C = gsw_C_from_SP(SP,t,p)
Calculates conductivity, C, from (SP,t,p) using PSS-78 in the range
2 < SP < 42. If the input Practical Salinity is less than 2 then a
modified form of the Hill et al. (1986) fomula is used for Practical
Salinity. The modification of the Hill et al. (1986) expression is to
ensure that it is exactly consistent with PSS-78 at SP = 2.
The conductivity ratio returned by this function is consistent with the
input value of Practical Salinity, SP, to 2x10^-14 psu over the full
range of input parameters (from pure fresh water up to SP = 42 psu).
This error of 2x10^-14 psu is machine precision at typical seawater
salinities. This accuracy is achieved by having four different
polynomials for the starting value of Rtx (the square root of Rt) in
four different ranges of SP, and by using one and a half iterations of
a computationally efficient modified Newton-Raphson technique (McDougall
and Wotherspoon, 2013) to find the root of the equation.
Note that strictly speaking PSS-78 (Unesco, 1983) defines Practical
Salinity in terms of the conductivity ratio, R, without actually
specifying the value of C(35,15,0) (which we currently take to be
SP = Practical Salinity (PSS-78) [ unitless ]
t = in-situ temperature (ITS-90) [ deg C ]
p = sea pressure [ dbar ]
(ie. absolute pressure - 10.1325 dbar)
SP & t need to have the same dimensions.
p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SP & t are MxN.
C = conductivity [ mS/cm ]
SP = [34.5487; 34.7275; 34.8605; 34.6810; 34.5680; 34.5600;]
t = [28.7856; 28.4329; 22.8103; 10.2600; 6.8863; 4.4036;]
p = [ 10; 50; 125; 250; 600; 1000;]
C = gsw_C_from_SP(SP,t,p)
Trevor McDougall, Paul Barker and Rich Pawlowicz [ email@example.com ]
3.05 (16th February, 2015)
Hill, K.D., T.M. Dauphinee and D.J. Woods, 1986: The extension of the
Practical Salinity Scale 1978 to low salinities. IEEE J. Oceanic Eng.,
OE-11, 1, 109 - 112.
IOC, SCOR and IAPSO, 2010: The international thermodynamic equation of
seawater - 2010: Calculation and use of thermodynamic properties.
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
UNESCO (English), 196 pp. Available from the TEOS-10 web site.
See appendix E of this TEOS-10 Manual.
McDougall, T.J. and S.J. Wotherspoon, 2013: A simple modification of
Newton’s method to achieve convergence of order "1 + sqrt(2)". Applied
Mathematics Letters, 29, 20-25.
Unesco, 1983: Algorithms for computation of fundamental properties of
seawater. Unesco Technical Papers in Marine Science, 44, 53 pp.
The software is available from http://www.TEOS-10.org