Sound speed in sea. NPL equation

Mathematical definition

$$\boxed{\begin{array}{l} C\left( {T,S,D} \right) = 1402.5 + 5T - 5.44 \times {10^{ - 2}}{T^2} + 2.1 \times {10^{ - 4}}{T^3}\\ + 1.33S - 1.23 \times {10^{ - 2}}ST + 8.7 \times {10^{ - 5}}S{T^2}\\ + 1.56 \times {10^{ - 2}}D + 2.55 \times {10^{ - 7}}{Z^2} - 7.3 \times {10^{ - 12}}{Z^3}\\ + 1.2 \times {10^{ - 6}}Z\left( {L - 45} \right) - 9.5 \times {10^{ - 13}}T{Z^3}\\ + 3 \times {10^{ - 7}}{T^2}Z + 1.43 \times {10^{ - 5}}SZ \end{array}}$$

Notation	Description	Units	Limits
$C$	sound speed	$\text{m/s}$
$T$	temperature	$^{\circ}\text{C}$	$-1 < T < 30$
$S$	salinity	$\text{‰}$	$0 < S < 42$
$D$	depth	$\text{m}$	$0 < D < 12000$

Octave/Matlab implementation

function C = sound_speed_sea_npl(T,S,D,L)
% Inputs
%   T: temperature \ degree Celsius \ -1 < T < 30 
%   S: salinity \ ppt \ 0 < S < 42
%   D: depth \ m \ 0 < D < 12000
%   L: latitude \ degree \ -90 < L < 90
% Outputs
%   C: speed of sound in seawater \ m/s

    C = 1402.5 + 5*T - (5.44e-2)*(T.^2) + (2.1e-4)*(T.^3) ...
        + 1.33*S - (1.23e-2)*S.*T + (8.7e-5)*S.*(T.^2) ...
        + (1.56e-2)*D + (2.55e-7)*(D.^2) - (7.3e-12)*(D.^3) ...
        + (1.2e-6)*D.*(L-45) - (9.5e-13)*T.*(D.^3) + (3e-7)*(T.^2).*D ...
        + (1.43e-5)*S.*D;
end

Computational examples

$D$\$T$	$0°\text{C}$	$10°\text{C}$	$20°\text{C}$	$30°\text{C}$	$40°\text{C}$
$10\ \text{m}$	$1442.56$	$1483.90$	$1516.14$	$1540.55$	$1558.38$
$1000\ \text{m}$	$1458.62$	$1499.98$	$1532.31$	$1556.85$	$1574.88$
$2000\ \text{m}$	$1475.31$	$1516.64$	$1548.98$	$1573.61$	$1591.78$
$5000\ \text{m}$	$1527.74$	$1568.04$	$1599.55$	$1623.51$	$1641.20$

References

1. Leroy, Claude C; Robinson, Stephen P; Goldsmith, Mike J, "A new equation for the accurate calculation of sound speed in all oceans", 2008