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/content.html.
Where:
c = speed of sound (m/s),
α = absorption coefficient (dB/m)
T = temperature (°C)
S = salinity (ppt)
D = depth (m)
P = pressure (kPa)
f = frequency (kHz)
where -2 < T < 30
25 < S < 40
0 < D < 8000
where -2 < T < 23
30 < S < 40
0 < D < 500
where 0 < T < 95
D = 0
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 (m/s) is a function of salinity, temperature and pressure.
T = Temperature with a valid range* of 0 to 40 degrees Celsius.
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).
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 |
where:
This algorithm applies to all oceanic conditions and 200 Hz < f < 1 MHz.
Note: The Francois & Garrison (1982) algorithm calculates the absorption coefficient in units of dB/km. Echoview displays the calculated absorption coefficient units in dB/m as recommended by MacLennan et al (2002).