2.3.2. Initial and Boundary Conditions

#### 2.3.2.1. Model Validation

Initial model calibration and validation were performed using data from the NOAA-NOS 1984–1985 circulation survey [7]. An "astronomical tides only" scenario was used to assess the model's capability of accurately representing the tidal dynamics. The model was further calibrated using observed data from 1984 to 2012 for model forcing and comparison. Roughness calibration was performed based on information from a sedimentological survey of the upper Delaware Estuary [8], leading to local roughness parameters ranging from 0.001 m in the downstream section of the model to 0.015 m in the coarser upstream section.

#### NOAA/NOS Survey 1984

The National Oceanic and Atmospheric Administration and National Ocean Service (NOAA/NOS) conducted a Delaware Bay and River circulation survey in 1984/1985. Stations within the model domain upstream of the Chesapeake and Delaware Canal were used for this study. The majority of measurements were conducted from February through April 1984. Five water level stations and seven current stations were available for model forcing, as reference, and to develop tidal constituents. In the tidal-only scenario the downstream open boundary was forced using the predicted water level for Delaware City based on 37 tidal constituents from contemporary water level data. The flow boundaries were forced using annual mean discharge from 23 USGS river gauges.

No observed water level was available for Delaware City in 1984 to force the hindcast scenario, thus the water level time series from the nearby Reedy Point station was shifted in phase to match the timing at Delaware City. Observed discharge from 23 USGS stations provided data for the flow boundaries. The bathymetry used for grid generation was assembled from individual sounding datasets downloaded from the NOAA National Geophysical Data Center, Digital Elevation Model Discovery Portal [9] and converted to NAVD88 using VDATUM [10]. Additional soundings of smaller tributaries of interest were conducted by PWD and integrated into the bathymetry data set.

#### PWD Long Term Current Survey 2012/13

In May 2012 PWD installed three buoy mounted ADCPs within the model domain to collect long term current measurements for additional model calibration and validation. The NOAA Physical Oceanographic Real-time System (PORTS) for the Delaware Bay provided current data at a station near Philadelphia (db0301) and water levels at five stations within the domain [11] (Figure 3). Observed water level data for Delaware City and discharge data from all gauged tributaries along the model domain were used to force the open boundaries. An area ratio based approach was used to estimate discharge for ungauged tributaries and for run off areas downstream of USGS gauges and along the Delaware River. Wind forcing data were generated from measurements at five stations within the domain obtained from the National Climatic Data Center [12].

#### 2.3.2.2. Dye Study 1997

The dye study was conducted in November 1997. Observed water levels were available for stations at Reedy Point and Philadelphia at this time. Reedy Point water level data was shifted in phase to be used as open boundary forcing and the Philadelphia water level data was compared to model results for validation. Observed discharge from USGS gauges were used as available and discharge for ungauged tributaries and runoff areas were estimated using an area ratio based approach. Since the dye study's main goal was to observe a wet weather event, all Philadelphia CSO inputs were included in the model forcing. The PWD Hydrologic and Hydraulic (H&H) modeling group maintains a validated Stormwater Management Model (SWMM) of each of Philadelphia's three wastewater plant drainage districts. The SWMM model utilizes precipitation data, geospatial data of the land cover of the contributing service area, and numeric representation of the combined sewer system to simulate CSO flows. A range of flow estimates for each of the City's 164 CSO regulators and reported flows from the three wastewater treatment plants were provided for the dye study simulation exercise.

For the study, dye was injected into the sewer line 180 m back from the end of pipe. An average dye concentration of 236 parts-per-billion (ppb) was measured downstream of the injection point at the end of the pipe. The dye was injected upstream of a regulator that directs flow to a treatment plant during dry weather and allows for overflows into the river during storms. Thus, a considerable amount of dye was likely redirected to the plant and did not reach the outflow where the concentration was measured. The reported discharge was back calculated based on the measured concentration and the total amount of dye injected. Application of the reported discharge resulted in overprediction of dye concentrations in the river. As an alternative, the modeled CSO discharge for this sewer line was used, which resulted in good agreement with observed dye concentrations in the river. Wind fields were generated from observed data of three NCDC stations within the model domain.

#### **3. Results and Discussion**

#### *3.1. Model Validation*

For the astronomic tidal-only simulation in February through April 1984, water level results at Philadelphia showed good agreement with predicted time series as shown in Table 1 below. Amplitude errors range from 0 to 6 cm for water level. A slight shift in phase exists compared to observed data, which explains higher values for the RMSE. The RMSE and Skill by Willmott [13] are 12 cm and 0.98, respectively. Results for all water level stations range from 9 to 15 cm for RMSE and 0.98 to 0.99 for Skill.


**Table 1.** Tidal-only harmonic constituents: predicted *vs.* model for water level and major velocity at Philadelphia NOAA stations 8545530 and C51.

Velocity results also showed good agreement with predicted time series at Philadelphia station C51 from the NOS Delaware River and Bay Circulation Survey. Velocity data were measured 8.5 m above bottom corresponding to model results from the second layer below surface. Amplitude errors ranged from 1 to 7 cm/s as shown in Table 1. The RMSE and Skill are 11 cm/s and 0.98 respectively. Results for currents range from 7 to 17 cm/s for RMSE and 0.42 to 0.98 for Skill at all stations.

For the hindcast simulation in August through September 2012, water level results showed good agreement with predicted time series with amplitude errors smaller than 3 cm as shown in Table 2 below. The RMSE and Skill are 7.7 cm and 0.99.

Velocity results also showed good agreement with predicted time series as shown in Table 2 below. Amplitude errors range from 0 to 7 cm/s. The RMSE and Skill are 8.5 cm/s and 0.98.


**Table 2.** Hindcast harmonic constituents, August–September 2012: observed *vs.* model for water level and major velocity at Philadelphia NOAA stations 8545240 and PWD Buoy B, layer 4.

#### *3.2. Dye Study 1997*

Dye simulation results were compared to in-situ fluoroscopy observations that were converted to ppb by weight. The most fully-developed plume is represented by Mapping 3, which is comprised of survey observations interpolated over the 3.5 h of Day 2, low-slack tide (Figure 4). Figure 5 below shows contour plot visualizations of simulated dye results for the corresponding Mapping 3 time, which successfully characterized the observed plume. The extent of the 0.01 ppb contour line, thus the total detectable plume, matched the observed extent very well.

Transect plots of the dye results are shown in Figure 6 in which generally good agreement with observed concentrations are shown. Less dye was transported in the downstream extent of the plume in the model simulation than was measured in the survey as seen at profile P2, but this result is within an acceptable range.

A strong wind co-aligned with the Delaware Bay longitudinal axis led to a setdown throughout the estuary, which is visible at the Philadelphia NOAA water level station as a drop in mean water level of approximately 0.6 m. This resulted in a barotropic emptying of the upper estuary that transported much of the dye mass out of the domain of the original study. The model response to this setdown showed good agreement by matching the outflow of volume as seen in a plot of the subtidal water level at Philadelphia (see Figure 7).

**Figure 4.** Mapping 3 contour plot of low-slack, Day 2 survey results. Inset shows location of dye-injection point. Model results of profiles P2, P3, P4 and P5 are shown in Figure 6.

**Figure 5.** Contour plots of simulated dye injection, at time of Mapping 3. Axes in kilometer, dye in ppb, and time in Julian days.

**Figure 6.** Model results *vs.* observed concentrations for profiles P2, P3, P4 and P5.

**Figure 7.** Water level and subtidal water level scenarios: (1) tidal-only boundary forcing with no local wind (**solid gray**); (2) observed boundary forcing with no local wind (**red**); and (3) observed boundary forcing with local wind (**blue**).

To demonstrate the impact of meteorological forcing on dye transport, three scenarios were simulated: (1) tidal-only boundary forcing comprised of harmonic constituents from the NOAA Delaware City station with no local wind; (2) observed water level that contained the down-bay setdown as a subtidal signal was applied at the lower model open boundary without a local wind field; and (3) the same observed boundary forcing was applied but along with a composite local wind field.

Comparison of the water level and subtidal plots between Scenarios 2 and 3 demonstrated the dominance of the down-bay subtidal set-down in both cases, but show only a very small impact on water levels from local wind within the model domain (Figure 7). This influence of along-estuary wind stress on subtidal fluctuations in the Delaware Estuary is consistent with the findings of Janzen and Wong [14].

**Figure 8.** Model dye results *vs.* observed: Scenario 1 and Scenario 3 showing impact of barotropic setdown on dye transport.

Comparison of observed and simulated dye concentrations in Scenario 3 during the setdown event also showed good agreement (see Figure 8). Results from Scenario 1 with tidal-only boundary forcing shows the range of error that would be experienced without simulating the effects of the estuarine setdown.

The influence of bathymetry on dye distribution can be seen in the extent of the plume. The mixing length, the length after which full lateral mixing can be expected in a channel, was previously estimated to be on the same order of magnitude as the tidal excursion in this area [15]. Thus, full lateral mixing could be expected within the first day of the dye study. Instead, the plume largely moved along the Pennsylvania shoreline, with its center of mass following the navigation channel (Figure 5). In areas where the navigation channel shifted between shores (Figure 9) or where the entire river cross section was deeper (Figure 10) the plume followed as well, further confirming bathymetrical steering induced by the presence of the navigation channel.

**Figure 9.** Modeled plume extent with shifting navigation channel. Bed elevation in meters, dye in ppb.

**Figure 10.** Modeled plume extent in deep river section.
