1. Introduction
While the effect of large-scale topography such as that found on Hispaniola or Taiwan on the overall structure and motion of tropical cyclones is well known, the impact of small-scale topography, whose maximum height is significantly less than the depth of the tropical cyclone boundary layer, on near-surface wind speeds in landfalling tropical cyclones and the resulting damage is not often appreciated. This is in spite of the fact that a theory for the calculation of these effects, which has been validated against both field and wind tunnel measurements and used extensively by the wind energy community to site wind turbines in areas of complex topography, has been in existence for over 35 years. For small-scale topography of this nature it is found that near-surface wind speeds near the crests of topographic features such as ridges and hills show marked increases when compared to the equivalent wind speeds measured at the same height above flat terrain. During the 1983 Askervein Hill field experiment on the island of South Uist in the Outer Hebrides, Scotland, for example, Salmon et al. (1988a) found that wind speeds measured at a height of 10 m above ground on the crest of the hill, 116 m above the surrounding terrain, were up to 90% higher than the corresponding wind speeds measured at the same height above ground at a reference station located in flat terrain upstream of the hill. Since wind loads on structures depend on the velocity squared, this represents an increase of 260% in the wind load that a structure on top of the hill would experience relative to the loads experienced by the same structure located in flat terrain. While many modern building codes explicitly require the consideration of topographic speed-up effects when calculating design wind loads, this speed-up effect clearly has major implications for warning of potentially damaging near-surface wind speeds in tropical cyclones making landfall in regions where topographic effects on surface wind speeds are likely to be significant. This would include many Caribbean and Pacific islands, as well as countries like Australia, Taiwan, and Japan.
In reviewing the effects of small-scale topography on the observed damage following landfalling tropical cyclones, it becomes clear that while there are many reports that qualitatively suggest there are topographic effects involved, there have been very few quantitative studies of these effects. In reviewing the observed effects of topography on the surface wind speeds of Cyclone Winifred, which made landfall on the North Queensland coast of Australia in February 1986, Walker et al. (1988) noted that the failure of at least one newer house, built within the previous 5 yr prior to the landfall of Winifred, could be attributed to topographical speed-up effects that were not taken into consideration at the time that the house was designed. The significance of this statement is that changes in the Australian wind loading code in the early 1980s explicitly required topographic speed-up effects to be taken into account when designing structures in areas with topography, and that this was not done for this particular house. Following the landfall of Cyclone Larry in the same region in March 2006, Henderson et al. (2006) noted that damage to houses in East Innisfail appeared to be concentrated in the vicinity of four hilltops and that there was a noticeable difference in damage levels when compared to houses of similar age in nearby flat terrain. It was also noted that there were a number of hilltop houses in the shoreline communities of Coquette and Flying Fish Points that had suffered some of the most significant damage in the area, yet newer homes in the same locations that had been designed to meet more recent versions of the building code that explicitly required topographic speed-up effects to be taken into account in their design suffered very little structural damage.
Similar effects were noted by Powell and Houston (1998) in reviewing the impact of Hurricane Marilyn on the island of St. Thomas following its passage over the island on 15–16 September 1995, where it was noted that damage surveys provided compelling evidence that structures located on hillsides and hilltops were more susceptible to wind damage than those located at lower elevations. Using topographic speed-up factors taken from the Caribbean Uniform Building Code (Caribbean Community Secretariat 1989), it was also noted that a marginal category 1 storm on the Saffir–Simpson scale could produce winds of category 3 intensity over steep hilltops and a weak category 2 storm could produce category 5 winds. In discussing the results of a postevent damage survey following the landfall of Super Typhoon Paka on Guam in December 1997, Houston et al. (2002) noted several instances where topographic effects appeared to have played a role in the resulting damage patterns. This included commenting on a newer Federal Aviation Administration radar dome that had been destroyed, yet which, in their opinion, should have been designed to withstand the higher wind loads imposed by its siting in an area of complex topography.
In this paper, we consider the impact of small-scale topography on the damage patterns observed following the passage of Hurricane Fabian over the island of Bermuda on 5 September 2003. The following section provides a brief review of boundary layer flow over small-scale, low-slope topography, while the third section of the paper presents some details on the topography of Bermuda, Hurricane Fabian, and its impact on the island. This is followed by a section discussing the methodology used in the study, including the reconstruction of the overland surface wind fields using the Hurricane Research Division Real-Time Hurricane Wind Analysis System (H*Wind) overwater surface wind field analyses in combination with wind field modification factors accounting for change of roughness and topographic speed-up effects, and the assessment of roof damage to structures on Bermuda using satellite imagery. The results of the study are then presented and discussed, followed by the conclusions.
2. Boundary layer flow over low-slope topography
Framework for interpreting atmospheric boundary layer flow over small-scale topography, showing the division of the flow into inner and outer regions together with the impact of the underlying topography on the wind speed profile at the crest relative to a reference profile measured above flat, level terrain.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-12-00050.1
Following the publication of Jackson and Hunt’s original paper, which considered two-dimensional flow, Mason and Sykes (1979) extended the theory to the three-dimensional case, this paper forming the basis for further developments by groups in both Canada (Walmsley et al. 1982; Taylor et al. 1983) and the United Kingdom (Mason and King 1985) to try and remove some of the limitations of the original theory. Hunt et al. (1988) further refined the original theory by splitting both the inner and outer layers into two further subregions, yielding a four-layer model that allowed for a wide range of upwind profiles. Much of the reason for the success of models based on the theory of Jackson and Hunt was that the use of Fourier transform techniques in combination with the linearized equations of motion allowed analytical solutions to be readily obtained for a wide variety of terrain types with minimal computational time when compared to the equivalent finite-difference solutions to the full nonlinear equations of motion. As a result, linearized models based on the theory of Jackson and Hunt were widely adopted within the wind energy community to assist in the siting of wind turbines in areas of topography, and models such as the Wind Atlas Analysis and Application Program (WAsP; Mortensen et al. 1993) are still used extensively today.
Validation of the linear theory against both field and wind tunnel studies showed that linear models worked well in predicting the magnitude of the speed-up on the windward side and crest of hill, but rather less successfully on the downwind side of the hill where nonlinear effects start to become important. Furthermore, once the slope of the hill starts becoming too steep, the linear theory also starts to overpredict the magnitude of the speed-up on the upwind slope, with Ayotte (2008) suggesting that these differences start becoming significant for slopes exceeding 0.3–0.4, depending on the underlying surface roughness. As the steepness of the hill increases, the likelihood of flow separation on the lee slope of the hill also increases, which is usually accounted for by assuming that the effect of flow separation is to modify the shape of the hill that the flow sees, giving an “effective” hill with a much gentler slope than would be apparent from examining the physical hill. For this reason, most building codes place a limit on the maximum slope of the hill, beyond which the value of the speed-up factor is taken to be a constant.
In more generally complex terrain the effects on both mean and gust wind speeds become somewhat harder to quantify. In these conditions the flow can no longer be considered as a perturbation to the undisturbed flow above flat, level terrain and, instead, the flow conditions start adjusting to the increased turbulent stresses due to the underlying terrain. The wind tunnel results of Miller and Davenport (1998) for a series of identical two-dimensional sinusoidal ridges show that while over the first ridge the flow behaves as though it were an isolated ridge, over subsequent ridges the speed-up effect is reduced relative to the isolated ridge case although it is important to emphasize that there is still a visible speed-up effect. The turbulence levels however increase significantly in response to the increased surface shear stress due to the underlying ridges. The net effect is that gust wind speeds in these situations tend to approach those that would be calculated for isolated ridges of the same shape and slope.
3. Bermuda and Hurricane Fabian (2003)
The island of Bermuda lies about 1000 km off the east coast of the United States in the North Atlantic Ocean, on the southern edge of an ancient volcanic caldera. Although the underlying base rock is igneous, the island is covered by a limestone cap that tends to form low rolling ridges running from the northeast to the southwest along the axis formed by the major islands of St David’s Island, St George’s Island, and Main Island, before turning to the north at the southern end of Main Island and onto Somerset Island, as can be seen in Fig. 2. The highest point on Bermuda is Town Hill at the northern end of Main Island, overlooking Harrington Sound with an elevation of 76 m above sea level. The underlying topography is therefore relatively low when compared to the height above the surrounding terrain of a number of the hills considered previously in field studies of boundary layer flow over low-slope topography, such as Brent Knoll [130 m; Mason and Sykes (1979), Askervein Hill [116 m; Salmon et al. (1988a)], Kettles Hill [100 m; Salmon et al. (1988b)], and Blashavel [100 m; Mason and King (1985)]. Since observations from all of these field studies have been used to successfully validate linearized models for boundary layer flow over topography based on the theory of Jackson and Hunt (1975), we shall assume that the application of such a model to the topography of Bermuda to predict the resulting topographic speed-up effects is valid.
Topography of Bermuda with elevations given in m. Labeled points correspond to locations at which wind speeds were observed during the passage of Hurricane Fabian over the island: Warwick Camp, WC; Cable and Wireless, CW; the Bermuda airport, A; and Bermuda Harbour Radio, HR.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-12-00050.1
Hurricane Fabian formed as a tropical depression about 680 km to the west of the Cape Verde Islands on 27 August 2003, as the result of deep convection associated with a vigorous tropical wave that had left western Africa several days earlier. The initial tropical depression became a tropical storm the following day, before subsequently reaching hurricane strength 2 days later on 30 August 2003 (Lawrence et al. 2005). Peak intensity in terms of the maximum 1-min mean wind speed was estimated to have been 125 kt, reached while Fabian was 490 km east-northeast of the northern Leeward Islands, while the hurricane maintained category 3 or 4 strength on the Saffir–Simpson scale for nearly a week. The initial motion of the storm was westward for several days, before turning first to the northwest then to the north, bringing the eastern eyewall of Fabian over the island of Bermuda at around 2000 UTC on the evening of 5 September 2003. The intensity of Fabian at the time was estimated to be close to 100 kt in the official National Hurricane Center (NHC) report, although H*WIND estimates of the intensity at the same time were somewhat lower at 89 kt.
Fabian caused considerable damage to both structures and vegetation on Bermuda, with property damage subsequently being estimated to be at least 300 million U.S. dollars, in addition to four deaths when a vehicle was swept off the causeway linking St George’s and Main Islands. Wind speeds were observed at four points on the island, as indicated in Fig. 2. Official wind speed measurements at Bermuda International Airport terminated due to storm surge inundation approximately half an hour before the peak of the storm, while continuous records were obtained at sites located at Warwick Camp, Cable and Wireless, and Bermuda Harbour Radio, although the record at Bermuda Harbour Radio was unfortunately subsequently lost due to a computer malfunction. The anemometers at all three locations are located at heights considerably above the standard 10 m above ground level (AGL) recommended by the World Meteorological Organization (WMO 2008), which means that the interpretation of wind speeds recorded at these sites requires careful consideration for both the effects of elevation and the underlying terrain. Measured peak gust wind speeds included 102 kt at 10 m AGL at the Bermuda airport prior to failure, 131 kt at the Cable and Wireless site at 50 m AGL, 148 kt at Bermuda Harbour Radio at 38 m AGL on top of a hill overlooking the harbour of St Georges prior to failure of the mast, and 125 kt at Warwick Camp at a height of 68 m AGL.
In reviewing the damage caused by Fabian, Rowe (2003) noted that while most of the limestone and concrete block buildings that form the prevalent building style on Bermuda successfully withstood the winds of Fabian, a significant portion of buildings with traditional Bermuda-style limestone slate roofs, or their modern equivalent, suffered partial roof failures. Much of this damage occurred along the leading edge of the roof on the side of the building facing into the direction of the strongest winds associated with Fabian, which were to the east and south. This pattern of damage is consistent with what is known about the aerodynamics of roofs with slopes typical of those found on Bermuda houses, in which suction (i.e., uplift) pressures act over much of the roof surface with the highest pressures occurring along the windward edge of the roof where the flow initially separates. It was also noted that the observed damage clearly demonstrated the importance of topography, with structures on the western and northern sides of hills remaining largely unscathed, while up to 80% of houses on some south-facing slopes suffered visible damage based on field observations and photographs taken at the time (M. Rowe 2012, personal communication). In this case houses on the western and northern slopes would have been on the lee side of the topography when the directions of the strongest winds associated with Fabian are taken into account, while houses on the southern and eastern slopes would have been on the windward side.
4. Data and methodology
a. Surface wind fields
The basis of the surface wind field reconstructions are the H*WIND surface wind field analyses prepared by the National Oceanic and Atmospheric Administration’s (NOAA) Hurricane Research Division (HRD). These are prepared in real time using data from a variety of platforms, including flight-level observations; dropsonde measurements; surface stations, including land, buoy, and ship observations; and satellite observations, which are then quality controlled and objectively analyzed to obtain the estimated 1-min mean overwater wind speed at a height of 10 m AGL. Further details on the processing and analysis methods may be found in Powell et al. (1996), Powell and Houston (1996), and Powell et al. (1998). These overwater wind fields are then modified to account for the effects of changes in surface roughness alone and the combined effects of changes in surface roughness and the underlying topography on the 1-min mean wind speeds calculated on a regular grid covering the island of Bermuda.
1) Overwater wind fields
The starting point for our surface wind field reconstructions are the four H*WIND surface wind analyses available at 1330, 1930, 2000, and 23:03 UTC on 5 September 2003, covering the time period during which Fabian was passing to the west of Bermuda. These surface wind field analyses were obtained as gridded data files, centered on the position taken to be the storm center at the time of analysis. The first step was to recenter the wind fields on a track obtained using the translating pressure fit method of Kepert (2005) on flight-level geopotential height measurements obtained during the same time frame. By fitting a spline curve to the center fixes obtained in this way, it was then possible to locate the four H*WIND surface wind analyses in both space and time. For intermediate locations and times, the surface wind field was first linearly interpolated in time from the two H*WIND analyses bracketing the time of interest, before then being recentered on the track obtained from the flight-level observations. The end result was a set of overwater wind fields spaced at 15-min intervals along the track between 1330 and 2303 UTC.
2) Calculation of change of roughness and topographic speed-up effects
To calculate the change of roughness and topographic speed-up effects, we use the MS-Micro version of the linearized model for boundary layer flow over low-slope topography described by Walmsley et al. (1986). This model is a development of the earlier model described by Walmsley et al. (1982) and Taylor et al. (1983), with the main difference being the inclusion of a linearized model for changes in surface roughness in addition to the effects of the underlying topography. The two effects are then calculated separately before being combined to obtain the final solution. As input, the model requires the specification of both the underlying topography and surface roughness in the form of separate regular meshes, or tiles, at the resolution that the model is to be run at. Since the model uses Fourier transforms to obtain analytical solutions to the linearized equations of motion, the final tile size used is a combination of the resolution of the input topography and surface roughness databases and the number of points used to define the mesh, which must be a power of 2. In this case we use a horizontal resolution of 10 m for the input topography and roughness databases in combination with a mesh defined using 1024 points in both directions, which yields a tile size of 10 240 m × 10 240 m.
For the topography, digital terrain data were obtained from the Bermuda Ministry of Works and Engineering and Housing and used to create a digital elevation model (DEM) of Bermuda with a horizontal grid resolution of 10 m in both directions. Defining the underlying surface roughness proved to be more problematical with an initial investigation into the Moderate Resolution Imaging Spectroradiometer (MODIS) 500-m MOD12Q1 yearly land cover dataset, showing that much of the land cover classification for Bermuda was questionable. Following a visual inspection of satellite imagery for Bermuda, the decision was made to simply classify the surface roughness as either overwater, with a roughness length of 0.001 m based on the work of Powell et al. (2003), or overland with a roughness length of 0.1 m (Wieringa 1993). While this is obviously a simplification, we would note that much of Bermuda is covered by housing and reasonably dense vegetation, which would justify the use of a roughness length of at least 0.1 m. Furthermore, the effect of an increase in surface roughness overland, regardless of the value chosen, will be to reduce the surface wind speed, while the impact of the underlying topography on the surface wind speeds is much more significant and variable.
To run the model, a grid of points covering the island and extending 200 m offshore was generated with a horizontal resolution of 200 m. For each grid point, tiles measuring 10 240 m × 10 240 m and centered on the selected point were extracted from the surface roughness and topography databases and then used as input to the model. Two sets of wind speed adjustment factors for the base open water wind speeds were then calculated at a height of 10 m AGL: one accounting for the effects of changes in surface roughness alone and one for the combined effects of changes in surface roughness and topography. In calculating the adjustment factors, 12 wind directions at 30° increments centered on 0°, 30°, etc. were used.
3) Overland wind fields
The overland wind fields were calculated by first overlaying each of the calculated open water wind fields on top of the grid used to determine the wind speed adjustment factors. For each grid point the wind speed and direction was then determined for every time step that an overwater wind field was available for. Using the wind direction derived from the open water wind field, the appropriate wind speed adjustment factors for both surface roughness changes only and roughness and topography combined were then determined by linearly interpolating the calculated values for the two wind directions bracketing the selected wind direction. The overwater wind speed was then multiplied by the calculated wind speed adjustment factor to obtain either an overland wind speed accounting for the effects of a change in surface roughness only or the combined effects of surface roughness changes and topography. In this way a time history of wind speeds at a particular grid point could be obtained. Finally, for each grid point the maximum wind speed associated with the overwater, roughness-only, and roughness and topography combined cases was extracted and used to create a swath map of maximum 1-min mean wind speeds for each of the three cases considered. To obtain estimates of the maximum wind speed at each building location, the locations of the building centroids were overlaid on the appropriate swath map before using bilinear interpolation in combination with the wind speed values at the four closest grid points around the building location to determine the wind speed at the building centroid.
b. Observed roof damage
Statistics on the observed roof damage were obtained through an analysis of satellite imagery from the QuickBird high-resolution satellite that was acquired on 11 September 2003, 6 days after Fabian’s passage over Bermuda. In this particular case we make use of the panchromatic (black and white) imagery obtained by this satellite with a horizontal resolution of 0.61 m. The acquired images were first georeferenced to the Bermuda National Grid 2000 (BNG2000), before being overlaid on a building footprint database, showing the footprint of every single building on Bermuda, obtained from the Bermuda Ministry of Works and Engineering and Housing. In processing the imagery, it was assumed that the presence of pixels associated with the color blue within individual building footprints indicated the presence of blue tarpaulins, which are typically used to provide temporary protection, on the roof of the structure, and that this in turn indicated that the structure had suffered some form of damage. This allowed damaged structures to be the first identified, before then attempting to work out the percentage damage to the structure by calculating the ratio of the internal footprint area of the structure covered by blue pixels to the overall area covered by the footprint of the structure.
The approach taken was validated by comparing the results obtained from the analysis of the satellite imagery with photographs taken on the ground during a damage survey undertaken by one of the authors (KB) in the same time frame that the satellite imagery was acquired. Figures 3 and 4 show photographs taken on the ground on 10 September 2003, looking northeast and northward, respectively, from the Harbour Radio site overlooking St Georges. In both cases houses with blue tarpaulins, showing up as darker areas on the roof, are clearly visible in the photographs. Several of these houses are identified and can be compared to the results of the satellite imagery analysis shown as an insert in the lower-left corner of each figure. In all cases the houses identified in the photographs are also identified as damaged from the satellite imagery analysis. Closer examination of all the photographs taken during the ground survey shows that there are several houses that can be identified as having tarpaulins on their roof; however, these have not been identified in the satellite imagery analysis. This appears to be a result of the fact that the tarpaulins used on these houses are not blue, but instead are of a much lighter color. Since the tarpaulin identification algorithm was optimized for the color blue, these lighter-colored tarpaulins have not been identified during processing. While in theory the tarpaulin identification algorithm could be recalibrated to identify tarpaulins of a lighter color, in practice this would be much more difficult because of the lack of distinction between tarpaulins of a lighter color and the white roofs characteristic of many of the buildings found on the island. In this regard, blue is a much easier color to distinguish from white than a much lighter color would be. A reasonable conclusion would be that the results of the analysis represent a lower bound on the total number of structures with damaged roofs, and that the true number is higher. Overall, the results of our analysis show that at least 1.2% of the total building stock on Bermuda suffered some form of visible roof damage.
View from Harbour Radio looking northeast. Indicated in the photograph are structures with visible blue tarpaulins, showing up as darker areas on the roof, and which are also identified by the darker color of the building footprint as being damaged in the inset, which shows the results of the corresponding satellite imagery analysis.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-12-00050.1
As in Fig. 3, but looking north.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-12-00050.1
In choosing to use identifiable roof damage to buildings as our primary damage indicator we would note that, in general, the performance of buildings in high wind speeds will depend on a number of factors, including the intended use of the building, the methods and materials used in the construction of the building, as well as the age and the building code requirements in force at the time of the construction of the building. In this regard the style of roof construction used for residential buildings in Bermuda tends to be very consistent from building to building, irrespective of the age of the building. The traditional Bermuda roof involves the use of 1-in. (2.54 cm) thick slates measuring 12 in. × 18 in. (0.3048 m × 0.4572 m) laid over an open batten supporting structure, and overlapped by 9 in. (0.2286 m). Slates were originally cut from limestone, but modern materials are now also used as an alternative to limestone. Once completed the roof is then given a cement wash before being whitewashed with lime or paint giving the distinctive white roofs associated with the island. This consistency in construction style over time provides some justification for using the observed roof damage to calculate the ratio of buildings with damaged roofs to undamaged buildings, without further classifying the buildings by other parameters such as the age of the structure or the construction materials used. We would also note that the current version of the Bermuda Building Code does not explicitly require topographic speed-up effects to be taken into account when designing a residential structure. To apply the same methodology used in this paper to a region such as Australia, where there have been significant changes to building codes over the last 30 yr, as well as prescriptive classifications for residential structures that take into account the structure’s location with regard to the surrounding topography and the resulting design loads, would require a detailed forensic examination of individual structures to group like structures with like structures.
In terms of the location of the majority of the damaged structures, Fig. 5 presents a close-up view of the southeast coast of Bermuda in which structures identified as having damaged roofs are shown in relation to the underlying topography. It is clear from Fig. 5 that the majority of damaged structures are to be found on slopes that would have been on the windward side or near the crests of topographic features where one would expect enhanced wind speeds due to topographic speed-up effects. Table 1, which shows the results of an analysis of the slope aspects on which damaged buildings are to be found, reinforces this impression, with 29.7% of damaged buildings being found on southeast-facing slopes. A further 28% are to be found on south-facing slopes, with smaller numbers on east- and southwest-facing slopes. There are virtually no damaged buildings to be found on slopes with northerly aspects, which is consistent with the observations of Rowe (2003).
Close-up of southeast coast of Bermuda showing identified structures with damaged roofs (black dots) in relation to the underlying topography. Line AA′ defines the line along which the profile of Fig. 6 was taken.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-12-00050.1
Terrain slope aspect vs percentage of total number of damaged buildings.
5. Results
To show the impact of roughness changes alone and roughness and topography combined on the surface overland wind speeds, Fig. 6 presents the calculated wind speed adjustment factors at a height of 10 m AGL for a southeasterly wind blowing along the line AA′ as indicated in Fig. 5. Also shown in Fig. 6 is a profile of the underlying topography along this line, as well as a second curve revealing the effects of a change of surface roughness from a roughness length of 0.001 to 0.1 m as calculated using the analytical model of Weng et al. (2010). Note that the vertical scale of the topography in this figure has been exaggerated by a factor of 10 when compared to the horizontal scale. In considering the impact of changes in surface roughness alone it is clear that the overall effect is to reduce the overland wind speeds relative to those observed over open water, and that the farther one moves from the point at which the surface roughness changes the greater is the reduction in the wind speed. It is also apparent that the internal boundary layer that develops at the change of surface roughness takes some time to grow to a depth sufficient for the effects to be observed at a height of 10 m, which means that locations along the coast and for a short distance inland will be exposed to the higher open water wind speeds. A comparison of the two models for surface roughness changes alone suggests that the change of roughness model incorporated into MS-Micro underestimates the impact of the change in surface roughness when compared to the analytical model of Weng et al. (2010), which was validated against a full numerical model described in the same paper, with the wind speeds predicted by the latter being reduced by a factor 0.83 at a distance of 1770 m when compared to the value of 0.93 predicted using the model incorporated into MS-Micro. The important point to note, however, is that for a change of surface roughness from overwater to overland the wind speed is always reducing with increasing distance from the change of surface roughness, until eventually the flow is in full equilibrium with the new surface.
Profile along line AA′ shown in Fig. 5 with (bottom) the underlying topography and (top) calculated wind speed adjustment factors at a height of 10 m AGL accounting for roughness-only and roughness and topography combined results for a southwesterly wind. Also shown is the curve for change of roughness effects from the analytical model of Weng et al. (2010). Note that the vertical scale of the topography profile has been exaggerated by a factor of 10.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-12-00050.1
In considering the combined effects of topography and roughness, it is clear that the underlying topography has a significant impact on surface wind speeds over very short distances. As one moves along the profile from left to right, the sheltering effect at the base of the first rise at 250 m can clearly be identified, as the wind speed adjustment factor drops below 1, before increasing to value of 1.24 on the crest of the feature. Subsequent topographic sheltering and speed-up effects can be seen and related to the underlying topography as one continues to move farther along the profile, reaching a maximum value of 1.29 at the crest of the second major topographic feature at 690 m. Comparing the relative heights of the two topographic features at 250 and 690 m, and the corresponding wind speed adjustment factors also reinforces the point that the magnitude of the speed up is not simply determined by the elevation of the underlying terrain, but by the terrain slope, as indicated in Eq. (5). The maximum value calculated for the wind speed adjustment factor value for any grid point on the island irrespective of wind direction is 1.58, which the results of Ayotte (2008) would suggest is toward the upper end of the range for the validity of linear model solutions when compared to the full nonlinear solutions. Given, however, that MS-Micro has been successfully validated against field studies such as those of Salmon et al. (1988a) or Salmon et al. (1988b), where the slopes and resulting observed speed-up factors have been higher, we consider the approach taken in this paper to be reasonable and without the computational cost of running a full nonlinear numerical model for the same terrain.
To validate the approach taken to reconstruct the surface wind field, Figs. 7 and 8 show comparisons of the modeled 1-min mean wind speed and direction, respectively, at a height of 68 m above ground with the corresponding observations for the Warwick Camp tower site on the southeast coast of the island. Both the modeled wind speed and direction show good agreement with the magnitudes of the observed values, particularly during the passage of the front-right quadrant of the eyewall over the site, with a maximum modeled wind speed of 59.4 m s−1 compared to a maximum observed value of 56.6 m s−1, although the timing of the modeled values leads the observed values. In terms of comparisons between roughness only and roughness and topographic effects combined, the proximity of the Warwick Camp tower site to the shoreline for southeasterly winds means that the only significant influence is that of the underlying topography, as at a height of 68 m above ground the anemometer is still in a marine exposure. As the wind swings around to a southwesterly direction following passage of the eyewall, roughness effects become increasingly apparent with the wind now blowing across the island. Even though the change of roughness model incorporated in MS-Micro tends to underpredict the impact of a change of surface roughness at heights of 10 m when compared to the analytical model of Weng et al. (2010), at a height of 68 m both models give very similar results because of the time taken for the internal boundary layer to develop and start affecting wind speeds at a height of 68 m above ground. The corresponding modeled wind speeds at a height of 10 m above ground at the same site show a much large variation, particularly those where the effects of both roughness and topography are included with the maximum 1-min mean wind speed being predicted to be 60.4 m s−1.
Observed 1-min mean wind speed at a height of 68 m at Camp Warwick compared to modeled wind speeds for roughness-only and roughness and topography results combined.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-12-00050.1
Observed 1-min mean wind direction at a height of 68 m at Camp Warwick compared to modeled wind direction.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-12-00050.1
The modeled values also show the distinct double peak of an eyewall passage over the Warwick Camp site, unlike the observed values, which do not. Since the observations represent the ground truth, and the chart record from the Cable and Wireless site also shows similar behavior, there are two possibilities for the presence of a double peak in the modeled wind speeds and not in the observed wind speeds at both sites. During the passage of the right-rear quadrant of the eyewall over the island, the wind direction is such that winds are blowing over the island from a southwesterly direction, which means that changes in roughness effects associated with the transition from an overwater to an overland exposure for winds from this direction would come into play. These effects would, however, need to be significantly larger than those calculated using either of the change of roughness models considered in this study to completely obscure the double peak of an eyewall passage at both the Warwick Camp and Cable and Wireless sites. The second possibility is that the issue lies with the H*WIND wind fields themselves, and that wind speeds in the right-rear quadrant of the eyewall were not as well defined at the time of the eyewall passage over the island as the H*WIND analyses would suggest. This would, however, require further investigation using alternative data sources such as radar to prove or disprove this conjecture.
Swath maps showing the modeled maximum 1-min mean wind speeds for open water, roughness only, and roughness and topography combined conditions, respectively, are shown in Figs. 9–11. The open water wind field shows very little variation over the island with modeled wind speeds ranging from 45.4 to 46.1 m s−1, which would place Fabian as a midrange category 2 storm on the Saffir–Simpson hurricane wind scale at the time of its passage over Bermuda. The roughness-only wind field shows the effect of the change of roughness from open-water to overland conditions with a pronounced wind speed gradient in a northwesterly direction across much of the island. This trend is consistent with maximum wind speeds being recorded during the passage of the right-front quadrant of the eyewall over the island, with maximum wind speeds at isolated locations being observed during the passage of the right-rear quadrant of the eyewall. The lowest modeled wind speed anywhere on the island is 40.9 m s−1, or at the upper end of the range for a category 1 hurricane. The use of the analytical model of Weng et al. (2010) would result in an even greater reduction in wind speeds across the island.
Modeled maximum 1-min mean “open water” wind speeds over Bermuda at a height of 10 m.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-12-00050.1
Modeled maximum 1-min mean wind speeds at a height of 10 m over Bermuda accounting for changes in surface roughness effects only.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-12-00050.1
Modeled maximum 1-min mean wind speeds at a height of 10 m accounting for changes in surface roughness and topographic effects combined.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-12-00050.1
Inclusion of the effects of both roughness and topography leads to a complex pattern of maximum 1-min mean wind speeds across the island that primarily reflects the effect of the underlying topography. Significant areas of topographically enhanced wind speeds can clearly be identified along the crests of ridges and other topographic features, while areas subjected to topographic sheltering can also be identified. Once again, the latter are primarily associated with winds from the southeast, which would place these areas on the lee slope of the underlying topography. In this case modeled wind speeds range from 30.7 to 68.9 m s−1, that is, from less than category 1 to upper-end category 4 on the Saffir–Simpson scale. A calculation of the relative areas of the island experiencing wind speeds by Saffir–Simpson category shows that about 26% of the island experienced category 1 wind speeds, 54% category 2 wind speeds, and 19% category 3 wind speeds, with 1% of the island experiencing category 4 wind speeds. It is important to realize that these high wind speeds are occurring in very localized areas and, as suggested by the profile shown in Fig. 6, are changing rapidly over very small horizontal distances. Estimates of the likely peak gust wind speeds are subject to considerable uncertainty; however, using Eq. (7) in combination with the calculated speed-up factors and a value of 1.23 for an onshore coastal 3-s to 1-min gust factor, as recommended by Harper et al. (2010), leads to predicted gust wind speeds ranging in value from 37.7 to 81.2 m s−1. The use of the corresponding recommended inland 3-s to 1-min gust factor of 1.49 leads to even higher values for the predicted peak gust wind speeds, with values ranging from 45.7 to 95.1 m s−1.
Finally, using the interpolated wind speeds at the building centroids, we consider the relationship between the building damage and the maximum 1-min mean wind speed experienced at that location. This was done by binning the building wind speeds in wind speed bands defined at 2.5 m s−1 intervals and then counting the number of damaged and undamaged buildings in each wind speed band. These numbers were then used to calculate a damage ratio based on the ratio of buildings with damaged roofs to the total number of buildings in each wind speed band. Intuitively, we expect the resulting damage, as defined by the ratio of structures with damaged roofs to the total number of structures in a given wind speed band, to increase with increasing wind speeds, with a clear point at which damage first starts occurring. Figure 12 shows the variation of the damage ratio with maximum 1-min mean wind speed for the roughness-only and roughness and topography combined cases. The open water case is not shown because the limited range of wind speeds found across the island for this case means that all structures on the island fall into a single wind speed band. The relatively narrow range of wind speeds for the roughness-only case is reflected in the fact that wind speeds for this case fall into one of three bands. While there is a trend toward increasing damage with increasing wind speed, it is very hard to say much more about the impact of surface roughness changes on the observed damage patterns on the basis of this figure alone. The use of the analytical model of Weng et al. (2010) would result in a larger decrease in wind speeds for locations on the lee side of the island, which would tend to extend the roughness-only curve to lower wind speeds, but this would not be expected to substantially change the results. On the other hand, the results for roughness and topography combined do show a very clear trend with increasing wind speeds, as well as suggesting a threshold wind speed of around 37.5 m s−1 for roof damage to structures to start occurring.
Damage ratio vs maximum 1-min mean wind speed for roughness-only and roughness and topography combined cases.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-12-00050.1
While the use of simple topographic indicators such as the local elevation or the local slope at individual building locations would appear at first glance to be an attractive option in further isolating the effects of the underlying topography on the observed damage patterns, neither of these indicators turns out to be suitable. As Eq. (5) shows, elevation by itself does not control the magnitude of the speed up, and neither does the local slope since the slope that appears in Eq. (5) is a measure of the average upwind slope of the topographic feature that is being considered. Furthermore, while the local slope on the crest of a topographic feature such as a ridge or hill will be zero, or very close to it, the magnitude of the topographically induced speed up reaches a maximum in the same location. This leaves only the modeled wind speeds themselves to try and further isolate the effects of the underlying topography on the resulting damage patterns.
In an attempt to do this, we first classify individual building locations by the roughness-only wind speed band that they fall into. For each of these wind speed bands, we then consider the variation of the ratio of damaged to undamaged buildings, using the roughness and topography combined wind speeds to bin the results into wind speed bands defined at 2.5 m s−1 intervals. The underlying assumption in this case is that the difference between the wind speeds at individual building locations for the roughness-only and roughness and topography combined cases is due only to the effect of the underlying topography. If the latter is influencing the observed damage patterns, then once again we intuitively expect to see a clear relationship between the wind speed and the ratio of damaged to undamaged buildings within a particular roughness-only wind speed band. In fact, as Fig. 13 shows, there is a very clear trend of increasing damage with increasing wind speeds for each of the three roughness-only wind speed bands, and which is particularly noticeable for structures falling within the 42.5–45.0 m s−1 wind speed band. This suggests that the combined effects of roughness and topography, and in particular the underlying topography, which was shown in Fig. 6 to have the greatest impact on wind speed variations across the island, are primarily responsible for the observed damage patterns. The use of other measures, such as the aspect of the slope that the building is located on, also leads to results similar to those shown in Fig. 13, that is, little or no variation in the damage when classified by the roughness only wind speeds, but a clear variation with the roughness and topography combined wind speeds, with increasing amounts of damage with increasing wind speeds.
Damage ratio vs maximum 1-min mean wind speed for roughness and topography combined cases split out by the roughness-only wind speed band.
Citation: Weather and Forecasting 28, 1; 10.1175/WAF-D-12-00050.1
6. Conclusions
While a number of previous studies of the damage following the landfall of tropical cyclones in areas with topography have qualitatively suggested that the observed damage patterns are related to the underlying topography, this study attempts to quantitatively explore the relationship between the observed damage and the underlying topography by examining the passage of Hurricane Fabian over the island of Bermuda on 5 September 2003. Using a well-established linearized model of atmospheric boundary layer flow over low-slope topography that also incorporates a model for changes in surface roughness in conjunction with overwater H*WIND surface wind field analyses, it was possible to reproduce the observed wind speeds and directions at an observing site located on the southeast coast of the island. Although the islands are relatively low lying, rising to a maximum elevation of 76 m above sea level, topographic speed-up effects are still significant, with winds speeds in highly localized areas reaching category 4 strength on the Saffir–Simpson hurricane wind scale, when the overwater strength was only category 2. Consideration of the variation in wind speeds due to the change in roughness on transitioning from overwater to overland showed that, while there was some variation with wind speed, this did not fully explain the observed damage patterns. On the other hand, consideration of the combined effects of roughness and topography showed that there was a very consistent trend of increasing damage with increasing wind speeds when the effects of topography on the near-surface wind speeds were taken into account.
Acknowledgments
We would like to acknowledge the contributions of the following people to this paper: Roger Williams, head of the Bermuda Weather Service at the time of Hurricane Fabian, for his invaluable assistance in data collection; Rodney Johnson and Paul Lethaby of what is now the Bermuda Institute of Ocean Sciences for processing the Warwick Camp wind speed data; and Edida Rajesh and coworkers at RMS India for processing the satellite imagery. We would also like to thank Bruce Harper, David Henderson, and two anonymous reviewers for their comments on an earlier draft of this paper. The Warwick Camp wind speed data were provided by the Bermuda Electric Light Company, while the digital terrain model of Bermuda and the building database were both provided by the Bermuda Ministry of Works and Engineering and Housing. The H*WIND surface wind field analyses used in this study were obtained from the website of NOAA’s Hurricane Research Division. Partial financial support for publication of this paper was provided by RMS.
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