MHKiT Upcrossing Analysis Example

The following example shows how to perform an upcrossing analysis on a surface elevation trace and plot quantities of interest (such as wave heights, periods, and crest exceedance probabilities).

% Clear variables and close figures
clear; close all;

Compute the Surface Elevation

% Define Peak Period and Significant Wave Height

Tp = 10; % Peak period in seconds

Hs = 2.5; % Significant wave height in meters

gamma = 3.3; % JONSWAP

% Define Frequency Vector using a return period of 1 hour

Tr = 3600; % Return period in seconds (1 hour)

df = 1 / Tr; % Frequency step size in Hz

f = 0:df:1; % Frequency vector

% Calculate JONSWAP Spectrum

spec = jonswap_spectrum(f, Tp, Hs, gamma);

% Sampling frequency for time vector

fs = 10.0; % Sampling frequency in Hz

t = 0:1/fs:Tr-1/fs; % Time vector

% Generate Surface Elevation

eta = surface_elevation(spec, t, "seed", 123);

% Plot Surface Elevation

figure('Position', [100, 100, 1600, 600]);

plot(eta.time, eta.elevation);

xlabel('Time (s)','interpreter','latex');

ylabel('$\eta (m)$','interpreter','latex');

title(['Surface Elevation for Tp = ' num2str(Tp) 's, Hs = ' num2str(Hs) 'm']);

grid on; set(gca,'TickLabelInterpreter','latex')

xlim([eta.time(1) eta.time(end)])

Plot the Individual Wave Heights and Periods

waveHeights = uc_heights(t, eta.elevation);

wavePeriods = uc_periods(t, eta.elevation);

figure('Position', [100, 100, 1600, 600]);

plot(wavePeriods, waveHeights, 'o');

xlabel('Zero Crossing Period (s)','interpreter','latex');

ylabel('Wave Height (m)','interpreter','latex');

grid on;set(gca,'TickLabelInterpreter','latex')

Plot the Crest Probability of Exceedance Distribution

crests = uc_peaks(t, eta.elevation);

crests_sorted = sort(crests);

% Number of crests

N = numel(crests_sorted);

% Exceedance probability (ascending crests)

Q = (N:-1:1) / N;

% Plot Exceedance Probability

figure('Position', [100, 100, 1600, 600]);

semilogy(crests_sorted, Q, 'o');

xlabel('Crest Height (m)','interpreter','latex');

ylabel('P(Exceedance)','interpreter','latex');

grid on; set(gca,'TickLabelInterpreter','latex');