Sound speed in sea. Mackenzie equation

Mathematical definition

$$\boxed{\begin{array}{l} C\left( {T,S,D} \right) = 1448.96 + 4.591T - 5.304 \times {10^{ - 2}}{T^2} + 2.374 \times {10^{ - 4}}{T^3}\\ + 1.340\left( {S - 35} \right) + 1.630 \times {10^{ - 2}}D + 1.675 \times {10^{ - 7}}{D^2}\\ - 1.025 \times {10^{ - 2}}T\left( {S - 35} \right) - 7.139 \times {10^{ - 13}}T{D^3} \end{array}}$$

Notation	Description	Units	Limits
$C$	sound speed	$\text{m/s}$
$T$	temperature	$^{\circ}\text{C}$	$-2 < T < 30$
$S$	salinity	$\text{‰}$	$25 < S < 40$
$D$	depth	$\text{m}$	$0 < D < 8000$

Octave/Matlab implementation

function C = sound_speed_sea_mackenzie(T,S,D)
% Inputs
%   T: temperature \ degree Celsius \ -2 < T < 30 
%   S: salinity \ ppt \ 25 < S < 40
%   D: depth \ m \ 0 < D < 8000
% Outputs
%   C: speed of sound in seawater \ m/s

    C = 1448.96 + 4.591*T - (5.304e-2)*(T.^2) + (2.374e-4)*(T.^3) ...
        + 1.340*(S-35) + (1.630e-2)*D + (1.675e-7)*(D.^2) ...
        - (1.025e-2)*T.*(S-35) - (7.139e-13)*T.*(D.^3);
end

Computational examples

$D$\$T$	$0°\text{C}$	$10°\text{C}$	$20°\text{C}$	$30°\text{C}$	$40°\text{C}$
$10\ \text{m}$	$1442.42$	$1483.78$	$1515.95$	$1540.36$	$1558.44$
$1000\ \text{m}$	$1458.73$	$1500.08$	$1532.24$	$1556.65$	$1574.72$
$2000\ \text{m}$	$1475.53$	$1516.83$	$1548.94$	$1573.30$	$1591.32$
$5000\ \text{m}$	$1527.95$	$1568.41$	$1599.69$	$1623.21$	$1640.40$

References

1. Mackenzie, Kenneth V, "Nine‐term equation for sound speed in the oceans", 1981