A Model Study on the Summertime Distribution of River Waters in Long Island Sound

Abstract

Long Island Sound (LIS), a large urban estuary in the northeastern USA, receives freshwater from many rivers along its northern shore. The size of these rivers varies widely in terms of basin area and discharge. The Regional Ocean Modeling System (ROMS) was applied with conservative passive tracers to identify the distribution, mixing, freshwater residence times, and storm response for all of LIS’s river systems during the summer of 2013. A watershed model was applied to overcome the lack of adequate river discharge observations for coastal watersheds. The Connecticut River was the largest contributor to riverine freshwater throughout the estuary despite its entry point near the mouth. The Connecticut River strengthened bulk stratification in the eastern LIS the most but acted to weaken stratification near the mouths of other rivers and in far western LIS by freshening waters at depth. The Housatonic and Hudson Rivers had the strongest influence on stratification in central and western LIS, respectively. Smaller coastal rivers were the most influential in strengthening stratification near the southwestern Connecticut shoreline. The influence of small coastal rivers was amplified after a major storm due to shorter storm response times relative to the larger rivers. Overall, river water was close to a well-mixed state throughout LIS, but more stratified near river mouths. Freshwater residence time estimates, meanwhile, indicated monthly to multi-seasonal time scales (43 to 180 days) and grew longer with greater distance from the LIS mouth.

Appendices

Appendix 1. GSFLOW Parameterization

Each of the coastal watersheds (Fig. 1) was identified as a hydrologic response unit (HRU) in GSFLOW with its own unique watershed properties. Land use, soil type, rock type, and watershed boundaries were obtained from the University of Connecticut Center for Land Use Education and Research (UCONN CLEAR, http://clear.uconn.edu) and from the Connecticut Department of Energy and Environmental Protection (www.ct.gov/deep/gisdata). These data were used to determine values for the model parameters for each HRU (Table 3). Note that GSFLOW was run using English (instead of metric) units, as it is in most applications. Fractions of land type (i.e., water, deciduous, coniferous, grass, developed, barren) were determined for each HRU. Using these fractions, cov_type was set to the most prevalent land type in each HRU. Summer and winter canopy densities (covden_sum and covden_win, respectively) were determined for each HRU using the land type fractions of coniferous and deciduous forests (summer canopy being the sum of both fractions and the winter canopy being only the fraction of coniferous forests). Summer and winter canopy storage capacities in GSFLOW (srain_intcp and wrain_intcp, respectively) were calculated using the fraction of deciduous and coniferous forests in each HRU and multiplying each fraction by its respective storage capacity. The storage capacities of deciduous (0.055 in. during summer and 0.028 in. for winter) and coniferous forests (0.063 in.) were based on values in Hörmann et al. (1996).

Table 3 GSFLOW parameter definitions per Markstrom et al. (2008)

Soil type was determined from the United States Department of Agriculture (USDA) Natural Resources Conservation Service (NRCS, http://www.nrcs.usda.gov/) which provided sand, silt, and clay percentages for different depth ranges at hundreds of locations in Connecticut. The most prevalent soil type was first determined for each soil profile, and then, each HRU soil type was set as the predominant soil type (sand, silt, or clay) among sampling locations within HRU boundaries.

The fraction of impervious surface area (hru_percent_imprev) and the minimum fraction of surface area that contributed to surface runoff (carea_min) were determined for each HRU using the UCONN CLEAR land use dataset. Impervious surface area fraction was set to the fraction of each HRU that was classified as being “developed” while the minimum fraction that could contribute to surface runoff was set to the fraction that was classified as being “water.” The maximum fraction that could contribute to surface runoff (carea_max), meanwhile, was set as the sum of carea_min and the fraction that was classified as flooding occasionally, frequently, or very frequently per the Soil Flood Class GIS dataset available from the CT DEEP.

The linear flow coefficient used for computing the gravity drainage to the groundwater reservoir (ssr2gw_rate) was set to 1 in. day⁻¹ multiplied by the fraction of glacial stratified drift (both coarse and fine grains) (F _{Glacial_Strat}) from the CT DEEP Surficial Stratified Drift GIS dataset. This method is similar to the approach of Bjerklie et al. (2010). The same fraction of glacial stratified drift was then used to compute a diffusivity (the numerator in equation 11) from the ratio of transmissivity and storativity of glacial stratified drift (T _gsd and S _gsd) and glacial till (T _till and S _till). T _gsd, S _gsd, T _till, and S _till were set to 10,000 ft² day⁻¹, 0.2, 200 ft² day⁻¹, and 0.01, respectively, per Bjerklie et al. (2010). Diffusivity was then divided by the square of a constant length scale (L) of 1000 ft. to obtain the linear flow coefficient for the routing of groundwater to streams in GSFLOW (gwflow_coef) per Eq. 11.

$$ \mathrm{gwflow}\_\mathrm{coef}=\frac{\left({F_{\mathrm{Glacial}\_\mathrm{Strat}}}^{\ast}\left(\frac{T_{\mathrm{gsd}}}{S_{\mathrm{gsd}}}\right)+\left(1-{F_{\mathrm{Glacial}\_\mathrm{Strat}}}^{\ast}\left(\frac{T_{\mathrm{till}}}{S_{\mathrm{till}}}\right)\right)\right)}{L^2} $$

(11)

This parameterization is based on a scaling of the groundwater flow equation (e.g., Goode and Konikow 1990). The flow from groundwater to the streams is determined by multiplying the gwflow_coef by the storage in the groundwater reservoir.

Nine additional parameters were set through an optimization scheme to minimize the root mean square error (RMSE) between the modeled and the observed discharges (described below). These parameters are listed in Table 4 with a description, and the value they were set to for each of the three subregions. The values of these parameters were determined by setting them to the default values provided in the GSFLOW manual (Markstrom et al. 2008), varying each parameter (one at a time) from its lowest to highest possible value on a one-tenth scale, and selecting the value that produced the lowest root mean square error between the model output and the observations for at least one river in each subregion. Upon completion of fitting the ninth parameter, the values that produced the smallest RMSE for each parameter were set as the updated initial values and the process was run again. At least five iterations were completed for each subregion’s parameter fitting; the fitting scheme was halted once the value for each parameter stopped changing between iterations. The fminsearch function in MATLAB (Nelder and Mead 1965) also was used in a similar manner, using the same initial default values and seeking a minimum in RMSE. The use of this function returned similar results to the first method. GSFLOW also was tested with seven of these parameters set to the corresponding HRU’s values from Bjerklie et al. (2010) and with the remaing two set to values suggested by Bjerklie (personal communication). Ultimately, the values determined with the iterative process previously described provided discharge estimates with lower RMSE and and higher r ² values when compared with observations.

Table 4 Nine GSFLOW parameters set via optimization for the lowest RMSE

The rivers selected for each subregion’s parameter fitting were selected because (1) USGS had several years of continuous gage data for comparison, (2) the gage data available were measured below most tributaries, and (3) they were not greatly regulated via damming. For the southwest subregion, the Sasco Brook (USGS gage no. 01208950) near Southport, CT, was used with a dataset spanning from 1 January 2005 to 1 December 2013. For the south central subregion, the Indian River (USGS gage no. 01195100) near Clinton, CT, was used with a dataset spanning the same period. For the southeast subregion, Latimer Brook (USGS gage no. 011277905) in East Lyme, CT, was used with a dataset spanning from 9 September 2008 to 31 October 2012. Prior to comparison of GSFLOW flow output to gage data, GSFLOW output for the corresponding HRU was scaled according to the gaged area. This was necessary because two of the three gages used had a drainage basin ~ 25% smaller than the GSFLOW output due to the gage location within the watershed. For observational comparison, the GSFLOW estimates of discharge from Sasco Brook, Indian River, and Latimer Brook were therefore multiplied by 0.72, 0.76, and 1.00, respectively. Statistics from the comparison of GSFLOW modeled discharge to gage measurements are shown in Table 5. Overall, percent error between the measured and the observed discharges ranged from 43 to 64% of the standard deviation of the observed discharge. This is comparable to the level of agreement in other watershed-modeling efforts (e.g., Bjerklie et al. 2010; Ely and Kahle 2012).

Table 5 GSFLOW discharge estimates and gaged discharge statistics for small coastal rivers

Appendix 2. Estimation of Exchange Flow at Coastal River Mouths

The GSFLOW daily river discharge (Q _river) was used in conjunction with salinity observations and ROMS results to constrain conditions at each small coastal river’s mouth. Discharge estimates from GSFLOW for small coastal rivers were modified using a steady-state salinity and volume balance based on the Knudsen relationship (Knudsen 1900; MacCready and Geyer 2010). The benefit of this was that the change in river water salinity and volume flux caused by the movement of saltier LIS water up the non-resolved river channels at depth could be represented. Hence, the volume flux (of mixed water) flowing out of each coastal river mouth into LIS (Q_outflow) was determined via Eq. 12.

$$ {Q}_{\mathrm{outflow}}=\left({Q}_{\mathrm{river}}\times {S}_{\mathrm{inflow}}\right)/\left({S}_{\mathrm{inflow}}-{S}_{\mathrm{outflow}}\right) $$

(12)

S _inflow was the lower-layer salinity flowing into the river’s estuary (and out of LIS) at depth and was set from the adjacent ROMS grid cell. It was calculated at each model time step from the vertically averaged salinity of the lower 17 of 20 equally spaced sigma levels. Note that because GSFLOW output was daily, its Q _river values were linearly interpolated to ROMS time steps. S _outflow (the upper-layer outflowing salinity) was then calculated as S _inflow − ΔS, where ΔS was based on field observations and held constant throughout the model run.

The field observations used to constrain ΔS consisted of conductivity, temperature, depth (CTD) casts made in 28 of the small coastal rivers. Each river was sampled on only 1 day. Sampling of all 28 rivers took place over a 2-week period in July 2013 on days that had no rainfall. All casts were made within 90 min of low slack tide from a bridge or dock near the river’s mouth via a YSI Sontek CastAway CTD. Each sampled river’s ΔS was set to the salinity difference between the average salinities above and below the measured pycnocline. For each of the 13 rivers without CTD measurements, the ΔS from the river with the closest basin size within the same subregion was applied. Each river’s outflow volume flux and salinity (Q _outflow and S _outflow) were calculated in ROMS for each time step and applied to the three upper sigma levels at the point source location. The volume flux and salinity flowing into each river mouth (Q _inflow and S _inflow) were distributed throughout the remaining lower levels; Q _inflow was calculated with equation 13:

$$ {Q}_{\mathrm{inflow}}=-\left({Q}_{\mathrm{outflow}}-{Q}_{\mathrm{river}}\right) $$

(13)

This approach does not include the full time variability of estuary exchange that occurs in nature but is considerably better than entirely neglecting the estuary processes that influence stratification at these coastal river mouths.

Appendix 3. Comparison of ROMS Output to Observations

LIS water survey data available from the CT DEEP were processed and compared to ROMS tidally averaged output for summer 2013. The observational stations are spaced along the LIS central axis from the head to the mouth. Model results were interpolated to the same locations, depths, and times of the survey observations. Figure 10 scatter plots model temperatures and salinities versus observations with the regression line and a reference 1:1 line. Figure 11, meanwhile, shows the seasonal average of the temperature and salinity measurements made by the CT DEEP and the corresponding seasonal average (only using observed times) temperature and salinity outputs from ROMS, as well as their differences.

Model output was too fresh (with a − 0.77-psu bias) and too warm (with a + 2.01 °C bias) for the June–August 2013 study period. Modeled salinity had an r ² of 0.83 and a point-to-point RMSE of 0.89 psu when compared to observations. Half of this RMSE was due to the bias. A linear fit produced a regression slope of 1.12. Modeled temperature, meanwhile, had an r ² of 0.82 and a point-to-point RMSE of 2.28 °C. Half of this was also due to the bias. A linear fit produced a regression slope of 1.06. Overall, modeled and observed salinity stratifications were close and the model thermal stratification was reasonably close with the observations being more thermally stratified.

Fig. 10

Comparison of CT DEEP temperature (a) and salinity (b) observations to interpolated ROMS model output from 13 June 2013 to 29 June 2013

Fig. 11

Average temperature and salinity measurements from CT DEEP water quality surveys from 13 June 2013 to 29 June 2013 (a, d), averaged ROMS output interpolated for the same times and locations as the CT DEEP measurements (b, e), and the difference between them (c, f)