Operational Formulas for Estimating Wind and Waves During a Hurricane

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

In the December 2006 issue of this journal Hsu (2006a and b) proposed several formulas for operational use, Eqs.(1) through (5) as follows:

Equation 1(1)
Equation 2(2)
Equation 3(3)
Equation 4(4)
Equation 5(5)
Equation 6(6)

In April 2007, Powell and Reinhold (2007) published their paper which presented a list of 19 hurricanes with four major parameters including the radius of maximum wind (Rmax), minimum sea-level pressure (Pmin), maximum sustained wind (Vmax = U10 max) and the distance from the eye where 34 kts (or 17 m/s) winds were located (R34 kts). These parameters are listed here in Table 1. Using this information, Eqs.(2) and (5) may be further validated.

First, to verify Eq.(2), we divide the left hand side by the argument containing Pmin on the right. The ratio (A) should be around 6.3 if it is to be acceptable. From Table 1, this value is found. Thus we can say that Eq.(2) is further verified.

Now, to verify Eq.(5), we need to get Pr and Rr which are the pressure and corresponding distance at r. Since a tropical storm begins at 34 kts or 17 m/s, we substitute U10 = 17 m/s into Eq.(1) and get Pr = 1006 hPa. Then we substitute Rr = R34 kts and Pr = 1006 hPa into Eq.(5). Using the dataset provided in Table 1, the ratio (B) of the argument on the left hand side and that on the right should be approximately one if Eq.(5) is operationally useful. It can be seen that B = 1.0. For operational applications, Eq.(5) is converted to Eq.(6). Since R34 kts and Pmin are both available from the Tropical Cyclone Advisories issued by the National Hurricane Center or Joint Typhoon Warning Center, the wave height at any distance r from the eye can be estimated using Eq.(3) with the input of Eqs.(4) and (6).

References

Hsu, S. A., (2006a), Nowcasting the significant wave height during a hurricane. Mariners Weather Log, 50(3), December 2006, pp. 6-7.

Hsu, S. A., (2006b), Estimating the wind speed during a hurricane at sea, Mariners Weather Log, 50(3), December 2006, pp. 8-9.

Powell, M. D. and Reinhold, T. A., 2007, Tropical cyclone destructive potential by integrated kinetic energy, Bulletin American Meteorological Society, 88(4), April 2007, pp. 513-526.

Table 1. Validations of Eqs. (2) and (5) based on data provided in Powell and Reinhold (2007).

Storm Year Month Time Rmax Pmin Vmax R34 kt A B
    Day UTC (km) (hPa) (m/s) (km) Eq.2 Eq.5
Andrew 1992 24-Aug 900 19 922 68 191 7.1 1.2
Camille 1969 18-Aug 430 15 909 65 230 6.4 0.9
Charley 2004 13-Aug 1930 7 941 63 156 7.4 0.4
Dennis 2005 10-Jul 1930 9 946 51 296 6.2 0.3
Emily 2005 20-Jul 130 24 948 54 291 6.7 0.7
Fabian 2003 5-Sep 1330 67 941 51 380 6 1.7
Frances 2004 5-Sep 130 52 960 46 319 6.3 1.2
Hugo 1989 22-Sep 400 37 934 58 317 6.5 1.3
Iris 2001 9-Oct 130 8 948 43 165 5.3 0.4
Isabel 2003 18-Sep 1630 87 957 47 532 6.3 1.2
Ivan (AL) 2004 16-Sep 730 35 946 49 326 6 1
Ivan (Jamaica) 2004 11-Sep 1330 17 925 70 314 7.5 0.7
Jeanne 2004 26-Sep 330 48 950 46 317 5.8 1.3
Katrina (FL) 2005 25-Aug 2230 15 984 33 115 6.1 0.5
Katrina (LA) 2005 29-Aug 1200 65 920 52 454 5.4 1.8
Katrina Peak Wind 2005 28-Aug 1200 26 909 71 349 7 1.1
Keith (Belize) 2000 1-Oct 2230 19 959 50 154 6.8 0.9
Michelle 2001 4-Nov 1930 28 949 50 335 6.3 0.7
Opal 1995 4-Oct 2235 98 942 50 353 5.9 2.7
Rita 2005 24-Sep 730 30 937 49 357 5.6 0.9
Wilma Peak Wind 2005 19-Oct 1930 7 892 62 326 5.6 0.4
Wilma (FL) 2005 24-Oct 1030 72 951 51 380 6.5 1.6
Wilma (Mexico) 2005 22-Oct 130 20 930 59 394 6.5 0.6
Mean  6.3 1.0
Standard Deviation  0.59 0.56