JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 117, C08033, doi:10.1029/2012JC007902, 2012
Relative importance of pelagic and sediment respiration in causing
hypoxia in a deep estuary
D. Bourgault,1 F. Cyr,1 P. S. Galbraith,2 and E. Pelletier1
Received 18 January 2012; revised 15 June 2012; accepted 28 June 2012; published 25 August 2012.
[1] Oxygen depletion in the 100-m thick bottom layer of the deep Lower St. Lawrence
Estuary is currently thought to be principally caused by benthic oxygen demand
overcoming turbulent oxygenation from overlying layers, with pelagic respiration playing
a secondary role. This conception is revisited with idealized numerical simulations,
historical oxygen observations and new turbulence measurements. Results indicate that a
dominant sediment oxygen demand, over pelagic, is incompatible with the shape of
observed oxygen profiles. It is further argued that to sustain oxygen depletion, the turbulent
diffusivity in the bottom waters should be ≪104 m2 s1, consistent with direct
measurements but contrary to previous model results. A new model that includes an
Arrhenius-type function for pelagic respiration and a parameterization for turbulence
diffusivity is developed. The model demonstrates the importance of the bottom boundary
layer in reproducing the shape of oxygen profiles and reproduces to within 14% the
observed change in oxygen concentration in the Lower St. Lawrence Estuary. The analysis
indicates that turbulent oxygenation represents about 8% of the sum of sediment and
pelagic oxygen demand, consistent with the low turbulent oxygenation required to
maintain oxygen depletion. However, contrary to previous hypotheses, it is concluded that
pelagic oxygen demand needs to be five time larger than sediment oxygen demand to
explain hypoxia in the 100-m thick bottom layer of the Lower St. Lawrence Estuary.
Citation: Bourgault, D., F. Cyr, P. S. Galbraith, and E. Pelletier (2012), Relative importance of pelagic and sediment respiration
in causing hypoxia in a deep estuary, J. Geophys. Res., 117, C08033, doi:10.1029/2012JC007902.
1. Introduction
[2] A general problem for understanding and modeling
hypoxia in marine systems is to determine the relative importance of benthic versus pelagic oxygen demand [Hetland and
DiMarco, 2008; Pena et al., 2010]. This determination has
important consequences in the choice of the model to adopt as
well as in the direction to concentrate research efforts. In
general, hypoxia in deep (≫100 m) marine systems is little
affected by sediment processes given the power-law decrease
with depth of particulate organic carbon fluxes [Buesseler
et al., 2007; Pena et al., 2010]. In shallow seas (<100 m),
sediment oxygen demand contributes more directly to hypoxia
[Pena et al., 2010; Rabalais et al., 2010] although Hopkinson
and Smith [2005] concluded that only 24% of total organic
inputs are respired by the benthos in shallow estuaries (10 m).
[3] Within this context we re-examine here the relative
importance of benthic and pelagic oxygen demand in
1
Institut des sciences de la mer de Rimouski, UQAR, Rimouski,
Québec, Canada.
2
Maurice-Lamontagne Institute, Fisheries and Oceans Canada, MontJoli, Québec, Canada.
Corresponding author: D. Bourgault, Institut des sciences de la mer de
Rimouski, UQAR, 310 allée des Ursulines, Rimouski, QC G5L 3A1,
Canada. ([email protected])
©2012. American Geophysical Union. All Rights Reserved.
0148-0227/12/2012JC007902
causing hypoxic conditions in the Lower St. Lawrence
Estuary (LSLE) (Figure 1). The case of the LSLE is particularly intriguing because it is a deep estuary (350 m) but,
contrary to general understanding, previous studies have
attributed a predominant sediment oxygen demand over
pelagic in contributing to hypoxia of its bottom waters.
[4] Oxygen concentration in the bottom one hundred
meters or so of the LSLE (Figure 1) has received considerable research attention since Gilbert et al. [2005] documented its spatial and temporal variability towards hypoxic
conditions [Benoit et al., 2006; Thibodeau et al., 2006;
Katsev et al., 2007; Gilbert et al., 2007, 2010; Lehmann et
al., 2009; Thibodeau et al., 2010a, 2010b; Genovesi et al.,
2011; Mucci et al., 2011]. The conceptual model of oxygen
depletion pictures an oxic deep (>200 m) water mass of
Atlantic origin pumped by an estuarine pressure gradient into
the Gulf of St. Lawrence through Cabot Strait and channeled
into the LSLE up to the Head of the Laurentian Channel
[Gilbert et al., 2005]. At an estimated pace of 1 cm s1
[Gilbert, 2004], this water mass spends about 2 years isolated
from the atmosphere in its journey from Cabot Strait to the
Head of the Laurentian Channel, a distance of approximately
750 km. During its course landward, oxygen is gradually
depleted due to benthic and pelagic respiration and organic
matter remineralization that overcomes turbulent oxygenation from oxygen-rich surface layers. Hypoxic conditions,
with oxygen concentration [O2] < 62.5 mmol L1, are
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Figure 1. Map of the Gulf of St. Lawrence and Lower St. Lawrence Estuary (LSLE). Each numbered square
box delimits regions within which oxygen data were extracted from the Ocean Data Management System
public database [Fisheries and Oceans Canada, 2011]. Each box is centered around stations 16–25 as defined
in Benoit et al. [2006] and Lehmann et al. [2009]. The Head of the Laurentian Channel is at station 25.
reached approximately off Baie-Comeau and further landward (Figures 1 and 2).
[5] Based on results from a transport and diagenetic
numerical model, Benoit et al. [2006] concluded that sediment
oxygen demand alone can generate hypoxic bottom waters
near the Head of the Laurentian Channel and hypothesized that
pelagic respiration has little influence on the oxygen budget.
This model-based conclusion was supported, although moderated, by Lehmann et al. [2009] who concluded, based on the
analysis of stable isotope ratios of dissolved oxygen, that about
two-thirds of oxygen depletion in the 100-m thick bottom
layer of the Laurentian Channel occurs from benthic bacterial
respiration with the remaining third attributed to the pelagos.
[6] To sum up, oxygen depletion in the 100-m thick bottom layer of the LSLE is thought to occur primarily because
turbulent oxygenation from overlying layers is small relative
to benthic oxygen demand. This poses a paradox. How can
the upper source of oxygen from vertical mixing be negligible while turbulent transmission throughout the 100-m
thick bottom layer from the benthos be important? Solving
this paradox is the main motivation of this paper.
[7] To help resolve the paradox it is informative to evaluate the level of turbulent diffusion required to prevent turbulent oxygenation of the 100-m thick bottom layer from
overlying layers. It could be argued that it should be such
that the diffusive time-scale t d be much greater than the
residence time t r of bottom waters. A scaling analysis of a
diffusive process leads to the following form for the diffusive time-scale
td ≡
Hb2
;
K
ð1Þ
where Hb is the thickness of the bottom layer subject to
oxygen depletion and K is the turbulent diffusivity of dissolved oxygen. The condition on turbulent diffusivity to
allow oxygen depletion (i.e. t d ≫ t r) then becomes
K≪
Hb2
:
tr
ð2Þ
[8] Taking Hb 102 m and t r = 2 years 108 s as representative of conditions prevailing in the bottom waters
of the LSLE gives K ≪ 104 m2 s1.
[9] However, this reasoning brings a contradiction with
the literature. In their modeling study, Benoit et al. [2006]
concluded, inversely, that diffusivity values <104 m2 s1
provided unrealistic results. This contradiction is in fact
another way to express the paradox mentioned above.
[10] To address this paradox, we carried out idealized
numerical simulations, examined historical oxygen profiles
and collected turbulence measurements in the Laurentian
Channel. The result of this analysis is a new conception
on the role of pelagic versus benthic respiration for
depleting oxygen and sustaining hypoxic conditions in the
deep LSLE.
2. Methods
2.1. Model
[11] We take a Lagrangian point of view where the temporal evolution of a water mass traveling from the Gulf and
into the LSLE is diagnosed. In this Lagrangian frame of
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Figure 2. Mean (2005–2011) dissolved oxygen concentration [O2] and temperature T fields along a transect extending from station 16 in the Gulf to station 25 at the Head of the Laurentian Channel (Figure 1).
These fields were interpolated from observations around stations 16 to 25, identified at the top of the figure. The color scale is saturated at 200 mmol L1 to visually highlight changes in bottom layers. For easier
intercomparison, model results presented below (Figures 3, 6, and 8) share the same color scale and aspect
ratio. The white horizontal line indicates the depth used in some of the model simulations (H = 325 m).
reference, the equation adopted here for dissolved oxygen
concentration [O2] is
∂½O2 ∂
∂½O2 ¼
K
R;
∂t
∂z
∂z
ð3Þ
where t is time, z is the vertical axis taken positive downward and R is an oxygen sink due to pelagic community
respiration, a term to be detailed later on as needed. For
dimensional consistencies the oxygen concentration in
equation (3) is expressed in mmol m3 although values in the
text and figures will be reported in mmol L1 for easier
comparison with the literature. With a change of variable
t = x/u, where x is the along-channel spatial coordinate and u
the water velocity, this time-dependant Lagrangian approach
is equivalent to the steady-state Eulerian approach adopted
by Benoit et al. [2006] since the time rate of change term
∂[O2]/∂t in equation 3 becomes an advective term u∂[O2]/∂x.
We neglect horizontal diffusion, a term kept in Benoit et al.
[2006] but shown to have little impact on their model
results compared to vertical diffusion. Vertical pumping from
the estuarine circulation is also neglected assuming that the
deep water (>200 m) is principally upwelled against the sill
at the Head of the Laurentian Channel [Koutitonsky and
Bugden, 1991]. Similar approaches were also used by
Ingram [1979] and Bugden [1991] to model the properties
of intermediate and deep waters. This approach is further
supported by the results of Cyr et al. [2011] who showed
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that the temporal evolution of the cold intermediate layer at
station 23 is principally driven by vertical diffusion. This
balance likely holds in the deep layer given that the vertical
flow must vanish at the bottom. It will be quantitatively shown
in section 3 that this equation (3), although simple and based
on a number of assumptions (2D flow without topography,
vertically-uniform lagrangian velocity, no vertical advection,
simple representation of pelagic respiration, etc.) captures
sufficiently well the observed variability of dissolved oxygen
to open up a discussion that challenges current understanding
of hypoxia in the St. Lawrence and deep estuaries.
[12] Unless otherwise stated, the seabed boundary condition is
K
∂½O2 ¼ Fb ;
∂z z¼zb
ð4Þ
where zb is bottom depth and Fb is the imposed sediment
oxygen demand, expressed in mmol m2 s1 in the equation
but reported in the text in mmol cm2 yr1 for easier comparisons with other studies. The value and form of this benthic oxygen flux will be detailed below as needed. At the top
boundary, the oxygen concentration is fixed to a constant
value (i.e. a Dirichlet boundary condition), as in Benoit et al.
[2006]. The influence of this boundary condition will be
discussed in the Results section (section 3) where the results
of Benoit et al. [2006] are revisited. Depending on simulations, the initial condition is either taken as an idealized or
observed oxygen profile representative for station 16 in the
middle of the Gulf (Figure 1).
[13] The vertical domain varies between simulations. In
revisiting the results of Benoit et al. [2006], two vertical
domains are examined, one between 200 ≤ z ≤ 300 m, as in
Benoit et al. [2006], and a thicker one between 150 ≤ z ≤
300 m for a sensitivity analysis. All other simulations use a
vertical domain between 0 ≤ z ≤ 325 m, that is the average
maximum depth along the Laurentian Channel in the LSLE.
The simulation period is set to t r = 2.2 years that is the
average residence time for a water parcel traveling the
700 km separating station 16 from station 25 at the Head of
the Laurentian Channel at u = 1 cm s1. This velocity, and
therefore the residence time used here, was determined by
Gilbert [2004] by calculating the maximum lagged correlation of temperature time series (1952–2003) between different regions of the gulf at depth 250 m. This value represents a
long-term average and is about twice as fast as determined
before by Bugden [1991]. Very little is known about the
variability of the deep circulation of the gulf. Results sensitivity to the residence time will be examined.
[14] Equation (3) is solved numerically with an explicit
forward-in-time, centered-in-space scheme on a vertical grid
size Dz = 1 m and time step Dt = 600 s. Results are negligibly sensitive to finer vertical or temporal resolutions.
Doubling the grid size resolution to 1/2 m while quadrupling
the time step resolution to 600/4 s leads to less than 0.1%
difference.
2.2. Oxygen Data
[15] Dissolved oxygen data were extracted from the Ocean
Data Management System public database [Fisheries and
Oceans Canada, 2011]. All data found in the database
between year 2005 and 2011 within a square box of side
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roughly the width of the Laurentian Channel and centered on
stations 16 to 25, except station 23 (Figure 1), were extracted
and grouped together per station. Station 23 is visited weekly
by scientists from the Maurice Lamontagne Institute since
1993 as part of a monitoring program and oxygen data started
to be collected there systematically since 2005. Oxygen data
at this station were obtained at the station and not within a
boxed region. Those stations were chosen because they have
been routinely visited in previous sampling campaigns [e.g.,
Benoit et al., 2006; Lehmann et al., 2009]. On average,
59 profiles were extracted per station. Station 23 contains the
highest number of profiles (n = 157) while station 25 contains
the least number (n = 10). Data obtained through this
database were collected with Sea-Bird Electronics SBE 43
oxygen sensors. These sensors were routinely calibrated
against bottled seawater samples by Winkler titration.
[16] Statistics such as means, 95% confidence intervals
on means and 95% spread of the data were computed for each
station. Confidence intervals on means were obtained by
performing 500 bootstrap replicates of the sampling set
[Efron and Gong, 1983]. For statistical robustness, the model
and analysis presented below rely on 7-year averages rather
than examining a single year.
2.3. Turbulence Data
[17] Turbulence measurements were collected at station
23 as well as along a cross-shore transect extending off
Rimouski over a three-year period (summers 2009–2011)
with two shear microstructure profilers VMP-500 manufactured by Rockland Scientific International (RSI). Those
profilers are equipped with Sea-Bird Electronics sensors for
fine-scale (1 dm) measurements of temperature T and
salinity and RSI sensors for micro-scale (1 cm) vertical
shear measurements ∂u′/∂z. See Cyr et al. [2011, Figure 8]
for a sample profile of some of these quantities at station 23.
[18] Of the 1558 profiles collected to date, 892 are presented in Cyr et al. [2011] in a study of the erosion of the cold
intermediate layer. The remaining 666 profiles were collected in summer 2011 and are used here to complement the
Cyr et al. [2011] data set. Of all 813 profiles collected to date
at station 23, 797 were sampled down to 150–180 m and only
4 throughout the entire water column, down to 330 m, where
we let the profiler hit the bottom. Those four profiles were
collected consecutively, within about a two hour period. We
therefore have little statistical confidence in the turbulence
within the bottom boundary layer at the deepest point of the
Laurentian Channel. However, Cyr et al. [2011] obtained
150 profiles through the bottom boundary layer in depths
varying between 20 and 140 m at stations along a crosschannel transect extending off Rimouski. Turbulence within
the bottom boundary layer will be determined principally
from those measurements.
[19] The methodology for inferring eddy mass diffusivity
from microstructure shear measurements is well established
and detailed in Cyr et al. [2011, and references therein].
Briefly, for well-developed, steady-state and isotropic turbulence, typical of coastal oceanographic conditions, the
eddy diffusivity is calculated from the microstructure shear
measurements as [Osborn, 1980]
4 of 13
K¼G
;
N2
ð5Þ
BOURGAULT ET AL.: HYPOXIA IN THE ST. LAWRENCE ESTUARY
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where G = 0.2 is the dissipation flux coefficient, N is the
background buoyancy frequency,
¼
15 ∂u′ 2
;
n
2
∂z
ð6Þ
is the dissipation rate of turbulent kinetic energy and n is the
molecular viscosity. The overbar is taken here as a 5-m
average which matches the typical vertical resolution used
in 3D numerical models of the Gulf [e.g., Smith et al., 2006].
In practice, the averaging is carried out in the spectral space
to remove instrumental noise. It is assumed here that dissolved oxygen diffusivity equals mass diffusivity in a turbulent flow. As with the oxygen data, confidence intervals on
means were obtained by performing 500 bootstrap replicates
of the sampling set.
[20] As suggested by Cyr et al. [ 2011], the effective
eddy diffusivity Ke in a cross-shore transect going through
station 23 is thought to be a combination of interior mixing
and mixing processes operating near lateral boundaries
where the water intersects the sloping bottom and where the
turbulence may be orders of magnitude higher. Cyr et al.
[2011] showed that the net effect of boundary mixing at
this cross-section is to increase the effective interior diffusivity by a factor of 1.8. Taking this into account, the effective eddy diffusivity considered in this study is
Ke ¼ 1:8K;
demand until hypoxic conditions are reached near the bottom of the Head of the Laurentian Channel.
[23] Benoit et al. [2006] justified using a Dirichlet condition at the top model boundary based on the observation that
the oxygen concentration at this level in summer 2003 did
not vary much along its path from the Gulf to the Head of the
Laurentian Channel (see their Figure 2). This is also
approximately seen in the 7-year mean (our Figure 2). This
approach would be justified as long as criterion (2) would be
respected. Otherwise, turbulent diffusion from overlying
well-oxygenated layers could oxygenate the 100-m thick
bottom layer. However, this possibility is greatly limited if
the oxygen concentration is fixed at the top boundary, an
aspect illustrated below with the next simulation.
[24] In this second simulation, we test the sensitivity of the
model results to the top boundary condition by extending the
domain thickness by 50 m upward. The initial condition is
adjusted to take into account the oxygen profile observed
between 150 and 200 m in summer 2003 from Benoit et al.
[2006]. For simplicity, the initial oxygen profile above
200 m is idealized as a linear increase, from 120 mmol L1 at
200 m to 220 mmol L1 at 150 m, as inferred visually from
the field observations presented in Figure 2 in Benoit et al.
[2006]. Mathematically, this is (in mmol L1)
½O2 ðz; t ¼ 0Þ ¼
ð7Þ
where K is the interior diffusivity measured at station 23.
3. Results
3.1. Benthic Respiration Only: Benoit et al. [2006]
Revisited
[21] As a test case, our model was first configured as in
Benoit et al. [2006] for their high carbon flux scenario, a
case where their model reproduced hypoxic conditions near
the Head of the Laurentian Channel (their Figures 9b and
9d). For this simulation, the integration domain lies between
200 ≤ z ≤ 300 m, that is the thickness Hb = 100 m of what is
generally considered to be the bottom waters of the LSLE.
The initial condition is set to [O2](z, t = 0) = 120 mmol L1,
which is equivalent to the seaward boundary condition
imposed by Benoit et al. [2006] in their Eulerian reference
frame. This vertically-uniform initial condition is an idealization of the oxygen profile observed between 200–300 m at
station 16 in July 2003 [see Benoit et al., 2006, Figure 2].
The top boundary condition is fixed at [O2](z = 200 m, t) =
120 mmol L1. The sediment oxygen demand, or benthic
oxygen flux Fb, along the Laurentian Channel is taken from
Figure 9b in Benoit et al. [2006] that we digitized (Figure 3,
top). The eddy diffusivity is set to K = 1.0 104 m2 s1
and pelagic respiration is R = 0. Note that this simulation
violates equation (2), to which we refer as criterion (2),
since K 104 m2 s1 is comparable to H2b/t r (100 m)2/
108 s = 104 m2 s1.
[22] The resulting oxygen spatial field for this simulation
is almost identical to that of Benoit et al. [2006] (compare
Figure 3a with their Figure 9b). Oxygen is gradually
depleted in the water column due only to sediment oxygen
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2z þ 520
120
for 150 ≤ z < 200 m
for 200 ≤ z ≤ 300 m:
ð8Þ
[25] The top boundary condition of this simulation is [O2]
(z = 200 m, t) = 220 mmol L1. Eddy diffusivity is as in the
previous simulation, set to K = 1.0 104 m2 s1. The
thickness of the layer subject to hypoxia is still Hb = 100 m
and criterion (2) still not satisfied.
[26] This second configuration is therefore a little more
realistic than the previous simulation and should in principle
provide better agreement with observations. However, the
resulting oxygen spatial field is completely different (compare Figure 3b with 3a). The 100-m thick bottom layer is
oxygenated, due to turbulent oxygenation from layers above
200 m, and hypoxic conditions are not reached. The results
thus depend on model depth and top boundary condition.
[27] A third simulation was carried out with the same
configuration as the previous one except that the diffusivity is
decreased to K = 1.0 105 m2 s1 in order to satisfy criterion (2). This time oxygen is depleted in the 50-m or so
above the bottom with hypoxic, and even anoxic, conditions
reached at the Head of the Laurentian Channel (Figure 3c).
The shape of the oxygen profile at the head of the channel is
unrealistic and concentrations are too low. Although this
third simulation produces unrealistic results, it illustrates the
importance of respecting condition (2). Here we see that
since the condition is respected the oxygen concentration
at level 200-m is little affected. This is a situation where,
if simplification is required, setting a Dirichlet boundary
condition at 200 m would be justified.
[28] As already noticed in Benoit et al. [2006], low diffusivity produces unrealistically low oxygen concentration
in a too thin bottom layer. On the other hand, high diffusivity induces too much turbulent oxygenation from overlying layers, as demonstrated here. The apparent ability of
the Benoit et al. [2006] model to reproduce realistic hypoxic
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Figure 3. Model results for the spatial field of oxygen concentration [O2](mmol L1) for three different
model configurations (Figures 3a, 3b, and 3c) but forced with the same sediment oxygen demand Fb (top
panel) and no pelagic respiration R = 0. Each sub-panel to the right shows the seaward (x = 700 km, dotted
line) and landward (x = 0, solid line) oxygen concentration profiles. The origin of the x-axis corresponds to
station 25 at the Head of the Laurentian Channel (see Figure 1). The sediment oxygen demand Fb of the
top panel was digitized from Figure 9 in Benoit et al. [2006]. (a) As in Benoit et al. [2006] with diffusivity
K = 1.0 104 m2 s1. This figure is to be compared with Figure 9b in Benoit et al. [2006]. (b) As in
Figure 3a but with the domain extended up by 50 m and using a seaward boundary oxygen profile between
150–200 m idealized from the field observations for July 2003 reported in Benoit et al. [2006]. K = 1.0 104 m2 s1. (c) Same as Figure 3b but with K = 1.0 105 m2 s1. For easier intercomparison, each
panel a, b and c shares the same color scale and aspect ratio as Figures 2, 6, and 8. Numbers on top refer
to sampling stations (Figure 1).
conditions using high diffusivity is attributed to a model
implementation and top boundary condition inconsistent
with criterion (2) and field observations. We conclude from
these exercises that it is not possible to reproduce realistic
oxygen field and hypoxic conditions in a 100 m thick bottom layer with only a sediment oxygen demand, neither using
low (105 m2 s1) or high (104 m2 s1) constant diffusivity.
This conclusion provided a motivation to examine in greater
details deep turbulent diffusion and pelagic oxygen demand
as detailed in the following sections.
below 275 m where only 4 profiles were collected. Within
the bottom boundary layer, eddy diffusivity increases
exponentially on average (Figure 5). Values reached at the
bottom are approximately one order of magnitude higher
than above the boundary layer.
[31] Taking the bottom boundary layer into consideration,
the following parameterization is proposed for the effective
diffusivity affecting oxygen depletion in the bottom waters
of the LSLE
3.2. Eddy Diffusivity and Turbulent Oxygenation
[29] It was argued in the Introduction that the vertical
diffusivity in the bottom waters of the LSLE should be
≪104 m2 s1 to sustain oxygen depletion. We now provide
a more accurate estimation of the eddy diffusivity before
proceeding with refined simulations.
[30] The profile of the mean effective eddy diffusivity
measured at station 23, below 100 m, is shown in Figure 4b.
The depth-averaged diffusivity, between 100 m and 275 m,
is K e ¼ ð2 1Þ 105 m2 s1. This mean excludes values
where H is the total water depth, Kb = (4 2) 104 m2 s1
is the eddy diffusivity at the sea bed and d = 3 1 m is a
scale height, both determined from a best fit to observations
in the bottom boundary layer (Figure 5). K e ¼ ð2 1Þ 105 m2 s1 is the deep pelagic eddy diffusivity discussed
above. The tilde is used to distinguish this parameterization
from the actual observations. The effect of the boundary
layer, i.e. the second term in equation (9), on near-bottom
oxygen profiles will be presented in the following section.
~ e ðzÞ ¼ K e þ Kb exp½ðz H Þ=d ;
K
6 of 13
ð9Þ
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Figure 4. (gray shades) Confidence intervals (95%) on deep (>100 m) mean profiles of oxygen concentration [O2], effective eddy diffusivity Ke and turbulent oxygen fluxes Fp at station 23, off Rimouski (gray
shades). Turbulent oxygenation of the bottom layers through a surface located at 100 m above the bottom,
i.e. here at 230 m depth, is highlighted in the third panel with the dashed lines as visual aids. The oxygen
turbulent flux through this surface is Fp = (4 1) 101 mmol cm2 yr1 (see text for details). The solid
line in the second panel is the effective eddy diffusivity parameterization defined by equation (9).
[32] Diffusivity and oxygen observations at station 23
(Figure 4) can be combined to provide the pelagic turbulent
oxygenation defined as
Fp ¼ Ke
∂½O2 :
∂z
ð10Þ
[33] The maximum downward flux is observed around
100 m with Fp 102 mmol cm2 yr1 and decreases
approximately exponentially with depth (Figure 4c). Close to
bottom the uncertainty is large because only 4 turbulence
profiles sampled to the bottom. At 100 m above the bottom,
i.e. a standard height for comparison with other studies
[e.g., Lehmann et al., 2009], the flux is Fp = (4 1) 101 mmol cm2 yr1.
3.3. Benthic and Pelagic Respiration as in Lehmann
et al. [2009]
[34] Using the parameterization for the deep turbulent
effective diffusivity developed above (equation (9)), we now
proceed with simulations that include both benthic and
pelagic respiration as inferred by Lehmann et al. [2009].
[35] For these simulations, the model depth is set to H =
325 m which corresponds to the average maximum depth of
the LSLE (see white horizontal line in Figure 2). The initial
condition is taken as the mean oxygen profile at station 16
(Figures 2 and 6, right).
[36] A Dirichlet boundary condition set to [O2](z = 0 m, t) =
300 mmol L1 is applied at the sea surface. Bottom waters
properties, below 100 m depth, are insensitive to this choice
since the diffusion time scale, with K e 105 m2 s1,
required to propagate the surface signal below 100 m depth
is much longer than the 2.2. year simulation period.
Figure 5. The bottom boundary layer in the LSLE represented with 1-m scale effective eddy diffusivity Ke as a function of height above bottom (hab). Light gray profiles were
collected in depths varying between 20 and 140 m by Cyr
et al. [2011]. The thin black lines are the four profiles that
hit the deepest point of the estuary (330 m) at station 23.
The darker gray shade is the 95% confidence interval on
the trimmed mean (5% removed each side) and the dashed~ e ).
line is the least-square best fit of equation (9) (K
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Figure 6. Modeled oxygen concentration field [O2](mmol L1) with sediment oxygen demand and
pelagic respiration rates as in Lehmann et al. [2009]. The right panel shows the seaward (x = 700 km, dotted
line) and landward (x = 0, solid line) concentration profiles. (top) Simulations using the eddy diffusivity
parameterization defined by equation (9) with an exponential increase through the bottom boundary layer.
(bottom) Same as the top panel but using a constant eddy diffusivity throughout the bottom boundary layer
i.e. K ¼ K e . Numbers on top refer to sampling stations (Figure 1).
[37] The sediment oxygen demand in the LSLE, i.e. at
times when the Lagrangian water mass reaches station 20
and further landward to station 25, is set to
Fb ¼ 354 mmol cm
2
1
yr ;
¼ 0:
R¼
ð11Þ
as inferred by Lehmann et al. [2009]. The eddy diffusivity is
~ e.
parameterized as in equation (9), i.e. K = K
[38] In the deeper Gulf (stations 16 to 20), where depth
reaches 400 m, the boundary condition at the deepest cell (z =
325 m) is set to
∂
∂½O2 K
∂z
∂z [40] The pelagic community respiration rate is included in
the bottom 100-m only and is set to
ð12Þ
z¼325m
[39] This boundary condition is introduced because there
is no indication in the oxygen field at 325 m in the Gulf that
would suggest direct influences of bottom oxygen demand at
that level. If this were the case the oxygen concentration
would decrease with depth below 325 m whereas observations show the opposite (Figure 2). Also, throughout the
Gulf section the exponential dependance of the eddy diffusivity (see equation (9)) is removed by setting K ¼ K e since
the deepest cell lies far above the bottom boundary layer.
0:0196 mmol cm3 yr1
0
for H z ≤ 100 m
otherwise
ð13Þ
again as inferred by Lehmann et al. [2009].
[41] The result of this model is a significant improvement
over the previous model (Figures 6, top, and 7). In particular,
the form of the near-bottom oxygen resembles much more
closely the observations. However, hypoxic conditions are
not reached. Minimum concentration at the bottom of station
25 are 100 mmol L1.
[42] A large part of the improvement is due to the exponential form of the eddy diffusivity in the bottom boundary
layer landward of station 20. To show this, a simulation was
carried out by removing the bottom boundary layer parameterization, i.e. with a constant diffusivity K ¼ K e throughout
the water column (equivalent to setting Kb = 0 in equation (9)).
This simulation leads to too severe hypoxia 30 mmol L1
near the Head of the LSLE (Figure 6, bottom). Furthermore,
the shape of the near-bottom oxygen profile is unrealistic
compared to field observations (Figure 7). This highlights the
importance of using a realistic representation of turbulent
processes throughout the bottom boundary layer of scale
height d (equation (9)).
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Figure 7. Comparison at three stations in the LSLE between observations (gray shades) and model
results of oxygen concentration in the deep layers (>100 m). The darker shades are the 95% confidence
intervals on means and the lighter shades are the 2.5%–97.5% percentiles spread of the data (statistics
made on years 2005–2011). The dashed lines are the results from the simulation that uses sediment oxygen
demand and pelagic respiration rates as in Lehmann et al. [2009] and the eddy parameterization
defined by equation (9). The misfit is e = 49% (see text for details on misfit definition). The dashed-dotted
lines are simulations using a constant eddy diffusivity throughout the bottom boundary layer, i.e. Kb = 0 in
equation (9). The solid lines are the results from the simulation that uses a temperature-dependant pelagic
respiration rate and sediment oxygen demand inferred from inverse modeling and the parameterization
defined by equation (9). The misfit is e = 14%. The vertical dashed line highlights the threshold for hypoxia.
[43] The model-observations overall misfit for the simulation that includes the exponential boundary layer diffusivity is evaluated as
25 ~
1X
O 2 i ½O2 i e¼
;
n i¼21 ½O2 16 ½O2 i ð14Þ
where ½O2i and ½Õ2i are, respectively, the observations and
model result at station i, the overbar is the average of the
data available below 100 m depth and n = 5 is the number of
stations in the LSLE. This quantifies the ability of the model
to reproduce oxygen concentration relative to the observed
difference between station 16 and i. The misfit for this
simulation is e = 49%.
3.4. An Arrhenius Model for Pelagic Respiration
[44] Based on the temperature dependance of chemical
reactions proposed by Arrhenius [Logan, 1982], Genovesi
et al. [2011] suggested that the 2 C warming of the deep
waters of the LSLE over the last century may have contributed
between 10–32% to oxygen depletion by increasing organisms metabolism and bacterial respiration rates. Inspecting
the temperature field along the Laurentian Channel shows
comparable longitudinal and vertical temperature change
in bottom waters (Figure 2). This leads us to consider a
temperature-dependent, Arrhenius parameterization for pelagic
respiration rate.
[45] In the following simulation, we test the following
Arrhenius model for pelagic respiration rate
R ¼ R0 eT0 =ðT Tf Þ ;
ð15Þ
where R0 is a reference respiration rate, T0 a temperature
scale, both to be determined with the procedure described
next, and Tf = 1.9 C the freezing point of seawater of
salinity 34.5 taken as the temperature below which pelagic
oxygen consumption is negligible. The temperature T
represents the 2005–2011 observed mean (Figure 2).
[46] This time, the coefficients R0 and T0 in equation (15),
as well as the sediment oxygen demand Fb and pelagic diffusivity K e , are not imposed a priori but are determined by
inverse modeling, or data assimilation. This provides a robust
statistical mean to evaluate those parameters while objectively scanning the parameter space. The other two coefficients used in the diffusivity parameterization defined by
equation (9), i.e., the bottom diffusivity Kb and scale
height d, are fixed but results sensitivity is diagnosed by
taking into account the uncertainties of those parameters.
Letting Kb and d as free parameters led the search algorithm
to converge towards unrealistic values.
[47] These four coefficients (R0, T0, Kb, K e) are determined
by minimizing the following least-square cost function,
9 of 13
C¼
k 2 25 X
2
X
~ 2 ½O2 i ;
O
i
i¼21 k1
ð16Þ
BOURGAULT ET AL.: HYPOXIA IN THE ST. LAWRENCE ESTUARY
C08033
C08033
Figure 8. Same as Figure 6 but for the simulation with a temperature-dependent pelagic respiration rate
and sediment oxygen demand inferred from inverse modeling. Numbers on top refer to sampling stations
(Figure 1).
where i is the station number, k1 the index of the cell located
at z = 100 m, k2 the index of the maximum depth at which
data are available for a given station i and, [Õ2] and [O2] are,
respectively, the modeled and observed oxygen concentrations. The depth z = 100 m for k1 is chosen as the depth below
which oxygen is unaffected from direct exchange with the
atmosphere associated with the winter mixed layer depth
[Galbraith, 2006]. The minimization is performed using the
Nelder-Mead method [Nelder and Mead, 1965]. All other
parameters and boundary conditions are set as in the previous
simulation.
[48] The algorithm returned the following values: K e ¼
ð2:40 0:02Þ 105 m2 s1, R0 = 0.0920 0.0006 mmol
cm3 yr1, T0 = 5.42 0.03 C and Fb = 203 100 mmol
cm2 yr1.
[49] Each of these values is realistic. The eddy diffusivity
K e returned by the algorithm is within the uncertainty of
direct measurements at station 23 (see equation (9)). The
sediment oxygen demand Fb returned is within the range of
values reported in the literature [Benoit et al., 2006; Katsev
et al., 2007]. When combined into the Q10 number, which
is commonly used to express metabolic rates [e.g. Genovesi
et al., 2011], the coefficients R0 and T0 give
Q10 ¼
RðT0 þ 10 CÞ
¼ 1:5;
RðT0 Þ
ð17Þ
which is within the range reported in the literature (see
Genovesi et al. [2011] for a review).
[50] The result of this simulation is a significant improvement relative to the previous simulation with misfit e = 14%
compared to e = 49% (Figures 7 and 8). The oxygen profile
near the bottom resembles the observed profiles and hypoxic
conditions are reached at station 25.
[51] The simulation above was carried out for a period of
2.2 years, which corresponds to the average residence time
for a water parcel traveling the 700 km separating station 16
to station 25 at the Head of the Laurentian Channel at u =
1 cm s1 [Gilbert, 2004]. However, previous estimates suggested a residence time twice as long [Bugden, 1991]. To test
the sensitivity of the results to the residence time we carried
out a simulation by doubling the residence time. The model
converged to the same oxygen field as the previous simulation with identical misfit e = 14%. The returned diffusivity
and reference pelagic respiration were twice as low with
K e = 1.2 105 m2 s1 and R0 = 0.046 mmol cm3 yr1.
However, the reference temperature T0 and sediment oxygen
demand Fb returned were identical to the previous simulation. This is to be kept in mind, but the rest of the discussion
presented below will be based on the results carried out with
the 2.2 years residence time for easier comparisons with
previous studies that have adopted this value for analysis
[e.g., Lehmann et al., 2009].
[52] The spatial pattern of the inferred pelagic community
respiration rate R is presented in Figure 9 for the 2.2 years
simulation (values could simply be divided by two for the
4.4. years simulation). For easier comparison with Lehmann
et al. [2009], values are expressed in nmol L1 d1. Values
between 50–100 m are comparable to the 33 6 nmol L1
d1 reported by Lehmann et al. [2009] for station 23, but
3–4 times higher in deep waters, with values reaching
120 nmol L1 d1. This difference is at the heart of the results
obtained here: our study requires much higher pelagic
respiration than inferred before to explain hypoxia in the
LSLE. This contradiction does not necessarily call into question the measurements published by Lehmann et al. [2009]
but rather that pelagic bio-chemical processes at station 23
may not be representative of pelagic processes occurring
throughout the Gulf and LSLE. This point will be further
discussed below supported with observations suggesting
important differences between pelagic processes occurring
in the Gulf and the LSLE.
[53] Note that the pelagic respiration model defined by
equation (15) has no depth-dependance. Such a depthdependance could be expected due to the power-law decrease
of organic matter fluxes [Buesseler et al., 2007]. There is
some visual indications of depth-dependant oxygen depletion rate in the Gulf region (between station 16 and 17) but
not so much in the LSLE (Figure 2). To test whether this
could improve model results, the following form of pelagic
respiration was implemented,
(
R¼
if z < z0
R0 eT0 =ðT Tf Þ
R0 ðz=z0 Þb eT0 =ðTTf Þ otherwise
ð18Þ
where z0 = 150 m is a reference depth and b an attenuation
coefficient [Buesseler et al., 2007] to be determined by
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BOURGAULT ET AL.: HYPOXIA IN THE ST. LAWRENCE ESTUARY
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C08033
Figure 9. Pelagic respiration R = f(T) (see equation (15)) inferred from the inverse model and calculated
with the temperature observations of Figure 2. Numbers on top refer to sampling stations (Figure 1).
minimization. Over the depth range and region simulated
here, this depth-dependant form of pelagic respiration did not
provide any improvement over the simpler depth-invariant
form (equation (15)). The minimization algorithm returned
a value close to 0 for the attenuation coefficient b which led
the model to converge towards the same solution as the
previous simulation.
3.5. The Oxygen Budget
[54] The relative importance of pelagic versus benthic
oxygen demand in producing hypoxic conditions in the
100-m thick bottom layer of the LSLE is now evaluated by
examining the modeled oxygen budget. The budget is
expressed as,
B ¼ F p F b F R;
ð19Þ
where
Fp ¼
1
L
Z
L
Fp ðz ¼ 225 mÞ dx
ð20Þ
0
is the average turbulent oxygenation from overlying layers,
where L = 700 km is the distance separating stations 16
and 25,
Fb ¼
1
L
Z
L
Fb dx
ð21Þ
0
is the average sediment oxygen demand, keeping in mind
that Fb = 0 between stations 16 and 21 for reasons
detailed earlier (see text around equation (12)), and,
FR ¼
1
L
Z
L
Z
H
R dz dx
0
225 m
is the depth-integrated pelagic respiration rate.
ð22Þ
[55] Given the 14% model error in reproducing the oxygen
field (see section 3.4), we cautiously provide here the budget
to only one significant figure. Once rounded, the calculation
gives F p = 4 101 mmol cm2 yr1, F b = 8 101 mmol
cm2 yr1, F R = 4 102 mmol cm2 yr1, and B = 5 102 mmol cm2 yr1.
[56] Turbulent oxygenation contributes approximately 8%
to the budget, consistent with low turbulent fluxes required
to maintain hypoxic conditions. However, contrary to previous hypotheses, pelagic oxygen demand is about 5 times
larger than benthic oxygen demand. This ratio decreases to
about 2.5 for the 4.4 years simulation (see section 3.4 for
details on sensitivity results to the simulation period).
4. Discussion
4.1. Caveat
[57] The model developed here assumes that a steady-state
exists in the upstream boundary condition. However, deep
Cabot Strait waters feeding the estuarine circulation have
become colder (and richer in dissolved oxygen) between
2003 and 2009 at a rate of 0.12 C yr1 (from Table 17 in
Galbraith et al. [2011]). This change can be treated as an
additional flux that can be compared to the terms of the
budget formulation (equation (19)). Gilbert et al. [2005]
estimated the change in dissolved oxygen associated with
changing water masses to have an upper bound of 24.4
mmol L1 C1. Thus, the upper bound for this advective
water mass anomaly flux is (24.4 mmol L1 C1) (0.12 C y1) = 2.9 mmol L1 yr1, which integrated over
the bottom 100 m of the water column corresponds to Fwm =
3 101 mmol cm2 yr1. This does not affect our budget
balance since it is one order of magnitude smaller than the
main term.
[58] Benoit et al. [2006] raised the idea that sediment
oxygen demand taking place along the sloped flanks of the
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BOURGAULT ET AL.: HYPOXIA IN THE ST. LAWRENCE ESTUARY
Figure 10. Mean observed (solid) and simulated (dashed)
bottom waters (225–325 m) dissolved oxygen concentration.
The gray shade highlights the LSLE. Numbers on top refer
to sampling stations (Figure 1).
Laurentian Channel may represent an additional sink to the
laterally-averaged budget. Such a localized benthic oxygen
demand operating throughout the depth of the bottom waters,
if important, could indeed be confused with pelagic oxygen
demand if the deep waters within the Laurentian Channel
were laterally well-mixed. The fraction f of the total channel
width affected by sediment oxygen demand taking place
along the sloped flanks can be evaluated as f = (2Hsod/s)/L,
where Hsod is the thickness over which sediment oxygen
demand is significantly felt, L is the width of the Laurentian
Channel in the Gulf, s is the slope of the sides of the channel
and the factor 2 is to take into account the effect of both sides
(see Cyr et al. [2011] for a similar geometric calculation).
Taking Hsod ≈ 2 101 m as a maximum value (see, for
example, Figure 3c), L ≈ 5 104 m and s ≈ 0.03 gives f = 3%.
This calculation suggests that the net contribution from sediment oxygen demand at sloped sidewalls is small relative to
the total channel width.
4.2. Benthic Versus Pelagic Respiration
[59] The model presented here captures reasonably well
the average oxygen depletion occurring along the bottom
waters of the Laurentian Channel, from the Gulf to the Head
of the Laurentian Channel (Figures 7 and 8). However, the
model does not capture the spatial details of this depletion.
This is best seen in examining the modeled and observed
along-channel oxygen concentration averaged between
225 m and 325 m depth (Figure 10). The largest observed
depletion rate occurs in the deep Gulf section and steadily
decreases towards the LSLE. The depletion rate in the Gulf,
near station 16, is at least 2 times larger than at the mouth of
the LSLE, near station 21. Within the LSLE there is in fact
little depletion and even some signs of oxygenation towards
the Head, presumably due to enhanced turbulent diffusion
near the sill [Forrester, 1974; Ingram, 1983; Saucier and
Chassé, 2000]. This spatial variability in the depletion rates
can also be seen from the interpolated oxygen field (Figure 2)
where horizontal gradients in bottom waters (between 225–
325 m) are significantly greater in the Gulf region than within
the LSLE. This fact alone suggests that the low oxygen
concentration observed throughout the bottom layers of the
LSLE is principally the result of pelagic processes that took
place months before in the Gulf region.
C08033
[60] The predominance of pelagic over benthic oxygen
sink discussed above is further supported by the oxygen
field that exhibits a minimum around 250 m in the Gulf
between stations 16 and 20 (Figure 2). This minimum would
be drawn to the bottom if benthic respiration were principally responsible for the depletion at that level in the Gulf.
Within the LSLE (Figure 2, stations 21–25), the minimum
sits indeed at the bottom which possibly reflects the direct
effect of sediment oxygen demand there, although it could
also be a coincidence of the raising sea floor that approximately coincides with the depth of the oxygen minimum
found in the Gulf. Regardless, as presented above, the deep
water mass that scrubs the bottom of the LSLE had already
been largely depleted in oxygen within the Gulf.
[61] Our analysis suggests that pelagic community respiration in deep waters (>150 m, Figure 9) is 3–4 times higher
than pelagic bacterial respiration reported by Lehmann et al.
[2009] for station 23. As presented above, there are indications in the mean oxygen field alone of larger depletion rate
in the Gulf than in the LSLE, an aspect not captured by our
model. Our model likely overestimates pelagic community
respiration in the LSLE, and underestimates it in the Gulf
(again suggested by Figure 10). Therefore, the difference
between Lehmann et al.’s [2009] measurements for station
23 and our inferred rate, meant to be representative of the
mean conditions along the entire transect, may indicate that
bio-chemical processes occurring at station 23 are not representative of pelagic processes occurring throughout the
Gulf and LSLE. This calls for more research on bio-chemical
processes in the Gulf section.
[62] As for turbulent diffusivity, the fact that the model
results converge to an average diffusivity comparable to that
observed at station 23 suggests little differences between the
deep turbulent field in the Gulf and the LSLE. If this is
verified with direct turbulence observations, yet to be collected in the Gulf, it would further support the hypothesis
that pelagic oxygen demand in the Gulf is greater than in the
LSLE.
5. Conclusions
[63] The following paradox appears in the literature on
hypoxia in the LSLE: Both high and low turbulent diffusivity
are implicitly invoked to explain hypoxia when sediment
oxygen demand is assumed to be the primary sink. On the
one hand, sufficiently high diffusion is required to deplete the
100-m thick bottom layer while, on the other hand, low diffusion is required to prevent turbulent oxygenation from
overlying layers. This paradox partly arose from the apparent
ability of the Benoit et al. [2006] model to reproduce realistic
hypoxic conditions in the bottom waters of the LSLE with
exclusively a sediment oxygen demand and constant high
turbulent diffusivity K. It is demonstrated here that the Benoit
et al. [2006] model reproduced realistic conditions due to the
implementation of a top boundary condition and domain
depth inconsistent with the high value used for K. The consequence of the inconsistency is to greatly limit turbulent
oxygenation from overlying layers. When the inconsistency
is removed, it is further shown that realistic hypoxic conditions throughout the 100-m thick bottom layer cannot be
reproduced with sediment oxygen demand alone, neither using
high or low diffusion. However, when pelagic respiration is
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BOURGAULT ET AL.: HYPOXIA IN THE ST. LAWRENCE ESTUARY
incorporated in the model as an exponential function of
water temperature along with a parameterization of turbulent
diffusivity based on field observations, realistic hypoxic
conditions are reproduced.
[64] Overall, the results of the analysis presented here,
based on inspection of historical oxygen profiles, new in situ
turbulence measurements and idealized simulations, suggest
that pelagic oxygen consumption is the dominant oxygen sink
responsible for hypoxia in the 100-m thick bottom waters of
the deep Estuary and Gulf of St. Lawrence, with benthic
oxygen demand playing a necessary but secondary role.
There are to date very few studies that have addressed pelagic
oxygen demand in the Estuary and Gulf of St. Lawrence.
In the light of the results presented here new research efforts
towards studying pelagic respiration are called for in order to
foresee the future of dissolved oxygen in the St. Lawrence
system and the impact on the marine ecosystem.
[65] Acknowledgments. This research was funded by the Natural
Sciences and Engineering Research Council of Canada, the Canada Foundation for Innovation, Fisheries and Oceans Canada, the Fonds de RechercheNature et Technologies Québec and is a contribution to the scientific
program of Québec-Océan. We would like to thank the external reviewers
as well as the Editor for their constructive criticism on a previous version
of the manuscript. We would also like to thank Denis Gilbert for general
discussions about hypoxia and for his comments on the manuscript as well
as Rémi Desmarais and Paul Nicot for their assistance in the summer 2011
field season. A special thanks as well to the people who maintain the Atlantic
Zonal Monitoring Program that provides invaluable information and historical data sets for understanding our oceans.
References
Benoit, P., Y. Gratton, and A. Mucci (2006), Modeling of dissolved oxygen
levels in the bottom waters of the Lower St. Lawrence Estuary: Coupling
of benthic and pelagic processes, Mar. Chem., 102, 13–32, doi:10.1016/
j.marchem.2005.09.015.
Buesseler, K. O., et al. (2007), Revisiting carbon flux through the oceans
twilight zone, Science, 316, 567–570, doi:10.1126/science.1137959.
Bugden, G. L. (1991), Changes in the temperature-salinity characteristics of
the deeper waters of the Gulf of St. Lawrence over the past few decades,
Can. Spec. Publ. Fish. Aquat. Sci., 113, 139–147, 1991.
Cyr, F., D. Bourgault, and P. S. Galbraith (2011), Interior versus boundary
mixing of a cold intermediate layer, J. Geophys. Res., 116, C12029,
doi:10.1029/2011JC007359.
Efron, B., and G. Gong (1983), A leisurely look at the bootstrap, the jacknife and cross-validation, Am. Stat., 37(1), 36–48.
Fisheries and Oceans Canada (2011), Oceanographic Data Management
System, <http://ogsl.ca/app-sgdo/en/accueil.html>, Maurice-Lamontagne
Inst., Mont-Joli, Québec, Canada, consulted on 25 October 2011.
Forrester, W. D. (1974), Internal tides in the St. Lawrence Estuary, J. Mar.
Res., 32, 55–66.
Galbraith, P. S. (2006), Winter water masses in the Gulf of St. Lawrence,
J. Geophys. Res., 111, C06022, doi:10.1029/2005JC003159.
Galbraith, P. S., J. Chassé, D. Gilbert, P. Larouche, D. Brickman, B. Pettigrew,
L. Devine, A. Gosselin, R. G. Pettipas, and C. Lafleur (2011), Physical
oceanographic conditions in the Gulf of St. Lawrence in 2010, Can. Sci.
Advis. Sec. Res. Doc., 2011/045, 86 pp., Fisheries and Oceans Canada,
Mont-Joli, Québec, Canada.
Genovesi, L., A. de Vernal, B. Thibodeau, C. Hillaire-Marcel, A. Mucci,
and D. Gilbert (2011), Recent changes in bottom water oxygenation
and temperature in the Gulf of St. Lawrence: Micropaleontological and
geochemical evidence, Limnol. Oceanogr., 56(4), 1319–1329, doi:10.4319/
lo.2011.56.4.1319.
C08033
Gilbert, D. (2004), Propagation of temperature signals along the north-west
Atlantic continental shelf edge and into the Laurentian Channel, paper
presented at ICES Annual Science Conference, Int. Counc. for the
Explor. of the Sea, Vigo, Spain.
Gilbert, D., B. Sundby, C. Gobeil, A. Mucci, and G. H. Tremblay (2005),
A seventy-year record of diminishing deep-water oxygen levels in
the St. Lawrence estuary: The northwest Atlantic connection, Limnol.
Oceanogr., 50, 1654–1666.
Gilbert, D., D. Chabot, P. Archambault, B. Rondeau, and S. Hébert (2007),
Appauvrissement en oxygène dans les eaux profondes du st-laurent
marin: Causes possibles et impacts écologiques, Nat. Can., 131, 67–75.
Gilbert, D., N. N. Rabalais, R. J. Diaz, and J. Zhang (2010), Evidence for
greater oxygen decline rates in the coastal ocean than in the open ocean,
Biogeosciences, 7, 2283–2296.
Hetland, R. D., and S. F. DiMarco (2008), How does the character of oxygen
demand control the structure of hypoxia on the Texas-Louisiana continental shelf?, J. Mar. Syst., 70, 49–62, doi:10.1016/j.jmarsys.2007.03.002.
Hopkinson, C. S., and E. M. Smith (2005), Estuarine respiration: an overview of benthic, pelagic, and whole system respiration, in Respiration in
Aquatic Ecosystems, edited by P. A. delGiorgio and P. J. le B. Williams,
chap. 8, pp. 122–146, Oxford Univ. Press, New York.
Ingram, R. G. (1979), Water mass modification in the St. Lawrence Estuary,
Nat. Can., 106, 45–54.
Ingram, R. G. (1983), Vertical mixing at the head of the Laurentian Channel,
Estuarine Coastal Shelf Sci., 16, 332–338, 1983.
Katsev, S., G. Chaillou, B. Sundby, and A. Mucci (2007), Impact of progressive oxygen depletion on sediment diagenesis and fluxes: a model
for the Lower St. Lawrence Estuary, Limnol. Oceanogr., 52, 2555–2568.
Koutitonsky, V. G., and G. L. Bugden (1991), The physical oceanography
of the Gulf of St. Lawrence: A review with emphasis on the synoptic variability of the motion, Can. Spec. Publ. Fish. Aquat. Sci., 113, 57–90.
Lehmann, M. F., B. Barnett, Y. Gélinas, D. Gilbert, R. J. Maranger,
A. Mucci, B. Sundby, and B. Thibodeau (2009), Aerobic respiration
and hypoxia in the Lower St. Lawrence Estuary: Constraints on oxygen
sink partitioning from stable isotope ratios of dissolved oxygen, Limnol.
Oceanogr., 54, 2157–2169, doi:10.4319/lo.2009.54.6.2157.
Logan, S. R. (1982), The origin and status of the Arhenium equation,
J. Chem. Educ., 59, 279–281.
Mucci, A., M. Starr, D. Gilbert, and B. Sundby (2011), Acidification of
Lower St. Lawrence Estuary bottom waters, Atmos. Ocean, 49(3),
206–218, doi:10.1080/07055900.2011.599265.
Nelder, J. A., and R. Mead (1965), A simplex method for function minimization, Comput. J., 7, 308–313.
Osborn, T. R. (1980), Estimates of the local rate of vertical diffusion from
dissipation measurements, J. Phys. Oceanogr., 10, 83–89.
Pena, M. A., S. Katsev, T. Oguz, and D. Gilbert (2010), Modeling dissolved
oxygen dynamics and hypoxia, Biogeosciences, 7, 933–957.
Rabalais, N. N., R. J. Díaz, L. A. Levin, R. E. Turner, D. Gilbert, and
J. Zhang (2010), Dynamics and distribution of natural and human-caused
hypoxia, Biogeosciences, 7, 585–619.
Saucier, F. J., and J. Chassé (2000), Tidal circulation and buoyancy effects
in the St. Lawrence Estuary, Atmosphere Ocean, 38(4), 1–52.
Smith, C. G., F. J. Saucier, and D. Straub (2006), Formation and circulation
of the cold intermediate layer in the Gulf of Saint-Lawrence, J. Geophys.
Res., 111, C06011, doi:10.1029/2005JC003017.
Thibodeau, B., A. de Vernal, and A. Mucci (2006), Recent eutrophication
and consequent hypoxia in the bottom waters of the Lower St. Lawrence
Estuary: Micropaleontological and geochemical evidence, Mar. Geol.,
231, 37–50, doi:10.1016/j.margeo.2006.05.010.
Thibodeau, B., A. de Vernal, C. Hillaire-Marcel, and A. Mucci (2010a),
Twentieth century warming in deep waters of the Gulf of St. Lawrence:
A unique feature of the last millennium, Geophys. Res. Lett., 37,
L17604, doi:10.1029/2010GL044771.
Thibodeau, B., M. F. Lehmann, J. Kowarzyk, A. Mucci, Y. Gélinas,
D. Gilbert, R. Maranger, and M. Alkhatib (2010b), Benthic nutrient
fluxes along the Laurentian Channel: Impacts on the N budget of the
St. Lawrence marine system, Estuarine Coastal Shelf Sci., 90(4), 195–205.
13 of 13