Synthesize ocean ambient noise as a sum of four physical mechanisms: turbulence, distant shipping, wind/surface, and Mellen thermal. Coates 1989 / Stojanovic 2007 closed-form fit to Wenz 1962 Figure 13.
Ocean ambient noise is not a single sound. It is a sum of identifiable physical mechanisms, each with a distinct frequency dependence and physical driver. Wenz (1962) compiled the first systematic decomposition, dividing prevailing noise into four broad bands: turbulent pressure (below ~10 Hz, near-field hydrodynamic flow noise on the sensor itself rather than propagating sound — what acousticians call "pseudo-sound"), distant shipping (10–300 Hz, anthropogenic, dominated by propeller cavitation and machinery from ships over the horizon), wind and surface processes (100 Hz to 30 kHz, radiated by breaking waves and the bubble clouds they inject into the upper few metres of water), and thermal noise (above 50 kHz, the absolute lower bound set by the kT kinetic energy of water molecules buffeting the hydrophone — equipartition theorem).
This demo synthesizes each component using the Coates 1989 / Stojanovic 2007 closed-form parameterization, a standard engineering fit to Wenz's Figure 13 widely used in the underwater communications literature. The formulas reproduce the shapes and qualitative slider responses of the Wenz curves; they are within about 5–10 dB of any specific digitization of Wenz Figure 13 at the lowest wind speeds (modern measurements such as Hildebrand 2021 give somewhat higher levels than the original Wenz figure at low Beaufort numbers, partially closing the gap).
The plot shows what the listener at the chosen depth would hear: four dashed lines, one per mechanism, summed (in linear power) into the solid black "theoretical" curve. The thin gray "live measured" trace is the actual audio output read back from an AnalyserNode — with a correct synthesis chain it should sit right on top of the black curve across the audible band. Mute or solo individual components to hear what each one sounds like in isolation. With shipping off and wind speed below 1 m/s, you hear essentially only the thermal floor (high-frequency hiss at the limit of equipartition). Turn shipping back on and push the density slider toward s = 1 (or click Busy Harbor) and the rumble of distant traffic emerges at 30–80 Hz. Push wind toward 15 m/s (Beaufort 7) and broadband noise from breaking surface waves takes over the entire mid-band. Then crank the depth slider up and listen to the high-frequency content roll off while the shipping rumble persists.
Each mechanism is driven by its own independent stream of unit-variance Gaussian white noise (so the four sources are uncorrelated, as they are physically). Each stream is shaped by a linear-phase FIR filter whose magnitude response is 10NL(f)/20, where NL(f) is the listener-level spectrum for that mechanism — i.e. the Wenz surface spectrum minus the depth-absorption correction described below (so at depth = 0 it is exactly the Wenz surface spectrum). The four filtered streams are summed and sent through a master gain and a brick-wall safety limiter to the speakers. Slider drag triggers a coalesced FIR redesign that hot-swaps onto a silent parallel ConvolverNode, then crossfades over 60 ms, keeping the audio click-free during continuous parameter changes.
Wind speed. Speed of the wind blowing over the ocean surface, in m/s (or equivalently Beaufort number). Drives the surface noise band (100 Hz – 30 kHz). Breaking waves and the bubbles they inject under the surface are the primary radiation mechanism (Wenz 1962; Knudsen, Alford, Emling 1948; Carey and Evans 2011). The Coates/Stojanovic formula has the wind 1 kHz spectrum level scaling roughly as 7.5 √U, giving a ~9 dB increase between gentle breeze (U = 5 m/s) and strong wind (U = 12 m/s).
Shipping density. Approximate density of distant commercial shipping, parameterized by the Coates/Stojanovic shipping activity factor s in [0, 1]. Drives the 10–300 Hz band. Anthropogenic; has measurably increased in the global ocean since the 1960s (Andrew et al. 2002, McDonald et al. 2006). At s = 1 with heavy traffic in busy lanes, the rumble can dominate the spectrum below 200 Hz. The slider does not go below s = 0; to silence shipping entirely (rather than reduce to "low traffic" levels), uncheck the on box for Shipping.
Hildebrand 2021 wind mode. Replaces the Coates/Stojanovic wind curve with a coarse approximation of the Hildebrand, Frasier, Baumann-Pickering, Wiggins (2021) empirical fit. Hildebrand 2021 gives somewhat higher levels than Wenz Figure 13 at low Beaufort numbers and similar levels at high Beaufort. The faithful per-Beaufort, piecewise- frequency original is in the companion MATLAB code; the curve here applies a Beaufort-dependent offset to the Coates/Stojanovic shape to capture the qualitative difference. Use it to A/B the two parameterizations.
Listener depth. A hydrophone at the sea surface, one moored at 100 m, and a deep-ocean sensor at 3 km hear noticeably different versions of the same soundscape: high-frequency wind hiss is absorbed by the water above the sensor, while low-frequency shipping rumble persists. This slider sets the listener's depth below the sea surface, log-spaced from surface (0 m, no correction) up to 5 km. Surface-generated components are attenuated by seawater absorption along an effective vertical path; the absorption coefficient α(f) uses the Ainslie–McColm 1998 three-term fit (boric-acid relaxation ~1 kHz, MgSO4 ~100 kHz, pure-water viscosity above 100 kHz) evaluated at fixed mid-latitude open-ocean defaults T = 10 °C, S = 35 psu, pH = 8.0 (not user- adjustable in this demo). Per mechanism:
At d = 0 every depth correction is exactly zero, so the listener spectrum and the audio reduce to the surface Wenz spectrum bit-for-bit. As you raise depth, the high-frequency hiss dies off first (large α above a few kHz) while the low-frequency shipping rumble persists, which is the qualitatively correct picture of why a deep hydrophone hears mostly shipping and very-low-frequency wave noise.
Component on / solo. Use these to isolate the contribution of each physical mechanism. Especially illuminating: solo "Thermal", set wind low, and turn up the volume until you can hear the high-frequency hiss; this is the absolute floor of any underwater hydrophone, set by water temperature alone.
The Coates/Stojanovic wind fit is approximate and overshoots the original Wenz 1962 Figure 13 at the lowest wind speeds by 5–10 dB. The shipping spectrum varies enormously by location, time of day, and traffic geometry; the fit here is an average. The demo synthesizes an "open mid-latitude ocean" average and does not model marine mammal vocalizations, ice cracking, snapping shrimp, rain, or other intermittent or local sources from Wenz's Figure 14.
The depth model is one-way direct-path seawater absorption only. It does not include: SOFAR-channel trapping (which can boost low-frequency shipping noise by 3–10 dB near the sound-channel axis); refraction or multipath from the local sound-speed profile; seasonal or geographic variation in T, S, or pH; or the angular structure of the surface noise field beyond a single 1.4× cone-factor. Typical residual error in the audio band: under about 3 dB above 1 kHz for depths below 1 km, growing to several dB at higher frequencies and greater depths, and up to ~10 dB optimistic for shipping near the SOFAR axis.
The thermal component is essentially inaudible in the audio band (NL_th(1 kHz) = −15 dB; NL_th(10 kHz) = 5 dB). It is plotted out to 200 kHz where it dominates, but its contribution to the audio synthesis is negligible.