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gsw_SP_from_C.m
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gsw_SP_from_C.m
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function SP = gsw_SP_from_C(C,t,p)
% gsw_SP_from_C Practical Salinity from conductivity
%==========================================================================
%
% USAGE:
% SP = gsw_SP_from_C(C,t,p)
%
% DESCRIPTION:
% Calculates Practical Salinity, SP, from conductivity, C, primarily using
% the PSS-78 algorithm. Note that the PSS-78 algorithm for Practical
% Salinity is only valid in the range 2 < SP < 42. If the PSS-78
% algorithm produces a Practical Salinity that is less than 2 then the
% Practical Salinity is recalculated with a modified form of the Hill et
% al. (1986) formula. The modification of the Hill et al. (1986)
% expression is to ensure that it is exactly consistent with PSS-78
% at SP = 2. Note that the input values of conductivity need to be in
% units of mS/cm (not S/m).
%
% INPUT:
% C = conductivity [ mS/cm ]
% t = in-situ temperature (ITS-90) [ deg C ]
% p = sea pressure [ dbar ]
% ( i.e. absolute pressure - 10.1325 dbar )
%
% t & p may have dimensions 1x1 or Mx1 or 1xN or MxN, where C is MxN.
%
% OUTPUT:
% SP = Practical Salinity on the PSS-78 scale [ unitless ]
%
% AUTHOR:
% Paul Barker, Trevor McDougall and Rich Pawlowicz [ help@teos-10.org ]
%
% VERSION NUMBER: 3.05 (27th January 2015)
%
% REFERENCES:
% Culkin and Smith, 1980: Determination of the Concentration of Potassium
% Chloride Solution Having the Same Electrical Conductivity, at 15C and
% Infinite Frequency, as Standard Seawater of Salinity 35.0000
% (Chlorinity 19.37394), IEEE J. Oceanic Eng, 5, 22-23.
%
% Hill, K.D., T.M. Dauphinee & D.J. Woods, 1986: The extension of the
% Practical Salinity Scale 1978 to low salinities. IEEE J. Oceanic Eng.,
% 11, 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 http://www.TEOS-10.org
% See appendix E of this TEOS-10 Manual.
%
% 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
%
%==========================================================================
%--------------------------------------------------------------------------
% Check variables and resize if necessary
%--------------------------------------------------------------------------
if ~(nargin == 3)
error('gsw_SP_from_C: Requires three input arguments')
end %if
[mc,nc] = size(C);
[mt,nt] = size(t);
[mp,np] = size(p);
if (mt == 1) & (nt == 1) % t scalar - fill to size of C
t = t*ones(size(C));
elseif (nc == nt) & (mt == 1) % t is row vector,
t = t(ones(1,mc), :); % copy down each column.
elseif (mc == mt) & (nt == 1) % t is column vector,
t = t(:,ones(1,nc)); % copy across each row.
elseif (nc == mt) & (nt == 1) % t is a transposed row vector,
t = t.'; % transposed then
t = t(ones(1,mc), :); % copy down each column.
elseif (mc == mt) & (nc == nt)
% ok
else
error('gsw_SP_from_C: Inputs array dimensions arguments do not agree')
end %if
if (mp == 1) & (np == 1) % p scalar - fill to size of C
p = p*ones(size(C));
elseif (nc == np) & (mp == 1) % p is row vector,
p = p(ones(1,mc), :); % copy down each column.
elseif (mc == mp) & (np == 1) % p is column vector,
p = p(:,ones(1,nc)); % copy across each row.
elseif (nc == mp) & (np == 1) % p is a transposed row vector,
p = p.'; % transposed then
p = p(ones(1,mc), :); % copy down each column.
elseif (mc == mp) & (nc == np)
% ok
else
error('gsw_SP_from_C: Inputs array dimensions arguments do not agree')
end %if
if mc == 1
C = C.';
t = t.';
p = p.';
transposed = 1;
else
transposed = 0;
end
%--------------------------------------------------------------------------
% Start of the calculation
%--------------------------------------------------------------------------
a0 = 0.0080;
a1 = -0.1692;
a2 = 25.3851;
a3 = 14.0941;
a4 = -7.0261;
a5 = 2.7081;
b0 = 0.0005;
b1 = -0.0056;
b2 = -0.0066;
b3 = -0.0375;
b4 = 0.0636;
b5 = -0.0144;
c0 = 0.6766097;
c1 = 2.00564e-2;
c2 = 1.104259e-4;
c3 = -6.9698e-7;
c4 = 1.0031e-9;
d1 = 3.426e-2;
d2 = 4.464e-4;
d3 = 4.215e-1;
d4 = -3.107e-3;
e1 = 2.070e-5;
e2 = -6.370e-10;
e3 = 3.989e-15;
k = 0.0162;
[Iocean] = find(~isnan(C + t + p));
t68 = t(Iocean).*1.00024;
ft68 = (t68 - 15)./(1 + k*(t68 - 15));
% The dimensionless conductivity ratio, R, is the conductivity input, C,
% divided by the present estimate of C(SP=35, t_68=15, p=0) which is
% 42.9140 mS/cm (=4.29140 S/m), (Culkin and Smith, 1980).
R = 0.023302418791070513.*C(Iocean); % 0.023302418791070513 = 1./42.9140
% rt_lc corresponds to rt as defined in the UNESCO 44 (1983) routines.
rt_lc = c0 + (c1 + (c2 + (c3 + c4.*t68).*t68).*t68).*t68;
Rp = 1 + (p(Iocean).*(e1 + e2.*p(Iocean) + e3.*p(Iocean).*p(Iocean)))./ ...
(1 + d1.*t68 + d2.*t68.*t68 + (d3 + d4.*t68).*R);
Rt = R./(Rp.*rt_lc);
Rt(Rt < 0) = NaN;
Rtx = sqrt(Rt);
SP = NaN(size(C));
SP(Iocean) = a0 + (a1 + (a2 + (a3 + (a4 + a5.*Rtx).*Rtx).*Rtx).*Rtx).*Rtx + ...
ft68.*(b0 + (b1 + (b2 + (b3 + (b4 + b5.*Rtx).*Rtx).*Rtx).*Rtx).*Rtx);
% The following section of the code is designed for SP < 2 based on the
% Hill et al. (1986) algorithm. This algorithm is adjusted so that it is
% exactly equal to the PSS-78 algorithm at SP = 2.
if any(SP(Iocean) < 2)
[I2] = find(SP(Iocean) < 2);
Hill_ratio = gsw_Hill_ratio_at_SP2(t(Iocean(I2)));
x = 400*Rt(I2);
sqrty = 10*Rtx(I2);
part1 = 1 + x.*(1.5 + x);
part2 = 1 + sqrty.*(1 + sqrty.*(1 + sqrty));
SP_Hill_raw = SP(Iocean(I2)) - a0./part1 - b0.*ft68(I2)./part2;
SP(Iocean(I2)) = Hill_ratio.*SP_Hill_raw;
end
% This line ensures that SP is non-negative.
SP(SP < 0) = 0;
if transposed
SP = SP.';
end
end