Sonar calculator algorithms

This page details the algorithms used in Sonar Calculator. The equations used by Mackenzie (1981), Chen and Millero (1977) are discussed by the National Physical Laboratory website (2018) Simple Equations [Online] Available at http://resource.npl.co.uk/acoustics/techguides/soundseawater/.

Where:

c = speed of sound (ms-1)

α = absorption coefficient (dBm-1)

T = temperature (°C)

S = salinity (ppt)

D = depth (m)

P = pressure (kPa)

f = frequency (kHz)

Speed of sound in salt water (Mackenzie, 1981)

Mackenzie (1981)

where -2 < T < 30

25 < S < 40

0 < D < 8000

Speed of sound in salt water (Leroy, 1969)

Leroy (1969)

where -2 < T < 23

30 < S < 40

0 < D < 500

Speed of sound in fresh water (Del Grosso and Mader, 1972)

Del Grosso and Mader (1972)

where 0 < T < 95

D = 0

Speed of sound (Chen and Millero, 1977)

Chen and Millero (1977). The Sonar calculator Pressure (kPa) is converted to units of bar for calculations.

Where:

c(S, T, P) = Speed of sound (ms-1) is a function of salinity, temperature and pressure.

T = Temperature with a valid range* of 0 to 40 °C.

S = Salinity with a valid range* of 0 to 40 ppt.

P = Pressure with a valid range* of 0 to 1000 bar.

*Valid range is sourced from Wong and Zhu (1995).

Table of Coefficients

Coefficient	Numerical value	Coefficient	Numerical value
C00	1402.388	A02	7.166E-5
C01	5.03830	A03	2.008E-6
C02	-5.81090E-2	A04	-3.21E-8
C03	3.3432E-4	A10	9.4742E-5
C04	-1.47797E-6	A11	-1.2583E-5
C05	3.1419E-9	A12	-6.4928E-8
C10	0.153563	A13	1.0515E-8
C11	6.8999E-4	A14	-2.0142E-10
C12	-8.1829E-6	A20	-3.9064E-7
C13	1.3632E-7	A21	9.1061E-9
C14	-6.1260E-10	A22	-1.6009E-10
C20	3.1260E-5	A23	7.994E-12
C21	-1.7111E-6	A30	1.100E-10
C22	2.5986E-8	A31	6.651E-12
C23	-2.5353E-10	A32	-3.391E-13
C24	1.0415E-12	B00	-1.922E-2
C30	-9.7729E-9	B01	-4.42E-5
C31	3.8513E-10	B10	7.3637E-5
C32	-2.3654E-12	B11	1.7950E-7
A00	1.389	D00	1.727E-3
A01	-1.262E-2	D10	-7.9836E-6

Absorption coefficient (Francois & Garrison, 1982)