source: Roms_tools/Preprocessing_tools/rho_eos.m @ 2

function [rho,bvf]=rho_eos(Tt,Ts,z_r,z_w,g,rho0)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% function [rho,bvf]=rho_eos(Tt,Ts,z_r,z_w,g,rho0)
%
% Computes density via Equation Of State (EOS) for seawater.
% If so prescribed, non-linear EOS of Jackett and McDougall (1995)
% is used.
%
% Tt potential temperature [deg Celsius].
% Ts salinity [PSU].
% Tz pressure/depth, [depth in meters and negative].
%
% K0, K1 and K2 are the pressure polynomial coefficients for secant
% bulk modulus, so that
%
%               bulk = K0 - K1 * z + K2 * z**2 ;
%
% while rho1 is sea-water density [kg/m^3] at standard pressure
% of 1 Atm, so that the density anomaly at in-sity pressure is
%
%               rho = rho1 / (1 + z / bulk) - 1000
%
% If so prescribed, it also computes the Brunt-Vaisala frequency
% [1/s^2] at horizontal RHO-points and vertical W-points,
%
%                   bvf = - g/rho0 d(rho)/d(z).
%
%  In computation of bvf the density anomaly difference is computed
%  by adiabatically lowering/rising the water parcel from RHO point
%  above/below to the W-point depth at "z_w".
%
%  Reference:
%
%  Jackett, D. R. and T. J. McDougall, 1995, Minimal Adjustment of
%  Hydrostatic Profiles to Achieve Static Stability, Journ of Atmos.
%  and Oceanic Techn., vol. 12, pp. 381-389.
%
% << This equation of state formulation has been derived by Jackett
%    and McDougall (1992), unpublished manuscript, CSIRO, Australia.
%    It computes in-situ density anomaly as a function of potential
%    temperature (Celsius) relative to the surface, salinity (PSU),
%    and depth (meters).  It assumes  no  pressure  variation along
%    geopotential  surfaces,  that  is,  depth  and  pressure  are
%    interchangeable. >>
%                                          John Wilkin, 29 July 92
%
% Check Values: T=3 C S=35.5 PSU Z=-5000 m rho=1050.3639165364 
%
% 
%  Further Information:  
%  http://www.brest.ird.fr/Roms_tools/
%  
%  This file is part of ROMSTOOLS
%
%  ROMSTOOLS is free software; you can redistribute it and/or modify
%  it under the terms of the GNU General Public License as published
%  by the Free Software Foundation; either version 2 of the License,
%  or (at your option) any later version.
%
%  ROMSTOOLS is distributed in the hope that it will be useful, but
%  WITHOUT ANY WARRANTY; without even the implied warranty of
%  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%  GNU General Public License for more details.
%
%  You should have received a copy of the GNU General Public License
%  along with this program; if not, write to the Free Software
%  Foundation, Inc., 59 Temple Place, Suite 330, Boston,
%  MA  02111-1307  USA
%
%  Copyright (c) 2001-2006 by Pierrick Penven 
%  e-mail:Pierrick.Penven@ird.fr  
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
[N,M,L]=size(Tt);

A00=+19092.56;A01=+209.8925;
A02=-3.041638;A03=-1.852732e-3;A04=-1.361629e-5;A10=104.4077;
A11=-6.500517;A12=+0.1553190;A13=2.326469e-4;AS0=-5.587545;
AS1=+0.7390729;AS2=-1.909078e-2;B00=+4.721788e-1;B01=+1.028859e-2;
B02=-2.512549e-4;B03=-5.939910e-7;B10=-1.571896e-2;B11=-2.598241e-4;
B12=+7.267926e-6;BS1=+2.042967e-3;E00=+1.045941e-5;E01=-5.782165e-10;
E02=+1.296821e-7;E10=-2.595994e-7;E11=-1.248266e-9;E12=-3.508914e-9;

QR=+999.842594;Q01=+6.793952e-2;Q02=-9.095290e-3;
Q03=+1.001685e-4;Q04=-1.120083e-6;Q05=+6.536332e-9;Q10=+0.824493;
Q11=-4.08990e-3;Q12=+7.64380e-5;Q13=-8.24670e-7;Q14=+5.38750e-9;
QS0=-5.72466e-3;QS1=+1.02270e-4;QS2=-1.65460e-6;Q20=+4.8314e-4;


sqrtTs=sqrt(Ts);

K0=A00+Tt.*(A01+Tt.*(A02+Tt.*(A03+Tt.*A04)))...
   +Ts.*(A10+Tt.*(A11+Tt.*(A12+Tt.*A13))...
   +sqrtTs.*(AS0+Tt.*(AS1+Tt.*AS2)));
K1=B00+Tt.*(B01+Tt.*(B02+Tt.*B03))...
   +Ts.*(B10+Tt.*(B11+Tt.*B12)+sqrtTs.*BS1);
K2=E00+Tt.*(E01+Tt.*E02)...
   +Ts.*(E10+Tt.*(E11+Tt.*E12));
rho1=QR+Tt.*(Q01+Tt.*(Q02+Tt.*(Q03+Tt.*(Q04+Tt.*Q05))))...
     +Ts.*(Q10+Tt.*(Q11+Tt.*(Q12+Tt.*(Q13+Tt.*Q14)))...
     +sqrtTs.*(QS0+Tt.*(QS1+Tt.*QS2))+Ts.*Q20);
rho=rho1./(1+0.1.*z_r./(K0-z_r.*(K1-z_r.*K2)));

if nargin > 3
  bvf=0.*z_w;
  cff=g./rho0;
  bvf(2:N,:,:)=-cff*(rho1(2:N,:,:)./...
              (1.+0.1.*z_w(2:N,:,:)./...
              ( K0(2:N,:,:)-z_w(2:N,:,:).*(K1(2:N,:,:)-z_w(2:N,:,:).*K2(2:N,:,:))))...
              -rho1(1:N-1,:,:)./( 1.+0.1.*z_w(2:N,:,:)./...
              ( K0(1:N-1,:,:)-z_w(2:N,:,:).*(K1(1:N-1,:,:)-z_w(2:N,:,:).*K2(1:N-1,:,:)))))...
              ./(z_r(2:N,:,:)-z_r(1:N-1,:,:));
else
  bvf=0;
end             
return