Auxiliary Material
Text S1:
Salinity structure of the Waquoit Bay coastal aquifer
Cross-sectional transects of the salinity structure of the Waquoit Bay coastal
aquifer have been measured numerous times (Fig. S1). These transects were completed
over ~10 days, at various stages of the tide and in various wave conditions. While there is
some variability in the structure/extent of the upper mixing zone, which is driven by
short-time scale tides and waves, the slope of the mixing interface is stable across the
three years (slope = 0.29±0.01, April 2003, June 2004 and June 2005). Locations of
samples are noted in black squares, while white squares mark the position of the
monitoring well used for the time series, which is approximately located at mean sea
level. The time series monitoring wells are within the stable region, thus salinity
oscillations during the time series reflect lateral movement of the deep mixing zone, not
shifts near the upper mixing zone where the interface has the highest slope. Note
horizontal distance in Fig. S1 is measured from the coastal well CCC1, the location of the
upland head in the model simulations (Fig. 1).
In addition, the salinity of the wells was monitored over a falling tide (October 15,
2004), to determine if salinity of the deep mixing zone varied across a tidal cycle (Fig.
S2). The salinity was stable despite a 0.8 m drop in sea level. Based on this evidence, we
expect the position of the deep mixing zone to respond to changes in the hydraulic
gradient on time scales longer than hours and to processes that are sustained on the order
of days to weeks to months. Thus, tidal components and wave conditions that lead to sea
level variability on longer time scales (i.e. the annual tidal components or sustained
winter storms), may impact the position of the interface, since they likely impact mean
sea level on this time scale.
Groundwater levels, sea level anomaly and aquifer salinity
Seasonal oscillations in inland groundwater levels (i.e. USGS well 10 km from
MSL) driven by groundwater recharge have been proposed to be the dominant forcing of
the coastal aquifer hydraulic gradient [Anderson and Emanuel, 2008, 2010; Michael et
al., 2005]. In this conceptual model, seasonal variability in precipitation and
evapotranspiration rates result in seasonally variable aquifer recharge, with a time lag in
aquifer head response due to 1) time for recharge to percolate into the aquifer, and/or 2)
time for landward recharge to equilibrate with groundwater discharge at the coast
[Michael et al., 2005]. In the case of the Waquoit Bay coastal aquifer, this model predicts
seaward movement of the interface and an increase in terrestrial SGD during
spring/summer following the winter peak in recharge. Conversely, following peak
summer evapotranspiration rates, the groundwater level would correspondingly decrease
and the interface would move landward during fall and winter.
In support of this conceptual model, both field data and numerical modeling at
Waquoit Bay have demonstrated that there is a time lag between peak recharge and peak
inland aquifer levels of approximately three to five months [Michael et al., 2005]. Direct
measurements of SGD with manual seepage meters in summer (June 2002 and 2003) and
via in situ hydraulic gradients in winter (February 2004) indicated greater SGD in
summer [Michael, 2004; Michael et al., 2003, 2005], but remain inconclusive since sea
ice cover during the winter prevented measurement of hydraulic gradients in the region
where the greatest groundwater discharge had been observed in the summer. It is
important to note that this conceptual model, which has been used previously to design
numerical models of seasonal coastal aquifer dynamics, also assumes either 1) sea level
varies symmetrically about mean sea level (MSL) such that longer-term MSL does not
change over time [Lu and Luo, 2010; Michael et al., 2005], or 2) seasonal sea level
variations serve to reinforce the seasonal pattern delineated above.
Here we calculate the head gradient according to the procedure outlined in Post et
al. [2007], since consideration must be given to the variable density ground and bay
water. We utilized cross correlation analysis to better understand how the various time
series were related. All time series were first set to a specific sampling interval (15 days
for the head gradient comparison between sea level and head gradient (Fig. S5a) and 30
days for the comparison between salinity and sea level, USGS and CCC1 groundwater
levels (Figs. S5b-c, S6 and S7)). The data was then standardized to a mean of 0 and
standard deviation of 1. Each time series was first auto correlated to determine the
effective sample number according to:
N* 
Nt
T
where N is the number of measurements, Δt is the time interval between points and T is

the integral time scale of the data series, given by:
T C
0 1
y
N nk1
 t 2[C (n
y
k
 t) Cy (nk )]
k 0
where Cy is the autocovariogram, normalized to the autocovariance at zero lag, of the

time series and nk is the kth lag of n [Glover et al., 2011]. The Matlab xcorr function was
used to perform the analysis. In the cross correlation analysis, one variable was
considered independent and one was dependent. For example, in Fig. S5a, sea level is the
independent variable while head gradient is dependent, since sea level can influence head
gradient, but head gradient will not alter sea level. Thus, positive lags indicate that the
dependent value occurs after a change in the independent value, i.e. the head gradient
response is lagged in time compared to sea level. Framed in this context, a negative lag
does not have a physically consistent meaning and is not shown. Only lags out to N/4 are
shown for each analysis. The 95% confidence interval was calculated as:
r 
1.96
N*  n  3
where r is the correlation, 1.96 is the Z-score for a 95% confidence interval, N* is the

number of independent measurements, and n is the number of lags [Glover et al., 2011].
This confidence interval is noted in all cross correlation plots as a dashed line. Note that
this type of analysis may show high correlations of opposite sign that are lagged half of
the period of the correlation. For instance, if two time series are in phase at 0 lag and both
oscillate with a seasonal signal, they likely have a negative correlation when one is
lagged 6 months in relation to the other.
The monthly groundwater level 3 km inland from Waquoit Bay (USGS
monitoring well #413525070291904) showed an approximately seasonal oscillation in
groundwater level of ~1 m, however the timing of the peak in groundwater levels was not
constant, ranging from late spring (2004 to 2008) to fall (2008 to 2010, Fig. S3a),
suggesting that the seasonality of groundwater levels on Cape Cod may not be primarily
controlled by evapotranspiration, as previously proposed, but also by precipitation. For a
portion of the time series (Jan. 2005 to June 2007), groundwater levels directly at the
coast (CCC1 and CCC2) were dampened (~10 cm) (Fig. S3b). The cross correlation
analysis revealed that coastal groundwater levels are correlated to sea level (r=0.66) with
a lag of 15 days and inland (USGS) groundwater levels (r=0.76) at a lag of 45 days (Fig.
S6).
A similar cross correlation of the time series salinity data with 1) head gradient, 2)
sea level, 3) coastal (CCC1) groundwater level and 4) inland (USGS) groundwater levels
revealed the highest correlation between sea level (r=0.56) and head gradient (r=-0.49) at
0 lag (Fig. S7). There was no significant correlation between salinity and coastal
groundwater head, while the inland groundwater head was correlated to salinity with a
two month lag (r=-0.54). Thus, while the previously proposed conceptual model of
Michael et al. (2005) agrees with our analysis of coastal and inland groundwater levels,
dynamic movement of the saltwater interface appears to be dominated by seasonal sea
level oscillations as discussed in depth in the main text.
References:
Anderson, W. P., and R. E. Emanuel (2008), Effect of interannual and interdecadal
climate oscillations on groundwater in North Carolina, Geophys. Res. Lett., 35(23), doi:
10.1029/2008gl036054.
Anderson, W. P., and R. E. Emanuel (2010), Effect of interannual climate oscillations on
rates of submarine groundwater discharge, Water Resour. Res., 46, doi:
10.1029/2009wr008212.
Glover, D.M., Jenkins, W.J. and Doney, S.C. 2011. Modeling Methods for Marine
Science. Cambridge University Press. ISBN-13: 978-0521867832. pp. 571.
Michael, H. A., J. S. Lubetsky, and C. F. Harvey (2003), Characterizing submarine
groundwater discharge: a seepage meter study in Waquoit Bay, Massachusetts, Geophys.
Res. Lett., 30(6), doi:10.1029/2002gl016000.
Michael, H. A. (2004), Seasonal dynamics in coastal aquifers: investigations of
submarine groundwater discharge through field measurements and numerical models,
PhD thesis, Massachusetts Institute of Technology.
Michael, H. A., A. E. Mulligan, and C. F. Harvey (2005), Seasonal oscillations in water
exchange between aquifers and the coastal ocean, Nature, 436(7054), 1145-1148.
Lu, C. H., and J. Luo (2010), Dynamics of freshwater-seawater mixing zone development
in dual-domain formations, Water Resour. Res., 46, doi:10.1029/2010wr009344.
Post, V., H. Kooi and C. Simmons (2007), Using hydraulic head measurements in
variable-density ground water flow analyses, Ground Water, 45, doi:10.1111/j.17456584.2007.00339.x.
Supplementary Figure Captions
Fig. S1: Salinity structure of the coastal aquifer in April 2003, June 2004 and June 2005.
Fig. S2: a) Tidal time series of salinity at monitoring wells and b) 6-minute Woods Hole
mean sea level during the same time period.
Fig. S3: Relationship between coastal aquifer salinity and inland and coastal groundwater
levels and sea level.
Fig. S4: a) Mean sea level anomaly along the northeast US coast Jan. 2004 to May 2011
and b.) Woods Hole, MA predicted sea level due to the solar annual tidal component and
measured sea level.
Fig. S5: Cross correlation analysis of head gradient and a) sea level, b) CCC1 coastal (46
m from MSL) groundwater levels and c) USGS inland (10 km from MSL) groundwater
levels. 95% confidence intervals are shown in dashed lines.
Fig. S6: Cross correlation analysis for coastal (46 m from MSL) groundwater levels and
a) inland (USGS, 10 km from MSL) groundwater and b) MSL. 95% confidence intervals
are shown in dashed lines.
Fig. S7: Cross correlation analysis for salinity and a) head gradient between CCC1 and
MSL, b) sea level, c) coastal CCC1 groundwater levels and d) inland USGS groundwater
levels. 95% confidence intervals are shown in dashed lines.
Fig. S8: Mean sea level anomaly from Woods Hole, MA, and three-month running mean
NAO index from a) Jan. 1980 to Oct. 2011 and b) Jan. 2004 to Oct. 2011, and c) cross
correlation between sea level and NAO. 95% confidence intervals are shown in dashed
lines.