Water sound speed calculator

OUTPUT: sound speed in m/s

INPUTS:
This function allows any or all inputs to be scalar or vectors. However, dimensions of all vector inputs must agree.

T_degrees_C is temperature in [°C]
P_kPa is absolute pressure [kPa]
S_ppt is salinity in ppt; most often close enough to psu for practical purposes. For freshwater use S_ppt = 0 or leave blank

If you have data from a CTD cast, you might have values for temperature, pressure, and salinity in the following format. (These example values are entirely hypothetical):
T_profile = [22 22 21 19 18];
P_profile = [101 150 199 240 300];
S_profile = [35.5 35 34.5 34 34.5];

Or you might have constant values for one or all of the input parameters:
T_const = 22;
P_const = 110;
S_const = 33;

ANY OF THE INPUTS FOLLOWING WILL WORK:
c_water(T_const,P_const,S_const)
c_water(T_const,P_const)
c_water(T_const)
c_water()
c_water
c_water(T_profile)
c_water(T_profile,P_profile)
c_water(T_profile,P_profile,S_profile)
c_water(T_profile,P_profile,S_const)
c_water(T_profile,P_const,S_profile)
c_water(T_profile,P_const,S_const)
c_water(T_const,P_profile,S_profile)
c_water(T_const,P_const,S_profile)
c_water(T_const,P_profile,S_const)
c_water(T_const,P_profile)
c_water(T_profile,P_const)

GRAPHICAL EXAMPLE
d = 0:5000; % for depth of 0 to 5 kilometers
p = 101.325+1025*9.81*d/1000; % pressure equivalent in kPa
t = [20:-10/500:10 10*ones(1,4500)]; % a very simplified thermocline model
c = c_water(t,p,32);
plot(c,-d)
ylabel('depth (m)')
xlabel('sound speed (m/s)')

Note: This calculator assumes a complete absence of bubbles. Even a small amount of gas in the water column may significantly affect sound speed. See Wood's model for the bulk sound speed of multiphase media.