About the Thermocline & Ocean Stratification
This simulation renders a vertical ocean cross-section from the surface to 4000 m, showing how temperature, sound speed and the SOFAR channel vary with depth. Temperature follows a sigmoid profile, T(z) = T_deep + (T_surf − T_deep) / (1 + exp((z − z_thermo) / scale)), which produces a sharp thermocline. Sound speed is computed from the Mackenzie (1981) equation, c = 1449.2 + 4.6T − 0.055T² + 0.00029T³ + (1.34 − 0.01T)(S − 35) + 0.016z.
The Surface Temperature, Thermocline Depth and Salinity sliders reshape the temperature and sound-speed curves, while the Season presets (summer, winter, tropical, polar) load realistic combinations. The SOFAR axis sits at the sound-speed minimum, and acoustic rays are traced with Snell's law so they refract back toward it. This channelling lets low-frequency sound travel thousands of kilometres, which underpins long-range sonar, submarine detection and whale communication.
Frequently Asked Questions
What is a thermocline?
A thermocline is a layer of water where temperature drops sharply with depth, separating the warm, sunlit surface mixed layer from the cold deep ocean. In this simulation it is centred on the Thermocline Depth slider value (100–600 m by default) and its sharpness is set by an internal scale parameter. It marks the transition zone shown by the steep part of the cyan temperature curve.
How does the simulation model temperature with depth?
It uses a sigmoid (logistic) function: T(z) = T_deep + (T_surf − T_deep) / (1 + exp((z − z_thermo) / scale)). T_surf comes from the Surface Temperature slider, T_deep is fixed near 2°C, z_thermo is the Thermocline Depth, and scale controls how abruptly the temperature changes. This gives a smooth warm-to-cold profile with a concentrated gradient at the thermocline.
What is the SOFAR channel?
SOFAR stands for Sound Fixing and Ranging. It is a horizontal layer at the depth where sound speed is at a minimum, typically several hundred to about a thousand metres down. Sound rays entering this layer are continually refracted back toward the axis, so acoustic energy is trapped and can propagate over very long distances with little loss.
How is sound speed calculated here?
The model applies the Mackenzie (1981) nine-term equation: c = 1449.2 + 4.6T − 0.055T² + 0.00029T³ + (1.34 − 0.01T)(S − 35) + 0.016z, where T is temperature in °C, S is salinity in PSU and z is depth in metres. Sound speed rises with temperature, salinity and pressure, so it falls through the thermocline then climbs again in the deep, creating the SOFAR minimum.
What do the on-screen controls do?
Surface Temperature (15–30°C) sets the warm top layer; Thermocline Depth (100–600 m) moves the gradient up or down; Salinity (30–38 PSU) shifts the sound-speed curve. The Season preset menu loads matched parameter sets, and the Display toggles switch layer labels, the SOFAR sound rays and the animated water particles on or off.
How are the sound rays traced?
Each ray starts at the SOFAR axis and is stepped through the water column using Snell's law, where cos(angle)/c stays constant. As the ray passes through layers of different sound speed its angle bends; when it would exceed the refraction limit it turns back, simulating total internal reflection. The result is the oscillating yellow ray paths that stay channelled around the minimum-speed depth.
What do the four statistics show?
SOFAR Depth is the depth of minimum sound speed for the current settings. Min Sound Speed is the speed at that axis in metres per second. Surface Speed is the sound speed at the surface. Gradient is the temperature change across the thermocline in degrees Celsius per roughly 100 m, measured 50 m above and below the thermocline depth.
Why does the polar preset have no real thermocline?
In polar waters the surface is already near freezing, so there is little temperature contrast between the surface and the deep ocean. The polar preset sets a surface temperature of about 2°C with a deep, gentle scale, producing an almost uniform profile. With no strong gradient the thermocline effectively disappears, which is why high-latitude seas are nearly isothermal.
Is this simulation physically accurate?
It uses the real Mackenzie (1981) sound-speed formula and a physically reasonable sigmoid temperature profile, so the qualitative behaviour, the SOFAR minimum, the refraction of rays and the seasonal contrasts, is faithful. It is simplified for clarity: it omits currents, salinity-with-depth variation, internal waves and full range-dependent acoustics, so it is an educational tool rather than an operational ocean model.
Why can submarines hide below the thermocline?
The sharp sound-speed change at the thermocline reflects and refracts surface sonar pulses, creating a shadow zone beneath it. A submarine diving below the layer can sit in this acoustic blind spot where surface ships find it much harder to detect. The same gradient that channels SOFAR sound also helps conceal vessels, which is why thermocline depth matters in naval operations.
How do whales use the SOFAR channel?
Baleen whales such as fin and blue whales produce very low-frequency calls that couple efficiently into the SOFAR channel. Because the channel traps and guides this sound with minimal loss, the calls can travel across entire ocean basins. This is widely thought to support long-range communication and may help whales navigate and locate one another over thousands of kilometres.