Semidiurnal perturbations to the surge of Hurricane Sandy


Corresponding author: A. Valle-Levinson, Civil and Coastal Engineering Department, University of Florida, Gainesville, FL, USA. (


[1] Hurricane Sandy drove storm surges throughout the eastern seaboard of the United States, from Miami to Maine, at the end of October 2012. The surge was particularly high (>3 m) in coastal New York. In the southeastern United States, the surge was <1 m but had striking semidiurnal perturbations that reached a range of ~0.5 m in northern Florida and southern Georgia. These oscillations are typically not considered in surge forecasts and their origin needs to be understood for future forecasts. Analytical and numerical approaches indicated that semidiurnal perturbations arose from an interaction between astronomical tide and wind forcing. This combination of forcing caused phase shifts between incident and reflected tidal waves that customarily produce quasi-standing tidal conditions in the area. Atmospheric forcing of sufficient strength, which threshold remains to be established, disrupted such quasi-standing tidal behavior through Coriolis accelerations and triggered the semidiurnal perturbations.

1 Introduction

[2] Hurricane Sandy was forecast as the storm of the century in the eastern United States. A southward moving low pressure Arctic system off the eastern coast of Canada, together with an eastward moving low pressure system from western Canada, converged with hurricane Sandy as it moved northward. The collision between tropical and Arctic atmospheric systems resulted in Sandy becoming a much more powerful and sizable storm than it would have been without the Arctic and western systems. The combination of two low pressure systems is known as the Fujiwhara effect [Fujiwhara, 1921]. Sandy caused a double Fujiwhara effect that, according to the National Oceanic and Atmospheric Administration forecasts, was expected to produce the highest storm surges of the last hundred years in the coasts of New Jersey and around New York City. And Sandy met the projections.

[3] The goal of this investigation was to describe the storm surge behavior related to hurricane Sandy along the eastern coast of the United States, from Miami, Florida, to Cape Cod, Massachusetts. A particular objective was to document and to explain the appearance of unexpected semidiurnal perturbations triggered by Sandy between Cape Hatteras and Miami. These objectives and goal were addressed with meteorological and sea level measurements along the United States’ (U.S.) eastern seaboard recorded in real time by the National Ocean Service of the National Oceanic and Atmospheric Administration.

[4] Long, along-shelf, transient free waves (periods > few minutes and up to inertial), or edge waves, are known to be excited by forced waves associated with storms (unusual atmospheric forcing) that move across a shelf break [Proudman, 1953; Garrett, 1970] or a sloping bathymetry [Greenspan, 1956]. The amplitude of these free oscillations will depend on whether they cause resonance or not [e.g., Vennell, 2010]. Resonance and wave periods will in turn depend on the properties of the atmospheric forcing, such as maximum sustained wind speed, barometric pressure, diameter of the storm, speed of its translation, and angle of attack relative to the shelf break or coast [e.g., Yankovsky, 2009; Vennell, 2010; Thiebaut and Vennell, 2011]. Resonance and wave periods will also depend on the characteristics of the shelf, such as water depth and slope. In essence, storms can generate different types of waves [Thiebaut and Vennell, 2011]: edge waves, which are oscillations trapped over the shelf or at the coast by refraction and can propagate up and downshelf; subinertial waves (usually called “continental shelf waves”), which propagate down the shelf; and Kelvin waves, which can be single (along either the coast or the shelf break) or double (along both the coast and the shelf break).

[5] The studies above neglect bottom friction as well as tidal influences or interaction of storms with tide. Tide-surge interactions can produce signals that become evident upon subtracting the astronomical tide from the observed water level [e.g., Sinha et al., 2008]. These signals can be called nontidal “residuals” and, for a progressive tide, occur most frequently in the rising tide [Horsburgh and Wilson, 2007]. In a standing wave, however, the greatest positive residuals should occur in the falling tide [Proudman, 1957]. Over the westernmost indentation of the South Atlantic Bight, in northern Florida and southern Georgia, semidiurnal residuals attained ranges of up to 0.5 m, 50% of the surge. An explanation for the semidiurnal perturbations occupies most of this presentation.

2 Data Compilation

[6] Atmospheric forcing data, in particular wind velocity and barometric pressure, as well as sea level data were obtained from coastal stations distributed along the US eastern seaboard (Figure 1a). Data are maintained by the National Ocean Service of the US National Ocean and Atmospheric Administration and readily available from their website “” Preliminary data are available from the website in real time but verified data are available a few weeks later. Verified water level data at 6 min intervals were compiled from 21 stations along the U.S. east coast (Figure 1a) from 25 October to 31 October 2012. Compiled water level data included predicted values, related to astronomical tide, and observed values. Detided values described the storm surge, which simply consisted of the difference between observed and predicted water level. Wind velocity and atmospheric pressure data were extracted from most of the same stations (not all water level stations had wind data available) and from a couple more stations where no water level data were available, Hatteras and Duck (both in North Carolina), for the period of interest. Three variables: atmospheric pressure, wind velocity and detided water level (storm surge) were used to construct Hovmöller diagrams. In these, variables are represented in the time and distance parameter space to readily detect the propagation of signals. The origin in distance was station 1 (Figure 1a) at the southern coast of Florida and in time it was 00:00 local time on 25 October 2012. All times were represented in local time, which was Eastern Daylight Saving Time for the period studied.

Figure 1.

(a) Track of Hurricane Sandy between 26 and 29 October 2012. Each date label appears at the beginning of the day (local time). Red circles are drawn every 6 h. Numbers on the coast indicate stations with sea level data available. Blue lines indicate de 100 and 500 m isobaths to indicate the limit of the continental shelf. (b) Storm properties (in a Lagrangian framework, obtained from the National Hurricane Center's website) during the life of Hurricane Sandy. Smooth lines represent three-point running average of each property to identify trends better. (c) Domain for 2-D numerical ROMS experiments that helped explain the origin of the semidiurnal surge.

3 Storm Trajectory

[7] Sandy first became a tropical storm late on 22 October 2012 in the Western Caribbean. It then became a hurricane shortly before making landfall on Jamaica on 24 October, with maximum sustained winds around 36 m/s. Sandy then intensified to winds of ~49 m/s as it affected Cuba on 25 October. On 26 October it moved over the Bahamas and began its trajectory toward the United States (Figure 1a) while losing strength, slowing down and gaining barometric pressure (Figure 1b). The storm then followed a trajectory that was nearly parallel to the shoreline of the U.S. southern states of the Atlantic seaboard during 27 and 28 October, with its eye at distances between 400 and 600 km from the coast. During this period, Sandy steadily moved faster from 3 to 7 m/s, lost barometric pressure from 970 to 950 hPa (or mb), but maintained maximum sustained wind speeds at ~33 m/s (Figures 1a and 1b). Upon reaching the latitude of Virginia (~37°N) on 29 October, Sandy started moving onshore at faster speeds of 7 to 12 m/s, while gaining strength and continuing to lose barometric pressure. When Sandy made landfall a few kilometers south of Atlantic City, New Jersey, at close to 20 h (local time) on 29 October, it was moving at 14 m/s and featured a barometric pressure of 940 hPa and maximum sustained winds of 41 m/s. During its trajectory, hurricane Sandy had winds spanning >1500 km and became the largest hurricane on record for the Atlantic Ocean.

4 Barometric Pressure and Winds Along the U.S. Eastern Seaboard

[8] The wind field related to hurricane Sandy was first influential over south Florida on 26 October (lower left part of Figure 2a). Directions were preferentially from the northeast and sustained magnitudes reached >12 m/s. The highest wind magnitudes along the U.S. southeastern coast were felt sequentially northward as the storm moved in that direction. Still around the southeastern coast, winds peaked at ~20 m/s gusts and typically showed a Gaussian-like ramp-up and decay with time. The standard deviation of this pulse was nearly 12 h. Once the storm moved past Cape Hatteras, winds over coastal stations intensified to >30 m/s gusts maintaining their northeasterly direction. As the storm continued its path along and across the eastern coast of the U.S., the cyclone winds and barometric pressure affected the entire coast from Cape Hatteras to Maine.

Figure 2.

(a) Hovmöller diagram of wind velocity (vectors) and atmospheric pressure (shaded contours) during the period influenced by Sandy. Vertical dotted lines align with semidiurnal S2 atmospheric pressure oscillations of amplitudes between 1 and 2 hPa. Numbered labels on the right correspond to numbers of Figure 1a. (b) Hovmöller diagram of detided water level (colored contours) during the period influenced by Sandy. Vertical dashed lines align with maxima in water level with M2 period. These correspond to signals that propagate southward (1100 km in 0.2 day) and northward (700 km in 0.25day) from Cape Hatteras. Numbered labels on the right correspond to numbers of Figure 1a. (c) Hovmöller diagram of predicted tide (colored contours) during the period influenced by Sandy for the coastal stretch between Florida and eastern Long Island Sound. Vertical dashed lines align with the pulses depicted in Figure 2b. Numbered labels on the right correspond to numbers of Figure 1a.

[9] Also along the southeastern coast of the United States, the barometric pressure exhibited semidiurnal oscillations with a period of 12 h and amplitudes of 1 to 2 hPa [Ray and Ponte, 2003] not associated with Sandy (Figure 2a). The hurricane caused Gaussian-like drops of ~20 hPa in barometric pressure at coastal stations. South of Cape Hatteras, Sandy effects persisted for roughly 4 days, but north of this site the effects were much more dramatic. At stations directly affected, markedly off New Jersey and New York, barometric pressure dropped from 1020 to 940 hPa over a 4 day period. Following the inverse barometer effect [Gill, 1982], only the drop in atmospheric pressure was expected to produce a storm surge of 0.8 m.

5 Storm Surge

[10] Storm surge in coastal New York, on the “right” side of the storm, reached ~3 m at the Battery station in downtown Manhattan. The highest surge recorded was ~4 m at Kings Point, on the western end of Long Island Sound. The funneling effect by the Sound must have contributed to the surge amplification [Friedrichs and Aubrey, 1994]. In comparison, at Atlantic City, New Jersey, just north of the landfall site, the surge was ~1.75 m. One of the most remarkable aspects of Sandy was that it caused storm surges throughout the Atlantic coast of the United States (Figure 2b). Surges were excited by the direct impact of atmospheric forcing from wind velocity and atmospheric pressure (Figure 2a), from South Florida to Maine (although the figures show only up to eastern Long Island Sound in New York). Most of the coast affected by Sandy was also influenced by coastal long waves forced by the storm, which moved along and across the shelf break.

[11] Long waves (periods >1 h) were triggered by the hurricane moving parallel to the shelf break and winds blowing onshore. Between Cape Hatteras and Miami, along the southeastern coast of the United States, long waves travelled rapidly at ~60 m/s (dashed lines in Figure 3b, between stations 1 “Vakey” and 10 “Beaufort”). Waves were most conspicuous during the northward translation of the storm from 26 to 28 October. Interestingly, the wave period was the same as the lunar semidiurnal tide M2, i.e., 12.4 h and emulated Kelvin waves in their direction of propagation. Moreover, these southward waves, like tides in the region [Blanton et al., 2004]), were amplified at the westward coastal indentation that forms the South Atlantic Bight (stations 4, 5, and 6). In contrast to the free shelf and edge waves that can be excited by a storm [e.g., Ke and Yankovsky, 2011; Vennell, 2010], these waves appear to have been forced by the storm, as explored in the Discussion. Their maximum amplitude (Figure 2b) was related to the passage of the storm off northern Florida and southern Georgia at 00:00 on 28 October (Figure 1a). Also, there appears to have been waves travelling from Cape Hatteras northward at 30 m/s, half the rate relative to the southward waves, but with the same period. The approach of the hurricane to the northern part of the domain (>1200 km from origin) must have masked the influence of the northward waves after 00:00 on 29 October. But Cape Hatteras, because of its protrusion offshore and its narrow continental shelf, seems to be a partition region between northward and southward propagating long waves.

Figure 3.

Top panel shows modifications to a semidiurnal standing wave η (emulating a predicted tide) by a phase-shifted pair of incident and reflected waves ηf superimposed on a subtidal surge ηS. The signal ηf + ηS is taken as the “observed” water level. The difference between observed and predicted (ηf + ηSη) represents the semidiurnal perturbations of Figure 2b. Lower panels show Hovmöller diagrams, similar to Figure 2b, for detided water level derived from six ROMS simulations as indicated in the labels.

[12] The character of the semidiurnal perturbations observed in the southeastern U.S. was different from the tidal waves as drawn from predictions (Figure 2c). South of Cape Hatteras, tidal waves down to central Florida (500 km on Figure 2c) are quasi-standing and move with similar speed as the storm-induced oscillations. However, in southern Florida, the tide exhibits some northward propagation. North of Cape Hatteras, tides propagate from New York to Virginia, i.e., southward, in opposition to the storm-induced waves. Comparison of the storm-induced waves (dashed lines) to the predicted tide (filled contours) clearly shows the contrast between the two. The mechanism of generation for these revealing semidiurnal storm-induced waves, which could also be regarded as “semidiurnal surge”, is explored next.

6 Discussion

[13] It is evident that the M2 semidiurnal surge caused by Sandy in the South Atlantic Bight, between 0 and 1300 km in Figure 2b, was not related to direct forcing from the S2 barometric pressure fluctuations. Semidiurnal barometric pressure oscillations were too small to produce the surge (Figure 2a). The likely mechanism for the generation of the semidiurnal surge arose from the interaction between tides and atmospheric forcing [e.g., McInnes and Hubbert, 2003]. In a semidiurnal surge, tides seem to be an essential component because of the surge period.

[14] In the South Atlantic Bight portion between Cape Hatteras and Cape Canaveral in Central Florida, the stretch between 500 km and 1250 km in Figure 2c, tides are quasi-standing [Blanton et al., 2004]. It is likewise evident, also from Figure 2c, that tides are quasi-standing in the Mid-Atlantic Bight (between 1300 and 200 km in Figure 2c). Standing waves require two waves traveling in opposite directions [e.g., Dean and Dalrymple, 1991]

display math(1)

where A1, A2 are the amplitude of the incident and reflected waves, respectively (A2 can be equal to A1), κ is the wave number in the cross-shore direction x, t is time, and ω is the wave frequency. The wave number and frequency are the same for incident and reflected waves.

[15] A likely scenario in the South Atlantic Bight was that the dynamics of the modified wave ηf were represented by a wave equation modified during the storm by wind stress τs, atmospheric pressure P, bottom stress τb, and Earth's rotation [e.g., Thiebaut and Vennell, 2011]

display math(2)

where ρ is water density, ∇ is the Del operator (//∂ x, //∂ y), f is the Coriolis parameter, h is water depth, and ζ is relative vorticity. The variable is the forcing that alters the standing wave (taken as a constant, locally, for the moment and for the sake of argument). In general, could represent modifications to water level from Earth's rotation (or vorticity) and from forcing related to a stress. The stress itself could be atmospheric stress or bottom stress; it could even be tidal stress in terms of the advective accelerations [Proudman, 1957]. A possible conceptual solution to equation (2) consists of oppositely directed waves affected by stresses and Earth's rotation (contained in ), i.e.,

display math(3)

where φ is a phase lag caused by stresses and Earth's rotation, and depends on / [ωc] (analogous to Horsburgh and Wilson [2007]). Yet another possibility is that only one wave is out of phase, e.g.,

display math(4)

[16] Equations ((3)) and ((4)) satisfy equation (2). The outcome at the coast does not change and is that the difference between η f (equations ((3)) or ((4))) and η (equation (1)) yields a wave with a periodicity of 12.42 h (Figure 3, top panel), just as observed during Sandy. The arguments of this paragraph are consistent with those in Horsburgh and Wilson [2007]. Therefore, it is proposed that the semidiurnal surge observed was caused by the interaction between the storm and the tide.

[17] The fact that varies in space and time was explored, in conjunction with tide-surge interactions, through numerical model scenarios of the storm over the eastern United States. Assessment of the terms in the cross-shelf momentum balance obtained from the model, allowed determination of the relative influence of bottom stress, nonlinear advection, atmospheric stress and Earth's rotation on the generation of the semidiurnal perturbations to the surge. The Regional Ocean Modeling System (ROMS) was implemented in two dimensions (depth-integrated) over a portion of the western North Atlantic Ocean (Figure 1c) to study water level response to a storm similar to Sandy. The numerical model is three-dimensional, free surface, terrain-following and solves finite-difference approximations of the Reynolds-Averaged Navier-Stokes equations. It uses the hydrostatic and Boussinesq approximations [Chassignet et al., 2000; Haidvogel et al., 2000] with a split-explicit time stepping algorithm [Shchepetkin and McWilliams, 2005; Haidvogel et al., 2008]. The model was forced with synthetic wind velocities, atmospheric pressure and tides derived from the Global Forecast System run by NOAA. Boundary conditions for tides were derived from the OSU/TPX7.2 global tidal database. Tidal elevations and currents were linearly interpolated from the OSU/TPX7.2 grid to the ROMS grid computational boundaries. A Flather boundary condition [Flather, 1976] for the barotropic currents was imposed at the open boundaries, allowing for the free propagation of wind-generated currents and tides. Six scenarios were run to test the appearance of semidiurnal perturbations associated with the storm surge. Scenario 1 considered water level response to forcing only from atmospheric pressure. Scenario 2 investigated the response to wind only. Scenario 3 included both wind and atmospheric pressure. Scenarios 1, 2, and 3 had no tides, so scenarios 4 and 5 explored the influence of tides and atmospheric pressure, and tides and wind, respectively. Finally, Scenario 6 determined the influence of tides and atmospheric forcing.

[18] It was clear that the storm-induced semidiurnal waves observed during Sandy required the presence of tides (Figure 3, Hovmöller diagrams). With no tides, only a subtidal surge was observed. However, the semidiurnal perturbations on the storm surge, similar to those observed, could be detected only with the combination of tides and wind forcing. The Hovmöller diagrams indicated that, in this specific storm, northeasterly winds over the continental shelf between Cape Hatteras and northern Florida contributed more than atmospheric pressure to the phase lag for incident and reflected tidal waves. The phase lag in wave propagation caused a rearrangement between observed and predicted waves that seem to affect the entire eastern seaboard. In other studies, storm-tide interactions have been dominated by bottom friction [e.g., Tang et al., 1996; Zhang et al., 2010] or by nonlinear advection [e.g., Proudman, 1957]. Inspection of the magnitude of terms in the cross-shelf momentum balance during Sandy at Fernandina Beach, near the border between Florida and Georgia, indicated another possibility (Figure 4). This was a site of amplification of semidiurnal perturbations to the storm surge. The cross-shelf momentum balance at that location showed increased influence of Coriolis accelerations during the period of maximum forcing from Sandy, from noon on 26 October to noon on 28 October. During that period, the balance was dominated by local accelerations, pressure gradient and Coriolis. The increase of cross-shelf Coriolis accelerations during Sandy was attributed to intensified northeasterly winds that drove along-shelf flows of similar or greater magnitude than tidal flows. Numerical results then point to a mechanism of storm-tide interactions associated with Coriolis accelerations. This mechanism is proposed as the main responsible for the semidiurnal perturbations to the surge observed during Sandy.

Figure 4.

Absolute value of the momentum balance terms extracted at the coast of Fernandina Beach, Florida. Three scenarios, 2, 4, and 6 are depicted by green, red, and blue lines, respectively. During Sandy’s influence at this location, from noon 26 October to noon 28 October, Coriolis accelerations contributed most to balance local and pressure gradient forces per unit mass in the scenario that considered tide-surge interactions (blue line). Bottom stress and advective accelerations had a small influence. These results indicated that Coriolis accelerations linked to along-shelf flows were responsible for the phase distortions in the standing tide that resulted in semidiurnal perturbations to the storm surge.

[19] A similar response was also detected during forcing from Hurricane Irene over the U.S. eastern seaboard in August 2011. Further studies that investigate thresholds of causing the phase shift in the tides are needed. Nonetheless, the most revealing finding of this study is that atmospheric forcing does not only cause subtidal perturbations to water level. It can also produce semidiurnal perturbations through Coriolis accelerations. Understanding these perturbations is fundamental for the accurate prediction of storm surges and for risk analysis throughout areas prone to storm influence.


[20] A.V.L. acknowledges funding from a Fulbright Fellowship that allowed a stay at the Instituto de Ciencias del Mar, Barcelona, where this study was undertaken. M.O. acknowledges funding from the “Cantabria Campus International Augusto Gonzalez Linares Program.” The comments from two anonymous reviewers are appreciated.

[21] The Editor thanks two anonymous reviewers for their assistance in evaluating this paper.