Explain How Individual Wave Heights Are Measured (Zero-Crossing Method)
explain_wave_height_measurement.RdEducational function explaining how individual wave heights like Hmax are measured, and how this differs from the statistical Hs calculation.
Examples
cat(explain_wave_height_measurement())
#>
#> HOW INDIVIDUAL WAVE HEIGHTS ARE MEASURED: THE ZERO-CROSSING METHOD
#> ===================================================================
#>
#> TWO DIFFERENT CONCEPTS - IMPORTANT DISTINCTION
#> ----------------------------------------------
#> 1. Hs (Significant Wave Height) = STATISTICAL parameter from continuous
#> surface elevation data (4 * standard deviation)
#>
#> 2. Hmax (Maximum Wave Height) = INDIVIDUAL wave height from discrete
#> wave-by-wave analysis using zero-crossing method
#>
#> THE ZERO-CROSSING METHOD
#> ------------------------
#> To measure individual wave heights, we need to define what constitutes
#> a single 'wave'. The standard method is ZERO UP-CROSSING:
#>
#> 1. ZERO UP-CROSSING: A point where the surface elevation rises through
#> the mean level (from below to above zero, after de-meaning)
#>
#> 2. ONE WAVE = The segment between two consecutive zero up-crossings
#>
#> 3. Within each wave segment:
#> - CREST = maximum elevation (highest point)
#> - TROUGH = minimum elevation (lowest point)
#> - WAVE HEIGHT H = Crest - Trough (vertical distance)
#>
#> VISUAL EXAMPLE
#> --------------
#> Crest
#> /\
#> / \
#> / \ <- One complete wave
#> / \
#> ------/--------\-------- Mean level (zero)
#> \ /
#> \ /
#> \ /
#> \/
#> Trough
#>
#> ^ ^
#> | |
#> Zero up-crossing Zero up-crossing
#> (wave starts) (wave ends, next starts)
#>
#> Wave Height H = Crest elevation - Trough elevation
#>
#> HOW Hmax IS DETERMINED
#> ----------------------
#> From a 17.5-minute measurement period:
#>
#> 1. De-mean the surface elevation time series
#> 2. Identify all zero up-crossings
#> 3. For each wave (segment between crossings):
#> - Find the maximum (crest)
#> - Find the minimum (trough)
#> - Calculate H = crest - trough
#> 4. Hmax = maximum of all individual wave heights
#>
#> TYPICAL RESULTS
#> ---------------
#> In a 17.5-minute period with 8-second average wave period:
#> - ~130 individual waves identified
#> - Each has its own height H_i
#> - Hmax is the single largest
#> - H_1/3 (Hs) is the average of the ~43 largest waves
#>
#> RELATIONSHIP BETWEEN Hs AND Hmax
#> --------------------------------
#> For Rayleigh-distributed waves (theoretical):
#> - Hmax/Hs depends on number of waves N
#> - Expected Hmax = Hs * sqrt(ln(N)/2) (approximately)
#> - For N=100 waves: Hmax ~ 1.5 * Hs
#> - For N=1000 waves: Hmax ~ 1.86 * Hs
#>
#> ROGUE WAVE CRITERION
#> --------------------
#> A rogue wave is defined when:
#> Hmax/Hs > 2.0 (or 2.2 in some standards)
#>
#> This exceeds the statistical expectation, suggesting
#> non-linear wave interactions (Benjamin-Feir instability,
#> wave-current interaction, or focusing effects).
#>
#> WHY TWO METHODS EXIST
#> ---------------------
#> 1. SPECTRAL METHOD (Hs = 4*sigma):
#> - Robust to noise
#> - Works with short records
#> - Standard for operational forecasting
#> - Related to wave energy (m0 = sigma^2)
#>
#> 2. ZERO-CROSSING METHOD (Hmax, H_1/3):
#> - Direct physical measurement
#> - Needed for structural design (maximum loads)
#> - Required for rogue wave detection
#> - Historical standard before FFT became practical
#>
#> BOTH METHODS SHOULD AGREE
#> -------------------------
#> For a proper Rayleigh sea, both methods give similar Hs:
#> - Spectral: Hs = 4 * sqrt(m0) = 4 * sigma
#> - Zero-crossing: Hs = H_1/3 (mean of highest third)
#>
#> Disagreement suggests:
#> - Bi-modal sea (swell + wind waves)
#> - Non-linear effects
#> - Data quality issues
#>
#> REFERENCES
#> ----------
#> 1. Tucker, M.J. & Pitt, E.G. (2001). Waves in Ocean Engineering.
#> Elsevier. Chapter 5: Wave statistics.
#>
#> 2. Goda, Y. (2010). Random Seas and Design of Maritime Structures.
#> World Scientific. Chapter 2: Statistical properties.
#>
#> 3. DNV-RP-C205 (2019). Environmental Conditions and Environmental Loads.
#> Section 3.5: Wave parameters.