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gsw_isopycnal_vs_ntp_CT_ratio.m
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function [G_CT, p_mid] = gsw_isopycnal_vs_ntp_CT_ratio(SA,CT,p,p_ref)
% gsw_isopycnal_vs_ntp_CT_ratio ratio of the gradient of
% Conservative Temperature in a potential density surface
% to that in a neutral tangent plane (i.e. in a locally
% referenced potential density surface) (75-term equation)
%==========================================================================
%
% USAGE:
% [G_CT, p_mid] = gsw_isopycnal_vs_ntp_CT_ratio(SA,CT,p,p_ref)
%
% DESCRIPTION:
% Calculates the ratio of the two-dimensional gradient of Conservative
% Temperature in a potential density surface (with reference sea pressure
% (p_ref)) versus that in the neutral tangent plane (see Eqns. (3.17.3)
% and (3.17.4) of IOC et al. (2010)). This ratio has been called the
% "isopycnal Conservative Temperature gradient ratio". This ratio is
% evaluated at the mid pressure between the individual data points in the
% vertical. The reference sea pressure of the potential density surface
% must have a constant value. This function uses the computationally
% efficient 75-term expression for specific volume in terms of SA, CT and
% p (Roquet et al., 2015)
%
% Note that this 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 )
% p_ref = reference sea pressure of the potential density surface [ dbar ]
% ( i.e. absolute reference pressure - 10.1325 dbar )
%
% SA & CT need to have the same dimensions.
% p & p_ref may have dimensions 1x1 or Mx1 or 1xN or MxN, where SA & CT
% are MxN
%
% OUTPUT:
% G_CT = the ratio of the gradient of CT in a potential density surface
% to that in a neutral tangent plane. G_CT is output on the
% same vertical (M-1)xN grid as p_mid, where M & N are the
% dimensions of SA. G_CT is dimensionless. [ unitless ]
% p_mid = mid pressure between the individual points of the p grid.
% That is, p_mid is on a (M-1)xN grid.
% p_mid has units of: [ dbar ]
%
% AUTHOR:
% Trevor McDougall, Paul Barker & David Jackett [ 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 Eqns. (3.17.3) and (3.17.4) of this TEOS-10 Manual.
%
% McDougall, T. J., 1987: Neutral surfaces. Journal of Physical
% Oceanography, 17, 1950-1964. See Eqn. (29) of this paper.
%
% 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 | nargin == 4)
error('gsw_isopycnal_vs_ntp_CT_ratio: Requires three or four inputs')
end %if
if ~(nargout == 2)
error('gsw_isopycnal_vs_ntp_CT_ratio: Requires two outputs')
end
if nargin == 3
% Assume reference pressure is 0 dbar.
p_ref = 0;
end
if ~isscalar(unique(p_ref))
error('gsw_isopycnal_vs_ntp_CT_ratio: The reference pressures differ, they should be unique')
end
[ms,ns] = size(SA);
[mt,nt] = size(CT);
[mp,np] = size(p);
if (mt ~= ms | nt ~= ns)
error('gsw_isopycnal_vs_ntp_CT_ratio: SA and CT must have same dimensions, p can be a vector')
end
if (ms*ns == 1)
error('gsw_isopycnal_vs_ntp_CT_ratio: There must be at least 2 values')
end
if (mp == 1) & (np == 1) % p scalar - must be two bottles
error('gsw_isopycnal_vs_ntp_CT_ratio: There must be at least 2 values')
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_isopycnal_vs_ntp_CT_ratio: Inputs array dimensions arguments do not agree')
end %if
if ms == 1
SA = SA.';
CT = CT.';
p = p.';
[mp,np] = size(p);
transposed = 1;
else
transposed = 0;
end
p_ref = unique(p_ref).*ones(mp-1,np); %resize the reference pressure
%--------------------------------------------------------------------------
% Start of the calculation
%--------------------------------------------------------------------------
Ishallow = 1:(mp-1);
Ideep = 2:mp;
p_mid = 0.5*(p(Ishallow,:) + p(Ideep,:));
SA_mid = 0.5*(SA(Ishallow,:) + SA(Ideep,:));
CT_mid = 0.5*(CT(Ishallow,:) + CT(Ideep,:));
dSA = SA(Ishallow,:) - SA(Ideep,:);
dCT = CT(Ishallow,:) - CT(Ideep,:);
[dummy, alpha, beta] = gsw_specvol_alpha_beta(SA_mid,CT_mid,p_mid);
[dummy, alpha_pref, beta_pref] = gsw_specvol_alpha_beta(SA_mid,CT_mid,p_ref);
%--------------------------------------------------------------------------
% This function calculates G_CT using the computationally-efficient
% 75-term expression for specific volume as a function of SA, CT and p.
% If one wanted to compute this with the full TEOS-10 Gibbs function
% expression for specific volume, the following lines of code will enable
% this.
%
% t_mid = gsw_t_from_CT(SA_mid,CT_mid,p_mid);
% alpha = gsw_alpha_wrt_CT_t_exact(SA_mid,t_mid,p_mid);
% beta = gsw_beta_const_CT_t_exact(SA_mid,t_mid,p_mid);
% alpha_pref = gsw_alpha_wrt_CT_t_exact(SA_mid,t_mid,p_ref);
% beta_pref = gsw_beta_const_CT_t_exact(SA_mid,t_mid,p_ref);
%
%------------This is the end of the alternative code-----------------------
numerator = dCT.*alpha./beta - dSA;
denominator = dCT.*alpha_pref./beta_pref - dSA;
G_CT = nan(size(SA_mid));
G_CT(denominator ~= 0) = numerator(denominator ~= 0)./denominator(denominator ~= 0);
if transposed
G_CT = G_CT.';
p_mid = p_mid.';
end
end