Chapter 3 – Tides, Storm Surge and Water Levels

From ‘Highways in the Coastal Environment: Second Edition’ by FHWA

Chapter 3 – Tides, Storm Surge and Water Levels

3.1 – 3.2 – 3.3 – 3.4

Water level fluctuations include astronomical tides, storm surges, and long-term sea level rise or fall. Water level is important in coastal processes and engineering in part because it controls the location of wave influence on shorelines and structures. Geologically, sea level controls the overall location and shape of the continental shoreline. The definitions of tidal datums and surveying datums can be important for the design of engineering works near the coast. Storm surge, which temporarily raises the water level, can control the design water level for engineering. Tidal currents can be significant as tides and storm surges enter and exit coastal bays through inlets.

The portion of the water level fluctuation controlled by the astronomical bodies, the moon and the sun, are referred to as the astronomical tide. Additionally, coastal water levels are often affected by meteorological conditions including storm surge in response to winds and wave sand local rainfall.

3.1 Astronomical Tides

The tide is the slow rise and fall of the ocean waters in response to the gravitational pull of the moon and the sun. The tide is essentially a very long ocean wave with a wave period of 12.4 hours. The usual interval between successive high tides is 12.4 hours as the arrival of the crests of these waves represent high tide. The moon exerts a greater influence on the tides than does the sun.

The astronomical tide is well understood and can be predicted for any time at many locations. Tidal predictions are well understood by most coastal residents and are often included in local daily newspapers and weather forecasts. The National Oceanic and Atmospheric Administration’s (NOAA) National Ocean Survey provides on-line tidal forecasts as well as other information about tides around the nation.[2] Along most coasts bordered by the ocean, the astronomical tide forecasts are within 1 ft of the actual tide elevation 90% of the time. The difference between the forecasts and actual water elevation measurements is normally a result of weather related phenomena (e.g., wind blowing from same direction over some period, i.e. a storm surge). Understanding some of the characteristics of tides is helpful in understanding some of the terminology used to define tides and tidal datums.

3.1.1 Characteristics of Astronomical Tides

In most locations in the United States, there are two high tides and two low tides every lunar day (24.8 hours). These are called”semidiurnal” tides (see Figure 3.1).At many locations the two high tides that occur each day are roughly of the same elevation. But at many other locations, there is a “mixed tide” with a clear “diurnal inequality” in the high tides as one is significantly higher than the other. Some places, like portions of the Gulf of Mexico, have only one high tide and one low tide per day. These tides are called “diurnal” tides.

Figure 3.1. Basic Definitions of Tides modified from /tidesandcurrents.noaa.gov.

Large differences in tide range occur at the same location throughout the month. The highest tides which occur at intervals of half a lunar month are called “spring tides.” They occur at or near the time when the moon is new or full, i.e., when the sun, moon and earth fall in-line, and the tide generation forces of the moon and sun are additive. When the tide range is at its lowest during the lunar month, the “neap tides” occur.

Large differences in the magnitude of the daily tide range occur at different locations in the US. These differences are caused by the interactions of the oceanic tidal motions with the continental land mass and the depths and shape of coastal bays and shelves. At Anchorage, Alaska, the tide range can vary up to almost 30 feet between high and low tide. At Pensacola, Florida, however the range can be less than 2 feet throughout a day. These differences in tidal range can occur within short distances along the coast and up bays. For example, the average tide range at Sandy Hook, New Jersey is about 5 feet but is only 2 feet just 125 miles away at Montauk Point, New York .

The basic astronomical tide producing forces go through a “tidal epoch, ” a cycle that lasts approximately 18.6 years. Thus, water level statistics related to tides, such as mean sea level, are computed by averaging over a complete epoch.

3.1.2 Tidal and Survey Datums

The distinction between tidal datums and surveying datums can be important in the design, construction, and operation of engineering works near the coast. Tidal datums are vertical datums based on the epoch-averaged tide levels at a specific location. Tidal datums are based on actual measurements at a specific tide gage. Since sea level is changing over the long-term, the tidal datums are re-established after every tidal epoch. The most recent tidal epoch ended in 2001 and NOAA’s National Ocean Survey has re-established the tidal datums for most of the United States’ tide gage locations for the 1983 -2001 tidal epoch.

There are a number of tidal datums. The mean high water datum (MHW) is the average, over an 18.6-year tidal epoch, of the high water elevations at a specific location. The mean higher high water datum (MHHW) is the average of the higher high water elevations. The difference between these two datums, MHW and MHHW, is greatest at locations with the greatest “diurnal inequality” in high tides during a typical day. Likewise, the mean low water datum (MLW) is an average of the low tide elevations and the mean lower low water datum (MLLW) is an average of the lower low tide elevations. MLLW is the basis for most navigation charts because it provides mariners with a consistent, somewhat conservative, estimate of the depth. The mean sea level datum (MSL) is the average of all the observations of water level over a tidal epoch.

Survey datums are specified for gegeodetic surveying and set by the NOAA’s National Geodetic Survey. The National Geodetic Verticalatum of 1929 (NGVD 29) and the North American Vertical Datum of 1988 (NAVD 88) are the two primary vertical survey datums used in the US. The older NGVD 29 geodetic datum was originally established using estimates of mean sea level at 26 tide gages around the nation. Thus, it was often referred to as just “mean sea level.”

However, it has long been recognized that it was not the mean sea level because mean sea level changes through time and survey datums do not. The National Geodetic Survey has not called NGVD 29 the”mean sea level” for decades. NAVD 88 was an improvement to the NVGD 29 and ha snow replaced it as the primary vertical datum for surveying. It normally will be near the mean sea level at the open coast but it is not the mean sea level.

The relationship between the survey datum, NAVD 88, and the tidal datums, e.g. MSL or MLLW, has been calculated by the NOAA National Ocean Service for many of the tide gages around the US. An example is shown in Figure 2.18 using the values for Charleston, South Carolina . The distances from a local tide station datum to the NAVD 88 and to the tidal datums for the 1983 to 2001 epoch are shown. The local tide station datum is meaningless except for that specific gage record. What are significant are the relative relationships between the survey datum and the tidal datums.

Figure 3.2 shows that the mean sea level(1983 to 2001 epoch) is -0.21 ft NAVD 88 at Charleston, SC. This relationship is not the same at other locations around the nation.

The relationship between the tidal datum sand NAVD 88 for different locations around the nation can be obtained directly from the NOAA NOS website (tidesandcurrents.noaa.gov/ in November 2006). Investigating the relationship between site specific upland surveys and tidal datums can be important.

Figure 3.2. An example of the relationship between the survey and tidal datums.

3.2 Storm Surge

Storm surge is the rise of water level above the astronomical tide as a result of meteorological forcing. This forcing is primarily wind but also includes the barometric pressure and, for some coast allocations, local rainfall runoff. Storm surge can be negative, i.e. winds can decrease water levels from the astronomical tide levels. Storm surge is highly influenced by geography including the shape of the coast and its bays, thundershower bathymetry, and the flooded topography. High storm surges occur along the coast where the landmass stops the hydrodynamic movements. The highest storm surge can occur in bays. Wind affects storm surge by placing a stress on the water surface, by generating oceanic currents and by generating waves. Breaking waves can contribute to storm surge by adding a component of mean water surface elevation called wave setup. Storm surge is an important coastal process for the design of coastal infrastructure primarily because it increases the design still water level and allows waves to attack higher elevations. Surge also can be an important component in tidal inlet hydrodynamics.

Figure 3.3 is an example of hurricane storm surge. The predicted tide is plotted along with measurements from a tide gage located on a pier in the Gulf of Mexico. The surge, the difference between the predicted and actual water level, extends for several days with a very dramatic peak of over 7 feet above the predicted high tide early on August 18. That high peak corresponds with the time that the hurricane made landfall with its eye just to the southwest of the tide gage.

Figure 3.3. Storm surge at Galveston, Texas, from Hurricane Alicia in 1983.

The hydrograph of a coastal storm surge is usually considered as the time variation of water surface elevation at a specific location. Both the magnitude and duration of a coastal storm surge can be important. During the most destructive coastal storm in United States history, Hurricane Katrina in 2005, the water level rose 27 feet higher than its predicted tide elevation due to storm surge along much of the coast near Bay St. Louis, Mississippi. Several inland locations had mean high water marks over 30 feet in elevation. This storm surge was unprecedented in United States history. But the previous high storm surge, 21 feet, was along this same stretch of coast in Hurricane Camille of 1969. Another of the most destructive storms in American history, the Nor’easter Ash Wednesday Storm of 1962, caused much of its damage due to its relatively long duration. The storm surge lasted for 2½ days over five semi-diurnal high tides, or “five high-tides.” This long duration allowed beach storm erosional processes to act that long and cause extensive property damage along the Atlantic coast.

3.2.1 Modeling Approaches

Storm surge hydrographs from specific storms can be modeled with modern hydrodynamic modeling techniques. The numerical modeling of coastal hydrodynamics is based on solving the fundamental fluid mechanics of motion, the continuity equation and the momentum equation, in a manner that is most efficient and appropriate for the problem. Different formulations of the equations and solution algorithms have been applied to the coastal hydrodynamics situation and there is a rich history of this modeling that has developed over the past thirty years in both the near shore physical oceanography and coastal engineering research communities. Much of the research and development of these models was done with funding from federal agencies with coastal interests including NOAA and the USACE. Research papers with the models and applications are available in a variety of publications. Many of the applications and models were presented at a series of specialty conferences called the International Estuarine and Coastal Modeling conferences that began in the early 1990’s and continue.

One of the available hydrodynamic models that can be used to estimate a storm surge hydrograph, as well as currents, associated with a specific storm is the storm surge and circulation model, ADCIRC (ADvanced CIRCulation, Luettich, et al. 1992; Blain, et al. 1994; Scheffner, et al. 1994; Westerink, et al. 1993; and Westerink, et al. 1994). ADCIRC’s two-dimensional version uses a finite element approach to solve the depth-integrated, nonlinear momentum and continuity equations in the time domain.

Input to ADCIRC includes the topography and bathymetry, distributions of wind velocity vector, and bottom drag coefficient, as well as boundary conditions. The output of ADCIRC includes the time series of surge elevation (this is the still water elevation without the wave crest elevations) at any location, the two-dimensional surface elevation and the water velocity fields at all grid locations.

The ADCIRC model has been used to develop an estimate of the storm surge hydrograph for Hurricane Katrina (Douglass, et al. 2006). The numerical grid used is shown in Figure 3.4. The grid extends out into the Gulf of Mexico beyond the shallow continental shelf but is focused on the shoreline and upland areas that flooded. A map of the estimated maximum surge predicted by the storm surge model is shown in Figure 3.5. The highest surge reached 333 ft (10 m) above the mean sea level (MSL). This value agrees with those reported in post-storm surveys.

Figure 3.4. Example of a numerical grid for a coastal hydrodynamic model (from Douglass, et al. 2006)

The detailed, estimated storm surge hydrograph at the location of the US Highway 90 bridge across Biloxi Bay that was destroyed by Katrina is shown in Figure 3.6. The peak surge is estimated to be 21.5 feet at 10:30 a.m. Also shown on Figure 3.6 are estimates of wave height from a SWAN model (see Douglass, et al. 2006). The shape of the hydrograph indicates that the bridge was exposed to surge elevations above 15 feet for three hours.

Figure 3.5 Estimates of the peak storm surge caused by Hurricane Katrina (from Douglass, et al. 2006)

Figure 3.6 Storm surge hydrograph as estimated by ADCIRC modeling for Hurricane Katrina at the US 90 bridge across Biloxi Bay, Mississippi (from Douglass, et al. 2006)

3.2.2 Design Water Levels

The selection of a design water level can be one of the most critical coastal engineering decisions for the designs and structures discussed in Part 3 of this document. For example, the design water level often controls the design wave height, stone size and extent of armoring on coastal revetments. Also, wave loads on elevated bridge decks are extremely sensitive to water level. Essentially, the water level dictates where waves can reach and attack.

Design water level decisions should be addressed using the traditional, risk-based approach of a “design return period” as is common in hydraulic engineering. For example, the “100-year storm surge level” is the surge elevation with a 1%-annual risk of exceedance. Each year, there is a 1% chance that a storm surge of this magnitude (or greater) will occur. Some coastal designs may justify a lower return period (e.g., 25- year or 50-year) in certain areas -balancing the greater risks affiliated with such design with engineering and economic considerations.

Three approaches for developing site-specific water level-return period relationships are: 1) use of available analyses, 2) historical analysis, and 3) numerical simulations with historic inputs. There is a great deal of literature and information on each of these approaches (including plusses and minuses). This document will only provide a brief synopsis of the key elements in each approach.

Some limited information on return periods for water levels is available from state and Federal agencies. FEMA, as part of their flood insurance mission, has estimated 100-year flood levels and areas of subsequent inundation along much of the United States coast. However, the precision of the FEMA results can be limited and they should be evaluated carefully before use in design.

Many emergency management agencies have coastal inundation maps that are based on results from hydrodynamic models. One commonly applied model is called SLOSH (Sea, Lake, and Overland Surges from Hurricanes). The SLOSH model is usually used to estimate the worst possible flood level for each of the Saffir-Simpson scale storm categories. These may provide an estimate of extremely rare storms but do not provide risk-based information for design. Some Corps of Engineers Districts have developed their own water level-return period relationship for design at many coastal locations. Some state resource management agencies, e.g. Florida’s Department of Environmental Protection’s Bureau of Beaches and Coastal Systems, have developed estimates of surge-return period relationships along the coast.

All available estimates of the surge-return period relationship should be collocated and evaluated carefully before use in design. Available estimates are often not adequate for design of site-specific coastal works without the review by a qualified coastal engineer. The Florida DOT has researched application of such analyses and developed a protocol that may be useful for others to review and adopt (Sheppard and Miller 2003).

Historical analysis on long-term tide gage data can provide water level-return period information. Typically, determining the return period associated with these tide station record involves application of log-Pearson Type III (or similar)statistical methods. Either graphical or analytical statistical approaches can be used. However, such analyses are typically restricted to locations near one of the NOAA/NOS long-term tide stations or a tide station operated by the Corps of Engineers; other local, state, or Federal agencies; or universities. In a situation familiar to practitioners trying to use riverine gaging station data, these tide stations are rarely close enough to the actual project site to allow direct application. However, unlike those stream flow driven riverine gages, the tide station may allow a practitioner to apply engineering judgment (and other, more formal techniques) and establish a reasonable “transfer function” that relates water levels at a location with a tide record to another nearby location. This could provide a reasonable estimate of the relationship for some locations.

New, independent analysis of the relationship between water level and return period is often appropriate for design of coastal highway solutions. For major projects, a probabilistic, numerical approach which uses a hydrodynamic model for storm surge simulations (see Section 3.2.1) and historical storm information can be used. The model must be calibrated appropriately. Input storm conditions for historical hurricanes for the past 150 years are available from the NOAA HURDAT database. There are two general approaches to assigning the proper probability to historical storms and other “hypothetical storms;” 1) the Joint Probability Method (JPM) which is typically used by FEMA in their coastal flood studies, and 2) the Empirical Simulation Technique (EST) which was developed by the Corps of Engineers to develop site-specific water level-return period relationships (US Army 2002 CEM). This sort of analysis likely requires the integration of a qualified, coastal engineer or scientist into the design team.

3.3 Sea Level Rise

The level of the oceans of the world has been gradually increasing for thousands of years. The important change is the relative sea level change, the combined effect of the ocean water elevation and the land-mass elevation change. Some of the United States land-mass near the coast is subsiding due to a variety of geologic factors including compaction and man-induced factors such as groundwater or oil and gas extraction. Some of the United States land-mass near the coast, however, is rebounding or emerging, due to glacial retreat. Relative sea level change, rise or fall, is the difference between these two, the ocean and the land elevation. The sea level fluctuations of the past twenty thousand years and the geologic impacts on beaches are discussed below.

Tide gages have measured relative sea level changes around the nation for the last century. Figure 3.7 (Atlantic and Gulf coasts) and Figure 3.8 (Pacific coast)show the variation in the average annual mean sea level (MSL) for a number of locations around the United States coast for the past century. The values are plotted relative to the MSL of the 1983 to 2001 tidal epoch. There is a clear upward trend, i.e. relative sea level rise, along much of the United States coasts. There are, however, some places with no clear trend or even a negative trend. For example, near the California/Oregon border and in much of Alaska, there is a relative sea level fall in the last century. The rate of sea level rise (or fall) varies significantly along the United States coast with the highest rates of rise in the areas with the most land-mass subsidence along the Gulf Coast.

The rate of relative sea level rise or fall can be evaluated by the change in mean sea level as measured at specific NOAA tide gages from one tidal epoch to the next. The change in mean sea level from the 1960 to 1978 tidal epoch to the 1983 to 2001 tidal epoch was +0.25 feet(sea level rise) at Charleston, South Carolina, and was -0.03 feet (sea level fall) at Juneau, Alaska.

The world-wide, average sea level, with land-mass subsidence effects removed, is called the eustatic sea level. The estimated eustatic sea level has been rising at a rate of 2 mm/year for the past century. In a very active research field, many atmospheric scientists have concluded that the earth is warming and that sea level rise rates will accelerate in response. While no acceleration in sea level rise rate has been measurable yet, the U.S. Environmental Protection Agency (USEPA) and many others have suggested future sea level rise acceleration scenarios for planning.

The impact of long-term sea level rise has rarely been taken directly into account in the design and planning of coastal highways. It has, however, been indirectly taken into account because of its effect on epoch-based tidal datums and its fundamental controlling effect on shoreline change and other coastal processes. It is likely that long-term sea level rise and other global climate change phenomenon, such as an increase in storminess, have already significantly impacted our coastal highway system. For example, it is possible that the frequency of coastal flooding and damage to highways has increased in the past several decades. Thus, long-term sea level rise probably will be more often accounted for in the planning and design of engineered systems near the coast in the coming decades.

Figure 3.7. Sea levels along the US Atlantic and Gulf coasts for the past century.

Figure 3.8. Sea levels along the US Pacific coast for the past century.

3.4 Lake Water Level Fluctuations

The Great Lakes, the Great Salt Lake, and other very large inland lakes are tide less. They are completely separated from the oceans and are too small for any astronomical tides of their own. Water levels in these large inland lakes have significant fluctuations however in response to rainfall in their drainage basins. For example, there is an annual rise and fall of between 1 and 2 feet on Lake Erie due to snowmelt in the spring. Multi-year wet and dry periods cause 3 to 5 feet of decadal-scale fluctuations. Many of these very large lakes have their own local lake level datums that are used for science and engineering related to the water level. A bulletin describing lake levels for the Great Lakes is available from the Detroit District of the USACE on-line at www.lre.usace.army.mil/glhh.