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 4Faculty of Forest Natural Resources
Management, SUNY-ESF, Syracuse, NY 13210

• 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).
Fig 8a
Phytoplankton density apparently increases with t
when nitrogen load is independent of flow
concentrations
mg/l

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.
Fig 8b
Phytoplankton density apparently decreases with t
when nitrogen load is based on fixed-concentration
riverine loads because t increases
with decreasing flow.
Figures 5, 6, and 7 show steady state behavior of
N, P, and Z 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 in Figures 5a, 6a, and 7a
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.
Log(L) 2.233 0.643Log (Q) R2 0.60

Fig 8c
The above system can be written as mass-balance
equations in the following form
In fact, flow and N load are correlated, but not
perfectly so (NOAA dataset, S.V. Smith, 2003
Loads derived from SPARROW model.)

• 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) and physical factors (light, temperature) may
be 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
Fig 2
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Steady-states of N, P, and Z simulations 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)
Steady-states of N, P, and Z simulations under
the assumption of Michaelis-Menten phytoplankton
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.
Steady-states of N, P, and Z simulations under
the assumption of Michaelis-Menten phytoplankton
limited grazing and denitrification as
characterized by Nixon et al (1996), ie
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
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.
Fig 3

where t is freshwater flushing time
(days). Denitrification suppresses phytoplankton
zooplankton levels below the baseline
case, presumably due to N limitation.
Fig 4