Relation Between Significant Wave Height and Wind Speed during Hurricanes

Professor S. A. Hsu
Louisiana State University
Email: Email: sahsu@lsu.edu

In the December 2015 Issue of this Journal, the author presented following formulas, for fetch-limited seas,

Formula 1

And for duration-limited seas,

Formula 2

Here U10 is the wind speed at 10 meters in m/s, Hs is the significant wave height in meters and Tp is the dominant wave period in seconds.

In this research note, more analyses of the relation between Hs and Tp are conducted. Our results are presented in Figure 1. The datasets are based on simultaneous measurements of Hs and Tp during Hurricanes Kate (1985), Lili (2002), Rita (2005) and Wilma (2005) by the National Data Buoy Center (NDBC) (see http://ndbc.noaa.gov and for hurricane tracks, see http://nhc.noaa.gov ). Figure 1 shows that, approximately,

Formula 3
Figure 1

Figure 1. Relation between Tp and Hs during four hurricanes.


Further verification of Equation (3) during Hurricanes Ivan (2004) and Katrina (2005) near Buoy 42040 is shown in Figure 2. The reason to employ the datasets from Ivan and Katrina is because they contain some extreme measurements of Hs and Tp.

Figure 2

Figure 2. Verification of Equation (3) during Ivan and Katrina near Buoy 42040.


Now, substituting Equations (3) into (1) or (2), we find that U10 and Hs are linearly related. However, in order to minimizing the effects of swell, the wind seas usually start when U10 > 7 m/s. Therefore, from statistical viewpoints, we need,

Formula 4

Here, "a" and "b" are the slope and the intercept of this proposed linear relation between Hs and U10, respectively. Note that these coefficients can vary with different storms and need to be determined from field measurements.

Now, on the basis of the datasets provided by the NDBC (http://ndbc.noaa.gov ) at Buoy 42003, which was located on the right-hand side the storms' track during Hurricanes Ivan (2004) and Katrina (2005), our result to verify Equation (4) is presented in Figure 3, which shows that

Formula 5

Since the correlation coefficient R = 96% is very high and the coefficient of determination (R2) = 0.92, meaning that 92% of the linear variation between Hs and U10 can be explained, Equation (5) is thus recommended for estimating Hs from U10 or vice versa.

Figure 3

Figure 3. Verification of the linear relation between Hs and U10 as suggested in Equation (4) during Ivan and Katrina near Buoy 42003.


Acknowledgements:

Buoy measurements provided by NDBC are greatly appreciated.

Back to top