# Wind-wave prediction equations for probabilistic offshore hurricane hazard analysis

## Abstract

The evaluation of natural catastrophe risk to structures often includes consideration of uncertainty in predictions of some measure of the intensity of the hazard caused by the catastrophe. For example, in the well-established method of probabilistic seismic hazard analysis, uncertainty in the intensity measure for the ground motion is considered through so-called ground motion prediction equations, which predict ground motion intensity and uncertainty as a function of earthquake characteristics. An analogous method for evaluating hurricane risk to offshore structures, referred to herein as probabilistic offshore hurricane hazard analysis, has not been studied extensively, and analogous equations do not exist to predict offshore hurricane wind and wave intensity and uncertainty as a function of hurricane characteristics. Such equations, termed here as wind and wave prediction equations (WWPEs), are developed in this paper by comparing wind and wave estimates from parametric models with corresponding measurements during historical hurricanes from 22 offshore buoys maintained as part of the National Data Buoy Center and located near the US Atlantic and Gulf of Mexico coasts. The considered buoys include observations from 27 historical hurricanes spanning from 1999 to 2012. The 27 hurricanes are characterized by their eye position, translation speed, central pressure, radius to maximum winds, maximum wind speed, Holland B parameter and direction. Most of these parameters are provided for historical hurricanes by the National Hurricane Center’s H*Wind program. The exception is the Holland B parameter, which is calculated using a best-fit procedure based on H*Wind’s surface wind reanalyses. The formulation of the WWPEs is based on two parametric models: the Holland model to estimate hurricane winds and Young’s model to estimate hurricane-induced waves. Model predictions are made for the 27 considered historical hurricanes, and bias and uncertainty of these predictions are characterized by comparing predictions with measurements from buoys. The significance of including uncertainty in the WWPEs is evaluated by applying the WWPEs to a 100,000-year stochastic catalog of synthetic hurricanes at three locations near the US Atlantic coast. The limitations of this approach and remaining work are also discussed.

## Keywords

Probabilistic offshore hurricane hazard analysis Hurricane risk Uncertainty quantification Offshore structures## List of symbols

- B
Pressure profile exponent (i.e., the Holland B parameter)

*F*_{X}Cumulative probability density function of random variable

*X*- GMPE
Ground motion prediction equation

*L*Fetch length

- MRP
Mean return period

*P*_{c}Hurricane central pressure

*P*_{n}Ambient pressure

- PGA
Peak ground acceleration

- PGV
Peak ground velocity

- POHHA
Probabilistic offshore hurricane hazard analysis

- PSHA
Probabilistic seismic hazard analysis

*R*_{max}Hurricane radius of maximum wind speed

*R*′Effective hurricane radius

*S*_{a}Spectral acceleration

*V*_{g}Sustained 10-min wind speed at gradient level

*V*_{max}Hurricane maximum wind speed

*V*_{tr}Hurricane translation speed

- WWPE
Wind and wave prediction equation

*d*Water depth

*f*_{X}Probability density function of random variable

*X**f*_{c}Coriolis parameter

*g*Acceleration due to gravity

*r*Radial distance measured from the center of the hurricane eye

*x*Variable representing modeled environmental intensities (e.g., sustained 1-min wind speed at 10-m elevation

*V*or significant wave height*H*_{s})*x*_{c}Variable representing bias-corrected modeled environmental intensities (e.g., bias-corrected sustained 1-min wind speed at 10-m elevation

*V*_{c}or bias-corrected significant wave height*H*_{s,c})- \(\hat{x}\)
Variable representing measurements or probabilistic realizations of environmental intensities (e.g., sustained wind speed \(\hat{V}\) or significant wave height \(\hat{H}_{\text{s}}\))

- \(\bar{y}\)
Vector of parameters characterizing a hurricane at a particular instant

- Φ
Standard normal cumulative probability distribution function

*ε*_{X}Normally distributed random variable representing the difference between the logarithms of measured and modeled values for

*X*. Positive values correspond to measured values greater than modeled values*θ*Hurricane direction angle measured relative to north (clockwise positive)

*μ*Mean

*ν*Annual rate of occurrence

*ρ*Air density

*σ*Standard deviation

## Notes

### Acknowledgments

This work is based upon work supported by the National Science Foundation under Grants CMMI-1234560 and CMMI-1234656, the Massachusetts Clean Energy Center, Northeastern University, and the University of Massachusetts, Amherst. Any opinions, findings and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the view of the National Science Foundation or other funding agencies.

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