underwater.sound_speed

Speed of sound in sea water (empirical equations).

Three coexisting equations for the sound speed c as a function of temperature, salinity and depth/pressure, selectable through model:

• "unesco" — the UNESCO / Chen & Millero (1977) algorithm, the international standard, in the Wong & Zhu (1995) ITS-90 recalculation. Default.
• "del_grosso" — the Del Grosso (1974) equation (Wong & Zhu 1995 form), a high-accuracy alternative over a narrower domain.
• "mackenzie" — the Mackenzie (1981) nine-term depth-based equation.

The UNESCO and Del Grosso equations use pressure, not depth, so a depth is first converted with the Leroy & Parthiot (1998) standard-ocean formula (depth_to_pressure). SoundSpeedProfile evaluates c over a depth profile and exposes the sound-speed gradient.

Sources (clean-room, implemented from the equations, validated by cross-model agreement and the canonical Mackenzie check value 1550.744 m/s at 25 °C, 35 ppt, 1000 m): NPL Technical Guide “Speed of Sound in Sea-Water” (Wong & Zhu 1995 coefficient tables), Mackenzie (1981) JASA 70, Del Grosso (1974) JASA 56, Leroy & Parthiot (1998) JASA 103.

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depth_to_pressure

depth_to_pressure(depth: float, latitude: float = 45.0) -> float

Gauge pressure at a given ocean depth (Leroy & Parthiot 1998), in MPa.

Standard-ocean formula (an ideal medium of 0 °C and 35 ppt); no local corrections are applied.

Parameters

Name	Description
depth	Depth below the surface Z, in metres (>= 0).
latitude	Latitude φ, in degrees (default 45°).

Returns: Gauge pressure, in megapascals.

Raises

Exception	When
ValueError	If the depth is negative or non-finite.

sea_water_sound_speed

sea_water_sound_speed(
    temperature: float,
    salinity: float,
    depth: float,
    *,
    model: str = 'unesco',
    latitude: float = 45.0,
) -> float

Speed of sound in sea water, in metres per second.

Parameters

Name	Description
temperature	Temperature T, in degrees Celsius.
salinity	Salinity S, in parts per thousand (PSU).
depth	Depth below the surface, in metres (>= 0).
model	"unesco" (default), "del_grosso" or "mackenzie".
latitude	Latitude for the depth→pressure conversion, in degrees (used by "unesco" and "del_grosso"; default 45°).

Returns: The sound speed c, in m/s.

Raises

Exception	When
ValueError	If model is unknown or an input is non-finite.

Note

Each equation is a fit over a bounded oceanographic domain and extrapolates silently outside it (e.g. Del Grosso abused at T = 40 °C, S = 0, z = 11 km returns an unphysical ~1995 m/s). Published validity domains: UNESCO/Chen-Millero T 0-40 °C, S 0-40, P 0-1000 bar; Del Grosso T 0-30 °C, S 30-40, P 0-1000 kg/cm²; Mackenzie T 2-30 °C, S 25-40, depth 0-8000 m.

sound_speed_profile

sound_speed_profile(
    depths: NDArray[np.float64] | list[float],
    temperatures: NDArray[np.float64] | list[float] | float,
    salinities: NDArray[np.float64] | list[float] | float,
    *,
    model: str = 'unesco',
    latitude: float = 45.0,
) -> SoundSpeedProfile

Evaluate a sound-speed profile over a depth column.

Parameters

Name	Description
depths	Depths, in metres (1-D, non-negative, increasing).
temperatures	Temperature per depth, in °C (array or a scalar broadcast to every depth).
salinities	Salinity per depth, in PSU (array or scalar).
model	Sound-speed equation (see sea_water_sound_speed).
latitude	Latitude for the depth→pressure conversion, in degrees.

Returns: A SoundSpeedProfile.

Raises

Exception	When
ValueError	If the inputs are invalid.

SoundSpeedProfile

SoundSpeedProfile(
    depth: NDArray[np.float64],
    sound_speed: NDArray[np.float64],
    gradient: NDArray[np.float64],
    model: str,
)

Sound-speed profile c(z) over a column of water.

Attributes

Name	Description
depth	Depths, in metres (increasing downward).
sound_speed	Sound speed at each depth, in m/s.
gradient	Vertical sound-speed gradient dc/dz, in (m/s)/m.
model	The equation used.

SoundSpeedProfile.plot()

SoundSpeedProfile.plot(
    ax: Axes | None = None,
    *,
    language: str = 'en',
    **kwargs: Any,
) -> Axes

Plot the sound-speed profile (speed vs depth, depth increasing down).