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The storm surge is a long gravity wave with a length scale similar to the size of the generating tropical cyclone, and lasts for several hours depending on the cyclone size and speed of movement. It is thus of a similar scale to an astronomical tide and should not be confused with short gravity wind waves, which have wave-lengths of metres and periods of seconds. The surge usually consists of a single passing wave that elevates or depresses the still water height. In some special situations, especially for cyclones moving parallel to the coast, secondary waves or resurgences can form behind the tropical cyclone.
The ocean response to tropical cyclones is quite different in deep water and in shallow, offshore water. In deep waters, far from a coast, the surface wind stress from a tropical cyclone creates a rotating mound, or vortex, of water by diffusing momentum downward. The ocean elevation is small, approximately the hydrostatic uplift in response to the low central pressure (the inverted barometer effect) and some minor long term Coriolis effects. Dynamic effects become pronounced as the tropical cyclone approaches a coast. On entering the shallow waters of a continental shelf, conservation of the potential vorticity of the mound requires development of marked divergence. Channelling by local bathymetry, and reflections from the coast also contribute to substantially amplify the surge height. Unlike the short-wavelength, propagating wind-waves, a translating surge wave does not break in shallow waters. As viewed by an observer facing out to sea, a tropical cyclone has onshore winds, with positive surge, to the right (left) in the Northern (Southern) Hemisphere, and offshore winds, with negative surge, to the right (left).
The radius of maximum winds provides an important scaling parameter for storm-surge calculations. A crude approximate measure for the wave length of the long gravity surge wave is 4 times the radius of maximum winds, discounting the effects of the pressure gradient body force on the surge wave. Tropical cyclone size, translation speed, residence time on the continental shelf, and angle of attack to the coast, together with local offshore bathometry and inland topography all play significant roles in surge generation and inland flooding.
Some confusion exists between storm tides and storm surges. In this report a storm surge is the elevation of water generated by a tropical cyclone above or below the normal astronomical tide. A storm tide, on the other hand, is the total elevation (including the astronomical tide) above or below a standard datum. The storm tides are predicted water heights issued in tropical cyclone advisories. The generic term "surges" is used interchangeably according to context. Storm surge can be computed with modelling efforts but the storm tide is difficult because of phasing uncertainties with astronomical tide.
Figure 4.1. Recorded storm-tide gauge trace at Steel Pier, Atlantic City, New Jersey, USA, generated by a hurricane on September 14-15, 1944, with predicted astronomical tide superimposed (numbers indicate the LST running from left to right). Subtracting the astronomical tide from the trace gives the surge generated by the hurricane.
Raw surge observations are always storm tides. Historical observations of storm tides are frequently scarce, haphazard, targets of chance and at times inconsistent with datum points for accurate post tropical cyclone analysis. It is remarkable how little effort is made to record and archive surge data after tropical cyclone passage throughout the world!
The best data are from a tide gauge trace of water levels against time, similar to an anemometer trace of winds (Fig. 4.1). Although short gravity wind waves normally are filtered out by the stilling well of the gauge, substantial wind-wave contamination may occur during a tropical cyclone, as may be seen by the high frequency "noise" in Fig. 4.1. The usual archive procedure is to visually average the surge at hourly times, which leads to inaccuracies as peaks and troughs may fall between hourly readings (as indicated on Fig. 4.1). Astronomical tide predictions are then subtracted from the record to produce the storm surge.
Staff gauge records are visually-averaged, still-water sightings of water levels, against time, from a scaled ruler anchored to the ground with respect to a known datum. These data are as good as tide gauge data, assuming a competent, trained observer remains nearby during the tropical cyclone passage.
Tide and staff gauges, unfortunately, are few and far between, and they frequently fail during core passage of a tropical cyclone. Post tropical cyclone surveys of high water marks against geodetic bench marks are therefore normally required for surge estimation. In the absence of tidal or staff gauge data, it is best to have a cluster of nearby high water observations for verification studies. A single, isolated high water mark or debris observation should be treated with caution because of inherent inaccuracy. A reliable surge model can approximate the occurrence time of high surge to enable removal of the astronomical tide to determine the peak storm surge at the observation point.
Statistical and empirical methods utilise historical data to develop a forecast technique by regression or other statistical approaches. Unfortunately, such an approach requires a large data base, which is non-existent in most regions. This lack of data is a handicap for statistical studies (Harris, 1956). Some incomplete data sets have been compiled in localised areas for developing empirical surge forecast techniques (Connor et al., 1957; Goudeau and Connor, 1968).
Numerical models provide the best approach to computing surges associated with tropical cyclones, albeit with qualifications. A surge model requires a geographical data base consisting of sea bathometry and, if inland inundation is to be computed, the complex inland topography surrounding the cyclone landfall point. The data must extend alongshore for the region of gale force winds and out to the edge of the continental shelf with a resolution of, at worst, several kilometres, and inland to the 10 m land contour with 1 m height resolution. Such data are referred to as a basin or basin data. Because of the lack of adequate meteorological data, a parameterised tropical cyclone model is used to provide the external forcing for the surge model. This cyclone model is initialised with the size, central pressure and track of the cyclone. Such a procedure is "diagnostic" since a surge model does not (and is not required to) forecast tropical cyclone conditions or tropical cyclone track. A surge model will accept any reasonable tropical cyclone parameters from an outside arbiter without regard to its pedigree. With this freedom, surge models are capable of answering "What if?" questions according to basin and tropical cyclone input data.
With the aid of desk computers, actual computer runs can be made in a timely fashion for coastal surges. Moreover, colour computer monitors can easily graph salient features of surges for instant display. Any tropical cyclone can be run with a particular basin, providing that the basin data have been prepared and that the requisite coastal surge model and parameterised tropical cyclone model have been programmed. One example of such an application is the personal-computer based surge model developed by Hubbert et al. (1990).
Coastal surge models are not useful for inland surge inundation associated with estuaries, bays, lakes, meandering rivers, canals, realistic coastlines with capes and coves, barriers (roads, levees, spoil banks, etc.), as well as flooding across low lying terrain. For these fragmentary, non-ideal conditions, a more sophisticated surge model is required.
Surge models can be run concurrently with an astronomical tide to include the interesting non-linear interactions that occur between these. However, the normal 6-hour error for tropical cyclone arrival in a 24-hour forecast period is roughly the time difference between high and low semi-diurnal astronomical tide. Thus, the direct inclusion of astronomical tides in surge models is inappropriate for operational forecasting. Instead, surge forecasters generally superimpose astronomical tide onto the computed surge using subjective estimates of the quality of the forecast track. If forecasting defensively, the high tide is usually superimposed on the surge.
The surge from most landfalling tropical cyclones affects 100-200 km of coastline for a duration of several hours. Unfortunately, tropical cyclone track forecasts have errors of a similar magnitude for the crucial 24 h leading up to landfall. Model surge computations cannot provide a valid surge estimate with such imprecision in the track forecast. An example for Hurricane Elena (1985) is shown in Figs. 4.2a,b using SLOSH (Jelesnianski et al., 1992) for storm-surge computation. The computed and observed surge values using the post-analysis best track were in good agreement (Fig. 4.2a). However, using the forecast track produced very poor surge estimates (Fig. 4.2b). The track forecast error at landfall was 40 km, which is excellent by meteorological standards, yet produced surge estimates that were radically different from those that were observed. This arises because the generated surge is sensitive to small errors with a track at an acute angle to the coast.
Figure 4.2. Comparison of observed/computed surges (ft) for Hurricane Elena, Aug. 29-Sept. 3, 1985: a) using best track positions; b) using the forecast track. Tropical cyclone parameters were supplied by the National Hurricane Center, Miami, Florida.
It is disagreeable, of course, to predict a non-occurrent high surge with a forecast track. Suppose, however, the predicted and real track were reversed and a low surge were predicted instead of a calamitous high surge? A reliable surge model can be used to indicate surge sensitivities peculiar to a given basin with complicated coastal and terrain features, thereby alerting users to possible surprises in surge generation.
One method of countering the problems with imprecise forecast tracks is to run a proven and reliable surge model with several alternate tracks, varying on either side of forecast landfall point. Similar procedures can be applied for possible changes in tropical cyclone intensity and size during a forecast period. In this way, a range of possible surge values is generated corresponding to the range of meteorological imprecision.
Figure 4.3. Nomogram for peak surge on the open coast. Entering arguments are pressure drop and radius of maximum winds. The maximum winds are valid for 10-min average at 10 m elevation for a stationary cyclone over water. The curves were computed for a standard tropical cyclone motion across a standard basin, as described in the main text.
Numerical models also can be used to develop nomograms for surge forecasting, which have appeal for their simplicity, but are subject to limitations of use in complex terrain and are usually restricted to coastal surges. The nomograms are usually prepared from pre-computations with a simplified numerical surge model, quasi-idealised basins and hypothetical tropical cyclone conditions. The basin requirements are bathymetric depths only and a coastline of long horizontal extent, small islands excluded. The basin geometry is idealised with a regular, unbroken coastline of mild curvature and an infinite height vertical wall at the coast to represent rapidly rising inland terrain, but has realistic offshore bathometry. For ease of presentation the cyclone components are restricted to time-invariant tropical cyclone parameters, straight line landfall tracks at any angle of attack to the coast, constant speed along tracks and a sequential series of coastal landfall points (Jelesnianski, 1972; Das, 1981; Das et al., 1974; Ghosh, 1977).
Figure 4.4. Nomogram of correction factors against vector tropical cyclone motion. The factor corrects Fig. 4.3 for non-standard tropical cyclone motion and the inset orientates the cyclone track angle relative to a coast.
Figure 4.5. Nomogram of shoaling correction factors for the Gulf coast of the USA. The factor corrects Fig. 4.3 for real, non-standard basins.
To determine a peak coastal surge, for any landfall tropical cyclone in a restricted area, consider, for example, the three nomograms in Figs. 4.3-4.5 (Jelesnianski, 1972). The first nomogram (Fig. 4.3) requires two cyclone parameters: radius of maximum winds (an indicator of cyclone size) and pressure drop (ambient pressure surrounding the tropical cyclone less central pressure of the tropical cyclone). These two arguments give a preliminary value of storm surge for a standard tropical cyclone moving perpendicular to the coast across a standard basin with a translational speed of 6 ms-1. The standard basin consists of a straight line coast cantered at latitude 30o, a 4 m depth at the coast, and a one-dimensional slope descending seaward at 0.6 m km-1.
Figure 4.6. A family of 12 westbound, hypothetical tracks. Hurricane symbols reference landfall points, the dots are eye positions 6 h apart and each track is identified by the distance in miles to the left side (LS) or right side (RS) of the harbor entrance to Miami, Florida.
Notice how the computed peak surges vary almost linearly with pressure drop and only mildly with tropical cyclone size. These are fortuitous features since tropical cyclone size is difficult to ascertain compared to central pressure. Since the maximum wind can vary with tropical cyclone size for a given pressure drop (Fig. 4.3) this suggests maximum wind by itself is too sensitive a parameter for surge studies. Also, surface pressure measurements are not contaminated with the same level of noise as are wind observations.
For non standard tropical cyclone motion, Fig. 4.4 corrects the preliminary surge value with a correction factor FM for any track angle of attack to the coast at any speed of motion. The nomogram was prepared with a standard basin, a tropical cyclone with radius 30 km, and a pressure drop of 62 mb. Two conclusions can be drawn from this figure: (1) tropical cyclones moving from land to water have much smaller surges than landfalling tropical cyclones (water to land); (2) higher tropical cyclone translational speed gives higher surges (up to a critical speed) for landfall tropical cyclones, but the reverse for cyclones moving out to sea. Nomograms of this nature will not work well with strongly curved coasts; that is, if the coastal radius of curvature is smaller than the radius of maximum winds. The correction factor, of course, is dependent on the choice of tropical cyclone parameters, but the variation is small for a large range of parameters.
Figure 4.5 further corrects the preliminary surge value for a composite of non-standard, real geographical basins via a shoaling factor FG developed from experience along the coasts of the Gulf of Mexico. The basins used have 2-dimension depth contours in which strongly curved and ragged coastlines were smoothed to mild curvature. The correction factor is invalid if applied to other regions of the world unless bathymetric depths correspond, latitude does not differ significantly, coastal curvature is mild and inland terrain rises rapidly. The nomogram was prepared with a standard tropical cyclone motion. Since the shoaling correction is mildly sensitive to tropical cyclone size but not pressure drop, two tropical cyclones of radii 20 and 40 km, were used. A nomogram of this nature is a useful tool since it lucidly portrays the relative surge potential along an extended coastal segment threatened by a tropical cyclone.
The preliminary surge value must be multiplied by both the correction factors, FG and FM, to compute the peak surge. Other nomograms can be prepared to include the envelope profile of the coastal storm surge (Ghosh, 1977). Once prepared for a specific region, these nomograms do not require the use of a computer and quickly give an answer for quasi-idealised conditions. Nomograms for alongshore, non-landfall, tropical cyclones can also be prepared but are unwieldy and of such complexity they lose their simplicity and appeal (Jelesnianski and Barrientos, 1975).
On site computations with several tracks, tropical cyclone intensities and sizes may require many computer runs. During a real time situation this can overload computer facilities and personnel, and require unacceptably time consuming analysis of the output. An alternate procedure both for surge forecasting and for evacuation and planning purposes is to prepare an atlas of pre-computed surges (Jarvinen, et. al., 1985).
To generate a data base of pre-computed atlases of storm surges for a particular basin with inland water bodies and complicated terrain features, recourse is made to a tropical cyclone climatology, which gives a broad view of the tropical cyclone types likely to affect a given region. Much ingenuity is required to optimally stratify meteorological parameters from sparse meteorological data within limited regions. Usually, historical tropical cyclones affecting a region are stratified into preferred track directions, intensities, and sizes. An example of a family of parallel tracks, idealised from climatology, is shown in Fig. 4.6 for Biscayne Bay, Florida, USA. Such a family of equally spaced, parallel tracks for surge computations need not follow great circles. They can gently curve to reflect climatological data, but should all correspond in the vicinity of the landfall points.
The family of tracks account for alternate landfall points for a given direction along a coastal area of interest (or else alternate distances from the coast for alongshore moving tropical cyclones). It should be recognised that the generated surge normally is strongly dependent on the angle the track makes with the coast, several hours before and after landfall. The remaining track segments affect the surge only mildly. Thus, although the location of a tropical cyclone far out to sea and its landfall point may be significantly in error, the family, or families, representing the broad approach to land can be used to estimate the likely surge consequences.
For simplification, it is often assumed that the cyclone translational speed, central pressure and size remain constant along the track. Alternate values of these parameters can be used for each track family to provide a more comprehensive data base. The embedded, identical tropical cyclone model in each family of tracks, also can be designed to alter the tropical-cyclone central pressure and size with time after landfall to represent any explosive filling and core changes of the tropical cyclone.
Care needs to be taken with using many parameters to develop a comprehensive surge data base. For example, using 3 families of tropical cyclone tracks, each family with 10 parallel, equally spaced tracks, 5 different central pressures, 2 different sizes and 2 different translational speeds, would require 3x10x5x2x2=600 model runs.
It is impossible to account for all possible eventualities. The atlas that is developed should be regarded as a good starting point to isolate the potential surge whenever a tropical cyclone is forecast to affect a given coastal region. After a study of potential surges with idealised tracks from the atlas, runs can then be made to fine tune a surge forecast, that includes relevant details from the actual cyclone.
An atlas of pre-computed surges can be a bulky document and collating the several possible tropical cyclone conditions from the many into a composite potential of surges is a demanding chore. Since each computer run gives an envelope of highest waters in a basin for the life history of a tropical cyclone, it is a simple computer chore to determine the highest possible surge at all vulnerable coastal locations from a particular family of tracks. The resulting map is called a Maximum Envelope of Waters, or MEOW.
To put the concept of a MEOW into perspective, consider how the SLOSH surge model (Jelesnianski, et al., 1984; Jarvinen and Lawrence, 1985) is used by the US National Hurricane Center. The model has been used widely and was designed in a universal sense that does not require specialised calibration for runs in any basin with any tropical cyclone. An example of a basin and its attendant, polar, telescoping grid for Biscayne Bay, Florida, is provided in Fig. 4.7a, and the overlapping basins used along the US coast are indicated in Fig. 4.7b.
Model runs were made using hypothetical tropical cyclones with central pressures stratified by the Saffir/Simpson scale of intensity categories and sizes from climatology. For example, the surface envelope of highest waters for a westbound tropical cyclone, moving at 5 ms-1 with Saffir/Simpson category 3, radius of maximum winds 30 km and landfall at Miami, Florida is depicted in Fig. 4.8a, for the window region of Fig. 4.7a.
Note the site 20 km south of the track in Fig. 4.8a, where no flooding is present (denoted by a star). If the same tropical cyclone moving in the same track direction made landfall 100 km further to the south, the resulting surge (Fig. 4.8b) would inundate this site.
Figure 4.7. a) The telescoping polar grid mesh for the SLOSH surge model for the Miami, Florida Basin, b) the 31 SLOSH basins along the East and Gulf coasts of the USA used by the SLOSH storm-surge model (several of which use an elliptic/hyperbolic grid). The boxed area in (a) is the domain depicted in Figs. 4.8-4.9.
Figure 4.8. Surface envelope of peak storm surge (ft) generated by a westbound, 5 ms-1, Saffir Simpson Category 3 hurricane with radius of maximum winds 30 km, landfalling at (a) and 100 km south (b) of Miami, Florida. The shaded areas are flooded regions.
Figure 4.9. A MEOW (ft) generated from the SLOSH surge model by the westbound tropical cyclones of Fig. 4.6 with the same parameters used in Fig. 4.8. The shaded areas are flooded regions.
To generate the MEOW, the maximum surge value from the entire family of cyclones at each grid square of a basin is saved, regardless of which cyclone was responsible. The resulting composite of peak surges makes up a MEOW such as that shown in Fig. 4.9 from the 12 tracks of Fig. 4.6. Other MEOWs can be developed for a range of cyclone profiles and conditions. This provides an easily accessible summary of the "worst case" surge scenario given the uncertainty in the current forecast situation (Jarvinen et al., 1985).
It is recommended that any atlas of pre-computed surges contain composite sets of MEOWS. When an offshore tropical cyclone is posed to strike inside a basin, such a set provides both a ready reckoner of the surge disaster potential and a quick summary of those cyclone tracks and types that need to be examined more carefully.
If all the computed surge data of an atlas are available for graphical display on a computer, a "mini" MEOW can be quickly assembled in real time. This is especially useful since it allows the user to select the most probable range of possible tracks and cyclone profiles for the present situation. Such a procedure, which is best utilised near landfall time, is utilised by the US National Hurricane Center to forecast storm surges. The user selects the range of scenarios from a display on the screen, consistent with anticipated forecast track errors, and then the computer prepares the composite envelope of maximum waters from a pre-computed atlas of surges.
During late September, 1989, a powerful tropical cyclone, Hurricane Hugo, was threatening the eastern coast of the United States. Its landfall time and position were uncertain and the central pressure and tropical cyclone size was evolving, but there was confidence in the prevailing track direction. Whilst Hugo was still far out to sea, the Charleston Basin (Fig. 4.7b) was chosen to study surge potential. From the computer data base, a MEOW (Fig. 4.10) was derived from a category 3 tropical cyclone family with radius of maximum winds of 40 km, travelling to the NW at 5 ms-1 and with landfall points 15 km apart. The processing was done using a personal computer based SLOSH, a menu driven, sophisticated, friendly and flexible procedure to explore surge potential from a vast data base of pre-computed hypothetical tropical cyclones. A zoom facility (Fig. 4.10b) was used to highlight the vulnerable Charleston city area.
The potential peak surge of around 5 m given by the MEOW was a most disturbing record surge for the region and difficult for many weather forecasters to accept, but based on this analysis surge forecasts of 4-5 m were issued. Hugo subsequently intensified to a category 4 hurricane and accelerated to a translational speed of over 10 ms-1. The SLOSH post-analysis using best track data (Fig. 4.11) gave a computed peak storm tide of over 6 m (20.3 ft), which agreed quite well with the available observations (shown as triangles in Fig. 4.11). Since the tropical cyclone made landfall at high astronomical tide, 1 ft needs to be added to the computed surge to arrive at the storm tide.
Figure 4.10. A MEOW generated by a family of cyclones characteristic of the forecast features of Hurricane Hugo (1989) moving along the parallel tracks (black lines). The extent of the basin is shown and white lines represent the coast: a) full basin, b) zoomed to highlight the Charleston region.
Figure 4.11. Computed surge (ft) using the SLOSH model on the best track for Hurricane Hugo (1989). Numbers in triangles indicate observations or estimates of actual surge height and an astronomical tide of 1 ft must be added to the surge to arrive at the storm-tide value.
The agreement between this actual cyclone analysis and the pre-computed MEOW is excellent and indicates that the MEOW can be very useful in defining the scale of the surge problem very well, given a reasonable estimate of the forecast uncertainties with the tropical cyclone. Not all examples will be this accurate, however, comparisons of computed surge values against available data from past historical tropical cyclones suggest an accuracy range of ±20% for SLOSH derived surges.
The MEOW scheme is applicable to any coastal region, but devising a SLOSH type procedure for a lengthy coastline is a laborious and time consuming project. Many basins are required (Fig. 4.7b), extracting geographical data onto grid schemes from bathymetric and topographic maps is a tedious task, as is developing a suitable cyclone climatology. Each basin then requires hundreds of individual runs with hypothetical tropical cyclones to stratify MEOW composites. Once the data base is secured in computer memory, however, both 'What if?' games and special studies, such as tropical cyclone evacuation procedures, can be undertaken with relative ease.
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