General. The Sea, Lake, and Overland Surges from Hurricanes (SLOSH) model is the latest and most sophisticated mathematical model yet developed by the National Weather Service to calculate potential surge heights from hurricanes. The SLOSH model is a two dimensional model that was developed for real-time forecasting of surges from actual hurricanes within selected Gulf and Atlantic coastal basins. In addition to furnishing surge heights for the open coast, the SLOSH model has the added capability to compute the routing of storm surge into bays, estuaries, or coastal river basins as well as calculating surge heights for overland locations. Significant natural and man-made barriers are represented in the model and their effects simulated in the calculations of surge heights within a basin.

The SLOSH model is designed for use in an operational mode; that is, for forecast/hindcast runs without controlled, local calibration, or observed winds. The rationale for this design is to avoid having the forecaster predict unavailable input data. The SLOSH model contains a storm model into which simple, time-dependent meteorological data are input and from which the driving forces of a simulated storm are calculated. These data are as follows:

SLOSH Grid Configuration. The SLOSH model utilizes telescoping coordinate grid systems within which particular coastal basins are represented. Due to the amount of coastline included in the southwest Louisiana study area, two different SLOSH grids were required. The Vermilion Bay Basin was used to model the area from Vermilion Parish to Lafourche parish and the Sabine Lake Basin was used to model the area from the Texas/Louisiana state line to Vermilion Parish. The SLOSH grids for the Vermilion Bay Basin and the Sabine Lake Basin are shown in Figure 2-1. The overlap in the grids ensures that the model results are consistent from one SLOSH basin to the next.

The Vermilion Bay Slosh grid is a telescoping polar coordinate system with 128 arcs (the curved lines) and 156 radials (the straight lines). The resolution of the model for inland locations nearest the grid’s pole is approximately 0.2 square miles per grid square. The size of the grid squares increase as the distance from the pole increases. The grid squares along the outer boundaries of the grid cover approximately 6 square miles. The Sabine Lake grid is a telescoping elliptical coordinate system with 120 arcs and 145 radials. The resolution of the model varies from 0.1 square miles per grid square nearest the grid’s pole to 1.4 square miles at the outer boundaries of the grid. The larger grid cells in the offshore region permits the inclusion of a large geographic area in the model so that model boundary effects on the dynamics of the storm are diminished. The advantage of this grid system is that it offers good resolution in areas of primary interest while conserving computer resources by minimizing the number of calculations required to model a storm.

The characteristics of a particular basin are constructed as input data within the model. These characteristics include the topography of inland areas; river basins and waterways; bathymetry of nearshore areas, bays and large inland water bodies; significant natural and man-made barriers such as barrier islands, dunes, roadbeds, floodwalls, levees, etc.; and a segment of the continental shelf. The SLOSH model simulates inland flooding from storm surge and permits the overtopping of barriers and flow through barrier gaps.

Verification of the Model. After a SLOSH model has been constructed for a coastal basin, verification experiments are conducted. The verification experiments are performed in a "hindcast" mode, using the real-time operational model code and meteorological input from historical storms. These input data consist solely of observed storm parameters and an initial observed sea surface height occurring approximately 48 hours before landfall. Ideally there would be a large number of actual storm events with well documented meteorology and storm surge histories which could be compared to the storm surge histories hindcast by the SLOSH model for the same storms. In reality, hurricanes are a rare meteorological event for any given region, and it is even rarer to find adequate, reliable measurements of storm surge elevations over a representative number of sites within a region due to the difficulty in making such measurements during hurricane conditions.

The computed surge heights are compared with those measured from historic storms and, if necessary, adjustments are made to the input or basin data. These adjustments are not made to force agreements between computed and measured surge heights from historical storms but to more accurately represent the basin characteristics or historic storm parameters. In those instances where the model gave realistic results in one area of a basin but not in another, closer examination of the basin often revealed inaccuracies in the representation of barrier heights or missing values in bathymetric or topographic charts. In the case of historic storms, most of the data was coarse; with parameters prescribed invariant with time and with an unrealistically smoothed storm track. When necessary, further analysis and subjective decisions are employed to amend the track or other parameters of the historic storms used in the verification process.

Model Output. The SLOSH model output for a modeled storm consists of a tabulated storm history containing hourly values of storm position, speed, direction of motion, pressure drop and radius of maximum winds; a surface envelope of highest surges; and, for preselected grid points, time-history tabulations of values for surge heights, wind speeds, and wind directions. If desired, the model can also furnish two-dimensional snapshot displays of surges at specified times during a simulation.

The highest water level reached at each location along the coastline during the passage of a hurricane is called the maximum surge. Maximum surges along the coastline do not necessarily occur at the same time. The time of the maximum surge for one location may differ by several hours from the maximum surge that occurs at another location. A plot of the maximum water surface elevation attained at each grid cell over the duration of the simulated storm does not represent a "snapshot" of the storm surge at a given instant of time. Instead, it represents the highest water level at each grid cell during a hurricane irrespective of the actual time of occurrence.

The printed envelope of highest surges from the SLOSH model shows the computed surge heights in feet NGVD in the center of each grid square. Other information depicted includes symbols for natural and man-made geographic features, latitude and longitude lines, and the storm path through the basin. In order to output computed surges on a line printer, the polar grid for a basin is transformed onto an image plane of equal spacing. Cells near the origin of the polar grid are thus expanded relative to their original size and cells near the outer portion of the polar grid are contracted relative to their original size. The result is that the model grid is represented by equally spaced parallel lines while Latitude and Longitude lines and all other geographic features within the basin are distorted.

The time-history data of surge heights, wind speeds, and wind directions are tabulated for each pre-selected grid point in the model. These data are listed for each grid point at ten-minute intervals for a 72-hour segment of a simulated storm track, starting 48 hours prior to landfall and continuing for 24 hours after landfall or closest approach. The surge heights are in feet NGVD; the wind speeds in miles per hour; and the wind directions in degrees azimuth from which the wind is blowing. Water depths are not computed because terrain height varies within a grid square. The depth of flooding is deduced by subtracting the actual terrain height from the model-generated surge height.

General. With over 250 miles of coastline included in the southwest Louisiana study area, two SLOSH model basins were required. The Sabine Lake basin SLOSH model and the Vermilion Bay SLOSH model were used in the Southwest Louisiana Hurricane Evacuation Study to determine potential surge heights and the limits of inundation. The Sabine Lake SLOSH Basin covers the area from Port Arthur, Texas to Abbeville, Louisiana. The Vermilion Bay SLOSH Basin covers the area from Abbeville, Louisiana to Golden Meadow, Louisiana. The SLOSH model grids are shown in Figure 2-1.

Topographic and Bathymetric Input. The accuracy of the SLOSH model depends heavily on the ability to accurately model the topographic and bathymetric features of the basin. Inaccuracies in modeling these features will contribute directly to errors in the modeling of storm surge. This is of particular importance for the Sabine Lake and Vermilion Bay basins, which include large areas of sea-level marsh, swamp and open water. The major barriers to storm surge in southwest Louisiana include natural ridges along many of the rivers and bayous and man-made features such as, levees, floodwalls, highways, and railroad embankments. The bathymetry of the coastline and the areas bays, lakes, rivers, canals, and bayous are also of importance in accurately modeling hurricane surge. Data was collected to establish the heights of both Federal and non-Federal levees and floodwalls, and to establish the existence of any gaps or other information that might affect the integrity of a barrier to hurricane surge. Other barrier heights were obtained from existing profiles or actual surveys of features critical to the limits of inundation. The bathymetry of the coastline and other bodies of water within the study area was obtained using hydrographic surveys, bathymetric maps, and U.S.G.S. quadrangle maps. Input to the model also included average ground elevations for each grid square within the basin.

Verification. The historical hurricanes used in the verification process were Hurricane Audrey in 1957(Sabine Lake Basin) and Hurricane Andrew in 1985(Vermilion Bay Basin).  Go to top

Simulated Hurricanes. As part of the Southwest Louisiana Hurricane Evacuation study, a total of 600 simulated hurricanes were modeled using the Sabine Lake Basin SLOSH model and another 850 simulated hurricanes were modeled using the Vermilion Bay Basin SLOSH model. The characteristics of the simulated hurricanes were determined from an analysis of historical hurricanes, which have occurred within the study area. The parameters selected for the modeled storms were the intensities, forward speeds, directions of motion, and radius of maximum winds. These parameters were defined based on a meteorological probability of occurrence within each of the SLOSH basins. A breakdown of the hypothetical hurricanes for the Sabine Lake Basin and the Vermilion Bay Basin are presented in Table 2-3 and Table 2-4, respectively.

A total of 60 different storm tracks were modeled for the Sabine Lake Basin. These tracks are shown in PDF Maps. A total of 85 different storm tracks were modeled in the Vermilion Bay Basin. These tracks are shown in PDF Maps. The simulated hurricanes moving along these tracks had combinations of parameters representing five categories of hurricane intensity, as described by the Saffir/Simpson Hurricane Scale; eight approach directions for landfalling and paralleling hurricanes (west, west-northwest, northwest, north-northwest, north, north-northeast, northeast, and east-northeast); two forward speeds of 5 and 15 miles per hour; and numerous landfall or closest approach locations separated by 20 miles or less along the coastline. The radius of maximum winds specified for all of the simulated hurricanes was 25 miles at landfall.  Go to top

Most hurricanes weaken after landfall because the central pressure increases (the storm fills) and the radius of maximum winds tends to increase. The terrain of southern Louisiana is very low, flat, and marshy and the transition to "land" from "water" is not abrupt. When Gulf waters are at above-normal heights, for example, during the approach of a hurricane, the "coastline" is somewhere north of that usually drawn by cartographers. A "virtual coastline," shown in Figure 2-2, was used for SLOSH model calculations. Modeled storms were assumed to have "over water" characteristics until they traversed the virtual coastline, where landfall was defined to occur.

The primary factor which determines the intensity or category of a hurricane is the difference between the central barometric pressure of the center of the storm and the ambient barometric pressure surrounding the system. The term for the difference in internal and external pressures of a tropical cyclone is delta-p (_p). Table 2-5 lists the categories of hurricanes modeled for the Southwest Louisiana Hurricane Evacuation Study, the ranges of pressures constituting each category, the central barometric pressures for the simulated storms, and the resulting pressure difference, assuming an ambient standard barometric pressure of 1010 millibars.

Based on observations from tide gauges throughout the Sabine Lake Basin and the Vermilion Bay Basin, tidal anomalies of about +1ft NGVD before arrival of a hurricane are not uncommon. These initial heights, known as the tide anomaly, represent the heights of the water surface above mean sea level existing several days in advance of approaching hurricanes. The values for the tide anomaly used in the SLOSH model represent the average sea surface heights recorded at tide gauges for historical hurricanes several days prior to landfall. To simulate conditions at high tide, an additional 1ft was added to the initial water heights within the SLOSH model. Thus, all SLOSH model runs were made with initial surface elevations of +2 ft. NGVD to simulate conditions at high tide.

Maximum Envelopes of Water. One of the outputs from the SLOSH model is a plot of the maximum water surface elevation at each grid cell within the basin affected by the storm, irrespective of when that water level was obtained. The imaginary surface defined by the maximum water level in each grid cell is termed the "envelope" of maximum water surface elevations. The largest individual water surface elevation within the entire basin for a particular storm is termed the "peak" surge. The location of the peak surge depends on where the eye of a hurricane crosses the coastline, its intensity, the bathymetry and topography of the basin, configuration of the coastline, the approach direction, and the size or radius of maximum winds of the hurricane. In most instances, the peak surge from a hurricane occurs to the right of the storm path near the radius of maximum winds. This is largely due to the counter-clockwise rotation of the windfield surrounding the eye of the hurricane. To the right of the point of landfall, winds blow toward the shoreline; to the left of the point of landfall, winds blow away from the shoreline. It should be noted that during an actual hurricane, the point of landfall is highly unpredictable.

Due to the inability to precisely forecast the ultimate landfall location, forward speed, direction of movement, or other characteristics of a threatening hurricane, the objective of the hazards analysis is to determine the potential peak surges for all locations within the study area. For that purpose, a "maximum envelope of water" (MEOW) is utilized. A maximum envelope of water is developed from an array of peak surges calculated for the individual hurricanes modeled within the Sabine Lake and the Vermilion Bay Basins. Maximum envelopes of water can be created for any specified storm parameter or sets of parameters desired. A total of 80 MEOW's were developed for the Sabine Lake and the Vermilion Bay Basins. Each MEOW represented a different combination of hurricane (intensity categories 1-5), direction of approach (8 different directions), and forward speed (2 forward speeds). The maximum envelope of water shows the peak surge heights for each grid cell within the basin, independent of where the hurricane actually crosses the coastline. Go to top

The results of the 80 original MEOW's were analyzed to determine which changes in storm parameters--i.e., intensity, forward speed, and direction of approach--resulted in the greatest differences in the values of the peak surges for all locations and which parameters could reasonably be combined to facilitate evacuation decision making. The topography of southwest Louisiana is generally low-lying with numerous bayous, lakes, and rivers. This creates a unique sensitivity to storm surge and care must be taken when combining various hurricane parameters. Relatively small increases in peak surge can place entire communities at risk to inundation.

The results of our analysis showed that a change in storm category accounted for the greatest change in the peak surge heights calculated for grid cells throughout the study area. Changes in forward speed of the simulated hurricanes also affected the peak surge values. Generally, the faster moving (15 miles per hour) storms produced higher surge levels at the open coast while the slower (5 miles per hour) storms resulted in higher surge levels within most lakes and overland locations within the basins. A review of the limits of inundation for each of the five categories of hurricanes revealed that the vulnerable population within the study area is not overly sensitive to the forward speed of the storm. Given the difficulty in accurately predicting the forward speed of hurricanes, the difference in the vulnerable population did not warrant the preparation of the surge inundation maps for forward speeds of 5 and 15mph. Therefore, the forward speeds were combined for each category of hurricane modeled.Go to top

The direction of approach also had a significant effect on the potential surge heights in the study area. However, the inherent difficulties in predicting the direction of approach for a hurricane in excess of 24 hours prior to landfall made the grouping of hurricanes by approach direction impracticable. Including the direction of approach would also add an unknown variable to the decision-making process. The approach directions were, therefore, combined for each category of hurricane modeled.

The MEOW's were then grouped according to overall similarities in the predicted envelopes of maximum water level throughout the entire basin. Additional sets of maximum envelopes of water (MEOW's of the MEOW's or MOM's) were developed combining all hurricane approach directions. The forward speeds were also combined for each of the 5 categories of storms. This final grouping was performed in order to provide for the development of hurricane scenarios to be used in the evacuation planning process. It is from these maximum envelopes of water that the surge inundation maps were developed. The surge maps depict the limits of inundation from peak storm surge heights potentially generated by the five categories of storm intensity. These maps do not predict the limits of inundation from a single storm, but rather delineate the areas that are threatened by storm surge.

Statistical Analysis. Hurricane evacuation decision-makers should keep in mind that the SLOSH model is a mathematical model and does not give perfect results. To determine the accuracy of the SLOSH model, runs were conducted by the National Weather Service for 10 historical landfalling hurricanes. A total of 523 observations of storm surge heights from tide gages and measured high water marks were made and compared to the SLOSH model values for the same locations (i.e., SLOSH model height minus observed height). A negative difference meant the SLOSH model underestimated the storm surge and a positive difference meant the model overestimated surge. Tide gage readings accounted for 14 percent of the observations, while the remainder were high water mark readings. Although the error range was from -7.1 feet to +8.8 feet, the standard deviation was only 2.0 feet. The mean absolute error in the surge height calculated by SLOSH was 1.4 ft. The arithmetic mean for these observations was -0.3 feet, which indicates a slight negative bias. This does not mean that the same negative bias will appear in future hurricane events.

Based on the results of the statistical analysis conducted by the National Weather Service, a +20 percent adjustment to the SLOSH values would eliminate most of the potential negative errors occurring from the model. However, such an adjustment would also add additional surge height to those values that already contain positive errors, possibly endangering the credibility of the SLOSH model results. With this in mind, southwest Louisiana emergency management officials elected not to make a general adjustment to the computed surge heights. Evacuation planners should remain cognizant of the potential for the SLOSH model to underestimate some of the surge values.

Variations in Hurricane Parameters. As mentioned earlier, the parameters of the 600 hurricanes modeled for the Sabine Lake Basin and the 850 hurricanes modeled for the Vermilion Bay Basin were: five categories of storm intensity, eight approach directions (west, west-northwest, northwest, north-northwest, north, north-northeast, northeast, and east-northeast), two forward speeds (5 and 15 miles per hour), radius of maximum winds of 25 miles and storm tracks separated by 20 miles or less. The parameters of future hurricanes having the greatest potential for variation from those modeled for the study are radius of maximum winds, forward speed, and central barometric pressure.  Go to top

Surge Heights Within Protected Areas. In addition to estimating surge heights along the open coast, the SLOSH model simulates the routing of the storm surge into bays, estuaries, and coastal river basins and calculates surge heights for overland locations. The surge heights for overland locations are based on average ground elevations assigned to individual grid cells. Of the greatest concern are the surge heights within the heavily developed areas, some of which are protected by hurricane surge barriers. The potential for flow through any gaps in the protection and for overlapping of the barriers increases the difficulty in modeling these areas. Special techniques are incorporated to model two-dimensional inland inundation, routing of surges inland when barriers are overtopped, the effect of trees, the movement of the surge up rivers, and flow through channels, cuts and over submerged sills.

Levee Performance. Portions of the southwest Louisiana study area are reliant on the levees and floodwalls (both Federal and non-Federal), which have been constructed as barriers to hurricane surge. The extent of flooding within these areas during a hurricane depends greatly on the ability of the barriers to function as intended. The performance of a levee or floodwall depends on many factors (design criteria, construction techniques, maintenance, severity of storm, etc.). The SLOSH model cannot account for these factors. The SLOSH model runs performed for the Sabine Lake Basin and the Vermilion Bay Basin assumed that the levees and floodwalls remained intact, even if overtopped. In past storms, such as Hurricane Betsy, Hurricane Juan, and Hurricane Andrew, portions of existing levees have failed. The failure of a levee or floodwall could significantly increase the extent and degree of flooding. Emergency management officials should be aware of the potential for failure in barriers that provide protection and the corresponding impacts.