Sound speed in sea. Coppens equation

Mathematical definition

$$\boxed{\begin{array}{l} C\left( {T,S,D} \right) = C\left( {T,S,0} \right) + \left( {16.23 + 0.253T} \right)D + \left( {0.213 - 0.1T} \right){D^2}\\ + \left( {0.016 + 0.0002\left( {S - 35} \right)} \right)\left( {S - 35} \right)TD \end{array}}$$

Notation	Definition	Units	Limits	Conversion
$C$	sound speed	$\text{m/s}$
$T$	temperature	$^{\circ}\text{C}$	$-2 < T < 35$	$T\left[ {{\rm{d^\circ C}}} \right] = T\left[ {{\rm{^\circ C}}} \right] \times {10^{ - 1}}$
$S$	salinity	$\text{‰}$	$0 < S < 42$
$D$	depth	$\text{m}$	$0 < D < 4000$	$D\left[ {{\rm{km}}} \right] = D\left[ {\rm{m}} \right] \times {10^{ - 3}}$

$$\begin{array}{l} C\left( {T,S,0} \right) = 1449.05 + 45.7T - 5.21{T^2} + 0.23{T^3}\\ + \left( {1.333 - 0.126T + 0.009{T^2}} \right)\left( {S - 35} \right) \end{array}$$

Octave/Matlab implementation

function C = sound_speed_sea_coppens(T,S,D)
% Inputs
%   T: temperature \ degree Celsius \ -2 < T < 35 
%   S: salinity \ ppt \ 0 < S < 42
%   D: depth \ m \ 0 < D < 4000
% Outputs
%   C: speed of sound in seawater \ m/s

    d = D.*(1e-3);
    t = T.*(1e-1);

    C = 1449.05 + 45.7*t - 5.21*(t.^2) + 0.23*(t).^3 ...
        + (1.333 - 0.126*t + 0.009*(t.^2)).*(S - 35) ...
        + (16.23 + 0.253*t).*d + (0.213-0.1*t).*(d.^2) ...
        + (0.016 + 0.0002*(S-35)).*(S-35).*t.*d;
end

Computational examples

$D$\$T$	$0°\text{C}$	$10°\text{C}$	$20°\text{C}$	$30°\text{C}$	$40°\text{C}$
$10\ \text{m}$	$1442.55$	$1483.85$	$1516.03$	$1540.46$	$1558.51$
$1000\ \text{m}$	$1458.83$	$1500.21$	$1532.46$	$1556.97$	$1575.10$
$2000\ \text{m}$	$1475.70$	$1516.96$	$1549.09$	$1573.47$	$1591.48$
$5000\ \text{m}$	$1528.86$	$1568.56$	$1599.12$	$1621.93$	$1638.38$

References

1. Coppens, Alan B, "Simple equations for the speed of sound in Neptunian waters", 1981