Hurricane generated waves as observed by satellite

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1 See discussions, stats, and author profiles for this publication at: Hurricane generated waves as observed by satellite Article in Ocean Engineering May 1996 DO: / (96) CTATONS 24 READS 39 2 authors, including: an R Young University of Melbourne 97 PUBLCATONS 3,561 CTATONS SEE PROFLE Available from: an R Young Retrieved on: 09 August 2016

2 Pergamon Ocean Enyng. Vol. 23, No. 8. pp. 7bL b Copyright Elsevier Science Ltd Pnnted in Great Britain. All rights reserved i96 $ S (96) HURRCANE GENERATED WAVES AS OBSERVED SATELLTE BY. R. Young and G. P. Burchell Dept. of Civil Engineering, University College, Univ. Of NSW, Canberra, Australia (Received 25 August 1995; accepted infnalform 27 October 1995) Abstract-A data set consisting of observations of significant wave height and wind speed within mature hurricanes has been obtained from the GEOSAT satellite mission. Due to the global coverage of the satellite, this data set is extensive, consisting of 100 hurricanes. n addition, as the satellite rapidly propagates across the region influenced by the hurricane wind field, an almost instantaneous cross-section through the hurricane is observed. These features mean that the data set is significantly more comprehensive than those previously presented. The observations confirm the importance of both the maximum wind speed within the hurricane and the velocity of forward movement in determining the magnitude and distribution of the significant wave height field. The data are presented in terms of a relatively simple parametric hurricane wave model. This model represents both a compact description of the data and a tool for engineering design. Copyright 0 19% Elsevier Scxnce Ltd 1. NTRODUCTON Hurricane wind fields are characteristically intense, spatially inhomogeneous and directionally varying. The large gradients in wind speed and the rapidly varying wind directions of the hurricane vortex generate extremely complex ocean wave fields. Typically, waves generated by hurricanes consist of a combination of both swell and wind sea. n addition, the directional distribution of the wind sea component is often skewed due to the rapid variation in the wind direction. The complexity of the wave generation process within hurricane wind fields provides an ideal and demanding test for numerical wind wave prediction models. ndeed, the complexity of the wind field represents a demanding test for our physical knowledge of wind wave generation. The collective data base under such conditions is, however, relatively small. The fact that hurricanes occur relatively infrequently and have tracks which are difficult to predict, means that observations under hurricane conditions are fortuitous. n addition, coincident observations of both wind and wave conditions are extremely rare. Hurricanes vary significantly in intensity, spatial scale and velocity of forward movement. A comprehensive data base would require observations throughout this three dimensional parameter space. Clearly, the likelihood of obtaining such a data base using conventional in situ instruments, such as buoys, is very small. This lack of a comprehensive data base places limitations on our ability to understand the complex physics of wind wave generation in such situations and to validate wind wave prediction models. One means of potentially overcoming this data deficiency is to use satellite remote sensing data. n particular, the GEOSAT satellite provided three years of global observations of wind speed and wave height. This paper presents data from

3 762. R. Young and G. P. Burchell hurricanes over flown by GEOSAT during its three year mission. n order to quantify the data in a concise manner, it is presented in the form of a parametric model which attempts to include the important physical properties of hurricane wave generation. The organization of this paper is as follows. n section 2, a short review of our current knowledge of hurricane wave generation is presented. This is followed in section 3 by a description of the GEOSAT data base to be used. Based on the GEOSAT observations of wind speed and wave height a parametric description of the wave height data is presented in section 4. Finally, conclusions are drawn in section HURRCANE GENERATED WAVES Our present understanding of the hurricane wave field has been gained from a combination of in situ measurements (both non-directional and directional) at single points during the passage of hurricanes, remote sensing data and the application of numerical models. Much of the hurricane wave data collected using in situ instruments has been obtained for commercial purposes and consequently, only a small fraction is in the public domain. The first comprehensive attempt to collect data under hurricane conditions was the Ocean Data Gathering Program (Shemdin, 1977). This program involved instruments on six offshore oil platforms in the Gulf of Mexico. These systems operated between 1968 and 1971, during which data was collected for four hurricanes, including Camille. The program has been described in detail by Ward (1974) and Hamilton and Ward (1974). Since 1972, the US NOAA Data Buoy Office has deployed buoys at various locations around the US coast (NOAA Data Buoy Office, 1973). Hurricane data from these buoys have been presented in a number of publications including Withee and Johnson (1975). n addition to the US data set a significant hurricane (tropical cyclone) wave data base has been established by the offshore oil industry on the north-west coast of Australia. Data have been obtained from more than 25 hurricanes over a period in excess of twenty years (Harper et al., 1993). Although non-directional observations of hurricane wave conditions are valuable, a more comprehensive understanding can be obtained from directional measurements. Directional spectral observations during the passage of hurricanes have been reported by For&all et al. (1978) and Black (1979). Remotely sensed data using Synthetic Aperture Radar have also provided insight into the directional properties of waves within hurricanes (Elachi et al., 1977; Ring and Shemdin, 1978; Shemdin, 1980; Gonzalez et al., 1982; McLeish and Ross, 1983; Beal et al., 1986; Holt and Gonzalez, 1986). Numerous models have been proposed for the prediction of waves within hurricanes. These range from the largely empirical (Bretschneider 1959, ; jima et al., 1968; Ross, 1976; Young, 1988) to those based on solutions to the radiative transfer equation (Patterson, 1972; Bea, 1974; Uji, 1975; Cardone et al., 1977; Young, 1987). ndeed, models have been used by Donoso et al. (1987) and Young (1988) to generate synthetic hurricane wave data bases which span a comprehensive range of hurricane wind field parameters. As the generation source, the hurricane wind field is central to an understanding of the resultant wave field. A number of models have been proposed to describe the hurricane vortex (Schloemer, 1954; Graham and Hudson, 1960; Smith, 1968; Gray and Shea, 1973; Shea and Gray, 1973; Simiu et al., 1976; Atkinson and Holliday, 1977; Wang, 1978; Holland, 1980). Although the details of these various models differ, the wind velocity UrO

4 Hurricane generated waves 763 (at reference height 10 m) at any point within the hurricane can be determined in terms of the central pressure, p,, (or maximum wind velocity, V_), the velocity of forward movement, V,, the radius to maximum winds, R and the direction of the hurricane forward movement, 0,. Based on such a description of the wind field and the composite data base of wave observations, a qualitative description of the hurricane wave field emerges. The wind field is asymmetric, with higher winds to the right (northern hemisphere) of the hurricane centre. The wave field has an even greater degree of asymmetry due to the combined influence of the asymmetry of the wind field and the extended fetch which exists within a translating hurricane. The wind vector in the intense wind region to the right of the storm centre (northern hemisphere) is approximately aligned with the direction of forward propagation. Hence, waves generated in this region tend to move forward with the hurricane and therefore remain in high wind regions for an extended period of time. n contrast, waves generated on the low wind side of the storm (left side in northern hemisphere) propagate in the opposite direction to the hurricane translation and rapidly move away from the high wind areas. This concept of an extended fetch is also important in determining the wave height within a hurricane. Not only is the wave height determined by the maximum wind speed, V but also by the period of time the waves remain within the intense wind region (Smhaxe;ndin, 1977). As V_ increases, the period of the waves generated and hence the speed at which they propagate also increases. Consequently, V, must also increase for the most severe wave conditions to occur. Should the hurricane move too slowly, the waves will outrun the hurricane whereas should the hurricane move too rapidly, the waves will be left behind. Consequently, for a given value of V_, the wave height could be expected to increase with increasing V, until a maximum is reached. A further increase in V will result in a decrease in wave height. Similarly, the spatial distribution of wave height (asymmetry) will also depend on both V_ and V,. An attempt to incorporate this qualitative understanding of the hurricane wave field into a quantitative model was made by Young (1988). Young (1988) assumed that the JON- SWAP (Hasselmann et al., 1973) relationships, originally developed for fetch limited conditions, could also be applied in hurricane wind fields with the specification of a suitable equivalent fetch. Based on a synthetic data base generated by a numerical model, the equivalent fetch was determined in terms of V_, V, and R. Although the model is empirical, it implicitly incorporates the intuitively consistent non-dimensional scaling of JON- SWAP, together with the parameters observed to be important in determining the wave field within a hurricane. As this model will be used to describe the present data set in a concise manner in section 4, it is presented here in detail. Given values of V_, V and R, Young (1988) found that an equivalent fetch, F, could be represented by the relationship F - = avz,, + bv,,,,,v, + c$,, + dv,, + evj, +f R where a = x 10p3, b = x lo-, c = x lo-, d = x lo-, e = x 10-l and f = x 10-l. The term R can be found in terms of R as R = 22.5 x 10310gR x lo3 (2) n Equation (1) and Equation (2) all terms are in standard S.. units (ie.

5 764. R. Young and G. P. Burchell V,,,,,V -[m/s]; F,R,R -[ml). The maximum significant wave height in the hurricane, p can then be determined from a modified form of the JONSWAP (Hasselmann et al., 1973) relationship!?h? -----= $$ vz max i max The spatial distributions of H, could then be determined in terms using a series of diagrams for different values of V,, and V,. 3. THE GEOSAT DATA BASE The US Navy satellite GEOSAT was launched in March, Following an initial classified mission, it commenced its Exact Repeat Mission (unclassified) in November, This mission continued until January, From March, 1989 onwards, however, the data quality progressively degraded. The satellite was placed in a polar orbit, repeating the same ground tracks to an accuracy of approximately 1 km every 17 days (called a 17 day repeat cycle). The resulting ground track separation at the equator was 150 km, this separation decreasing towards the poles. The altimeter on board the satellite measured a value of wind speed and wave height once every second, resulting in a ground track separation of approximately 6.5 km between observations. The pre-launch specification for the accuracy of the GEOSAT altimeter measurements of wave height was +lo% or 0.5 m, whichever is larger. A number of post-launch validations against buoy measurements (Dobson et al., 1987; Glazman and Pilorz, 1990; Carter et al., 1992; Guillaume and Mognard, 1992) have confirmed that the altimeter performance is within these specifications. Post-launch validations of wind speed measurements from the GEOSAT altimeter have been conducted by Dobson et al. (1987), Shuhy et al. (1987), Toumadre and Ezraty (1990) and Guillaume and Mognard (1992). Although less conclusive than validations of wave height, the evidence suggests that in the wind speed range 0 to 15 m/s, wind speed can be measured to an accuracy of f2 m/s. At wind speeds above 15 m/s the error increases. Young (1993) and Young and Holland (1996) suggest that at these higher wind speeds the accuracy is of order +20% Hurricane occurrence Data on the occurrence and parameters defining the wind fields of all hurricanes which occurred during the 3 year GEOSAT mission were obtained from the Australian Bureau of Meteorology (Australian region), the Joint Typhoon Warning Center, Guam (S.E. Asian region) and the US National Oceanographic and Atmospheric Administration (US region). The GEOSAT data set was then searched to find satellite tracks in the vicinity (within 500 km) of the reported positions of these hurricanes. The resulting data set consisted of 100 passes of the satellite above reported hurricanes. Each pass consists of a cross-section through the hurricane with values of wind speed and wave height measured at an approximately 6.5 km interval. Only storms in deep water and distant from any influence of a coastline were considered. Hurricanes are typically characterized in terms of the parameters of the wind field. These parameters include: central pressure, po; velocity of forward movement, V,,; direction of forward movement, 0, and radius to maximum winds, R. The data provided by the respective meteorological institutes enabled the calculation of all parameters except R. (3)

6 Hurricane generated waves 765 Histograms showing the distributions of po, V,, R and latitude of the hurricanes are shown in Fig. 1. The full set of parameters for the data set are presented in appendix A. The wide parameter range covered by the data set is clear, with p. spanning values from barely cyclonic at 999 HPa to extremely intense at 904 HPa. Similarly, V spans values from near stationary to extremely rapid translation in excess of 12 m/s. The radius to maximum winds is a difficult parameter to estimate from synoptic data and consequently, is not routinely available. t is typically estimated in the case of landfalling hurricanes from in situ measurements of atmospheric pressure and wind speed. n the present context wind speed data is available in the form of the GEOSAT observations along the cross-sections through the respective hurricanes. n order to estimate the value of R for each hurricane, the hurricane wind field model of Holland (1980) was adopted. This model assumes that the wind field can be represented in a relatively simple parametric form. The gradient wind can be expressed as u = AWn-po) R exp(-alp) + T o.5 ti 2 P s where U, is the gradient wind at radius r from the centre of the storm, f is the Coriolis parameter, p the air density, p. the central pressure, and pn the ambient atmospheric pressure far from the storm. The parameters A and B can be expressed in terms of the radius to maximum winds, R, as (4) (5) 950 pa Wa) O % (m/s) (4 2or Latitude (deg) Fig. 1. Histograms showing the distribution of the parameters represented by the data set. (a) Central pressure, po, (b) Velocity of forward movement, V fmr (c) Radius to maximum winds, R and (d) Latitude of the positions of the hurricane centres.

7 766. R. Young and G. P. Burchell The dimensionless parameter B defines the shape of the wind field with increasing distance from the centre of the hurricane. ncreasing B concentrates more of the pressure drop near R. Holland (1980) has shown that B can be related to the central pressure p,,. A linear fit to his data yields B = (980 - pj120 (6) where p. is expressed in hectopascals (or millibars). Following Shea and Gray (1973), the radial winds are assumed to spiral in toward the centre of the storm with a constant inflow angle of 25. Also, a first-order asymmetry has been applied to the wind field by adding the hurricane forward speed V to the symmetric flow and rotating the maximum to an angle of 70 to the direction of the cyclone forward motion (to the left in southern hemisphere and to the right in northern hemisphere). These modifications are consistent with the results of Shea and Gray (1973) and Shapiro (1983). Naturally, there can be variability in all these parameters, particularly the angle to the maximum winds, which can vary significantly between storms (Shapiro, 1983). The gradient wind velocity U, was reduced to U,, (1 -min. average) by the application of a factor of 0.8 (Powell, 1980). Hence the full wind field is defined by the specification of the position of the centre of the storm, the central pressure po, radius to maximum winds, R, and the direction and velocity of forward translation. With the adoption of this model the full two-dimensional wind field can be determined provided that the wind field parameters of po, V,, 0, and R are known. As all parameters with the exception of R are known a non-linear least squares technique (ie. Levenberg- Marquardt method, Press et al., 1986) was used to fit the Holland (1980) model to the GEOSAT wind observations, yielding the optimal estimate of R. A histogram showing the estimated values of R is shown in Fig. 1. An example of the agreement between the GEOSAT observations of wind speed and the optimal Holland (1980) model results are shown in Fig. 2. To aid comparison of hurricanes within the data set, a simple co-ordinate transformation was performed to ensure the direction of forward movement was the same for all storms. n addition, southern hemisphere storms were mirror reversed to ensure the wind direction circulation was anti-clockwise for all storms (ie. maximum winds to the right of the direction of forward movement). With the co-ordinate system transformed in this manner and with the spatial scale expressed in terms of the radius to maximum winds, R, passes through different hurricanes can be compared. n order to aid such inter-comparisons, the hurricanes within the data base were binned based on their values of V, and po. Figure 3 show two examples of measured values of significant wave height, H, from hurricanes with similar wind field parameters. Figure 3a presents results for passes through three storms with p. = HPa and V = m/s. n contrast, Fig. 3b presents H,, for passes through less intense but faster moving hurricanes (p. = f 2.5 HPa, v, = m/s). The ability to group passes from separate hurricanes with similar wind field parameters yields data on the spatial distribution of the wave height field which has previously not been possible with in situ instruments. Although Fig. 3 is included to give an impression of the data and its consistency, some interesting features of the hurricane wave field are obvious. The wave field is clearly asymmetric with higher waves to the right of the storm centre than to the left. n addition, the central pressure, p. which largely determines the

8 Hurricane generated waves 767 1: Distance along track (km) Fig. 2. A comparison between the wind speed, U,, as observed by GEOSAT and the predictions of the Holland (1980) model for hurricane CO36NO4 (see appendix A). The short line at the bottom of the plot marks the point of closest approach of the satellite ground track to the centre of the hurricane (37.0 km). maximum winds within the hurricane is only one factor in determining the magnitude of the wave heights generated. The group of less intense but more rapidly propagating hurricanes shown in Fig. 3b clearly have higher significant wave heights than the more intense but slowly propagating hurricanes shown in Fig. 3a. 4. PARAMETRC DESCRPTON OF DATA n order to present the data in a concise manner it is convenient to represent the results in terms of the characteristic hurricane parameters. As the parametric model of Young (1988) appears to represent the basic physical quantities essential to the description of the hurricane wind field, this model has been adopted as an initial description of the data. As indicated in section 2, given values of V_ (related to po), V, and R the model of Young (1988) yields an equivalent fetch, F, Equation (l), which can be used in the modified JONSWAP relationship, Equation (3), to determine the maximum significant wave height, fl-. The determination of H, at any other point in the hurricane required the use of an appropriate spatial distribution chart. n the present context we desire to be able to determine the model prediction of H, at each location for which there exists a GEOSAT observation. This is typically of order 200 points for each of the 100 hurricanes in the data base. n order to process this quantity of data the full set of spatial distribution diagrams presented by Young (1988) were digitized, enabling the full model predictions to be performed in an automated fashion. n order to assess model performance against the GEOSAT data, the following error statistics were defined

9 R. Young and G. P. Burchell C008Ni 2 - H= 4.4 m C045N04 - H= 4.7 m C050Nll - H= 6.4 m R=59.6 km C019N04 - H= 7.2 m R=39.4 km (a) C099N04 - H= 7.2 m R=90.73 km C083N12 - H= 4.4 m R=80.41 km R=73.48 km (b) R=87.77 km Fig. 3. Values of observed significant wave height along the GEOSAT ground track. The ground track is shown by the thick line. The significant wave height is proportional to the magnitude of the shaded region measured perpendicular to the ground track. The radial grid is expressed in term of the radius to maximum winds with radial lines being drawn every 2R. The hurricane reference numbers are shown at the top of each panel (see appendix A), along with the maximum recorded significant wave height. The value of radius to maximum winds is shown at the bottom of each panel. The point along the ground track where the maximum significant wave height was recorded is shown by the asterisk. All hurricanes have been rotated so that they propagate to the right as shown by the arrow and converted so as to be in a northern hemisphere configuration (maximum wind to the right of propagation direction). The hurricanes have been grouped based on their respective wind field parameters. The hurricanes in group (a) are within the parameter range p0 = f 2.5 HPa and V, = 2.6 f 0.7 m/s whereas those in group (b) are p0 = HPa and Vfm = 6.8 f 0.7 m/s. RMS = N where &= (HY - Hyd) H s and N is the number of GEOSAT observations of H, for that hurricane, WY= is the value of H, as measured by the GEOSAT satellite and c d is the corresponding value of H, predicted by the Young (1988) model. The basic premise of the Young (1988) model is that H, is a function of both V_, and V,. n order to investigate this premise, the values of Bias obtained from (8) are shown in Fig. 4 as a function of V,,,,, and V. A negative Bias indicates that the model overpredicts the values of H,y whereas a positive Bias indicates the model underpredicts H,. For clarity the negative and positive values have been plotted in separate panels in Fig. 4. Although there is scatter in the data, a clear trend emerges. The model underpredicts H,

10 Hurricane generated waves 769 (a) -ve Bias - Overprediction 14 (b) +ve Bias - Underprediction / U V,, (m/s) V,, (m/s) Fig. 4. Values of the Bias, see Equation (8), for each hurricane as a function of V,, and V,. Panel (a) shows negative values of Bias whilst panel (b) shows positive values. The size of the symbols is proportional to the magnitude of the Bias. for small V,, and large V and overpredicts H,y for large V,_ and small V m. The diagonal line shown on Fig. 4 represents an approximate delineation between these two regions. This systematic trend in the Bias indicates a systematic error in the equivalent fetch, F as predicted by Equation (1). The values of F above the diagonal appear too small whilst those below this line appear too large. n view of the scatter in the data only the lowest order correction to F appears warranted. One such correction would involve a factor with which to multiply Equation (1) in order to generated values of F more consistent with the data. The correction factor should have a value of one along the diagonal shown in Fig. 4 and, to the lowest order, would vary linearly away from this line. The slope of this correction, which takes the form of a plane in two-dimensional V,,, - V,, space, can then be determined to yield optimal agreement with the GEOSAT data. With the diagonal defining a line along which the correction plane takes a value of one, only the value of the plane at one other point is required to fully define the equation to the plane. For convenience, the value of the plane (called =o) at the point V max = 6Om/s, Vfi = 0 m/s has been adopted. Hence, the diagonal represents a hinge about which the plane rotates as the value o changes. A value of o = indicates a horizontal surface of uniform value one (ie. no correction to the original values of F). Values of o < 1 would indicate a decrease in F below the diagonal and an increase above (ie. the desired result). As w is varied both the Bias and RMS errors will change. The optimal solution should yield the minimum values of both these quantities averaged over the full data set. As an indication of the improvement in the model, additional error statistics are defined RMS = t 5 RMSi j=l Bias = & 5 Biasj j=l (11)

11 710. R. Young and G. P. Burchell - - where RMS and Bias represent the average RMS error and average Bias, respectively for the full data set and M is equal to the number of hurricanes in the data set (100 in this case). Figure 5 shows the variation in E and RMS as the slope of the correction plane, as represented by w, is varied. The optimal result is achieved for a value of o slightly less than zero. Such a result is physically unrealistic as it implies negative values of F and hence H, for large V_ and small V, (ie. lower right corner of Fig. 4). ndeed, even small positive values of o would imply that for a stationary or slowly moving hurricane, as V_ increases H, would increase to some point and then decrease. As there is no data, including the present, to support such a result it seems unrealistic. The fact that the optimal correction to the model yields these unrealistic results is an indication that (a) the data set is scattered, showing the natural variability of hurricane wind fields and (b) that although the present data set is extensive, it is still lacking in some regions of the parameter space. To overcome these problems two side conditions are imposed on the optimization: (a) the equivalent fetch should not be negative and (b) for constant V as V_ increases i, should not decrease. With the inclusion of these side conditions an optimal result is achieved with a value of o = The equation to the plane representing the correction factor is c = -O.OlSV,, + o.o431v, (12) where V_ and V, have units of [m/s] and C is a dimensionless correction factor to be applied to Equation (1) r 1 +Bias RMS 0.44;, R 8 --m m m t * + * % m ( + T + * x * m '+ %%% , Fig. 5. Values of RMS (see Equation (10)) and & (see Equation (11)) as a function of the parameter O. The vertical solid line at o = 1 represents no modification to the original model of (Young (1988)). The dashed vertical line represents the optimum value of o with the inclusion of the side conditions. W * x m at m +

12 Hurricane generated waves 711 : V,, Ws) Fig. 6. (a) Contours of the equivalent fetch, F as a function of maximum wind velocity within the hurricane, V_ and velocity of forward movement, Vh as predicted by the model of Young Contours of the equivalent fetch, F as a function of maximum wind velocity witbin the hurricane, V,, and velocity of forward movement, V after application of the correction factor, C, (see Equation (12)) to the model of Young (1988).

13 172. R. Young and G. P. Burchell Figure 6 shows a comparison between values of equivalent fetch, F obtained from the original model of Young (1988) compared with those obtained after application of the correction factor C, (12). The dependence of F on V,,, and V,, is appreciably changed. n particular, in the original model F was a monotonically increasing function of V,,, for constant V,. The GEOSAT data indicates that this is not always the case. n some regions of the parameter space, for constant V, F firstly increases as a function of V,, but then decreases. Due to the nature of the JONSWAP function Equation (3), however, H, continues to increase. ndeed, this was one of the side conditions imposed in the determination of the correction factor. 5. CONCLUSONS The data presented in this paper represents the most comprehensive set of observations of the significant wave height distribution within hurricanes gathered to date. Data have been obtained from 100 hurricanes covering a wide range of wind field parameters. n addition, the data are in the form of near instantaneous cross-sections across the twodimensional hurricane wave field. Such data are far easier to interpret than data obtained from a fixed in situ instrument. Although the hurricane may move past such an instrument yielding similar data to that obtained here, it does so over a number of days, during which time the parameters of the hurricane wind field are seldom constant. The data provide a confirmation that both the maximum wind speed in the hurricane, V,,,r and the velocity of forward movement, V, play significant roles in determining the significant wave height, H,. The dependence on these two parameters proposed by Young (1988) on the basis of results from a spectral wave model have been found to be systematically biased. A simple correction has, however, been proposed to overcome this bias. Although the parametric representation of the data proposed here yields results which are, in the mean, consistent with the observed data base there is significant scatter in the data. This is attributed to the natural variability of hurricane wind fields and to the difficulty of accurately determining the wind field parameters. Wind field models such as those of Holland (1980) present a very idealized representation of the flow in hurricanes and there is much variability about this mean representation. Finally, although the data set presented here is much more comprehensive than has been available to date, it is still deficient in many respects. t is desired to investigate the twodimensional wave field which is itself a function of three hurricane wind field parameters V,,,, V and R. To fully define this five-dimensional space requires an enormous quantity of data. n addition, the GEOSAT altimeter data presented here provides no information on wave period of direction of propagation, both of which are required to obtain a full understanding of the wave field. As the quantity of available satellite data continues to grow, these addition questions may be answered. REFERENCES Atkinson, G.D. and Holliday, C.R Tropical cyclone minimum sea level pressure-maximum sustained wind relationship for western North Pacific. Mon. Weather Rev. 105, Bea, R.G Gulf of Mexico hurricane wave heights, 6th Offshore Technology Conf., Houston, OTC, Beal, R.C., Gerling, T.W., rvine, D.E., Monaldo, F.M. and Tilley, D.G Spatial variations of ocean wave directional spectra from the Seasat Synthetic Aperture Radar. J. Geophys. Res. 91, Black, J.L Hurricane Eloise directional wave energy spectra, 1 lth Offshore Technology Conf., Houston, OTC, Bretschneider, C.L Hurricane design-wave practices. Trans. ASCE 124,

14 Hurricane generated waves 173 Bretschneider, CL A non-dimensional stationary hurricane wave model, 4th Offshore Technology Conf., Houston, OTC, Cardone, V.J., Ross, D.B., Ahrens, M.R An experiment in forecasting hurricane generated sea states, Proc. 1 lth Tech. Conf. on Hurricanes and Tropical Met., Miami. Carter, D.J.T., Challenor, PG. and Srokosz, M.A An assessment of Geosat wave height and wind speed measurements. J. Geophys. Res. 97, l Dobson, E., Monaldo, F. and Goldhirsh, J Validation of Geosat Altimeter-derived wind speeds and significant wave heights using buoy data. J. Geophys. Res. 92, l Donoso, M.C.., Le Mehaute, B. and Long, R.B Data base of maximum sea states during hurricanes. J. Waters. Port Coastal Ocean Eng., ASCE 113, 31 l-326. Elachi, C., Thompson, T.W. and King, D.B Observations of the ocean wave pattern under Hurricane Gloria with Synthetic Aperture Radar. Science 198, Forristall, G.Z., Ward, E.G., Cardone, V.J. and Borgmann, L.E The directional spectra and kinematics of surface gravity waves in Tropical Storm Delia. J. Phys. Oceanogr. 8, Glazman, R.E. and Pilorz, S.H Effects of sea maturity on satellite altimeter measurements. J. Geophys. Res. 95, Gonzalez, F.., Thompson, T.W., Brown, W.E. and Weissman, D.E Seasat wind and wave observations of Northeast Pacific Hurricane va, August 13, J. Geophys. Res. 87, Graham, H.E. and Hudson, G.N Surface winds near the center of hurricanes (and other cyclones), NHRP Rep. 39, Govt. Print. Office, 200. Gray, W.M. and Shea, D.J The hurricane s inner core region, : Thermal stability and dynamic characteristics. J. Atmos. Sci. 30, Guillaume, A. and Mognard, N.M A new method for the validation of altimeter-derived sea state parameters with results from wind and wave models. J. Geophys. Rex 97, Hamilton, R.C. and Ward, E.G Ocean Data Gathering Program-Quality and reduction of data, 6th Offshore Technology Conf., Houston, OTC 2108-A. Harper, B.A., Mason, L.B. and Bode, L Tropical Cyclone Orson-A Severe test for modelling, 1 lth Aust. Conf. Coastal and Ocean Eng., Townsville, Hasselmann, K Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP). Dtsch. Hydrogh. Z. Suppl. A 8, 12. Holland, G.J An analytical model of the wind and pressure profiles in hurricanes. Mon. Weather Rev. 108, Holt, B. and Gonzalez, F SR-B Observations of dominant ocean waves near Hurricane Josephine. J. Geophys. Res. 91, jima, T., Soejima, T. and Matsuo, T Ocean wave distribution in typhoon area, Proc. Coastal Eng. in Japan, 2, King, D.B. and Shemdin, O.H Radar observations of hurricane wave directions, 16th nt. Conf. on Coastal Eng., Hamburg, McLeish, W. and Ross, D.B maging radar observations of directional properties of ocean waves,./. Geophys. Res. 88, NOAA Data Buoy Office Practical experience with buoys developed by the NOAA Data Buoy Oflice, US Dept. of Commerce. Patterson, M.M Hindcasting hurricane waves in the Gulf of Mexico, Sot. Pet. Eng., Powell, M.D Evaluations of diagnostic marine boundary layer models applied to hurricanes. Mon. Weather Rev. 108, , Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T Numerical Recipes, Cambridge University Press, 818. Ross, D.B A simplified model for forecasting hurricane generated waves, Bull. A.M.S., 113. Schloemer, R.W Analysis and synthesis of hurricane wind patterns over Lake Okechobee, FL, Hydromet Rep. 31, Govt. Print. Office 49. Shapiro, L.J The asymmetric boundary layer flow under a translating hurricane. J, Amro.~. Sci. 40, Shea, D.J. and Gray, W.M The hurricane s inner core region, : Symmetric and asymmetric structure. J. Atmos. Sci. 30, Shemdin, O.H Hurricane waves, storm surge and currents: An assessment of the state of the art, US- South East Asia Symp. on Eng. for Natural Hazards Protection, Manila. Shemdin, O.H Prediction of dominant wave properties ahead of hurricanes, 17th nt. Coastal Eng. Conf., ASCE, Sydney, Shuhy, J.L., Grunes, M.R., Uliana, E.A. and Choy, L.W Comparison of Geosat and ground-truth wind and wave observations: Preliminary results. Johns Hopkins APL Tech. Dig. 8,

15 114. R. Young and G. P. Burchell Simiu, E., Patel, V.C. and Nash, J.F Mean speed profiles of hurricane winds. J. Eng. Mech. Div., ASCE 102, Smith, R.K The surface boundary layer of a hurricane. Tellus 20, Toumadre, J. and Ezraty, R Local climatology of wind and sea state by means of satellite radar altimeter measurements. J. Geophys. Res. 95, Uji, T Numerical estimation of the sea wave in a typhoon area. Papers in Meteorology and Geophysics 26, Wang, G.C Sea level pressure profile and gusts within a typhoon circulation. Mon. Weather Rev. 106, Ward, E.G Ocean Data Gathering Program-An overview, 6th Offshore Technology Conf., Houston, OTC 2108-B. Withee, G.W. and Johnson, A Data report: Buoy observations during Hurricane Eloise (September 19 to October 11, 1975), Environmental Science Div., Data Buoy Office, NOAA, US Dept. of Commerce. Young, LR A shallow water spectral wave model. J. Geophys. Res. 93, Young, LR A parametric hurricane wave prediction model. J. Waterw. Port Coastal Ocean Eng., AXE 114, Young, LR An estimate of the Geosat altimeter wind speed algorithm at high wind speeds. J. Geophys. Res. 98, Young,.R. and Holland, G.J Atlas of the Oceans Wind and Wave Climate, p. 241, Pergamon Press, SBN o APPENDX Table 1. Summary of hurricane parameters in the data set ndex Name Latitude Longitude (deg) (deg) p. (HP4 vfi Ws) R (km) Closest approach to hurricane centre (km) COOlN COO4NO COO4N COO5Nll 15.6 COO5N COO5N COO7NOl 8.4 C007NO C007N C013N C016NOl C016N C016N C019N C019N C019N C020N CO2ONO C021N C025N C026N C028N C029N C029N C031N C032N C033N

16 Hurricane generated waves 775 Table 2. Summary of hurricane parameters in the data set (continued) ndex Name Latitude Longitude (deg) (deg) p. (HPa) q+n (m/s) R (km) Closest approach to hurricane centre (km) C036NO4 C036NlO C038N04 CO39NO3 C039N07 CO40NO 1 CO44N03 CO45N03 CO45N04 CO45NO7 CO46N02 CO47NO2 CO48N04 CO48N05 CO48N07 C050N04 CO5ON 10 C050Nll C059N03 C066N02 CO69N02 C075N05 C075Nll C075N14 C077N05 C077N07 C083Nll C083N12 C083N13 C085N03 C086N07 C088N05 CO9ONOl CO90NlO CO90N14 CO90N17 C093N02 C093N

17 116. R. Young and G. P. Burchell Table 3. Summary of hurricane parameters in the data set (continued) ndex Name Latitude Longitude (deg) (deg) p. (HPa) v, (m/s) R (km) Closest approach to hurricane centre (km) CO94N04 C094N05 C099N02 C099N03 C099N04 ClOON03 C 102N02 Cl02N03 C103N04 C103N08 C103NlO C103N12 C112NOl Cl 12N04 C118N05 C118N08 Cl 19NOl C121N05 C121N07 C121N08 C 122N03 C124N08 C128N05 C131N07 C132NOl C138N02 C140NlO C 143N05 C143N07 C148N18 C 149N03 C 149N06 C149N12 C 150NOO C150N