Sound speed in sea. Del Grosso equation

Mathematical definition

$$\boxed{C\left( {T,S,P} \right) = {C_{000}} + \Delta {C_T} + \Delta {C_S} + \Delta {C_P} + \Delta {C_{STP}}}$$

Notation	Description	Units	Limits	Conversion
$C$	sound speed	$\text{m/s}$
$T$	temperature	$^{\circ}\text{C}$	$0 < T < 35$
$S$	salinity	$\text{‰}$	$29 < S < 43$
$P$	pressure	$\text{kPa}$	$0 < P < 98000$	$P\left[ {{\rm{at}}} \right] = P\left[ {{\rm{kPa}}} \right] \times 1.019716 \times {10^{ - 2}}$

$$\Delta {C_T}\left( T \right) = {C_{T1}}T + {C_{T2}}{T^2} + {C_{T3}}{T^3}$$

$$\Delta {C_S}\left( S \right) = {C_{S1}}S + {C_{S2}}{S^2}$$

$$\Delta {C_P}\left( P \right) = {C_{P1}}P + {C_{P2}}{P^2} + {P_{P3}}{P^3}$$

$$\begin{array}{l} \Delta {C_{STP}}\left( {T,P,S} \right) = {C_{TP}}TP + {C_{T3P}}{T^3}P + {C_{TP2}}T{P^2}\\ + {C_{T2P2}}{T^2}{P^2} + {C_{TP3}}T{P^3} + {C_{ST}}ST\\ + {C_{ST2}}S{T^2} + {C_{STP}}STP + {C_{S2TP}}{S^2}TP + {C_{S2P2}}{S^2}{P^2} \end{array}$$

Coefficient	Value	Coefficient	Value
$C_{000}$	$1402.392$	$C_{ST}$	$-0.1275936\times10^{-1}$
$C_{T1}$	$0.5012285\times10^{1}$	$C_{TP}$	$0.6353509\times10^{-2}$
$C_{T2}$	$-0.551184\times10^{-1}$	$C_{T2P2}$	$0.2656174\times10^{-7}$
$C_{T3}$	$0.221649\times10^{-3}$	$C_{TP2}$	$-0.1593895\times10^{-5}$
$C_{S1}$	$0.1329530\times10^{1}$	$C_{TP3}$	$0.5222483\times10^{-9}$
$C_{S2}$	$0.1288598\times10^{-3}$	$C_{T3P}$	$-0.4383615\times10^{-6}$
$C_{P1}$	$0.1560592$	$C_{S2P2}$	$-0.1616745\times10^{-8}$
$C_{P2}$	$0.2449993\times10^{-4}$	$C_{T2S}$	$0.9688441\times10^{-4}$
$C_{P3}$	$-0.8833959\times10^{-8}$	$C_{S2TP}$	$0.4857614\times10^{-5}$
$C_{STP}$	$-0.3406824\times10^{-3}$

Octave/Matlab implementation

function C = sound_speed_sea_delgrosso(T,S,P)
% Inputs
%   T: temperature \ degree Celsius \ 0 < T < 35 
%   S: salinity \ ppt \ 29 < S < 43
%   P: pressure \ kPa \ 0 < P < 98000 
% Outputs
%   C: speed of sound in seawater \ m/s

    C000 = 1402.392;
    CT1 = 0.5012285e1;
    CT2 = -0.551184e-1;
    CT3 = 0.221649e-3;
    CS1 = 0.1329530e1;
    CS2 = 0.1288598e-3;
    CP1 = 0.1560592;
    CP2 = 0.2449993e-4;
    CP3 = -0.8833959e-8;
    CST = -0.1275936e-1;
    CTP = 0.6353509e-2;
    CT2P2 = 0.2656174e-7;
    CTP2 = -0.1593895e-5;
    CTP3 = 0.5222483e-9;
    CT3P = -0.4383615e-6;
    CS2P2 = -0.1616745e-8;
    CST2 = 0.9688441e-4;
    CS2TP = 0.4857614e-5;
    CSTP =-0.3406824e-3;

    p = P*1.019716e-2;

    CT = CT1*T + CT2*(T.^2) + CT3*(T.^3);
    CS = CS1*S + CS2*(S.^2);
    CP = CP1*p + CP2*(p.^2) + CP3*(p.^3);
    CSTP = CTP*T.*p + CT3P*(T.^3).*p + CTP2*T.*(p.^2) + ...
        CT2P2*(T.^2).*(p.^2) + CTP3*T.*(p.^3) + ...
        CST*S.*T + CST2*S.*(T.^2) + CSTP*S.*T.*p + ...
        CS2TP*(S.^2)*T.*p + CS2P2*(S.^2).*(p.^2);

    C = C000 + CT + CS + CP + CSTP;
end

Computational examples

$D$\$T$	$0°\text{C}$	$10°\text{C}$	$20°\text{C}$	$30°\text{C}$	$40°\text{C}$
$10\ \text{m}$	$1442.55$	$1483.85$	$1516.04$	$1540.44$	$1558.37$
$1000\ \text{m}$	$1458.67$	$1500.30$	$1532.61$	$1556.65$	$1573.49$
$2000\ \text{m}$	$1475.45$	$1517.18$	$1549.48$	$1573.14$	$1588.94$
$5000\ \text{m}$	$1528.32$	$1569.16$	$1600.96$	$1623.67$	$1637.27$

References

Del Grosso, Vincent A, "New equation for the speed of sound in natural waters (with comparisons to other equations)", 1974
Wong, George SK; Zhu, Shi‐ming, "Speed of sound in seawater as a function of salinity, temperature, and pressure", 1995