# Modeling Storm Surge and Inundation in Washington, DC, during Hurricane Isabel and the 1936 Potomac River Great Flood

^{1}

^{2}

^{*}

## Abstract

**:**

^{2}equal to 0.93 and 0.98 at the Wisconsin Avenue and Washington gauges, respectively. A simulation was also conducted for reconstructing the historical 1936 Potomac River Great Flood that inundated downtown. It was identified that the flood water, with a velocity exceeding 2.7 m/s in the downstream of Roosevelt Island, pinched through the bank northwest of East Potomac Park near DC. The modeled maximum inundation extents revealed a crescent-shaped flooding area, which was consistent with the historical surveyed flood map of the event.

## 1. Introduction

^{2}) [8] and LiDAR (light detection and ranging) data was applied to study the effect of distributed roughness on flows in the flood plain [9]. Wang et al. (2014) [10] successfully used the semi-implicit formulation combined with sub-grids in simulating inundation in the New York City during Hurricane Sandy.

^{3}/s, which was 39-times the normal daily flow, and water levels of 8.5 m and 5.7 m were observed at the Chain Bridge and at the Key Bridge (3.2 km apart), respectively [11]. In the Upper Potomac River, the flow passes through the fall-line as a fluvial river, transitions into a tidal river and eventually becomes a major estuary downstream. In the process, the direction of currents, flow pattern, frictional resistance, the geomorphology and the sediment characteristics are all subject to change as the flow regimes change. Works have been attempted to make predictions in the region for the combined storm surge and riverine flooding, but with shortcomings or limited success. The USGS has developed a hydrodynamic model for simulating unsteady flow in a network of open channels and implemented the model for the tidal Potomac River [12]. The effect of freshwater inflow, tidal currents and meteorological conditions were tested, but have not been applied for storm conditions. Recently, Mashriqui et al. (2010) [13] initiated the CERIS (Coastal, Estuary, River Information Services) system to provide an integrated suite of water information for hazard mitigation, water resources and ecosystem management. The unsteady HEC-RAS (Hydrologic Engineering Centers River Analysis System) model was developed and tested for a 2003 Hurricane Isabel simulation, but the phase lagged by 4–6 h and the peak elevation under-predicted by 30–50 cm when compared with the observations measured at NOAA’s Washington, DC, waterfront station. The National Weather Service’s (NWS) Advance Hydrologic Prediction Service was responsible for the forecast of the river discharge into the Upper Tidal Potomac River, but with a disclaimer that their forecasts do not include the wind-induced storm surge. Lastly, EA Engineering, Inc. of Hunt Valley, MD (2001) [14] applied RMA2, RMA4 and SED2D, a suite of finite element hydrodynamic, transport, and sediment models developed by Army Corps of Engineers, in the upper reach of the Potomac River only for the dye-tracer and turbidity plume studies.

## 2. Study Area

^{3}/s; the flow may be less than 40 m

^{3}/s in the summer and reaches 3800 m

^{3}/s during flood periods. The tide in the Potomac is an integral part of the Chesapeake Bay system; originating from the Atlantic Ocean and propagating upstream along the main stem of the bay into the Potomac River. It can reach up to the Chain Bridge, where the tidal influence ends. The mean tidal range at Wisconsin Avenue is approximately 0.9 m. The tidal phase lags 11.5 h behind that at Hampton Roads at the mouth of the Chesapeake Bay. The model grid was constructed from the Little Falls (USGS Station 01646500; latitude 38°56′59.2′′ longitude 77°07′39.5′′), MD, at the fall line to Colonial Beach, VA, with a total length of about 120 km, as shown in Figure 2a. The domain covers about 2/3 of the tidal Potomac River area and contains a total of 18,259 base grids in square elements with a resolution of 200 m × 200 m and incorporates sub-grids (the sub-grids will be described in detail in Section 3). The bathymetry and topography associated with the model domain ranging from −10 m to 10 m (minus represents above ground) are displayed in Figure 2b. The observation stations used for the study include Little Falls, MD (USGS), Wisconsin Avenue (USGS), Washington, DC, waterfront (NOAA), Colonial Beach, VA (NOAA), and Lewisetta, VA (NOAA), whose locations are marked by solid symbols shown in the left panel of Figure 1. Among these stations, Washington, DC, is one of the longest-serving tide stations in the nation, which started operation 15 April 1931. For this study, the mean sea level is used as the datum.

**Figure 1.**(Left) The Potomac River modeling domain (shaded) and observation stations used for the study; (right) the zoom-in map of Washington, DC, and the Upper Tidal Potomac River.

## 3. Storm Surge and Inundation Model Incorporating Sub-Grids in the Upper Tidal Potomac River

#### 3.1. Model Description

^{2}(Unstructured Tidal Residual Intertidal Mudflat Model, power 2 version). The model is governed by the three-dimensional shallow-water equations with the Boussinesq approximation and is solved for free surface elevation, water velocities and salinity in a Cartesian coordinate system. The model was formulated with an efficient semi-implicit, Eulerian-Lagrangian scheme on unstructured orthogonal grids that includes both 3D barotropic and baroclinic processes pertaining to tide, wind and gravitationally-driven circulation on an f-plane [15,16,17]. The Potomac River is one of the major tributaries of the Chesapeake Bay, whose drainage area is 38,000 km

^{2}, and the mean annual mean river discharge is 360 m

^{3}/s. The Upper Tidal Potomac River is dominated by fresh water discharge, wind and tide. The tide from downstream can reach up to the Chain Bridge near DC, whereas the salt water intrusion normally only reaches up to the U.S. Route 301 Bridge near Colonial Beach. The length of the salt intrusion upstream from the lower Potomac River varies with the season depending on the magnitude of the freshwater discharge, but in general, the transition zone moves around Colonial Beach. The temperature-induced stratification is small because of the shallowness of the estuary. Thus, the region from the fall line to Colonial Beach, which was chosen as the model domain, can be reasonably considered as the vertically well-mixed tidal fresh zone with the downstream side ends in the transition zone. Because the interest of the present paper is focused on barotropic motions driven by the river, tide and wind-induced surge in the Upper Tidal Potomac River, using the vertically-averaged 2D version of the model (but including 2D temperature) for the domain chosen is thus appropriate.

**Figure 2.**(

**a**) The Potomac River grid domain including land area around Washington, DC; (

**b**) the combined bathymetry data (30-m resolution) and LiDAR-derived topography (10-m resolution) used.

_{j}is sub-grid velocity, ϛ the surface elevation and cf is a dimension-less friction coefficient for which a formulation, such as Chezy’s or Manning’s, can be given.

_{j}is not a function of time. From this, it follows that the equation can be rewritten as u

_{j}= Ω

_{j}$\sqrt{\zeta}$

_{x}. Assuming the pressure gradient is constant on each edge (but velocity, friction and depth are variable), it can be shown that the velocity of the individual sub-grid can be obtained by the base grid velocity times the ratio of the hydraulic conveyance of the sub-grid to that of base grid on each side of the grid edge, based on the following formula:

_{j}||, Ω

_{j}) and (||U||, Ω) are the velocity and conveyance for the sub-grid and base grid, respectively, and J defines the total number of wet sub-grids within a base grid.

#### 3.2. Incorporation of LiDAR-Derived DEM into the Sub-Grid Model Domain

**Figure 3.**Three example of bathymetric transects in the Upper Potomac River used to verify bathymetry interpolation, with corresponding sounding data published in EA Engineering (2001) [14] (bottom left) and the model’s sub-grid bathymetry (bottom right) in the vicinity of the Washington aqueduct.

**Figure 4.**Detailed feature of the based grid vs. sub-grids in Washington, DC, near Roosevelt Island. The thicker white line shows the 200-m base grid with each grid cell containing a 20 × 20 of 10 m × 10 m sub-grid cells. The resolution is such that LiDAR data are in 10-m resolution and bathymetry in 30-m resolution. An example of the bathymetry cross-section is shown in the lower left corner.

## 4. Modeling the 2003 Hurricane Isabel Event

^{3}/s recorded at the USGS Little Falls, MD, station at the fall line.

#### 4.1. Model Setup

_{f}is the friction slope.

_{10}(at 10 m height) for wind speed greater than 40 m/s [24]. Model simulations began on 00:00 GMT 1 September 2003 and ended at 00:00 GMT 1 October 2003 with a five-day spin up period.

#### 4.2. Results

^{2}(R-squared value), RMS (root mean square) and peak difference were 0.94, 14.3 cm and 9.2 cm for Wisconsin Avenue and 0.98, 7.3 cm and 2.4 cm for Washington, DC, respectively, as shown in Table 1. For a hurricane event with the peak water level reaching 3 m, the prediction skill of the current model is quite reasonable. In further analysis of the individual uncertainties over the comparisons, the largest uncertainties, based on NOAA Co-OPS’s user manual, were associated with the seasonal effect of the tidal river, local wind and weather patterns and thermal expansion. The errors can also be associated with the datum selected (1–5 cm) and the measurement technique (1–2 cm). In our effort in simulating storm tide of the 2003 Hurricane Isabel, the observed wind, pressure, river discharge and temperature fields were prescribed to the model; thus, seasonal effects were not be a major issue for the uncertainty. There were still base errors, which were embedded in the datum selection and the measurement itself, which amounts to about 2–7 cm. Our water level prediction at the Washington, DC, station was close to this lower limit.

Statistic | Wisconsin Ave. | Washington, DC |
---|---|---|

R² | 0.94 | 0.98 |

RMS | 14.3 cm | 7.3 cm |

MAE | 11.4 cm | 4.8 cm |

Peak Difference | 9.2 cm | 2.4 cm |

^{3}/s and 4000 m

^{3}/s. These two peak flows did not arrive until two and four days after the Hurricane passed, an indication of the delay of the watershed in collecting the precipitation dumped by the hurricane. To test the hypothesis quantitatively that the second and third peak were indeed the river discharge induced, a sensitivity tests was conducted with a scenario in which the no flux boundary condition was assigned at the head of the river. The scenario was dubbed “without” river discharge. The model results, under “without” river discharge, under-predicted the observed water level (along with the “with” river discharge model results) during the high flow period by about 1 m for the second peak and about 0.5 m for the third peak at Wisconsin Avenue station, as shown in Figure 6a. The under-prediction of water level during high flow periods was obvious at the Wisconsin Avenue station; however, it was not as clear at the Washington, DC, station.

**Figure 5.**The 2003 Hurricane Isabel model simulation results for (

**a**) Wisconsin Avenue and (

**b**) for Washington, DC, compared with the gauge measurement. Model results are shown in red and observation in blue; also included is the Potomac River discharge at Little Falls, MD, shown in green (with the scale on the right-hand side scale).

**Figure 6.**The 2003 Hurricane Isabel model simulation results for (

**a**) Wisconsin Avenue and (

**b**) for Washington, DC, similar to Figure 5, except using zero upstream river discharge at Little Falls, MD. Although not used as an upstream boundary condition, the Potomac River discharge (in green) at Little Falls, MD, was retained for reference.

**Figure 7.**The modeled 2003 Hurricane Isabel-induced inundation in the City of Alexandria, VA. The photograph depicts a high water mark at the intersection of King Street and Union Street showing that the floodwater reached 10.2 feet, approximately 5.5 feet (1.7 m) above the ground level, which is consistent with the modeled inundation at the location, which is between 4.9 and 6.6 feet (1.5–2.0 m).

## 5. Inundation Simulation for the Potomac River Great Flood of 1936

^{3}/s, which is 39-times of the normal daily flow.

#### 5.1. Model Setup

#### 5.2. Results

^{3}/s using the scale on the right-hand side.

^{2}, RMS and peak difference were 0.98, 5.8 cm and 2.9 cm for the “with” sub-grid approach but 0.77, 41 cm and 23.8 cm for the “without” sub-grid approach at the Washington gauge station. The errors of using the “without” sub-grid approach were almost 8-times larger, and the R-squared drops below 0.8. The mismatch of the phase was well-documented in the USGS and NOAA’s prior efforts. The fact that the “without” sub-grid approach encountered similar problems in producing the incorrect tidal phase, but can be overcome, highlighted the power of the high-resolution sub-grid approach and the nonlinear solver it uses. In terms of uncertainties in the model-data comparison, we feel that the sub-grid approach has reduced the large errors imbedded in the “without sub-grid” approach to the point that it reached the inherent error associated with the datum selection and equipment measurement itself at about 2–7 cm, as shown in Table 2. The comparison of water level and river discharge time series revealed that the peak water level can reach Washington, DC, with very little delay from the time when the flood peak passes the fall line. Having over several million people living in the metropolitan area, this means that Washington, DC, will have very little time to prepare and evacuate for a flash river flooding without a proper early warning system.

**Figure 8.**Time series plots comparing modeled results for (

**a**) Wisconsin Avenue and (

**b**) for Washington, DC “with” 10 m × 10 m sub-grids (red) and “without” sub-grids (gray dashed line) during the 1936 Potomac River Great Flood. The comparison was made at the Wisconsin Avenue (top) and Washington, DC, stations (bottom). The observation record was available only at the Washington, DC, station; river discharge from Little Falls, MD, is superposed (green) for reference.

**Table 2.**Statistical comparison of modeled time series results with and without a 10-m sub-grid at Washington, DC, during the 1936 Potomac River Flood.

Statistic | “With” Sub-Grid | “Without” Sub-Grid |
---|---|---|

R^{2} | 0.98 | 0.77 |

RMS | 5.8 cm | 41.0 cm |

MAE | 3.7 cm | 36.0 cm |

Peak Difference | 2.9 cm | 23.8 cm |

**Figure 9.**Visualization of the velocity vectors and water level (background color) from sub-grid model simulation results for the Washington, DC, metropolitan area during the 1936 Potomac River Great Flood. The shoreline is shown superposed in black. It is revealed that at the height of the flooding, the river bank north of East Potomac Park near DC was pinched by large (>2.7 m/s) velocities deflected from Roosevelt Island and subsequently flooded the downtown area.

**Figure 10.**Modeled maximum inundation extent for the Greater Washington, DC (

**a**), and surveyed downtown DC flood area (

**b**) during the 1936 Potomac River Great Flood.

**Table 3.**Model simulated inundation region in different parts of the DC area during the 1936 Potomac Great Flood. The individual (top) and total square km and miles (bottom) are listed.

Modeled Flood Area | m^{2} | km^{2} | mi^{2} |
---|---|---|---|

Potomac Park & Golf Course | 3,118,210.81 | 3.12 | 1.20 |

Washington DC Crescent * | 2,466,778.05 | 2.47 | 0.95 |

Washington Harbor | 1,167,493.83 | 1.17 | 0.45 |

DC Naval Yard | 633,843.92 | 0.63 | 0.24 |

Reagan Airfield | 1,819,267.96 | 1.82 | 0.70 |

Virginia Parks | 1,778,806.55 | 1.78 | 0.69 |

Anacostia-Bolling Base & Park | 1,632,464.54 | 1.63 | 0.63 |

Total | 12,616,865.65 | 12.62 | 4.87 |

* DC Crescent Modeled Flood Area | m^{2} | km^{2} | mi^{2} |

Upper Crescent | 1,815,294.67 | 1.82 | 0.70 |

Lower Crescent | 651,483.375 | 0.65 | 0.25 |

Total | 2,466,778.05 | 2.47 | 0.95 |

## 6. Discussion and Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

USACE | US Army Corps of Engineers, Department of Defense |

NOAA Co-OPS | National Oceanic and Atmospheric Administration, Center for Operational Oceanographic Products and Services |

NAVD88 | North America vertical datum of 1988 |

NAD83 CORS96 | North America datum of 1983, readjusted based on the Continuous Operating Reference Stations (CORS) |

## References

- Heaps, N.S. On the numerical solution of the three-dimensional hydrodynamic equations for tides and storm surge. Mem. Soc. R. Soc. Sci. Liėge Coll Huit
**1972**, 2, 143–180. [Google Scholar] - Reid, R.O.; Bodin, R.O. Numerical model for storm surges in Galveston Bay. J. Waterw. Harbor Div.
**1968**, 94, 33–57. [Google Scholar] - Davis, A.M. Three-dimensional modelling of surge. In Flood due to High Winds and Tides; Peregrine, D.H., Ed.; Academic Press: London, UK, 1981; pp. 45–74. [Google Scholar]
- Jelesnianski, C.P.; Chen, J.; Shaffer, W.A. SLOSH: Sea, Lake, and Overland Surges from Hurricanes; National Weather Service: Silver Spring, MD, USA, 1992. [Google Scholar]
- Kerr, P.C.; Donahue, A.S.; Westerink, J.J.; Luettich, R.A., Jr.; Zheng, L.Y.; Weisberg, R.H.; Huang, Y.; Wang, H.V.; Teng, Y.; Forrest, D.R.; et al. US IOOS coastal and ocean modeling testbed: Inter-model evalulation of tides, waves, and hurricane surge in the Gulf of Mexico. J. Geophys. Res.
**2013**, 118, 5129–5172. [Google Scholar] - Chen, C.; Beardsley, R.C.; Luettich, R.A., Jr.; Westerink, J.J.; Wang, H.; Perrie, W.; Xu, Q.; Donahue, A.S.; Qi, J.; Lin, H.; et al. Extratropical storm inundation testbed: Intermodel comparisons in Situate, Massachusetts. J. Geophys. Res. Oceans
**2013**, 118, 5054–5073. [Google Scholar] - Roland, Aron; Zhang, Y.; Wang, H.V.; Meng, Y.; Teng, Y.; Maderichd, V.; Brovchenkod, I.; Dutour-Sikirice, M.; Zankea, U. A fully coupled 3D wave-current interaction model on unstructured grids. JGR Oceans
**2012**, 117, C00J33. [Google Scholar] [CrossRef] - Neelz, S.; Pender, G. Sub-gird scale parameterisation of 2D hydrodynamic models of inundation in the urban area. Acta Geophys.
**2007**, 55, 65–72. [Google Scholar] [CrossRef] - Casas, A.S.; Lane, N.; Yu, D.; Benito, G. A method for parameterizing roughness and topographic sub-grid scale effects in hydraulic modelling from LiDAR data. Hydrol. Earth Syst. Sci. Discuss.
**2010**, 7, 2261–2299. [Google Scholar] - Wang, H.V.; Loftis, J.D.; Liu, Z.; Forrest, D.; Zhang, J. The storm surge and sub-grid inundation modeling in New York City during Hurricane Sandy. J. Mar. Sci. Eng.
**2014**, 2, 226–246. [Google Scholar] - United States Geological Survey (USGS). Part3. Potomac, James, and Upper Ohio Rivers (Water-Supply Paper 800). In The floods of March 1936; United States Geological Survey: Denver, CO, USA, 1937. [Google Scholar]
- Schaffranek, R. A Flow Simulation Model of the Tidal Potomac River—A Water-Quality Study of the Tidal Potomac River and Estuary; United States Geological Survey: Denver, CO, USA, 1987; p. 2234-D. [Google Scholar]
- Mashriqui, H.S.; Halgren, J.S.; Reed, S.M. Toward Modeling of river-estuary-ocean interactions to enhance operational river forecasting in the NOAA National Weather Service. In Proceedings of the 2nd Joint Federal Interagency Conference, Las Vegas, NV, USA, 27 June–1 July 2010.
- EA Engineering, Science, and Technology, Inc. Water Quality Studies in the Vicinity of the Washington Aqueduct; Baltimore District, US Army Corps of Engineers, Washington Aqueduct Division: Washington, DC, USA, October 2001. [Google Scholar]
- Casulli, V. A semi-implicit finite difference method for non-hydrostatic, free-surface flows. Int. J. Numer. Methods Fluids
**1999**, 30, 425–440. [Google Scholar] [CrossRef] - Casulli, V.; Walters, R.A. An unstructured grid, three-dimensional model based on the shallow water equations. Int. J. Numer. Methods Fluids
**2000**, 32, 331–348. [Google Scholar] [CrossRef] - Casulli, V.; Zanolli, P. High resolution methods for multidimensional advection-diffusion problems in free-surface hydrodynamics. Ocean Model.
**2005**, 10, 137–151. [Google Scholar] [CrossRef] - Casulli, V. A high-resolution wetting and drying algorithm for free-surface hydrodynamics. Int. J. Numer. Methods Fluid Dyn.
**2009**, 60, 391–408. [Google Scholar] [CrossRef] - Casulli, V.; Stelling, G. Semi-implicit sub-grid modeling of three-dimensional free-surface flows. Int. J. Numer. Methods Fluid Dyn.
**2011**, 67, 441–449. [Google Scholar] [CrossRef] - Loftis, J.D.; Wang, H.V.; Hamilton, S.E.; Forrest, D.R. Combination of LiDAR Elevations, Bathymetric Data, and Urban Infrastructure in a Sub-Grid Model for Predicting Inundation in New York City during Hurricane Sandy. Comput. Environ. Urban Syst.
**2015**. under review. [Google Scholar] - Casulli, V.; Zanolli, P. A three-dimensional semi-implicit algorithm for environmental flows on unstructured grids. In Proceedings of the Conference on Methods for Fluid Dynamics, University of Oxford, Oxford, UK; 1998; pp. 57–70. [Google Scholar]
- Hederson, F.M. Open Channel Flow. 1996; The Macmillan Company: New York, NY, USA; p. 522.
- Garratt, J.R. Review of drag coefficients over oceans and continents. Mon. Weather Rev.
**1977**, 105, 915–929. [Google Scholar] [CrossRef] - Powell, M.D.; Vickery, P.J.; Reinhold, T.A. Reduced drag coefficient for high wind speeds in tropical cyclones. Nature
**2003**, 422, 279–283. [Google Scholar] [CrossRef] [PubMed] - Stamey, B.; Wang, H.V.; Koterba, M. Predicting the Next Storm Surge Flood. Sea Technol.
**2007**, 48, 10–15. [Google Scholar] - Arnold, J.L. The Evolution of the Flood Control Act of 1936; United States Army Corps of Engineers: Fort Belvoir, VR, USA, 1988. [Google Scholar]
- VIMS Physical Science. 1936 Potomac River flood simulation. Available online: http://web.vims.edu/physical/3DECM/DC19360301/ (accessd on 11 July 2015).
- National Capital Planning Commission (NCPC). Flooding and Stormwater in Washington, DC, 2008. Available online: http://www.ncpc.gov/DocumentDepot/Publications/FloodReport2008.pdf (accessed on 17 January 2008).
- Loftis, J.D.; Wang, H.V.; DeYoung, R.J.; Ball, W.B. Integrating LiDAR Data into a High-Resolution Topo-bathymetric DEM for Use with Sub-Grid Inundation Modeling at NASA Langley Research Center. J. Coast. Res.
**2015**, in press. [Google Scholar] - Loftis, J.D. Development of a Large-Scale Storm Surge and High-Resolution Sub-Grid Inundation Model for Coastal Flooding Applications: A Case Study during Hurricane Sandy. Ph.D. Thesis, College of William & Mary, Williamsburg, VA, USA, 2014. [Google Scholar]
- Smith, W. Climate Change Symposium, Washington Metropolitan Council of Governments, May 21, 2012. Available online: http://www.mwcog.org/environment/climate/adaptation/Presentations/5-%20Smith.pdf (accessed on 22 May 2012).

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**MDPI and ACS Style**

Wang, H.V.; Loftis, J.D.; Forrest, D.; Smith, W.; Stamey, B.
Modeling Storm Surge and Inundation in Washington, DC, during Hurricane Isabel and the 1936 Potomac River Great Flood. *J. Mar. Sci. Eng.* **2015**, *3*, 607-629.
https://doi.org/10.3390/jmse3030607

**AMA Style**

Wang HV, Loftis JD, Forrest D, Smith W, Stamey B.
Modeling Storm Surge and Inundation in Washington, DC, during Hurricane Isabel and the 1936 Potomac River Great Flood. *Journal of Marine Science and Engineering*. 2015; 3(3):607-629.
https://doi.org/10.3390/jmse3030607

**Chicago/Turabian Style**

Wang, Harry V., Jon Derek Loftis, David Forrest, Wade Smith, and Barry Stamey.
2015. "Modeling Storm Surge and Inundation in Washington, DC, during Hurricane Isabel and the 1936 Potomac River Great Flood" *Journal of Marine Science and Engineering* 3, no. 3: 607-629.
https://doi.org/10.3390/jmse3030607