Sept. 25, 2003
A generalized biological model for marine ecosystems
Rucheng C. Tian*, Pierre F. Lermusiaux
James J. McCarthy and Allan R. Robinson
Harvard University
Department of Earth and Planetary Sciences
29 Oxford Street
Cambridge
MA 02138
*Present address and correspondence:
Rucheng Tian
School of Marine Science and Technology
University of Massachusetts
706 South Rodney French Blvd.
New Bedford, MA 02744, USA
e-mail: rtian@umassd.edu
Fax: 1-508-910-6342
Tel.: 1-508-910-6383
Key words: Marine, ecosystems, generalized, model
1
Abstract
Marine ecosystems function through a series of highly integrated interactions among
biota and the habitat and dynamic links among food web components. The high degree of
trophic complexity prohibits the development of a single model with fixed structure,
which can be applied to various ocean ecosystems and a large number of various
biological models have been proposed in the literature. In this paper we presented a
generalized and flexible biological model which can be applied to various ecosystems.
The generalized biological model consists of 7 functional groups of state variables:
nutrients (Ni), autotrophs (Ai), heterotrophs (Hi), detritus (Di), dissolved organic matter
(DOMi), bacteria (Bi) and auxiliary state variables (Xi). Auxiliary state variables represent
oceanic properties that are not independent components in food web structure and trophic
dynamics, but their field usually depends on other biological variables (e.g. chlorophyll,
dissolved oxygen, CO2, DMS, bioluminescence, etc). In contrast to classical biological
models in which the number of state variables is fixed, the number of components of each
functional group in the generalized model is a variable (varying from 1 to n). Also, the
symbolic state variables are not prescribed to a specific biological species or chemical
and detrital pools, but their biological correspondents are defined by users for each
specific application. The definition of the biological correspondents resides in the
parameter values that control biological and biogeochemical dynamics and trophic links.
An application with 3 different model configurations is presented to illustrate the
functionality of the generalized biological model.
2
1. Introduction
Marine ecosystems consist of a complex network comprising from inorganic
nutrients, through phytoplankton, bacteria, zooplankton and fish to marine mammals.
Marine ecosystems are usually modeled by compartment models, with each compartment
representing a trophic level or taxonomic group such as phytoplankton, zooplankton and
nutrient. There are organisms of unnumbered species, at various stages and of different
sizes. The structural design is thus critical in determining its adequacy and capability to
simulate ecosystem function.
Since the first marine ecological model of phytoplankton (Fleming, 1939), there is
a trend of increasing complexity in ecological model structure. For example, Andersen et
al. (1987) found that it was necessary to divide the phytoplankton compartment into
diatoms and flagellates and zooplankton into copepods and appendicularia. Moloney and
Field (1991) divided the autotrophs into pico-, nano- and net-phytoplankton and
heterotrophs into bacteriplankton, heterotrophic flagellates, microzooplankton and
meosozooplankton. Moisan and Hofmann (1996) considered gelatinous zooplankton,
copepods and euphausiids whereas Pace et al. (1984) simulated bacteriaplankton,
protozoa, grazing zooplankton, carnivorous zooplankton, mucous net feeders and pelagic
fishes at the heterotrophic level. Wroblewski (1982) considered five life stages of
copepod: eggs, nauplii, early copepodites (CI-III), copepodites (CIV-CV) and adult.
Armstrong (1994) proposed a model with n parallel food chains, with each consisting of a
phytoplankton species Pi and it’s dedicated zooplankton predator Zi classified in size.
Nihoul and Djenidi (1998) presented a conceptual food web model in which
3
phytoplankton was divided into cynobacteria, ultraphytoflagellates, phytoflagellates,
diatoms and autotrophic dinoflagellates and zooplankton was divided into heterotrophic
flagellates, ciliates, heterotrophic dinoflagellates, arthropod and gelatinous zooplankton.
Although most of the biological models are nitrogen driven, Lancelot et al. (2000)
considered five types of nutrients (Si(OH)4, PO4-, NO3-, NH4+ and Fe). Armstrong (1999)
argued that ecological models need to reflect both taxonomic and size structure of the
planktonic community. Cousins (1980) suggested a conceptual trophic continuum model
in which an ecosystem was divided into three basic trophic levels (autotrophs,
heterotrophs and detritus), with each component representing a size continuum from
small to large organisms or particles.
The high degree of trophic complexity prohibits the development of a single
model with fixed structure, which can be applied to various marine ecosystems. Given
the complexity and diversity in marine ecosystems, we present in this paper a generalized
and flexible biological model, which can be adapted to various marine ecosystems and
scientific objectives.
2. Model structure
Marine ecosystems function through a series of highly integrated interactions among
biota and the habitat and trophic links among food web components. Nutrient availability
is the primary limiting factor in oceanic productivity. Phytoplankton photosynthesis
represents the first step in food web dynamics in the ocean, followed by secondary
production of zooplankton, fish and so on. Organisms at each trophic level can be
classified on various criteria, such as size, weight, age and taxonomic groups. Based on
4
the energy resources harvested from the ocean, however, marine organisms can be
divided into autotrophs and heterotrophs (Cousins, 1980). Autotrophs are organisms that
obtain all their energy from inorganic material whereas heterotrophs require organic
substances as energy resource. We adopted this general classification in order that the
state variables of the generalized biological model represent a large range of marine
organisms. Dissolved organic matter is fundamentally different from particular organic
matter or detritus in biogeochemical dynamics and bacteria have specific impacts on
remineralization of organic matter and energy transfer. Based on these trophic and
biogeochemical dynamics, the generalized biological model is constituted of 7 functional
groups of state variables (Fig. 1): nutrients ( Ni), autotrophs (Ai), heterotrophs (Hi),
detritus (Di), dissolved organic matter (DOMi), bacteria (Bi) and auxiliary state variables
(Xi). In this paper we focus on discussion of the pelagic ecosystem. However, the
generalized biological model has the potential to extend to benthic ecosystems and to
higher trophic levels. For example, apart from phytoplankton in pelagic ecosystems,
autotrophs can include other marine plant such as macrophytes and sea grass. At the
heterotroph level, the model has potential to extend from zooplankton to fish level and
other marine animals.
In contrast to classical biological models in which the number of state variables is
fixed, the number of components of each functional group in the generalized biological
model is a variable (varying from 1 to n). Also, the symbolic state variables are not
prescribed to a specific biological species or chemical and detrital pools, but their
biological correspondents are defined by users for each specific application. We describe
below some examples of state variable assignments, but different assignments are
5
feasible.
Nutrients include ammonium (NH4+), nitrate (NO3-), phosphate (PO4-), silicate
(Si(OH)4) and iron (Fe). Autotrophs essentially represent phytoplankton in pelagic
ecosystems. Phytoplankton can be classified as picophytoplankton, nanophytoplankton
and microphytoplankton, or as small and large phytoplankton according to their size.
Taxonomic groups can also be used for state variable assignment, such as cyanobacteria,
dinoflagellates and diatoms, or detailed species. Heterotrophs in pelagic systems are
essentially zooplankton that can range from protozoa, through ciliates, copepodes to net
mucous feeders, or represent different stages or different weights of zooplankton.
Detritus are usually classified by size, but other classifications are also possible, e.g.
based on chemical composition. DOM can be classified according to their chemical
composition (e.g., DOC and DON) or at the molecular level (e.g., high and low molecular
weight DOM). The bioavailability of DOM is of particular importance in determining
biogeochemical cycles, remineralization, energy transfer and microbial activities.
Consequently DOM is often classified as labile, semi-labile and refractory categories
(Carlson and Ducklow, 1995; Anderson and Williams, 1999). The bioavailability of
DOM consists of a continuum from labile to refractory so that DOM can be divided into a
large number of classes. Numerous classifications are possible for marine bacteria. In
ecological modeling, it is important to parameterize bacterial response to environmental
factors. For example, bacteria can be divided into aerobic and anaerobic species.
According to their response to temperature, bacteria can be divided into psychrophiles
(optimal temperature Topt between 4 and 7 C), tolerant psychrophiles (Topt=7-20 C),
psychrotrophs (can develop over a large range of temperature), tolerant psychrotrophs
6
(Topt=20-20 C) and mesophiles bacteria (Topt>30 C) (Delille and Perret, 1989).
Auxiliary state variables represent oceanic properties that are not independent
components in food web structure and trophic dynamics and their field depends on other
biological variables (e.g., chlorophyll, CO2, dissolved oxygen, DMS, optics, acoustic
properties, bioluminescence, toxin of harmful algae, etc).
In order that the model is flexible, energy flows between food web components are not
determined in advance. All heterotrophs can feed on all autotrophs and all other
heterotrophs. The specific energy flow between two biological pools will be determined
by users by assigning a specific value to the corresponding preference coefficient (Fig.
2). For example, omnivorous and carnivorous copepods may have raptorial feeding with
narrow-size window of prey whereas mucous-net feeder such as appendicularia, salps,
and doliolids can collect particles ranging from bacteria (0.2-5 m in diameter) to large
diatoms (8x100 m) (Madin and Deibel, 1997). Energy flows are quite different between
these two types of zooplankton although they can be represented by the same symbolic
state variable in the model. Detailed trophic links are determined based on state variable
assignment in a specific application. This will be illustrated by the application presented
in the following sections.
The basic unit (or currency) of the model is also determined by users. The commonly
used unit in ecological and biogeochemical models are in carbon or nitrogen. Generally
the unit is unique for a single biological model. In a specific model, however, there can
be more than one unit if it is so desired for observational or scientific/modeling reasons.
Transfer coefficients (i.e. conversion factors) from one unit to another is provided in this
generalized model by a specific elemental ratio for each trophic component.
7
3. Parameterization
A wide variety of mathematical formulations have been developed to describe
biological processes and forcing functions, such as light, nutrient and temperature forcing
on
phytoplankton
growth
rate,
zooplankton
grazing
and
predation.
Theses
parameterizations are usually based on empirical relationships between variables that can
be measured. The ecological or physiological processes underlying the observed
correlation are not explicit in these relationships. There is no sound statistical or
physiological basis to reject one or another formulation (Sakshaug et al., 1997), but the
choice between them can be critical in respect with the model behavior (Gao et al., 2000;
Gentleman et al., 2003). In this paper, we present one set of parameterizations selected as
the a priori equations of the generalized biological model. These parameterizations have
been selected based on their flexibility and completeness. For example, parameterization
of light forcing on phytoplankton growth rate with photoinhibition have been selected
over that without photoinhibition. Grazing functions with switching functional response
have been selected over that without switching functional response. Mechanistic
parameterizations have been selected over empirical relationships. Formulations that can
simulate various functional responses have been selected over monotone functions (Tian,
in preparation).
3.1. Autotrophs
The partial differential equation for autotrophs (phytoplankton) Ai is written as:
Ai
A nh
m
 (1  rASi ) i Ai  a ADi Ai Ai  rAS i Ai  s Ai i   G Aji
t
z j 1
(1)
8
where i, aADi, mi, rASi, rASi, spi are the growth rate, mortality (including aggregation) rate
and power index, biomass-based and growth-based exudation of DOM and sinking
velocity og autotroph Ai, i(0, np) and j(0, nz) are autotroph and heterotroph index varying
from 0 to na and nh, and na and nh are the total number of autotrophs and heterotrophs
respectively.
Temperature tends to influence the maximum phytoplankton growth rate so that
multiplication with other limiting factors is usually used to compute the combined effect.
However, both multiplication and the minimum of light- and nutrient-dependent
phytoplankton growth rates are used in the literature:
 i (1)   i (T ) min(  i ( E ),  i ( N1, 2 ),  i ( N 3 ), , ,  i ( N nn ))
(2)
 i ( 2)   i ( E ) i (T ) min(  i ( N1, 2 ),  i ( N 3 ), , ,  i ( N nn ))
(3)
where i(T), i(E) and i(Nj) are temperature, light and nutrient-dependent growth rate of
autotroph Ai, respectively. Both of these two formulations are hypothetical. Experimental
and field data often showed that the combined effects of light and nutrient limitation is
between the minimum and multiplication (Rhee and Gotham, 1981; Redalje and Laws,
1983). Consequently we suggest combining the minimum and multiplication formulation:
 i   i  i (1)  (1   i ) i (2)
(4)
where 0<<1.
Light forcing on phytoplankton growth rate is formulated as:
i ( E )  (1  e 
Ai E / Pmi
)e
  Ai E / Pmi
(5)
where E represents photosynthetically active radiation (PAR), Pmi is the theoretical
maximum growth rate, Ai is the initial slope of photosynthesis-irradiance relationship
9
and Ai is the photoinhibition coefficient (Platt et al. 1980).
Temperature forcing on phytoplankton growth rate is parameterized as:
 i (T )  Pmi e
T TOAi
TAi
(6)
where T is the temperature of sea water, TOAi and ∆TAi are the optimal temperature and
the temperature interval determining the initial slope of the relationship between
temperature and phytoplankton growth rate. This function can simulate the optimal
temperature at which phytoplankton growth rate reaches a maximum and ∆TAi can be
determined from Q10.
Limitation of phytoplankton growth by nutrient availability is parameterized by the
combined Michaelis-Menten and Droop function:
 i ( N ( j )) 
N j  N 0 ji
N j  K SNJi  N 0 ji
(7)
where Nj, N0ji and KSNji are concentration, threshold and half-saturation constant of
nutrient Nj for autotroph Ai (Caperon and Myer, 1972; Paasche; 1973; Dugdale, 1977;
Droop, 1983). Ammonium inhibition on nitrate uptake is formulated as:
i ( N (2)) 
N 2  N 02
K SN1i

N 2  N 02  K SN 2i N1  N 01  K SN1i
(8)
where N1, N2, KSN1i and KSN2i are concentration of and half-saturation constants of
ammonium and nitrate for autotroph Ai (Parker 1993).
DOM exudation from phytoplankton is linked to both biomass and growth rate
representing basic and active respiration, respectively (Bannister, 1979; Laws and
Bannister, 1980; Spitz et al., 2001). Mortality (senescence) is usually parameterized as a
linear function whereas aggregation loss as a quadratic function of phytoplankton
10
biomass. Both mortality and aggregation of phytoplankton result in formation of biogenic
detritus. We have combined the two mechanisms by using an adjustable power function
(2nd term in Eq. 1). Linear and quadratic functions will be simulated when the power
order mAi is set to 1 and to 2 respectively. The grazing term (5th term in Eq. 2) will be
described in the following section.
3.2 Heterotrophs
The general equation for heterotrophs Hj is written as:
H j
t
na
nh
nd
nb
i 1
k 1
l 1
m 1
  e HAjiG Aji   (e HHjk G Hjk  G Hkj )   e HDjk G Djl   e HBjmG Bjm
  HDj H
mHj
 rHj H j  w j
(9)
H j
z
where GAji, GHjk, GDjl and GBjm are the total grazing (or predation) amounts of heterotroph
Hj on autotroph Ai, heterotroph Hk, detritus Dl and bacteria Bm, respectively, eHAji, eHHjk
eHDjl and eHBjm are the corresponding gross growth efficiency of Hj, GHkj is the predation
loss of Hj by other heterotrophs, mHDj, mHj are the power indices of heterotroph mortality,
rHj is the biomass-based respiration coefficient and wj is the vertical migration speed of
heterotrophs Hj.
Heterotroph grazing function is written as:
G Aji  g j (T ) H j
p
( Ai  A0i )
mGj
HAji
na
R j   ( p HAji ( Ai  A0i ))
i 1
nd
  ( p HDjl ( Dl  D0l ))
l 1
(10)
1 Rj
mGj
mGj
nh
  ( p HHjk ( H k  H 0 k ))
k 1
nb
  ( p HBjm ( Bm  B0 m ))
mGj
(11)
mGj
m 1
where gj(T) is the temperature-dependent grazing rate determined using Eq. 6, pHAji, pHHjk,
11
pHDjl and pHBjm are the preference coefficients for autotroph Ai, heterotroph Hk, detritus Dl
and bacteria Bm, A0i, H0k, D0l and B0m are the thresholds under which the feeding amount
of heterotroph Hj on the corresponding food item is negligible (Gismervik and Andersen,
1997). Other feeding amount (GHjk, GDjl and GBjm ) are also computed by Eq. 10 in which
the numerator is replaced by the corresponding prey item. This function has the flexibility
to capture various functional responses and feeding behaviors. The power order mGj
determines the degree of switching feeding. The higher mGj is, the more switching
feeding occurs. When mGj=1, no switching occurs. When mGj, this formulation
generates an exclusive switching feeding.
Heterotroph mortality represents the model closure term and is often parameterized as
a linear or quadratic function of biomass. Heterotroph pools in numerical models usually
represent a large range of size, species and stages of organisms. The quadratic function is
justified by predation within the same heterotroph pool. Following Edwards and Yool
(2000), we have formulated the mortality as a modulable power function of heterotroph
biomass (5th term in Eq. 9). The power order mHj can be set to 1 for linear function and to
2 for quadratic function or to any other alternative order. Heterotroph respiration
represents the metabolic processes that lead to the remineralization of organic matter to
inorganic nutrients. Metabolic processes consists of basic metabolism at resting and
active metabolism such as locomotion activity, feeding, assimilation, substance
transformation and etc (Parson et al., 1984; Clarke, 1987; Carlotti et al., 2000). We have
linked the basic metabolism to the heterotroph biomass (6th term in Eq. 9) and the active
metabolism as a linear function of the feeding amount (see “Nutrient” section below).
Excretion of dissolved organic matter (DOM) and defecation are parameterized as a
12
fraction of the feeding quantity which are presented in the euqations of DOM and
detritus, respectively.
Zooplankton diurnal vertical migration represents a new aspect in marine ecological
modeling. Few modelling applications have tried to included migration process
(Anderson and Nival, 1991; Tian et al., 2004). The driving mechanisms underlying
zooplankton vertical migration are complex, including environmental factors (e.g. light,
food abundance, temperature, salinity, gravity, dissolved oxygen, turbulence, predation,
etc) and biological factors (e.g. species, age, sex, state of feeding, reproduction, energy
conservation, biological cycles and so forth; Forward, 1988; Ohman, 1990; Anderson and
Nival, 1991). Light has been shown to be an important driving force due to the fact that
zooplankton migrate beneath the euphotic zone during the day to escape predation and
return to surface waters for feeding during the night (Forward, 1988; Frank and Widder,
1997). Following Tian et al. (2004), only light and food abundance are parameterized as
driving forces of zooplankton vertical migration in this model. Light-induced migration
speed (wl) is linked to the change in percentage of solar radiation at the sea surface (I0):
 100 I 0 

wlj  wbj 
 I 0 t 
3
(12)
where wbj is a constant representing the slope between migration speed and light change
(Anderson and Nival, 1991; Tian et al., 2004). The absolute value of wlj is set to wmaxj
when Eq. 38 gives values >wmaxj and to -wmaxj (i.e., upward) when ∂I0/∂t is undetermined
during the night. To preclude zooplankton ascending to the euphotic zone with solar
radiation decreasing (e.g., in the afternoon), wlj is set to zero when light intensity in the
water column is higher than a critical value (I(z)>0.01I0). Light-induced upward
migration velocity is also set to zero when the food gradient is positive, i.e., food
13
abundance increases with depth (Ft/z>0). When upward migrating zooplankton reach
the chlorophyll maximum, for example, they are thus assumed to stop migrating further
to surface layers where foods are scarce. In this case, the migration speed is determined
only by food abundance. Food-dependent vertical migration speed (wfj) is calculated
using an exponential function:

w fj  ardj wmax j 1  e
 k fj R j

(13)
where ardj is randomly equal to 1 or –1 with 50% probability each at each migration time
step, and kfj is a constant describing the slope between migration speed and total food
abundance (Rj). Seasonal migration and overwintering was modeled using a critical food
abundance (Rmin) below which light-induced migration speed is set to zero. When food
abundance in winter is lower than Rmin, mesozooplankton overwinter at depth.
3.3 Bacteria
The general equation for bacterial state variables Bj is:
B j
t
ns
nh
i
k 1
  eBSjiU DOMji  eBNjU NH 4 j   GBkj  rBj B j
(14)
where UDOMji and UNH4j are the uptake amount of DOMi and NH4+ by the bacterial pool
Bj, eBSji and eBNj are the corresponding gross growth efficiency, GBkj is the consumption of
bacteria Bj by heterotrophs Hk and rBj is the respiration rate of bacteria Bj. The DOM and
NH4+ uptakes are determined by:
U DOMji   Bj (T ) B j
U NH 4 j   Bj (T ) B j
p DOMji ( DOM i  DOM 0i )
1  R Bj  S j
Sj
1  RBj  S j
(15)
(16)
14

S j  min( p NHj ( NH 4  NH 4

0j
), j RDONj )
(17)
ns
RBj   p DOMji ( DOM i  DOM 0 ji )
(18)
i 1
ns
RDONj   p DONji ( DON i  DON 0i )
(19)
i 1
where Bj(T) is the temperature-dependent growth rate of bacteria Bj determined by Eq. 6,
DOMi, DOM0i, NH4+ and NH4+0j, pDOMji and pNH4j are the concentration, threshold and
preference coefficient of DOMi and NH4+ for bacteria Bj, respectively, RBj and RDONj
represent DOM and DON substrates available for bacteria uptake. When the model unit is
in nitrogen, DOM is DON. When the model unit is in carbon, for example, DOM is DOC
and DON is calculated from DOC and the corresponding C:N ratio. j is the uptake ratio
between NH4+ and DON. A prescribed value of  is used when the model unit is in
nitrogen (Kantha, 2004). When the model unit is in carbon however,  is calculated by:
j 
eBSji ( N : C ) Bj
eBNj ( N : C ) DOMi
1
(20)
where (N:C)Bj and (N:C)DOMi are the nitrogen to carbon ratio of bacteria Bj and of DOMi
respectively (Fasham et al., 1990; Bissett et al., 1999; Tian et al., 2004).
3.4 DOM
The general equation for DOM state variables is:
nd
nb
DOM i na
  ( rASji  rASji  j ) A j   DSmi Dm  U DOMki
t
j 1
m 1
k 1
nh
nd
nb
 na




G


G


G


G





HASkji
Akj
HHSkli
Hkl
HDSkmi
Dkm
HBSkni
Bkn


k 1  j 1
l 1
m 1
n 1

  SSii1 DOM i   SSi1i DOM i 1
nh
(21)
15
where rASji and rASji are the coefficients of biomass-based and growth-based exudation of
DOMi from autotroph Aj. The sum of rASji and the sum of rAsji (i=1 to ns) equal the terms
rASj and rASj in Eq. 1. The second term on the right side of Eq. 21 represents the feeding
losses to DOM from heterotroph including sloppy feeding, defecation and excretion. The
third and forth terms are detritus dissolution and bacterial uptakes. The fifth and sixth
terms represent transformation between DOM pools, such as aging when DOM is
classified according to their bioavailability (Keil and Kirchman, 1994).
The elemental ratio between nutrients and the unit element (e.g. carbon or nitrogen) in
living organisms (i.e. autotrophs, heterotrophs and bacteria) are prescribed with specific
value for each organism pools. The elemental ratio in dissolved and detrital pools (i.e.
DOM and detritus) are computed according the elemental ratio in each of the source and
sink terms. The elemental ratio (aSji) between nutrient Ni and the unit element in DOMj is
determined as:
a Sji
t
nh

na
   a
k 1

na
nd
nb
j 1
m 1
k 1
 (  a Aji ( rASji  rASji  j ) A j   a Dmi DSmi Dm  a Sji  U DOMkj
j 1

 HASkjiG Akj   a HHkli HHSkliG Hkl   a HDkmi HDSkmiG Dkm   a HAkni HBSkniG Bkn  (22)
HAkji
nh
nd
nb
l 1
m 1
n 1
 a Sj SSjj1 DOM j  a Sj 1i SSj1 j DOM
j 1
) /( DOM j 
DOM
t
j

)  a Sji
where aSji, aAji, aDmi, aHAkji, aHHkli, aHDkmi, aHAkni are the elemental ratio between nutrient Ni
and carbon in DOMj, in autotroph Aj, in detritus Dm, and in feeding losses to DOMj from
heterotroph Hk feeding on autotroph Aj, on heterotroph Hl, on detritus Dm and on bacteria
Bn respectively. The elemental ratios in feeding losses aHAkji from heterotroph Hk feeding
on prey Aj is calculated by:
16
 HAkji 
 Aji  eHAkj a Hki
(23)
1  eHAkj
where aAji and aHki and aHAkji are the elemental ratio between nutrient Ni and the unit
element (e.g. carbon or nitrogen) in prey Aj and heterotroph Hk, and eHAkj is the
corresponding growth efficiency (Landry et al., 1993; Tian et al., 2004).
3.5 Detritus
The general equation for detritus is:
na
nh
Di
m
  ADji A j j   HDki H kmk   DDi1 Di21   DDi Di2   Ddi 1 Di 1   Dd1 Di   DSi Di
t
j 1
k 1
nh
nd
nb

Di nh  na
 s Di
    HADkjiG Akj   HHDkliG Hkl   HDDkmiG Dkm   HBDkniG Bkn  G Dki 
z k 1  j 1
l 1
m 1
n 1

(24)
The first two terms on the right-hand side of Eq. 22 are the mortality of autotrophs and
heterotrophs which lead to the formation of biogenic detritus. The third and fourth terms
represent aggregation gain and loss formulated as a quadratic function. The fifth the sixth
terms are the gain and loss due to particle breakage. The seventh and eighth terms are
particle dissolution and sinking and the last term represents heterotroph feeding losses to
detritus including both sloppy feeding and defecation and heterotroph consumption. The
elemental ratio in detritus pools are computed in the same way as for DOM pools.
3.6 Nutrients
The general equation for nutrients Ni is:
na
nh
nd
nb
N i nh


  a Hji  rHj H j  rHj  G Ajh rHj  G Hjk  rHj  G Djl  rHj  G Bjm 
t
j 1
h 1
k 1
l 1
m 1


 ns
 na
    a BSkli (1  eBSkl )U DOMkl  e BNkU NH 4 k  a Bki rBk Bk    a Ami  m Am
k 1  l
 m
nb
(25)
17
where aHji, aBki and aAmi are the ratio between element Ni and the unit element in
heterotroph Hj, bacteria Bk and autotroph Am respectively. rHj and rBk are the biomassbased respiration of heterotroph Hj and bacteria Bk. rHj is the active respiration
coefficient of heterotroph Hj based on grazing amount or assimilation. The active
respiration coefficient of nutrient Ni from heterotroph Hj grazing on autotroph Ah is
determined by:
rHAjhi  rHj
 Ahi  e HAjha Hji
(26)
1  e HAjh
where rHj is the active respiration rate of heterotroph Hj, aAhi and aHji are the ratio
between element Ni and the unit element in autotroph Ah and heterotroph Hj, and eHAjh is
the gross growth efficiency of heterotroph Hj grazing on autotroph Ah. The active
respiration coefficient of other terms including the active respiration of bacteria aBSkli are
also determined by Eq. 26 by using the corresponding terms.
When nitrogen is concerned, NH4+ is released from biological metabolism and
respiration. Consequently, Eq. 25 applies to NH4+ only. NO3- is formed through
nitrification of NH4+ as source term and consumed by autotroph photosynthesis. The
proportion between NH4+ and NO3- uptakes is governed by Eqs. 7 and 8. Ammonium is
nitrified to nitrate through nitrifying bacteria, which is known to be photoinhibited in
surface waters (Olson, 1981). Nitrification rate (QAN) is thus linked to light intensity in
the model:
QAN
0, E (t , z )  0.1Emax

  0.1ER  E (t , z )
max
 AN NH 4 ,

0
.
1
E
max

(25)
E (t , z )  0.1Emax
where AN is the nitrification coefficient and Emax is the maximum solar radiation in
18
surface waters (i.e. at noon; Tian et al., 2000).
3.7 Auxiliary state variables
We imply by auxiliary state variables oceanic properties that change over time in
function of other simulated biological pools. At the present stage of the model
development, we have only parameterized chlorophyll-a. Other auxiliary state variables
will be considered in future versions of the model.
The chlorophyll a concentration depends on phytoplankton biomass and the
chlorophyll-a:carbon ratio of phytoplankton. Chl:C ratio can be influenced by daylength
(D), irradiance (E), nutrient (N) and temperature (T), i.e., the DENT model. It can also be
influenced by other factors such as species and life history (Cullen, 1993; Claustre et al.,
1994). Two options of Chl:C ratio have been implemented in the generalized biological
model. The first option is to prescribe a Chl:C value to each autotroph pools. When
several autotroph groups are considered and given that each autotroph group has its
specific C:Chl ratio, these different prescribed values can allow to simulate to certain
extent the Chl:C variability in the autotroph community through the changes in relative
importance among the different groups (Claustre et al. 1994; Tian et al., 2001).
Alternatively, the Chl:C ratio can be calculated at each time step by the following
equation:
Chl : C  mi
i
I i
(26)
where i is the growth rate of autotroph Ai, which is forced by nutrient, light and
temperature (Eq. 1),  is the initial slope between PAR and autotroph growth rate (Eq. 5)
19
and m and  are the maximum and actual Chl:C ratio (Geider and MacIntyre, 1996;
Geider et al., 1997; Spitz et al., 2001). Based on Eq. 1 of autotrophs, the general equation
for chlorophyll a is thus:
nh


i
A
Chl na 
m
  (1  rASi )mi
Ai   i  ADi Ai i  rASi Ai  s Ai i   G Aji  


t
 i i E
z j 1
i 1 


(27)
The four terms on the right-hand side represent changes in chlorophyll concentration due
to phytoplankton growth, aggregation (or mortality), respiration (or exudation), cell
sinking and zooplankton grazing, respectively. All the symbols are defined in Eqs. 1 and
26.
4. Model configuration
The generalized biological has been coupled with the Harvard Ocean Prediction
System which consists of a physical general circulation model and multiple data
assimilation schemes (Robinson, 1996). The coupled system has been applied to the
Monterey Bay (MB) area during the AOSN-II research program. We present here only
the configuration of the generalized biological model to illustrate its functionality and
applicability.
Three model configurations were tested during the application. The first model
configuration has 4 state variables (Fi. 3), 2 nutrients (NH4+ and NO3-), 1 autotrophs
(phytoplankton) and 1 heterotroph (zooplankton). The model configuration represents
thus the NPZ model. The second configuration was based on the model presented in
Fasham et al. (1990). In this configuration, there are 2 nutrients (NH4+ and NO3-), 1
autotroph (phytoplankton), 1 heterotroph (zooplankton), 1 detritus, 1 DOM (DON) and 1
bacteria. We call this configuration the Fasham model configuration in the following text.
20
The third model configuration was based on the model presented in Tian et al. (2000). In
this configuration, there are 2 nutrients (NH4+ and NO3-), 2 autotrophs (small and large
phytoplankton), 2 heterotrophs (micro- and mesozooplankton), 2 detritus (small
suspended and large sinking detritus), 1 DOM (DON), 1 bacterial pool and 3 auxiliary
state variables (prokaryotic, eukarytic and total chlorophyll). This configuration allows to
simulate both the microbial food web (DON, bacteria, small phytoplankton and
microzooplankton) and the mesoplankton food chain (large phytoplankton and
mesozooplankton). As this model configuration appears to be the most suitable to
simulate an upwelling ecosystem in MB, we call this configuration the a priori model
configuration in the following text. The model unit is set in mmol nitrogen per meter
cube (mM N m-3).
In the NPZ model configuration, phytoplankton take up NO3- and NH4+ for growth and
are lost through zooplankton grazing and mortality (Table 1 A). Zooplankton take their
resource from phytoplankton and loses biomass through mortality and respiration leading
to NH4+ regeneration. Since no detrital pools is included in this model configuration,
biomass loses through the mortality of phytoplankton and zooplankton were considered
being exported out of the euphotic zone (Spitz et al., 2001). NH4+ is formed through
zooplankton respiration, lost through phytoplankton uptake and nitrified to NO3-.
The Fasham model configuration has 3 more state variables compared to the NPZ
model: bacteria, DON and detritus (Table 1 B). All the biological dynamics
parameterized in the NPZ model was included in the Fasham model configuration.
Instead being considered exported from the euphotic zone in the NPZ model, the biomass
loses through the mortality of phytoplankton and zooplankton result in the formation of
21
biogenic detritus. Bacteria consume DON, NH4+ and detritus (by attached bacteria) and
are consumed by zooplankton. Both the passive and active respiration of bacteria result in
NH4+ regeneration. No mortality of bacteria was considered in the model by assuming
that respiration and zooplankton consumption are the major biomass losses of bacteria.
DON is formed through phytoplankton exudation and zooplankton feeding losses and
remineralized through bacterial activities.
In the a priori model configuration, phytoplankton, zooplankton and detritus are all
divided into large- and small-sized pools, respectively (Table 1 C). Small phytoplankton
are consumed by microzooplankton and large phytoplankton by mesozooplankton. In the
MB
application,
microzooplankton
consumption
of
large
phytoplankton
and
mesozooplankton grazing on small phytoplankton are considered negligible by assign the
corresponding preference coefficient to 0. The mortality of small phytoplankton and
microzooplankton results in the formation of small detritus and the mortality of large
phytoplankton and mesozooplankton results in the formation of large detritus.
Microzooplankton consume bacteria, small phytoplankton and small detritus (sources)
whereas
mesozooplankton
feed
on
large
phytoplankton,
large
detritus
and
microzooplankton. Mortality of living organisms and feeding losses ( sloppy feeding and
defecation) are the major sources of detritus. The two detritus pools are linked through
aggregation from small to large detritus and disaggregation of large to small detritus. The
dissolution of large detritus is ignored by considering that this flux is included in the
disaggregation term to small detritus the dissolution of which leads to the formation of
dissolved organic matter DON.
Detailed discussion and validation of parameter values were presented in a joint paper
22
(Tian et al., submitted). We focus here on the differences of parameter values among the
3 model configurations (Table 2). The model structure is determined by the number of
state variables of each functional group. The total number of nutrients nn was assigned to
2 for all the 3-model configurations. The total numbers of phytoplankton and
zooplankton were set as 1 for the NPZ and Fasham model configuration, but to 2 for the a
priori model configuration. The total numbers of bacteria and DOM were set to 0 for the
NPZ model configuration and 1 for the Fasham and the a priori model configurations.
The total number of detritus was 0 in the NPZ model configuration, 1 in the Fashma
model configuration and 2 in the a priori model configuration, while the total number of
auxiliary state variables was 1 for the NPZ and Fasham model configuration and 3 for the
a priori model configuration. The biological and biogeochemical pools corresponding to
each state variables were presented in the preceding subsection.
The theoretical maximum growth rate (Pm) of small and large phytoplankton were set
based on previous studies in the a priori model configuration (Tian et al., submitted). The
theoretical maximum growth rate of the total phytoplankton pool in the NPZ and Fasham
model were determined based on the a priori model setup. The average simulated ratio
between large and small phytoplankton was approximately 3:1 in Monterey Bay. The Pm
were 1.05 and 3.15×10-5 mmol N mg Chl-1 s-1 for large and small phytoplankton in the a
priori simulation, respectively. Based on these values, the Pm for total phytoplankton
pool was set as 1.6×10-5 mmol N mg Chl-1 s-1. The values of the initial slope Ai and the
photoinhibition coefficient Ai were estimated in a similar way.
Since the phytoplankton exudation was not parameterized in the NPZ model
configuration, a relatively higher mortality was used than that in the other 2
23
configurations. High nutrient half-saturation constants were used for large phytoplankton
than that for small phytoplankton in the a priori simulation. A values in between were
thus used for total phytoplankton pool in the NPZ and Fasham model configurations.
The Chl:N values were based on field data collected during the summer season in MB.
The averaged C:Chl of field observations was 43. Assuming phytoplankton have a
Redfield C:N ratio of 6.625 in mole, the Chl:N ratio is thus determined as 1.85 for the
total phytoplankton pools. The Chl:N ratio for large and small phytoplankton in the a
priori simulation were also based on filed measurement (Tian et al., submitted). The
sinking velocity of large phytoplankton was assumed as 1 m d-1 and the averaged sinking
velocity of the total phytoplankton pool in the NPZ and Fasham model configuration was
assumed as the half of that conventional value. All other parameter values were identical
among the 3 different model configurations (see justification in Tian et al., submitted).
5. Simulation comparison
We focus here on the simulation comparison of the 3 model configurations. A brief
description of the context of the experiment is provided below for a better understanding
of the inter-model comparison. Detailed description of the Monterey Bay (MB)
application and oceanographic interpretation are presented in a joint paper (Tian et al.,
submitted). The AOSN II experiment was carried out from Aug. 6 to Sept. 10, 2003.
During the early experiment from Aug 6 – 18, a strong upwelling event occurred due to
dominated northwesterly upwelling-favorable winds. We called this period the “Strong
upwelling period” in the following text. From Aug. 18-23, southeasterly winds prevailed
and upwelling ceased. We called this period the “Relaxation period”. Moderate upwelling
24
events occurred late in the experiment and we call this period the “Moderate upwelling
period”. Two upwelling centers were identified during the experiment, one near Año
Nuevo to the north of MB and the other close to Point Sur to the south of MB.
High chlorophyll abundance was simulated in Monterey Bay by all the 3 models,
particularly in Northeastern MB (Fig. 5). This part of MB is called the “upwelling
shadow” where stable hydrographic conditions persist during the upwelling season. High
chlorophyll concentration are usually observed in this part of the bay ((Broenkow and
Smethie, 1978). A band of high chlorophyll concentration was simulated by the 3 models,
extending southwestward from MB. It was located in the upwelling plume of the Año
Nuevo upwelling center to the north of MB and the upwelling fronts of the Point Sur
upwelling center to the south of MB. Hydrographic conditions were more suitable to
phytoplankton development in upwelling plumes and fronts than within the upwelling
centers during strong upwelling events. However, the a priori model seemed to have
overestimated chlorophyll concentration in the offshore regions compared with the NPZ
and Fasham model simulations. The difference among the 3 model structures is that the a
priori model has explicit parameterization of the microbial food web including
picophytoplakton, microzoopankton, bacteria, DON and suspended biogenic detritus.
Upwelling ecosystems are usually dominated by large-sized mesoplankton food web. The
microbial food web can be thus overestimated in the a priori model simulation. The
simulated vertical distribution of chlorophyll and NO3- were almost identical, with the
nitricline around 40 m depth and upwelling activities in nearshore regions where the
nitricline was pushed upward (Fig. 6, 7).
No significant difference in the NO3- distribution in surface waters can be observed
25
among the 3 simulations (Fig. 8). During the strong upwelling event early in the
experiment, high NO3- concentration was simulated in MB and in the plume region to the
southwest of MB. These NO3- stocks were essentially advected from the Año Nuevo
upwelling center into MB. During the relaxation period, high spot in NO3- distribution
was simulated in the upwelling shadow in Northeast MB, which was advected from the
Point Sur upwelling center by the reversed northward current (Tian et al., submitted).
During the moderate upwelling event late in the experiment, NO3- concentration was
significant lower than during the strong upwelling period in all the 3 simulations. The
simulated NH4+ fields were significantly different among the 3 simulations (Fig. 9). The
NPZ simulation had the highest NH4+ values reaching ca 0.8 mmol N m-3, the a priori
simulation had the lowest NH4+ values <0.5 mmol N m-3, whereas the Fasham model
simulation had NH4+ values in between. As identical respiration rate of heterotrophic
zooplankton was used among the 3 model configurations, the low NH4+ values in the a
priori model simulation was due to the picophytoplankton uptake of NH4+. In the model,
relatively lower half-saturation constant of NH4+ was used for small cells than for large
phytoplankton by assuming that small cells can self-sustained in oligotrophic
environments by taking up regenerated NH4+.
The simulated zooplankton fields were similar between the NPZ model and the
Fasham model simulations (Fig. 10), with high value in MB and particularly in the
upwelling shadow. The comparison between the a priori model simulation and the other
2 simulations was more difficult because of its 2 zooplankton pools whereas 1 single
zooplankton pool was simulated in the other simulations. However, the simulated
mesozooplankton and micrzooplankton fields of the a priori model showed similar
26
distribution with the zooplankton fields of the other 2 model simulations, with high
values in the upwelling shadow and in MB. Patchness in the zooplankton distribution was
observed in the simulated fields due to upwelling activities and horizontal advection.
The general distribution pattern and magnitude of total phytoplankton production rates
were similar among the 3 simulations. High phytoplankton production rates were
simulated in the upwelling shadow and in MB. Similar to the phytoplankton biomass
distribution, relatively elevated phytoplankton production rate was simulated in the
upwelling plume and front region between the 2 upwelling centers during the strong
upwelling event (Fig. 11, Aug 15). During the relaxation (Fig. 11, Aug. 22) and during
the moderate upwelling event (Fig. 11, Aug. 29), the a priori model predicted relatively
elevated phytoplankton production in the offshore regions than the other 2 models, which
can explain in part the elevated phytoplankton biomass in the a priori model simulation
in the offshore regions.
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Tian, R.C., Deibel, D., Rivkin, R.B. and Vézina, A.F., 2004. Biogenic carbon and
nitrogen export in a deep-convection region: simulations in the Labrador Sea. DeepSea Research Part I, 51, 413-437.
Tian, R.C., Vézina, A.F., Legendre, L., Ingram, R.G., Klein, B., Packard, T., Roy, S.,
Savenkoff, C., Silverberg, N., Therriault, J.C., Tremblay, J.E., 2000. Effects of pelagic
food-web interactions and nutrient remineralization on the biogeochemical cycling of
carbon: a modeling approach. Deep-Sea Research Part II 47, 637-662.
Tian, R.C., Vézina, A.F., Starr, M., Saucier, F., 2001. Seasonal dynamics of coastal
ecosystems and export production at high latitudes: a modeling study. Limnology and
Oceanography 46, 1845-1859.
Wroblewski, J.S. 1982. Interaction of currents and vertical migration in maintaining
Calanus marchallae in the Oregon upwelling zone - a simulation. Deep-Sea Research 29,
665-686.Figure captions
Fig. 1. Generalized biological model. N: Nutrients; A: Autotrophs; H: Heterotrophs; D:
Biogenic detritus; DOM: Dissolved organic matter; B: Bacteria; X: Auxiliary state
variables; nn, na, nh, nd, ns and nx are total numbers of state variables of the
corresponding functional groups. The width of arrows and lines is proportional to the
33
number of processes represented (e.g., the fecal pellets and mortality line contains 3
processes: autotrophs mortality, heterotrophs mortality and defecation).
Black dots represent state variables between 2 and n that are not specifically depicted.
Fig. 2. Example of processes interface: heterotroph grazing on autotrophs with a specific
grazing preference coefficient pji between each heterotroph and autotroph.
Fig. 3. NPZ (upper panel) and Fasham (low panel) model configurations for the
Monterey Bay application. NPZ model configuration has 2 nutrients (NH4+, NO3-), 1
autotrophs (phytoplankton) and 1 heterotrophs (zooplankton). The Fasham model
configuration (Fasham et al., 1990) has 2 nutrients (NH4+, NO3-), 1 autotrophs
(phytoplankton), 1 heterotrophs (zooplankton), 1 detrital pool, 1 DOM (DON) and 1
bacterial pool.
Fig. 4. A priori model configuration for the Monterey Bay application: 2 nutrient (NH4+,
NO3-), 2 autotrophs (small and large phytoplankton), 2 heterotrophs (microzooplankton
and mesozooplankton), 2 detritus (small and large detritus), 1 DOM (DON), 1 bacteria
and three auxiliary state variables (small, large and total chlorophyll).
Fig. 5. Simulated surface chlorophyll distribution by the three model configurations at the
early experiment (Aug. 8), strong upwelling event (Aug. 15), relaxation period (Aug. 22)
and moderate upwelling event (Aug. 29).
34
Fig. 6. Simulated chlorophyll (mg Chl m-3) transectional distribution by the three model
configurations. Dates were selected according to field observation.
Fig. 7. Simulated NO3- (mmol N m-3) transectional distribution by the three model
configurations. Dates were selected according to field observation.
Fig. 8. Simulated NO3- distribution field by the three model configurations at the early
experiment (Aug. 8), strong upwelling event (Aug. 15), relaxation period (Aug. 22) and
moderate upwelling event (Aug. 29).
Fig. 9. Simulated NH4+ distribution field by the three model configurations at the early
experiment (Aug. 8), strong upwelling event (Aug. 15), relaxation period (Aug. 22) and
moderate upwelling event (Aug. 29).
Fig. 10. Simulated zooplankton distribution field by the three model configurations at the
early experiment (Aug. 8), strong upwelling event (Aug. 15), relaxation period (Aug. 22)
and moderate upwelling event (Aug. 29).
Fig. 11. Simulated primary production (mmol N m-2 d-1) by the three model
configurations at the early experiment (Aug. 8), strong upwelling event (Aug. 15),
relaxation period (Aug. 22) and moderate upwelling event (Aug. 29).
35
36
Fig. 1. Generalized biological model. N: Nutrients; A: Autotrophs; H: Heterotrophs; D:
Biogenic detritus; DOM: Dissolved organic matter; B: Bacteria; X: Auxiliary state
variables; nn, na, nh, nd, ns and nx are total numbers of state variables of the
corresponding functional groups. The width of arrows and lines is proportional to the
number of processes represented (e.g. the fecal pellets and mortality line contains 3
processes: autotrophs mortality, heterotrophs mortality and defecation).
Black dots represent state variables between 2 and n that are not specifically depicted.
37
Fig. 2. Example of processes interface: heterotroph grazing on autotrophs with a specific
grazing preference coefficient pji between each heterotroph and autotroph.
38
Fig. 3. NPZ (upper panel) and Fasham (low panel) model configurations for the
Monterey Bay application. NPZ model configuration has 2 nutrients (NH4+, NO3-), 1
autotrophs (phytoplankton), 1 heterotrophs (zooplankton). The Fasham model
configuration (Fasham et al., 1990) has 2 nutrients (NH4+, NO3-), 1 autotrophs
(phytoplankton), 1 heterotrophs (zooplankton), 1 detrital pool, 1 DOM (DON) and 1
bacterial pool.
39
Fig. 4. A priori model configuration for the Monterey Bay application: 2 nutrient (NH4+,
NO3-), 2 autotrophs (small and large phytoplankton), 2 heterotrophs (microzooplankton
and mesozooplankton), 2 detritus (small and large detritus), 1 DOM (DON), 1 bacteria
and three auxiliary state variables (small, large and total chlorophyll).
40
Fig. 5. Simulated surface chlorophyll distribution by the three model configurations at
the early experiment (Aug. 8), strong upwelling event (Aug. 15), relaxation period (Aug.
22) and moderate upwelling event (Aug. 29).
41
Fig. 6. Simulated chlorophyll (mg Chl m-3) transectional distribution by the three model
configurations. Dates were selected according to field observation.
42
Fig. 7. Simulated NO3- (mmol N m-3) transectional distribution by the three model
configurations. Dates were selected according to field observation.
43
Fig. 8. Simulated NO3- distribution field by the three model configurations at the early
experiment (Aug. 8), strong upwelling event (Aug. 15), relaxation period (Aug. 22) and
moderate upwelling event (Aug. 29).
44
Fig. 9. Simulated NH4+ distribution field by the three model configurations at the early
experiment (Aug. 8), strong upwelling event (Aug. 15), relaxation period (Aug. 22) and
moderate upwelling event (Aug. 29).
45
Fig. 10. Simulated zooplankton distribution field by the three model configurations at the
early experiment (Aug. 8), strong upwelling event (Aug. 15), relaxation period (Aug. 22)
and moderate upwelling event (Aug. 29).
46
Fig. 11. Simulated primary production (mmol N m-2 d-1) by the three model
configurations at the early experiment (Aug. 8), strong upwelling event (Aug. 15),
relaxation period (Aug. 22) and moderate upwelling event (Aug. 29).
47
Table 1. Trophic links between state variables. “x” implies that the state variable in the
first column is a source of the sate variable in the first row and “y” implies a sink. “0”
indicates that the link (or preference) coefficient was assigned to 0 in this application and
“-“ implies no link between the two corresponding state variables.
A. NPZ model configuration.
NH4+ NO3- P
Z
x
-
P
y
y
NO3-
y
y
B. Fasham model configuration.
NH4+ NO3- P
Z
B
D
DON
xy
-
-
-
y
DON
-
-
y
y
y
D
-
-
y
xy
Z
x
-
y
P
y
y
NO3-
y
C. A priori model configuration.
NH4+ NO3- SP
LP
B
MiZ
y
MeZ
SD
LD
xy
-
-
-
x
0
y
-
DON
-
-
y
y
y
y
y
0
LD
-
-
0
x
0
xy
xy
SD
-
-
y
0
xy
0
MeZ
x
-
0
y
y
MiZ
x
-
y
0
LP
y
y
-
SP
y
y
DON
y
48
NO3-
y
49
Table 13. Variables and parameters in the generalized biological model (values in
parentheses are for small phytoplankton).
Symbol
definition
unit
value
nn
na
nh
ns
nb
nd
nx
Nb of nutrient
Nb of autotrophs
Nb of heterotrophs
Nb of DOM
Nb of bacteria
Nb of detritus
Nb of auxiliary variables
Ai
Initial slope of the E-u function

ADi
HDi
an
HAS1
DDi
DSi
Ai
eHAji
eHHji
eHDji
eHBji
eBSji
eBNji
gmj
Proportion between
multiplication and minimum of
light and nutrient limiting
factors
Mortality of phytoplankton
Mortality of zooplankton
Nitrification rate
Formation of DON from
feeding loss
Quadratic aggregation
coefficient of detritus
Linear dissolution coefficient
of small detritus
Photoinhibition coefficient of
phytoplankton
Growth efficiency of
zooplankton grazing on
phytoplankton
Growth efficiency of mesozoo.
predation of microzoo.
Growth efficiency of
zooplankton feeding on
detritus
Growth efficiency of
microzoo. feeding on bacteria
Growth efficiency of bacteria
feeding on DON
Growth efficiency of bacteria
uptake of NH4+
Maximum grazing rates of
zooplankton
unitless
unitless
unitless
unitless
unitless
unitless
unitless
10-7 mmolN
mgChl-1 s-1 (W m2 -1
)
NPZ
2
1
1
0
0
1
1
Fasham
2
1
1
1
1
1
1
a priori
2
2
2
1
1
2
2
3.2
3.2
2.1(6.3)
unitless
0.5
0.5
0.5
10-7 s-1
10-7 s-1
10-7 s-1
6.94
2.31
4.63
4.63
2.31
4.63
4.63
2.31(1.16)
4.63
fraction
0.2
0.2
0.2
10-7 s-1
0.0
0.0
2.31(0.0)
10-6 s-1
5.79
5.79
5.79
10-8 mmol N mg
Chl-1 s-1 (W m-2)-1
1.6
1.6
1.05(3.15)
fraction
0.3
0.3
0.3
fraction
0.3
0.3
0.3
fraction
0.3
0.3
0.3
fraction
-
0.4
0.4
fraction
-
0.3
0.3
fraction
-
1.0
1.0
10-5 s-1
1.16
1.16
1.16(2.31)
50
KSANj1
KSANj2
mHAji
mHi
mAi
ηB1
Pmi
pHAji
pHHji
pHBji
pHDji
pBDOMji
pBNH4ji
N0I
A0i
D0I
DOM0i
θmaxi
rASi
ruASi
rHi
rgHi
rBi
rBi
sAi
Half-saturation concentration
of NO3Half-saturation concentration
of NH4+
Power coefficient of
zooplankton feeding
Power coefficient of
zooplankton mortality
Power coefficient of
phytoplankton mortality
Ratio between NH4+ and DON
uptake by bacteria
Theoretical maximum growth
of phytoplankton
Preference coefficient of
zooplankton on phytoplankton
Preference coefficient of
mesozoo. on microzoo
Preference coefficient of
microzoo. on bacteria
Preference coefficient of
zooplankton on detritus
Preference coefficient of
bacteria for DOM
Preference coefficient of
bacteria for NH4+
Threshold of nitrogen for
phytoplankton uptake
Threshold for zooplankton
grazing
Threshold of bacteria feeding
on small detritus
Threshold for bacteria feeding
on DON
Chl:N of phytoplankton
Biomass-based DOM
exudation of phytoplankton
Growth-based DOM exudation
of phytoplankton
Passive respiration of
zooplankton
Active respiration of
zooplankton
Passive respiration of bacteria
Active respiration of bacteria
Sinking velocity of large
mmol N m-3
1.5
1.5
2.0(0.8)
mmol N m-3
0.8
0.8
1.5(0.5)
unitless
1.0
1.0
1.0
unitless
1.5
1.5
1.5
unitless
1.0
1.0
1.0
fraction
-
0.3
0.3
10-5 mmol N mg
Chl-1 s-1)
1.6
1.6
3.15&
1.05
(mmol N m-3)-1
2.0
2.0
2.0 (0.0)
(mmol N m-3)-1
-
-
1.0
(mmol N m-3)-1
-
5.0
0.0(5.0)
(mmol N m-3)-1
-
0.0
0.0(1.0)
(mmol N m-3)-1
-
0.5
0.5
(mmol N m-3)-1
-
1.0
1.0
mmol N m-3
0.0
0.0
0.0
mmol N m-3
0.02
0.02
0.02
mmol N m-3
0.02
0.02
0.02
mmol N m-3
-
6.0
6.0
mg Chl/mM N
1.85
1.85
3.18(0.96)
10-7 s-1
-
1.74
1.74
fraction
-
0.1
0.1
10-7 s-1
9.26
9.26
9.26
fraction
0.3
0.3
0.3
10-6 s-1
fraction
10-5 m s-1
0.58
4.63
0.56
0.58
4.63
0.56
1.16
51
sDi
TOAi
∆TAi
BMi
phytoplankton
Sinking velocity of large
detritus
Optimal temperature for
phytoplankton, zooplankton
and bacteria
Temperature scale of Q10 for
phytoplankton, zooplankton
and bacteria
Maximum growth rate of
bacteria
10-4 m s-1
-
2.31
2.31
ºC
20
20
20
ºC
14.5
14.5
14.5
10-5 s-1
-
1.39
1.39
52