Short-Term Probability of Maximum Wave Height Exceedance (Forristall)

Computes P(H_max > h | H_s, T_z, D) for a stationary sea state of significant wave height H_s, mean zero-crossing period T_z, lasting duration D, using the Forristall (1978) Weibull short-term distribution for individual wave heights.

Forristall (1978) gives P(H > h | H_s) = exp(-(h / (alpha * H_s))^beta) with alpha = 0.681 and beta = 2.126 (calibrated on Gulf of Mexico storm data). For N independent waves in the window, P(H_max <= h) = (1 - P(H > h))^N, so P(H_max > h) = 1 - (1 - exp(-(h/(alpha*H_s))^beta))^N, with N = D / T_z.

Reference: Forristall, G. Z. (1978). On the statistical distribution of wave heights in a storm. Journal of Geophysical Research, 83(C5), 2353-2358.

Usage

p_hmax_exceedance(h, hs, tz, duration_s = 3600, alpha = 0.681, beta = 2.126)

Arguments

h

Numeric vector of wave heights to evaluate (m).

hs

Numeric significant wave height (m), length 1 or length(h).

tz

Numeric mean zero-crossing period (s), length 1 or length(h).

duration_s

Numeric window duration in seconds (default 3600 = 1 hour).

alpha

Forristall scale parameter (default 0.681).

beta

Forristall shape parameter (default 2.126).

Value

Numeric vector of P(H_max > h) values in [0, 1]. Returns NA where hs <= 0, tz <= 0, or any input is NA.

See also

Other storm-alert: beaufort_to_description(), create_storm_alert_email(), detect_storm_events(), fetch_all_forecasts(), fetch_all_marine_forecasts(), fetch_met_eireann_warnings(), fetch_open_meteo_forecast(), fetch_open_meteo_marine(), knots_to_beaufort(), send_storm_alert(), summarise_forecast_rogue_risk()

Examples

# Probability of a 20 m wave during a 1-hour window with Hs = 10 m, Tz = 9 s
p_hmax_exceedance(20, hs = 10, tz = 9, duration_s = 3600)
#> [1] 0.02028495