Wave Reflection Analysis

This tool implements the three-wave-probe reflection analysis used by Lamsal, Haus & Rhode-Barbarigos (2026), An experimental study on wave transmission over submerged SEAHIVE® breakwaters, Coastal Engineering Journal (doi:10.1080/21664250.2026.2661171).

Following the methodology of Goda & Suzuki (1976) and Kobayashi, Cox & Wurjanto (1990), incident and reflected wave heights are separated from co-linear capacitance wave-probe records using linear wave theory. The free surface is modeled at each frequency as a superposition of incident and reflected linear waves; the Fourier coefficients of each gauge are combined to solve a 2×2 system for the incident and reflected amplitudes a_i, a_r: A_j = a_ie^−ikx_j + a_re^+ikx_j. The wave number k follows from the linear dispersion relation ω² = gk tanh(kd), solved by Newton–Raphson iteration from a Fenton–McKee seed. A Bluestein-algorithm DFT handles records of arbitrary length.

The method is valid when the probe spacing Δx satisfies 0.05 ≤ Δx/L ≤ 0.45, where L is the local wavelength. The tool checks this band and the 2×2 inversion conditioning at every frequency and discards bins that fail either test; the fraction of measured spectral energy that survives this filter is reported as the retained-energy fraction. Incident and reflected spectra are integrated to the spectral significant wave heights H_m0 = 4√m₀, and the coefficients are defined as K_r = H_r/H_i and (when two arrays are present) K_t = H_i,2/H_i,1.

Method selection. The default analysis is the redundant three-probe array of spectral.js (reflectionAnalysis): the three probe pairs are averaged at every valid frequency, and the result is reported as long as it retains at least 80 % of the spectral energy. When the three-probe inversion is ill-conditioned, the tool falls back to the best admissible two-probe pair and flags the row with a small "2P" badge in the results table (otherwise a "3P" badge is shown). The Analysis method dropdown in the settings panel lets the user override this selection: force three-probe with no fallback, force two-probe on the best pair, or force a specific two-probe pair (1–2, 1–3 or 2–3) — useful for cross-checking a published result with a different method.

Input files: 2, 3 or 6 numeric columns, detected automatically. Two columns run two-probe Goda–Suzuki on the single pair (only X₁₂ is used); three columns run a three-probe array (with automatic two-probe fallback); six columns run two three-probe arrays in the same file (channels 1–3 seaward, channels 4–6 shoreward). Water depth is set below and may be overridden per file (auto-read from "Depth=d" in the file name when present). The browser tool calls the same per-frequency Goda–Suzuki routines as the Python WaveLabX package (two_probe_goda, three_probe_array and reflection_analysis); an automated cross-implementation test in the WaveLabX test suite confirms that the two interfaces produce numerically equivalent results on identical inputs.