**4. Hindcasts**

Post-storm hindcast surge (S) and surge-plus-tides (ST) simulations were run for the SLOSH ny3 basin to determine the accuracy of the results. The hindcast simulation that generated surgeonly water levels was forced by wind parameters from the Hurricane Sandy Best Track to drive the SLOSH model.

A second hindcast simulation was run with surge plus tides. First, tides were spun up for 720 h. After this 30-day spin-up period with tides alone, a 100-hour SLOSH hindcast simulation was run with both tides and Best Track wind forcing.

The results were then compared with the water surface elevations recorded at NOAA tide gauge stations, measurements from temporary USGS storm surge sensors (SSS) and high water mark (HWM) estimates made by the USGS.

#### *4.1. NOAA Stations vs. SLOSH Water Levels*

The tide and total water levels were extracted from 13 NOAA stations (Figure 2) located in New York (NY), New Jersey (NJ), Rhode Island (RI), Connecticut (CT), and Massachusetts (MA) within the ny3 basin area and compared to the SLOSH water levels from the surge-only and surgeplus-tide hindcast simulations.

The time evolution of the observed *vs.* modeled water levels is shown in Figure 11 for the surgeonly (left panels) and surge-plus-tides (right panels) runs.

**Figure 11.** Hydrographs of surge **(left panels**) and surge + tides (**right panels**) at NOAA stations (**red**) *vs.* SLOSH simulations (**blue**) with RMS error and correlation calculated between the two time series. Time is in month/day and hours UTC (horizontal axis) and water elevations are in meters (vertical axis). The station numbers in the time series plots correspond to the locations shown in Figure 2.

**Figure 11.** *Cont.*

The water levels for surge and total water levels (surge-plus-tides) at the NY stations are in good agreement with the observations, as evidenced by root mean square errors (RMSE) of 0.17–0.36 m for surge and 0.19–0.51 for total water levels. SLOSH seems to underestimate the surge, but not the total water levels at CT stations. The RMSE ranges from 0.18 to 0.28 m (0.19 to 0.35 m) for surge (surge-plus-tides), respectively, in that state. The modeled surge and total water levels are slightly underestimated at RI and MA stations, with RMSEs of 0.15–0.19 m (0.22–0.26 m). The simulated

water surface elevations at NJ stations are characterized by RMSEs between 0.22 and 0.24 m (0.32 and 0.47 m) for surge (surge-plus-tides), respectively. The Cape May, NJ station is located near a SLOSH boundary, thus the phase is slightly accelerated (the simulated surge arrives too early) relative to the observations. Preliminary experiments, in which the boundary condition in the SLOSH grid was modified from deep to shallow water (since it is so close to the coast) at that model boundary, seem to improve the results for this station. It is anticipated that this adjustment will be included when a new higher-resolution SLOSH New York grid is built. The highest resolution in the current ny3 basin is 213 m. Considering only those stations away from the basin boundary, the correlations between the model-simulated and measured water surface elevations range from 0.83 to 0.94 for the surge-only, and 0.81 to 0.95 for the surge-plus-tides simulations.

Table 4 shows a summary of the NOAA stations and SLOSH surge (S) and surge-plus-tide (ST) simulation results. The observed peak of S arrived earlier than the observed peak of ST, except at Bergen Point, NY, Cape May, NJ, Chatham, MA and Nantucket, MA. The same timing was replicated in the SLOSH simulations, except at Bergen Point and Cape May where the peaks of S were simulated to arrive earlier than the peaks of ST. The RMS errors range from 0.15 to 0.41 m. The correlations range from 0.80 to 0.95.

**Table 4.** Summary of the NOAA stations *vs.* SLOSH surge (S) and surge-plus-tides (ST) simulation results. Times are in elapsed hours from the start of the model run—03:00 UTC, 27 October 2012. The numbers in column 1 correspond to the locations shown in Figure 2 and the time series plots in Figure 11.


Panels in Figure 12 display the maximum water levels for (a) surge and (b) surge-plus-tides and the time-of-arrival of the peaks for (c) surge and (d) surge-plus-tides, measured at NOAA stations *vs.* those simulated by SLOSH. Figure 12a,b shows the stations that fall within the 10% height error (dark orange) cone, 20% error (orange) cone and 30% error (yellow) cone. In Figure 12a the simulated surge at station locations in NJ and at two station locations in NY show errors between 10% (dark orange) and 20% (orange cone), while at station locations far from the point of landfall the modeled maximum surge is underestimated, The simulated surge-plus-tides water surface elevation errors at most station locations in Figure 12b are within the 10%–20% range. In Figure 12c,d the stations that fall in the ±3 h error range for the time-of-arrival of the peak are within the orange band and the ±6 h error range are within the yellow band.

**Figure 12.** NOAA stations *vs.* SLOSH maximum water levels for (**a**) surge and (**b**) surge-plus-tides and the time-of-arrival of the peak water levels for (**c**) surge and (**d**) surge-plus-tides. In (**a**) and (**b**), the dark orange cone depicts 10% error, the orange cone depicts 20% error and the yellow cone depicts 30% error. In panel (**a**) the simulated surge at 3 NJ and at 2 NY station locations show errors between 10% and 20%, while at station locations far from the point of landfall the modeled maximum surge is underestimated. In panel (**b**) the simulated surge-plus-tides water surface elevation errors at most station locations are within the 10%–20% range. In panels (**c**) and (**d**) the stations that fall in the ±3 h error range for the time-of-arrival of the peak are within the orange band and the ±6 h error range are within the yellow band. The simulated peak arrival times at most sensor locations are within 3 h of that which was observed, except at stations in RI and MA far from the landfall location in panel (**c**), and at Cape May (8536110) in panel (**d**) which is close to the boundary of the model grid.

The simulated peak arrival times at most sensor locations are within 3 h of that which was observed, except at stations in RI and MA far from the landfall location in panel (c), and at Cape May (station 8536110) in panel (d) because, as mentioned above, the station is located too close to the model boundary.

#### *4.2. USGS Storm Surge Sensors vs. SLOSH Water Levels*

The USGS deployed a temporary network of water level and barometric pressure sensors at 224 locations along the Atlantic coast from Virginia (VA) to Maine (MN). This was the second-largest deployment of storm-tide sensors, exceeded only by the number distributed during Hurricane Irene (2011), which made landfall in the same area of the US [3]. 145 water level and 9 wave-height sensors were deployed at 147 locations while 8 rapid deployment gauges (RDGs), and 62 barometric pressure sensors were deployed at additional locations. The water level sensors recorded water levels at 30-second intervals, the wave sensors recorded data every 2 s, the RDG sensors recorded water levels and meteorological data every 15 min and the barometric pressure sensors recorded at 30-second intervals. The water levels were recorded in feet above NAVD88. Unfortunately, 7 water level sensors were lost or the structures to which they were attached were damaged, 4 water level sensors and 1 wave sensor did not record (the water did not rise high enough to be measured) and 2 RDGs were destroyed by flood. This temporary monitoring network augmented the existing tide gauge networks and helped characterize the height, extent and timing of the storm tides.

Table 5 shows the USGS storm surge sensors (SSS) deployed in each state that were used to compare water level measurements against results from the SLOSH surge-plus-tides simulation.


**Table 5.** The numbers of USGS storm surge sensors (SSS) deployed in each state, eliminated from the analysis, and used to verify the SLOSH model surge-plus-tides simulation results (\* denotes that the sensor was both outside the SLOSH basin and measured waves, not surge or tides).

Of the 154 sensors, only 81 were located in the ny3 basin. 9 sensors that recorded highfrequency wave heights could not be used for verification purposes because the coupled surge (SLOSH) plus wave (SWAN, Simulating WAves Nearshore) modeling system is still undergoing development and testing. 12 sensors were close to the SLOSH basin boundary or were sited in locations that were contaminated by local effects (some sensors were buried under the sand attached to an underground piling, others were surrounded by high marsh grass/weeds, some sensors were mounted on structures that block flow in most directions, other sensors were located in narrow alleys between buildings where extreme, unrepresentative channeling can occur, *etc.*). These sub-grid scale features and geomorphologies are not modeled or resolved by the SLOSH grid, so those sensors were not employed in the verification process. Therefore, 60 SSS sensors (Figure 13a) were compared with the model results (Figure 13b).

**Figure 13.** (**a**) Map of USGS Storm Surge Sensor (SSS) locations; (**b**) Hydrographs of inundation recorded by USGS SSS (**red**) *vs.* SLOSH-simulated surge-plus-tides water levels above ground level (AGL) (**blue**) with RMS error and correlation calculated between the two types of time series. Time is in month/day and hours UTC (horizontal axis) and water elevations are in meters (vertical axis). The sensor numbers in the time series plots in (**b**) correspond to the locations shown in panel (**a**).

A comparison between the SSS sensor measurements and SLOSH-simulated water levels AGL, displayed in Figure 13b, show the extent and degree of inundation and how well the model values agree with the observed water levels. The hydrographs at the SSS stations show excellent agreement in both amplitude and phase with the SLOSH model-simulated surge-plus-tides results.

Figure 14a shows the SSS sensor measurements that fall within the 10% error (dark orange) cone, 20% error (orange) cone and 30% error (yellow) cone. The SLOSH-simulated surge-plus-tides values at most station locations are within the 10%–20% error range. Figure 14b shows the stations that fall in the ±3 h error range in the arrival time of the peak (orange) and ±6 h error (yellow). Most of the simulated peak arrival times are accurate within 3 h of the observed arrival times.

Table 6 compares the USGS storm surge sensor (SSS) *vs.* SLOSH maximum water surface elevations from the SLOSH surge-plus-tides simulation, the timing of the peak water levels, and

**Figure 13.** *Cont.*

calculations of the RMS errors and the correlations. Tables 7, 8 and 9 provide summary statistics for the data in Table 6. The RMSE of the SSS *vs.* SLOSH-simulated water levels show that 80% of the values simulated at station locations are less than 0.5 m (1.6 ft) in error and have correlations greater than 0.60. The SLOSH-simulated relative errors are less than 0.30 at 92% of the SSS sensor locations.

**Figure 14.** USGS SSS sensor *vs.* SLOSH-simulated surge-plus-tides (**a**) maximum water levels (m) and (**b**) time-of-arrival (hours) of the peak water levels. In (**a**), the dark orange cone depicts the 10% error, the orange cone depicts 20% error and the yellow cone depicts the 30% error. The water surface elevation errors at most sensors are within the 10%–20% range. In (**b**) the stations that fall in the ±3 h error range for the timing of the peak are within the orange band and the ±6 h error range are within the yellow band. Most sensors' observed *vs.* modeled peak arrival times are within 3 h.

**Table 6.** USGS Storm Surge Sensors *vs.* SLOSH Peak Arrival Times and Water Levels. Times are in elapsed hours from the start of the model run—03:00 UTC, 27 October 2012.


**Table 6.** *Cont.*



**Table 6.** *Cont.*

**Table 7.** Partition of USGS storm surge sensors (SSS) *vs.* SLOSH root mean square errors (m).


**Table 8.** Partition of USGS storm surge sensors (SSS) *vs.* SLOSH correlations.


**Table 9.** Partition of USGS storm surge sensor (SSS) *vs.* SLOSH relative errors.

