Auxiliary material for
Mean Sea Level Variability along the Northeast American Atlantic Coast
and the Roles of the Wind and the Overturning Circulation
Philip L. Woodworth 1, Miguel Á. Morales Maqueda 1, Vassil M. Roussenov 2,
Richard G. Williams 2 and Chris W. Hughes 2,1
(1) National Oceanography Centre, Joseph Proudman Building, 6 Brownlow Street,
Liverpool L3 5DA, United Kingdom
(2) School of Environmental Sciences, University of Liverpool, Liverpool L69 3GP, United
Kingdom
Introduction
This Auxiliary Material provides additional information to be read alongside the main part of the
paper.
Standard Deviation Model Sea Level
Figure S1 shows the standard deviation of detrended annual mean values of sea level from the
higher resolution version of the LHC model for the full model run 1950-2009. A corresponding
figure for 1993-2009 for comparison to altimeter data is given in Figure 5.
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Bermuda Mean Sea Level
Figure S2 demonstrates that the Liverpool/Hadley Centre (LHC) model works well at Bermuda
in the centre of the gyre. It shows the observed MSL record (black points) detrended over the
period 1950-2009 and corrected for the inverse barometer effect and the equilibrium lunar nodal
tide. Other points are from the LHC model higher resolution version (red), 1-degree version
(light blue) and 1-degree version without wind forcing (green), similarly detrended.
Comparison of secular trends simulated by the LHC model to those obtained from altimeter and
thermosteric data
Figure S3 shows trends in North Atlantic sea level during 1993-2009 from (a) the higher
resolution version of the LHC model and (b) satellite altimetry, and (c) trend in thermosteric sea
level relative to the 700m reference level. Area weighted average values of -0.17, 2.50 and 1.67
mm/year for the North Atlantic region (70-10° W, 10-70° N) have been removed from plots (a-c)
respectively. Contours are shown for 0, ±1 and ±2 mm/year.
The figure is provided to show that the LHC model can simulate adequately the spatial patterns
of trends in North Atlantic altimetric sea level and thermosteric sea level during 1993-2009,
2009 being the last year of model run. (‘Thermosteric’ refers to density-related change in sea
level resulting from change in temperature; the data set was provided by the National
Oceanographic Data Center, www.nodc.noaa.gov). The linear trend in MSL in the North Atlantic
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observed by altimetry is known to correspond closely to that of thermosteric sea level, together
with a more spatially-uniform trend due to change in ocean mass [Meyssignac and Cazenave,
2012]. The area-weighted trend, which has been removed from the maps, is larger for the
altimetry than for the thermosteric sea level because the former contains contributions from
ocean mass change, while the latter is relative to the 700 m reference level only. The areaweighted trend for the model is close to zero owing to its volume-conserving (Boussinesq)
formulation.
Other ocean models used in the analysis
The main ocean model that we used in this analysis was the Liverpool/Hadley Centre (LHC)
model. However, we also investigated other ocean models, including the Nucleus for European
Modelling of the Ocean (NEMO) models [e.g. Madec, 2008; Blaker et al., 2012; Deshayes et al.,
2013]. Data from a number of runs at 1/4 and 1/12° resolution are available using different
forcing fields (see Table 1 of Deshayes et al. [2013]). In our case, most use was made of the 1/4°
run spanning 1958-2007, although owing to spin-up transient effects we use data for 1963onwards only. The model is known to have drifts, particularly in the global salinity field due to
deficiencies in fresh water forcing. The 1/12° model run spans 1988-2010.
We also used a shorter run (1988-2004) of the 1/12° version of the Ocean Circulation and
Climate Advanced Modelling Project (OCCAM) ocean circulation model [Webb et al., 1997],
together with sea levels provided by a 1975-2004 run of a barotropic (depth averaged) version of
OCCAM on a 1/4° grid [Hughes and Stepanov, 2004]. A modified form of NCEP wind forcing
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was used for the former [Marsh et al., 2009], with European Centre for Medium-Range Weather
Forecasts (ECMWF) reanalysis (ERA-40) winds employed for the latter.
These additional ocean models investigated provide contrasting results to those for the LHC
model discussed in the main text. The NEMO 1/4° model demonstrates similar values of
correlation and gain over the shelf to those of the LHC model. It also has a minimum in
variability at the shelf edge, similar to the LHC model, and it has a similar level of agreement
with the tide gauges although the model run spans the shorter period 1963-2007 only. Its pattern
of variability in the Gulf Stream gyre is closer to that of the altimetry than for the LHC model
because the NEMO simulation allows a fully resolved eddy field to develop (see the main text).
The 1/12° version of NEMO provides less plausible findings, with little or no shelf edge
variability minimum, if one accepts the pattern of variability from altimetry as being correct.
OCCAM presents relatively low variability of 2 cm or less on the shelf (consistent with Bingham
and Hughes [2009]) and no marked shelf edge minimum. The barotropic version of OCCAM,
being essentially a storm surge model and which we have included for completeness, has an
expected low variability of only ~5 mm on the shelf.
Quadratic coefficients from the 20CR project
Figure S4 shows quadratic coefficients from the 20CR project over the period 1871-2012, as
discussed in the text. (Units are 10-4 N/m2 per year2.)
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Coherence of wind stress in the western North Atlantic
Figure S5 (a) shows correlations between the zonal component of surface wind stress at (74°W,
40.5°N), which is the point of the NCEP reanalysis closest to Sandy Hook, and the zonal
component of surface wind stress elsewhere in the North Atlantic. The correlations have been
calculated using annual mean zonal wind stresses for the period 1948-2013 (first and last years
included) from the NCEP reanalysis. The white contour encompasses the area within which
correlations are greater than 0.87 (i.e. more than 75% of the zonal wind stress variance within the
contour is explained by zonal wind stress variability at Sandy Hook). (b) As (a) but for the
meridional component of the surface wind stress.
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Auxiliary Material References
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Pole de modélisation. Institut Pierre Simon Laplace, Technical Report 27, ISSN No. 1288-1619.
Blaker, A.T., J.J-M. Hirschi, B. Sinha, B. de Cuevas, S. Alderson, A. Coward, and G. Madec
(2012), Large near-inertial oscillations of the Atlantic meridional overturning circulation, Ocean
Modelling, 42, 50-56, doi:10.1016/j.ocemod.2011.11.008.
Deshayes, J., A.-M. Tréguier, B. Barnier, A. Lecointre, J. Le Sommer, J.-M. Molines, T.
Penduff, R. Bourdallé-Badie, Y. Drillet, G. Garric, R. Benshila, G. Madec, A. Biastoch, C.W.
Böning, M. Scheinert, A.C. Coward, and J.J.-M. Hirschi (2013), Oceanic hindcast simulations at
high resolution suggest that the Atlantic MOC is bistable, Geophys. Res. Lett., 40, 3069-3073,
doi:10.1002/grl.50534.
Hughes, C.W., and V.N. Stepanov (2004), Ocean dynamics associated with rapid J2 fluctuations:
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Figure S1
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Figure S2
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Figure S3(a)
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Figure S3(b)
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Figure S3(c)
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Figure S4
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Figure S5
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