We have considered U(P,N) in the form of a Michaelis-Menten relation in N and proportional to P, ie, U(P,N)=VPvnN/(kn N). Grazing, G(P,Z) is regarded as proportional to Z, and has been considered either as Michaelis-Menten in P or proportional to P

1
TOWARD A MODEL-BASED SYSTEM OF ESTUARINE
CLASSIFICATION   D.P. Swaney1 ,R.W. Howarth1,
R.M. Marino1, D. Scavia2, M. Alber3 and E.W.
Boyer4 1Dept of Ecology Evolutionary Biology,
Cornell University, Ithaca, NY, 14850 2School of
Natural Resources Environment, University of
Michigan, Ann Arbor, MI, 48109 3Dept of Marine
Sciences, University of Georgia, Athens, GA
30602 4Dept of Environmental Science, Policy
Management, U C Berkeley, Berkeley, CA 94720

• What are the apparent relationships between flow,
  t, and effect of nutrient loads?

Nutrient loads can result from flow dependent
sources (riverine flows, groundwater seepage,
precipitation) or be essentially independent of
terrestrial flows and atmospheric water flows
(point sources).
 ABSTRACT There is a very large range of
estuarine biological responses to nitrogen
loadings and other anthropogenic driving
variables, determined in part by the magnitude,
frequency, and other characteristics of the
drivers, but also by intrinsic characteristics of
the estuarine systems. Such intrinsic
characteristics can include both
physical/chemical factors (depth, salinity, water
residence time, etc) and biological factors
(nature of ecological communities, trophic
interactions, etc). To address the richness of
estuarine response to driving variables, we aim
to establish a simple estuarine classification
scheme, at least for a river-dominated subset of
estuarine systems. Toward this goal, we are
investigating a class of models, the
nutrient-phytoplankton-zooplankton (NPZ) models,
which have been used to examine a range of
subjects including effects of nutrient limitation
and zooplankton predation on phytoplankton
dynamics (eg, Steele and Henderson, 1981) and
fish predation (eg, Scheffer et al., 2000), and
can admit a wide range of behavior, including
multiple steady states and oscillatory behavior
(Edwards and Brindley, 1999) .
Figure 9a
Phytoplankton density apparently increases with t
when nitrogen load is independent of flow
concentrations
mg/l
Figures 6, 7 and 8 show simulated steady state
behavior of phytoplankton over a range of tau (ie
residence time, or more properly freshwater
flushing time) for five different N loading
levels. Here, loads are assumed to be
independent of freshwater flow. Dashed lines
indicate the NOAA-defined breakpoints of 5, 20,
and 60 ugChl/l as definitions of thresholds
between Low, Medium, High, and Hyper Eutrophic
conditions, translated into phytoplankton
nitrogen equivalents.
Figure 9b
We have considered U(P,N) in the form of a
Michaelis-Menten relation in N and proportional
to P, ie, U(P,N)VPvnN/(knN). Grazing, G(P,Z)
is regarded as proportional to Z, and has been
considered either as Michaelis-Menten in P or
proportional to P (G(P,Z)(1-a)VZvpP /(kpP) or
G(P,Z)(1-a)VvpPZ ). The nutrient recycling term
R(P,Z) is proportional to G, ie R(P,Z)a/(1-a)
G(P,Z). The grazing loss to phytoplankton
biomass is GU, ie either VvpPZ /(kpP) or
VvpPZ.
Phytoplankton density apparently decreases with t
when nitrogen load is based on fixed-concentration
riverine loads because t increases
with decreasing flow.
Figure 6. Steady-states of phytoplankton
simulations under the assumption of
Michaelis-Menten phytoplankton limited grazing
and denitrification as characterized by Nixon et
al (1996), ie Denitrification Nload (0.208
log(t)-0.085)
where t is freshwater flushing time
(days). Denitrification suppresses phytoplankton
zooplankton levels below the baseline
case, presumably due to N limitation.

The above system can be written as mass-balance
equations in the following form
Figure 9c
In fact, flow and N load are correlated for 139
estuaries in the NOAA database, but not perfectly
so. (S.V. Smith, et al. 2003) Loads derived from
SPARROW model Flow from NCPDI.)
Figure 7. Simulated steady-states of
phytoplankton under the assumption of
Michaelis-Menten limited grazing and no
denitrification (baseline case). Plankton density
increases and levels off as t increases above
100 N levels decline as P and Z increase, and
are suppressed at all load levels above t 30
days.

• Conclusions and future challenges

Even simple models of estuarine system biology
can exhibit a variety of behaviors in response
to different levels of environmental drivers,
such as freshwater flow or nutrient load. These
include various steady-states, regular
oscillations, and irregular fluctuations that may
serve as a basis for classification of coastal
ecosystems. To date, we have explored only a few
functional forms of grazing and have focused on
the response of phytoplankton to changes in
residence time and N load. Other nutrients (P,
Si, O2) and physical factors (light, temperature)
are important as well. Future investigations
will more fully explore these relationships as
well as effects of seasonality and other
time-varying characteristics of driving variables.
The equations can be solved numerically to
determine the steady-state values of N,P, and Z,
if such a state exists (fig 1). Increasing load
or changing parameter values may result in
oscillatory or other non-steady state behavior.
Fig 2 shows the effect of increasing
N concentration in load from 5 to 15 mg/l.
Switching on denitrification removes the
oscillatory behavior, effectively reducing the
increased load (fig 3). More complex behavior
can result by changing values of model
parameters.
Fig 1
Figure 8. Simulated steady-states of
phytoplankton under the assumption of grazing
jointly proportional to phytoplankton and
zooplankton, and no denitrification. At t less
than 100 days, the phytoplankton response is
similar to that of the other scenarios. At longer
time scales, phytoplankton density is higher than
in the other scenarios. Zooplankton and N are
suppressed (note changes of scale)
References Edwards, A.M. and J. Brindley. 1999.
Zooplankton Mortality and the Dynamical Behaviour
of Plankton Population Models. Bulletin of
Mathematical Biology. 61303339. Nixon et al.
1996. The fate of nitrogen and phosphorus at the
land-sea margin of the North Atlantic Ocean.
Biogoechemistry 35 141-180 Scheffer et al.,
2000. Effects of fish on plankton dynamics a
theoretical analysis. Canadian Journal of
Fisheries and Aquatic Sciences.
571208-1219 Smith, S.V., S. Bricker and P.
Pacheco. 2003. Preliminary NOAA dataset.
(http//drysdale.kgs.ku.edu/estuary/hp_firststep.c
fm ) Steele, J. H. and E.W. Henderson. 1981. A
Simple Plankton Model. The American Naturalist.
117676-691.
Fig 2
Fig 4. shows the effect of generating
irregular fluctuations in phytoplankton
by reducing the recycling of nutrients from
the grazing interaction from 0.7 to 0.3
Fig 3

Acknowledgements This work has been supported by
an EPA STAR grant, Developing regional-scale
stressor models for managing eutrophication in
coastal marine ecosystems, including interactions
of nutrients, sediments, land-use change, and
climate variability and change, EPA Grant Number
R830882, R.W. Howarth, P.I.
Contact information Email dps1_at_cornell.edu pr
oject website http//www.eeb.cornell.edu/biogeo/E
PA-STAR/EPASTAR.htm
Fig 4