6.2. Influence of Wind and Freshwater Discharge
Forcing from wind and freshwater discharge is summarized in Figure 6
, as presented in Section 5
. The wind forcing during the simulation period was induced by winds with speeds of up to 9 m s−1
, predominantly from the south, southwest, and west. The freshwater forcing was associated with constant discharge from WWTPs and intermittent CSOs during three rainfall events. The model results for July 15 to 25 August 2015 showed that Jamaica Bay’s deep channels (e.g., North Channel and Beach Chanel) varied from well-mixed to partially-stratified estuarine conditions. During and after spring tides, the vertical (top-to-bottom) density differences were smaller than 1 kg m−3
, and after the neap tide, the density differences were up to 2 kg m−3
(differences over a 10 m water column). Density differences were predominantly driven by salinity, except in stagnant areas of the bay, such as Grassy Bay, where the differences in summer are occasionally driven equally by saline and thermal stratification.
The results shown in Table 3
indicate that excluding the wind forcing (model NW) caused a slight reduction in the calculated mean residence times. The contribution of wind forcing to the residence time in Jamaica Bay and Grassy Bay increased to 6% and 2%, respectively. The subtle influence of the wind forcing on residence time could be due to the low speed of prevailing winds during the simulation period. Winds were occasionally above 6 m s−1
and winds of this magnitude could impact the flushing of shallow regions, such as the central area of Jamaica Bay where the water depth changes between tens of centimeters to about 2 m. However, most the tracer mass was in deep areas, as the bay’s average depth is about 5 m. In these areas, except for a thin layer near the water surface, the influence of wind-induced shear stress on transport processes during the simulation period was of secondary importance. To better evaluate the impact of wind forcing on the residence time in Jamaica Bay, we ran the model ALL with idealized wind scenarios, i.e., westerly and easterly winds with a constant speed of 6 m s−1
. The calculated residence time for the idealized wind forcing was about 11% larger than the residence time from the model NW (no wind forcing). We also ran the model for a higher constant wind speed (10 m s−1
) and found that, regardless of the direction of the winds (westerly or easterly), stronger winds further increased the residence time in Jamaica Bay (an increase of about 14%).
The wind-induced increase in the mean residence time can be related to the impacts of wind forcing on physical transport processes. Depending on the wind speed, duration, and fetch, the momentum transfer from the wind to the water column can influence transport processes, such as advection and diffusion, and vertical mixing and circulation. For example, using a 3-D hydrodynamic model, [62
] showed that up- and down-estuary winds can reduce stratification in Chesapeake Bay. Based on observations from the York River Estuary, [63
] found that wind forcing can impact the vertical shear and, thus, can either increase or decrease vertical stratification. For high-speed wind events, local surface waves (and swells) can further influence transport processes through wave-current interactions (e.g., as seen by [64
]), wave-generated turbulence, orbital velocity, and momentum transfer from breaking waves to the mean flow. Jamaica Bay is a back-barrier coastal system and is sheltered from ocean swells by the Rockaway Peninsula. However, local waves generated by high-speed winds, especially during winter storms, could influence the water circulation of the bay. No study has yet been devoted to the wind and wave effects on the physical processes in Jamaica Bay. A comprehensive estuarine circulation study would improve our understanding of the important physical processes in Jamaica Bay that are influenced by wind forcing.
The model results in Table 3
show that excluding freshwater discharge (model NF) caused a substantial increase in calculated mean residence times. In Jamaica Bay, the model with all forcing (ALL) computed a residence time of 17.94 days, whereas the residence time calculated by the model neglecting freshwater discharge (NF) was 22.61 days. In Grassy Bay, excluding freshwater discharge increased the residence time from 10.65 days to 13.02 days. Therefore, the influence of freshwater discharge on residence time during the simulation period was to reduce it 21% in Jamaica Bay and 18% in Grassy Bay.
The reduction in mean residence time caused by freshwater discharge may have been due to changes in the baroclinic flow, barotropic flow, vertical mixing, or circulation. To better evaluate the influence of freshwater discharge on residence time, we compared the vertical profiles of the calculated time-averaged velocity in the presence and absence of freshwater discharge. The time-averaged velocity was defined as the velocity averaged over the first 30 days of the residence time simulation period. Note that the majority of the tracers left Jamaica Bay in the first 30 days. Figure 7
shows the vertical profiles of the time-averaged velocity at two sites: one at North Channel (lat = 40.627, lon = −73.882, depth = 11 m), which is the deep channel on the northern side of the bay, and the other at Beach Channel (lat=40.584, lon = −73.836, depth = 12 m), which is the bay’s southern deep channel. Velocities were rotated into their principle axes-the angle of maximum variance of the flow-to determine streamwise and transverse components of the velocity field. At the site located at North Channel, the streamwise up-estuary flow direction was 37 degrees counterclockwise from east (positive/negative flows indicate approximately northeastward/southwestward flows). At the site at Beach Channel, the streamwise up-estuary flow direction was 12 degrees counterclockwise from east (positive/negative flows indicate approximately eastward/westward flows). Figure 7
indicates that the freshwater discharge importantly influenced the streamwise velocities in both the northern and southern deep channels. Freshwater inputs strongly enhanced the two-layer estuarine gravitational circulation and vertical shear, enhancing shear dispersion and giving a likely explanation for the reduction in residence time (e.g., [65
]). Vertical profiles of time-averaged velocities over the channel banks, not shown here, also indicate that freshwater inputs strengthened residual circulation.
Freshwater discharge during the simulation period was mainly from WWTPs, which provided a background freshwater flow of 10 m3
and 84% of total freshwater discharge during the period. This is because Jamaica Bay has a very small watershed, only a few times larger than the bay itself, and about 2 million residents and their associated municipal water use [19
]. This water helps to promote bay flushing, yet also carries a high nitrogen load from wastewater treatment. Three rainfall events generated excessive CSOs and abrupt spikes in the total amount of freshwater inflow to the system (Figure 6
b). The largest inflow occurred 35 days after the tracers were released into the system (i.e., August 21), during a storm event with a total daily rainfall of 6.3 cm. On the other hand, the model results showed that the residence time in Jamaica Bay was 17.94 days. Therefore, the intense rainfall event of August 21st did not overlap with the period of the calculated residence time. To better evaluate the impact of an intense rainfall event on the residence time, we performed a freshwater timing sensitivity experiment by running the model (ALL) for a scenario where the rainfall event of August 21st occurred on July 17, i.e., two days after the tracers were released in the domain. We used “model ALLfts
” to refer to this freshwater timing sensitivity experiment. Table 4
shows the calculated residence times from model ALLfts
and compares them with the results from model ALL. The comparisons show that the early occurrence of excessive CSO on August 21st changed the residence time in Jamaica Bay from 17.94 days to 16.89 days, a reduction of about 6%. The residence time in Grassy Bay was reduced from 10.65 to 10.15 days, about 5%. The results presented here show only a minor importance of the timing of rainfall events, suggesting that the system may have a relatively uniform residence time year-round.
6.3. Spatial Distribution of Tracer Concentration
We also investigated the spatial distribution of tracer concentration in the study area. Figure 8
shows snapshots of tracer concentration for a case where the tracers were released in Grassy Bay. During flood tides, e.g., the snapshot at time = 0.2 day, the tracers were pushed farther into Grassy Bay, whereas during ebb tides, e.g., the snapshot at time = 0.5 day, the tracers were transported outside the domain. The tracer concentration near the extension of J.F.K. airport’s runway 4L remained higher than the concentration in other regions. For example, after 11.3 days, the concentration in this part of Grassy Bay was still above 0.5, whereas the concentration in other regions was below 0.3. The model results also revealed the existence of a transport pathway along Broad Channel on the western side of Grassy Bay. The tracers within this pathway left Grassy Bay throughout its northwestern and southern outlets within a relatively short time. The tracers that left Grassy Bay were first transported to the shallow regions in the center of Jamaica Bay (day 2.8) and were later dispersed very broadly towards the Rockaway Inlet (day 6.6).
As illustrated in Figure 8
, the eastern part of Grassy Bay near the extension of J.F.K. airport’s runway 4 L retained the tracers much longer than other regions. Therefore, this region could have the highest mean biological oxygen demand and concentration of nitrogen and phosphorus, the lowest amount of dissolved oxygen and diversity of species, and the largest percent of clay on the bottom sediment. Moreover, the mean residence time of Grassy Bay certainly underestimates the retention time of tracers in this poorly-circulated, nearly stagnant region.
shows snapshots of the spatial distribution of tracer concentration for the case where the tracers were released into Jamaica Bay. The snapshots at time = 17.3 and 24.8 days recap the long-term retention of tracers near the extension of J.F.K. airport’s runway 4L. Moreover, the arms (tributaries) of Jamaica Bay retained the tracers longer than the bay’s central region and the deep channels in the perimeter of the bay. For example, after 24.8 days, the tracer concentration in Shellbank Basin, Thurston Basin, Motts Basin, and Norton Basin was still above 0.6, whereas the concentration in the center of the bay was below 0.3. Therefore, the mean residence time of Jamaica Bay should not be used as a transport time scale in these poorly-circulated parts of the bay. Separate simulations should be carried out to determine space-dependent residence times in Jamaica Bay. A Lagrangian particle tracking model (e.g., [14
]), even though it can be computationally expensive, would provide more information about the spatially varying residence time in Jamaica Bay.
6.4. Results from Tidal Prism Method
To estimate the mean residence time using the tidal prism method, we first determined the surface area and average volume of water in the study area. The computational grid of Jamaica Bay (JEM grid) indicates that the surface area and volume of water are, respectively, about 5.52 × 107 m2 and 24.71 × 107 m3 in Jamaica Bay (excluding its inlet), and about 0.86 × 107 m2 and 4.84 × 107 m3 in Grassy Bay. We used an average tidal range of 1.6 m (averaged between neap and spring tides) to calculate the tidal prism. The results of our tide modeling, not shown here, revealed that the tidal range is between about 1.57 m and 1.65 m in the study area, including Grassy Bay. Using the water surface area and the average tidal range, the tidal prism was approximated to be 8.84 × 107 m3 for Jamaica Bay and 1.38 × 107 m3 for Grassy Bay. By setting the return flow factor, b, to a default value of 0.5 and the tidal period to 12.4 h, the calculated residence time was 2.89 days for Jamaica Bay and 3.64 days for Grassy Bay, which were significantly smaller than the values calculated by sECOM (17.94 and 10.65 days). The tidal prism method calculated a larger residence time for Grassy Bay than Jamaica Bay. This was because of the larger ratio between the mean volume of water and the tidal prism (V/P, see Equation (8)) in Grassy Bay.
The remarkable difference between the calculated mean residence times based on the numerical model sECOM and the tidal prism theoretical method might be due to the assumptions used in the theoretical method, e.g., the assumption of a well-mixed tidal system. However, the major cause of such large discrepancies may be due to an inappropriate return flow factor used in the tidal prism method, as previous studies have shown that the prediction of tidal flushing is quite sensitive to this factor. For example, [58
] applied the tidal prism method to the Bay Colony Marina in Indian River Bay, DE, and found that a recommended return flow factor of 0.5 caused significant errors in the calculated residence time. Using measurements of dilution of the plume of dye, they calibrated the return flow factor and found that it greatly deviated from the recommended value. Herein, using the model results presented in the previous section, we carried out a calibration process to determine the return flow factor, b
, of the tidal prism method for Jamaica Bay and Grassy Bay.
To calibrate b
, we replaced Tr,TP
in Equation (7) with the mean residence time calculated by sECOM (i.e., the values in Table 3
) and back calculated the return flow factor. Table 5
shows the calibrated b
for each numerical experiment tested in the previous section. In Jamaica Bay, the calibrated b
ranged from 0.90 to 0.95, whereas it ranged from 0.81 to 0.88 in Grassy Bay. Larger return flow factors in Jamaica Bay may be due to the different hydrodynamic characteristics of different regions in the study area. Ref. [58
] identified that “the phase of tidal flow in the connecting channel relative to the flow along the coast, the strength of the channel flow relative to the strength of the coastal flow, and the amount of mixing that occurs once the basin water has been ejected into coastal waters” significantly impact the return flow factor. The outlets of Jamaica Bay and Grassy Bay are located in regions with different hydrodynamic properties, which greatly affects the fraction of tracers returning to the system during flood tides. While the outlet of Jamaica Bay is bordered with the Rockaway Inlet, a deep 7 km-long channel with strong currents, Grassy Bay’s outlets are located near shallow wide areas dominated by wetlands and weak currents.
The large return flow factor in Jamaica Bay may be also due to the effect of the inlet, which was not included in the control volume that represents Jamaica Bay. Tracers that leave the bay remain in the inlet during a few tidal cycles before entering the ocean. We did not include the inlet as part of the control volume because the presence of strong currents in the inlet leads to a well-circulated system compared to the bay, which suffers poor circulation and issues related to water quality.
To cross check the calibrated return flow factors, we used the time series of tracer concentration calculated by the numerical model to estimate the percentage of tracers that returned to the system during flood tides. We calculated the return flow factor by comparing the amount of tracers that left the domain of interest during the ebb tide with the amount of tracers that entered the domain during the successive flood tide. The amount of tracers that left the domain during the ebb tide was calculated by subtracting the total volumetric concentration of tracers at the time of low tide (i.e., when the tidal level in the outlet of Jamaica Bay was at low tide) from that at the time of the preceding high tide. The amount of tracers that entered the domain during the flood tide was calculated by subtracting the total concentration of tracers at the time of low tide from that at the time of the successive high tide. The results from the model ALL showed that between 75% and 100% (with an average of 85%) of tracers that left Jamaica Bay during ebb tides returned to the system during flood tides, which satisfactorily agrees with the return flow factors calibrated for the tidal prism method.
Previous studies have used widely different values for the return flow factor b
. For example, ref. [66
] set b
equal to 0.3 to determine the flushing time in a large number of marinas along the Spanish coast, whereas [67
] set b
to 0.7 for Mundaú Lagoon in Brazil. The small value of b
used by [66
] may be due to the fact that most coastal systems along the Spanish coast are coastal systems open to the sea and, thus, tracers that leave the system immediately are diluted into the sea and only a small portion of tracers return to the system. Ref. [67
] found that the tidal prism method (with b
= 0.7) significantly underestimated the flushing time of Mundaú Lagoon. While their numerical simulation based on the e-folding theory calculated a flushing time on the order of months, the tidal prism method calculated a flushing time on the order of days. They adopted the return flow factor of 0.7 based on salinity data analysis in Mundaú Lagoon carried out by [68
], who specified that only 30% of the flood flow contained new water from the ocean. Ref. [67
] used a control region that excluded the long, narrow inlet of Mundaú Lagoon. A return flow factor larger than 0.7 could take into account the effect of returning flows from the inlet to the control region and consequently result in a flushing time which is at the same order of magnitude as the flushing time calculated by the numerical model. For example, using the information about tides and water volume in Mundaú Lagoon provided by [67
] and adopting a return flow factor of 0.95, the calculated flushing time would be on the same order of magnitude as the flushing time calculated by the e-folding method for Mundaú Lagoon.
By knowing the flow return factor b
in our study area, we could use the tidal prism method (Equation (7)) to generate a time series of the total tracer concentration in the study area. Figure 10
compares the time series of the tracer concentration calculated by the tidal prism method and sECOM. While the calculated time series from the tidal prism method with b
= 0.5 considerably mismatched the modeled time series from sECOM, the time series produced based on a calibrated b
were in good agreement with those from sECOM. Figure 10
shows that a return flow factor of 0.5 caused the tidal prism method to significantly overestimate the tracer concentration decay in Jamaica Bay. On the other hand, the tidal prism method based on a calibrated b
accurately duplicated the temporal variations in tracer concentration. The time series from sECOM showed profound tide-induced variations in tracer concentration, especially during the first few days of the simulation period, which cannot be captured using the tidal prism method. In each tidal cycle, ebb tides carried the tracers near the domain outlet to Rockaway Inlet, whereas flood tides returned the tracers back into the domain. The impact of tidal cycles gradually diminished as the tracer concentration in Jamaica Bay decreased over time. The time series also revealed that at the end of the simulation, between 16% and 25% of the released tracers remained within Jamaica Bay. The largest portion of unflushed tracers remained in the east and southeast of the bay, i.e., in Grassy Bay, Thurston Basin, Motta Basin, and Morton Basin.