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();
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();
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();
semilogy(crests_sorted, Q, 'o');
xlabel('Crest Height (m)','interpreter','latex');
ylabel('P(Exceedance)','interpreter','latex');
grid on; set(gca,'TickLabelInterpreter','latex');
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