*4.3. USGS High Water Marks vs. SLOSH Maximum Water Levels*

The observational measurements for Hurricane Sandy were supplemented by an extensive dataset of post-flood high water marks (HWMs). The USGS flagged, surveyed and collected more than 950 HWMs. Of those 950 HWM, 650 were classified to be independent (greater than 1000 ft apart from each other), and 257 flagged in CT, RI and MA were not surveyed due to lack of funding. Vertical accuracy was 0.26 ft in all counties except 0.47 ft in NJ-Union, Middlesex and Monmouth counties [3]. 559 HWMs were inside the SLOSH ny3 basin, and 312 had valid data, so excluding those close to the SLOSH boundaries, 284 HWMs were analyzed and 17 outliers (a HWM estimated from a streak on the wall of a steel shipping container, another identified by a mud line inside a small enclosed room under an air-conditioning unit, *etc.*) were removed. The remaining 268 HWMs distributed in different states (Table 10) were then compared to SLOSH-simulated inundation values AGL.

A comparison of the HWM estimates *vs.* SLOSH surge-plus-tides maximum water levels is shown in Figure 15. 34% of the simulated height at HWM locations have relative errors less than or equal to 10% (dark orange), 72% have errors less than or equal to 20% (orange cone) and 89% have errors less than or equal to 30% (yellow cone).


**Table 10.** Number of USGS High Water Marks (HWM) used to verify SLOSHsimulated maximum water levels for each state.

**Figure 15.** USGS High Water Marks (HWM) *vs.* SLOSH model-simulated surge-plustides maximum height of inundation (m) AGL. The dark orange cone depicts the 10% error, the orange cone depicts 20% error and the yellow cone depicts 30% error. The water surface elevation errors at most stations are within the 10%–20% range.

Table 11 summarizes the relative error of the HWM *vs.* SLOSH maximum water levels. Almost 90% have errors less than or equal to 30%. Of the remaining HWM locations where the relative error exceeds 30%, there were 17 locations where the SLOSH-simulated maximum water levels were greater than HWM and 13 locations where the SLOSH-simulated maximum water levels were less than HWM, so there is no clear error bias.


**Table 11.** Summary of USGS High Water Marks (HWM) *vs.* SLOSH-simulated maximum water level relative errors.

#### *4.4. Horizontal Distribution of Observations vs. SLOSH*

Figure 16 shows the SLOSH-simulated surge-plus-tides maximum envelope of water (relative to NAVD88) for Hurricane Sandy. Observations at NOAA stations (squares), SSS (triangles) and HWM (circles) have been added with the same color range for comparison. For the most part, the observations are in good agreement with the model results. Some HWMs have higher water level values than those simulated (red circles), particularly in west Raritan Bay, NY. It seems the water in the East River is not flowing through the grid properly. There could be many reasons for this including: unsimulated features in the wind field, the formulations of the surface and bottom stresses, lack of coupling to a wave model, and/or sophistication of the boundary conditions; however of particular significance is a lack of resolution in that area and a non-optimal orientation angle of the grid lines with respect to the river. More detailed investigation needs to be conducted and a new New York basin might need to be built to remedy this retardation of the water flow.

The distribution of the relative error between the observed and modeled maximum heights is shown in Figure 17. Errors are less than 10% in the Long Island Sound, the CT and RI coastlines and 20% along the south shore of Long Island (Breezy Point, Atlantic Beach, Long Beach, Jones Beach the Hamptons). Some isolated areas along the east NJ coastline (Surf City) exhibit higher relative errors.

The SLOSH model-simulated surge-plus-tides AGL results over land and maximum envelope of water over the ocean, as rendered by the interactive SLOSH Display Program [19], are compared to the Federal Emergency Management Agency (FEMA) Modeling Task Force (MOTF) fieldverified, "ground-truth" Hurricane Sandy Impact Analysis graphic [20], which depicts the final high-resolution storm surge extent (grey) and very high-resolution extent in NYC (blue) in Figure 18 to provide a more detailed verification of the inundation area. The geographical patterns of inundation agree quite well, especially at Breezy Point, Rockaway, the low-lying areas surrounding JFK airport and further east along the shores of East Bay and South Oyster Bay. The SLOSH wetting-and-drying algorithm performs skillfully inland to the west, in the area extending from south to north along the west bank of the Hudson River from Hoboken to Union City, NJ and further west in the larger Jersey City, Secaucus and Ridgefield area. Flooding over the river banks is also accurately simulated to the south along the Raritan River, the Washington Canal and the South River. The inundation area calculated from the SLOSH Best Track hindcast simulation was 561 km2 (216 sq mi).

**Figure 16.** SLOSH model-simulated surge-plus-tides maximum envelope of water (relative to the NAVD88 vertical datum) for Hurricane Sandy. Observations at NOAA stations (squares), SSS (triangles) and HWM (circles) have been added with the same color range for comparison. Water levels are in meters.

**Figure 17.** Geographical distribution of the relative error between the observed and SLOSH-simulated maximum water levels.

**Figure 18.** (**a**) SLOSH model-simulated inundation (ft) above ground level (AGL) over land and maximum envelope of water over the ocean, as rendered by the interactive SLOSH Display Program; and (**b**) Modeling Task Force (MOTF) field-verified, "ground-truth" Hurricane Sandy Impact Analysis graphic (courtesy of FEMA), which depicts the final high-resolution storm surge extent (**grey**) and very high-resolution extent in NYC (**blue**).

#### **5. Conclusions**

The verification analyses conducted in this study show that the NWS SLOSH storm surge prediction model is able to simulate the height, timing, evolution and extent of the water that was driven ashore by Hurricane Sandy (2012) with a high degree of fidelity. Upgrades to the numerical model in 2013, including the incorporation of astronomical tides with 37 harmonic constituents, have increased its hindcast accuracy and will enable forecasters to better predict the timing and extent of the total water level and inundation.

In addition, the model's extreme computational efficiency enables it to run large, automated ensembles of predictions in real-time to account for the high variability in atmospheric forcing that can occur in tropical cyclone forecasts, which makes the guidance designed to alert the public and prevent the loss of life more robust and reliable.

Quantitative comparisons (Figure 19, summary provided in Table 12) of SLOSH simulation results against water surface peak elevations measured at all 13 NOAA tide gauge stations, by 60 storm surge sensors deployed by the USGS prior to the storm, and from 268 HWMs collected by USGS—a total of 341 observations—reveal that the SLOSH model-simulated water levels at more than one-third (34%) of the data measurement locations have less than 10% error (dark orange cone), while 71% (89%) have less than 20% (30%) error (orange and yellow cones, respectively). The RMS error between the observed and modeled peak water levels is 0.47 m (1.5 ft) (Table 13).

**Figure 19.** Comparison of water levels (m) at all NOAA tidal gauges, USGS storm surge sensors (SSS) and High Water Marks (HWM) *vs.* SLOSH model-simulated maximum water levels (m). Water surface elevation errors at most locations are within the 10%–20% range (dark orange cone).

**Table 12.** Partition of relative error between observed and SLOSH-simulated maximum water elevation for all measurements: NOAA tide gauge stations and USGS storm surge sensors (SSS) and high water marks (HWM), cumulative (Cum) and individual (Ind).


**Table 13.** Root mean square error between observed and SLOSH-simulated maximum water elevation for all measurements: NOAA tide gauge stations and USGS storm surge sensors (SSS) and high water marks (HWM), cumulative (Cum) and individual (Ind).


The arrival times of the peaks in the water elevation observations at NOAA and USGS SSS stations and their SLOSH-simulated counterparts are in good agreement, as demonstrated by the hydrographs and the statistical calculations (RMSE and correlation) from the time series.

The SLOSH simulations underestimated the surge in some areas far from the point of landfall and far from the center of the SLOSH grid where the resolution is coarser (CT, MA, RI) and in the Raritan Bay where the resolution (2 grid cells) across the East River might not be allowing the water to flow freely into the bay. Many other factors may have contributed to the underestimation of water levels in these locations: grid resolution, basin size, boundary conditions, lack of waves in the simulations, the tidal method, wind field, surface stress, bottom stress, *etc*. In this case, the most likely reason for the error is the coarseness of the grid. Previous SLOSH studies [21] have shown that larger and higher resolution SLOSH grids and different parameterizations of the surface and bottom stresses can improve the accuracy of the storm surge results. Efforts are currently underway to test and validate a coupled SLOSH + SWAN modeling system [21] that includes surge, tides and waves.

The highly complex structure of Hurricane Sandy presented an operational challenge for the standard tropical version of SLOSH. Figure 20 shows a comparison between the winds produced by the SLOSH parametric wind model and the real-time multi-platform satellite surface wind analysis at 00 UTC on 30 October 2012 from the NOAA National Environmental Satellite, Data and Information Service (NESDIS), the Cooperative Institute for Research in the Atmosphere (CIRA) Regional and Mesoscale Meteorology Branch (RAMMB) at Colorado State University (CSU) [22] as Hurricane Sandy made landfall northeast of Atlantic City, NJ. The wind analysis combines information from five different data sources to create a mid-level wind analysis, which is then adjusted to the surface using empirical, radially varying coefficients obtained from reconnaissance aircraft and GPS dropwindsonde data. Despite the simplicity of the SLOSH parametric wind model, the simulated winds are remarkably realistic. There is strong wavenumber 1 asymmetry due to the storm's forward motion. The 50 kt (25.72 ms<sup>í</sup><sup>1</sup> ) isotachs in panels (a) and (b) are similar in orientation, shape and extent. The SLOSH surface friction simulates a reduction in wind speed of about 10 knots (5.14 ms<sup>í</sup><sup>1</sup> ) over Long Island Sound due to the downwind effects of the Long Island land cover. The wind directions in both panels also compare quite favorably.

**Figure 20.** Comparison of wind speeds from (**a**) the SLOSH parametric wind model and (**b**) the multi-platform surface wind analysis (courtesy of NOAA/NESDIS and CSU/CIRA/RAMMB). The white square in panel (**a**) depicts the area where the wind analysis (**b**) was conducted. Wind speeds are in kts for comparison (1 kt = 0.52 ms<sup>í</sup><sup>1</sup> ).

The basis of this study was to assess a baseline skill level of SLOSH and compare it to its latest improvements demonstrated by the inclusion of tidal constituents in SLOSH. Implementing gridded wind fields, an improved parametric wind model [12], and a combination thereof are planned upgrades to SLOSH.

The ExtraTropical Storm Surge Model (ETSS), developed by the NOAA/NWS Meteorological Development Laboratory (MDL), is a variation of the NWS SLOSH that runs operationally on NCEP's central computing system four times daily. The model is forced by real-time output of winds and pressures from the NCEP Global Forecast System (GFS) and produces numerical storm surge guidance for extratropical systems in 6 grids that cover the US East Coast, Gulf of Mexico, West Coast, Gulf of Alaska, Bering Sea and Arctic. This modeling system does not currently include overland flooding or tides. Work is currently underway to combine the ETSS and the newer versions of SLOSH, which include tides and inundation, via nesting from the coarser ETSS grids down to the latest higher resolution SLOSH grids.

An improved version of the Mattocks and Forbes [12] asymmetric parametric wind model, GWAVA (Gradient Wind Asymmetric Vortex Algorithm), is currently being incorporated into SLOSH. Blending the near-field winds from this more advanced parametric wind model with gridded far-field winds from the GFS or other numerical weather prediction models will potentially improve storm surge prediction by providing more realistic multi-scale wind forcing at the ocean surface and its hydrodynamic response.

The value of future upgrades to the SLOSH model and basin refinements can later be compared to this baseline study. This analysis will also be instrumental in the evaluation of other modeling systems and to assess how they might contribute to operational forecasting as NHC moves toward a multi-model ensemble.

#### **Author Contributions**

Cristina Forbes developed AutoSurge, ran the operational forecast and hindcast simulations, generated graphics and did the analysis and validation of observations vs. SLOSH results; Jamie Rhome provided his expertise in operational storm surge forecasting and communication of the storm surge threat; Craig Mattocks contributed his knowledge on the atmospheric forcing of storm surge simulations, forecast ensembles, parametric wind models, optimization of numerical models and visualization of the results; Arthur Taylor provided his expertise on the SLOSH model and implementation of the various upgrades used in the operational and hindcast simulations.

#### **Conflicts of Interest**

The authors declare no conflict of interest.

#### **References**


Miami, FL, USA, 2013; pp. 1–300. Available online: http://www.nhc.noaa.gov/data/tcr/AL182012\_Sandy.pdf (accessed on 26 November 2013).

