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A numerical study of the effect of hurricane wind asymmetry on storm surge and inundation
Ocean Modelling 36 (2011) 71–79
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A numerical study of the effect of hurricane wind asymmetry on storm surge and inundation Lian Xie a,⇑, Huiqing Liu a,⇑, Bin Liu a, Shaowu Bao b,c a
Department of Marine, Earth and Atmospheric Sciences, North Carolina State University, Box 8208, Raleigh, NC 27695, United States Earth System Research Laboratory, National Oceanic and Atmospheric Administration Boulder, CO 80307, United States c Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado, Boulder, CO 80307, United States b
a r t i c l e
i n f o
Article history: Received 28 March 2010 Received in revised form 23 September 2010 Accepted 7 October 2010 Available online 13 October 2010 Keywords: Storm surge Inundation Wind asymmetry Hurricane Floyd
a b s t r a c t The influence of the asymmetric structure of hurricane wind field on storm surge is studied with five types of numerical experiments using a three-dimensional storm surge model. The results from the case of Hurricane Floyd (1999) show that Floyd-induced peak surge would have been much higher had the region of maximum wind rotated 30–90° counterclockwise. The idealized cases (the hypothetical hurricanes) with a wind speed asymmetry of 20 m s1 show that the peak (negative) surge varied from 4.7 to 6.0 m (5 to 5.7 m) or equivalent to 8.8% and 16.3% (2.8% and 10.4%) differences as compared to the control experiment. The area of flooding varied from 3552 to 3660 km2. The results from two other idealized cases of varying degree of wind speed asymmetry further show that with decreasing (increasing) asymmetry of wind fields, the variations of peak surge and peak negative surge caused by the rotation of wind fields decrease (increase) accordingly. The results suggest that in storm surge simulations forced by winds derived from balanced models, considerable uncertainty in storm surge and inundation can result from wind asymmetries. This is true even if all other storm parameters, including maximum wind speed, the radius of maximum winds (storm size), minimum central pressure, storm translation speed, drag coefficient, and model settings (domain size and resolution) are identical. Thus, when constructing ensemble and probabilistic storm surge forecasts, uncertainty in wind asymmetry should be considered in conjunction with variations in storm track, storm intensity and size. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction With the increase in the US coastal population, hurricanes have become a major threat to the lives and property of residents living in vulnerable coastal regions, particularly along the Gulf of Mexico and the Atlantic seaboard. While storm winds are damaging per se, the storm-induced surge and inundation are threatening to life and property during hurricane landfall. Accurate forecast of the storm surge and inundation is critical to hurricane preparedness and evacuation planning. Though knowing the amount of precipitation accompanying a storm is a key factor in forecasting inland flooding, accurate wind forcing is the most important factor ensuring the accuracy of storm surge and inundation forecasts. Due to high computational expenses, numerical weather prediction models have not yet been widely adopted for forecasting the hurricane winds for storm surge prediction. Axis-symmetric parametric hurricane vortex models based on gradient wind or cyclostrophic wind balance (Holland, 1980; Depperman, 1947; DeMaria et al., 1992) ⇑ Corresponding authors. Address: NCSU/MEAS, Box 8208, Raleigh, NC 276958208, United States. Tel.: +1 919 513 2325. E-mail addresses: [email protected] (L. Xie), [email protected] (H. Liu). 1463-5003/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ocemod.2010.10.001
are still often used to compute the wind forcing for storm surge and inundation forecasting. However, these axis-symmetric models are not able to describe the true spatial structure of the wind fields of real hurricanes, which are rarely axis-symmetric. It is well known that as a result of the storm motion, the winds in a hurricane’s right-front quadrant relative to the hurricane’s translation direction are generally stronger than the winds in other quadrants. However, hurricane wind asymmetry can arise from many other factors as well, including friction (Shapiro, 1983), vertical shear and environmental conditions (Wang and Holland, 1996), the near discontinuity of the surface friction and the latent heat flux (Chen and Yau, 2003), and the beta (b) effect (Ross and Kurihara, 1992). Bell and Ray (2004) used the National Oceanic and Atmospheric Administration’s (NOAA) Hurricane Research Division (HRD) flight-level data archive of 1977–99 North Atlantic hurricanes to create probability distribution of hurricane-force wind radius in different quadrants for minimal and major hurricanes. Their results showed that the largest hurricane-force wind radius could be possibly located at any of quadrants relative to the hurricane’s translation direction, but it tend to be in the right-rear quadrant for minimal hurricanes and in the front quadrant for the major hurricanes. We analyzed the HRD surface wind analysis data (from 2000
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to 2009 North Atlantic hurricanes) and got the similar results for distribution of maximum wind. Strongest winds could be possibly located at any of the four quadrants, but is most likely located at the right-front or right-rear quadrants. Therefore, several attempts have been made to incorporate hurricane asymmetric structures into parametric hurricane wind models (e.g., Georgiou, 1985; Jelesnianski et al., 1992; Houston, 1999; Xie et al., 2006). Houston (1999) showed that the difference between HRD surface wind analysis data and the data from the wind model used to drive NOAAs Sea, Lake and Overland Surges Hurricane (SLOSH) model (Jelesnianski et al., 1992), is the cause of some of the significant differences (around 0.8 m) in the computed storm surge for Hurricane Emily (1993) versus the observational storm surge. However, the effect of the asymmetric spatial structure of hurricane wind field on storm surge has not yet been systematically investigated. Questions which remain unanswered are the following: What would be the difference in the storm surge and inundation when the model is driven by the hurricane wind fields with the same size (radius of maximum wind) and intensity (maximum wind speed), but with different asymmetric spatial distributions? How much error would be introduced due to neglecting hurricane wind asymmetries under the same hurricane size and intensity? In this study, idealized and real-case numerical experiments were conducted to investigate the effect of the asymmetry in hurricane wind field on storm surge and inundation both qualitatively and quantitatively. In Section 2, the storm surge and inundation model used in this study as well as the design of experiments are described. Section 3 presents the modeling results, followed by conclusions and summary in Section 4. 2. Model description and experiment design The storm surge and inundation component of the Coastal Marine Environmental Prediction System (CMEPS) (Xie et al., 2002, 2004, 2008; Pietrafesa et al., 2003; Peng et al., 2004; Liu and Xie, 2009) developed at North Carolina State University (NCSU) is used in this study to simulate hurricane-induced storm surge and inundation. The hydrodynamic core of CMEPS incorporates the Princeton Ocean Model (POM) for ocean circulation and the Simulating Waves Nearshore (SWAN) model for sea surface waves. Other components of CMEPS include an inundation scheme, a tidal forcing processor, an empirical runoff model, and a hurricane wind model. POM uses a terrain-following coordinate in the vertical. The turbulent mixing parameterization scheme invokes the Mellor-Yamada turbulent closure model (Mellor and Yamada, 1974). In this study, CMEPS does not include the effects of the river input, surge–tide interactions, or surge–wave interactions in order to isolate the effect of wind asymmetry. Five types of experiments are conducted in this study. First, the storm surge model is calibrated by using the assimilated wind and water level data for Hurricane Floyd (1999) (Control experiment of Case 1). Next, the assimilated wind field of Hurricane Floyd is rotated to examine the effect of wind asymmetry on storm surge and inundation (Sensitivity experiments of Case 1). Then, a hypothetical hurricane is constructed with a prescribed wind asymmetry of 20 m s1, in which the wind asymmetry is defined as the difference between the maximum and the minimum wind speed at the radius of maximum winds. The sensitivity of the storm surge and inundation in a simplified coastal setting to the spatial distribution of the wind asymmetry is studied by rotating the wind field of the hypothetical hurricane (Case 2). After that, Cases 3 and 4 repeat the experiments for the hypothetical hurricane, but with smaller (10 m s1) and larger (30 m s1) wind asymmetries, respectively. The model domain used in the Hurricane Floyd case (Case 1) is shown in Fig. 1. A 48-h simulation (21Z 14 September to 21Z 16
September) is conducted for each sensitivity experiment. The topography and bathymetry data from National Geophysical Data Center (NGDC, http://www.ngdc.noaa.gov/) are used in this study. A two-level nesting technique is employed. The outer domain is 75.5–82.5° W, 31.0–34.5° N with a grid spacing of 1 min and an internal time step of 150 s. The inner domain is 79.0–81.0° W, 32.0–33.5° N, with 20 s as the spatial grid size and 50 s as the internal time step. The outer domain provides the inner domain with lateral boundary conditions including the water level and horizontal currents through a one-way nesting-down procedure (Xie et al., 2008). In the Hurricane Floyd case (Case 1), the hurricane wind fields were generated using an asymmetric hurricane wind model (Xie et al., 2006) for the control experiment. This asymmetric hurricane wind model, for forecast purposes, is optimized by determining its basic parameters using National Hurricane Center (NHC) forecast guidance and real-time observations, such as buoy data. For hindcast purposes, this asymmetric hurricane wind model can incorporate wind data from various data sources such as the Eta Data Assimilation System (EDAS), North American Regional Reanalysis (NARR), and NOAA HRD surface wind analyses (HWind, Powell et al., 1996; Powell and Houston, 1996) to optimize its parameters. Both EDAS and NARR data contain North American regional wind reanalysis data. EDAS data have a horizontal resolution of 80 km and a time interval of 6 h, while NARR data have a higher horizontal resolution of 32 km and a shorter time interval of 3 h. However, the NARR data are still too coarse for our purposes and the resulting hurricane vortex is too weak to be used directly in the simulation of hurricane-induced storm surge and inundation. The poorly resolved and weak hurricane vortex is first removed using a smooth filter (Kurihara et al., 1993) to obtain the environmental flow field. Then, hurricane winds generated via the asymmetric parametric hurricane wind model were implanted into the environmental flow. Besides, in regions where the HWind data are available, the HRD high resolution wind analysis data were embedded in the above wind field, obtaining the final combined hurricane wind field. The wind field employed in the control experiment at 22:30Z 15 September 1999 is shown in Fig. 2a. The maximum wind is located to the right of the storm track. The wind speeds along the latitude of 31.73° N (shown as the line AB in Fig. 2a) are shown in Fig. 2b. The maximum wind speed reached 40.0 m s1 on the right side of the storm whereas only about 36.0 m s1 on the left side. In the sensitivity experiments of Case 1 (Table 1), the environmental flow fields remain unchanged, but the embedded high-resolution hurricane vortexes are rotated (counter-clockwise) by an angle ranging from 30° to 330° relative to the storm translation direction. For example, the wind field at 22:30Z 15 September 1999 for EXP 5, in which the hurricane vortex is rotated by 150°, is shown in Fig. 2c. The maximum wind is located to the rear-left of the storm translation direction after rotation. The wind speeds along the east–west cross-section of 31.73° N (shown as the line CD in Fig. 2c) are shown in Fig. 2d. The maximum wind in the western side of the storm reached 40.0 m s1, while only about 36.0 m s1 on the eastern side. An idealized experiment (Case 2) is conducted to simulate a hypothetical hurricane with asymmetric wind structures approaching a north–south oriented east coast (Fig. 3a). The idealized topography and bathymetry are assumed uniform in the north–south or alongshore (Y) direction and vary perpendicularly to the coast (X direction) from 20 m above the mean sea level on the western boundary to 140 m below the mean sea level (MSL) on the eastern boundary (Fig. 3b) in a nominal 500 500 km box. The horizontal grid spacing in the X and Y directions is set to be 2 km. Ten sigma levels are used in the vertical. The time step is set to 120 s for the internal mode. The hypothetical hurricanes
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Fig. 1. Domain configuration for the simulation of Hurricane Floyd (1999) together with the storm track (the line marked by asterisks). The inner rectangle indicates the highresolution nested domain.
Fig. 2. (a) The wind fields used in the Floyd case control experiments; (b) the wind speed cross-section along line AB; (c) the wind fields used in the real case EXP5; (d) the cross-section along line CD. The wind fields used in the real case (e) EXP1, (f) EXP2, (g) EXP3, and (h) EXP8. Contours are winds speed in m s1 and arrows are winds vector.
started at a distance of 500 km away from the eastern boundary and moved westward at a constant translation speed of 10 m s1. In the control experiment of Case 2, the maximum wind was
located in the rear of the storm (Fig. 3a). Seven sensitivity experiments of Case 2 were conducted to study the effect of the wind asymmetry on storm surge and inundation. In each of the
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Table 1 Sensitivity experiments for Hurricane Floyd. Experiment #
1
2
3
4
5
6
7
8
9
10
11
Angle (°)
30
60
90
120
150
180
210
240
270
300
330
Fig. 3. Domain configuration for the idealized experiments: (a), model domain with the vertical line (AB) representing the idealized coastline, the hypothetic Hurricane wind field (contours in every 5 m s1), and the arrow showing the moving direction of the storm; (b), model topography and bathymetry for a east–west cross-section.
sensitivity experiments, the hurricane wind speed field is rotated (counter-clockwise) by 45–315°, in 45° intervals (Table 2). In the control and sensitivity experiments, the maximum wind speed is held as a constant of 55 m s1. A 36-h simulation is carried out for each idealized experiment. Cases 3 and 4 are identical to Case 2 except with a smaller and larger wind asymmetry of 10 m s1 and 30 m s1 respectively.
north–northeast of the hurricane eye, while within the southwest sector, the winds were opposite in direction, with a maximum wind speed of 36.0 m s1. Fig. 4 shows the comparison between the time series of the observed and simulated water levels. The observed water level was recorded by the NOAA National Ocean Service (NOS) Center for Operational Oceanographic Products and Services (CO-OPS) coastal station located at Cooper River mouth, Charleston, SC (32.7817° N 79.9250° W). The first observed peak water level, which occurred at 21:00Z 15 September (the 24th hour of simulation), was 0.80 m, while the simulated peak surge valid at this time was 0.84 m. After the first peak, the simulated water level retreated and the lowest water level reached a level of 0.32 m below MSL, shallower than the observed 0.70 m below MSL. Consequently, this under-estimated retreat also caused the simulated second peak of 0.51 m, to be higher than the observed value of 0.36 m. While we are focusing on the effects of the asymmetric structure of the hurricane wind field on coastal water level, other factors may also have influenced the simulated water level, such as the lack of consideration of river input, surge–tide interactions, and surge–wave interactions – none of which were taken into consideration in this study. The discrepancy between the simulated and the observed water levels may be caused by the exclusion of these processes. However, in general, the simulation of the effects of the hurricane wind field on the variation of water level agreed reasonably well with the observations, and therefore provided a basis for further sensitivity experiments. Fig. 5 shows the water level evolution due to the hurricane wind forcing in the control run of the real case simulations. Fig. 5a shows that at the initial time, the water level was set to zero throughout the domain. At the 14th hour (Fig. 5b) winds associated with the hurricane started to influence the study region and caused the water level to rise in the southern portion of the domain, with an accompanying increase in water level of around 0.2 m. At the
3. Results and discussion 3.1. Storm surge and inundation induced by Hurricane Floyd Hurricane Floyd (1999) was a Saffir-Simpson category-4 hurricane at 21:00Z 14 September 1999, when the storm surge model was initialized. The actual hurricane entered the region represented by the coarse domain at 21:00Z 15 September as a category-3 hurricane with a maximum wind speed of 45 m s1. As actually occurred, Floyd weakened throughout the simulation until it became a tropical storm with a maximum wind speed of 25 m s1 when the simulation was terminated. Fig. 2a shows the hurricane wind field of the control experiment at 22:30Z 15 September. At this time, the maximum southerly to southeasterly winds were larger than 40.0 m s1, and were located to the
Table 2 Idealized sensitivity experiments. Experiment #
1
2
3
4
5
6
7
Angle (°)
45
90
135
180
225
270
315
Fig. 4. Comparison of the time series of the observed (triangles) and simulated (solid line) water levels in the control experiment at the Charleston station.
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Fig. 5. The evolution of water level (contours in every 0.2 m) due to the hurricane wind (gray arrows) forcing in the real case simulation (the control experiment) for Hurricane Floyd (1999). (a) initial time; (b) 14th hour; (c) 24th hour and (d) 29th hour.
24th hour (Fig. 5c), the hurricane center moved into the domain and the water level increased rapidly. At this time, the water level at the Charleston station reached its first peak of 0.8 m. At the 29th hour (Fig. 5d), the hurricane moved to the northern part of the domain The on-shore winds near the northern coast led to a 1.6 m water level rise. In the southern part of the domain where the winds blew offshore, the water level decreased to 1 m below prestorm water levels. The maximum storm surge caused by Hurricane Floyd is relatively small in our study domain. This is because the maximum wind of the storm remained outside our computational domain. In the next section, the influence of the maximum wind location in an asymmetric hurricane wind field on hurricane-induced storm surge will be discussed. 3.2. Sensitivity of Hurricane Floyd’s surge to hypothetical wind asymmetry In this section, we consider the sensitivity of the storm surge induced by a set of hypothetical hurricanes with surface winds
resembling that of Hurricane Floyd except that the wind field is rotated (counter-clockwise) by 30–330° relative to the storm motion at 30° intervals for each experiment (Table 1). Fig. 6 shows the maximum (thick line) and minimum (thin line) water levels during the simulation in the control experiment and the sensitivity experiments. The maximum water level reached 2.22 m in EXP 2 (39% larger than that in the control experiment), in which the wind field was rotated by 60°. Note that the maximum water levels increased significantly in EXPs 1–3 (rotated by 30–90°), whereas the variation in the maximum water levels in other experiments was relatively small compared to the control experiment, ranging from 1.68 m to 1.74 m. The difference between EXPs 1–3 and the other experiments is that the maximum winds were located near the coast in EXPs 1–3, but far away from coastal areas in the other experiments (Fig. 2a, c, e, f, g and h). It can be seen from Figs. 2a, c, e, f, g and h and 6 that the maximum water level increased when the maximum winds were located near the coast. Generally, the maximum storm surges occur near the coast. Therefore, when maximum winds were located near the
Fig. 6. The domain-wide maximum (thick line) and minimum (thin line) water levels during the simulation in the control experiment and sensitivity experiments in the real case simulation for Hurricane Floyd (1999).
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coast as after rotation, the maximum storm surge increased. The minimum water levels were also sensitive to the wind asymmetries. In EXP 7, in which the wind field was rotated by 210°, the water level dropped to 3.63 m below the MSL; whereas in EXP 2, in which the wind field was rotated by 60°, the minimum water level was only about 1.80 m below the MSL, 50% smaller than that in EXP 7. Fig. 7 shows the locations of the maximum (dark ellipse in Fig. 7a and b) and minimum (dark ellipse in Fig. 7c and d) water levels over the whole domain during the pass of Hurricane Floyd, and the wind vectors and wind speed contours just before the occurrence of the maximum or minimum water levels. Fig. 7a–d correspond to EXP 2, EXP 10, EXP 7 and EXP 2, respectively. In EXP 2 (Fig. 7a), the region of maximum winds was rotated to the coastal area (by 60°). The region denoted by ‘‘E-MAX” was under the influence of maximum onshore winds (47 m s1), and therefore it experienced the largest increase in water level (2.22 m) among the experiments. However in EXP 10 (Fig. 7b), the maximum winds were rotated to offshore regions. The region denoted by ‘‘E-MAX” was never directly influenced by the maximum wind speed. Therefore, it experienced a relatively smaller water level increase (1.73 m) compared to EXP 2. In Fig. 7c, the area indicated by ‘‘E-MIN”, was influenced by the strongest offshore winds, therefore it experienced the largest drop in water level of about 3.63 m below the MSL. In Fig. 7d, the area marked ‘‘E-MIN” was influenced
by weakest offshore winds, and thus experienced the smallest drop in water level of only 1.80 m below MSL. The rotation of the hurricane wind field affected not only the domain-wide maximum and minimum water levels but also the time series of the water level at a specific location. Fig. 8 shows the time series of the water levels experienced at the Charleston station. The triangle indicates the observed data and the solid line reflects the simulated water level time series in the control and sensitivity experiments. It shows that rotation of the wind field can cause the first simulated peak surge to vary from 0.6 to 1.7 m, the second simulated peak surge to vary from 0.98 m below MSL to 0.95 m above MSL, and cause the lowest water level to vary from 1.2 to 0.1 m below MSL. 3.3. Idealized control experiments Consider now a set of idealized hurricanes with constructed wind fields. In all idealized experiments, the hypothetical hurricane is set to move from the eastern side of the domain at a constant translation speed of 10 m s1 toward the west (Fig. 3a). During the hurricane’s landfall, the coastal region to the north of the storm track experiences on-shore winds that induce a rise in water level and inundation, whereas the region to the south experiences offshore winds and a decrease in water level. Fig. 9a shows the hurricane wind field (gray solid contour) and water levels
Fig. 7. The locations (dark ellipses) of the maximum (in a and b) and minimum (in c and d) water levels, and the wind vector (arrows) and wind speed (contours in every 10 m s1) just before the occurrence of the maximum (a and b) and minimum (c and d) water levels.
Observed Angle=0 Angle=210 Angle=60
Fig. 8. Time series of the water levels experienced at the Charleston station in the control and sensitivity experiments.
L. Xie et al. / Ocean Modelling 36 (2011) 71–79
a
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b
Fig. 9. The hurricane wind speed (gray contours in every 5 m s1) and water level (dark contours in every 2 m) at the 23th hour for (a) the control experiment and (b) EXP 6.
(black solid contour) at the 23rd hour in the control experiment. The maximum rise of water level reached 5.18 m (not shown) and the maximum drop of water level was 4.90 m (not shown). In Fig. 9a, line AB shows the original coastline. Fig. 10 shows the time series of the domain-wide maximum (black solid line), the minimum water levels (black dashed line) and the number of flooded grids (gray line). The maximum increase in water level reached about 5.18 m at the 23rd hour, when the hurricane reached the coast. After landfall, the increase in water level gradually diminished to near zero at the 32nd hour. The water level in the southern portion of the domain dipped to 5.53 m below the MSL at the 24th hour, and then gradually returned to pre-storm level in about 12 h. The inundation began at the 19th hour and the flooded area reached 3300 km2 by the 25th hour. 3.4. Idealized sensitivity experiments In addition to the control experiment, seven sensitivity experiments are conducted (Table 2). In each sensitivity experiment, the idealized hurricane wind field is rotated by 45–315° at 45° intervals. Therefore, the maximum wind speeds in the sensitivity experiments are located at different azimuth angle relative to the storm motion. However, the maximum wind speeds in the sensitivity experiments are the same for all cases. As an illustration, Fig. 9b shows the hurricane wind field (gray solid contour) and water level variation (black solid contour) induced by the hurricane at the 23rd
hour in sensitivity EXP 6. In this experiment, the wind speed field was rotated by 270° counterclockwise. Due to the rotation, the maximum wind speed that was located in the eastern half of the storm in the control experiment was shifted to the southern side of the domain. Consequently, the northern part of the coastal region, where hurricane winds reached more than 50 m s1 in the control experiment, now experienced a wind speed of less than 40 m s1. Therefore, the northern part of the coastal region experienced a maximum increase in water level of only 4.71 m at the 23rd hour, less than the 5.18 m increase in the control experiment. Along the southern portion of the coastline, the maximum wind speed reached about 50 m s1 leading to a decrease in the water level of about 5.13 m in EXP 6. Fig. 11 shows the variations in the maximum and minimum water levels (black solid and dashed lines) and accumulated number of inundated grids (gray line) in the 36-h simulation in the sensitivity experiments. It is clearly shown that both water level and inundation were influenced by rotation of the wind fields. Maximum water levels ranged from 4.73 m (EXP 5) to 6.04 m (EXP 2), while the minimum water levels ranged from 5.70 m (EXP 7) to 4.97 m (EXP 3). In EXP 2, the number of flooded grids is 915 (approximately 3660 km2), while in EXP 5, the number is only 888 (approximately 3552 km2). To illustrate the relative influence of wind asymmetry on water level, the percentage of water level variation in the sensitivity experiments to that in the control experiment was defined as:
VP ¼ ðELs ELc Þ=jELc j
ð1Þ
where ELs are maximum (minimum) water levels from sensitivity experiments and ELc is maximum (minimum) water level from control experiment. Fig. 12a and b shows the maximum and minimum water level variation percentages of seven sensitivity experiments, respectively. It is clearly shown that the rotation of the wind fields can cause the maximum water level to increase by 16.29% or decrease by 8.80%, and cause the magnitude of the minimum water level to reduce by 10.41% or increase by 2.76%. The differences depicted in Fig. 12a and b are attributed to the differences in the spatial distribution of maximum and minimum winds. The differences in storm surge and inundation will also depend on the measure of the asymmetry of the wind. Let us define the wind speed asymmetry as the difference between the maximum and the minimum wind speed at the radius of maximum winds:
ASY ¼ U ma U mi Fig. 10. Time series of the maximum (black solid line) and minimum water level (black dashed line) and the number of flooded grids (gray line) in the control experiment.
ð2Þ
To quantify the effect of wind speed asymmetry (ASY) on storm surge and inundation, two additional sets of sensitivity experiments (Cases 3 and 4) – one for ASY = 10 m s1 and the other for
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Fig. 11. Maximum (black solid line) and minimum water levels (black dashed line) and accumulated number of inundated grids (gray line) in the 36-h simulation in the idealized sensitivity experiments.
Fig. 12. Water level variation percentage of sensitivity experiments to control experiment for domain wide (a) maximum water level and (b) minimum water level.
ASY = 30 m s1 – were conducted. Water level variation percentage (VP) of these two sets of experiments and the original set of experiments (ASY = 20 m s1) are shown in Table 3 for maximum water level and Table 4 for minimum water level. The VP caused by the rotation of wind fields increases with increasing ASY of wind field, for both the maximum and the minimum water levels.
Table 3 VP of sensitivity experiments for maximum water level. ASY (m s1)
10 20 30
Angle (°) 45
90
135
180
225
270
315
5.70 10.39 15.42
7.81 16.29 26.03
5.65 10.45 17.59
0.45 3.74 3.92
4.61 8.80 11.20
5.81 8.57 10.73
3.34 5.85 7.28
Table 4 VP of sensitivity experiments for minimum water level. ASY (m s1)
10 20 30
Angle (°) 45
90
135
180
225
270
315
3.34 2.89 7.72
6.38 7.73 12.54
7.03 10.41 13.73
6.33 10.14 11.17
4.08 3.91 7.94
0.60 0.51 5.49
0.29 2.76 7.37
4. Conclusions Extensive efforts have been made in the past to improve storm surge and inundation forecasts, such as incorporating impacts of sea surface waves and tides into storm surge and inundation models, increasing the model resolution or changing 2-dimensional storm surge model to 3-dimensional. However, these factors can only improve the accuracy of storm surge forecast based on accurate wind forcing fields. Hence accurate wind forcing is a fundamental factor ensuring the accuracy of storm surge and inundation forecasts. Axis-symmetric parametric hurricane wind models are still often used to compute the wind forcing for storm surge and inundation forecasting. However, it is well known that the wind fields of real hurricanes are rarely axis-symmetric. It is important to understand how asymmetric spatial structure of wind fields affects storm surge and inundation forecasts. The results from this study show that when maximum winds were rotated to the coast, the maximum storm surge increased. The minimum water levels were also sensitive to the wind asymmetry. This implies that the relative rotation of otherwise identical hurricane wind fields will have a strong influence on hurricane-induced storm surge, flooding and inundation. For a real case simulation of Hurricane Floyd (1999), there could have been as much as 38% (50%) difference in maximum (minimum) water levels at the coast if the wind field were rotated. It also shows that the time history of water level at a specific station is sensitive to the
L. Xie et al. / Ocean Modelling 36 (2011) 71–79
asymmetry in wind fields. In the first set of idealized hurricane experiments, it was shown that the rotation of the asymmetric wind fields had a significant influence on storm surge and inundation. This caused the maximum water level to vary from 4.73 m to 6.04 m (8.80% to 16.29% compared to control results), minimum water level to vary from 5.70 m to 4.97 m (10.41% to 2.76%) and inundation areas to vary from 3552 to 3660 km2. The results from the additional two sets of idealized hurricane experiments showed that such sensitivity is also dependant on the degree of asymmetry in wind fields. The percentage of water level variation would decrease with decreasing asymmetry of wind fields. It varies from 5.81% to 7.81% for maximum water level and from 7.03% to 0.60% for minimum water level when asymmetry of wind fields dropped from 20 m s1 to 10 m s1. Meanwhile, when the asymmetry of wind fields increased from 20 m s1 to 30 m s1, the percentage of maximum water level changes ranged from 11.20% to 26.03% for high water, and from 13.73% to 7.37% for low water. In summary, the results showed that there is significant sensitivity of storm surge and inundation to the asymmetry in hurricane wind field. This implies that even if other parameters, such as the maximum wind speed, the radius of maximum winds and the central pressure are correctly estimated, considerable error in the simulation of storm surge will result from neglecting the asymmetric characteristics of the hurricane wind field. Acknowledgements This study is supported by the National Oceanic and Atmospheric Administration Grant #UF-EIES-0704029-NCS via a subcontract from the University of Florida. We thank Katie Costa for providing proofreading. We also appreciate the comments of two anonymous reviewers and editor. References Bell, K., Ray, P.S., 2004. North Atlantic hurricanes 1977–99: surface hurricane-force wind radii. Monthly Weather Review 132, 1167–1189. Chen, Y., Yau, M.K., 2003. Asymmetric structures in a simulated landfalling hurricane. Journal of the Atmospheric Sciences 60 (18), 2294–2312. DeMaria, M., Aberson, S., Ooyama, K., 1992. A nested spectral model for hurricane track forecasting. Monthly Weather Review 120, 1628–1640.
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Depperman, R.C., 1947. Notes on the origin and structures of Philippine typhoons. Bulletin of the American Meteorological Society 28, 399–404. Georgiou, P., 1985. Design Wind Speeds in Tropical Cyclone Prone Regions. Ph.D. Thesis, University of Western Ontario. Holland, G.J., 1980. An analytic model of the wind and pressure profiles in hurricanes. Monthly Weather Review 108, 1212–1218. Houston, S.H., Shaffer, W.A., Powell, M.D., Chen, J., 1999. Comparisons of HRD and SLOSH surface wind fields in hurricanes: implications for storm surge modeling. Weather and Forecasting 14 (5), 671–686. Jelesnianski, C., Chen, J., Shaffer, W., 1992: Slosh: sea, lake and overland surges from hurricane. Technical report, National Weather Service, silver springs, MD. Kurihara, Y., Bender, A.M., Rebecca, R.J., 1993. An initialization scheme of hurricane models by vortex specification. Monthly Weather Review 121, 2030. Liu, H., Xie, L., 2009. A numerical study on the effects of wave–current–surge interactions on the height and propagation of sea surface waves in Charleston Harbor during Hurricane Hugo 1989, Continental Shelf Research, doi: 10.1016/ j.csr.2009.03.013. Mellor, G.L., Yamada, T., 1974. A hierarchy of turbulence closure models for planetary boundary layers. Journal of the Atmospheric Sciences, 1791– 1806. Peng, M., Xie, L., Pietrafesa, L., 2004. A numerical study of storm surge and inundation in the croatan-albemarle-pamlico estuary system. Estuarine, Coastal and Shelf Science 59, 121–137. Pietrafesa, L., Xie, L., Dickey, D., Peng, M., Bao, S., 2003. The North Carolina State University coastal and estuary storm surge and flood prediction system. Ecosystems and Sustainable Development 4, 100–109. Powell, M.D., Houston, S.H., Reinhold, T.A., 1996. Hurricane Andrew’s landfall in South Florida. Part I: Standardizing measurements for documentation of surface wind fields. Weather Forecast 11, 304–328. Powell, M.D., Houston, S.H., 1996. Hurricane Andrew’s landfall in South Florida. Part II: Surface wind fields and potential real-time applications. Weather Forecast 11, 329–349. Ross, R.J., Kurihara, Y., 1992. A simplified scheme to simulate asymmetries due to the beta effect in barotropic vortices. Journal of the Atmospheric Sciences 49 (17), 1620–1628. Shapiro, L., 1983. The asymmetric boundary layer flow under a translating hurricane. Journal of the Atmospheric Sciences 40 (8), 1984–1998. Wang, Y., Holland, G.J., 1996. Tropical cyclone motion and evolution in vertical shear. Journal of the Atmospheric Sciences 53 (22), 3313–3332. Xie, L., Bao, S., Pietrafesa, L., Foley, K., Fuentes, M., 2006. A real-time hurricane surface wind forecasting model: formulation and verification. Monthly Weather Review 134, 1355–1370. Xie, L., Pietrafesa, L.J., Wu, K., 2002. Interannual and decadal variability of landfalling tropical cyclones in the Southeast coastal states of the United States. Advances in Atmospheric Sciences 19, 677–686. Xie, L., Pietrafesa, L.J., Peng, M., 2004. Incorporation of a mass-conserving inundation scheme into a three-dimensional storm surge model. Journal Coastal Research 20, 1209–1223. Xie, L., Liu, H., Peng, M., 2008. A numerical study on the effect of wave–current interactions on the storm surge and inundation associated with Hurricane Hugo 1989. Ocean Modelling 20, 252–269.
Contents lists available at ScienceDirect
Ocean Modelling journal homepage: www.elsevier.com/locate/ocemod
A numerical study of the effect of hurricane wind asymmetry on storm surge and inundation Lian Xie a,⇑, Huiqing Liu a,⇑, Bin Liu a, Shaowu Bao b,c a
Department of Marine, Earth and Atmospheric Sciences, North Carolina State University, Box 8208, Raleigh, NC 27695, United States Earth System Research Laboratory, National Oceanic and Atmospheric Administration Boulder, CO 80307, United States c Cooperative Institute for Research in Environmental Sciences (CIRES), University of Colorado, Boulder, CO 80307, United States b
a r t i c l e
i n f o
Article history: Received 28 March 2010 Received in revised form 23 September 2010 Accepted 7 October 2010 Available online 13 October 2010 Keywords: Storm surge Inundation Wind asymmetry Hurricane Floyd
a b s t r a c t The influence of the asymmetric structure of hurricane wind field on storm surge is studied with five types of numerical experiments using a three-dimensional storm surge model. The results from the case of Hurricane Floyd (1999) show that Floyd-induced peak surge would have been much higher had the region of maximum wind rotated 30–90° counterclockwise. The idealized cases (the hypothetical hurricanes) with a wind speed asymmetry of 20 m s1 show that the peak (negative) surge varied from 4.7 to 6.0 m (5 to 5.7 m) or equivalent to 8.8% and 16.3% (2.8% and 10.4%) differences as compared to the control experiment. The area of flooding varied from 3552 to 3660 km2. The results from two other idealized cases of varying degree of wind speed asymmetry further show that with decreasing (increasing) asymmetry of wind fields, the variations of peak surge and peak negative surge caused by the rotation of wind fields decrease (increase) accordingly. The results suggest that in storm surge simulations forced by winds derived from balanced models, considerable uncertainty in storm surge and inundation can result from wind asymmetries. This is true even if all other storm parameters, including maximum wind speed, the radius of maximum winds (storm size), minimum central pressure, storm translation speed, drag coefficient, and model settings (domain size and resolution) are identical. Thus, when constructing ensemble and probabilistic storm surge forecasts, uncertainty in wind asymmetry should be considered in conjunction with variations in storm track, storm intensity and size. Ó 2010 Elsevier Ltd. All rights reserved.
1. Introduction With the increase in the US coastal population, hurricanes have become a major threat to the lives and property of residents living in vulnerable coastal regions, particularly along the Gulf of Mexico and the Atlantic seaboard. While storm winds are damaging per se, the storm-induced surge and inundation are threatening to life and property during hurricane landfall. Accurate forecast of the storm surge and inundation is critical to hurricane preparedness and evacuation planning. Though knowing the amount of precipitation accompanying a storm is a key factor in forecasting inland flooding, accurate wind forcing is the most important factor ensuring the accuracy of storm surge and inundation forecasts. Due to high computational expenses, numerical weather prediction models have not yet been widely adopted for forecasting the hurricane winds for storm surge prediction. Axis-symmetric parametric hurricane vortex models based on gradient wind or cyclostrophic wind balance (Holland, 1980; Depperman, 1947; DeMaria et al., 1992) ⇑ Corresponding authors. Address: NCSU/MEAS, Box 8208, Raleigh, NC 276958208, United States. Tel.: +1 919 513 2325. E-mail addresses: [email protected] (L. Xie), [email protected] (H. Liu). 1463-5003/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.ocemod.2010.10.001
are still often used to compute the wind forcing for storm surge and inundation forecasting. However, these axis-symmetric models are not able to describe the true spatial structure of the wind fields of real hurricanes, which are rarely axis-symmetric. It is well known that as a result of the storm motion, the winds in a hurricane’s right-front quadrant relative to the hurricane’s translation direction are generally stronger than the winds in other quadrants. However, hurricane wind asymmetry can arise from many other factors as well, including friction (Shapiro, 1983), vertical shear and environmental conditions (Wang and Holland, 1996), the near discontinuity of the surface friction and the latent heat flux (Chen and Yau, 2003), and the beta (b) effect (Ross and Kurihara, 1992). Bell and Ray (2004) used the National Oceanic and Atmospheric Administration’s (NOAA) Hurricane Research Division (HRD) flight-level data archive of 1977–99 North Atlantic hurricanes to create probability distribution of hurricane-force wind radius in different quadrants for minimal and major hurricanes. Their results showed that the largest hurricane-force wind radius could be possibly located at any of quadrants relative to the hurricane’s translation direction, but it tend to be in the right-rear quadrant for minimal hurricanes and in the front quadrant for the major hurricanes. We analyzed the HRD surface wind analysis data (from 2000
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to 2009 North Atlantic hurricanes) and got the similar results for distribution of maximum wind. Strongest winds could be possibly located at any of the four quadrants, but is most likely located at the right-front or right-rear quadrants. Therefore, several attempts have been made to incorporate hurricane asymmetric structures into parametric hurricane wind models (e.g., Georgiou, 1985; Jelesnianski et al., 1992; Houston, 1999; Xie et al., 2006). Houston (1999) showed that the difference between HRD surface wind analysis data and the data from the wind model used to drive NOAAs Sea, Lake and Overland Surges Hurricane (SLOSH) model (Jelesnianski et al., 1992), is the cause of some of the significant differences (around 0.8 m) in the computed storm surge for Hurricane Emily (1993) versus the observational storm surge. However, the effect of the asymmetric spatial structure of hurricane wind field on storm surge has not yet been systematically investigated. Questions which remain unanswered are the following: What would be the difference in the storm surge and inundation when the model is driven by the hurricane wind fields with the same size (radius of maximum wind) and intensity (maximum wind speed), but with different asymmetric spatial distributions? How much error would be introduced due to neglecting hurricane wind asymmetries under the same hurricane size and intensity? In this study, idealized and real-case numerical experiments were conducted to investigate the effect of the asymmetry in hurricane wind field on storm surge and inundation both qualitatively and quantitatively. In Section 2, the storm surge and inundation model used in this study as well as the design of experiments are described. Section 3 presents the modeling results, followed by conclusions and summary in Section 4. 2. Model description and experiment design The storm surge and inundation component of the Coastal Marine Environmental Prediction System (CMEPS) (Xie et al., 2002, 2004, 2008; Pietrafesa et al., 2003; Peng et al., 2004; Liu and Xie, 2009) developed at North Carolina State University (NCSU) is used in this study to simulate hurricane-induced storm surge and inundation. The hydrodynamic core of CMEPS incorporates the Princeton Ocean Model (POM) for ocean circulation and the Simulating Waves Nearshore (SWAN) model for sea surface waves. Other components of CMEPS include an inundation scheme, a tidal forcing processor, an empirical runoff model, and a hurricane wind model. POM uses a terrain-following coordinate in the vertical. The turbulent mixing parameterization scheme invokes the Mellor-Yamada turbulent closure model (Mellor and Yamada, 1974). In this study, CMEPS does not include the effects of the river input, surge–tide interactions, or surge–wave interactions in order to isolate the effect of wind asymmetry. Five types of experiments are conducted in this study. First, the storm surge model is calibrated by using the assimilated wind and water level data for Hurricane Floyd (1999) (Control experiment of Case 1). Next, the assimilated wind field of Hurricane Floyd is rotated to examine the effect of wind asymmetry on storm surge and inundation (Sensitivity experiments of Case 1). Then, a hypothetical hurricane is constructed with a prescribed wind asymmetry of 20 m s1, in which the wind asymmetry is defined as the difference between the maximum and the minimum wind speed at the radius of maximum winds. The sensitivity of the storm surge and inundation in a simplified coastal setting to the spatial distribution of the wind asymmetry is studied by rotating the wind field of the hypothetical hurricane (Case 2). After that, Cases 3 and 4 repeat the experiments for the hypothetical hurricane, but with smaller (10 m s1) and larger (30 m s1) wind asymmetries, respectively. The model domain used in the Hurricane Floyd case (Case 1) is shown in Fig. 1. A 48-h simulation (21Z 14 September to 21Z 16
September) is conducted for each sensitivity experiment. The topography and bathymetry data from National Geophysical Data Center (NGDC, http://www.ngdc.noaa.gov/) are used in this study. A two-level nesting technique is employed. The outer domain is 75.5–82.5° W, 31.0–34.5° N with a grid spacing of 1 min and an internal time step of 150 s. The inner domain is 79.0–81.0° W, 32.0–33.5° N, with 20 s as the spatial grid size and 50 s as the internal time step. The outer domain provides the inner domain with lateral boundary conditions including the water level and horizontal currents through a one-way nesting-down procedure (Xie et al., 2008). In the Hurricane Floyd case (Case 1), the hurricane wind fields were generated using an asymmetric hurricane wind model (Xie et al., 2006) for the control experiment. This asymmetric hurricane wind model, for forecast purposes, is optimized by determining its basic parameters using National Hurricane Center (NHC) forecast guidance and real-time observations, such as buoy data. For hindcast purposes, this asymmetric hurricane wind model can incorporate wind data from various data sources such as the Eta Data Assimilation System (EDAS), North American Regional Reanalysis (NARR), and NOAA HRD surface wind analyses (HWind, Powell et al., 1996; Powell and Houston, 1996) to optimize its parameters. Both EDAS and NARR data contain North American regional wind reanalysis data. EDAS data have a horizontal resolution of 80 km and a time interval of 6 h, while NARR data have a higher horizontal resolution of 32 km and a shorter time interval of 3 h. However, the NARR data are still too coarse for our purposes and the resulting hurricane vortex is too weak to be used directly in the simulation of hurricane-induced storm surge and inundation. The poorly resolved and weak hurricane vortex is first removed using a smooth filter (Kurihara et al., 1993) to obtain the environmental flow field. Then, hurricane winds generated via the asymmetric parametric hurricane wind model were implanted into the environmental flow. Besides, in regions where the HWind data are available, the HRD high resolution wind analysis data were embedded in the above wind field, obtaining the final combined hurricane wind field. The wind field employed in the control experiment at 22:30Z 15 September 1999 is shown in Fig. 2a. The maximum wind is located to the right of the storm track. The wind speeds along the latitude of 31.73° N (shown as the line AB in Fig. 2a) are shown in Fig. 2b. The maximum wind speed reached 40.0 m s1 on the right side of the storm whereas only about 36.0 m s1 on the left side. In the sensitivity experiments of Case 1 (Table 1), the environmental flow fields remain unchanged, but the embedded high-resolution hurricane vortexes are rotated (counter-clockwise) by an angle ranging from 30° to 330° relative to the storm translation direction. For example, the wind field at 22:30Z 15 September 1999 for EXP 5, in which the hurricane vortex is rotated by 150°, is shown in Fig. 2c. The maximum wind is located to the rear-left of the storm translation direction after rotation. The wind speeds along the east–west cross-section of 31.73° N (shown as the line CD in Fig. 2c) are shown in Fig. 2d. The maximum wind in the western side of the storm reached 40.0 m s1, while only about 36.0 m s1 on the eastern side. An idealized experiment (Case 2) is conducted to simulate a hypothetical hurricane with asymmetric wind structures approaching a north–south oriented east coast (Fig. 3a). The idealized topography and bathymetry are assumed uniform in the north–south or alongshore (Y) direction and vary perpendicularly to the coast (X direction) from 20 m above the mean sea level on the western boundary to 140 m below the mean sea level (MSL) on the eastern boundary (Fig. 3b) in a nominal 500 500 km box. The horizontal grid spacing in the X and Y directions is set to be 2 km. Ten sigma levels are used in the vertical. The time step is set to 120 s for the internal mode. The hypothetical hurricanes
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Fig. 1. Domain configuration for the simulation of Hurricane Floyd (1999) together with the storm track (the line marked by asterisks). The inner rectangle indicates the highresolution nested domain.
Fig. 2. (a) The wind fields used in the Floyd case control experiments; (b) the wind speed cross-section along line AB; (c) the wind fields used in the real case EXP5; (d) the cross-section along line CD. The wind fields used in the real case (e) EXP1, (f) EXP2, (g) EXP3, and (h) EXP8. Contours are winds speed in m s1 and arrows are winds vector.
started at a distance of 500 km away from the eastern boundary and moved westward at a constant translation speed of 10 m s1. In the control experiment of Case 2, the maximum wind was
located in the rear of the storm (Fig. 3a). Seven sensitivity experiments of Case 2 were conducted to study the effect of the wind asymmetry on storm surge and inundation. In each of the
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Table 1 Sensitivity experiments for Hurricane Floyd. Experiment #
1
2
3
4
5
6
7
8
9
10
11
Angle (°)
30
60
90
120
150
180
210
240
270
300
330
Fig. 3. Domain configuration for the idealized experiments: (a), model domain with the vertical line (AB) representing the idealized coastline, the hypothetic Hurricane wind field (contours in every 5 m s1), and the arrow showing the moving direction of the storm; (b), model topography and bathymetry for a east–west cross-section.
sensitivity experiments, the hurricane wind speed field is rotated (counter-clockwise) by 45–315°, in 45° intervals (Table 2). In the control and sensitivity experiments, the maximum wind speed is held as a constant of 55 m s1. A 36-h simulation is carried out for each idealized experiment. Cases 3 and 4 are identical to Case 2 except with a smaller and larger wind asymmetry of 10 m s1 and 30 m s1 respectively.
north–northeast of the hurricane eye, while within the southwest sector, the winds were opposite in direction, with a maximum wind speed of 36.0 m s1. Fig. 4 shows the comparison between the time series of the observed and simulated water levels. The observed water level was recorded by the NOAA National Ocean Service (NOS) Center for Operational Oceanographic Products and Services (CO-OPS) coastal station located at Cooper River mouth, Charleston, SC (32.7817° N 79.9250° W). The first observed peak water level, which occurred at 21:00Z 15 September (the 24th hour of simulation), was 0.80 m, while the simulated peak surge valid at this time was 0.84 m. After the first peak, the simulated water level retreated and the lowest water level reached a level of 0.32 m below MSL, shallower than the observed 0.70 m below MSL. Consequently, this under-estimated retreat also caused the simulated second peak of 0.51 m, to be higher than the observed value of 0.36 m. While we are focusing on the effects of the asymmetric structure of the hurricane wind field on coastal water level, other factors may also have influenced the simulated water level, such as the lack of consideration of river input, surge–tide interactions, and surge–wave interactions – none of which were taken into consideration in this study. The discrepancy between the simulated and the observed water levels may be caused by the exclusion of these processes. However, in general, the simulation of the effects of the hurricane wind field on the variation of water level agreed reasonably well with the observations, and therefore provided a basis for further sensitivity experiments. Fig. 5 shows the water level evolution due to the hurricane wind forcing in the control run of the real case simulations. Fig. 5a shows that at the initial time, the water level was set to zero throughout the domain. At the 14th hour (Fig. 5b) winds associated with the hurricane started to influence the study region and caused the water level to rise in the southern portion of the domain, with an accompanying increase in water level of around 0.2 m. At the
3. Results and discussion 3.1. Storm surge and inundation induced by Hurricane Floyd Hurricane Floyd (1999) was a Saffir-Simpson category-4 hurricane at 21:00Z 14 September 1999, when the storm surge model was initialized. The actual hurricane entered the region represented by the coarse domain at 21:00Z 15 September as a category-3 hurricane with a maximum wind speed of 45 m s1. As actually occurred, Floyd weakened throughout the simulation until it became a tropical storm with a maximum wind speed of 25 m s1 when the simulation was terminated. Fig. 2a shows the hurricane wind field of the control experiment at 22:30Z 15 September. At this time, the maximum southerly to southeasterly winds were larger than 40.0 m s1, and were located to the
Table 2 Idealized sensitivity experiments. Experiment #
1
2
3
4
5
6
7
Angle (°)
45
90
135
180
225
270
315
Fig. 4. Comparison of the time series of the observed (triangles) and simulated (solid line) water levels in the control experiment at the Charleston station.
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Fig. 5. The evolution of water level (contours in every 0.2 m) due to the hurricane wind (gray arrows) forcing in the real case simulation (the control experiment) for Hurricane Floyd (1999). (a) initial time; (b) 14th hour; (c) 24th hour and (d) 29th hour.
24th hour (Fig. 5c), the hurricane center moved into the domain and the water level increased rapidly. At this time, the water level at the Charleston station reached its first peak of 0.8 m. At the 29th hour (Fig. 5d), the hurricane moved to the northern part of the domain The on-shore winds near the northern coast led to a 1.6 m water level rise. In the southern part of the domain where the winds blew offshore, the water level decreased to 1 m below prestorm water levels. The maximum storm surge caused by Hurricane Floyd is relatively small in our study domain. This is because the maximum wind of the storm remained outside our computational domain. In the next section, the influence of the maximum wind location in an asymmetric hurricane wind field on hurricane-induced storm surge will be discussed. 3.2. Sensitivity of Hurricane Floyd’s surge to hypothetical wind asymmetry In this section, we consider the sensitivity of the storm surge induced by a set of hypothetical hurricanes with surface winds
resembling that of Hurricane Floyd except that the wind field is rotated (counter-clockwise) by 30–330° relative to the storm motion at 30° intervals for each experiment (Table 1). Fig. 6 shows the maximum (thick line) and minimum (thin line) water levels during the simulation in the control experiment and the sensitivity experiments. The maximum water level reached 2.22 m in EXP 2 (39% larger than that in the control experiment), in which the wind field was rotated by 60°. Note that the maximum water levels increased significantly in EXPs 1–3 (rotated by 30–90°), whereas the variation in the maximum water levels in other experiments was relatively small compared to the control experiment, ranging from 1.68 m to 1.74 m. The difference between EXPs 1–3 and the other experiments is that the maximum winds were located near the coast in EXPs 1–3, but far away from coastal areas in the other experiments (Fig. 2a, c, e, f, g and h). It can be seen from Figs. 2a, c, e, f, g and h and 6 that the maximum water level increased when the maximum winds were located near the coast. Generally, the maximum storm surges occur near the coast. Therefore, when maximum winds were located near the
Fig. 6. The domain-wide maximum (thick line) and minimum (thin line) water levels during the simulation in the control experiment and sensitivity experiments in the real case simulation for Hurricane Floyd (1999).
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coast as after rotation, the maximum storm surge increased. The minimum water levels were also sensitive to the wind asymmetries. In EXP 7, in which the wind field was rotated by 210°, the water level dropped to 3.63 m below the MSL; whereas in EXP 2, in which the wind field was rotated by 60°, the minimum water level was only about 1.80 m below the MSL, 50% smaller than that in EXP 7. Fig. 7 shows the locations of the maximum (dark ellipse in Fig. 7a and b) and minimum (dark ellipse in Fig. 7c and d) water levels over the whole domain during the pass of Hurricane Floyd, and the wind vectors and wind speed contours just before the occurrence of the maximum or minimum water levels. Fig. 7a–d correspond to EXP 2, EXP 10, EXP 7 and EXP 2, respectively. In EXP 2 (Fig. 7a), the region of maximum winds was rotated to the coastal area (by 60°). The region denoted by ‘‘E-MAX” was under the influence of maximum onshore winds (47 m s1), and therefore it experienced the largest increase in water level (2.22 m) among the experiments. However in EXP 10 (Fig. 7b), the maximum winds were rotated to offshore regions. The region denoted by ‘‘E-MAX” was never directly influenced by the maximum wind speed. Therefore, it experienced a relatively smaller water level increase (1.73 m) compared to EXP 2. In Fig. 7c, the area indicated by ‘‘E-MIN”, was influenced by the strongest offshore winds, therefore it experienced the largest drop in water level of about 3.63 m below the MSL. In Fig. 7d, the area marked ‘‘E-MIN” was influenced
by weakest offshore winds, and thus experienced the smallest drop in water level of only 1.80 m below MSL. The rotation of the hurricane wind field affected not only the domain-wide maximum and minimum water levels but also the time series of the water level at a specific location. Fig. 8 shows the time series of the water levels experienced at the Charleston station. The triangle indicates the observed data and the solid line reflects the simulated water level time series in the control and sensitivity experiments. It shows that rotation of the wind field can cause the first simulated peak surge to vary from 0.6 to 1.7 m, the second simulated peak surge to vary from 0.98 m below MSL to 0.95 m above MSL, and cause the lowest water level to vary from 1.2 to 0.1 m below MSL. 3.3. Idealized control experiments Consider now a set of idealized hurricanes with constructed wind fields. In all idealized experiments, the hypothetical hurricane is set to move from the eastern side of the domain at a constant translation speed of 10 m s1 toward the west (Fig. 3a). During the hurricane’s landfall, the coastal region to the north of the storm track experiences on-shore winds that induce a rise in water level and inundation, whereas the region to the south experiences offshore winds and a decrease in water level. Fig. 9a shows the hurricane wind field (gray solid contour) and water levels
Fig. 7. The locations (dark ellipses) of the maximum (in a and b) and minimum (in c and d) water levels, and the wind vector (arrows) and wind speed (contours in every 10 m s1) just before the occurrence of the maximum (a and b) and minimum (c and d) water levels.
Observed Angle=0 Angle=210 Angle=60
Fig. 8. Time series of the water levels experienced at the Charleston station in the control and sensitivity experiments.
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a
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b
Fig. 9. The hurricane wind speed (gray contours in every 5 m s1) and water level (dark contours in every 2 m) at the 23th hour for (a) the control experiment and (b) EXP 6.
(black solid contour) at the 23rd hour in the control experiment. The maximum rise of water level reached 5.18 m (not shown) and the maximum drop of water level was 4.90 m (not shown). In Fig. 9a, line AB shows the original coastline. Fig. 10 shows the time series of the domain-wide maximum (black solid line), the minimum water levels (black dashed line) and the number of flooded grids (gray line). The maximum increase in water level reached about 5.18 m at the 23rd hour, when the hurricane reached the coast. After landfall, the increase in water level gradually diminished to near zero at the 32nd hour. The water level in the southern portion of the domain dipped to 5.53 m below the MSL at the 24th hour, and then gradually returned to pre-storm level in about 12 h. The inundation began at the 19th hour and the flooded area reached 3300 km2 by the 25th hour. 3.4. Idealized sensitivity experiments In addition to the control experiment, seven sensitivity experiments are conducted (Table 2). In each sensitivity experiment, the idealized hurricane wind field is rotated by 45–315° at 45° intervals. Therefore, the maximum wind speeds in the sensitivity experiments are located at different azimuth angle relative to the storm motion. However, the maximum wind speeds in the sensitivity experiments are the same for all cases. As an illustration, Fig. 9b shows the hurricane wind field (gray solid contour) and water level variation (black solid contour) induced by the hurricane at the 23rd
hour in sensitivity EXP 6. In this experiment, the wind speed field was rotated by 270° counterclockwise. Due to the rotation, the maximum wind speed that was located in the eastern half of the storm in the control experiment was shifted to the southern side of the domain. Consequently, the northern part of the coastal region, where hurricane winds reached more than 50 m s1 in the control experiment, now experienced a wind speed of less than 40 m s1. Therefore, the northern part of the coastal region experienced a maximum increase in water level of only 4.71 m at the 23rd hour, less than the 5.18 m increase in the control experiment. Along the southern portion of the coastline, the maximum wind speed reached about 50 m s1 leading to a decrease in the water level of about 5.13 m in EXP 6. Fig. 11 shows the variations in the maximum and minimum water levels (black solid and dashed lines) and accumulated number of inundated grids (gray line) in the 36-h simulation in the sensitivity experiments. It is clearly shown that both water level and inundation were influenced by rotation of the wind fields. Maximum water levels ranged from 4.73 m (EXP 5) to 6.04 m (EXP 2), while the minimum water levels ranged from 5.70 m (EXP 7) to 4.97 m (EXP 3). In EXP 2, the number of flooded grids is 915 (approximately 3660 km2), while in EXP 5, the number is only 888 (approximately 3552 km2). To illustrate the relative influence of wind asymmetry on water level, the percentage of water level variation in the sensitivity experiments to that in the control experiment was defined as:
VP ¼ ðELs ELc Þ=jELc j
ð1Þ
where ELs are maximum (minimum) water levels from sensitivity experiments and ELc is maximum (minimum) water level from control experiment. Fig. 12a and b shows the maximum and minimum water level variation percentages of seven sensitivity experiments, respectively. It is clearly shown that the rotation of the wind fields can cause the maximum water level to increase by 16.29% or decrease by 8.80%, and cause the magnitude of the minimum water level to reduce by 10.41% or increase by 2.76%. The differences depicted in Fig. 12a and b are attributed to the differences in the spatial distribution of maximum and minimum winds. The differences in storm surge and inundation will also depend on the measure of the asymmetry of the wind. Let us define the wind speed asymmetry as the difference between the maximum and the minimum wind speed at the radius of maximum winds:
ASY ¼ U ma U mi Fig. 10. Time series of the maximum (black solid line) and minimum water level (black dashed line) and the number of flooded grids (gray line) in the control experiment.
ð2Þ
To quantify the effect of wind speed asymmetry (ASY) on storm surge and inundation, two additional sets of sensitivity experiments (Cases 3 and 4) – one for ASY = 10 m s1 and the other for
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Fig. 11. Maximum (black solid line) and minimum water levels (black dashed line) and accumulated number of inundated grids (gray line) in the 36-h simulation in the idealized sensitivity experiments.
Fig. 12. Water level variation percentage of sensitivity experiments to control experiment for domain wide (a) maximum water level and (b) minimum water level.
ASY = 30 m s1 – were conducted. Water level variation percentage (VP) of these two sets of experiments and the original set of experiments (ASY = 20 m s1) are shown in Table 3 for maximum water level and Table 4 for minimum water level. The VP caused by the rotation of wind fields increases with increasing ASY of wind field, for both the maximum and the minimum water levels.
Table 3 VP of sensitivity experiments for maximum water level. ASY (m s1)
10 20 30
Angle (°) 45
90
135
180
225
270
315
5.70 10.39 15.42
7.81 16.29 26.03
5.65 10.45 17.59
0.45 3.74 3.92
4.61 8.80 11.20
5.81 8.57 10.73
3.34 5.85 7.28
Table 4 VP of sensitivity experiments for minimum water level. ASY (m s1)
10 20 30
Angle (°) 45
90
135
180
225
270
315
3.34 2.89 7.72
6.38 7.73 12.54
7.03 10.41 13.73
6.33 10.14 11.17
4.08 3.91 7.94
0.60 0.51 5.49
0.29 2.76 7.37
4. Conclusions Extensive efforts have been made in the past to improve storm surge and inundation forecasts, such as incorporating impacts of sea surface waves and tides into storm surge and inundation models, increasing the model resolution or changing 2-dimensional storm surge model to 3-dimensional. However, these factors can only improve the accuracy of storm surge forecast based on accurate wind forcing fields. Hence accurate wind forcing is a fundamental factor ensuring the accuracy of storm surge and inundation forecasts. Axis-symmetric parametric hurricane wind models are still often used to compute the wind forcing for storm surge and inundation forecasting. However, it is well known that the wind fields of real hurricanes are rarely axis-symmetric. It is important to understand how asymmetric spatial structure of wind fields affects storm surge and inundation forecasts. The results from this study show that when maximum winds were rotated to the coast, the maximum storm surge increased. The minimum water levels were also sensitive to the wind asymmetry. This implies that the relative rotation of otherwise identical hurricane wind fields will have a strong influence on hurricane-induced storm surge, flooding and inundation. For a real case simulation of Hurricane Floyd (1999), there could have been as much as 38% (50%) difference in maximum (minimum) water levels at the coast if the wind field were rotated. It also shows that the time history of water level at a specific station is sensitive to the
L. Xie et al. / Ocean Modelling 36 (2011) 71–79
asymmetry in wind fields. In the first set of idealized hurricane experiments, it was shown that the rotation of the asymmetric wind fields had a significant influence on storm surge and inundation. This caused the maximum water level to vary from 4.73 m to 6.04 m (8.80% to 16.29% compared to control results), minimum water level to vary from 5.70 m to 4.97 m (10.41% to 2.76%) and inundation areas to vary from 3552 to 3660 km2. The results from the additional two sets of idealized hurricane experiments showed that such sensitivity is also dependant on the degree of asymmetry in wind fields. The percentage of water level variation would decrease with decreasing asymmetry of wind fields. It varies from 5.81% to 7.81% for maximum water level and from 7.03% to 0.60% for minimum water level when asymmetry of wind fields dropped from 20 m s1 to 10 m s1. Meanwhile, when the asymmetry of wind fields increased from 20 m s1 to 30 m s1, the percentage of maximum water level changes ranged from 11.20% to 26.03% for high water, and from 13.73% to 7.37% for low water. In summary, the results showed that there is significant sensitivity of storm surge and inundation to the asymmetry in hurricane wind field. This implies that even if other parameters, such as the maximum wind speed, the radius of maximum winds and the central pressure are correctly estimated, considerable error in the simulation of storm surge will result from neglecting the asymmetric characteristics of the hurricane wind field. Acknowledgements This study is supported by the National Oceanic and Atmospheric Administration Grant #UF-EIES-0704029-NCS via a subcontract from the University of Florida. We thank Katie Costa for providing proofreading. We also appreciate the comments of two anonymous reviewers and editor. References Bell, K., Ray, P.S., 2004. North Atlantic hurricanes 1977–99: surface hurricane-force wind radii. Monthly Weather Review 132, 1167–1189. Chen, Y., Yau, M.K., 2003. Asymmetric structures in a simulated landfalling hurricane. Journal of the Atmospheric Sciences 60 (18), 2294–2312. DeMaria, M., Aberson, S., Ooyama, K., 1992. A nested spectral model for hurricane track forecasting. Monthly Weather Review 120, 1628–1640.
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