## 1. Introduction

Studying the spatial patterns, time variability, and forcing factors for subtidal exchange is central to understanding estuaries. Along- and across-estuary subtidal exchange influences physical water properties (e.g., temperature and salinity), biochemical properties (e.g., dissolved oxygen), cycling of nutrients, and contaminant distribution. The nature of subtidal exchange varies among estuaries. This study investigates subtidal exchange near the mouth of Long Island Sound (LIS), a major estuary on the U.S. East Coast located between Connecticut and New York. A recent review of the physical oceanography of LIS states that “much remains to be learned about the flow and rates of exchange of materials between the Sound and adjacent waters” (O’Donnell et al. 2014, p. 84). It is important to study how riverine freshwater and salt are transported out of and into LIS in order to better understand how the terrestrial and oceanic waters interact in this large estuary.

The main research questions of this observational and modeling study are as follows: 1) what is the spatial structure of the tidal-averaged velocity and salinity fields in eastern LIS, 2) how do these fields and subtidal fluxes of freshwater and salt vary over time, and 3) how is the temporal variability related to tidal, river, and wind forcing? This study focuses on an eastern LIS observational cross-estuary transect; it is the transect closest to the mouth that does not include island passes. The paper concentrates mostly on low wind regimes with different tidal and river discharge conditions, since Whitney and Codiga (2011) studied the response to wind events. Background on LIS, prior research, and analytical scalings for exchange-dominated estuaries (MacCready and Geyer 2010) are described in the next section. Section 4 describes the main features of the subtidal salinity and velocity fields, observations and corresponding model results, salinity and velocity fields for different tidal and river discharge forcing regimes, and exchange and net fluxes of freshwater and salt. In section 5, results are compared to the analytical scalings (MacCready and Geyer 2010), multivariate regressions are calculated to quantitatively assess the relative influence of each forcing (tides, discharge, and winds), and the net freshwater and salt fluxes are decomposed following the approach of Lerczak et al. (2006). In section 6, LIS results are placed in context with prior results for LIS and findings from other estuaries. The model results for exchange flux also are compared to observation-based values from eastern LIS (Codiga and Aurin 2007) and the net salt flux decomposition is discussed in light of prior estimates (Gay et al. 2004) and flux decompositions from other estuaries. Major finding are summarized in the conclusions (section 7).

## 2. Background

LIS is an example of a large (168 km) and wide (19-km average width) macrotidal estuary with significant riverine freshwater inputs. The tides are amplified because the estuary is resonant for semidiurnal lunar tides (Redfield 1950; Wong 1991). Tidal currents exceed 1 m s^{−1} in the eastern LIS and are sheared throughout much of the water column due to bottom stress (O’Donnell et al. 2014). Thus, tidal shear–driven mixing can be strong (Bowman and Esaias 1981). The largest freshwater source is the Connecticut River. It accounts for 72% of the total mean river input (Koppelman et al. 1976) and enters near the mouth on the Connecticut (northern) coast (Fig. 1). Estuary waters are partially to well mixed (O’Donnell et al. 2014), except for the highly stratified, near-field plumes of the Connecticut (Garvine 1974), Thames (closer to the mouth), and Housatonic (closer to the head) Rivers. LIS belongs in the fjord classification with the Puget Sound and Baltic Sea in the Geyer and MacCready (2014) parameter space, since it has strong tidal mixing relative to stratification (assessed with their mixing parameter) and a small velocity associated with river volume flux relative to the density front propagation speed [assessed with the freshwater Froude number of Geyer (2010)].

LIS is a glacially formed estuary. The connection to the “ocean,” actually Block Island Sound, is through breaks in the glacial moraine that forms the LIS south coast (Fig. 1). The largest and deepest pass, through which the largest fraction of tidal volume flux and exchange occurs, is the race between Plum Island (to the west) and Fishers Island (to the east). There are two other passes: between the mainland Connecticut coast and Fishers Island and between Plum Island and Long Island. Eastern LIS is deep (25-m average depth and 95-m maximum depth) with many scoured areas, while central and western LIS are shallower (17-m average depth) with many thick sediment depositional areas (Lewis and DiGiacomo-Cohen 2000). The overall trend is deepening from head to mouth, though this trend is interrupted by features such as Stratford Shoals and Mattituck Sill (Whitney et al. 2014). The overall width trend is widening from the head through the central LIS and narrowing through the eastern LIS to the mouth, though many headlands and embayments modulate the width (Fig. 1). The complex bathymetry and geometry leads to spatial variations in the tidal and subtidal flow fields. The interaction of the strong tidal currents with these features can lead to tidal rectification that generates subtidal flow. The scales for the gravitational circulation (Wilson 1976) and tidally rectified flow (Ianniello 1981) from two-dimensional models suggest density-driven and tidally driven influences on subtidal flow are the same order of magnitude (Ianniello 1981). The observed subtidal exchange flow along an eastern LIS ferry route has an outward-flowing wedge on the south side overlying and next to a larger inflow area (Codiga and Aurin 2007). The maximum, observed, subtidal, along-estuary velocity is 0.30 m s^{−1} for the transect. The spatial structure of the velocity field shows relatively little seasonal variability. The exchange flow amplitude for summer months is 67% stronger than the winter months; the peak exchange is lagged at least a month after the spring high river discharge (Codiga and Aurin 2007). Salinity and temperature sections were not available for this prior study, so the salt fluxes were not estimated. The average observed inward exchange flux is 2.3 × 10^{4} m^{3} s^{−1} (Codiga and Aurin 2007); this value is close to the 1.8 × 10^{4} m^{3} s^{−1} estimate from Riley (1956) and several others discussed in O’Donnell et al. (2014). In contrast, Gay et al. (2004) inferred a much weaker exchange flux based on inverse modeling results involving salinity and river discharge observations.

Many studies have investigated salt fluxes in estuaries. The net along-estuary salt flux often is decomposed (e.g., Lerczak et al. 2006) into contributions from section-averaged salinity and velocity (associated with uniform flow, often from river inputs), steady shear dispersion (associated with spatially varying exchange flow and spatial salinity variations), and tidal oscillatory salt flux (associated with diffusive processes such as tidal pumping, trapping, and lateral stirring; Fischer et al. 1979; Banas et al. 2004). Gay et al. (2004) concluded that the annual-mean outward salt flux linked to riverine flow and the inward tidal diffusive salt flux for eastern LIS are the same order of magnitude: both contributions are many times larger than the net salt flux from the exchange flow (steady shear dispersion). The Gay et al. (2004) exchange flow estimate, however, is considerably weaker than other observational estimates (e.g., Riley 1956; Codiga and Aurin 2007), as discussed above. Thus, the relative importance of salt flux contributions remains unclear for eastern LIS. For the nearby lower Hudson River, the net salt flux switches from inward during neap tides, when steady shear dispersion (and exchange flow) is strongest, to outward during spring tides, when shear dispersion is smaller and the uniform flow term dominates (Lerczak et al. 2006). In contrast, Ralston et al. (2010) found that tidal oscillatory salt flux is more important than the other contributions for the Merrimack River, especially near the mouth. Aristizabal and Chant (2013) modeled the partially stratified Delaware Bay and found that both the steady shear dispersion and tidal oscillatory salt flux increase from spring to neap tide with the steady shear dispersion dominating for high discharge. Sutherland et al. (2011), by applying the salinity class partitioning of the total exchange flow methodology (MacCready 2011), found inward and outward exchange fluxes increase from neap to spring tides near the Puget Sound mouth. Freshwater volume flux in this system varies with river discharge, the spring–neap cycle, and winds; the usually outward net freshwater flux reverses directions several times each month (Sutherland et al. 2011). The large and wide Delaware Bay and Puget Sound have more similarities to the LIS than either the Hudson or Merrimack Rivers. These examples point to the wide range of possibilities for mechanisms controlling LIS freshwater and salt fluxes.

*u*

_{r}, calculated as the river discharge divided by the entire cross-sectional area. This discharge velocity is scaled by a constant reference internal wave speed

*c*

_{o}that is the square root of the average total water depth and the reduced gravity based on the density difference between river and ocean water (involving a constant ocean salinity

*S*

_{o}). The MacCready and Geyer (2010) scalings for top-to-bottom salinity difference

*δS*and maximum exchange velocity

*u*

_{e}are

*T*

_{adj}:

*h*is total water depth,

*u*

_{tide}is mean tidal current amplitude,

*γ*has a value between 1 and 6 (3 is the theoretical value), and the numeric coefficient arises from the analytical solution and the mixing parameterizations (as in MacCready 2007). Time scale

*T*

_{adj}varies from several days to weeks for large partially stratified estuaries like the Delaware and San Francisco Bays (MacCready 2007). The actual adjustment time is likely to be shorter following discharge increases than after discharge decreases; the asymmetric response is diagnosed in Chen (2015). It is important to note that even though the scalings in Eq. (1) suggest the fully adjusted state depends only on river discharge, significant shorter-term variations can be caused by spring–neap tidal modulation and wind events (MacCready and Geyer 2010).

## 3. Methods

Observations for the eastern LIS cross-estuary transect (Fig. 1) are from surveys conducted onboard the R/V *Weicker* during spring and summer 2010. Temperature and salinity data were collected with an Acrobat towed, undulating vehicle and currents were collected with a ship-mounted RDI 600-kHz acoustic Doppler current profiler. Three surveys that map conditions throughout tidal cycles during low wind conditions are discussed in this paper (Table 1): the 29 April survey during mean tides and mean discharge, the 4 May survey during neap tides and mean discharge, and the 12 August survey toward the end of spring tides and low discharge. Water property and current measurements are averaged into cells 1 km wide and 4 m thick. Tidal-averaged fields are estimated by first removing M_{2} variations via one-constituent harmonic analysis and then temporally averaging these detided results. The surveys have between 6 and 11 crossings to resolve the tidal cycle. Each crossing took approximately 30 min to complete and each survey spanned 1 to 4 days (Table 1). The estuary width (13.5 km) and the operational requirements of the shipboard observations prevented more repeated crossings over a tidal cycle and limited the temporal resolution. The 4 May survey has the fewest crossings and the estimated tidal-averaged fields may not accurately represent true tidal averages; results may be biased toward flood tidal conditions. These observations show the spatial structure of tidal-averaged fields and their variability with tidal amplitude and river discharge conditions.

Observational surveys during 2010, including the survey name, dates, and crossings that resolve the tidal cycle, Connecticut River discharge conditions, and tidal conditions for each survey.

Simulating conditions in LIS is accomplished with the Regional Ocean Modeling System (ROMS; Haidvogel et al. 2008). The model domain includes the tidal reaches of each major river, the entire LIS, and the adjacent continental shelf. The entire domain is shown in Whitney and Codiga (2011); Fig. 1 shows LIS and nearby shelf regions. Horizontal resolution is 0.5 km across estuary and 1 km along estuary. Vertical resolution is 5% of the water column. Whitney and Codiga (2011) provide a detailed description of model domain, resolution, boundary conditions, and settings. Tides are forced along the open boundary with the M_{2}, S_{2}, N_{2}, K_{1}, and O_{1} constituents from the TPXO ocean tidal model (Egbert and Erofeeva 2002). As reported in Whitney and Codiga (2011), the root-mean-square error (RMSE) is 0.07 m s^{−1} (11% of the variance) between depth-averaged tidal current results and observations for eastern LIS ferry data (Codiga and Aurin 2007) and current meters throughout LIS (Bennett et al. 2010).

River discharge is based on 28 USGS stream gauge daily discharge records; values are scaled up by the ratio of total to gauged area for each watershed. River inflow points are at the geographic locations of the estuary heads for the six major rivers (Pawcatuck, Thames, Connecticut, Quinnipiac, Housatonic, and Hudson) and the river mouths of 37 smaller rivers that drain watersheds along the Connecticut coast. River inflows are imposed with 0 salinity (on the practical salinity scale) and an average annual temperature cycle with temperatures ranging from 0° (on February 1) to 25°C (on 1 August) each year; the temperature cycle is based on USGS observations from the Hudson and Connecticut Rivers. The Hudson River is included because some of the Hudson waters enter LIS at its head via the East River connection (actually a tidal strait).

Surface forcing includes hourly wind speed and direction, air temperature, sea level air pressure, and relative humidity from the central LIS buoy maintained and operated by the University of Connecticut (NOAA buoy 44039). Data gaps in the central LIS buoy record are filled with eastern LIS buoy data (NOAA buoy 44060); any remaining gaps are filled with data from New London Ledge Light in eastern LIS (NOAA station LDLC3). Cloud cover data are from the Sikorsky Memorial Airport in Bridgeport, Connecticut (NOAA station KBDR). Short-wave heat flux is calculated using the buoy air temperature observations and cloud cover data and algorithms for clear-sky radiation by Parkinson and Washington (1979), cloud corrections by Reed (1977), and ocean albedo by Payne (1972). Surface wind stress and heat fluxes are calculated in ROMS using COARE 3.0 bulk flux algorithms (Fairall et al. 2003) with the surface observations and calculated short-wave heat flux as inputs.

The model is initialized from rest with homogeneous (5.3°C; 32 salinity) water on 1 January 2008 and evolved over a 5-yr period ending 31 December 2012. The first model year is excluded from analysis in this study. Much of the analysis involves tidal-averaged fields of salinity and currents calculated in ROMS by averaging results over four M_{2} tidal cycles. Model results along the eastern LIS transect (Fig. 1) are compared to shipboard observations during the days corresponding to surveys in 2010 (Tables 1 and 2).

Salinity and along-estuary velocity ranges for observations and corresponding model results during each survey period. Positive velocities are directed outward toward the estuary mouth.

Tidal elevation amplitude at the transect, Connecticut River discharge, and wind stress magnitude are used to identify different forcing regimes (Table 3; Fig. 2). Tidal conditions are split into neap (low; 0.30–0.47 m), mean (0.47–0.63 m), and spring (high; 0.63–0.80 m) amplitudes; the mean tide bin is centered on the mean amplitude value (0.55 m), and each tidal bin is the same width. A running mean (averaging over the previous 30 days) is applied to river discharge for the regime analysis (discussed in section 4c) and multivariate regressions (discussed in section 5b); the guiding principle is the recent discharge history influences salinity and velocity fields in large estuaries. The mean discharge bin (492–883 m^{3} s^{−1}) is centered on the mean discharge value (688 m^{3} s^{−1}) and is one standard deviation wide; the low discharge (<492 m^{3} s^{−1}) and high discharge (>883 m^{3} s^{−1}) groups include everything above and below the mean discharge group, respectively. Low wind conditions include all wind stress magnitudes (averaged over four tidal cycles) less than 0.025 Pa (approximately 4 m s^{−1} wind speed). With this definition, low winds occur during 1156 M_{2} tidal cycles over 4 yr (41% of the time); these conditions are most frequent in spring and summer. Moderate to high wind conditions are more frequent in fall and winter. Whitney and Codiga (2011) describe wind response in LIS and found that along-estuary winds drive downwind flows flanking a deeper central upwind flow (apparent in observations and model results). This study focuses on the response to tidal and river discharge forcing; therefore, low wind regimes are analyzed. Regime-averaged fields for neap, mean, and spring tidal conditions with mean discharge are compared to study tidal influences. Regime-averaged fields for low, mean, and high discharge with mean tidal amplitudes are compared to investigate discharge effects. The importance of wind forcing relative to tidal and discharge forcing is assessed with multivariate regressions in section 5b.

Number of M_{2} tidal cycles in each low wind (<0.025 Pa) forcing regime. The corresponding percentages relative to the total M_{2} tidal cycles in the 4-yr analysis period are listed in parentheses. Moderate to high wind conditions account for the remaining 59% of the analysis period.

Forcing time series: (a) Connecticut River daily discharge (blue) and 30-day running average lagged discharge (black), (b) daily tidal elevation amplitude at the main transect, and (c) wind stress magnitude. Black dashed horizontal lines indicate thresholds for determining forcing regimes (described in section 3 and Table 3). Black vertical lines indicate the approximate timing of observational surveys (Table 1).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Forcing time series: (a) Connecticut River daily discharge (blue) and 30-day running average lagged discharge (black), (b) daily tidal elevation amplitude at the main transect, and (c) wind stress magnitude. Black dashed horizontal lines indicate thresholds for determining forcing regimes (described in section 3 and Table 3). Black vertical lines indicate the approximate timing of observational surveys (Table 1).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Forcing time series: (a) Connecticut River daily discharge (blue) and 30-day running average lagged discharge (black), (b) daily tidal elevation amplitude at the main transect, and (c) wind stress magnitude. Black dashed horizontal lines indicate thresholds for determining forcing regimes (described in section 3 and Table 3). Black vertical lines indicate the approximate timing of observational surveys (Table 1).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

## 4. Results

### a. Patterns of salinity and subtidal circulation

The average modeled surface salinity field for the mean tide, mean discharge, low wind regime shows that the eastern LIS has strong along- and across-estuary salinity gradients (Fig. 3). The freshest (most stratified) waters are associated with the Connecticut River plume (originating on the north coast 6 km west of the transect). These plume waters can flow eastward past the transect during ebb tides and can sweep back through the transect on flood tides. All significant river inflows enter along the northern coast (except for some Hudson waters entering at the LIS head via the East River), yet there is low-salinity water along the southern coast of this wide estuary. These salinity patterns are similar to those described in Whitney and Codiga (2011) and in Whitney et al. (2014). The across-estuary component of subtidal surface flow indicates some pathways that transport freshwater from the north side to the estuary center (Fig. 3). Surface along-estuary flow tends to have a westward component (toward the head) along the northern side and an eastward component (toward the mouth) along the southern side. Flow pathways into or out of the estuary can be indirect; there are anticyclonic and cyclonic areas. Near-bottom flow is directed into the estuary in most eastern LIS locations (Fig. 3). Near the transect, there is southwestward, near-bottom flow along the southern side that is roughly parallel to the coast. The salinity and velocity fields exhibit considerable spatial variability. Consequently, conditions along the eastern LIS transect likely are most highly representative of only the 6-km-long region between the Connecticut River mouth and the first island opening of the mouth. Flow into and out of most of the estuary does pass through this transect, however, and circulation patterns are much less complicated than through the three island openings of the mouth.

Salinity (color contoured) and subtidal currents (vectors) at (a) the surface and (b) near the bottom. Model results are regime averaged for the mean tide, mean discharge, and low wind regime. The main transect is marked with a gray line.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Salinity (color contoured) and subtidal currents (vectors) at (a) the surface and (b) near the bottom. Model results are regime averaged for the mean tide, mean discharge, and low wind regime. The main transect is marked with a gray line.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Salinity (color contoured) and subtidal currents (vectors) at (a) the surface and (b) near the bottom. Model results are regime averaged for the mean tide, mean discharge, and low wind regime. The main transect is marked with a gray line.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

### b. Observations and model results for 2010 surveys

During the 29 April survey (Tables 1 and 2; mean tides and mean discharge), the tidal-averaged salinity field has considerable vertical and lateral structure (Fig. 4). The lowest salinities are at the surface near the southern side and the highest salinities are at the bottom in the deepest area near the LIS center. Stratification is present throughout the transect. Isohalines are sloped upward with the freshest water to the south (despite the absence of rivers on this side) and saltiest waters to the north. There are no data for the 3 km closest to the northern coast; it is possible that the signature of the near-field Connecticut River plume exists within this data gap. Subtidal flow toward the mouth is strongest at the surface 3 km from the southern coast, and flow into the estuary is strongest near the bottom in the center of the transect (Fig. 5). There is weak surface flow into the estuary on the northern side. The outflow extends down to 20 m deep (⅔ of the water column) and spans the area with the freshest waters. The salinity and subtidal flow patterns are reminiscent of a geostrophically adjusted buoyant plume exiting a wide estuary, but the outflow is 4 times wider than the internal deformation radius (2.2 km), and the importance of advection and friction indicates dynamics are not geostrophic (e.g., Whitney and Codiga 2011; Whitney et al. 2014). Note that the rotational frictional semianalytical solution from Kasai et al. (2000), although it does not include advection, has similar exchange flow patterns and has been applied to eastern LIS by Codiga and Aurin (2007).

Observed and modeled tidal-averaged salinity sections for the main transect. Observations for (a) 29 Apr 2010 (mean tide, mean discharge), (b) 4 May 2010 (neap tide, mean discharge), (c) 12 Aug 2010 (spring tide, low discharge). Corresponding model results for (d) 29 Apr 2010, (e) 4 May 2010, and (f) 12 Aug 2010. The south side (near Long Island) is on the left and the north side (near Connecticut) is on the right. Integer salinities (e.g., 29 and 30) are marked with black isohalines.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Observed and modeled tidal-averaged salinity sections for the main transect. Observations for (a) 29 Apr 2010 (mean tide, mean discharge), (b) 4 May 2010 (neap tide, mean discharge), (c) 12 Aug 2010 (spring tide, low discharge). Corresponding model results for (d) 29 Apr 2010, (e) 4 May 2010, and (f) 12 Aug 2010. The south side (near Long Island) is on the left and the north side (near Connecticut) is on the right. Integer salinities (e.g., 29 and 30) are marked with black isohalines.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Observed and modeled tidal-averaged salinity sections for the main transect. Observations for (a) 29 Apr 2010 (mean tide, mean discharge), (b) 4 May 2010 (neap tide, mean discharge), (c) 12 Aug 2010 (spring tide, low discharge). Corresponding model results for (d) 29 Apr 2010, (e) 4 May 2010, and (f) 12 Aug 2010. The south side (near Long Island) is on the left and the north side (near Connecticut) is on the right. Integer salinities (e.g., 29 and 30) are marked with black isohalines.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Observed and modeled tidal-averaged along-estuary velocity sections for the main transect. (top) Observations and (bottom) corresponding model results. The dates are shown in the same order as the Fig. 4 salinity sections. Positive velocities are eastward (outward toward the mouth), negative velocities are westward (inward), and the 0 m s^{−1} isotach is marked with a thick black curve. Black isotachs are included at a 0.1 m s^{−1} interval.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Observed and modeled tidal-averaged along-estuary velocity sections for the main transect. (top) Observations and (bottom) corresponding model results. The dates are shown in the same order as the Fig. 4 salinity sections. Positive velocities are eastward (outward toward the mouth), negative velocities are westward (inward), and the 0 m s^{−1} isotach is marked with a thick black curve. Black isotachs are included at a 0.1 m s^{−1} interval.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Observed and modeled tidal-averaged along-estuary velocity sections for the main transect. (top) Observations and (bottom) corresponding model results. The dates are shown in the same order as the Fig. 4 salinity sections. Positive velocities are eastward (outward toward the mouth), negative velocities are westward (inward), and the 0 m s^{−1} isotach is marked with a thick black curve. Black isotachs are included at a 0.1 m s^{−1} interval.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

The 4 May survey was carried out during neap tides and similar mean discharge conditions (Tables 1 and 2). Tidal-averaged salinities span twice the range (2.73 range) of the prior mean tide survey (1.33 range; Fig. 4). The surface waters and bottom waters are, respectively, fresher and saltier than the prior survey, but the locations of the freshest and saltiest waters are similar to the first survey. Stratification is twice as strong and distributed throughout most of the water column (except near bottom). The isopycnal slopes are similar to the mean tide conditions, indicating a similar lateral structure. The flow toward the mouth is somewhat weaker than the prior survey (Fig. 5), while the inflow is of similar magnitude (Table 2). The vertical and lateral structure are similar to mean tide conditions, except the areas with the strongest outflow and inflow are wider and are shifted 1–3 km across the estuary toward the northern side. Based on this comparison, the most pronounced differences between mean and neap tides during mean discharge conditions is higher stratification and wider inflows and outflows during neap tides.

The 12 August survey includes conditions toward the end of spring tides during low discharge (Tables 1 and 2). Salinities are higher everywhere than the mean discharge surveys, and the 0.73 range of salinity is half the range of the first survey (Fig. 4). Correspondingly, the stratification is weaker. The lowest-salinity water and strongest stratification is at the surface on the south side, but there is some stratification throughout the transect. Isohalines are sloped in the same sense as in the other surveys. The maximum outflow and inflow velocities are similar to other surveys. The cores of the inflow and outflow regions are concentrated in narrower areas near the surface on the south side and near bottom at the estuary center. There also is a weaker secondary part of the outflow region on the north half that extends deep into the water column. It is bounded by an inflowing region occupying the entire water column near the north coast. As in the other surveys, across-estuary velocities tend to have a northward component at the surface and a southward component at depth. The salinity field is starkly different from the mean discharge surveys, but the exchange flow has similar magnitudes and some similar patterns to the earlier surveys.

The observed, mean, subtidal salinity and current fields have been created by first removing M_{2} tidal variability (via harmonic analysis) then temporally averaging the detided fields. The difficulty of extracting an accurate representation of the mean subtidal structure (during each survey) grows as the signal to noise ratio (SNR) decreases. An appropriate SNR for this application is the spatial variance of the mean subtidal field divided by the spatial-averaged temporal variance of the detided fields. The salinity SNR values are 6.8, 21.4, and 4.6 for the April, May, and August surveys, respectively. SNR values for along-estuary velocities are smaller but still above one; they are 1.9, 6.5, and 1.8 for the April, May, and August surveys, respectively. The SNR values for the across-estuary velocities are below one (ranging from 0.6 to 0.7). The observed across-estuary velocities fields are not shown or discussed due to the low confidence reflected by the lower SNR values.

The tidal-averaged model results (averaged over four M_{2} cycles) corresponding to the April mean tide, mean discharge survey have a larger than observed salinity range (Table 2; Fig. 4). Correspondingly, model results have twice the observed stratification. Nevertheless, the locations of the freshest and saltiest waters are the same as observed. The lateral structure and isohaline slope are similar too. The model shows fresher water associated with the Connecticut River plume near the north coast that is outside the observational data coverage area. It is important to note that the observations from 27 and 30 April were combined to map one full tidal cycle; therefore, there is not an exact timing match between the model and observations. This inherent mismatch may explain some of the differences between modeled and observed salinity fields. The along-estuary exchange flow has maximum outflow and inflow magnitudes (within the observed area) that are comparable to observed values (Table 2; Fig. 5). Model results and observations have similar velocity structure, though the zero crossing in the model is 3 m shallower. The observed inflow region on the northern side may not reach the surface, since model results show a shallow outflow layer here (above the observed depth range). Despite the stratification mismatch, both model results and observations show a wedge of low-salinity water flowing toward the mouth on the south side of the estuary that overlies a laterally offset salty water inflow. A possible explanation for the similar flow structure may be that stratification is not the strongest controlling factor for the subtidal flow here.

For the May, neap tide, mean discharge survey, maximum and minimum salinity results are much closer to observations (Table 2; Fig. 4). The model has higher stratification at the midwater column, but isopycnal slopes and lateral structure are representative of observed conditions. Model results are more stratified for neap tide forcing than mean tide conditions. Within the observed area, maximum outflow is somewhat stronger than observed (Table 2; Fig. 5). Model results for the August low discharge survey are very similar to the observed salinity range and structure (Table 2; Fig. 4). There are similarities between the modeled and observed along-estuary velocity fields, but the velocity range in the model is somewhat smaller than observed, and the surface maximum is less offset to the south than observed (Table 2; Fig. 5). Overall, the observed and modeled velocity fields have structural similarities for all surveys. One way to assess the velocity structure is with the lateral alignment index (LAI) that varies between zero for entirely vertically layered inflows and outflows to one for entirely laterally offset inflows and outflows (Whitney and Codiga 2011). The LAI for observations (0.5) and model results (0.4) indicate LIS is near the middle of the range with both vertical and lateral layered; the lower LAI for model results is consistent with the higher stratification.

Point-to-point statistical comparisons between model results and observations (Table 2) reveal a high level of correlation measured by the Pierson correlation coefficient squared *r*^{2}. The *r*^{2} values indicate correlations represent 96% of the salinity variance and 83%–94% of the along-estuary velocity variance (Table 2). The RMSE values, however, indicate significant differences that represent 57%–120% of the observed salinity standard deviation (and 15%–35% of the range) and 33%–62% of the along-estuary velocity standard deviation (and 8%–13% of the range). Some of this mismatch is due to limitations in calculating observed tidal-averaged fields from a limited number of crossings, but it is clear that model limitations (e.g., higher than observed stratification) significantly contribute to the error. Nevertheless, both observations and model results indicate there are pronounced changes in salinities and stratification between mean and low discharge conditions that are accompanied by smaller changes in exchange flow. Notwithstanding the differences between observations and the model, the paper will proceed with further model analysis.

### c. Forcing regime variability

The response to a broader range of tidal and discharge forcing conditions can be explored via the forcing regime averages of model results (described in section 3 and Table 3). The subtidal salinity fields for all nine low wind regimes have isohalines sloped upward toward the north (except near each coast) and stratification throughout most of the water column (Fig. 6). Stratification increases as tidal amplitude decreases and discharge increases; this is consistent with reduced tidal mixing and increased freshwater inputs for low tidal amplitudes and high discharge. The neap tide, high discharge case is the lowest salinity and most stratified situation, while the spring tide, low discharge case is the saltiest and most mixed. With increasing discharge, the surface salinity minimum moves northward across the estuary and the near-field Connecticut River plume region (next to the north coast) grows more pronounced. The spatial standard deviation (SSD) of the regime-averaged salinity fields is a good metric to quantify changes with forcing conditions (Table 4). For mean discharge conditions, the SSD for neap tides and spring tides, respectively, is 41% higher and 27% lower than during mean tides. The salinity field is more sensitive to river discharge variations. The SSD for low and high discharge (at neap tides), respectively, is 35% lower and 53% higher than for mean discharge.

Regime-averaged salinity sections. Spring tide regimes for (a) low discharge, (b) mean discharge, and (c) high discharge. Mean tide regimes for (d) low discharge, (e) mean discharge, and (f) high discharge. Neap tide regimes for (g) low discharge, (h) mean discharge, and (i) high discharge. All regimes are for low wind (<0.025 Pa) conditions. Integer salinities (e.g., 29 and 30) are marked with black isohalines.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Regime-averaged salinity sections. Spring tide regimes for (a) low discharge, (b) mean discharge, and (c) high discharge. Mean tide regimes for (d) low discharge, (e) mean discharge, and (f) high discharge. Neap tide regimes for (g) low discharge, (h) mean discharge, and (i) high discharge. All regimes are for low wind (<0.025 Pa) conditions. Integer salinities (e.g., 29 and 30) are marked with black isohalines.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Regime-averaged salinity sections. Spring tide regimes for (a) low discharge, (b) mean discharge, and (c) high discharge. Mean tide regimes for (d) low discharge, (e) mean discharge, and (f) high discharge. Neap tide regimes for (g) low discharge, (h) mean discharge, and (i) high discharge. All regimes are for low wind (<0.025 Pa) conditions. Integer salinities (e.g., 29 and 30) are marked with black isohalines.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

SSD over the main transect for each regime-averaged section shown in Figs. 6 and 7. SSD values for salinity, along-estuary velocity (m s^{−1}), and across-estuary velocity (m s^{−1}) are listed sequentially.

Subtidal along-estuary velocity fields show structural similarities among different forcing regimes (Fig. 7). All cases have outward flow with strongest surface velocities south of the estuary center overlying an inflow that rises to the surface near the north coast. Several of the regimes also have outward flow in a shallow, near-surface wedge at the north coast. This outflow is associated with the Connecticut River plume and is most apparent in the neap tide, low and mean discharge regimes. Inflow velocities increase as tidal amplitude decreases. Inflow velocities change to a lesser degree with discharge, with mean discharge regimes having slightly faster velocities. Outflow velocities are fastest for the neap and mean tide regimes with mean discharge. Unlike the salinity field, the velocity field SSD varies more for changing tidal conditions than for varying discharge (Table 4). The largest change from the mean tide/mean discharge is 115% for salinities and only 30% for subtidal velocities. The regime analysis and the intercomparison of observational survey results both indicate that temporal variability of the salinity field is more pronounced than the variability of the subtidal velocities.

Regime-averaged along-estuary velocity sections. Regimes are shown in the same order as in Fig. 6 and Table 3. Positive velocities are outward, negative velocities are inward, and the 0 m s^{−1} isotach is marked with a thick black curve (as in Fig. 5).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Regime-averaged along-estuary velocity sections. Regimes are shown in the same order as in Fig. 6 and Table 3. Positive velocities are outward, negative velocities are inward, and the 0 m s^{−1} isotach is marked with a thick black curve (as in Fig. 5).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Regime-averaged along-estuary velocity sections. Regimes are shown in the same order as in Fig. 6 and Table 3. Positive velocities are outward, negative velocities are inward, and the 0 m s^{−1} isotach is marked with a thick black curve (as in Fig. 5).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

### d. Time series

The time series of the spatial average salinity and salinity SSD further indicate how salinities decrease and spatial variability (due to vertical and lateral layering) increases following high discharge events (Fig. 8). Throughout the salinity SSD time series, there also is a clear tidal signal with increased spatial variability during neap tides. Along-estuary velocity SSD has variability associated with the spring–neap cycle throughout the record (Fig. 8). The spring–neap response indicates the velocity SSD (and exchange flow) is higher during neap tides. The velocity SSD time series also shows a lagged response to the highest and lowest discharge periods. Relative sensitivity to tides, discharge, and winds and associated lag times will be assessed via regression analysis in section 5b.

Time series (green) of (a) section-averaged salinity, (b) spatial standard deviation of salinity, and (c) spatial standard deviation of along-estuary velocity at the main transect. Regression time series (gray) are calculated from Eq. (6) with the best-fit coefficients in Table 6 and then dimensionalized using the 〈〈*Y*〉〉 and *σ*_{y} values in Table 5.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Time series (green) of (a) section-averaged salinity, (b) spatial standard deviation of salinity, and (c) spatial standard deviation of along-estuary velocity at the main transect. Regression time series (gray) are calculated from Eq. (6) with the best-fit coefficients in Table 6 and then dimensionalized using the 〈〈*Y*〉〉 and *σ*_{y} values in Table 5.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Time series (green) of (a) section-averaged salinity, (b) spatial standard deviation of salinity, and (c) spatial standard deviation of along-estuary velocity at the main transect. Regression time series (gray) are calculated from Eq. (6) with the best-fit coefficients in Table 6 and then dimensionalized using the 〈〈*Y*〉〉 and *σ*_{y} values in Table 5.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

*F*is defined as 1−

*S*/

*S*

_{o}, where

*S*is the salinity and

*S*

_{o}= 32 for this application. Selecting an appropriate

*S*

_{o}can be challenging for observational studies, but in this modeling application it is straightforward to select the constant salinity used for model initialization. The instantaneous, advective, freshwater volume flux (instantaneous freshwater flux for short) through a vertical cross section with area

*A*is the product of

*F*and the instantaneous along-estuary velocity

*u*[Eq. (3a)]. Averaging the instantaneous freshwater flux over at least one tidal period yields the subtidal freshwater flux [Eq. (3b)]:

*A*that covers the entire estuary cross section. The amplitude of the exchange flux also is of interest; the outward (or inward) subtidal freshwater flux is found by integrating only over the area where the subtidal volume flux is outward (or inward) as in Whitney et al. (2014).

The net subtidal freshwater flux (Fig. 9) is almost always outward, and the mean value is 823 m^{3} s^{−1}. The net flux is consistent with the river discharge entering the estuary and passing through the section toward the mouth. The outward freshwater flux is at least twice the net flux, and the inward flux is slightly larger than the net flux. All fluxes have larger magnitudes during high discharge periods. There are peaks during spring freshet, but also there are peaks associated with high discharge at other times that vary from year to year. Spring–neap variability also is evident; flux magnitudes are greater during neap tides (as determined with regression analysis in section 5b) when stratification and exchange flow both are larger.

Time series of (a) freshwater fluxes and (b) salt fluxes through the main transect. Outward fluxes are positive and shown for freshwater and salt fluxes in blue and red, respectively. Net fluxes are shown for freshwater and salt fluxes in cyan and magenta, respectively. Regression time series (gray) are calculated from Eq. (6) with the best-fit coefficients in Table 6 and then dimensionalized using the 〈〈*Y*〉〉 and *σ*_{y} values in Table 5.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Time series of (a) freshwater fluxes and (b) salt fluxes through the main transect. Outward fluxes are positive and shown for freshwater and salt fluxes in blue and red, respectively. Net fluxes are shown for freshwater and salt fluxes in cyan and magenta, respectively. Regression time series (gray) are calculated from Eq. (6) with the best-fit coefficients in Table 6 and then dimensionalized using the 〈〈*Y*〉〉 and *σ*_{y} values in Table 5.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Time series of (a) freshwater fluxes and (b) salt fluxes through the main transect. Outward fluxes are positive and shown for freshwater and salt fluxes in blue and red, respectively. Net fluxes are shown for freshwater and salt fluxes in cyan and magenta, respectively. Regression time series (gray) are calculated from Eq. (6) with the best-fit coefficients in Table 6 and then dimensionalized using the 〈〈*Y*〉〉 and *σ*_{y} values in Table 5.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

*ρ*in Eq. (4) convert salinity fluxes to salt fluxes. The net salt flux alternates between outward and inward, with outward net flux tending to correspond to mean tides following spring tides (as shown via regression analysis in section 5b). It is hard to see river discharge variability in the net flux time series, but both the outward and inward exchange salt fluxes tend to increase following high discharge periods. The outward and inward exchange fluxes are nearly equal to each other on average. They both also show spring–neap variability with stronger magnitudes during spring tides (like the freshwater exchange fluxes). The long-term average net salt flux is 4.8 × 10

^{3}kg s

^{−1}into the estuary (for the entire analysis period); the net flux standard deviation and long-term average exchange flux are 19 and 96 times greater, respectively. The small, long-term, average flux would take (in a hypothetical situation) more than 10 yr to equal the total salt volume in the estuary. This reflects an approximate, long-term, steady-state situation with respect to salt. The small, long-term, average net salt flux into the estuary is consistent with a flux out of the East River through the LIS head, the same direction as found in Gay et al. (2004).

## 5. Analysis

### a. Scalings

The bulk stratification and velocity scalings [Eq. (1)] for fully adjusted exchange-dominated estuaries from MacCready and Geyer (2010) may be appropriate for LIS. The appropriateness can be assessed by comparing the exact discharge-dependent (and tide independent) scalings [Eq. (1)] to model results averaged over the M_{2}–N_{2} spring–neap cycle. The assessment is completed graphically (without computing fit statistics), since this is sufficient when dealing with scalings. For these calculations, the river discharge is divided by *A* to convert it to discharge velocity *u*_{r}; the cross-sectional area *A* at the transect is 445 500 m^{2}. The 33-m mean depth and 0.24 m s^{−2} reduced gravity (for the river to ocean water salinity difference with *S*_{o} = 32) are used to calculate the reference internal wave speed (*c*_{o} = 2.8 m s^{−1}); *c*_{o} is much greater than the observed and modeled subtidal flow. The salinity difference scaling [Eq. (1a)] agrees quite well with 3 × SSD for salinity (Fig. 10); the scaling collapses the data and the scaling line has a slope similar to the data. Comparing the exchange velocity scaling [Eq. (1b)] to (3/2) × SSD for along-estuary velocity shows reasonable agreement (Fig. 10), but there is considerable scatter away from the scaling line.

Scaled (a) spatial range of salinity, (b) spatial range of along-estuary (exchange) velocity, (c) eastward (outward) exchange freshwater flux, and (d) eastward (outward) salt flux vs Connecticut River discharge scaled by section area and the reference internal wave speed *c*_{o}. The blue circles are model results averaged over the spring–neap cycle. The green curves are scalings for a fully adjusted exchange-dominated estuary with functional forms and coefficients based on MacCready and Geyer (2010).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Scaled (a) spatial range of salinity, (b) spatial range of along-estuary (exchange) velocity, (c) eastward (outward) exchange freshwater flux, and (d) eastward (outward) salt flux vs Connecticut River discharge scaled by section area and the reference internal wave speed *c*_{o}. The blue circles are model results averaged over the spring–neap cycle. The green curves are scalings for a fully adjusted exchange-dominated estuary with functional forms and coefficients based on MacCready and Geyer (2010).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Scaled (a) spatial range of salinity, (b) spatial range of along-estuary (exchange) velocity, (c) eastward (outward) exchange freshwater flux, and (d) eastward (outward) salt flux vs Connecticut River discharge scaled by section area and the reference internal wave speed *c*_{o}. The blue circles are model results averaged over the spring–neap cycle. The green curves are scalings for a fully adjusted exchange-dominated estuary with functional forms and coefficients based on MacCready and Geyer (2010).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

The agreement encourages estimates of exchange fluxes based on these scalings. Flux estimates also involve the vertical structure for the salinity and velocity exchange terms (involving u_{e}) in the two-dimensional analytical solution for subtidal circulation written in MacCready and Geyer (2010). The derived scaling for outward exchange volume flux is 0.26 × *A* × *u*_{e} [where the *u*_{e} scaling is shown in Eq. (1b)]. This volume flux scaling curve passes through the model outward volume flux data points, but the curve is not included in the figure, since it is simply a multiple of the velocity SSD curve.

*S*〉〉. The outward freshwater flux scaling [Eq. (5a)] compares well to model results (Fig. 10) and approximately depends on the square root of discharge. For this weakly stratified estuary, both terms in the freshwater flux scaling [Eq. (5a)] contribute significantly, whereas the first term is an order of magnitude larger than the second in the salt flux scaling [Eq. (5b)]. Consequently, the exchange salt flux approximately is the exchange volume flux multiplied by the record-averaged salinity (and density); the flux scaling depends on discharge to the ⅓ power (as does the exchange velocity).

The adjustment time scale [Eq. (2)] in response to discharge changes can be calculated using parameters representative of the entire estuary. The parameters are 20-m depth, 4 × 10^{5} m^{2} cross-sectional area, 10^{3} discharge (approximate mean total discharge into LIS), and 1 m s^{−1} *u*_{tide}. The time scale *T*_{adj} is 67, 133, and 400 days for *γ* values of 6, 3, and 1 [minimum, mean, and maximum values in MacCready (2007)], respectively. Even though the *γ* value is relatively unconstrained for the LIS, the adjustment time scale is a least 2 months for this large system. This result suggests that averaging over only one M_{2}–N_{2} spring–neap period is too short for truly fully adjusted results and can explain some of the scatter about the scaling curves in Fig. 10. Overall, the scalings based on MacCready and Geyer (2010) are effective at representing the long-term average LIS exchange characteristics indicated by the model results.

### b. Regressions

Multivariate linear regressions are pursued to quantitatively rate the relative influence of river discharge, tidal, and wind forcing factors on salinities, exchange velocities, and fluxes. It also is worth investigating how much of the subtidal variability in eastern LIS can be represented by these regressions. The agreement of the fully adjusted scalings for long-term averaged results encourages testing the same power relationships for river discharge (specified again below) on the tidal-averaged results that include short-term variability that is not fully adjusted. As discussed in MacCready and Geyer (2010), short-term variability includes response to spring–neap variability and wind events. Spring–neap variations in spatial salinity variations (and mixing) are expected to be proportional to tidal shear, which in turn is proportional to tidal current amplitude. Spring–neap variations in exchange flow may be linked to mixing variations or tidal residuals (e.g., Whitney et al. 2014); both are related to tidal current amplitude. The amplitudes of tidal elevation and currents are proportional to each other via shallow-water wave dynamics. Tidal elevation amplitude is selected for the regression analysis because it is typically more readily available in observations. Prior research indicates that wind events are a significant factor in modulating the exchange flow; this modulation is proportional to the along-estuary wind stress (Whitney and Codiga 2011). Salinity stratification (and mixing) also may have a wind-related signal that is proportional to wind stress. The prior research collectively indicates that the regressions should involve different powers of river discharge and linear relationships with tidal amplitude and wind stress components.

*X*are the same as used in the regime analysis: tidal elevation amplitude, 30-day running-averaged Connecticut River discharge (with an exponent described below), and along- and across-estuary wind stress averaged over four M

_{2}tidal cycles. The dependent variables

*Y*analyzed are the spatial-averaged salinity, SSD of subtidal salinity and along-estuary velocity, and the outward, inward, and net subtidal freshwater and salt fluxes. The discharge exponents applied to multivariate regressions are 1 for spatial-averaged salinity, ⅔ for salinity SSD [guided by Eq. (1a)], ⅓ for along-estuary velocity SSD [guided by Eq. (1b)], ½ for outward and inward freshwater flux, ⅓ for exchange salt flux, and 1 for net freshwater and salt fluxes [implied by Eqs. (1a) and (1b) combined]. The selected exponent for inward and outward freshwater flux is between the value used for salinity and velocity, since both are involved in its calculation [Eq. (5)]. The regression equation with dimensionless coefficients is

*X*〉〉 and 〈〈

*Y*〉〉) and then dividing by the temporal standard deviation (

*σ*

_{x}and

*σ*

_{y}) for the 4-yr analysis period. Table 5 lists the statistics used to standardize each variable. Since the variables are standardized, the offset

*b*

_{o}should be zero, and the dimensionless coefficients

*b*

_{i}indicate the relative sensitivity to tides, discharge, and winds. The 95% confidence interval on regression coefficients is calculated using the effective degrees of freedom

*N*

_{eff}calculated based on the first location where the lagged autocorrelation falls below ½ (Gille 2005).

Statistics for the independent *X* and dependent *Y* variables used in regressions [Eq. (6)]. The dimensional variables are standardized by subtracting the time-averaged value (〈〈*X*〉〉 and 〈〈*Y*〉〉) and dividing by the temporal standard deviation (*σ*_{x} and *σ*_{y}) for the 4-yr analysis period. Note that *Q* is the running-mean river discharge (averaged over the preceding 30 days), and *τ*_{x} and *τ*_{y} are the along- and across-estuary wind stress components.

Regression results are shown in Table 6 and Figs. 8 and 9; all fits are significantly different from zero at the 95% confidence level (or better). The section-averaged salinity has a strong, negative relationship with discharge and much weaker dependence on tidal amplitude and winds. The spatial structure of salinity (represented by the SSD) increases both with decreasing tidal amplitude and increasing discharge; the wind dependence is weak. The regressions account for over 60% of the variance for these salinity variables; maximum correlations occur when all forcings have zero lag (though the 30-day running-mean discharge has a built-in lag of approximately 15 days).

Regression results including the coefficients *b*_{i} for the independent variables used in Eq. (6). All independent and dependent variables are standardized using the statistics in Table 4. All coefficients are dimensionless and indicate the relative sensitivity to each forcing; the 95% confidence interval around each regression coefficient and *N*_{eff} is also listed. All offsets *b*_{o} are zero. The squared correlation coefficient *r*^{2} also is given. All correlations are significantly different from zero at a 95% confidence level. The B superscript indicates a 39.3-day (76 M_{2} tidal cycles) lag was applied for discharge, the C superscript indicates a 6.21-day (12 M_{2} tidal cycles) lag was applied for tidal amplitude, and no superscript indicates zero lag.

The SSD of the along-estuary velocity increases with decreased tidal amplitude, increased lagged discharge, and to a lesser extent with winds blowing toward the estuary mouth (eastward) and northward across the estuary. The wind dependence for velocity is stronger than for salinity. This regression accounts for half of the variance. The maximum correlation occurs when the 30-day running-mean discharge is lagged by 39.3 days (76 M_{2} tidal cycles) and other forcings have zero lags. The exchange volume flux is related to the SSD of the along-estuary velocity; both tend to be largest during the early summer months, similar to the timing observed by Codiga and Aurin (2007). The volume flux is lagged behind the discharge and salinity SSD that tend to peak in late spring. This long lag suggests the LIS system adjusts to river discharge over time scales of several months.

The outward subtidal freshwater flux depends on all forcings in the same sense as the salinity and along-estuary velocity SSDs (Table 6), but the sensitivity to river discharge is stronger. The regression accounts for approximately 70% of the variance. Results are similar for the inward freshwater flux except that coefficients signs are switched, since the inward flux is negative. The net freshwater flux is correlated with forcings in the same sense as the outward flux, though the net flux has less sensitivity to river discharge. The maximum correlation for freshwater fluxes occurs when all forcings have zero lag. Flux magnitudes tend to be larger during neap tides.

The regression for outward salt flux is similar to the along-estuary velocity SSD results except that the tidal dependence is stronger than discharge (instead of at parity). The inward salt flux regression results have opposite signs (because the inward flux is negative) but are otherwise similar. Note that all salt flux regressions apply the same discharge lag as used with along-estuary velocity. The regression with net salt flux is a considerably worse fit than for the other variables; it accounts for only 26% of the variance. There is no clear dependence on river discharge. The net salt flux is most sensitive to tides. The tides had to be lagged by 6.21 days (12 M_{2} tidal cycles) to achieve the maximum correlation. This lag corresponds to approximate ¼ of the M_{2}–N_{2} spring–neap cycle. Outward and inward peaks in net salt flux tend to occur near mean tides following spring and neap tides, respectively. Response to along- and across-estuary wind stress is in the same direction for net salt and freshwater fluxes, but the sensitivity is weaker for salt flux.

The regression analysis indicates that salinities, velocities, and fluxes have statistically significant relationships with discharge, tides, and winds. Overall, the regression analyses indicate river discharge and tides are the primary forcing factors, and winds exert a secondary but significant influence. Most variables (except exchange velocities and salt fluxes) have the strongest dependence on river discharge. These results collectively suggest that a significant portion of the salinity and velocity response can be estimated using easily obtained tidal, river discharge, and wind information. These findings are consistent with intercomparison of the regime-averaged results, except that the velocity dependence on discharge is more apparent for the regression results because a nonzero lag is used; this lag is also applied for salt fluxes. This long lag (approximately 40 days), along with the fact that the 30-day running-mean discharge yields a higher correlation than with instantaneous daily discharge (not shown), implies a long response time between subtidal circulation and discharge of almost 2 months. This lag is consistent with the lower range of *T*_{adj} estimates (with *γ* = 6) calculated in section 5a.

### c. Flux decomposition

*T*subscript and having zero means) and tidal averaged (denoted with 〈 〉):

*F*=

*F*

_{T}+ 〈

*F*〉 and

*u*=

*u*

_{T}+ 〈

*u*〉. The net freshwater flux associated with tidal oscillatory diffusion (Fflux

_{TO}) is defined as the tidal-averaged area integral of

*F*

_{T}

*u*

_{T}. In practice, it is easier to calculate the tidal oscillatory diffusion from model results by subtracting the flux calculated from tidal-averaged quantities from the total flux (calculated from 4b):

*F*〉 and 〈

*u*〉.

Time series of contributions to net (a) freshwater and (b) salt fluxes. The total freshwater flux (black) is calculated from Eq. (3), tidal oscillatory dispersion (green) is calculated from Eq. (7), and the remaining contributions from the spatial means (blue) and spatial variations (red) are calculated from Eq. (8). The total salt flux is calculated from Eq. (4), and the contributions are calculated in analogous fashion to Eqs. (7) and (8).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Time series of contributions to net (a) freshwater and (b) salt fluxes. The total freshwater flux (black) is calculated from Eq. (3), tidal oscillatory dispersion (green) is calculated from Eq. (7), and the remaining contributions from the spatial means (blue) and spatial variations (red) are calculated from Eq. (8). The total salt flux is calculated from Eq. (4), and the contributions are calculated in analogous fashion to Eqs. (7) and (8).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Time series of contributions to net (a) freshwater and (b) salt fluxes. The total freshwater flux (black) is calculated from Eq. (3), tidal oscillatory dispersion (green) is calculated from Eq. (7), and the remaining contributions from the spatial means (blue) and spatial variations (red) are calculated from Eq. (8). The total salt flux is calculated from Eq. (4), and the contributions are calculated in analogous fashion to Eqs. (7) and (8).

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Contributions to the long-term average net freshwater and salt fluxes. Positive values are outward toward the mouth.

*F*〉′ and 〈

*u*〉′ are biggest. The flux contribution associated with the net volume flux [first term on the rhs of Eq. (8c)] switches between inward and outward and varies with river discharge, tidal amplitude, and winds; it adds 9% on average to the net flux. This contribution increases with discharge and is modulated by the spring–neap cycle; it peaks in its outward flux approximately 6 days after spring tides. As with the net salt flux, the outward and inward peaks occur near mean tides following the M

_{2}–N

_{2}spring and neap tides, respectively. Overall, the decomposition indicates that the net freshwater flux is chiefly driven by subtidal shear dispersion but modified by tidal oscillatory diffusion and the freshwater flux associated with the net volume flux. The long-term average net freshwater flux and all three contributions are directed outward toward the estuary mouth (Table 7).

Since many studies (e.g., Lerczak et al. 2006; Ralston et al. 2010; Aristizabal and Chant 2013) analyze salt flux, it is also worthwhile to decompose salt fluxes in analogous fashion to the freshwater flux analysis. The net salt flux variations are chiefly due to the product of the net volume flux and the spatially averaged salinity (Fig. 11). The net salt and net volume fluxes both have outward and inward peaks near mean tides following M_{2}–N_{2} spring and neap tides, respectively. The much smaller contributions associated with steady shear dispersion and tidal oscillatory diffusion are consistently into the estuary; these two terms are of similar magnitude except when shear dispersion grows larger during high discharge. One factor contributing to the dominance of the net volume flux term is the spatially averaged salinity (around 30) is an order of magnitude larger than spatial variations of salinity (of order ±2), as in other partially to well-mixed estuaries. Focusing on the net freshwater flux variations, however, yields additional insights beyond the net salt flux because taking the difference between the local and reference salinity (the numerator of *F*) diminishes the term associated with spatial averages relative to the one associated with spatial salinity variations.

Over the 2009–12 model study period, the mean values of the net salt flux contributions are an order of magnitude smaller than their variations (Table 7). Unlike the variations, however, the mean values are not dominated solely by the uniform flow contribution. The long-term average net salt flux (directed into the estuary) arises from inward exchange flow (steady shear dispersion) and diffusion (tidal oscillatory flux) contributions that are partially countered by the outward uniform flow contribution. Results indicate that long-term average steady shear dispersion is twice as large as the tidal oscillatory diffusion.

The freshwater and salt flux analyses provide different perspectives, since the former tracks river waters, while the latter tracks salt supplied by the shelf. The long-term average net freshwater flux is outward and consistent with the mean river discharge. In contrast, the long-term average net salt flux is inward and is consistent with a corresponding flux out of the East River through the LIS head (as in Gay et al. 2004). The steady shear dispersion contribution is outward for freshwater flux because the outflowing layer of the exchange flow has more freshwater (and less salt) than the inflowing layer, as in a typical estuary (e.g., MacCready and Geyer 2010). The inward salt flux via steady shear dispersion indicates the outflowing exchange flow exports less salt than the inflowing exchange flow imports. The tidal oscillatory diffusion also exports freshwater and imports salt; this pattern is consistent with the tidal pumping occurring near estuary mouths (Fischer et al. 1979; MacCready 2004). The uniform flow contribution is outward for both flux types because the average volume flux is outward, but the contribution is small for freshwater flux and large for salt flux.

## 6. Discussion

Codiga and Aurin (2007) calculated inward, subtidal volume fluxes from ferry-based observations along a diagonal estuary crossing east of the main transect for this study. Their results indicate the average annual cycle for volume flux has values ranging from 1.8–3.0 × 10^{4} m^{3} s^{−1}; the maximum flux period is May through August. While every study year is unique, the average annual cycle for inward volume flux is computed using the model results for the main transect (Fig. 12). Values range from 1.3–1.9 × 10^{4} m^{3} s^{−1} and the maximum flux period is May through July. The differences in flux magnitudes between observations and model results is not surprising considering the different years covered, uncertainties in both observations and model results, and the different transect locations. The overall pattern of the observed and modeled annual cycles is similar with peak volume fluxes occurring in the late spring to summer. This timing reflects a delayed response to the typical spring peak discharge; model results for volume and salt fluxes are lagged approximately 45 days after peak discharge. The lag could explain some of the scatter between model results and the exchange velocity scaling from MacCready and Geyer (2010) that assumes no lag besides what is included by using the 30-day running-mean discharge (Fig. 10). It is important to emphasize that the average annual cycle for freshwater fluxes has peak values in April and May, coincident with peak discharge and earlier than peak volume fluxes (Fig. 12). The 1.6 × 10^{4} m^{3} s^{−1} mean exchange volume flux amplitude (for 2009–12) for model results is close to the 2.3 ± 0.5 × 10^{4} m^{3} s^{−1} (Codiga and Aurin 2007) and the ~1.8 × 10^{4} m^{3} s^{−1} (Riley 1956) observational estimates. The 0.4 × 10^{4} m^{3} s^{−1} Gay et al. (2004) value is less than ¼ the model flux and other observational values; thus, the Gay et al. (2004) value is a low outlier.

Average annual flux cycles for the 2009–12 model period for (a) volume, (b) freshwater, and (c) salt fluxes. Outward (blue, positive), inward (red, negative), and net (green) subtidal fluxes are shown.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Average annual flux cycles for the 2009–12 model period for (a) volume, (b) freshwater, and (c) salt fluxes. Outward (blue, positive), inward (red, negative), and net (green) subtidal fluxes are shown.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Average annual flux cycles for the 2009–12 model period for (a) volume, (b) freshwater, and (c) salt fluxes. Outward (blue, positive), inward (red, negative), and net (green) subtidal fluxes are shown.

Citation: Journal of Physical Oceanography 46, 8; 10.1175/JPO-D-15-0107.1

Over the 2009–12 model study period, the inward net salt flux arises from inward steady shear dispersion and tidal oscillatory diffusion (half the size) which are partially countered by the uniform flow contribution (the single largest term). The Gay et al. (2004) mean annual estimate (involving inverse modeling with salinity and discharge observations) has flux contributions in the same directions as the model results of the present study, but the tidal diffusion contribution is over 8 times greater than the steady shear dispersion term. Since other observational estimates of volume fluxes are several times larger than the Gay et al. (2004) value, it is likely that exchange flow contributes much more to the mean net salt flux than Gay et al. (2004) concluded.

The net salt flux results can be compared to other estuaries. Despite obvious differences between the wide and weakly stratified LIS and the narrow, more stratified Hudson, there are similarities in their net salt flux contributions. The mean contributions in each estuary include outward flux associated with uniform flow opposed by inward steady shear dispersion and a smaller influence from inward tidal oscillatory diffusion (Lerczak et al. 2006). The differences arise with the variability of net salt flux and its contributions. From spring to neap tides in the Hudson, the steady shear dispersion grows from a smaller contribution to the largest term and the net salt flux switches from outward to inward (Lerczak et al. 2006). LIS also has spring–neap variability, but the timing of maximum outward and inward fluxes occur near mean tides following the M_{2}–N_{2} spring and neap tides, respectively. The biggest difference from the Hudson is the salt flux associated with net volume flux always dominates variations. Results are starkly different from the Delaware (Aristizabal and Chant 2013) and the Merrimack (Ralston et al. 2010), since tidal oscillatory diffusion is a much smaller contributor to the net salt flux through the eastern LIS section.

## 7. Conclusions

This study has analyzed the spatial structure of salinity and subtidal velocity, the time variability of these fields and associated fluxes, and connections to forcing conditions. Observations and model results during the low wind survey times indicate that stratification substantially decreases with increased tidal amplitude and decreased river discharge. The subtidal flow field also varies among surveys, but the degree of similarity in magnitudes and patterns is remarkable considering the stark differences in stratification. Overall modeled and observed salinities and velocities have similar patterns and are highly correlated. Nevertheless, the RMSE errors that are a significant fraction of the spatial range of observed fields point to model limitations. Model results (averaged over spring–neap variations) are broadly consistent with salinity and velocity scalings for fully adjusted estuaries (MacCready and Geyer 2010). Multivariate regressions between model results and forcing indicate strong sensitivities to both tides and river discharge, with discharge response strongest for salinity and freshwater flux and tidal response larger for velocities, volume flux, and salt flux. Wind influence is a secondary forcing factor, but it is significant for velocity-related variables and most pronounced during winter months. The response of along-estuary velocities, volume flux, and salt flux to river discharge is lagged by several weeks. Consequently, volume and salt exchange tend to peak during early summer following the spring high discharge season, while minimum salinity and maximum freshwater flux occur during high discharge.

The freshwater and salt flux analyses provide different perspectives, since the former tracks river waters while the latter tracks salt supplied by the shelf. The inward exchange freshwater flux and net freshwater flux are comparable in magnitude, whereas exchange salt fluxes are considerably larger than net salt flux. The long-term average net freshwater flux is outward and consistent with the mean river discharge. In contrast, the long-term average net salt flux is inward and is consistent with a corresponding flux out of the East River through the LIS head (as in Gay et al. 2004). Both flux types show contributions from steady shear dispersion (associated with exchange flow), tidal oscillatory diffusion, and uniform flow, but the relative magnitudes and directions of these contributions differ. For net freshwater and salt fluxes, subtidal shear dispersion is twice the tidal oscillatory diffusion, and both contributions are in the same direction as the net flux. The steady shear dispersion contribution is outward for freshwater flux because the outflowing layer of the exchange flow has more freshwater (and less salt) than the inflowing layer, as in a typical estuary (e.g., MacCready and Geyer 2010). The inward salt flux via steady shear dispersion indicates the outflowing exchange flow exports less salt than the inflowing exchange flow imports. The tidal oscillatory diffusion also exports freshwater and imports salt; this pattern is consistent with the tidal pumping near many estuary mouths (Fischer et al. 1979; MacCready 2004). The uniform flow contribution is outward for both flux types because the average volume flux is outward, but the contribution is small for freshwater flux and large for salt flux. A following paper will continue the analysis by exploring the momentum balances influencing the subtidal dynamics in eastern Long Island Sound.

## Acknowledgments

This study was supported by NSF Grant 0825812 (Physical Oceanography) “Collaborative research: Investigating tidal influences on subtidal estuary coast exchange using observations and numerical simulations” and NSF Grant 0955967 (Physical Oceanography) “CAREER: The influence of distributed river inputs and coastal embayments on dynamics in large estuaries.” The observational study was helped considerably by Turner Cabaniss at UCONN Marine Sciences and Jim Fontaine (Exeter Science Services). This manuscript was improved through the helpful comments of the anonymous reviewers and the editor.

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