TOWARD A MODEL-BASED
SYSTEM OF ESTUARINE CLASSIFICATION
Nitrogen
(N)
QN
R(P,Z)
IN+QCN
U(P,N)
D.P. Swaney1 ,R.W. Howarth1, R.M. Marino1, D. Scavia2, M. Alber3 and E.W. Boyer4
1Dept
Phytoplankton
Biomass (P)
QP
IP+QCP
G(P,Z)
βsPV
D
Predation on
Zooplankton
G(P,Z)+R(P,Z)
Settling of P
Benthic flux ~ settled phyto?
s = sinking velocity
sPV
D
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
IZ+QCZ
λZ
Zooplankton
Biomass (Z)
Phytoplankton vs residence time for several N loads
0.5
10
0.4
12500
25000
0.3
37500
50000
0.2
"High"
"Medium"
0.1
ABSTRACT
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,
R(P,Z) = nutrient recycling from zooplankton
"Low"
0.0
There is a very large range of estuarine biological responses to nitrogen loadings and other anthropogenic “driving variables”, determined in part by the
G(P,Z) = grazing on phytoplankton by zooplankton
Q= freshwater flow
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”).
QZ
U(P,N) = N uptake
D= system depth
What are the apparent relationships between flow, t,
and effect of nutrient loads?
P (mg N/l)
Denitrification
Fig 8a
1
10
Phytoplankton vs residence time for several N loads
concentrations
dominated subset of estuarine systems. Toward this goal, we are investigating a class of models, the nutrient-phytoplankton-zooplankton (NPZ) models, which
Ii = flow-independent source of component i (N,P,Z)
have been used to examine a range of subjects including effects of nutrient limitation and zooplankton predation on phytoplankton dynamics (eg, Steele and
0.5
0.01mg/l
0.4
P (mg N/l)
QCi= riverine source of component i (N,P,Z)
1000
Phytoplankton density apparently increases with t when nitrogen load
is independent of flow
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-
V= system volume
100
Tau(days)
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
1.26
2.51
0.3
3.75
5
0.2
"High"
"Medium"
0.1
(Edwards and Brindley, 1999).
Fig 8b
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
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.
Phytoplankton vs residence time for several N loads
0.5
0.5
0.4
25005
0.3
50000
1.0E-04
600
800
200
400
600
800
"Low"
1
10
0.08
12508
25005
0.06
37503
50000
0.04
100
12508
25005
37503
50000
100
Fig 4
P (mg N/l)
Fig 4. shows the effect
of generating irregular
fluctuations in
Fig 3
phytoplankton by
reducing the recycling
of nutrients from the
grazing interaction
from 0.7 to 0.3
1.0E+00
"Low"
eutrophy
"Medium"
eutrophy
"High"
eutrophy
1.0E-02
1.0E-04
0
200
400
600
800
1000
Time (days)
1.0E+02
P
1.0E+00
"Low"
eutrophy
"Medium"
eutrophy
"High"
eutrophy
1.0E-02
1.0E-04
0
200
400
600
Time (days)
800
1000
25005
1.5E-03
37503
12508
50000
25005
2.0E-02
37503
50000
1000
Estuarine N concentration vs residence time
for several N loads
4.0E-03
10
3.0E-02
12508
25005
2.0E-02
37503
50000
10
3.0E-03
25005
1.0E-03
0.0E+00
0.0E+00
0.0E+00
10 Tau(days) 100
1000
37503
50000
1.0E-02
1
12508
2.0E-03
1.0E-02
1000
10 Tau(days) 100
Fig 7b
4.0E-02
1
10 Tau(days) 100
Fig 6c
Fig 7c
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
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
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)
where t is freshwater flushing time (days).
Denitrification suppresses phytoplankton
zooplankton levels below the baseline case,
presumably due to N limitation.
6
7
8
9
10
11
Log(Q+ppt-evap)
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.
1000
Fig 5c
Denitrification  Nload (0.208 log( t )  0.085)
Phytoplankton vs time
2.0E-03
1
1.0E+02
P
10
0.0E+00
1000
10
5
In fact, flow and N load are correlated, but not perfectly so (NOAA
dataset, S.V. Smith, 2003; Loads derived from SPARROW model.)
1000
2.5E-03
Estuarine N concentration vs residence time
for several N loads
12508
100
5.0E-04
10 Tau(days)
Fig 8c
4
Conclusions and future challenges
Fig 6b
3.0E-02
Tau(days)
1.0E-03
1
4.0E-02
10 Tau(days) 100
10
3.0E-03
0.00
1000
6
Zooplankton vs residence time for several N loads
0.02
10 Tau(days)
"Low"
1
10
0.00
1
Phytoplankton vs time
"Medium"
0.1
0.10
0.02
1
"High"
3.5E-03
0.04
7
3
50000
Fig 7a
0.06
8
0.0
1000
0.08
Log(L) = 2.233 + 0.643Log (Q) R2 = 0.60
4
37503
0.2
0.12
Estuarine N concentration vs residence time
for several N loads
Time (days)
100
1000
5
25005
0.3
Zooplankton vs residence time for several N loads
Fig 5b
1000
Tau(days)
100
12508
Fig 6a
Z (mg N/l)
Z (mg N/l)
P
N (mg N/l)
P (mg N/l)
1000
10
"Low"
eutrophy
"Medium"
eutrophy
"High"
eutrophy
0
Tau(days)
100
0.10
P
1.0E-04
"Medium"
0.12
1.0E+02
1.0E-02
"High"
Zooplankton vs residence time for several N loads
1000
1.0E+00
50000
0.2
Fig 5a
Phytoplankton vs time
P (mg N/l)
1.0E+09
5
1.0E+07
5.00
0.05
0.05
2
0.03
1.000
1.000
1
0.4
1
0.7
0.1
0.5
0.15
0.10
0.10
0.10
400
10
Time (days)
More complex behavior can result by changing values
Fig 2
of model parameters.
“Default” values of model parameters
Volume (m3)
Depth (m)
Q (m3/day)
N concentration in Load (g N/m3)
P concentration in Load (g C/m3 )
Z concentration in Load (g C/m3)
Max phyto growth rate (day-1)
Phyto growth half saturation const (g N/m3)
a (N/C ratio in phytoplankton)
aa (N/C ratio in grazing recycling)
Max zoo grazing rate (day-1)
Zoo grazing half saturation const (g C/m3)
b (phytoplankton C required per unit grazer C)
alpha (fraction of grazing recycled)
beta (fraction of benthic flux recycled)
Phyto sinking rate, s (m/day)
lambda (1st order predation on zooplankton)
Initial Condition N (g N/m3)
Initial Condition P (g C/m3)
Initial Condition Z (g C/m3)
200
37503
0.0
1
"Low"
eutrophy
"Medium"
eutrophy
"High"
eutrophy
0
0.3
0.1
"Low"
N (mg N/l)
P (mg N/l)
dN
 sP
V
 I N  Q (C N  N )  U ( N , P )  R ( P, Z )  V
 Denitr
dt
D
dP
sP
V
 I P  V (C P  P )  U ( N , P )  G ( P, Z )  U ( P, Z )  V
dt
D
dZ
Phytoplankton vs time
V
 I Z  Q (C Z  Z )  G ( P, Z )   VZ
1.0E+02
dt
0.0
1.0E-02
"High"
0.4
25005
Tau(days)
9
10
12508
"Medium"
The above system can be written as mass-balance equations in the following form:
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
Fig 1
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).
37503
0.2
0.1
1.0E+00
0.4
12508
P (mg N/l)
P (mg N/l)
VvpPZ.
10
10
10
0.5
10
1
Phytoplankton density apparently decreases with t when nitrogen load
is based on fixed-concentration riverine loads because t increases with
decreasing flow.
Phytoplankton vs residence time for several N loads
P (mg N/l)
grazing loss to phytoplankton biomass is G+U, ie either VvpPZ /(kp+P) or
Phytoplankton vs residence time for several N loads
Z (mg N/l)
nutrient recycling term R(P,Z) is proportional to G, ie R(P,Z)=a/(1-a) G(P,Z). The
N (mg N/l)
proportional to P (G(P,Z)=(1-a)VZvpP /(kp+P) or G(P,Z)=(1-a)VvpPZ ). The
0.0
Log (Load kg/yr)
QN,QP,QZ=
flushing loss
of N,P,Z
the sea
We have considered
U(P,N)
in thetoform
of a Michaelis-Menten relation in N and
"Low"
References
For those interested in the full citations of publications referred to
herein, or in a copy of the poster, please tack your email address to the
poster and we will email them to you!
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.