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gsw_enthalpy.m
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gsw_enthalpy.m
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function enthalpy = gsw_enthalpy(SA,CT,p)
% gsw_enthalpy specific enthalpy of seawater
% (75-term equation)
%==========================================================================
%
% USAGE:
% enthalpy = gsw_enthalpy(SA,CT,p)
%
% DESCRIPTION:
% Calculates specific enthalpy of seawater using the computationally-
% efficient expression for specific volume in terms of SA, CT and p
% (Roquet et al., 2015).
%
% Note that the 75-term equation has been fitted in a restricted range of
% parameter space, and is most accurate inside the "oceanographic funnel"
% described in McDougall et al. (2003). The GSW library function
% "gsw_infunnel(SA,CT,p)" is avaialble to be used if one wants to test if
% some of one's data lies outside this "funnel".
%
% INPUT:
% SA = Absolute Salinity [ g/kg ]
% CT = Conservative Temperature (ITS-90) [ deg C ]
% p = sea pressure [ dbar ]
% ( i.e. absolute pressure - 10.1325 dbar )
%
% SA & CT need to have the same dimensions.
% p may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & CT are MxN.
%
% OUTPUT:
% enthalpy = specific enthalpy [ J/kg ]
%
% AUTHOR:
% Trevor McDougall, David Jackett, Claire Roberts-Thomson and Paul Barker.
% [ help@teos-10.org ]
%
% VERSION NUMBER: 3.05 (27th January 2015)
%
% REFERENCES:
% 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 Eqn. (A.30.6) of this TEOS-10 Manual.
%
% McDougall, T.J., 2003: Potential enthalpy: A conservative oceanic
% variable for evaluating heat content and heat fluxes. Journal of
% Physical Oceanography, 33, 945-963.
% See Eqns. (18) and (22)
%
% McDougall, T.J., D.R. Jackett, D.G. Wright and R. Feistel, 2003:
% Accurate and computationally efficient algorithms for potential
% temperature and density of seawater. J. Atmosph. Ocean. Tech., 20,
% pp. 730-741.
%
% Roquet, F., G. Madec, T.J. McDougall, P.M. Barker, 2015: Accurate
% polynomial expressions for the density and specifc volume of seawater
% using the TEOS-10 standard. Ocean Modelling.
%
% The software is available from http://www.TEOS-10.org
%
%==========================================================================
%--------------------------------------------------------------------------
% Check variables and resize if necessary
%--------------------------------------------------------------------------
if ~(nargin == 3)
error('gsw_enthalpy: requires three inputs')
end
[ms,ns] = size(SA);
[mt,nt] = size(CT);
[mp,np] = size(p);
if (mt ~= ms | nt ~= ns)
error('gsw_enthalpy: SA and CT must have same dimensions')
end
if (mp == 1) & (np == 1) % p scalar - fill to size of SA
p = p*ones(size(SA));
elseif (ns == np) & (mp == 1) % p is row vector,
p = p(ones(1,ms), :); % copy down each column.
elseif (ms == mp) & (np == 1) % p is column vector,
p = p(:,ones(1,ns)); % copy across each row.
elseif (ns == mp) & (np == 1) % p is a transposed row vector,
p = p.'; % transposed then
p = p(ones(1,ms), :); % copy down each column.
elseif (ms == mp) & (ns == np)
% ok
else
error('gsw_enthalpy_: Inputs array dimensions arguments do not agree')
end %if
if ms == 1
SA = SA.';
CT = CT.';
p = p.';
transposed = 1;
else
transposed = 0;
end
%--------------------------------------------------------------------------
% Start of the calculation
%--------------------------------------------------------------------------
% This line ensures that SA is non-negative.
SA(SA < 0) = 0;
% % Set lower temperature limit for water that is approx. 1C colder than the
% % freezing termperature.
% CT_frozen = -1.79e-2 - 6.7157e-2.*SA - 9.2708e-4.*p;
%
% if any(CT(:) < (CT_frozen(:) - 1))
% [Icold] = find(CT < CT_frozen - 1);
% CT(Icold) = NaN;
% end
cp0 = 3991.86795711963; % from Eqn. (3.3.3) of IOC et al. (2010).
sfac = 0.0248826675584615; % sfac = 1/(40*(35.16504/35)).
offset = 5.971840214030754e-1; % offset = deltaS*sfac.
x2 = sfac.*SA;
xs = sqrt(x2 + offset);
ys = CT.*0.025;
z = p.*1e-4;
h001 = 1.0769995862e-3;
h002 = -3.0399571905e-5;
h003 = 3.3285389740e-6;
h004 = -2.8273403593e-7;
h005 = 2.1062306160e-8;
h006 = -2.1078768810e-9;
h007 = 2.8019291329e-10;
h011 = -1.5649734675e-5;
h012 = 9.2528827145e-6;
h013 = -3.9121289103e-7;
h014 = -9.1317516383e-8;
h015 = 6.2908199804e-8;
h021 = 2.7762106484e-5;
h022 = -5.8583034265e-6;
h023 = 7.1016762467e-7;
h024 = 7.1739762898e-8;
h031 = -1.6521159259e-5;
h032 = 3.9639828087e-6;
h033 = -1.5377513346e-7;
h042 = -1.7051093741e-6;
h043 = -2.1117638838e-8;
h041 = 6.9111322702e-6;
h051 = -8.0539615540e-7;
h052 = 2.5368383407e-7;
h061 = 2.0543094268e-7;
h101 = -3.1038981976e-4;
h102 = 1.21312343735e-5;
h103 = -1.9494810995e-7;
h104 = 9.0775471288e-8;
h105 = -2.2294250846e-8;
h111 = 3.5009599764e-5;
h112 = -4.7838544078e-6;
h113 = -1.8566384852e-6;
h114 = -6.8239240593e-8;
h121 = -3.7435842344e-5;
h122 = -1.18391541805e-7;
h123 = 1.3045795693e-7;
h131 = 2.4141479483e-5;
h132 = -1.72793868275e-6;
h133 = 2.5872962697e-9;
h141 = -8.7595873154e-6;
h142 = 6.4783588915e-7;
h151 = -3.3052758900e-7;
h201 = 6.6928067038e-4;
h202 = -1.7396230487e-5;
h203 = -1.6040750532e-6;
h204 = 4.1865759450e-9;
h211 = -4.3592678561e-5;
h212 = 5.5504173825e-6;
h213 = 1.8206916278e-6;
h221 = 3.5907822760e-5;
h222 = 1.46416731475e-6;
h223 = -2.1910368022e-7;
h231 = -1.4353633048e-5;
h232 = 1.5827653039e-7;
h241 = 4.3703680598e-6;
h301 = -8.5047933937e-4;
h302 = 1.87353886525e-5;
h303 = 1.6421035666e-6;
h311 = 3.4532461828e-5;
h312 = -4.9223558922e-6;
h313 = -4.5147285423e-7;
h321 = -1.8698584187e-5;
h322 = -2.4413069600e-7;
h331 = 2.2863324556e-6;
h401 = 5.8086069943e-4;
h402 = -8.6611093060e-6;
h403 = -5.9373249090e-7;
h411 = -1.1959409788e-5;
h421 = 3.8595339244e-6;
h412 = 1.2954612630e-6;
h501 = -2.1092370507e-4;
h502 = 1.54637136265e-6;
h511 = 1.3864594581e-6;
h601 = 3.1932457305e-5;
dynamic_enthalpy = z.*(h001 + xs.*(h101 + xs.*(h201 + xs.*(h301 + xs.*(h401 ...
+ xs.*(h501 + h601.*xs))))) + ys.*(h011 + xs.*(h111 + xs.*(h211 + xs.*(h311 ...
+ xs.*(h411 + h511.*xs)))) + ys.*(h021 + xs.*(h121 + xs.*(h221 + xs.*(h321 ...
+ h421.*xs))) + ys.*(h031 + xs.*(h131 + xs.*(h231 + h331.*xs)) + ys.*(h041 ...
+ xs.*(h141 + h241.*xs) + ys.*(h051 + h151.*xs + h061.*ys))))) + z.*(h002 ...
+ xs.*(h102 + xs.*(h202 + xs.*(h302 + xs.*(h402 + h502.*xs)))) + ys.*(h012 ...
+ xs.*(h112 + xs.*(h212 + xs.*(h312 + h412.*xs))) + ys.*(h022 + xs.*(h122 ...
+ xs.*(h222 + h322.*xs)) + ys.*(h032 + xs.*(h132 + h232.*xs) + ys.*(h042 ...
+ h142.*xs + h052.*ys)))) + z.*(h003 + xs.*(h103 + xs.*(h203 + xs.*(h303 ...
+ h403.*xs))) + ys.*(h013 + xs.*(h113 + xs.*(h213 + h313.*xs)) + ys.*(h023 ...
+ xs.*(h123 + h223.*xs) + ys.*(h033 + h133.*xs + h043.*ys))) + z.*(h004 ...
+ xs.*(h104 + h204.*xs) + ys.*(h014 + h114.*xs + h024.*ys) + z.*(h005 ...
+ h105.*xs + h015.*ys + z.*(h006 + h007.*z))))));
enthalpy = cp0.*CT + dynamic_enthalpy.*1e8; %Note. 1e8 = db2Pa*1e4;
% db2Pa = 1e4; % factor to convert from dbar to Pa
%--------------------------------------------------------------------------
% This function calculates enthalpy using the computationally-efficient
% expression for specific volume in terms of SA, CT and p. If one wanted
% to compute enthalpy from SA, CT, and p with the full TEOS-10 Gibbs
% function, the following lines of code will enable this.
%
% t = gsw_t_from_CT(SA,CT,p);
% enthalpy = gsw_enthalpy_t_exact(SA,t,p);
%
% or call the following, it is identical to the lines above.
%
% enthalpy = gsw_enthalpy_CT_exact(SA,CT,p)
%
%-----------------This is the end of the alternative code------------------
if transposed
enthalpy = enthalpy.';
end
end