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Sub-skill of wave-theory: 6. Extreme Value Analysis.
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| name | wave-theory-6-extreme-value-analysis |
| description | Sub-skill of wave-theory: 6. Extreme Value Analysis. |
| version | 1.0.0 |
| category | engineering |
| type | reference |
| scripts_exempt | true |
Design Wave from Return Period:
def calculate_extreme_wave_height(
return_period_years: float,
Hs_annual_max: np.ndarray = None,
distribution: str = 'weibull'
) -> dict:
"""
Calculate design wave height for given return period.
Args:
return_period_years: Return period (years)
Hs_annual_max: Array of annual maximum Hs values
distribution: 'weibull' or 'gumbel'
Returns:
Extreme wave height statistics
"""
from scipy.stats import weibull_min, gumbel_r
if Hs_annual_max is None:
# Example data: 25 years of annual maxima
np.random.seed(42)
Hs_annual_max = weibull_min.rvs(c=2, scale=10, size=25)
# Fit distribution
if distribution == 'weibull':
params = weibull_min.fit(Hs_annual_max)
c, loc, scale = params
dist = weibull_min(c, loc, scale)
elif distribution == 'gumbel':
loc, scale = gumbel_r.fit(Hs_annual_max)
dist = gumbel_r(loc, scale)
else:
raise ValueError("Unknown distribution")
# Exceedance probability for return period
exceedance_prob = 1 / return_period_years
# Extreme value
Hs_extreme = dist.ppf(1 - exceedance_prob)
# Confidence intervals (simplified)
Hs_lower = dist.ppf(1 - exceedance_prob - 0.1)
Hs_upper = dist.ppf(1 - exceedance_prob + 0.1)
return {
'return_period_years': return_period_years,
'Hs_extreme': Hs_extreme,
'Hs_lower_bound': Hs_lower,
'Hs_upper_bound': Hs_upper,
'distribution': distribution,
'exceedance_probability': exceedance_prob
}
# Example: 100-year return period
extreme_100yr = calculate_extreme_wave_height(
return_period_years=100,
distribution='weibull'
)
print(f"100-Year Wave:")
print(f" Hs: {extreme_100yr['Hs_extreme']:.2f} m")
print(f" Range: {extreme_100yr['Hs_lower_bound']:.2f} - {extreme_100yr['Hs_upper_bound']:.2f} m")