E T
tion into water. It is expressed in mg dry weight. It is the sum of phytoplankton converted to dry weight with C 1 ratio, the detritus compartment and of zooplankton biomass, converted to dry weight with C 2 ratio. TSS = P C~ + D E T + C2~,Z i.
3.5. Simulation The simulations were made in the following order: the model with grazing and defecation processes was calibrated on pond A data and then applied to pond B data; the same model, but without grazing and defecation processes, was applied to both ponds. To go from simple to more complex, we present, firstly, the results of the simulations without grazing (Fig. 6), followed by those with grazing (Fig. 7). As can be seen in Fig. 6, the model without grazing simulates roughly the seasonal cycle of chlorophyll a concentration in pond A with the maxima in summer and the minima in winter. In pond B, the winter minima are adequately simulated, but unlike pond A there are also minima in summer. The differences between observed and
pond A
7 6
~5
•
°
I
~4
I
o
3
+ Phytoplankton death - Grazing + Defecation - Mineralization [DET]ppV/O - D E T / O + D P C 1
1 0
)ond B
7
- ~,[DET]FRZiZi1.066 (r- 2°) + (E[P],FRZiZi)rCll.066 (r-2°) + (~,[DET]FRZiZi)rCt 1.066 (r-2°) - D E T R 1.066 (T- 20).
~4 ~3
The evolution of this compartment (TSS) has to be simulated because it affects light penetra-
eeQee
• •
~2 1 0
3.4. Total suspended solids submodel
.
~6
m Spring
Summer 1988
Fall
Winter
Spring Summer 1989
Fall
Fig. 6. Model without grazing process: comparison of observed (points) and simulated (solid lines) chlorophyll a concentrations (P) in ponds A and B.
F. Mespl~ et al. ~Ecological Modelling 78 (1995) 25-36 8 7
pond
A
,,
:
o "~3 ~ g2
"
~
o ~3 ea ,EE 2 1
• • "o
"
ee
,,
•e , e**
e
•
we
~***•
•
•
0 Spring
Summer 1988
Fall
Winter
Spring Summer 1989
Fall
Fig. 7. Model with grazing process: comparison of observed (points) and simulated (solid lines) chlorophyll a concentrations (P) in ponds A and B.
simulated data are more apparent in summer 1988 than in summer 1989 for both ponds. It seems that a major phenomenon (more important the first year than the second, and more important in pond B than in pond A) is not taken into account in the model. The computed concentration of chlorophyll a depends on solar radiation and temperature cycles; taking into account only these variables in the model does not allow simulation of the chlorophyll a concentration on a scale shorter than seasonal. The evolution of the chlorophyll a concentration, computed with the model with grazing, is shown in Fig. 7. For pond A, we notice an improvement of the simulation during the summers of both 1988 and 1989. In pond B, the simulation of the chlorophyll a concentration during both summers is nearer the observed data. Thus, the phenomenon that was not accounted for in the first model is probably the grazing process.
4. Discussion
The differences between simulated - with the model without grazing - and observed data dur-
33
ing summer are far more important for pond B than pond A. This originates from differences in retention times between both ponds; indeed, when retention time decreases, the species for which the generation time is longer than retention time are flushed out. First, zooplankton has the longest generation time. Therefore, if other conditions are identical in A and B ponds, the zooplankton is expected to grow better in the pond with the longest retention time (pond B). The grazing effect should therefore be more important in pond B than in pond A. Taking into account grazing processes allows simulation of the chlorophyll a concentration on a short temporal scale, in the order of a month, while the model without grazing only allows rough seasonal estimates for pond A and even false estimates in summer for pond B. To optimize the management of these types of pond, it is therefore necessary to use a model with grazing, unless suppressing the zooplankton development by physical (decreasing retention time, placing mesh screens of 50 /zm porosity in the channels for a period each day) or chemical means (increasing temporarily free ammonia to 20 mg 1-1, using mercaptothione, or reducing the pH to 3.5 for a few hours and neutralizing it after) (Richmond, 1986). The disadvantage of using chemical substances or nets is the increase in cost, while decreasing retention time limits phytoplankton development and decreases the removal efficiency. Taking into account the grazing process was achieved (see Results) at the price of an important forcing by (i) phytoplankton structure and (ii) biomass of the three zooplankton groups. But this forcing is successful since we observe a clear improvement of the simulations. The aim now must be to eliminate these forcing variables. To do this, we have to represent the phytoplankton by a different measure than chlorophyll a, which is too integral and which does not permit us to know, at any time, the size distribution of algal cells in the pond. Indeed, this may be particularly important since it is mainly the size of the algae which determines their grazing by zooplankton, although chemical phenomena may also interfere (Sterner, 1989). For taking into account
34
F. Mesplg et al. / Ecological Modelling 78 (1995) 25-36
information on the size of the phytoplankton cells, it is possible, as we have done, to consider the taxonomy. However, taxonomic determination is time consuming, tedious, and allows only a posteriori information; obviously therefore such a method does not allow predictions. This impossible situation can be overcome if we use several state variables to describe the phytoplankton compartment. The number of phytoplankton taxa is too important to represent each taxon as a state variable, but it is possible to pass from a taxonomic to a functional description of the phytoplankton structure using size class; only a restricted number of classes need be used. The phytoplankton species regrouped in these state variables should have homogeneous physiologies (growth rates, death rates, etc.), they must react in the same way to variations in temperature, radiation, nutrients concentrations, etc. One can consider this state achieved, at first approximation, because physiology measurements, and especially the maximal growth rate, are related to cell volume (Stra~kraba and Gnauck, 1985). The zooplankton has also to be divided into state variables corresponding to homogeneous groups related to their effect on phytoplankton; the species inside these groups should have the same maximal filtration rate, the same filtration threshold and should graze the same sizes of algal cells. Concerning the evolution of these phytoplankton and zooplankton groups (each one represented by a state variable), the difficulty is not conceptual because the same processes, represented by the same mathematical functions, apply within the phytoplankton or zooplankton compartment; only the parameters vary from one group to another, and they are not known with enough accuracy to allow simulation of the evolution of one group in the presence of others, and their successions. We believe that the H R A P is an ecosystem in which the successions of the phytoplankton taxa depend on interspecific competition, apart from zooplankton grazing. The phytoplankton taxa best adaptated to the ecosystem characteristics (especially light and temperature) will grow faster than the others. The problem is to characterize each state variable, repre-
senting a phytoplankton size class, by optimal temperature and irradiance, as Dauta (1983) started to do for different taxa. The seasonal evolutions of these groups will depend on meteorological conditions, while the shorter scale evolutions will depend on the presence or absence of grazers. It is impossible to know the date of appearance of a particular phytoplankton taxon within a week. The primary requirement to allow the development of algae is the presence of at least one cell in the pond. The data from the primary pond effluent (data not shown) show that some taxa had grown in both ponds which were not detected in the effluent.
5. Conclusions
We have underlined the importance of zooplankton grazing on the growth patterns of chlorophyll a in our experimental HRAP, and shown the clear improvement of the simulations when grazing is taken into account. For such an HRAP, with an actively growing community of grazers, it seems impossible not to take into account their effects on the evolution of the phytoplankton population. Some mathematical models which allow computation of primary production in a H R A P (Martin and Fallowfield, 1989; Grobbelaar et al., 1990; Fallowfield et al., 1992), in an attempt to optimize the pond's management, were constructed and calibrated without taking into account the zooplankton compartment. For low zooplankton abundance (as in pond A), a rough seasonal estimate of the variations in phytoplankton biomass is possible without consideration of zooplankton grazing. In contrast, when its abundance is high (pond B), the error in the simulation, even on a seasonal scale, is very significant. Although it is possible to simulate the chlorophyll a growth pattern a posteriori with forcing variables (phytoplankton structure and zooplankton biomass), as we have done, it seems unlikely, for the near future at least, that it will be possible to construct a predictive model on a taxonomic
F. Mesplg et al. ~Ecological Modelling 78 (1995) 25-36
basis, because of the high number of state variables (genus or species) to be considered. It would be more promising, in the case of an ecosystem study, with the help of deterministic modelling, to describe the biological variables by their functional characteristics (especially size), rather than by their taxonomy.
Acknowledgements The authors gratefully acknowledge the EEC for financial support through the grant EV4V0071-C (EDB) and thank H. Zulkifli, S. Canovas, S. Moersidik and H. E1 Halouani for their authorization to use their data.
References Bahlaoui, M.A., 1990. Lagunage ~ haut rendement exp6rimental: dynamique des diffErents groupes bactEriens et performances 6puratrices sanitaires. Th~se de doctorat, UniversitE de Montpellier II, 186 pp. Bannister, T.T., 1974. Production equations in terms of chlorophyll concentration, quantum yield, and upper limit to production, Limnol. Oceanogr., 19: 1-12. Bougis, P., 1974. Ecologie du Plancton Marin. II. Le Zooplancton. Masson et Cie, Paris, 200 pp. Buhr, H.O. and Miller, S.B., 1983. A dynamic model of the high-rate algal-bacterial wastewater treatment pond. Water Res., 17: 29-37. Canovas, S., 1991. Structure du zooplancton en traitement des eaux usEes par lagunage ~ haut rendement. Th~se de doctorat, UniversitE de Montpellier I, 170 pp. Dauta, A., 1982. Conditions de dEveloppement du phytoplancton. Etude comparative du comportement de huit esp~ces en culture. I. DEtermination des param~tres de croissance en fonction de la lumi~re et de la temperature. Ann. Limnol., 18: 217-262. Dauta, A., 1983. Conditions de dEveloppement du phytoplancton. I. Mod61isation de culture d'algues. Une approche des conditions de succession. Ann. Limnol., 19: 73-86. Di Toro, D.M., O'Connor, D.J. and Thomann, R.V,, 1971. A dynamic model of the phytoplankton population in the Sacramento-San Joaquin delta. Advances in Chemistry, No. 106, American Chemical Society, pp. 131-180. El Halouani, H., 1990. Lagunage ~ haut rendement: caractErisation physicochimique de l'ecosyst~me. Etude de son aptitude ?~ l'elimination de l'azote et du phosphore
35
dans l'epuration des eaux us6es. Th~se de doctorat, UniversitE de Montpellier I, 154 pp. Fallowfield, H.J. and Garrett, M.K., 1985. The treatment of wastes by algal culture. J. Appl. Bacteriol., Symposium Supplement, 187S-205S. Fallowfield, H.J. and Martin, N.J., 1988. The operation, performance and computer design of high rate algal ponds. In: Aquacultural Engineering: Technologies for the Future. Institute of Chemical Engineers Symposium Series No. 111, EFCE Publication Series No. 66, pp. 389-403. Fallowfield, H.J., MesplE, F., Martin, N.J., Casellas, C. and Bontoux, J., 1992. Validation of computer models for high rate algal pond operation for wastewater treatment using data from mediterranean and scottish pilot scale systems: implications for management in coastal regions. Water Sci. Tech., 25: 215-224. Fee, E.J., 1969. A numerical model for the estimation of photosynthetic production, integrated over time and depth, in natural waters. Limnol. Oceanogr., 14: 906-911. Goldman, J.C., 1979. Outdoor algal mass cultures. II. Photosynthetic yield limitations. Water Res., 13: 119-136. Grobbelaar, J.U., Soeder, C.J. and Stengel, E., 1990. Modeling algal productivity in large outdoor cultures and waste treatment systems. Biomass, 21: 297-314. Harris, G.P., 1980. Temporal and spatial scales in phytoplankton ecology. Mechanisms, methods, models, and management. Can. J. Fish. Aquat. Sci., 37: 877-900. Kirk, J.T.O., 1983. Light and Photosynthesis in Aquatic Ecosystems. Cambridge University Press, Cambridge, 401 PP. Martin, N.J. and Fallowfield, H.J,, 1989. Computer modelling of algal waste treatment systems. Water Sci. Tech., 21: 1657-1660. Oswald, W.J., 1988. Large-scale systems (Engineering aspects). In: M.A. Borowitzka and L.J. Borowitzka (Editors), Micro-algal Biotechnology. Cambridge University Press, Cambridge, pp. 357-394. Oswald, W.J., Gotaas, H.B., Ludwig, H.F. and Lynch, V., 1953. Algae symbiosis in oxidation ponds. 1II. Photosynthetic oxygenation. Sewage Ind. Wastes, 25: 692-705. Peters, R.H. and Downing, J.A., 1984. Empirical analysis of zooplankton filtering and feeding rates. Limnol. Oceanogr., 29: 763-784. Picot, B., E1 Halouani, H., Casellas, C., Moersidik, S. and Bontoux, J., 1991. Nutrient removal by high rate pond system in a meditteranean climate (France). Water Sci. Tech., 23: 1535-1541. Richmond, A., 1986. Handbook of Microalgal Mass Culture. CRC Press, Boca Raton, FL, 528 pp. Sciandra, A., 1986. Study and modelling of a simple planktonic system reconstituted in an experimental microcosm. Ecol. Model., 34: 61-82. Steele, J.H., 1962. Environmental control of photosynthesis in the sea. Limnol. Oceanogr., 7: 137-150. Sterner, R.W., 1989. The role of grazers in phytoplankton succession. In: U. Sommer (Editor), Plankton Ecology:
36
F. Mespl£ et al. / Ecological Modelling 78 (1995) 25-36
Succession in Plankton Communities. Springer-Verlag, Berlin, pp. 107-170. Stra~kraba, M. and Gnauck, A.H., 1985. Freshwater Ecosystems: Modelling and Simulation. Elsevier, Amsterdam, 313 pp. Thomann, R.V. and Mueller, J.A., 1986. Principles of Surface
Water Quality Modeling and Control. Harper & Row, New York, 643 pp. Zulkifli, H., 1992. Traitement des eaux us6es par lagunage haut rendement: structure et dynamique des peuplements phytoplanctoniques. Th~se de doctorat, Universit6 de Montpellier I, 206 pp.
Ecological Modelling 78 (1995) 25-36
Some difficulties in modelling chlorophyll a evolution in a high rate algal pond ecosystem Fabrice Mespl6 a,,, Claude Casellas a, Marc Troussellier b, Jean Bontoux
a
a Ddpartement Sciences de l'Environnement et Santd Publique, URA CNRS 1355, Facultd de Pharmacie, Avenue C. Flahault, F-34060, Montpellier, France b Laboratoire d'Hydrobiologie Marine et Continentale, URA CNRS 1355, Universitd Montpellier lI, F-34095, Montpellier, France
Received 30 January 1993; accepted 1 February 1994
Abstract The High Rate Algal Pond (HRAP) is an efficient treatment for controlling wastewater pollution by reducing the organic matter and the inorganic nutrient content. Deterministic modelling of temporal evolution of algae could provide a rational basis for pond management. An experimental H R A P was set up in M~ze (France) and sampled weekly over 24 months. Models simulating the evolution of chlorophyll a concentration and nutrients (N and P) were constructed using Stella II software. The seasonal pattern of chlorophyll a concentrations results from the annual cycle of solar irradiance and temperature, whereas shorter trends (1 to 4 weeks) are dependent on the evolution of zooplankton groups. The first difficulty is to determine the functional relationships of the phytoplankton and zooplankton groups. In the model the evolution of the phytoplankton taxa is considered to be dependent on (i) inherent parameters of phytoplankton taxa (mortality rate, growth rate, saturating light intensity, etc.) and on (ii) parameters of zooplankton taxa (filtration rate, size selectivity, etc.). To take all these taxa as state variables, and all the associated parameters, into account is impossible: to solve such a problem, we forced the evolution of the biomass of the phytoplankton and zooplankton taxa. This approach improves the agreement between the simulated and observed chlorophyll a concentration values. The second difficulty concerns the determinism of appearance of the phytoplankton and zooplankton taxa used in the model: up to now we are only able to force these appearances. Thus, even in quite simple ecosystems, using deterministic modelling as a predictive tool requires a full understanding of the exact biological succession and interaction processes. Keywords: Algae; Chlorophyll; Pond
1. Introduction
* Corresponding author. Present address: Laboratoire d'Hydrobiologie Marine et Continentale, URA CNRS 1355, Universit6 Montpellier II, Place E. Bataillon, F-34095, Montpellier Cedex 05, France.
H i g h R a t e A l g a l P o n d ( H R A P ) is an efficient t r e a t m e n t system for c o n t r o l l i n g w a s t e w a t e r pollution t h r o u g h o p t i m i z a t i o n of algal g r o w t h (Picot et al., 1991). T h e p e r f o r m a n c e o f high r a t e p o n d s
0304-3800/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0304-3800(94)00115-X
26
F. Mespld et aL / Ecological Modelling 78 (1995) 25-36
(HRAPs) depends mainly on the climatic conditions of the pond's location because the major factors affecting the pond's performance, on a seasonal scale, are solar irradiance and water temperature (Goldman, 1979). To optimize the performance of this low-cost and simple-technology wastewater treatment system, one needs a quantitative understanding of the relationships between these keys parameters and the growth of the algae. Computer modelling provides a valuable tool to explore the factors controlling this relationship and to provide information on the design and operation of the ponds. Models simulating the different parts of a HRAP's ecosystem have already been developed. Fallowfield and Martin (1988) and Martin and Fallowfield (1989) described a model to predict the evolution of algal productivity (as dry matter) over the year. Buhr and Miller (1983) presented a model of algae and bacterial growth on a day scale. However, there is still a need for a model simulating the weekly evolution of the phytoplankton compartment over the year. This frequency is adequate to describe phytoplankton dynamics in the ponds (Harris, 1980).
2. Materials and methods
.q
12, m
waTwate~ ~
°'~
I paddle wheel depth = 0.35 m
Fig. 1. Schematic view of a H R A P (~ flow speed).
from the village of M~ze (8500 inhabitants in winter and 20000 in summer), which was screened, grit and oil removed, and treated in an open unmixed primary settling tank with an 8-day retention time.
2.2. Model calibration data The sampling program lasted two years, from February 1988 to February 1990. Measurements of the inflow from the primary pond and in the HRAP were made at the same frequency. Water
INPUT ~
S~aolar r a d i ~
-- -- - R ~ e n c e f i m ~ - -
~
-- -{
.--
2.1. High rate algal ponds Two experimental HRAPs were operated at M6ze in southern France (03°35'E, 43°25'N) where a facultative pond treatment existed since 1980. The experimental ponds are 12 m by 4 m with a volume of 16.8 m 3 at 0.35 m depth with a central baffle. A circulation flow of 15 cm s -1 was maintained with a six-bladed paddle wheel mounted transversely across one channel (Fig. 1). Pond A was run at a seasonally variable retention time calculated using Oswald's (1988) empirical formula, and pond B was run at a fixed retention time of 8 days; pond B is used as a reference to determine the influence of a variable retention time (pond A) on the ecosystem and on the outflow water quality. The inflow for the ponds was sewage water
[
I - - ' 1 : State variables
~
/
p
: Forcing variables
J
I~
O
: Sink
Fig. 2. Conceptual model of chlorophyll a evolution in a HRAP. The so-called "model without grazing process" does not take into account grazing and defecation processes and the "model with grazing process" takes all processes into account.
F. Mespld et al. / Ecological Modelling 78 (1995) 25-36
temperature and chlorophyll a (French standard A F N O R T 90-117) were measured weekly. Phytoplankton and zooplankton populations, and their biomass, were determined weekly. Daily light intensity was obtained from the FrEjorgues meteorological station 35 km away.
27
2.3. Modelling A conceptual model (Fig. 2) was first developed based on knowledge of algal evolution in a eutrophic ecosystem (Richmond, 1986). The model was constructed using the simulation pro-
Table 1 Model parameters, definitions, values and sources for H R A P chlorophyll a model Symbol
Name
Values/Units
Source
total phytoplankton in pond TSS minus P total suspended solids in pond
mg chlorophyll a mg dry weight mg dry weight
pond data TSS - P pond data
Ly d a y - t oC pond A: 2 to 12 days pond B: 8 days
meteorological station pond data pond data
State variables P DET TSS
Forcing functions t~
photoperiod
Forcing variables It T 0
solar radiation water temperature residence time
Phyto structure
phytoplankton structure total biomass of i in the pond (i = cladocerans, rotifers or copepods) TSS concentration in primary pond P concentration in primary pond D E T concentration in primary pond
Zi [TSS]pp [P]pp [DET]pp
mg fresh weight
pond data pond data
mg dry weight 1- i mg chlorophyll a l mg dry weight 1- 1
primary pond data primary pond data primary pond data
1 day -1 16800 1 3 day- 1 Ly d a y - 1
pond data calibration
Parameters and coefficients Q V Gpmax Ia Ke Ks Kc h D FRZimax
flow rate ( = V/O) water volume in the pond phytoplankton maximal growth rate m e a n solar irradiance during the photoperiod ( = It/4~) total extinction coefficient specific extinction coefficient of TSS minus P specific extinction coefficient of chlorophyll a water depth mortality rate m a x i m u m filtration rate of i (i = cladocerans, rotifers or copepods)
CI
chlorophyll a/dry weight ratio
C2
dry w e i g h t / f r e s h weight ratio for zooplankton d e f e c a t e d / i n g e s t e d ratio mineralization rate threshold u n d e r which filtration rate is independent from food concentration
r R [F]0
m-1 0.05 m - 1 (rag dry weight l - i ) - i 0.016 m e mg - I chlorophyll a 0.35 m 0.15 d a y - 1 1day- i mg- 1 fresh weight zooplankton FRZcladma x = 0.12 FRZRotmax = 0.005 FRZcoomax = 0.12 70 mg dry weight mg i chlorophyll a 0.13 0.3 0.005 day 1 2 mg dry weight 1- t
pond data Richmond, 1986 pond data Sciandra, 1986
T h o m a n n and Mueller, 1986 calibration T h o m a n n and Mueller, 1986 Dauta, 1982
Bougis, 1974 Sciandra, 1986 Sciandra, 1986 Stra~kraba and Gnauck, 1985
F, Mesplget al. / EcologicalModelling 78 (1995)25-36
28
gram STELLA II © (High Performance Systems, Inc.) on an Apple Macintosh S E / 3 0 microcomputer. Simulations used a second-order R u n g e Kutta technique and an integration interval of 1 day. The model with grazing was calibrated with pond A 1988 and 1989 data, and run on pond B. Then the same model without grazing was run on pond A and B. The model parameters, definitions, values and their sources are given in Table 1.
V/O), where V is the volume of the pond and 0 is the residence time; then Input X = [ X ]ppV/O. For the same state variable X, the total output of X via the outflow from the H R A P is: Output X = X/O, where X is the total quantity of a state variable.
3.2. Phytoplankton submodel 3. Results
3.1. Hydrology submodel The hydrology submodel depicts inflow and outflow of wastewater in the pond, with a retention time (0) varying from 2 to 12 days for pond A and constant (8 days) for pond B (Fig. 3). The H R A P is assumed to be homogeneous and not vertically stratified, as confirmed by tracer experiments using chemical (El Halouani, 1990) and bacterial markers (Bahlaoui, 1990). We do not take into account sedimentation because the low depth and the continuous mixing prevent sludge accumulation (Fallowfield and Garrett, 1985). Considering a state variable X, the total input of X via the inflow from the primary treatment tank, is: Input X = [ X ] p p . Q , where [X]pp is the concentration of the state variable in the inflow, Q is the flow rate (Q =
We have chosen to represent the phytoplankton compartment by chlorophyll a which is an integral variable, simple to measure. Knowing the concentration of chlorophyll a in the primary pond ([P]pp) and the residence time (0), we can determine the phytoplankton input and output per day (see Section 3.1): Input P = [P]ppV/O, Output P = P/O.
Growth As the H R A P is continuously supplied with sewage water, phosphates and nitrates are never rate limiting; the mean pond N-NH 4 concentration of 9 mg 1-1 (range 0 . 0 3 - > 30 mg 1-1) remains well above the half-saturation constant of 15 ~ g 1-1 for N-NH 4 (Thomann and Mueller, 1986). Mean P-PO 4 concentrations of 4.6 mg 1-1 (range 0 . 4 5 - > 8 mg l - t ) also greatly exceed the half-saturation constant of 2.5 /zg l -x (Thomann and Mueller, 1986). We therefore only consider light energy and temperature as controlling growth:
Gp=Gpmax[f(lt)] [ f ( T ) l , 14.
Gp being the instantaneous growth rate, Gpmax the maximal growth rate, f ( I t) and f ( T ) the
12 1o .....
influence of solar radiation and temperature, respectively.
.....
Influence of solar radiation Spring S u m m e r Fall 1988
Winter
Spring S u m m e r 1989
Fall
Fig. 3. Residence time (0) in ponds A (solid line) and B (dashed line).
B e e r - L a m b e r t ' s law describes the light I at a depth h, in a light-absorbing medium (Kirk, 1983): I = Io exp(-Keh),
F. Mespldet al. / Ecological Modelling 78 (1995)25-36 where I 0 is the surface irradiance and K e the overall extinction coefficient. This law has been experimentally verified for dense algal cultures (Oswald et al., 1953). Several authors (Steele, 1962; Fee, 1969; Bannister, 1974) have shown that, at a constant temperature, as the irradiance increases, photosynthesis increases to a maximum. Further increase in irradiance tends to result in a decrease in photosynthesis due to photoinhibition. The response of photosynthesis to irradiance is modelled by Steele's (1962) equation, which takes into account the effects of photoinhibition at high light intensities. All irradiances are expressed in Langleys.
g( I ) = Gpmax( I / I s ) exp(1 - I / I s ) , where g ( I ) is the growth rate at irradiance 1 and I s is the saturating light intensity. The model combines B e e r - L a m b e r t ' s and Steele's equations to calculate the daily production rate, using the simplification of Di Toro et al. (1971) about the incident irradiance I0: during the photoperiod I 0 = I a = It/4, and outside the photoperiod I 0 = 0, with I a the mean solar irradiance during the photoperiod, I t the total daily irradiance and 4' the photoperiod in a day. Over the day, for a water depth h (see Di Toro et al., 1971): f ( I t ) = 2.718 4'[exp(--o/1)
--
exp(ao)]/(Keh),
where
Ol1
=
( I./Is) exp(-Keh )
and
c% = l a / I s. The extinction coefficient ( K e) equals: K e = K w + Ks([TSS ] - [ P ] C 1 ) + K c [ P ] , where K w is the extinction coefficient of pure water, K S is the specific extinction coefficient of the total suspended solids minus phytoplankton, expressed in dry weight ( [ T S S ] - [ P ] C 1 ) , K c is the specific extinction coefficient of chlorophyll a, and [P] is the concentration of chlorophyll a. In such ponds - containing wastewater - there
29
is no significant influence of the pure water coefficient of extinction (Kw) on K~. At the latitude of M6ze, we have simulated the evolution of the photoperiod & as: 4, = 12.6 - 3.97 cos[2~-(t + 3 9 ) / 3 6 5 ] / 2 4 , where t is days from 1 January.
Influence of temperature The effect of temperature ( f ( T ) ) o n G p m a x is approximated (Thomann and Mueller, 1986) by: f ( T ) = 1.066 (r-z°), where T is the temperature in °C.
Death Death rate (D) is considered constant over the year. Grazing This process is taken into account only in the model incorporating the grazing process. Modelling the grazing process requires us to focus, firstly, on zooplankton and phytoplankton community structures and secondly on the interactions between these two compartments. The zooplankton compartment cannot be considered as a black box because the structure of the zooplankton community is highly complex and is constantly changing. The study made by Canovas (1991) has shown that this compartment is divided into 5 taxa: Cladocerans, Ostracods, Rotifers, Copepods and Ciliates. As Ostracod biomass is less than 6% of the total zooplankton biomass and Ciliate biomass is less than 10% (Canovas, 1991), these two taxa are neglected in the model. Each taxon possesses different parameters associated with the grazing process (Peters and Downing, 1984; Thomann and Mueller, 1986). Fig. 4 shows the explosive evolution of these groups, which appear difficult to simulate. Indeed, this is why the evolution of each of the zooplankton groups is forced by the variables Zi, representing respective biomass. With regard to the phytoplankton, the chlorophyll a variable is too integral to be able to simulate the grazing process. Moreover, as the zooplankton groups graze different sizes of phytoplankton cells, we have to take into account the size structure of the
F. Mespl~ et al. / Ecological Modelling 78 (1995) 25-36
30
-
-
Cladocerans
----a-- Rotifers
Copepods
1000. pond A o~
~,~, 400
~g
260 o
~,
1750
pond B
E ~ 1500 O.E .~
looo
~
750 250 Spring Summer Fall 1988
Winter Spring Summer Fall 1989
Fig. 4. Evolution of the zooplankton biomass in ponds A and B.
phytoplankton population and its temporal evolution in the model. Unfortunately, it is impossible to calibrate a model taking into account ten phytoplankton taxa as state variables, because the number of associated parameters (growth rate, death rate, saturating light intensity, temperature optimum, etc.) to determine accurately is too large. As with the zooplankton, a forcing variable is used; this is "Phyto structure", which represents the daily taxonomic composition of the phytoplankton population as a percentage of the total biomass (Fig. 5). Only the total mass of chlorophyll a is computed, and then distributed in each taxon in proportion to their biomass. The taxa observed in the ponds during sampling are: Ankistrodesmus, Astasia, Dictyosphora,
Chlorella, Chloridella, Chloromonas, Coelastrum, Diatoms, Euglena, Golenkinia, Kirchneriella, Micractinium, Microcystis, Oocystis, Pediastrurn and Scenedesmus. Taxa that appeared less than 7 times during the two-year sampling period, with a relative biomass of less than 10% are neglected; these taxa are: Dictyosphora, Chloridella, Coelastrum, Golenkinia and Micractinium in pond A, and Astasia, Dictyosphora, Chloridella, Codastrum, Golenkinia, Kirchneriella, Micractinium and Oocystis in pond B.
The third point to take into account is the interaction between phytoplankton and zooplankton. The phytoplankton groups do not react similarly to different zooplankton groups, mainly because of cell sizes. This information has also to be considered by the model, and can be presented as a table, in which the columns are the zooplankton groups, the rows the phytoplankton taxa, and the cells the potential connections between the prey and the grazer (Table 2). Let us consider a group of zooplankton i, represented by its biomass, Z i ( i - Cladocerans, Rotifers or Copepods). The mass of chlorophyll a grazed by this zooplankton group, for a time step dt, is equivalent to: Graz Z i = [ P ] i F R Z i Z i f ( T ) , where [P]i is the chlorophyll a concentration edible by one of the three groups of zooplankton, FRZi is the filtration rate per day, Z i is the total biomass of one of three groups of zooplankton, and f ( T ) is the influence of temperature.
[ ] Microcvstis
[ ] Pediastrum
k~ Astasia
[ ] Ankistrodesmus [ ] Chlorella
[ ] $¢¢nedesmus
[ ] Diatoms
[ ] Euglena
•
i 100%
0 100%'
[ ] Kirchneriena
[ ] Oocystis
Chloromonas
.....
iiiiiiiii i i i i|I l ii l l l l | l | l l ,
"~ 0 50o/=
0"/, Spring Summer Fall Winter Spring Summer Fall 1988 1989
Fig. 5. Taxonomicstructures of phytoplanktoncommunitiesin ponds A and B, expressed in relative biomass.
F. Mespld et al. ~Ecological Modelling 78 (1995) 25-36
31
Table 2 "Edible" (Y) and "inedible" (n) algal taxa to zooplankton taxa, relating to their diameter (@) Cladocerans "edible" algal sizea: 3-20/xm
Copepods "edible" algal sizea: 10-50/xm
Rotifers "edible" algal sizea: < 20/~m
y
y
Y
y
y
Y
y
y
Y
y
y
Y
n (because of hard cell walls)
Y
Y
n
Y
n
y
n
n
n (because of gelatinous sheath)
Y
(calibration) Y
y
y
Y
n
n
n
n
Y
n
Ankistrodesmus (@ = 6.8 _ 1.2 tzm b)
Astasia (@ = 15.8 _+ 2.5 Ixm b)
Chlorella (@ = 5.1 ± 0.3 tzm b)
Chloromonas (@ = 18.3 _+ 4.4/xm b)
Diatoms ( 0 = 13.2 _+ 2 . 4 / z m b)
Euglena (@ = 29.8 ± 3.4/~m b)
tO'rchneriella (@ = 6.2 _4- 1.5/Lm
b)
Microcystis (@ = 13.2 _+ 2.4 ~ m b)
Oocystis (@ = 17.6 _+ 4 . 2 / x m b)
Pediastrum ( 0 = 54.2 + 2.1 ~ m b)
Scenedesmus ( ~ = 22.6 ± 4.2 tzm b)
a Sterner, 1989; b Zulkifli, 1992.
Under a certain concentration of food ([F]0), the filtration rate is independent from the food concentration and equal to FRZima~; above this level, the filtration rate decreases (Stra~kraba and Gnauck, 1985). F R Z / = FRZirnax, if
ature effect with the same function as for phytoplankton growth: f ( T ) = 1.066 (T-2°). Finally, we may write the instantaneous variation of phytoplankton, represented by chlorophyll a, as:
[F]~<[F]0;
F R Z i = exp(FRZim~[F]o/In[F]),
d P / d t = Input P - Output P + Growth - Death -
if [ F ] > [F]0. Food concentration ([F]) is the sum of phytoplankton concentration and detritus concentration (see below). The temperature effect on grazing varies from one species to another (Di Toro et al., 1971) and it is difficult to simulate the effect while the zooplankton groups are not divided into species. As a first approximation we simulate the temper-
=
Grazing
[P]ppV/O
-
P/O + PGpmax[2.718~b[exp((--Ia/Is)
-
exp(-K~h))
-
e x p ( I J l s ) ] / ( K¢h)] 1.066 (v- 2°)
- DP - Y~[P]iFRZiZi1.066 (T-2°).
F. Mesplg et al. / Ecological Modelling 78 (1995) 25-36
32
3.3. Detritus submodel The state variable D E T regroups the detritus of the model, i.e. phytoplankton necromass and faecal pellets. Knowing the concentration of chlorophyll a and total suspended solids in the inflow, we are able, by difference, to calculate the detritus concentration [DET]pp. The detritus input and output per day are: Input D E T = [DET]opV/O, Output D E T = D E T / 0 . This compartment is supplied by the flow "phytoplankton death" (expressed in chlorophyll a per day) converted to dry weight using the chlorophyll a/dry weight ratio, C 1. This ratio is constant when the algal cells are not deprived of nutrients (Dauta, 1983). The zooplankton also graze this compartment. The grazing process is represented by the same equation as phytoplankton grazing. When zooplankton graze phytoplankton and detritus, faecal pellets add to this state variable. One can consider that the input of these faecal pellets is a fraction, r, of the grazed matter. Considering phytoplankton, this fraction is computed in chlorophyll a and then converted to dry weight with C 1 ratio. The organic matter in this compartment is mineralized at a rate R, related only to temperature by f ( T ) . The instantaneous variation of D E T is therefore: d D E T / d t = Input D E T - Output D E T
tion into water. It is expressed in mg dry weight. It is the sum of phytoplankton converted to dry weight with C 1 ratio, the detritus compartment and of zooplankton biomass, converted to dry weight with C 2 ratio. TSS = P C~ + D E T + C2~,Z i.
3.5. Simulation The simulations were made in the following order: the model with grazing and defecation processes was calibrated on pond A data and then applied to pond B data; the same model, but without grazing and defecation processes, was applied to both ponds. To go from simple to more complex, we present, firstly, the results of the simulations without grazing (Fig. 6), followed by those with grazing (Fig. 7). As can be seen in Fig. 6, the model without grazing simulates roughly the seasonal cycle of chlorophyll a concentration in pond A with the maxima in summer and the minima in winter. In pond B, the winter minima are adequately simulated, but unlike pond A there are also minima in summer. The differences between observed and
pond A
7 6
~5
•
°
I
~4
I
o
3
+ Phytoplankton death - Grazing + Defecation - Mineralization [DET]ppV/O - D E T / O + D P C 1
1 0
)ond B
7
- ~,[DET]FRZiZi1.066 (r- 2°) + (E[P],FRZiZi)rCll.066 (r-2°) + (~,[DET]FRZiZi)rCt 1.066 (r-2°) - D E T R 1.066 (T- 20).
~4 ~3
The evolution of this compartment (TSS) has to be simulated because it affects light penetra-
eeQee
• •
~2 1 0
3.4. Total suspended solids submodel
.
~6
m Spring
Summer 1988
Fall
Winter
Spring Summer 1989
Fall
Fig. 6. Model without grazing process: comparison of observed (points) and simulated (solid lines) chlorophyll a concentrations (P) in ponds A and B.
F. Mespl~ et al. ~Ecological Modelling 78 (1995) 25-36 8 7
pond
A
,,
:
o "~3 ~ g2
"
~
o ~3 ea ,EE 2 1
• • "o
"
ee
,,
•e , e**
e
•
we
~***•
•
•
0 Spring
Summer 1988
Fall
Winter
Spring Summer 1989
Fall
Fig. 7. Model with grazing process: comparison of observed (points) and simulated (solid lines) chlorophyll a concentrations (P) in ponds A and B.
simulated data are more apparent in summer 1988 than in summer 1989 for both ponds. It seems that a major phenomenon (more important the first year than the second, and more important in pond B than in pond A) is not taken into account in the model. The computed concentration of chlorophyll a depends on solar radiation and temperature cycles; taking into account only these variables in the model does not allow simulation of the chlorophyll a concentration on a scale shorter than seasonal. The evolution of the chlorophyll a concentration, computed with the model with grazing, is shown in Fig. 7. For pond A, we notice an improvement of the simulation during the summers of both 1988 and 1989. In pond B, the simulation of the chlorophyll a concentration during both summers is nearer the observed data. Thus, the phenomenon that was not accounted for in the first model is probably the grazing process.
4. Discussion
The differences between simulated - with the model without grazing - and observed data dur-
33
ing summer are far more important for pond B than pond A. This originates from differences in retention times between both ponds; indeed, when retention time decreases, the species for which the generation time is longer than retention time are flushed out. First, zooplankton has the longest generation time. Therefore, if other conditions are identical in A and B ponds, the zooplankton is expected to grow better in the pond with the longest retention time (pond B). The grazing effect should therefore be more important in pond B than in pond A. Taking into account grazing processes allows simulation of the chlorophyll a concentration on a short temporal scale, in the order of a month, while the model without grazing only allows rough seasonal estimates for pond A and even false estimates in summer for pond B. To optimize the management of these types of pond, it is therefore necessary to use a model with grazing, unless suppressing the zooplankton development by physical (decreasing retention time, placing mesh screens of 50 /zm porosity in the channels for a period each day) or chemical means (increasing temporarily free ammonia to 20 mg 1-1, using mercaptothione, or reducing the pH to 3.5 for a few hours and neutralizing it after) (Richmond, 1986). The disadvantage of using chemical substances or nets is the increase in cost, while decreasing retention time limits phytoplankton development and decreases the removal efficiency. Taking into account the grazing process was achieved (see Results) at the price of an important forcing by (i) phytoplankton structure and (ii) biomass of the three zooplankton groups. But this forcing is successful since we observe a clear improvement of the simulations. The aim now must be to eliminate these forcing variables. To do this, we have to represent the phytoplankton by a different measure than chlorophyll a, which is too integral and which does not permit us to know, at any time, the size distribution of algal cells in the pond. Indeed, this may be particularly important since it is mainly the size of the algae which determines their grazing by zooplankton, although chemical phenomena may also interfere (Sterner, 1989). For taking into account
34
F. Mesplg et al. / Ecological Modelling 78 (1995) 25-36
information on the size of the phytoplankton cells, it is possible, as we have done, to consider the taxonomy. However, taxonomic determination is time consuming, tedious, and allows only a posteriori information; obviously therefore such a method does not allow predictions. This impossible situation can be overcome if we use several state variables to describe the phytoplankton compartment. The number of phytoplankton taxa is too important to represent each taxon as a state variable, but it is possible to pass from a taxonomic to a functional description of the phytoplankton structure using size class; only a restricted number of classes need be used. The phytoplankton species regrouped in these state variables should have homogeneous physiologies (growth rates, death rates, etc.), they must react in the same way to variations in temperature, radiation, nutrients concentrations, etc. One can consider this state achieved, at first approximation, because physiology measurements, and especially the maximal growth rate, are related to cell volume (Stra~kraba and Gnauck, 1985). The zooplankton has also to be divided into state variables corresponding to homogeneous groups related to their effect on phytoplankton; the species inside these groups should have the same maximal filtration rate, the same filtration threshold and should graze the same sizes of algal cells. Concerning the evolution of these phytoplankton and zooplankton groups (each one represented by a state variable), the difficulty is not conceptual because the same processes, represented by the same mathematical functions, apply within the phytoplankton or zooplankton compartment; only the parameters vary from one group to another, and they are not known with enough accuracy to allow simulation of the evolution of one group in the presence of others, and their successions. We believe that the H R A P is an ecosystem in which the successions of the phytoplankton taxa depend on interspecific competition, apart from zooplankton grazing. The phytoplankton taxa best adaptated to the ecosystem characteristics (especially light and temperature) will grow faster than the others. The problem is to characterize each state variable, repre-
senting a phytoplankton size class, by optimal temperature and irradiance, as Dauta (1983) started to do for different taxa. The seasonal evolutions of these groups will depend on meteorological conditions, while the shorter scale evolutions will depend on the presence or absence of grazers. It is impossible to know the date of appearance of a particular phytoplankton taxon within a week. The primary requirement to allow the development of algae is the presence of at least one cell in the pond. The data from the primary pond effluent (data not shown) show that some taxa had grown in both ponds which were not detected in the effluent.
5. Conclusions
We have underlined the importance of zooplankton grazing on the growth patterns of chlorophyll a in our experimental HRAP, and shown the clear improvement of the simulations when grazing is taken into account. For such an HRAP, with an actively growing community of grazers, it seems impossible not to take into account their effects on the evolution of the phytoplankton population. Some mathematical models which allow computation of primary production in a H R A P (Martin and Fallowfield, 1989; Grobbelaar et al., 1990; Fallowfield et al., 1992), in an attempt to optimize the pond's management, were constructed and calibrated without taking into account the zooplankton compartment. For low zooplankton abundance (as in pond A), a rough seasonal estimate of the variations in phytoplankton biomass is possible without consideration of zooplankton grazing. In contrast, when its abundance is high (pond B), the error in the simulation, even on a seasonal scale, is very significant. Although it is possible to simulate the chlorophyll a growth pattern a posteriori with forcing variables (phytoplankton structure and zooplankton biomass), as we have done, it seems unlikely, for the near future at least, that it will be possible to construct a predictive model on a taxonomic
F. Mesplg et al. ~Ecological Modelling 78 (1995) 25-36
basis, because of the high number of state variables (genus or species) to be considered. It would be more promising, in the case of an ecosystem study, with the help of deterministic modelling, to describe the biological variables by their functional characteristics (especially size), rather than by their taxonomy.
Acknowledgements The authors gratefully acknowledge the EEC for financial support through the grant EV4V0071-C (EDB) and thank H. Zulkifli, S. Canovas, S. Moersidik and H. E1 Halouani for their authorization to use their data.
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