A wind-driven, spatially coherent mode of nonseasonal, depth-independent variability in the Canadian inland seas (i.e., the collective of Hudson Bay, James Bay, and Foxe Basin) is identified based on Gravity Recovery and Climate Experiment (GRACE) retrievals, a tide-gauge record, and a barotropic model over 2003–2013. This dominant mode of nonseasonal variability is correlated with the North Atlantic Oscillation and is associated with net flows into and out of the Canadian inland seas; the anomalous inflows and outflows, which are reflected in mean sea level and bottom pressure changes, are driven by wind stress anomalies over Hudson Strait, probably related to wind setup, as well as over the northern North Atlantic Ocean, possibly mediated by various wave mechanisms. The mode is also associated with mass redistribution within the Canadian inland seas, reflecting linear response to local wind stress variations under the combined influences of rotation, gravity, and variable bottom topography. Results exemplify the usefulness of GRACE for studying regional ocean circulation and climate.
Hudson Bay, James Bay, and Foxe Basin together constitute the Canadian
inland seas (CIS; Fig. 1). This set of marginal seas connects to the
Labrador Sea and North Atlantic through Hudson Strait and Ungava Bay
in the east, and to the Arctic Ocean through Fury and Hecla Strait and
the Gulf of Boothia in the north. These seas are shallow, having
depths of
Shading is the logarithm of ocean depth from ETOPO5 5
The CIS play an important role in the ocean general circulation. Numerical simulations suggest that Hudson Strait is one of the most important regions in the world ocean for the dissipation of tidal energy (Egbert and Ray, 2001; Webb, 2014). Barotropic models show how, on synoptic timescales, dynamic response of Hudson Bay to barometric pressure drives flows through Hudson Strait, which generate coastal waves that subsequently affect sea level downstream as they propagate over the continental shelf (Wright et al., 1987; Greatbatch et al., 1996). Direct measurements of the baroclinic boundary current by a moored current array deployed in Hudson Strait reveal that the outflow through Hudson Strait is responsible for a substantial portion of the fresh water supplied to the Labrador Current and the North Atlantic Ocean (Straneo and Saucier, 2008a).
This region is also of interest in the context of changes ongoing in the Arctic system (White et al., 2007). Passive microwave data reveal that concentrations and extents of seasonal sea ice have decreased in Hudson Bay over recent decades, while historical climate data show that surface air temperatures around Hudson Bay have warmed since 1950 (Hochheim and Barber, 2010; Hochheim et al., 2011). Hydrometric data indicate strong interannual changes in Hudson Bay streamflow along with a marked shift in the seasonality of river discharge (Déry and Wood, 2004; Déry et al., 2011). However, it remains unclear whether the subsurface waters of the CIS have also undergone change.
Despite their relevance to circulation and climate, the CIS have been grossly undersampled: due to their vast expanse, harsh conditions, and remote location, few campaigns have been dedicated to continuously measuring their subsurface waters; even estimates of the bathymetry in this region can show large uncertainties, especially in the more northern reaches of the CIS. Early observational descriptions of circulation patterns and current structures are derived from sparse data (Prinsenberg, 1986b, c; Drinkwater, 1986). More recent data have facilitated more nuanced descriptions, for example, of the spatial structure of the boundary currents and the role of synoptic eddies in transporting fresh water through Hudson Strait (Straneo and Saucier, 2008a; Sutherland et al., 2011) and the mean state and seasonal cycle in the circulation and hydrography in Hudson and James bays (St-Laurent et al., 2012). However, continuous measurements of subsurface properties remain sparse, leaving open basic questions regarding regional ocean behavior on nonseasonal periods longer than a few days.
Concerns over impacts of climate change (Laidler and Gough, 2003) motivate best use of extant data to provide an understanding of anomalous behavior in this region. While a tide gauge situated at Churchill in southwestern Hudson Bay has measured sea level fluctuations since 1940, and the Gravity Recovery and Climate Experiment (GRACE) spacecraft have observed changes in the mass of ocean and ice over the CIS since 2002, only a few studies have made use of these data to understand the nature of variability in the CIS. Based on the Churchill tide gauge and hydrometric data, Gough and Robinson (2000) posit that sea level variations observed at Churchill partly result from local discharge from the Churchill River. Considering GRACE and an atmospheric reanalysis, Piecuch and Ponte (2014) submit that wind setup could effect mass changes in Hudson Bay. However, these hypotheses are based on statistical metrics (correlation coefficients and coefficients of determination), and it remains to test them using a more dynamically rigorous approach.
In this paper, we investigate nonseasonal oceanic behavior in the CIS. We provide an exploration and interpretation of the data from GRACE and the tide-gauge measurements mostly based on a coarse-resolution barotropic model driven by surface wind stress. The remainder of this paper is organized as follows: in Sect. 2, we describe and contrast the observational data; in Sect. 3, we describe the ocean model, comparing it to the available observations as well as output from a higher-resolution ocean/sea-ice model, and then use it to understand the leading mode of nonseasonal behavior of the CIS; in Sect. 4, we summarize and discuss our results.
Since their launch in March 2002, the twin GRACE satellites have been
monitoring the exchange of water mass between the land and the sea
(e.g., Boening et al., 2012). We use monthly ocean bottom pressure
estimates derived from Release-05 GRACE time-variable gravity
coefficients over the period 2003–2013 to study mass variability in
the CIS. The data are taken from the GRACE Tellus server (data version
RL05.DSTvDPC1409) and are processed at the University of Texas Center
for Space Research (Bettadpur, 2012). Postprocessing by Don
P. Chambers (University of South Florida) follows methods described by
Chambers and Bonin (2012). Relevant for our purposes, the data are
smoothed with a 500 km Gaussian filter, which reduces errors with
short wavelengths in the satellite recoveries, but which can also attenuate
the magnitudes of the oceanic signals. Relative to Chambers and
Bonin (2012), updated estimates are used for degree 2 order 0
coefficients (Cheng et al., 2011) and glacial isostatic adjustment
(A et al., 2013). Global spatial-mean values are subtracted from the
ocean mass estimates at each time step. The values are provided on a
regular
Given our interest in nonseasonal behavior, we remove a seasonal cycle from all time series, which we compute by averaging together all January entries, February entries, etc., over 2003–2013 into a 12 month time series. To circumvent difficulties of interpreting the gravity data over the ocean in the presence of large rates of glacial isostatic adjustment over Canada and cryospheric mass loss from Greenland (e.g., Tamisiea et al., 2007; Velicogna, 2009; Rignot et al., 2011), linear trends are removed from all time series using least squares.
A tide gauge maintained by the Canadian Hydrographic Service has
measured relative sea level at the mouth of the Churchill River in
Churchill, Manitoba (Fig. 1), for more than 70
A set of adjustments is applied to the tide-gauge data. As with the
gravimetric estimates, a seasonal cycle and a linear trend are removed.
To focus on ocean dynamical signals, we also
subtract from the tide-gauge record a global mean sea level time series based on altimetry data
(Ablain et al., 2009) as well as the inverted barometer response
based on monthly Interim European Centre for Medium-Range Weather
Forecasts Reanalysis (ERA-Interim) (Dee et al., 2011) mean sea level
pressure fields and Eq. (1) of Ponte (2006). We note that removal of
the global mean and inverse barometer signals reduces the detrended
monthly variance in the tide-gauge sea level time series over
2003–2013 by 40
One concern of using GRACE ocean bottom pressure estimates over the
CIS is that they might be contaminated by transient terrestrial water
storage from surrounding watersheds. Root mean square values of
monthly water storage estimated by a land hydrology model can be
5–10
To determine whether the ocean bottom pressure estimates are polluted
by leakage of terrestrial water storage, we consider nonseasonal time
series of GRACE bottom pressure averaged over the CIS alongside GRACE
water storage GRACE terrestrial water storage estimates were
processed at the University of Texas Center for Space Research and postprocessed by
Sean Swenson (National Center for Atmospheric Research). The gridded
estimates, provided on a The Hudson Bay drainage basin has been defined as the union
of the Hudson Bay seaboard and Nelson River basins, determined
based on watersheds data provided by the Commission for Environmental
Cooperation (
As an additional check on the GRACE ocean data quality, and also to
give physical insight, we compare bottom pressure estimates averaged
over the CIS to sea level observed at the Churchill tide gauge
(Fig. 2b). Notwithstanding the difference in amplitude, which probably
partly reflects attenuation of the true ocean bottom pressure signal
by the spatial averaging involved in the postprocessing (see
Sect. 2.1.1), there is close correspondence between the two curves
(Fig. 2b). The overall correlation coefficient between the nonseasonal
sea level and bottom pressure (0.58) is statistically significant at
the 95
The main drivers of mass redistribution in a homogeneous ocean are
surface loading and wind stress (Hughes, 2008). In the case of
synoptic timescales (i.e., periods of a few days), surface loading by
barometric pressure can drive a relatively large non-equilibrium sea
level response on the continental shelf (standard deviations
To assess this expectation, we consider numerical solutions from the
Massachusetts Institute of Technology general circulation model
(MITgcm; Marshall et al., 1997). The setup solves the primitive equations on
a coarse-resolution (
This framework is admittedly simple; many effects (e.g., mesoscale eddies, sea ice, river runoff, wind stress over the Arctic Ocean) have been precluded. On account of the coarse grid resolution, we do not resolve the topographic gyres and current separations induced by bathymetry in Hudson Bay discussed by Wang et al. (1994) in the context of a finer-resolution model. Due to the lack of ocean stratification, we do not capture the baroclinic boundary current in Hudson and James bays discussed by St-Laurent et al. (2012) among others. Given the lack of an interactive sea-ice model, we do not simulate any role played by sea ice in mediating the transfer of momentum between the atmosphere and the ocean (St-Laurent et al., 2011). However, to the extent that our model agrees with the data of interest, we can conclude that any omitted physics is unimportant in the present context.
Before comparing it to the GRACE ocean data, we smooth the model bottom
pressure using the same 500 km spatial filter used in the GRACE
postprocessing (Chambers and Bonin, 2012) and then average over the
CIS, interpolating onto the GRACE ocean grid. The statistically significant correlation coefficient between the
model and data bottom pressure is 0.69, with the model curve explaining
47
For comparing against the tide-gauge observations, we consider model
sea level from the grid cell whose centroid is the closest to the
Churchill site (Fig. 3b). The model time series roughly reproduces the
gross features of the observed sea level curve. However, the model
underestimates the data amplitudes: standard deviations of the observed and simulated
signals are 5.7 and 3.0
To gauge the influence of horizontal resolution and missing physics (ocean
stratification, sea-ice dynamics,
etc.) on the correspondence between the data and our model,
we also consider a higher-resolution ocean/sea-ice model. Monthly sea
level and bottom pressure from the Estimating the Circulation
and Climate of the Ocean Phase-II (ECCO2; Menemenlis et al., 2005)
cube92 solution were obtained for 2003–2012.
This estimate of the ocean/sea-ice state, generated by the MITgcm
coupled with a fully interactive sea-ice model, is defined
on a global “cubed sphere” topology, with a nominal horizontal resolution
of
Comparable ECCO2 curves for nonseasonal ocean bottom pressure averaged over the CIS and sea level at the Churchill tide-gauge location are overlaid in Fig. 3a and b, respectively. Perhaps surprisingly, for the common period 2003–2012, our simple barotropic model simulation performs as well as (if not better than) the ECCO2 cube92 solution in reproducing the data. While the ECCO2 solution explains 36 and 54 % of the variances in the GRACE and tide-gauge time series, respectively, the barotropic simulation explains 50 and 58 % of the respective observed variances (Fig. 3).
Results in Fig. 3 show that our simple dynamical framework is sufficient to capture the lowest-order monthly nonseasonal behavior observed in the CIS across a range of spatial scales, and imply that the influences of ocean stratification, sea ice, and surface fluxes of mass and buoyancy are higher order. The realism of the model encourages its further exploration to more fully understand the nonseasonal variability in the CIS. In what follows, we focus on sea level, but note that, since sea level and bottom pressure are equivalent quantities in a barotropic ocean, the results also apply to bottom pressure.
The relationship between observed sea level and bottom pressure changes (Fig. 2b) led us to hypothesize the existence of a bay-wide depth-independent oscillation. To determine more rigorously whether there is in fact such a wind-driven nonseasonal barotropic fluctuation of the CIS, we perform an empirical orthogonal function (EOF) analysis, which boils down to solving for the eigenvalues and eigenvectors of the covariance matrix of a scalar that varies in space and time (von Storch and Zwiers, 1999).
Leading empirical orthogonal function (EOF) of nonseasonal sea level
determined from the barotropic model in the Canadian inland seas.
The leading eigenvector of simulated sea level over the CIS shows
a single-signed spatial structure (Fig. 4a), but values are larger
over the deep interior region and smaller in the shallow boundary
area. The mode could be caused by a combination of local and remote
effects, perhaps with remote mechanisms forcing water into and out of
the domain and local drivers acting to redistribute mass within the
domain. This leading empirical mode explains 69.4
The leading expansion coefficients show variability across all
accessible timescales, and a dominant period is not visually obvious
(Fig. 4b), while an estimate of the associated power spectral density
is slightly red in nature (not shown). We observe that the
expansion-coefficient time series is essentially equivalent to the
bay-mean sea level signal: the correlation coefficient between the two
curves is
Looking further afield, we compute correlation coefficients between the expansion coefficients (Fig. 4b) and nonseasonal sea level time series at each model grid cell over the global ocean (not shown). A statistically significant in-phase relationship is apparent between fluctuations in the CIS, Baffin Bay, and the Mediterranean Sea, while a significant out-of-phase relationship is evident between the expansion coefficients and variations over the midlatitude North Atlantic and along parts of the North Sea. These relationships are similar to those suggested by Piecuch and Ponte (2014), who computed correlations between the leading mode of nonseasonal bottom pressure variability over the midlatitude North Atlantic and anomalous bottom pressure elsewhere based on GRACE data (e.g., their Fig. 3a).
Assuming geostrophy, fluctuations in sea level are proportional to variations in the barotropic stream function, and therefore this mode can be physically interpreted in terms of ocean circulation changes. For example, the domed shape of the eigenvector in Hudson Bay (Fig. 4a) suggests anomalous anticyclonic (cyclonic) circulation when the expansion coefficients are positive (negative). Given the cyclonic sense of Hudson Bay's mean circulation (e.g., St-Laurent et al., 2012), this mode thus corresponds to spin-up and -down of the barotropic component of the mean circulation in Hudson Bay roughly during positive and negative NAO periods, respectively.
Model results in Fig. 4 corroborate our earlier suspicion based on data that there exists a wind-driven barotropic fluctuation of the CIS that explains most of the nonseasonal sea level variance across a range of spatial scales. What is more, this mode of oscillation is correlated with the NAO, implying that some of the anomalous sea level behavior in the CIS is tied to climate variability more broadly over the North Atlantic sector, consistent with suggestions made by Gough and Robinson (2000). It remains to be determined, however, what the important regions of wind forcing are, and what the relevant ocean dynamics are. We turn to these questions in the next section.
Seeing as the leading expansion coefficients are correlated with the NAO
(Fig. 4b), we now consider the structure of nonseasonal wind stress forcing
over the northern North Atlantic sector (Fig. 5). Standard deviations of
nonseasonal wind stress are on the order of a few hundredths of
a N
Standard deviations of nonseasonal
To suggest relationships between wind stress over the northern North Atlantic and sea level in the CIS, we compute correlations between the expansion coefficients (Fig. 4b) and nonseasonal zonal and meridional wind stress (Fig. 5). Zonal winds over a broad swath extending from Hudson Bay and the Labrador Sea across the northern North Atlantic Ocean to the North, Norwegian and Barents seas are significantly negatively correlated with sea levels over the CIS (Fig. 6a). Sea levels over the CIS are significantly negatively correlated with meridional winds over eastern Hudson Bay and the western Labrador Sea as well as from the northeastern North Atlantic to the Norwegian Sea, while positive correlations are seen off the southwestern coast of Greenland (Fig. 6b). Given the correlation between the expansion coefficients and the NAO (Fig. 4b), these correlation patterns are consistent with wind stress anomalies associated with the NAO; for example, anomalous westerly winds occur during positive phases of the NAO (e.g., Marshall et al., 2001), when sea levels over the CIS are anomalously negative (Fig. 4b).
Correlation coefficients between the expansion coefficients of the
leading empirical orthogonal function (Fig. 4b) and nonseasonal
The strongest correlations between the expansion coefficients and zonal winds occur over Hudson Strait (Fig. 6a), suggesting that the sea level in the CIS might be influenced by wind stress variations over adjacent regions. For example, wind stress along Hudson Strait directed towards the CIS would force flow into the CIS until dynamic balance is established between the along-strait sea level gradient and wind stress, i.e., a wind setup (e.g., Csanady, 1981); in the absence of additional boundary forcing, the CIS would undergo barotropic adjustment in response to the mass inflow, likely resulting in a horizontally uniform sea level increase. (An analogous scenario can be entertained for winds over Hudson Strait directed away from the CIS.)
To establish what the influence of wind stress over Hudson Strait is, we perform another numerical simulation based on the model framework described previously (Sect. 3.1) by setting the surface wind stress to zero everywhere except over Hudson Strait (see Fig. 5), all else (e.g., the time period of integration) being equal. This Hudson Strait winds experiment captures some of the variability in the CIS from the baseline experiment examined in Fig. 4. Namely, winds over Hudson Strait effect bay-wide changes in sea level over the CIS, and the correlation between the leading sea level expansion coefficients from the baseline and Hudson Strait winds experiments is 0.58 (Fig. 7), demonstrating that Hudson Strait winds are important to variability in the region.
But there are also disagreements between behaviors generated by the two experiments. Wind stress over Hudson Strait effects sea level changes over the CIS whose amplitudes are horizontally uniform, implying that this experiment lacks important local effects (e.g., winds over the CIS) responsible for generating the spatially varying amplitudes that are manifested in the baseline experiment. What is more, the bay-mean sea level changes from the Hudson Strait winds experiment are smaller than those from the baseline experiment (cf. amplitudes in Figs. 4a and 7a), indicating that wind driving in remote regions (e.g., over the North Atlantic Ocean) is also important in forcing water into and out of the CIS.
As in Fig. 4 but shown for the experiment driven only by wind stress
over Hudson Strait. In
To more completely account for the behavior from the baseline experiment,
another simulation is performed over the same time period by driving the
model with wind stress only over regions where the correlation coefficient
between wind stress and baseline expansion coefficients is statistically
significant (see the colored regions in Fig. 6). This correlated winds
experiment generates variability in the CIS that is extremely close to the
behavior produced by the baseline simulation (Fig. 8), explaining
95
As in Fig. 4 but shown for the experiment driven only by wind stress
over regions of statistically significant correlation coefficients shown in
Fig. 6. In
The remote surface forcing is potentially communicated to the CIS by a variety of physical mechanisms that can influence sea level in and around Hudson Strait. We speculate that these could include, for example, coastally trapped propagating waves forced over shallow areas (e.g., around Cape Farewell, Greenland), and planetary and topographic Rossby waves forced by wind curl patterns over the deep ocean.
Finally, to infer what the relevant local dynamics are producing the spatial structure of the variability inside the bay (Fig. 4a), we run a suite of experiments treating the western entrance of Hudson Strait (surrounding Mill, Nottingham, and Salisbury islands) as an open boundary, with flow into and out of the CIS (i.e., bay-mean sea level changes) from the baseline experiment specified a priori. Simulations are identical in all respects other than that we choose to either variously “turn off” one of the terms in the model's momentum equations (e.g., advection, Coriolis, surface forcing, pressure gradient) or change the topography of the CIS.
Turning off winds over the CIS results in a leading mode of sea level
variability whose spatial structure is horizontally uniform, similar to the
Hudson Strait winds experiment case (Fig. 7a). In contrast, removal of
quadratic bottom drag or nonlinear terms from the model dynamics has no
perceptible effect, and the variable spatial structure from the baseline
experiment is recovered (cf. Fig. 4a). Finally, setting the depth to
a constant value (of about 250
Using satellite gravimetry, a tide gauge, and a barotropic model, we identified a wind-driven nonseasonal barotropic fluctuation of the Canadian inland seas (CIS) that is correlated with the NAO (Figs. 2–6). Anomalous inflows and outflows, which are reflected in spatially averaged changes in sea level and bottom pressure over the CIS, are driven by wind stress over Hudson Strait (Fig. 7), probably through a wind setup, and the northern North Atlantic Ocean (Fig. 8), possibly communicated by means of wave mechanisms. Anomalous mass redistribution within the CIS, which relates to changes in the depth-mean circulation, is governed by the linear ocean response to more local wind stress variations under the joint influences of rotation, gravity, and variable bottom topography. We observe that, while it suggests broad regions of wind forcing over the northern North Atlantic potentially contributing to CIS variability (Fig. 6), our analysis does not unambiguously pinpoint which forcing regions are most relevant – in fact, it could be that forcing over just one small area of the northern North Atlantic is the main driver. An adjoint model – capable of quantifying the sensitivity of a particular modeled quantity at a specific place and time to all model inputs and states at preceding times – could be used to shed more light on which regions of wind forcing most influence the CIS, as is done by Fukumori et al. (2007) to elucidate a near-uniform basin-wide sea level fluctuation of the Mediterranean Sea, but such an analysis is beyond our scope and deferred to future study.
Our findings complement previous modeling work on Hudson Bay (Wang et al., 1994; Saucier and Dionne, 1998; Saucier et al., 2004; St-Laurent, 2011, 2012). Whereas past studies tend to regard Hudson Strait as an open boundary, specifying inflow and outflow at the outset, our forcing experiments highlight wind stress changes over adjacent and remote areas responsible for driving mean sea level changes in the CIS (Figs. 7 and 8), emphasizing the need for accurate estimates of atmospheric variability for modeling the circulation in the CIS. Our ability to reproduce qualitatively the data (Fig. 3) without recourse to ice–ocean interactions accords with St-Laurent et al. (2011), who find that ice plays only a small role in mediating seasonal momentum transfer between air and sea, reflecting the loose, mobile nature of sea ice in Hudson Bay. Similar to Wang et al. (1994), we find that the effects of variable bottom topography, which are ignored in the flat-bottomed conceptual model of Hudson and James bays due to St-Laurent et al. (2012), are an important determinant of circulation changes in the CIS. (We note that St-Laurent et al. (2012) recover some of the effects of topographic steering by assuming that there is a strong current in the boundary region.)
Investigating all periods from monthly data between 1974 and 1994, and
based on a correlation analysis, Gough and Robinson (2000) conclude
that 43
One of the challenges of using GRACE data over the ocean in near-coastal regimes is separating oceanic signals from non-oceanic noise (Chambers and Schröter, 2011). In the case of the CIS, this is an especially difficult task, given the large rates of mass loss from the Greenland ice sheet, ongoing postglacial rebound over Canada, and any terrestrial water storage tied to changes in river discharge. Our results (Figs. 2 and 3) suggest that meaningful estimates of nonseasonal ocean bottom pressure behavior can be derived from GRACE retrievals over the CIS.
Support came from NASA (GRACE grant NNX12AJ93G) and NSF (grant
OCE-0961507). Helpful comments and useful suggestions from the editor
and two anonymous reviewers are gratefully acknowledged. GRACE ocean and land data were
processed by Don P. Chambers and Sean Swenson, respectively,
supported by the NASA MEaSUREs Program, and are available at