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gsw_isopycnal_slope_ratio.m
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function isopycnal_slope_ratio = gsw_isopycnal_slope_ratio(SA,CT,p,p_ref)
% gsw_isopycnal_slope_ratio ratio of the slopes of isopycnals
% on the SA-CT diagram for p and p_ref
% (75-term equation)
% =========================================================================
%
% USAGE:
% isopycnal_slope_ratio = gsw_isopycnal_slope_ratio(SA,CT,p,p_ref)
%
% DESCRIPTION:
% Calculates the ratio of alpha/beta at pressure, p, to that at reference
% pressure, p_ref. 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 )
% pr = reference pressure [ dbar ]
% ( i.e. absolute reference pressure - 10.1325 dbar )
%
% SA & CT need to have the same dimensions.
% p and p_ref may have dimensions 1x1 or Mx1 or 1xN or MxN, where
% SA and CT are MxN
%
% OUTPUT:
% isopycnal_slope_ratio
% = The ratio of alpha/beta evaluated at [ unitless ]
% pressure, p, to that at reference pressure, p_ref.
%
% 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 Eqn. (3.17.2) of this TEOS-10 Manual.
%
% 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.
%
% This software is available from http://www.TEOS-10.org
%
%==========================================================================
%--------------------------------------------------------------------------
% Check variables and resize if necessary
%--------------------------------------------------------------------------
if ~(nargin == 4)
error('gsw_isopycnal_slope_ratio: Requires four inputs')
end %if
[ms,ns] = size(SA);
[mt,nt] = size(CT);
[mp,np] = size(p);
[mpr,npr] = size(p_ref);
if (mt ~= ms | nt ~= ns)
error('gsw_isopycnal_slope_ratio: 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_isopycnal_slope_ratio: Inputs array dimensions arguments do not agree')
end %if
if (mpr == 1) & (npr == 1) % p_ref scalar - fill to size of SA
p_ref = p_ref*ones(size(SA));
elseif (ns == npr) & (mpr == 1) % p_ref is row vector,
p_ref = p_ref(ones(1,ms), :); % copy down each column.
elseif (ms == mpr) & (npr == 1) % p_ref is column vector,
p_ref = p_ref(:,ones(1,ns)); % copy across each row.
elseif (ns == mpr) & (npr == 1) % p_ref is a transposed row vector,
p_ref = p_ref.'; % transposed then
p_ref = p_ref(ones(1,ms), :); % copy down each column.
elseif (ms == mpr) & (ns == npr)
% ok
else
error('gsw_isopycnal_slope_ratio: Inputs array dimensions arguments do not agree')
end %if
if ms == 1
SA = SA.';
CT = CT.';
p = p.';
p_ref = p_ref.';
transposed = 1;
else
transposed = 0;
end
%--------------------------------------------------------------------------
% Start of the calculation
%--------------------------------------------------------------------------
[dummy, alpha, beta] = gsw_specvol_alpha_beta(SA,CT,p);
[dummy, alpha_pref, beta_pref] = gsw_specvol_alpha_beta(SA,CT,p_ref);
%--------------------------------------------------------------------------
% This function calculates isopycnal_slope_ratio 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 = gsw_pt_from_CT(SA,CT,p);
% alpha = gsw_alpha_wrt_CT_t_exact(SA,t,p);
% beta = gsw_beta_const_CT_t_exact(SA,t,p);
% tr = gsw_pt_from_t(SA,pt,p_ref0,p_ref);
% alpha_pref = gsw_alpha_wrt_CT_t_exact(SA,tr,p_ref);
% beta_pref = gsw_beta_const_CT_t_exact(SA,tr,p_ref);
%
%--------------This is the end of the alternative code---------------------
isopycnal_slope_ratio = NaN(size(SA));
isopycnal_slope_ratio(alpha_pref ~= 0) = (alpha(alpha_pref ~= 0).*beta_pref(alpha_pref ~= 0))./ ...
(alpha_pref(alpha_pref ~= 0).*beta(alpha_pref ~= 0));
if transposed
isopycnal_slope_ratio = isopycnal_slope_ratio.';
end
end