Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches

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Eldridge PM and Roelke DL (2011) Hypoxia in Waters of the Coastal Zone: Causes,
Effects, and Modeling Approaches. In: Wolanski E and McLusky DS (eds.) Treatise
on Estuarine and Coastal Science, Vol 9, pp. 193–215. Waltham: Academic Press.
© 2011 Elsevier Inc. All rights reserved.

Author's personal copy
9.11 Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling
Approaches*
PM Eldridge
†
and DL Roelke, Texas A&M University, College Station, TX, USA
© 2011 Elsevier Inc. All rights reserved.
9.11.1 Introduction 193
9.11.2 Drivers of Hypoxia 193
9.11.3 Effects of Hypoxia on Biota 197
9.11.4 Mitigation of Hypoxia 198
9.11.5 Assessment of Mitigation 198
9.11.6 Modeling Approaches 199
9.11.7 The Edge of Ockham’s Razor: Building a Hypoxia Model 201
9.11.7.1 A Modeling Framework 204
9.11.7.2 The Surface Mixed Layer 204
9.11.7.3 The Plankton Community 205
9.11.7.4 Vertical Flux of Organic Matter 207
9.11.7.5 Dissolved Organic Matter 208
9.11.7.6 Geochemical Processes 208
9.11.7.7 Gas Exchanges and Physical Circulation 208
9.11.8 Model Validation and Simulation Analysis 209
9.11.9 Future Hypoxia Models 211
References 212
Abstract
Hypoxia is one of the greatest threats to coastal zone ecosystems, where in extreme cases vast dead zones result. Primary
drivers of hypoxia include nutrient loading from anthropogenic sources and physical processes that lead to stratification.
Models are useful tools for the study of hypoxia. Their frameworks, however, vary tremendously ranging from simplified
portrayals of biota and the physical environment (productivity and metabolism simulated in a box model) to complex food-
web representations within three-dimensional circulation schemes. Much knowledge has been gained through the study of
simple models. However, to further our understanding of factors influencing hypoxia, the development of additional
complex models followed by an analysis of similarity in their qualitative behaviors is needed.
9.11.1 Introduction
Balancing environmental protection and sustainable resource use
is a challenging endeavor. Nowhere is this more evident than in
ecosystems of the coastal zone. Nearly 75% of the world’shuman
population lives within coastal watersheds (Vitousek et al., 1997)
with highest human population densities within 100 km of the
shoreline. Human activities in this region have led to the loss of
marsh and forest habitats leaving coastlines vulnerable to storm
events, diversion of freshwater flows resulting in salinification of
estuaries and bays, and overharvesting of fisheries leading to
drastic changes in ecosystem functioning (to name a few).
Human activities need not be in proximity of the coastal zone
to have an impact there. This is the case for one of the greatest
threats to coastal zone ecosystems, hypoxia.
Hypoxia is a condition of low dissolved oxygen (DO). It is
typically defined when DO drops below 2.8 mgO
2
l
−1
(Altieri
and Witman, 2006). Simply stated, it occurs when the demand
*In memory of Peter Eldridge, a colleague, mentor, and friend of so
many.
†
Deceased.
for oxygen exceeds the rate of supply. In addition to DO, there
are diverse chemicals from which oxygen can be used in reducing
environments, which include nitrate, nitrite, sulfate, and dis-
solved organic carbon (DOC). These chemicals are consumed
in reducing environments, producing ammonia, hydrogen sul-
fide, and methane. When DO drops to hypoxic levels, and, in
some cases, decreases to undetectable levels (anoxia), detrimen-
tal effects to biota ensue that in the extreme involves death. Not
only does the low availability of DO bring about adverse effects,
but also the increasing concentrations of ammonia and hydro-
gen sulfide exacerbate the condition. The alarming rate of
increase in hypoxia and the expanded magnitude and duration
of these events has fueled international interest to better under-
stand the phenomena and mitigate its impact.
9.11.2 Drivers of Hypoxia
Organic carbon loading, the process of eutrophication (Nixon,
1995), coupled to restricted circulation is the primary mechan-
ism and system condition that leads to hypoxia. Organic carbon
loading may result from inorganic nutrient loading if the marine
193
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194 Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches
system is nutrient limited. Under this condition, the added
inorganic nutrients stimulate primary productivity. Produced
organic carbon then not only supports bacterial production,
zooplankton grazing, and fisheries production, but also leads
to increased flux of organic material to bottom waters and sedi-
ments. There it is metabolized, consuming DO. Under
conditions of restricted circulation, DO is not replenished and
hypoxia can result (Andersson and Rydberg, 1988; Justić et al.,
2003; Turner and Rabalais, 1994; Dagg and Breed, 2003; Paerl
et al., 2006). Direct loading of organic material from allochtho-
nous sources can also bring about hypoxia.
The incidences of hypoxia are natural phenomena. For
example, in the open waters of the Black Sea, hypoxia has
existed for thousands of years due to poor water exchanges
with the Mediterranean Sea (Tolmazin, 1985; Zaitsev, 1992;
Mee, 2001). Similarly, the bathymetry of fjords restricts water
exchanges with the open ocean, leading to hypoxia in systems
with high organic carbon loading. This is observed in fjords of
Canada, Chile, New Zealand, Scotland, Norway, and Sweden
(Nordberg et al., 2001; Gray et al., 2002). Ocean systems along
some continental shelves during periods of upwelling experi-
ence hypoxia when the source waters are nutrient rich with low
DO. This was observed in shelf waters adjacent to Chile, Peru,
Namibia, South Arabia, and western United States (Gray et al.,
2002; Grantham et al., 2004; Helly and Levin, 2004; Chan
et al., 2008; Cullen and Boyd, 2008). In many systems, the
onset of vertical stratification by the formation of haloclines
and thermoclines can also lead to hypoxia (Wu, 2002).
While hypoxia events are natural phenomena, some anthro-
pogenic activities result in their proliferation, and increased
magnitude and duration. To illustrate, over the period of
1980–99, the area in the East China Sea afflicted by hypoxia
increased from <1000 to ~13700 km
2
. Similarly, the area in
the northern Gulf of Mexico (GOM) affected by hypoxia
increased from ~9000 to ~20000 km
2
over the period of
1985–92 (Rabalais, 2001; Rabalais et al., 2002a; Justić et al.,
2005). Alarmingly, the proliferation of hypoxia is pandemic
(UNEP, 2004). A partial list of systems around the world now
experiencing hypoxia is listed in Gray et al. (2002). The magni-
tude and duration of these events range from irregular short-
term phenomena to seasonal events lasting months, and, in
extreme cases, hypoxia is a permanent feature. Governmental
policy groups, such as the Joint Group of Experts on Scientific
Aspects of Marine Pollution and the US Commission on Ocean
Policy, consider hypoxia to be one of the most important
environmental problems threatening marine ecosystems in
modern times (GESAMP, 2001; USCOP, 2004).
Direct loading of organic material accelerates eutrophication.
However, inorganic nutrient loading quickens this process even
more so. Intensive farming, application of fertilizers, deforesta-
tion of watersheds, and discharge of domestic wastewaters are
the primary human activities leading to increased nutrient load-
ing to marine systems (Nixon, 1995; Howarth et al., 1996;
Zimmerman and Canuel, 2000; Diaz, 2001; Talaue-McManus
et al., 2001; Hong et al., 2002; Wu, 2002; Diaz et al., 2004; Druon
et al., 2004; Bagheri et al., 2005; Paerl, 2006; Zhang et al., 2007).
Historical records show that over recent decades nutrients that
commonly limit productivity in marine systems have increased
dramatically, that is, three- to fivefold for nitrogen and 2- to 20-
fold for phosphorus. This was observed for the Baltic, Black, and
North Seas, and from coastal waters of China, Japan, Germany,
the Netherlands, Australia, and the US (Rabalais et al., 2002a;
Wu, 2002). In addition to entering marine systems through
rivers, nutrients can enter through atmospheric deposition. This
occurs in industrialized regions and in areas of intensive livestock
production where gaseous forms of nitrogen are emitted in large
quantities (Paerl et al., 2002).
This increased nutrient loading has stimulated primary pro-
ductivity and resulted in higher flux of organic material to
deeper waters and the sediments (Figure 1). This is evidenced
in sediment cores of the Chesapeake Bay in the US. Lipid
biomarker distributions showed 35–50% increases in sediment
organic carbon content coincident with the timing of wide-
spread use of fertilizers within the watershed (Zimmerman
and Canuel, 2000). In addition, hypoxia was observed in
areas of the Chesapeake Bay adjacent to developed regions of
the watershed, but was not observed in areas of the bay adja-
cent to forested regions (King et al., 2005). The effects of
increased nutrient loading were also observed in the northern
GOM. Here, relationships were detected between agricultural
activities in the Mississippi River watershed and incidence of
hypoxia. In this system, it was approximated that >70% of the
nitrogen and phosphorus loaded onto the Louisiana Shelf
originated from agricultural activities. Interestingly, the loca-
tions where nitrogen and phosphorus loadings were highest
were geographically distinct (Figure 2). The largest sources of
nitrogen were located in areas of corn and soybean production,
whereas the locations of largest phosphorus sources were in
areas of pasture rangeland (generation of animal manure)
combined with production of corn and soybean (Alexander
et al., 2008). These studies, the ones referenced above, and
numerous other works, provide clear evidence of the causal
relationship between nutrient loading and hypoxia.
Predicting magnitude and duration of hypoxia from nutri-
ent loading is not straightforward because other processes and
system conditions come into play. In marine systems domi-
nated by small-sized phytoplankton, much of the primary
production remains in surface waters, where it is consumed
by micrograzers and recycled through the microbial loop,
with little sinking to bottom waters and sediments (Kiørboe
et al., 1996). Larger-sized phytoplankton taxa tend to outper-
form smaller-sized taxa when nutrient concentrations are
elevated. Consequently, nutrient loading tends to shift com-
munity composition within the phytoplankton toward larger-
sized taxa. When this occurs, less of the productivity is recycled
in surface waters, with more sinking to bottom waters and
sediments. In addition, the greater sinking rates of the larger-
sized phytoplankton shorten the time particles that are in the
water column. Thus, the effects of stimulated primary produc-
tivity and phytoplankton assemblage shifts are combined
(Riegman, 1995). In addition, the edibility of phytoplankton
affects the downward flux of organic matter, where less edible
forms tend to result in greater downward flux (Paerl, 2006).
The difficulty in predicting the increased downward flux of
organic material through this process arises from the difficulty
inherent in foretelling phytoplankton succession (Roelke et al.,
1997, 2003; Huisman and Weissing, 2001; Roelke and
Eldridge, 2008, 2009), as to which phytoplankton taxa emerge
as dominants following the increased nutrient loading will
determine the particle sinking characteristics.
The mode in which nutrients are loaded into a system may
also influence the supply of organic carbon to deeper waters and
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Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches 195
Figure 1 Inorganic nutrient loading accelerates the process of eutrophication. In this schematic, nutrient sources are agricultural, industrial, and
residential. Once transported through runoff and river inflows, excess inorganic nutrients stimulate primary productivity and result in a higher flux of
excessive organic matter sediments to deeper water where O
2
supply may be restricted. Decomposition of organic matter under these conditions can lead
to hypoxia. Reproduced from Paerl, H.W., Valdes, L.M., Peierls, B.L., Adolf, J.E., Harding, L.W., 2006. Anthropogenic and climatic influences on the
eutrophication of large estuarine ecosystems. Limnology and Oceanography 51, 448–462.
sediments. Some studies suggest that when nutrients are loaded
in a pulsed fashion, such as when river inflows are episodic,
plankton productivity is enhanced. This was demonstrated using
numerical models of the Nueces River Estuary in the US (Roelke
et al., 1999; Roelke, 2000) and experiments using natural plank-
ton assemblages from San Antonio and Corpus Christi Bays in
the US (Buyukates and Roelke, 2005; Miller et al., 2008). In
natural systems, this process might increase the downward flux
of organic material. Indeed, with a constant loading of nutrients,
organic matter remineralization appears to occur mostly within
surface waters with little downward flux. However, when nutri-
ent loadings are pulsed, there is significant downward flux of
organic material (Gray et al., 2002).
Further complicating the relationship between nutrient
loading and hypoxia is the reactivity of organic carbon.
Chemical forms of organic carbon are metabolized with differ-
ing efficiencies. For example, glucose is metabolized very
quickly compared to an equal weight of cellulose. Similarly,
the organic carbon produced by phytoplankton is metabolized
more quickly than organic carbon originating from vascular
plants (Tenore and Hanson, 1980; Graf et al., 1982; Aubert,
1990). A mismatch between oxygen consumption and supply
rate is more likely to occur when organic matter is metabolized
quickly. Therefore, it is not only the amount of organic carbon
loading into a system, but also the reactivity of this organic
carbon that is important to hypoxia formation. In the northern
GOM, allochthonous sources of organic carbon originating
mostly from vascular plants are approximately threefold greater
than organic carbon loading from phytoplankton production.
The incidence of hypoxia, however, is a function of both
organic supply and reactivity (Green et al., 2006).
The DO supply rate also complicates the relationship
between nutrient loading and hypoxia. Physical processes lead-
ing to stratification affect the DO supply rate to bottom waters
and sediments, and, in some systems, it is the onset of stratifi-
cation that controls hypoxia. This was observed in the Swan
River Estuary, Australia and the Chesapeake Bay (Kuo and
Neilson, 1987; Kurup and Hamilton, 2002; Kemp et al.,
2005). In addition, suppression and termination of hypoxia
are related to stratification breakdown, which was observed in
the Neuse River Estuary in the US and in Tokyo Bay where
cooling periods coincided with relief from hypoxia (Buzzelli
et al., 2002; Kodama et al., 2006). This was also observed in
Tokyo Bay, the Pearl and Neuse River Estuaries, and Pensacola
Bay in the US, where during strong storms wind-induced mix-
ing obliterated stratification and disrupted hypoxia (Glasgow
and Burkholder, 2000; Yin et al., 2004; Hagy et al., 2006;
Kodama et al., 2006).
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196 Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches
Percent of stream flux
<10 10–25 25–50
50–75 75–90 90–100
(a) Total nitrogen
(b) Total phosphorus
Figure 2 Increased loading of nitrogen and phosphorus to the northern Gulf of Mexico has stimulated primary productivity and resulted in higher flux of
organic material to deeper waters and sediments, fueling hypoxia. Locations where nitrogen and phosphorus loadings were highest were geographically
distinct within the Mississippi River watershed. The largest sources of nitrogen (a) were located in areas of corn and soybean production, whereas the
locations of largest phosphorus sources and (b) were in areas of pasture rangeland (generation of animal manure) combined with production of corn and
soybean. Reproduced from Alexander, R.B., Smith, R.A., Schwarz, G.E., Boyer, E.W., Nolan, J.V., Brakebill, J.W., 2008. Differences in phosphorus and
nitrogen delivery to the Gulf of Mexico from the Mississippi River basin. Environmental Science and Technology 42, 822–830.
Other physical processes affecting the DO supply rate and
hypoxia are tidal mixing and circulation. Hypoxia suppression
from tidal mixing was documented in lagoonal systems of
Portugal (Lopes et al., 2008) and in the Tone River Estuary of
Japan (Ishikawa et al., 2004). Similarly, estuarine circulation
driven by wind and freshwater inflows affected the spatial
extent of hypoxia, as observed in Tokyo Bay and the Pearl
River Estuary (Fujiwara and Yamada, 2002; Yin et al., 2004;
Kodama et al., 2006). From coastal ocean systems, seasonal
and decadal patterns of hypoxia are linked to circulation. This
was demonstrated in the Benguela upwelling system, where
hypoxia was controlled by circulation from the equatorial and
polar regions, and from seasonal shifts in shelf advection (van
der Plas et al., 2007; Monteiro et al., 2008). Similarly, hypoxia
along the Chilean coast, areas of the Adriatic and North Seas,
and the New York Bight were related to physical conditions
influencing DO supply (Falkowski et al., 1980; Druon et al.,
2004; Paulmier et al., 2006).
The interplay between organic carbon loading and physical
processes influencing DO supply leads to periodicity in
hypoxia in some areas. Seasonal patterns are common, where
physical processes forced by climate include freshwater
discharges, wind-driven circulation, and deep-water mixing.
Seasonal patterns of hypoxia have been observed in estuaries,
bays, coastal shelf waters, and confined seas (Fujiwara and
Yamada, 2002; Gray et al., 2002; Kodama et al., 2006;
Paulmier et al., 2006). Processes acting over longer periods
also influence hypoxia. For example, during El Niño years,
DO supply is higher and areas of hypoxia can be reduced,
which was observed along the Chilean shelf (Helly and Levin,
2004; Figure 3). In smaller systems, periodic hypoxia events
can occur over much shorter periods. Diurnal patterns are
frequently observed where high primary productivity leads to
DO supersaturation during daylight hours and high respiration
leads to hypoxia during night. This was observed in shallow
tidal creeks, lagoons, and estuaries (D’Avanzo and Kremer,
1994; Wenner et al., 2001; Moore, 2004; Shen et al., 2008).
In some areas, however, hypoxia is perennial. As mentioned
above, the bathymetry of some systems restricts water exchange
and DO supply, and hypoxia events are natural. These systems
include not only fjords and estuaries, but also large systems
such as the Gulf of Finland and areas of the Baltic, Black, and
Caspian Seas. While hypoxia is persistent in these systems,
there is evidence that the spatial magnitude of hypoxia has
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North
Pacific
Ocean
Andes Mountains
South
Oxygen minimum zone during an El Niño event
Oxygen minimum zone during non-El Niño periods
Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches 197
Figure 3 Incidence and magnitude of low oxygen are sometimes periodic, in phase with some physical drivers. In this image, showing the western
coastline of South America (Northern Chile in the south and Peru toward the north), the extent of the oxygen minimum zone during an El Niño event is
confined to the area colored red. Because upwelling is weaker during non-El Niño periods, the aerial extent of low dissolved oxygen is greater (red- and
yellow-colored areas combined). Reproduced from Helly, J.J., Levin, L.A., 2004. Global distribution of naturally occurring marine hypoxia on continental
margins. Deep-Sea Research I 51, 1159–1168.
increased due to culturally enhanced eutrophication (Gray
et al., 2002). In addition, cultural eutrophication likely caused
perennial hypoxia in some systems where it did not occur
previously, such as in areas of the Gulf of St. Lawrence
(Gilbert et al., 2005).
9.11.3 Effects of Hypoxia on Biota
As mentioned previously, ammonia and hydrogen sulfide are
produced under chemically reducing conditions. Both the che-
micals are toxic to many marine organisms. The presence of
these chemicals confounds understanding of hypoxia effects on
marine organisms. However, ammonia and hydrogen sulfide
are quickly oxidized when diffused into oxygenated waters,
even when oxygen is in short supply. Because the residence
times of these chemicals in oxygenated environments are
brief, it is generally accepted that observed hypoxia effects on
organisms are attributed mostly to low DO (Gray et al., 2002).
The most extreme hypoxia effect on organisms is death. In
areas where hypoxia persists for extended periods, vast dead
zones can develop where sedentary organisms perish and
motile organisms flee. One of the largest dead zones is that of
the northern GOM, where an expanse of the benthic shelf
environment exceeding 27000 km
2
hosts few life forms
(Rabalais et al., 2002b). Organism mortalities due to hypoxia
have been reported in coastal marine environments worldwide,
as reviewed in Wu (2002). Some hypoxia events develop
rapidly, ensnaring even motile organisms and causing fish
kills. These occur mostly in shallow water systems and are
particularly detrimental to the long-term viability of many
populations that use these habitats as nurseries (D’Avanzo
and Kremer, 1994; Shen et al., 2008). Tolerances for hypoxic
conditions vary among organisms. Fish tend to be the least
tolerant, followed by crustaceans, then annelids, and then
bivalves (Rosenberg et al., 1991; Nilsson and Rosenberg,
1994; Levin, 2000; Gray et al., 2002; Rabalais et al., 2002b;
Wu, 2002; Seitz et al., 2003; Lim et al., 2006). Larval stages and
juveniles are generally less tolerant than adults for many fish
and crustacean populations (Miller et al., 1995), and macro-
fauna are generally less tolerant than meiofauna (Sagasti et al.,
2000; Gray et al., 2002).
Recovery rates from hypoxia events vary among populations,
and this can also bring about food-web shifts. Mussel bed com-
munities were destroyed by hypoxia in Narragansett Bay on the
US east coast. Predators of mussels recovered more quickly than
mussels, preventing reestablishment of the original community.
In this case, hypoxia changed the long-term ecosystem structure
and function, decreasing the system’s filtration capacity and
energy transfer from the pelagic to benthos (Altieri and
Witman, 2006). Community composition shifts arising from
differential tolerances and recovery rates from recurrent hypoxia
can also result in biomass distribution changes, with less biomass
encompassed in benthic populations and more in pelagic popu-
lations, with fewer capstone species and more opportunistic
species (Wu, 2002; Lim et al., 2006), or simplyareduction in
overall biomass (Montagna and Ritter, 2006).
The spatial and temporal extent of hypoxia also controls the
distribution of many organisms, some commercially impor-
tant. For example, the mantis shrimp, Oratosquilla oratoria,
becomes immobile when DO declines below 2.3 mg l
−1
and
dies when DO drops below 0.5 mg l
−1
(Hamano and
Yamamoto, 2005). In Tokyo Bay, O. oratoria recruitment during
autumn only occurred in areas beyond the hypoxia edge where
DO was >2.1 mg l
−1
. However, as winter progressed and the
extent of hypoxia abated, O. oratoria expanded their distribu-
tion to follow the retreating hypoxia edge (Kodama et al.,
2006). Similarly, swimming and feeding behavior of Atlantic
cod, Gadus morhua, is proportional to DO. When DO drops
below 20% of the air saturation, these activities cease and fish
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198 Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches
survival is jeopardized. Observations from the Kattegat and
Baltic Seas and the Gulf of St. Lawrence show that G. morhua
completely avoid waters below this saturation level (Chabot
and Claireaux, 2008). The authors further suggested these same
behaviors are likely for European sea bass, Dicentrarchus labrax,
common sole, Solea solea, and turbot, Psetta maxima.
Food-web disturbances caused by habitat compression result
from hypoxia because motile organisms can detect and avoid
low DO waters, immigrating into adjacent and oxygenated
habitats (Pihl et al., 1991; Breitburg, 1992; Wannamaker and
Rice, 2000; Eby and Crowder, 2002; Bell et al., 2003; Craig and
Crowder, 2005). This migration can disrupt localized food webs
by resulting in population densities greater than the carry capa-
city of the habitat, shifting predator-to-prey ratios, and causing
population growth rates to plummet (Eby and Crowder, 2002;
Gray et al., 2002; Wu, 2002; Craig and Crowder, 2005; Eby et al.,
2005; Shoji et al., 2005; Kodama et al., 2006; Sell and Morse,
2006).
9.11.4 Mitigation of Hypoxia
Reversing eutrophication through reduced inorganic nutrient
loading is the primary strategy for hypoxia mitigation. In agri-
cultural areas, this involves decreasing fertilizer application
rates, which is of concern because this may affect crop yield.
Modifying tilling practices, however, may enable reduced ferti-
lizer application while maintaining crop yield. For example, in
the mid-western US, an area that supplies a large amount of
nitrogen to the northern GOM, fertilizers are typically applied
during fall. At this time of year, the soils are dry and the cost of
fertilizer is low. When fertilizers are applied this far in advance
of crop production, much of the nitrogen is lost from the
fertilizer through nitrification and leaching. However, the
application of fertilizer in the spring, closer to the start of
crop production, may prevent this loss (Gowda et al., 2008).
In turn, this may enable lower fertilizer application rates with
no reduction in crop yield, and lessen hypoxia in the northern
GOM.
Nutrient load reductions can also be achieved by creating
buffer zones between areas of nonpoint sources and water
bodies. A type of buffer zone, artificial wetlands, is effective at
reducing nutrient loads from diverted nutrient-rich waters.
Findings from many artificial wetland systems in the mid-
western US and northern Europe indicate reductions up to
88% for total phosphorus (Braskerud et al., 2005) and 37%
for total nitrogen (Kovacic et al., 2000). Furthermore, the effi-
ciency of artificial wetlands may be enhanced when multiple
systems are employed concurrently (Ng and Eheart, 2008).
Additional nutrient loading reduction measures in agricultural
systems include changing cropping systems and advancing
animal waste treatment methods. In urban areas, reduction of
nutrient loadings can be accomplished by decreasing dis-
charges from municipal and industrial water treatment plants,
increasing combustion engine fuel efficiency, switching to
alternative power sources with lower nitrogen oxide emissions,
and using less fertilizer during lawn care and landscaping
(CENR, 2003).
There may be additional strategies to combat hypoxia that
are complementary to reducing nutrient loading. For example,
it may be that top-down pressure on phytoplankton could be
enhanced, thereby preventing excessive organic material load-
ing through primary production. This was suggested for the
Chesapeake Bay, where some believe that the oyster population
decline resulted in less system filtration capacity, thereby
exacerbating the effects of eutrophication and hypoxia (Kemp
et al., 2005; Newell et al., 2005). This hypothesis is controver-
sial, however, because the predicted impact of oyster
restoration depends on the attributes of the model used to
study the system. Models that emphasize organic matter trans-
port through littoral zones suggest a strong link between
hypoxia in deeper areas of the bay and community structure
of fringing habitats. In these models, oyster restoration
decreases hypoxia (Newell, 1988; Newell et al., 2007).
De-emphasis of the these processes leads to temporal and
spatial mismatches between oyster filtration and primary pro-
ductivity, and predicts that oyster restoration will have little
effect on hypoxia (Pomeroy et al., 2006). Other discrepancies
between these contradicting models involve the temperature
dependence of filtration rate, and the role of fecal material as
an organic matter-loading agent (Cerco and Noel, 2007;
Fulford et al., 2007; Pomeroy et al., 2007). In the Chesapeake
Bay, as in many other systems, the idea of mitigating hypoxia
through top-down control of primary production requires
further investigation.
Another approach complementary to reducing nutrient
loading is manipulating hydraulic flushing. With this
approach, the timing of inflows is important. For example,
during periods of low inflow, deeper waters can become
entrained in regions where the estuary’s bathymetry restricts
flushing, and hypoxia can develop. Waters stored in reservoirs
during wetter periods of the year, however, could be used as
source water to maintain critical inflows necessary to flush
bathymetric regions susceptible to hypoxia. This approach to
mitigating hypoxia was suggested for the Swan River Estuary
(Kurup and Hamilton, 2002) and the Danshuei River Estuary,
Taiwan (Liu et al., 2005). Manipulating inflows in such a way
as to reduce the growth of less edible phytoplankton taxa
would also likely reduce hypoxia, as less of the organic matter
produced through primary productivity would sediment and
more would transfer up the food web (Roelke et al., 1997,
1999; Roelke, 2000; Buyukates and Roelke, 2005; Paerl, 2006;
Miller et al., 2008). The efficacy of such approaches to hypoxia
mitigation must consider a region’s water supply, and how this
supply will likely change with population growth and climate
change.
9.11.5 Assessment of Mitigation
There is good reason to believe that nutrient loading reductions
will reduce the effects of hypoxia. Evidence for this is seen in
the Black Sea, a system with perennial hypoxia. Cultural eutro-
phication during the post-World War II era worsened the extent
of hypoxia in this system (Tolmazin, 1985; Zaitsev, 1992; Mee,
2001). Fertilizer application declined, however, with the
decline in agricultural subsidies that followed the Soviet
Union collapse. In the decades that followed, nutrient loading
decreased and hypoxia effects were lessened (Mee, 2001).
Similarly, model simulations of the northern GOM suggest
that a 30% decrease in nitrogen loading would result in a
37% decrease in the frequency of hypoxia (Justić et al., 2003),
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Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches 199
and that reduced nutrient loads would substantially decrease
the spatial extent of hypoxia (Eldridge and Roelke, 2009). In
addition, model simulations of the Danshuei River Estuary
indicate that the completion of various sewage treatment pro-
jects will result in 75% reduction in nutrient loads and will
prevent DO from dropping below 1 mg l
−1
(Liu et al., 2005).
However, assessment of mitigation efforts will be complex.
For example, discharge volume also affects hypoxia because it
relates to stratification. The Justić et al. (2003) and Eldridge and
Roelke (2009) models of the northern GOM indicate that
modest increases in river discharge volume can offset the ben-
efit of reduced nutrient loading and hypoxia remains
unchanged. Further complicating the interaction between
nutrient loading and discharge volume is that not all systems
will likely be affected in the same manner. While increased
discharge volume in the northern GOM will likely expand
hypoxia, increased discharge volume in the Hudson River
Estuary will likely lessen the extent of hypoxia. These systems
respond differently to changing inflows because they vary in
their trophic state, bathymetry, and physical circulation char-
acteristics (Justić et al., 2005). Furthermore, ecosystem
response to changing nutrient loads will have lag times that
are dependent on the amount of organic matter stored within
the system. Remineralization of this organic matter will recycle
nutrients, stimulating productivity. Lag times may range from
years to decades (Rabalais et al., 2002a).
9.11.6 Modeling Approaches
The above-mentioned studies only skim the number of pub-
lished works on hypoxia in marine systems. From these it is
seen that environmental conditions leading to hypoxia are not
universal. For example, hypoxia occurs in shallow and deep
systems, small and large. It occurs when the water column is
stratified and well mixed. It occurs in areas with permanent and
temporary frontal systems, and in systems with and without
bathymetry that restricts water exchange (see reviews in Gray
et al., 2002; Rabalais et al., 2002a; Wu, 2002). Environmental
conditions leading to hypoxia are clearly not universal.
Consequently, the tools developed to study hypoxia are also
not universal. Modeling is one of the many tools used to study
hypoxia. Approaches to modeling are diverse, and include
qualitative approaches that are conceptual, and quantitative
approaches that are statistical and mathematical, and of varied
complexity.
Conceptual models are the frameworks of understanding
from which other models can be based. Early conceptual mod-
els linked system response with nutrient load (Figure 4(a)).
Cloern, 2001; The system response was typically chlorophyll a
concentration, primary productivity, community metabolism,
or DO, and the nutrient load was often characterized by a single
element, usually nitrogen. A simplified conceptual modeling
approach was useful for the management and restoration of
many lakes, as the relationship between nutrient load and
system response is robust between many inland water bodies
(Vollenweider, 1976; Hecky and Kilham, 1988). This simple
relationship proved less robust for marine systems because the
processes acting at the system level are fundamentally different
from those acting on lakes, and they are system specific.
Conceptual models of marine systems evolved from a
simple system understanding, and now account for greater
system complexity, which includes factors that drive transport
and hydraulic residence time, optical properties, benthic–
pelagic coupling, and tidal energy. Each of these processes can
buffer (or filter, as termed in Cloern, 2001) the effect of
increased nutrient loading on primary productivity and DO.
For example, when system flushing is high, when light is limit-
ing, or when particle removal rate by suspension feeders is
high, the degree to which productivity is stimulated by nutrient
loading can be lessened. Similarly, when tidal energy is high,
stratification is reduced and oxygen reentry is enhanced,
thereby lessening the degree to which DO is depleted with
organic matter loading. Conceptual models in marine systems
have also evolved to incorporate direct and indirect effects of
nutrient loading. These include the roles of multiple stressors,
seasonal dynamics, community composition shifts, and sedi-
ment stores of organic matter (Figure 4(b)).
Statistical models linking observations of routinely mea-
sured parameters can be very useful for predictive purposes.
For example, Hagy et al. (2004) developed statistical rela-
tionships between inflow and nutrient loading to the
volume of hypoxia for the Chesapeake Bay, where changes
in inflow couldbeusedtopredict the extentofhypoxia.
The advantages of a statistical modeling approach are that
the data needed for the model are readily available and the
uncertainty of the relationship is quantified. The disadvan-
tage is that the relationships are only correlative, and the
use of the model to predict system response under varied
conditions or in other systems is limited.
Hybrid models that blend statistical relationships with
simulation modeling have increased utility and still offer the
advantage of using readily available data. For example, Scavia
et al. (2006) estimated nutrient loading by employing log-
linear statistical relationships based on historical observations
of total nitrogen concentrations and flows, whereas biological
oxygen demand and oxygen flux were mechanistic functions
based on first-order rate constants for decomposition and prin-
ciples of diffusion and advection. With this approach, a greater
degree of realism is built into the model. In some models,
parameter values are periodically forced with new data.
Druon et al. (2004) simulated the North and Adriatic Seas
with hydrodynamics, while changes in biota are recalibrated
using satellite chlorophyll a observations and associated pro-
ductivity relationships. From this blended modeling approach,
they are able to generate a continuous risk index with a high
degree of certainty over short periods.
Mathematical models can also be fully mechanistic with no
reliance on statistics or data forcing. They also vary in their
complexity and how they are used. A mathematical model
can be as simple as a single ordinary differential equation
requiring few parameters, or as complex as sets of partial
differential equations requiring many parameters. Steady-state
solutions to mathematical models can be used to study
ecosystem attributes when the system is nonchanging, and
time-dependent behavior of mathematical models can be
used to study dynamic behaviors of systems.
By assuming that the system is not changing, as with steady-
state models, and imposing values for some components and
material fluxes that are readily determined empirically, other
components and material fluxes that are more difficult to
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(a) Early conceptual model
Changes in:
Nutrient loading Responses Chlorophyll
Primary production
System metabolism
Dissolved oxygen
Nutrient loading Responses
(b) Evolved conceptual model
Direct
Nutrient loading Filter responses Indirect
responses
Changes in:
Chlorophyll
Primary production Changes in:
Macroalgal biomass Benthos biomass
Sedimentation of orgainc C Benthos community
Si:N and N:P ratios Vascular plants
Toxic-harmful algal blooms Habitat quality/diversity
Phytoplankton community Water transparency
Organic C in sediments
Sediment biogeochemistry
Bottom-water dissolved oxygen
Responses Seasonal cycles
Mortality of fish/invertebrates
Reversible Nutrient cycling
Food-web structure
200 Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches
Figure 4 Conceptual models describing the response of marine systems to nutrient loading has evolved. Early models (a) were strongly influenced by
our understanding of responses to nutrient loading in freshwater systems, where the prevailing thought was that more nutrient loading would evoke a
greater response. Evolved conceptual models (b) better account for attributes of marine systems that filter the affect of nutrient loading, such as tidal
mixing and flushing, light limitation, and benthic–pelagic coupling. In addition, there are many indirect responses in marine systems to nutrient loading,
which in turn affect the direct responses, which are also accounted for in modern conceptual models. Reproduced from Cloern, J.E., 2001. Our evolving
conceptual model of the coastal eutrophication problem. Marine Ecology Progress Series 210, 223–253.
measure can be estimated. Van der Plas et al. (2007) employed
this modeling approach as they explored factors affecting
hypoxia in bottom waters and sediments of the central
Benguela upwelling system. In their model, nutrient and parti-
culate organic carbon in bottom waters and profiled through
the sediments were imposed, as they were based on empirical
data from the system. Fluxes were calculated using tempera-
ture-dependent reaction rates and principles of molecular
diffusion, and also based on the assumption that under varied
boundary conditions the system did not vary with time. Using
their steady-state model, they determined that processes acting
external to the bottom water and sediments were stronger
drivers of hypoxia than local processes. The authors acknowl-
edged the limitation of their modeling approach in that
insights of system dynamics were limited, which is true for
steady-state models in general.
In some systems, available data are greatly underdeter-
mined preventing adequate parametrization of the equations
describing the system. An alternative approach to solving
underdetermined models involves inverse analysis (Vezina
and Platt, 1988; Vezina, 1989). With this approach, upper
and lower bounds on components and material fluxes
described by the conceptual model are imposed. The range
over which the upper and lower bounds span reflects the con-
fidence interval, where broad ranges are used for components
and material fluxes that are poorly understood. A unique
solution to an underdetermined model can be found by accept-
ing only the solution meeting a predefined mathematical
criterion. Green et al. (2006) employed this modeling
approach as they explored seasonal attributes of the carbon
budget in waters of the northern GOM. They used a detailed
food-web model composed of small and large phytoplankton,
bacteria, three size classes of zooplankton, DOC, and detritus
(see Breed et al., 2004). They used simplified physical circula-
tion based on flows between large regions defined by salinity.
The food-web component of the model in each of the
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   
Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches 201
regions was underdetermined, so season-specific constraints on
components and material fluxes were used. The solution that
minimized the sum of squares including all material fluxes was
accepted. Green et al. (2006) were able to use this modeling
approach to explore seasonal attributes of the carbon budget,
that is, organic carbon partitioned into various plankton com-
ponents, primary productivity and community respiration, and
vertical flux, by performing several inverse analyses guided by
monthly time series data (generated by compiling data from 21
cruises). Their findings underscored the importance of primary
productivity and the generation of labile organic matter as a
contributing factor to hypoxia, especially during the spring and
summer months.
Ecosystem dynamics can be investigated through the analysis
of time-dependent behavior of differential equations. When
equations are simple, analytical solutions can be determined.
When equations are complex and nonlinear, as is the case with
most marine ecosystem models, numerical methods are
employed to find solutions. Numerical methods are not limit-
less, however. Computational power often limits the complexity
of models that are to be solved numerically, as models encom-
passing a greater number of differential equations requiring
simultaneous solution demand more processing power. In addi-
tion, some differential equations are unstable, where solutions
can rapidly diverge based on the numerical solving routine
employed. Furthermore, models with a high degree of realism
represented in their differential equations often require a greater
level of parametrization than simple models, which is not
always supported by available empirical data. As such, tradeoffs
exist as to the level of realism described in a numerical model
with what is practical to sample.
This tradeoff manifests itself in the frameworks of simulation
models (see Table 1). Some modeling efforts employ simple
representations of biota and physics. Shen et al. (2008),intheir
simulation of tidal creeks to the Chesapeake Bay, depicted only
two biotic groups, a phytoplankter and a macroalga. They
assumed the system was completely mixed, a spatial area of
~0.4 km
2
, which enabled them to employ a dimensionless box
modeling approach, that is, no physical circulation within the
framework. Similarly, Justić et al. (2003) represented biota in
their simulation of the northern GOM simply as organic matter
and net productivity, and assumed a well-mixed surface and
bottom layer over an area of ~20000 km
2
, where the bottom
layer was in contact with sediments that were also uniform in
their attributes over this area. Keeping biota and physical circula-
tion simple in these models allowed for ease of implementation.
However, a drawback was that insights regarding how aspects of
biota and physical circulation affect hypoxia were limited.
Other modeling efforts kept the representation of biota
simple and employ detailed simulation of physical circulation
(Table 1). These involve three- and two-dimensional frame-
works. Three-dimensional frameworks describe aerial and
vertical gradients (Druon et al., 2004; Hetland and DiMarco,
2008). A two-dimensional framework can be used to describe
circulation along a longitudinal and vertical gradient (Kurup
and Hamilton, 2002; Ishikawa et al., 2004; Liu et al., 2005;
Benoit et al., 2006; Scavia et al., 2006) or circulation within an
aerial surface with no vertical gradient (Lopes et al., 2008).
Three- and two-dimensional model frameworks are repre-
sented using partial differential equations. For example,
equations of a two-dimensional framework describing laterally
integrated dynamics of particles (e.g., phytoplankton) or dis-
solved substances (e.g., inorganic nutrients) suspended in the
water column would take the form:
∂ðCBÞ ∂ðCBuÞ ∂ðCBwÞ
þ þ
∂t ∂x ∂z
∂ ∂C ∂ ∂C
¼ kxB þ KzB þ CSi þ CSe ½1
∂x ∂x ∂z ∂z
where t is the time (days), x and z are the length and depth of the
targeted system (m), B is the width of the system (m) over which
the particle or dissolved substance is integrated, C is the laterally
averaged concentration of the particle or dissolved substance
(mmol m
−3
), u and w are the laterally averaged velocities in
the x and z directions (m d
−1
), K
x
and K
z
are the turbulent
diffusion coefficients in the x and z directions (m
2
d
−1
), S
i
is
the internal rate of change of C through biogeochemical pro-
cesses (mmol m
−3
d
−1
), and S
e
is the rate of change of C through
external processes acting at the boundaries (mmol m
−3
d
−1
). This
equation represents the mass balance of salt or sediment.
Models employing three- and two-dimensional frameworks
can be computationally expensive and challenging to solve
numerically. In the references listed above, the roles of biota
in hypoxia formation and persistence were not well described,
as representations of biota are simplified in these models. On
the other hand, physical processes such as stratification and
entrainment were well simulated in these models, which
enabled exploration of these processes as drivers of hypoxia.
Still other modeling efforts employ detailed depictions of
biota while keeping the simulation of physical circulation simple
(Table 1). These involve multiple competing phytoplankton
groups with varying ecosystem functions, bacterial and zooplank-
ton components, and complex biota-driven diagenetic processes
(Eldridge and Morse, 2008; Green et al., 2008; Eldridge and
Roelke, 2009). These models allow for the study of biotic pro-
cesses as they relate to hypoxia, but sacrifice the influence that
physical circulation processes might play. In the case study pre-
sented below, this will be discussed in greater detail.
Finally, recent modeling efforts represent detailed biota and
physical circulation (Table 1). These involved multiple plank-
ton groups with varying ecosystem functions and full three-
dimensional circulation. This class of model is the most pro-
mising as it allows for the interplay and biota and physical
processes to be studied as they affect hypoxia (Lin et al., 2007;
Sohma et al., 2008). However, this class of model also requires
the greatest amount of parametrization that may not be sup-
ported by empirical observations. It is also the most difficult to
validate. It may be that these models will be most useful when
investigating short-term ecosystem behavior where the model
inputs and parameters can be frequently recalibrated with new
data (see Justić et al., 2007). This coupling of empirical obser-
vation and modeling has worked well in meteorology with
regard to weather forecasting.
9.11.7 The Edge of Ockham’s Razor: Building
a Hypoxia Model
In the thirteenth century, William of Ockham noted “Entities
should not be multiplied unnecessarily,” a philosophy with
origins dating back to Aristotle. More commonly, the
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Table
1
Recent
numerical
models
focused
on
hypoxia
System
Biotic
components
Environmental
framework
Elements
Dimensions
Temporal
scale
Citation
Simplified
biota,
simplified
hydrodynamics
Small
tributary
of
Single
groups
for
phytoplankton
and
Shallow,
well-mixed
tidal
creek;
box
model
O
~0.4
km
2
area,
average
Diurnal
dynamics
Shen
et
al.
Chesapeake
Bay,
macroalgae
1.6
m
depth
over
30
days
(2008)
USA
Northern
Gulf
of
Net
productivity,
organic
matter
Single-layered
surface
and
bottom
waters;
O,
C
~20
000
km
2
Seasonal
dynamics
Justić
et
al.
Mexico
sediments;
box
model
over
decades
(2003)
Simplified
biota,
detailed
hydrodynamics
Northern
Gulf
of
Respiration
categories
Three-dimensional
hydrodynamics;
O
~120
000
km
2
Daily
dynamics
over
Hetland
and
Mexico
sediments;
7750
regions
months
DiMarco
Ria
de
Aveiro
Single
phytoplankton
group;
multiple
Elongated,
shallow
and
vertically
well-mixed
O,
N
450
km
2
area,
average
Diurnal
dynamics
(2008)
Lopes
et
al.
Lagoon,
Portugal
categories
of
biological
oxygen
demand
lagoon;
two-dimensional
hydrodynamics
1
m
depth
over
30
days
(2008)
(x,
y)
with
173
964
segments
St.
Lawrence
Respiration;
labile
and
refractory
organic
Bottom
layer
with
sediments;
two- O,
C
~700
km
length,
Steady
state
Benoit
et
al.
Estuary,
Canada
matter
dimensional
(x,
z)
with
10
locations
spanning
depths
100–
(2006)
300
m
Chesapeake
Bay,
organic
matter
Two-layered
water
column
(surface
and
O,
N
220
km
length
Steady
state
Scavia
et
al.
USA
bottom)
along
one
horizontal
dimension
(2006)
with
220
segments
Danshuei
River
Single
phytoplankton
group
Connected
river
estuaries
that
are
elongated,
O,
N,
P
33,
14,
and
37
km
Daily
dynamics
over
Liu
et
al.
Estuary,
Taiwan
shallow
and
stratified
with
sediment
regions,
varying
in
1
year
(2005)
boundary;
two-dimensional
(x,
z)
depth
between
1
and
hydrodynamics
with
84
segments
total
6m
North
Sea
and
Empirically
forced
productivity
and
Three-dimensional
hydrodynamics;
3770
n/a
~75
400
and
Monthly
dynamics
Druon
et
al.
Adriatic
Sea
respiration
and
7225
regions,
respectively
~350
000
km
2
,
over
a
year
(2004)
respectively
Tone
River
Estuary,
Oxygen
consumption
for
water
column
and
Elongated,
shallow
and
stratified
river
estuary
O
18
km
length,
Hourly
dynamics
Ishikawa
et
al.
Japan
sediments
with
sediment
boundary;
two-dimensional
~8
m
depth
over
100
days
(2004)
(x,
z)
hydrodynamics
Swan
River
Oxygen
consumption
for
bottom
waters
and
River
estuary
with
sediment
boundary;
two
O
50
km
length,
average
Hourly
dynamics
Kurup
and
Estuary,
Australia
sediments
dimensional
(x,
z)
hydrodynamics
depth
of
2.1
m
over
60
days
Hamilton
(2002)
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Biotic
complexity,
simplified
hydrodynamics
Northern
Gulf
of
Multiple
phytoplankton
functional
groups,
Single-layered
surface
and
multiple
layered
O,
C,
~20
000
km
2
Periodic
seasonal
Eldridge
and
Mexico
single
groups
for
zooplankton
and
detritus;
deep
waters;
sediments;
4
regions
N,
P
dynamics
Roelke
dissolved
labile
and
refractory
organic
(2009)
matter,
diagenetic
processes
Northern
Gulf
of
Productivity
and
respiration;
labile
and
Single-layered
surface
and
bottom
waters;
O,
C,
Zero-dimensional
Seasonal
dynamics
Eldridge
and
Mexico
refractory
organic
matter,
diagenetic
sediments
N,
S,
Morse
processes
Fe
(2008)
Northern
Gulf
of
Two
phytoplankton
and
two
zooplankton
Single-layered
surface
waters
O,
N
Zero-dimensional
Steady
state
Green
et
al.
Mexico
groups,
single
groups
for
bacteria
and
(2008)
detritus;
dissolved
organic
nitrogen
Complex
biota,
detailed
hydrodynamics
Tokyo
Bay,
Japan
Single
groups
for
phytoplankton,
zooplankton
Three-dimensional
hydrodynamics;
O,
C,
~900
km
2
area
Periodic
seasonal
Sohma
et
al.
benthic
algae,
suspension
and
deposit
sediments;
26
regions
N,
P
dynamics
(2008)
feeders,
and
detritus;
dissolved
labile
and
refractory
organic
matter,
biogeochemical
processes
Pamlico
Sound,
Three
phytoplankton
groups,
labile
and
Three-dimensional
hydrodynamics;
two- O,
N,
~5335
km
2
area,
average
Steady
state
Lin
et
al.
USA
refractory
organic
matter,
biogeochemical
layered
sediments;
~6586
segments
P,
Si
4.5
m
depth
(2007)
processes
Note:
The
models
are
grouped
according
to
the
complexity
of
the
simulated
biota
and
hydrodynamics.
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204 Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches
philosophy is written “Things should be made simple, but not
simpler” (sensu Albert Einstein). Despite its ancient origins, the
philosophy of Ockham’s razor is highly relevant today, espe-
cially in the area of hypoxia modeling. Some argue that simple
model frameworks are more useful than complex frameworks
because they are easier to validate with time-series data, inspir-
ing greater confidence (Williams, 2006; Justić et al., 2007).
Simple hypoxia models, however, provide a limited under-
standing of the mechanisms governing the development and
duration of hypoxia. Hypoxia models of greater mechanistic
complexity resemble natural systems more, when the complex-
ity correctly represents the processes. However, validation is far
more challenging.
In the case of the northern GOM, there is a need to simulate
the spatial and temporal scales of hypoxia, and explore how
they might change in response to impending nutrient loading
regulations and climate change. Some recent models of this
system provided a useful foundation for understanding pro-
duction and sinking of organic material that leads to hypoxia
(Breed et al., 2004; Green et al., 2006, 2008). These models do
not predict the temporal and spatial scale of hypoxia, however.
Other models explicitly included sediment processes (Bierman
et al., 1994; Rowe, 2001; Eldridge and Morse, 2008), but are
limited because they were either based on steady-state analyses
or designed to describe hypoxia development, not the spatial
scales of hypoxia. The mentioned models are already based on
complex frameworks, but none were designed to simulate both
the spatial and the temporal scales of hypoxia. To address the
challenges of hypoxia mitigation in the northern GOM, models
of greater complexity may be needed. In other words, these
models may be on the too simple side of Ockham’s razor.
In the subsequent sections, we present the development of
the model described in Eldridge and Roelke (2009), hereafter
referred to as the ER model, the most recent of the northern
GOM hypoxia models. Aspects of the model’s framework as
well as attributes of the surface mixed layer, plankton commu-
nity, vertical flux of organic matter, dynamics of dissolved
organic matter, geochemical processes, gas exchanges, and phy-
sical circulation are discussed.
The ER model was developed, in part, from previous publica-
tions that described plankton community interactions (Roelke
et al., 1999; Roelke, 2000) and biogeochemical processes (Morse
and Eldridge, 2007; Eldridge and Morse, 2008). Development of
this model followed a reductionist approach to reformulating
these models. In other words, the minimum mathematics
needed to describe the interactions among inorganic nutrients,
organic matter, and horizontal and vertical fluxes were
employed. Even so, the combined mixed layer, bottom water,
and sediment models produced a complex model. The most
relevant formulations from the ER model are presented below,
as well as some alternative modeling approaches.
9.11.7.1 A Modeling Framework
Models designed for predictive purposes have a framework
representative of the target system. The ER model was devel-
oped for the purposes of exploring the effect of river discharge
and nutrient loading on the spatiotemporal scale of hypoxia in
the northern GOM. The ER model simulated four regions that
were west of the point of discharge for the Mississippi River
into the northern GOM (Figure 5). Each of these model regions
had a surface mixed layer, bottom water layers, and a sediment
layer (Figure 6). A westward water flow from the Mississippi
River through the regions and out of the model domain was
simulated (Breed et al., 2004). Following this approach, the
volume of each modeled segment was fixed. Consequently, the
hydraulic residence time of each model segment varied as a
function of the river discharge and the water exchange with
ocean waters from the GOM. Thus, the horizontal material
fluxes varied as a function of the river discharge and ocean
water exchange, and the concentrations of materials in the
upstream model segment and the ocean waters from the
GOM. This simplified approach to the physical circulation
employed by the ER model enabled a more detailed simulation
of the system’s biology (discussed below).
External inputs to the mixed layer component of the ER
model included inorganic nutrients, sediments, and exchange
of oxygen and carbon dioxide with the atmosphere. All of the
materials imported to the mixed layer were either transformed
through primary production, grazing or recycling processes to
diffuse through the pycnocline, flow into the next region or
eventually sink. The bottom-water component of the model
was composed of four layers through which sinking phyto-
plankton, fecal pellet, and other organic material passed.
Diagenetic processes acted on sinking organic particles as they
passed through each successive layer. Organic particles that
survived the passage to the bottom were deposited in the sedi-
ment layer and acted on by sediment diagenetic processes.
Recycled inorganic nutrients were released from each of the
bottom water layers and the sediment where a portion of
these nutrients diffused back to the mixed layer.
9.11.7.2 The Surface Mixed Layer
There are many abiotic and biotic processes that influence
phytoplankton production, succession, and biomass accumu-
lation (Sommer et al., 1986; Odum et al., 1995; Roelke et al.,
1999; Roelke, 2000), all of which influence hypoxia formation.
Models that explain taxonomic or functional group dynamics
and extreme events, such as algal blooms, require simulation of
physiological characteristics and predator–prey interactions
that are specific to the varied taxonomic or functional groups
(see Sommer, 1989; Roelke and Buyukates, 2001). In the ER
model, the detailed food web simulated in Roelke (2000) was
simplified. Multiple phytoplankton groups competing for
nitrogen and phosphorus resources, and a crustacean grazer,
were simulated. The microbial food web and biological
dependences involving silica, however, were omitted. This sim-
plification of the plankton community enabled a more detailed
depiction of biogeochemical aspects, which included simulat-
ing equilibrium of dissolved CO
2
, carbonic acid and
bicarbonate (Whitfield and Turner, 1986), atmospheric CO
2
(Eldridge and Cifuentes, 2000), and O
2
exchange (Justić et al.,
1996). These chemicals were needed for the biogeochemical
modeling.
Shading and inorganic nutrient effects were also considered
in the mixed layer of the ER model. Shading affected the
irradiance extinction coefficient, where the total extinction
was a function of absorption by water, chlorophyll, river-
derived suspended particulate matter (SPM), and chromopho-
ric dissolved organic matter (CDOM). SPM and CDOM
originated from the river and progressively decreased in each
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Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches 205
N 030N 3028
N  027
Louisiana
20 m
1
2
3
4
60 m
100 m
300 m 500 m
Gulf of Mexico
0 20 40 80 120 160
km
9130 W 900 W30 W 88
Figure 5 The ER model employed a simplified physical circulation framework. Four regions that were west of the point of discharge for the Mississippi
River into the northern Gulf of Mexico were depicted, where a westward water flow from the Mississippi River through the regions and out of the model
domain was simulated (Breed et al., 2004). The volume of each modeled segment was fixed, so the hydraulic residence time of each segment varied as a
function of the river discharge and the water exchange with ocean waters from the Gulf of Mexico. This simplified physical circulation framework enabled a
more detailed simulation of the system’s biology (see Figure 6). Reproduced from Eldridge, P.M., Roelke, D.L., 2009. Origins and scales of hypoxia on the
Louisiana shelf: importance of seasonal plankton dynamics and river nutrients and discharge. Ecological Modelling. doi:10.1016/j.ecolmodel.2009.04.054.
of the four model segments as a function of sinking and
dilution.
9.11.7.3 The Plankton Community
Autotrophic productivity is a major source of organic matter
that fuels hypoxia development. In coastal systems, this pro-
ductivity is primarily through growth of phytoplankton. In the
ER model, the term of the phytoplankton population differen-
tial equation (see below, eqn [10]) that describes reproductive
growth of phytoplankton (Growth
−
, cells m
3
d
−1
) was deter-
mined by the specific rate of growth and the population
density. It was expressed as
Growth ¼ μ ½2
with μ
−1
 being the specific growth rate (d ) and  the cell
density (cells m
−3
).
While  was a state variable whose differential equation was
solved numerically (eqn [10], see below), μ was a variable that
was determined instantaneously. That is, the value of μ at a
given time step was a function of conditions at that time step.
In the ER model, μ was approximated as a function of
available nutrients and irradiance, as it was for many other
models (Somlyody and Koncsos, 1991; Montealegre et al.,
1995; Legovic and Cruzado, 1997; Roelke, 2000). The quantity
μ can be further influenced by other environmental condi-
tions, such as temperature and salinity (see Baker et al., 2007,
2009; Grover et al., 2009), but those were not accounted for the
ER model.
With regard to nutrient availability, there are different
approaches to estimate the specific growth rate. An approach
not employed in the ER model, but worthy of note here due to
its simplicity, is a formulation relating specific growth rate to
ambient nutrient concentration (sensu Monod, 1950), as
follows:
S
μ ¼ μ;max ½3

S þ KS
where μ; max is the maximum specific growth rate (d
−1
), S is
an inorganic nutrient concentration (mmol m
−3
), and K
S
is
the half-saturation coefficient for nutrient-limited growth
(mmol m
−3
). The Monod relationship is used frequently in
ecological models, and offers numerical stability and straightfor-
ward parametrization (Fasham et al., 1990; Aksnes et al., 1995).
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Light
Atmosphere–water interface O2 and CO2 exchange
Zoop
N and P
All
SPM P1 P2 P3 P4 P5 P6
O2DIC N P
Pyncnocline
Organic matter
mineralization
O2DIC N P
Sediment
206 Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches
Figure 6 In the ER model, each of the four hydrographic regions (see Figure 5) had a surface mixed layer, bottom water layers, and a sediment layer. The
plankton was depicted using six phytoplankton functional groups spanning a gradient of fast-growing, edible forms to slower-growing, less edible forms,
and a crustacean grazer. Chemicals used in the model included dissolved oxygen, dissolved inorganic carbon, nitrogen, and phosphorus. Organic matter
was pooled into refractory and labile components, and a full diagenetic model was employed in the sediments. Reproduced from Eldridge, P.M.,
Roelke, D.L., 2009. Origins and scales of hypoxia on the Louisiana shelf: importance of seasonal plankton dynamics and river nutrients and discharge.
Ecological Modelling. doi:10.1016/j.ecolmodel.2009.04.054.
Furthermore, incorporating the Monod relationship in models
where multiple nutrients can become limiting to phytoplankton
growth is straightforward, where Liebig’s law of the minimum
can be applied (see DeBaar, 1994):
μ ¼ MIN
μ−S1 ;μ−S2 ;…;μ−Sn ½4
where μ−S1, μ−S2 through μ−Sn are the specific growth rates
under conditions where S1, S2 through Sn (the potentially
limiting inorganic nutrients) are predictors of growth rate.
Specific growth rate of phytoplankton correlates better to
intracellular nutrient pools (or cell quota), however, than it
does to ambient nutrient concentrations (Droop, 1973, 1983).
In addition, models incorporating the cell quota concept
performed more accurately than models based on Monod
growth kinetics in dynamic settings (Grover, 1991; Sommer,
1991a, 1991b). The ER model simulated phytoplankton speci-
fic growth rate following the cell-quota concept. To achieve
this, equations describing intracellular nutrient pools and
nutrient uptake were used. The rate of phytoplankton specific
growth was
Q
μ ¼ �μ;max 1 − min ½5
Q 
with �μ;max being the maximum specific growth rate (d
−1
),
Q
min
the minimum intracellular nutrient content required for
survival (mmol cell
−1
), and Q the cell quota (mmol cell
−1
).
Values from the literature for �
μ;max are higher than reported
values for μ;max of Monod-based models because μ�
;max is a
theoretical value that can only be reached at infinite cell quota
(Sommer, 1989). The ER model employed Liebig’s law of the
minimum (eqn [4]) to determine which of the multiple nutri-
ents was limiting specific growth rate for each time step of the
simulation.
Regarding nutrient uptake rate, the ER model employed a
relationship with ambient nutrient concentration that followed
Michaelis–Menten kinetics (Dugdale, 1967):
S
ρ ¼ ρ½6
max ðS þ kSÞ
with ρ being the nutrient uptake rate (mmol cell
−1
d
−1
), ρmax
the maximum nutrient uptake rate (mmol cell
−1
d
−1
), and k
S
the half-saturation constant for nutrient uptake (mmol m
−3
).
Incorporating this nutrient uptake rate equation into multi-
nutrient models requires modification of eqn [6] to account for
nutrient uptake when some other resource is limiting growth.
Otherwise, the cell quota of nonlimiting nutrients would
increase to unrealistically high levels. In the ER model, where
two nutrients (nitrogen and phosphorus) potentially limited
growth, uptake of the nonlimiting nutrient was expressed using
S1 S2
ρS1 ¼ ρmax − S1 ½7
ðS1 þ kS1 Þ S2 þ aS2 kS2
with ρS1 being the uptake rate of the nonlimiting nutrient,
ρmax − S1 the maximum uptake rate of this nutrient, S
1
and S
2
the concentrations of the nonlimiting and limiting nutrients,
respectively, kS1 and kS2 the half saturation constants for uptake
of the nonlimiting and limiting nutrients, respectively, and aS2
was a scaling factor (see Zonneveld, 1996; Roelke et al., 1999).
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
Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches 207
In a multinutrient model, the nutrient that limits growth
can change over the course of the simulation. Thus, the equa-
tion used to simulate uptake rate of a particular nutrient can
also change (between eqns [6] and [7]). Therefore, it is neces-
sary to determine the limiting nutrient at each time step of the
model. In the ER model, this was achieved by comparing the
ratio of the available nutrients (e.g., S1:S2) to the ratio between
minimum cell quotas (e.g., Q
minS
1
:Q
minS
2
)(Rhee and Gotham,
1980; Elrifi and Turpin, 1985; Roelke et al., 1999).
Irradiance can also limit autotrophic production. In the ER
model, specific growth rate of phytoplankton as a function of
irradiance (d
−1
) was estimated using
− A ÞV ¼ V;max 1− e½8
with V being the light-dependent specific growth rate (d
−1
),
V;max the light-dependent maximum specific growth rate
(d
−1
), and A a scalar factor (Platt et al., 1984) defined as
αI
A ¼ ½9
V; max
with α being the slope of the photosynthesis-irradiance curve
(cm
2
s quanta
−1
d
−1
) for phytoplankton and I the irradiance
(quanta cm
−2
s
−1
), and other symbols are the same as pre-
viously defined. In the ER model, limitation of autotrophic
productivity due to light was considered along with the affects
of nutrient availabilities using eqn [4,] Liebig’s law of the
minimum (DeBaar, 1994; Legovic and Cruzado, 1997).
The Roelke et al. (1999) and Roelke (2000) models were
specifically formulated to evaluate the role of inorganic nutri-
ent loading magnitude, mode, and ratio on planktonic food-
web dynamics. As these were the same loading factors being
evaluated by the management community to control the size
and frequency of hypoxia in the northern GOM (Dodd, 2006;
Rabalais et al., 2007), they were used as the framework for the
simulated plankton community in the ER model.
Briefly, the plankton food-web component of the ER model
incorporated multiple phytoplankton groups, multiple limit-
ing resources, and a crustacean zooplankter (Figure 6). There
were six phytoplankton groups that covered a range of physio-
logical parameters consistent with nutrient preferences and
growth dynamics of coastal phytoplankton. Population
changes were influenced by the factors that affected specific
growth rate, as described above, and also respiration and mor-
tality losses, grazing losses, advection, and eddy diffusion. The
time-dependent differential equation describing population
changes for each phytoplankton group followed the form
d γG
¼ μ − rμ − m −  advection
dt QfixV; 
 eddy diffusion ½10
with r being a scalar factor describing the proportion of
growth lost to respiration, m a specific mortality rate (d
−1
),
γ the copepod grazing rate in terms of volume of prey (µm
3
individual
−1
d
−1
), G was the concentration of copepods
(individuals m
−3
), QfixV; was the fixed cellular volume of
the phytoplankton group (µm
3
cell
−1
), and all other
parameters were the same as previously defined.
To provide physiological parameters that bound the
expected physiologies of Louisiana shelf phytoplankton,
the ER model utilized physiological parameters for one of the
dominant shelf species, that is, the diatom Skeletonema costatum
(DeMarche et al., 1979; Dortch, 1982; Rabalais et al., 1996).
A range of physiological parameters for the six phytoplankton
groups was created based on these parameters. A parallel set of
edibility parameters such that fast growing r-selected groups
were more edible and slow growing K-selected groups were less
edible (Sommer et al., 1986) was also created in the ER model.
A vector of edibility and growth parameters for the six phyto-
plankton groups was calculated as an equally spaced gradient
bounded by upper (Up = 1.0) and lower (Dn = 0.05)
coefficients.
Up − Dn
Vector ¼ Up −    ni ;n
5 i ¼ 0; 1; 2; …; 5 ½11
Following this procedure, the ER model simulated phytoplank-
ton represents functional groups of varying growth potential
and edibility, not individual species.
In the ER model, lability of phytoplankton was related to
nitrogen content such that increasing the critical nitrogen cell
quota (Q
minN
) provided a relative index of the expected reac-
tivity of sinking phytoplankton. While evidence that nitrogen
content and reactivity are related in phytoplankton is lacking,
there is evidence that this relationship occurs in submerged
aquatic plants (Benner et al., 1991). Similar to other metabolic
processes, the ER model defined the relationship as hyperbolic:
− ðQn=Qmin =krÞ
ω ¼ 1 − e½12
with ω being the labile fraction of the phytoplankton cell and
kr an adjustable parameter.
Copepods represented zooplankton in the ER model
because of their abundance in coastal systems (Dagg et al.,
1991; Buskey, 1993) and their ability to effectively crop pri-
mary production. Growth of zooplankton was determined by
applying Liebig’s law of the minimum to the total N and P
ingested from phytoplankton relative to the fixed intracellular
N and P composition of the zooplankton. The zooplankton
prey choices were the six groups of phytoplankton. Total N and
P ingestion for copepods was a function of the copepod grazing
rate and a sloppy feeding correction, where the grazing rate was
based on a prey-saturation curve that asymptotically
approached the maximum grazing rate (see Roelke, 2000).
A dynamic cell quota of N and P was consumed with
each phytoplankton prey. The zooplankton were assumed to
have a fixed stoichiometry for N and P, thus N or P in excess of
this stoichiometry was excreted. Because the ER model did not
include a detailed bacterial component, losses to sloppy
feeding were converted directly into dissolved inorganic N
and P. Respiration and death were biomass-dependent func-
tions (Roelke, 2000).
9.11.7.4 Vertical Flux of Organic Matter
Remineralization of organic matter in bottom waters and
sediments is a function, in part, of the organic matter flux, as
discussed previously. Consequently, the process which contri-
butes to sinking is of importance and should be included in a
model. The mixed-layer biophysical formulations of the ER
model incorporated phytoplankton populations, zooplankton,
and transport processes whose omissions were thought to be
responsible for the poor correlation between primary
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4x 3y
ðCH2OÞx ðNH3 Þy ðH3PO −
4 z þ
Þ þ NO
5 3
R2=x
2x þ 4yx −3y 10z
! N
52 þ
þ CO
52
4x þ 3y −10z
þ
5 HCO−
3þ z HPO2−
4
3x þ 6y þ 10z
þ H O
½14
52
with x, y, and z being the components of oxidation contributed
by CH
2
O, NH
3
, and H
3
PO
4
(revised from Van Cappellen and
Wang, 1995).
Reactivities of organic matter broadly range from 2 to –5
(log k (yr
−1
)) depending on the age of the organic matter
(Burdige, 2006). Burdige (1991), however, was able to relate
reactivities of 8 and 1 yr
−1
to sediment organic matter with C:N
ratios of ~6 and ~35, respectively. Soetart et al. (1996) used a
broader range of end member reactivities (26 and 0.26 yr
−1
). In
the ER model, the refractory end member value from Burdige
(1991) and a doubling of the labile end member value from
208 Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches
production and flux rates in previous studies (see Redalje et al.,
1994). There were three categories of organic matter considered
in the ER model, which were phytoplankton, copepod fecal
pellets, and riverine allochthonous material.
Sinking rates for phytoplankton can vary considerably
based on vertical diffusivity (Huisman and Sommeijer, 2002),
and phytoplankton size and shape (Bienfang, 1980). Marine
snow formation further complicates sinking rate (Jackson,
1990, 2001; Hill, 1998; Hill et al., 2000). For depths of 24
and 40 m and phytoplankton ranging from 3 to 20 μm max-
imum linear dimension, Bienfang (1980) measured sinking
rates of 0.72  0.05 and 0.83  0.05 m d
−1
, so these sinking
rates were used in the ER model. The high sinking rate of
fecal pellets and the relatively shallow depth of the Louisiana
shelf made the ER model insensitive to the rate of sinking for
fecal pellets. The sinking rate used for allochthonous material
in the ER model was the same as used by other investigators
working in the northern GOM (e.g., Green et al., 2008). Owing
to high sinking rates used in the ER model, as much as 90% of
detrital sediment from the river sank from the mixed layer
within 5 km of the discharge (see Dagg and Breed, 2003).
9.11.7.5 Dissolved Organic Matter
Terrestrially derived CDOM may adsorb light within the
Mississippi River plume well into the mid salinity zone of the
ER model’sdomain(Figure 5). Although there are no good
estimates of CDOM export from the river, it is known that export
of dissolved organic matter (DOC) is ~4 times greater than
export of POC, and that half of this DOC is still present in the
mixed layer at a salinity of 20 (Dagg et al., 2004). In addition, it
was shown that most of the river-derived DOC was relatively
unreactive (Dagg et al., 2004; Del Castillo, 2005)except during
brief periods of low particle density when photo-oxidation
became important. In the ER model, the influence of CDOM
on light attenuation was estimated assuming that the DOC was
unreactive on the residence timescales of shelf waters and that
there was a strong relationship between CDOM adsorption and
DOC concentration (Del Castillo, 2005).
9.11.7.6 Geochemical Processes
Remineralization of organic material and consumption of
oxygen occur throughout the water column and in the sedi-
ments (Eldridge and Morse, 2008). The framework of the ER
model allowed diagenetic processes to act on sinking organic
particles as they passed through each successive layer to the
sediments where they resided until they were mineralized
(Figure 6). The diagenetic formulations of the ER model
were simplified from Morse and Eldridge (2007) so that
only carbon (in the forms of CH
2
O, HCO
3
−
,and CO
2
),
nitrogen (NH
3
,NO
3
−
,and N
2
), and phosphate (H
3
PO
4
and
HPO
42−
) cycles were considered for the diagenesis of labile
and refractory organic matter. Equations describing the
organic matter oxidations were
ðCH2OÞx ðNH3 Þy ðH2PO4 Þz þðx þ 2yÞO2 þðy þ 2zÞHCO−
3
R1=x
! ðx þ y þ 2zÞCO2 þ yNO−
3 þ zHPO2−
4
þðx þ 2y þ 2zÞH2O ½13
(Soetart et al., 1996) were used. The labile end member was
doubled in the ER model in order to generalize the diagenetic
equations for bottom water where recently deposited phyto-
plankton were rapidly metabolized and for sediments where
less reactive detritus entered the sediment water interface.
Because of the initial differences in the stoichiometry of the
phytoplankton groups, the fecal pellets and the riverine SPM,
and their differing sinking rates, each of these components were
treated separately in the ER model. Because nitrate serves as an
electron donor under anoxic conditions, ammonium and
nitrate were treated separately in the ER model, except when
entering the surface mixed layer where they were combined to a
single DIN pool. The kinetic rates for OM mineralization were
temperature sensitive assuming a Q
10
factor of 2.
9.11.7.7 Gas Exchanges and Physical Circulation
As mentioned previously, the oxygen supply rate is just as impor-
tant as the organic matter flux when considering hypoxia. The ER
model’s governing equations for the vertical transport processes
were similar to those described in Justić et al. (1996),where
oxygen and ΣCO
2
transport in the vertical direction were driven
by diffusion gradients between the atmosphere and the surface
waters, and DO gradients in the surface and bottom water
(Figure 6). While the transport formulation for DO was the
same as described by Justić et al. (1996), Whitfield and Turner’s
(1986) semi-closed system calculations for exchange with the
atmosphere were used in the ER model, as reformulated by
Eldridge and Cifuentes (2000). The concentration of dissolved
inorganic carbon (DIC) at any point within the four regions of
the model was a function of transport, respiration and primary
production, and losses or gains from the atmosphere (F
CO
2
).
D ½pCO2 atK0ðt; sÞ 1000 − ½H2CO3
FCO2 ¼ ½15
z ðZs þ ZbÞ 100
with D/z being the combined diffusion through water and
thickness of atm–water layer (cm s
−1
), p
CO
2
the atmosphere
concentration (μatm), K
0
(t, s) a thermodynamic constant cal-
culated from temperature–salinity-dependent algorithms
(Whitfield and Turner, 1986), and Z
s
and Z
b
the depths of the
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 
Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches 209
surface and bottom layers (m). Multiplication by 1000 and
division by 100 provides units of mmol-C m
−2
s
−1
. To deter-
mine the distribution of DIC species (H
2
CO
3
*, HCO
3
−
, and
CO
3
−2
) in surface waters, bottom waters, and the sediments
within each of the four regions, the ER model assumed that
alkalinity was a conservative property. Hence, there was a lim-
ited exchange of pCO
2
from the atmosphere allowing
calculation of alkalinity from pH and [DIC] using the closed
system equilibrium model of Stumm and Morgan (1981).
Similar to oxygen and ΣCO
2
, in the ER model, the nutrients
(phosphate, nitrate, and ammonium) were transported
through concentration gradients between the surface waters,
bottom water, and sediments based on Fick’s law.
Horizontal transport in the ER model was calculated as the
proportion (p) of water in region k + 1 derived from region k
(see Breed et al., 2004) as follows:
S35 − Smk þ1
Pk þ1 ¼ for regions k ¼1; …; 4 ½16
ðS35 − Smk Þ
with S
35
being standard seawater salinity and S
m
the middle
salinity in a region (Breed et al., 2004). The outputs from
models of each region simulation were used as inputs to the
next region after being adjusted for dilution. For cases in which
relative increases or decreases in Mississippi River flow (Q
m
)
were simulated, p
k+1
was simply multiplied by the factor (Q
case
)
to get a new p
k+1
. Following this approach, waters from the first
model segment were diluted with river water and blue ocean
water entering the region (B
flux
). Waters for each of the remain-
ing model segments were diluted with waters entering the
region from the upstream model segment and blue ocean
water, where the increasing salinity gradient from east to west
was used to determine the amount of blue ocean water entering
a region (B
mix
):
Bflux ¼Bc Bmix ð1 − pk þ1Þ for regions k ¼1; …; 4 ½17
with Bc the concentration of a blue water component (DIN,
PO
4
, etc.). Although eqn [16] could be used to calculate other
properties of surface water in each region, the ER model uti-
lized additional time series of salinity data (S
C6
) from Buoy C6
available for a point in region 3 (Justić et al., 1996). Data were
used to adjust the salinity in each region for seasonal variations
not considered in the vector of annually averaged Sm used in
eqn [16]:
Smk
Si ¼SC6 for regions k ¼1; …; 4 ½18
Sm3 Qcase
9.11.8 Model Validation and Simulation Analysis
Model validation involves comparing simulation results with
empirical evidence. The framework of the model and available
data influences the approach to validation. For example, the
target system modeled in Shen et al. (2008) was a well-mixed
tidal creek that was depicted with a box model. The biotic
components of the model were kept simple, phytoplankton
and macroalgae, and oxygen was the primary element modeled
(Table 1). In this case, the validation approach involved com-
parison of the model’s predicted fluctuations in DO with easily
obtained high-frequency measurements of DO in this system
over a 30-day period. The strong match between simulation
results and empirical evidence inspires confidence in the model
when system conditions are similar to the model’s framework
and assumptions. Using their validated model, the authors
went on to test the possible effects of varied rates of re-aeration,
sediment oxygen demand, carbon and oxygen loading, etc.
In more complex models, however, mismatches between
model capabilities and supporting data often exist. For exam-
ple, in Lopes et al. (2008), simulation of the Ria de Aveiro
Lagoon, Portugal, an elongated, shallow and vertically well-
mixed system, the model’s performance was evaluated over
timescales of hours for a period of 30 days. Diurnal dynamics
were pronounced in this simulation. However, supporting data
used for model validation (DO, chlorophyll, NH
4
, and NO
3
)
were collected at ~5-day intervals over a period of 30 days.
Similarly, Sohma et al. (2008) simulation of Tokyo Bay pro-
duced system-wide results over hourly time steps that involved
three-dimensional hydrodynamics coupled to sediment pro-
cesses. Times series data from the system (phytoplankton,
total organic matter, dissolved organic matter, NO
3
,NH
4
,
DON PO
4
, suspension and deposit feeders, and DO), however,
was from a few monitoring stations sampled at weekly to
monthly intervals. In this case, subsets of the model output
matching the locations of monitoring stations were used in the
validation. In the case of the ER model, where a complex
plankton community and biogeochemical processes were
simulated in a simplified physical circulation framework,
times series data in the spatial domain of the model did not
exist. Instead, empirical data were compiled from many inde-
pendent research efforts in the target system. From these data,
ranges in values of various parameters were determined for the
four subregions of the model, which were then compared to
the simulated ranges. These examples illustrate that for more
complex models there is usually greater uncertainty during
model validation. Consequently, best use of these models
may be to study relationships between forcing factors and
ecosystem properties, such as general trends linking river dis-
charge and nutrient loading to the scale of hypoxia, as
discussed below (see also final section 9.11.9 article).
A common use of hypoxia models is to investigate the
affects of nutrient loading and river discharge, which was the
case for the ER model. In this model, daily variations in nutri-
ent loading were determined based on monthly averages of
nutrients and water flow measured over a 7-year period for
the Mississippi River (Bratkovich et al., 1994; Justić et al.,
1996). This averaged condition of river flow and nutrient con-
centration was considered the base case. It was assumed that
years with increased or decreased flows and nutrients could be
simulated as multiples of the base case. The ER model was then
run repeatedly where with each simulation the river flow and
nutrient concentrations were varied. The range over which
these conditions varied spanned 50% of the base case. This
range was selected because nutrient loading reductions by as
much as 40% are being considered for the Mississippi River
watershed (Scavia et al., 2003; Rabalais et al., 2007) and pre-
dicted changes to river discharge due to climate change range
from 43% decreases to 96% increases (Miller and Russell,
1992).
The multiple phytoplankton functional groups simulated in
the ER model show varied spatiotemporal dynamics
(Figure 7). A dominance of edible phytoplankton near the
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210 Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches
Chlorophyll-a
20
)
–1
l
15
g µ(
10
5
)
0
–1
Carbon flux
0
d
2−
m-C (mmol
−50
Oxygen concentration
)
3−
m
2
-O(mmol
200
100
0
Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov Jan Mar May Jul Sep Nov
West East
Region 4 Region 3 Region 2 Region 1
−100
300
Figure 7 Annual dynamics of phytoplankton, carbon flux, and bottom water DO for regions 1 through 4 of the ER model. Phytoplankton are in the order
of black (most edible), blue, red, magenta, green, and cyan lines (least edible). Sinking fluxes of organic matter are color-coded blue for algae, green for
fecal material, and red for SPM. The chlorophyll a concentration is comprised mostly of fast-growing edible phytoplankton earlier in the year, which are
then replaced with slow-growing inedible forms. The black dashed line is the total chlorophyll a. Simulations are oriented from the most easterly
simulation (region 1, right side, where edible groups dominated most of the year) to the most westerly simulation (region 4, left side, where inedible
groups dominated most of the year). Model simulations of low salinity regions (1 and 2) have reductions of DO that result in hypoxia, whereas at the higher
salinity regions (3 and 4) DO drawdown is not sufficient to cause hypoxia. Reproduced from Eldridge, P.M., Roelke, D.L., 2009. Origins and scales of
hypoxia on the Louisiana shelf: importance of seasonal plankton dynamics and river nutrients and discharge. Ecological Modelling. doi:10.1016/j.
ecolmodel.2009.04.054.
river (region 1, see Figure 5), a gradual shift to a dominance
of less edible forms in the mid-salinity regions (regions
2 and 3), to a strong dominance of the less edible forms in
the high salinity zone (region 4) was predicted in the base
case simulation. The westward decrease in edible phyto-
plankton and the accompanying changes in grazing
produced a temporal and spatial dynamic that featured a
single annual bloom of edible phytoplankton near the
river, a bloom of edible phytoplankton early in the year
followed by a second bloom of less edible phytoplankton
later in the year in the mid-salinity regions, and finally a
single continuous bloom of less edible phytoplankton in the
higher-salinity regions. This pattern is similar to what has
been observed extensively in freshwater systems where edible
forms of phytoplankton are more prevalent early in the year,
but are eventually grazed down and replaced by less-edible
phytoplankton forms (e.g., Sommer et al., 1986; Roelke
et al., 2004, 2007). In the ER model, r-selected phytoplank-
ton groups persisted in areas of low salinity because of the
high hydraulic flushing from the river, while in high-salinity
areas hydraulic flushing from the river inflow was low and
K-selected phytoplankton groups persisted.
While similar succession patterns are observed in some
marine systems (Roelke et al., 1997; Schapira et al., 2008;
Silva et al., 2008; Morais et al., 2009), there are technological
limitations of detailed spatiotemporal sampling in large coastal
ocean environments that prevent observation of succession of
phytoplankton groups at this level. It is possible, however, to
evaluate the spatial distribution of phytoplankton groups. For
example, in the Mississippi River plume less edible species such
as large and toxic Pseudonitzschia spp. are more common in
regions of higher salinity (Thessen et al., 2005), as are smaller
cell-sized phytoplankton (Wawrik et al., 2004) that are less
edible due to their size relative to mesozooplankton (Hansen
et al., 1994).
The ER model predicted that the organic matter flux to
deeper waters and sediments mirrored chlorophyll-a concen-
tration and grazing activity in the surface layer (Figure 7). In
the base case of the simulation analysis, the resulting oxygen
consumption led to hypoxia in regions 1 through 3 with
hypoxic conditions being the longest near the river mouth
where salinity difference between surface and bottom waters
was greatest and phytoplankton sedimentation was augmented
with an equal amount of river-derived allochthonous detritus.
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West East
Region 4 Region 3 Region 2 Region 1
Nutrient effects River flow effects
300
250
200
150
100
50
0
1.5 1.5 1.5 1.5 1.5
1 1
Flushing
Nutrients
1 1
1 1 1 1
0.5 0.5 0.5 0.5
Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches 211
Figure 8 Results from the simulation analysis showing the predicted number of days per year of bottom water hypoxia under different conditions of
Mississippi River discharge and inorganic nutrient concentrations. The base-case river discharge and nutrient concentration simulation are represented
were the values are equal to 1. Values of 0.5 represent the simulation where the base-case was reduced by 50%, and values of 1.5 represent the simulation
where the base-case was increased by 50%. Simulations are oriented from the most easterly simulation (region 1, right side) to the most westerly
simulation (region 4, left side). The arrows indicate the continuum of river flow or nutrient concentrations tested in the simulations where hypoxia was
initiated (red), where the hypoxia increase is maximum (green), and where hypoxia increase asymptotically approached a constant value (blue).
Reproduced from Eldridge, P.M., Roelke, D.L., 2009. Origins and scales of hypoxia on the Louisiana shelf: importance of seasonal plankton dynamics and
river nutrients and discharge. Ecological Modelling. doi:10.1016/j.ecolmodel.2009.04.054.
The simulation analysis of the ER model involving varied
river discharge and nutrient concentrations revealed different
system responses that were dependent on proximity to the
point of river discharge (Figure 8). The model predicted that
hypoxia duration in the low-salinity area of the northern GOM
(region 1) is nearly insensitive over the range of river flows and
nutrient concentrations tested. In the model, this was due to
light limitation of primary production in this area. Further
away from the point of river discharge (region 2), the model
predicted hypoxia duration to be sensitive to changes in
river flow, where decreased river flow resulted in weakened
stratification allowing greater supply of O
2
to deeper waters
through wind mixing. Even further from the point of river
discharge (regions 3 and 4), hypoxia duration should be sensi-
tive to both river flows and nutrient concentrations, as
predicted by the ER model.
The hyperbolic relationship between nutrients and the
duration of hypoxia observed in the ER model suggests that
areas further from the point of river discharge (region 3 and to a
lesser degree region 4) are nearly saturated relative to nutrients,
and that trends in hypoxia there would be determined predo-
minately by changes in river flow. In other words, in these
regions the salinity difference between surface and bottom
waters and the resulting vertical mixing is more influential
than nutrients regarding the duration of hypoxia. Findings
from the ER model support the notion that a 40% decrease in
nutrient loading would substantially reduce the duration and
aerial extent of GOM hypoxia under present-day inflows
(Rabalais et al., 2007; Scavia et al., 2003). However, the simu-
lations also show that river discharge is a stronger factor
influencing hypoxia than nutrients and that a relatively small
increase in river discharge would offset a large reduction in river
nutrient concentration. Global climate change models predict
increasing precipitation for the mid-west region of the conti-
nental USA (Miller and Russell, 1992) so that increased river
discharge is a real possibility unless offset by irrigation and
municipal water projects.
9.11.9 Future Hypoxia Models
As mentioned earlier, complex hypoxia models are challenging
to validate, and this directly influences the confidence in simu-
lation results. A method of increasing confidence in complex
models involves the use of multiple, independent models. All
ecosystem models are simplifications of the natural environ-
ment, and they are constrained by tradeoffs between realism,
precision, and generality (Levins, 1966). Because no single
model can maximize all three, we can learn more from multi-
ple models by identifying similar qualitative behaviors
between them, despite differences in the model frameworks.
These qualitative similarities are likely more robust than find-
ings from any single model. In other words, the truth may best
be found at the intersection of independent lies.
There are many hypoxia models with a high degree of
variance in their framework complexity. The models listed in
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212 Hypoxia in Waters of the Coastal Zone: Causes, Effects, and Modeling Approaches
Table 1 are only more recent publications, and the list is by no
means exhaustive. There is a clear need for a meta-analysis of
simulations produced by these models in search of qualitative
similarities. For example, the ER model suggests that river dis-
charge is the dominant factor in stimulating hypoxia, a notion
supported by many other modeling studies. Qualitatively, it is
very likely that this notion is true. On the other hand, the ER
model also predicts that there is a hyperbolic hypoxic response
to river nutrients that can be mapped across the Mississippi
River plume salinity continuum that is affected by river dis-
charge, nutrient loading, phytoplankton succession, and lower
food-web dynamics. The ER model also suggests that slight
increases in river inflow would offset large decreases in nutrient
loading, a finding paramount to policy decisions regarding
watershed practices in parts of North America. Unfortunately,
there are few models of this complexity level to include in a
meta-analysis. In other words, there are not enough indepen-
dent lies from which to look for intersections. Similarly, there
are few models that capture the three-dimensional circulation
of systems impacted by hypoxia. Again, it is difficult to search
for common qualitative behavior regarding the roles of peri-
odic upwelling, eddy entrainment, and other physical factors
that influence hypoxia. Therefore, while there is a clear need for
meta-analyses of model behaviors, there is also a need for the
development of more complex models, that is, those that
employ detailed biota and three-dimensional hydrology.
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