Development of an over-water gust factor model for hurricane conditions

One measure of the variability of surface winds in a hurricane is the gust factor, G, defined as the ratio of the peak gust, averaged over time t, to the mean wind averaged over some longer period, T. Engineers frequently use the gust factor to determine wind loading conditions for design, while a secondary issue is the standardisation of winds averaged over different time periods to a common averaging period. To date very little information has been gathered on gust factors in hurricanes due to the scarcity of observations, Black(1993) providing a useful summary. In this paper we examine the possibility of developing a gust factor model, using extreme value statistics, for over-water hurricane conditions.

We start by assuming that the deviation of the wind fluctuations, averaged over time t, from a longer-term mean, averaged over time T, are Gaussian in nature. This allows us to write an expression for the gust factor of the form:

G(t,T)=1 + k(t,T)s (t,T)

(1)

where s (t,T) is a measure of the standard deviation of the fluctuations about a longer-term mean, normalised by the mean wind over time T, and k(t,T) is the standard normal extreme deviate associated with an exceedance probability of t/T. In general we note that the value of k(t,T) will be dependent on the criteria used to define the normal extreme distribution (i.e. median, average, 95% percentile, etc.). In this case we have chosen to use the average value associated with an exceedance probability of t/T.

Initial results calculated using a digital time series recorded by the US Army’s Field Research Facility (FRF) at Duck, NC, during the passage of Hurricane Bonnie in August 1998 allow us to firstly show that the deviations of the short-term fluctuations about a longer-term mean are, to a good approximation, Gaussian in nature. We also find that average values for k(t,T) fall on the curve defining the 60% percentile of the normal extreme distribution, close to the expected values for the average of the normal extreme. Finally we note that s (t,T) is dependent on both the choice of averaging periods, and the wind speed, a trend which is reflected in the behaviour of the observed gust factors with increasing winds.

Work on analysing several other digital time series recorded by the FRF in a similar fashion is currently in progress. We hope to supplement this data set with a larger data set of over-water gust factors derived from hurricane winds recorded by NOAA C-MAN and buoy stations over the period 1984-1998. While there is considerable scatter for low winds (< 10 m/sec), for winds above 10 m/sec, gust factors measured by both the buoy and C-MAN stations show evidence of the previously observed trend with increasing winds. Furthermore, this data set shows no dependence on atmospheric stability as measured by conditions at the air-sea interface.