The UNESCO equation: Chen and Millero

The international standard algorithm, often known as the UNESCO algorithm, is due to Chen and Millero (1977), and has a more complicated form than the simple equations above, but uses pressure as a variable rather than depth. For the original UNESCO paper see Fofonoff and Millard (1983)Wong and Zhu (1995) recalculated the coefficients in this algorithm following the adoption of the International Temperature Scale of 1990 and their form of the UNESCO equation is:


c(S,T,P) =   Cw(T,P) + A(T,P)S + B(T,P)S3/2 + D(T,P)S2
Cw(T,P) = (C00 + C01T + C02T2 + C03T3 + C04T4 + C05T5) +
  (C10 + C11T + C12T2 + C13T3 + C14T4)P +
  (C20 +C21T +C22T2 + C23T3 + C24T4)P2 +
  (C30 + C31T + C32T2)P3
A(T,P) =   (A00 + A01T + A02T2 + A03T3 + A04T4) +
  (A10 + A11T + A12T2 + A13T3 + A14T4)P +
  (A20 + A21T + A22T2 + A23T3)P2 +
  (A30 + A31T + A32T2)P3
B(T,P) = B00 + B01T + (B10 + B11T)P
D(T,P) = D00 + D10P
  T = temperature in degrees Celsius
S = salinity in Practical Salinity Units (parts per thousand)
P = pressure in bar

Range of validity: temperature 0 to 40 C, salinity 0 to 40 parts per thousand, pressure 0 to 1000 bar (Wong and Zhu, 1995).

Please note that for consistency, within the interactive version, the pressure must be input in kPa.

Table of Coefficients
Coefficients Numerical values Coefficients Numerical values
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


(1)C-T. Chen and F.J. Millero, Speed of sound in seawater at high pressures (1977) J. Acoust. Soc. Am. 62(5) pp 1129-1135

(2)N.P. Fofonoff and R.C. Millard Jr. Algorithms for computation of fundamental properties of seawater (1983), UNESCO technical papers in marine science. No. 44, Division of Marine Sciences. UNESCO, Place de Fontenoy, 75700 Paris.

(3)G.S.K. Wong and S Zhu, Speed of sound in seawater as a function of salinity, temperature and pressure (1995) J. Acoust. Soc. Am. 97(3) pp 1732-1736