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gsw_oceanographic_toolbox.c
11495 lines (10409 loc) · 471 KB
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gsw_oceanographic_toolbox.c
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/*
** $Id: gsw_oceanographic_toolbox-head,v c61271a7810d 2016/08/19 20:04:03 fdelahoyde $
** Version: 3.05.0-3
**
** This is a translation of the original f90 source code into C
** by the Shipboard Technical Support Computing Resources group
** at Scripps Institution of Oceanography -- sts-cr@sio.ucsd.edu.
** The original notices follow.
**
==========================================================================
Gibbs SeaWater (GSW) Oceanographic Toolbox of TEOS-10 (Fortran)
==========================================================================
This is a subset of functions contained in the Gibbs SeaWater (GSW)
Oceanographic Toolbox of TEOS-10.
Version 1.0 written by David Jackett
Modified by Paul Barker (version 3.02)
Modified by Glenn Hyland (version 3.04+)
For help with this Oceanographic Toolbox email: help@teos-10.org
This software is available from http://www.teos-10.org
==========================================================================
gsw_data_v3_0.nc
NetCDF file that contains the global data set of Absolute Salinity Anomaly
Ratio, the global data set of Absolute Salinity Anomaly atlas, and check
values and computation accuracy values for use in gsw_check_function.
The data set gsw_data_v3_0.nc must not be tampered with.
gsw_check_function.f90
Contains the check functions. We suggest that after downloading, unzipping
and installing the toolbox the user runs this program to ensure that the
toolbox is installed correctly and there are no conflicts. This toolbox has
been tested to compile and run with gfortran.
cd test
make
./gsw_check
Note that gfortran is the name of the GNU Fortran project, developing a
free Fortran 95/2003/2008 compiler for GCC, the GNU Compiler Collection.
It is available from http://gcc.gnu.org/fortran/
==========================================================================
*/
#include "gswteos-10.h"
#ifdef __cplusplus
# define DCOMPLEX std::complex<double>
#else
# define DCOMPLEX double complex
# define real(x) creal(x)
# define log(x) clog(x)
#endif
#include "gsw_internal_const.h"
/*
!==========================================================================
subroutine gsw_add_barrier(input_data,lon,lat,long_grid,lat_grid,dlong_grid,dlat_grid,output_data)
!==========================================================================
! Adds a barrier through Central America (Panama) and then averages
! over the appropriate side of the barrier
!
! data_in : data [unitless]
! lon : Longitudes of data degrees east [0 ... +360]
! lat : Latitudes of data degrees north [-90 ... +90]
! longs_grid : Longitudes of regular grid degrees east [0 ... +360]
! lats_grid : Latitudes of regular grid degrees north [-90 ... +90]
! dlongs_grid : Longitude difference of regular grid degrees [deg longitude]
! dlats_grid : Latitude difference of regular grid degrees [deg latitude]
!
! output_data : average of data depending on which side of the
! Panama canal it is on [unitless]
*/
void
gsw_add_barrier(double *input_data, double lon, double lat,
double long_grid, double lat_grid, double dlong_grid,
double dlat_grid, double *output_data)
{
GSW_SAAR_DATA;
int above_line[4];
int k, nmean, above_line0, kk;
double r, lats_line, data_mean;
k = gsw_util_indx(longs_pan,npan,lon);
/* the lon/lat point */
r = (lon-longs_pan[k])/(longs_pan[k+1]-longs_pan[k]);
lats_line = lats_pan[k] + r*(lats_pan[k+1]-lats_pan[k]);
above_line0 = (lats_line <= lat);
k = gsw_util_indx(longs_pan,npan,long_grid);
/*the 1 & 4 lon/lat points*/
r = (long_grid-longs_pan[k])/
(longs_pan[k+1]-longs_pan[k]);
lats_line = lats_pan[k] + r*(lats_pan[k+1]-lats_pan[k]);
above_line[0] = (lats_line <= lat_grid);
above_line[3] = (lats_line <= lat_grid+dlat_grid);
k = gsw_util_indx(longs_pan,6,long_grid+dlong_grid);
/*the 2 & 3 lon/lat points */
r = (long_grid+dlong_grid-longs_pan[k])/
(longs_pan[k+1]-longs_pan[k]);
lats_line = lats_pan[k] + r*(lats_pan[k+1]-lats_pan[k]);
above_line[1] = (lats_line <= lat_grid);
above_line[2] = (lats_line <= lat_grid+dlat_grid);
nmean = 0;
data_mean = 0.0;
for (kk=0; kk<4; kk++) {
if ((fabs(input_data[kk]) <= 100.0) &&
above_line0 == above_line[kk]) {
nmean = nmean+1;
data_mean = data_mean+input_data[kk];
}
}
if (nmean == 0)
data_mean = 0.0; /*errorreturn*/
else
data_mean = data_mean/nmean;
for (kk=0; kk<4; kk++) {
if ((fabs(input_data[kk]) >= 1.0e10) ||
above_line0 != above_line[kk])
output_data[kk] = data_mean;
else
output_data[kk] = input_data[kk];
}
return;
}
/*
!==========================================================================
subroutine gsw_add_mean(data_in,data_out)
!==========================================================================
! Replaces NaN's with non-nan mean of the 4 adjacent neighbours
!
! data_in : data set of the 4 adjacent neighbours
!
! data_out : non-nan mean of the 4 adjacent neighbours [unitless]
*/
void
gsw_add_mean(double *data_in, double *data_out)
{
int k, nmean;
double data_mean;
nmean = 0;
data_mean = 0.0;
for (k=0; k<4; k++) {
if (fabs(data_in[k]) <= 100.0) {
nmean++;
data_mean = data_mean+data_in[k];
}
}
if (nmean == 0.0)
data_mean = 0.0; /*errorreturn*/
else
data_mean = data_mean/nmean;
for (k=0; k<4; k++) {
if (fabs(data_in[k]) >= 100.0)
data_out[k] = data_mean;
else
data_out[k] = data_in[k];
}
return;
}
/*
!==========================================================================
function gsw_infunnel(sa,ct,p)
!==========================================================================
! "oceanographic funnel" check for the 75-term equation
!
! sa : Absolute Salinity [g/kg]
! ct : Conservative Temperature [deg C]
! p : sea pressure [dbar]
!
! gsw_infunnel : 0, if SA, CT and p are outside the "funnel"
! 1, if SA, CT and p are inside the "funnel"
!
! Note. The term "funnel" (McDougall et al., 2003) describes the range of
! SA, CT and p over which the error in the fit of the computationally
! efficient 75-term expression for specific volume in terms of SA, CT
! and p was calculated (Roquet et al., 2015).
*/
int
gsw_infunnel(double sa, double ct, double p)
{
return !(p > 8000 ||
sa < 0 ||
sa > 42 ||
(p < 500 && ct < gsw_ct_freezing(sa, p, 0)) ||
(p >= 500 && p < 6500 && sa < p * 5e-3 - 2.5) ||
(p >= 500 && p < 6500 && ct > (31.66666666666667 - p * 3.333333333333334e-3)) ||
(p >= 500 && ct < gsw_ct_freezing(sa, 500, 0)) ||
(p >= 6500 && sa < 30) ||
(p >= 6500 && ct > 10.0)
);
}
/*
!==========================================================================
function gsw_adiabatic_lapse_rate_from_ct(sa,ct,p)
!==========================================================================
! Calculates the adiabatic lapse rate from Conservative Temperature
!
! sa : Absolute Salinity [g/kg]
! ct : Conservative Temperature [deg C]
! p : sea pressure [dbar]
!
! gsw_adiabatic_lapse_rate_from_ct : adiabatic lapse rate [K/Pa]
*/
double
gsw_adiabatic_lapse_rate_from_ct(double sa, double ct, double p)
{
int n0=0, n1=1, n2=2;
double pt0, pr0=0.0, t;
pt0 = gsw_pt_from_ct(sa,ct);
t = gsw_pt_from_t(sa,pt0,pr0,p);
return (-gsw_gibbs(n0,n1,n1,sa,t,p)/gsw_gibbs(n0,n2,n0,sa,t,p));
}
/*
!==========================================================================
elemental function gsw_adiabatic_lapse_rate_ice (t, p)
!==========================================================================
!
! Calculates the adiabatic lapse rate of ice.
!
! t = in-situ temperature (ITS-90) [ deg C ]
! p = sea pressure [ dbar ]
! ( i.e. absolute pressure - 10.1325 dbar )
!
! Note. The output is in unit of degrees Celsius per Pa,
! (or equivalently K/Pa) not in units of K/dbar.
!--------------------------------------------------------------------------
*/
double
gsw_adiabatic_lapse_rate_ice(double t, double p)
{
return (-gsw_gibbs_ice(1,1,t,p)/gsw_gibbs_ice(2,0,t,p));
}
/*
!==========================================================================
function gsw_alpha(sa,ct,p)
!==========================================================================
! Calculates the thermal expansion coefficient of seawater with respect to
! Conservative Temperature using the computationally-efficient 48-term
! expression for density in terms of SA, CT and p (IOC et al., 2010)
!
! sa : Absolute Salinity [g/kg]
! ct : Conservative Temperature [deg C]
! p : sea pressure [dbar]
!
! gsw_alpha : thermal expansion coefficient of seawater (48 term equation)
*/
double
gsw_alpha(double sa, double ct, double p)
{
GSW_TEOS10_CONSTANTS;
GSW_SPECVOL_COEFFICIENTS;
double xs, ys, z, v_ct_part;
xs = sqrt(gsw_sfac*sa + offset);
ys = ct*0.025;
z = p*1e-4;
v_ct_part = a000
+ xs*(a100 + xs*(a200 + xs*(a300 + xs*(a400 + a500*xs))))
+ ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030
+ xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys ))))
+ z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs)))
+ ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys)))
+ z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012
+ xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys))
+ z*(a003 + a103*xs + a013*ys + a004*z)));
return (0.025*v_ct_part/gsw_specvol(sa,ct,p));
}
/*
!==========================================================================
function gsw_alpha_on_beta(sa,ct,p)
!==========================================================================
! Calculates alpha divided by beta, where alpha is the thermal expansion
! coefficient and beta is the saline contraction coefficient of seawater
! from Absolute Salinity and Conservative Temperature. This function uses
! the computationally-efficient expression for specific volume in terms of
! SA, CT and p (Roquet et al., 2014).
!
! sa : Absolute Salinity [g/kg]
! ct : Conservative Temperature [deg C]
! p : sea pressure [dbar]
!
! alpha_on_beta
! : thermal expansion coefficient with respect to [kg g^-1 K^-1]
! Conservative Temperature divided by the saline
! contraction coefficient at constant Conservative
! Temperature
*/
double
gsw_alpha_on_beta(double sa, double ct, double p)
{
GSW_TEOS10_CONSTANTS;
GSW_SPECVOL_COEFFICIENTS;
double xs, ys, z, v_ct_part, v_sa_part;
xs = sqrt(gsw_sfac*sa + offset);
ys = ct*0.025;
z = p*1e-4;
v_ct_part = a000
+ xs*(a100 + xs*(a200 + xs*(a300 + xs*(a400 + a500*xs))))
+ ys*(a010 + xs*(a110 + xs*(a210 + xs*(a310 + a410*xs)))
+ ys*(a020 + xs*(a120 + xs*(a220 + a320*xs)) + ys*(a030
+ xs*(a130 + a230*xs) + ys*(a040 + a140*xs + a050*ys ))))
+ z*(a001 + xs*(a101 + xs*(a201 + xs*(a301 + a401*xs)))
+ ys*(a011 + xs*(a111 + xs*(a211 + a311*xs)) + ys*(a021
+ xs*(a121 + a221*xs) + ys*(a031 + a131*xs + a041*ys)))
+ z*(a002 + xs*(a102 + xs*(a202 + a302*xs)) + ys*(a012
+ xs*(a112 + a212*xs) + ys*(a022 + a122*xs + a032*ys))
+ z*(a003 + a103*xs + a013*ys + a004*z)));
v_sa_part = b000
+ xs*(b100 + xs*(b200 + xs*(b300 + xs*(b400 + b500*xs))))
+ ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030
+ xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys))))
+ z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs)))
+ ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021
+ xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys)))
+ z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012
+ xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys))
+ z*(b003 + b103*xs + b013*ys + b004*z)));
return (-(v_ct_part*xs)/(20.0*gsw_sfac*v_sa_part));
}
/*
!==========================================================================
function gsw_alpha_wrt_t_exact(sa,t,p)
!==========================================================================
! Calculates thermal expansion coefficient of seawater with respect to
! in-situ temperature
!
! sa : Absolute Salinity [g/kg]
! t : insitu temperature [deg C]
! p : sea pressure [dbar]
!
! gsw_alpha_wrt_t_exact : thermal expansion coefficient [1/K]
! wrt (in-situ) temperature
*/
double
gsw_alpha_wrt_t_exact(double sa, double t, double p)
{
int n0=0, n1=1;
return (gsw_gibbs(n0,n1,n1,sa,t,p)/gsw_gibbs(n0,n0,n1,sa,t,p));
}
/*
!==========================================================================
elemental function gsw_alpha_wrt_t_ice (t, p)
!==========================================================================
!
! Calculates the thermal expansion coefficient of ice with respect to
! in-situ temperature.
!
! t = in-situ temperature (ITS-90) [ deg C ]
! p = sea pressure [ dbar ]
! ( i.e. absolute pressure - 10.1325 dbar )
!
! alpha_wrt_t_ice = thermal expansion coefficient of ice with respect
! to in-situ temperature [ 1/K ]
!--------------------------------------------------------------------------
*/
double
gsw_alpha_wrt_t_ice(double t, double p)
{
return (gsw_gibbs_ice(1,1,t,p)/gsw_gibbs_ice(0,1,t,p));
}
/*
!==========================================================================
function gsw_beta(sa,ct,p)
!==========================================================================
! Calculates the saline (i.e. haline) contraction coefficient of seawater
! at constant Conservative Temperature using the computationally-efficient
! expression for specific volume in terms of SA, CT and p
! (Roquet et al., 2014).
!
! sa : Absolute Salinity [g/kg]
! ct : Conservative Temperature (ITS-90) [deg C]
! p : sea pressure [dbar]
! ( i.e. absolute pressure - 10.1325 dbar )
!
! beta : saline contraction coefficient of seawater [kg/g]
! at constant Conservative Temperature
*/
double
gsw_beta(double sa, double ct, double p)
{
GSW_TEOS10_CONSTANTS;
GSW_SPECVOL_COEFFICIENTS;
double xs, ys, z, v_sa_part;
xs = sqrt(gsw_sfac*sa + offset);
ys = ct*0.025;
z = p*1e-4;
v_sa_part = b000
+ xs*(b100 + xs*(b200 + xs*(b300 + xs*(b400 + b500*xs))))
+ ys*(b010 + xs*(b110 + xs*(b210 + xs*(b310 + b410*xs)))
+ ys*(b020 + xs*(b120 + xs*(b220 + b320*xs)) + ys*(b030
+ xs*(b130 + b230*xs) + ys*(b040 + b140*xs + b050*ys))))
+ z*(b001 + xs*(b101 + xs*(b201 + xs*(b301 + b401*xs)))
+ ys*(b011 + xs*(b111 + xs*(b211 + b311*xs)) + ys*(b021
+ xs*(b121 + b221*xs) + ys*(b031 + b131*xs + b041*ys)))
+ z*(b002 + xs*(b102 + xs*(b202 + b302*xs))+ ys*(b012
+ xs*(b112 + b212*xs) + ys*(b022 + b122*xs + b032*ys))
+ z*(b003 + b103*xs + b013*ys + b004*z)));
return (-v_sa_part*0.5*gsw_sfac/(gsw_specvol(sa,ct,p)*xs));
}
/*
!==========================================================================
function gsw_beta_const_t_exact(sa,t,p)
!==========================================================================
! Calculates saline (haline) contraction coefficient of seawater at
! constant in-situ temperature.
!
! sa : Absolute Salinity [g/kg]
! t : in-situ temperature [deg C]
! p : sea pressure [dbar]
!
! beta_const_t_exact : haline contraction coefficient [kg/g]
*/
double
gsw_beta_const_t_exact(double sa, double t, double p)
{
int n0=0, n1=1;
return (-gsw_gibbs(n1,n0,n1,sa,t,p)/gsw_gibbs(n0,n0,n1,sa,t,p));
}
/*
!==========================================================================
function gsw_c_from_sp(sp,t,p)
!==========================================================================
! Calculates conductivity, C, from (SP,t,p) using PSS-78 in the range
! 2 < SP < 42. If the input Practical Salinity is less than 2 then a
! modified form of the Hill et al. (1986) formula is used for Practical
! Salinity. The modification of the Hill et al. (1986) expression is to
! ensure that it is exactly consistent with PSS-78 at SP = 2.
!
! The conductivity ratio returned by this function is consistent with the
! input value of Practical Salinity, SP, to 2x10^-14 psu over the full
! range of input parameters (from pure fresh water up to SP = 42 psu).
! This error of 2x10^-14 psu is machine precision at typical seawater
! salinities. This accuracy is achieved by having four different
! polynomials for the starting value of Rtx (the square root of Rt) in
! four different ranges of SP, and by using one and a half iterations of
! a computationally efficient modified Newton-Raphson technique (McDougall
! and Wotherspoon, 2012) to find the root of the equation.
!
! Note that strictly speaking PSS-78 (Unesco, 1983) defines Practical
! Salinity in terms of the conductivity ratio, R, without actually
! specifying the value of C(35,15,0) (which we currently take to be
! 42.9140 mS/cm).
!
! sp : Practical Salinity [unitless]
! t : in-situ temperature [ITS-90] [deg C]
! p : sea pressure [dbar]
!
! c : conductivity [ mS/cm ]
*/
double
gsw_c_from_sp(double sp, double t, double p)
{
GSW_TEOS10_CONSTANTS;
GSW_SP_COEFFICIENTS;
double p0 = 4.577801212923119e-3, p1 = 1.924049429136640e-1,
p2 = 2.183871685127932e-5, p3 = -7.292156330457999e-3,
p4 = 1.568129536470258e-4, p5 = -1.478995271680869e-6,
p6 = 9.086442524716395e-4, p7 = -1.949560839540487e-5,
p8 = -3.223058111118377e-6, p9 = 1.175871639741131e-7,
p10 = -7.522895856600089e-5, p11 = -2.254458513439107e-6,
p12 = 6.179992190192848e-7, p13 = 1.005054226996868e-8,
p14 = -1.923745566122602e-9, p15 = 2.259550611212616e-6,
p16 = 1.631749165091437e-7, p17 = -5.931857989915256e-9,
p18 = -4.693392029005252e-9, p19 = 2.571854839274148e-10,
p20 = 4.198786822861038e-12,
q0 = 5.540896868127855e-5, q1 = 2.015419291097848e-1,
q2 = -1.445310045430192e-5, q3 = -1.567047628411722e-2,
q4 = 2.464756294660119e-4, q5 = -2.575458304732166e-7,
q6 = 5.071449842454419e-3, q7 = -9.081985795339206e-5,
q8 = -3.635420818812898e-6, q9 = 2.249490528450555e-8,
q10 = -1.143810377431888e-3, q11 = 2.066112484281530e-5,
q12 = 7.482907137737503e-7, q13 = 4.019321577844724e-8,
q14 = -5.755568141370501e-10, q15 = 1.120748754429459e-4,
q16 = -2.420274029674485e-6, q17 = -4.774829347564670e-8,
q18 = -4.279037686797859e-9, q19 = -2.045829202713288e-10,
q20 = 5.025109163112005e-12,
s0 = 3.432285006604888e-3, s1 = 1.672940491817403e-1,
s2 = 2.640304401023995e-5, s3 = 1.082267090441036e-1,
s4 = -6.296778883666940e-5, s5 = -4.542775152303671e-7,
s6 = -1.859711038699727e-1, s7 = 7.659006320303959e-4,
s8 = -4.794661268817618e-7, s9 = 8.093368602891911e-9,
s10 = 1.001140606840692e-1, s11 = -1.038712945546608e-3,
s12 = -6.227915160991074e-6, s13 = 2.798564479737090e-8,
s14 = -1.343623657549961e-10, s15 = 1.024345179842964e-2,
s16 = 4.981135430579384e-4, s17 = 4.466087528793912e-6,
s18 = 1.960872795577774e-8, s19 = -2.723159418888634e-10,
s20 = 1.122200786423241e-12,
u0 = 5.180529787390576e-3, u1 = 1.052097167201052e-3,
u2 = 3.666193708310848e-5, u3 = 7.112223828976632e0,
u4 = -3.631366777096209e-4, u5 = -7.336295318742821e-7,
u6 = -1.576886793288888e+2, u7 = -1.840239113483083e-3,
u8 = 8.624279120240952e-6, u9 = 1.233529799729501e-8,
u10 = 1.826482800939545e+3, u11 = 1.633903983457674e-1,
u12 = -9.201096427222349e-5, u13 = -9.187900959754842e-8,
u14 = -1.442010369809705e-10, u15 = -8.542357182595853e+3,
u16 = -1.408635241899082e0, u17 = 1.660164829963661e-4,
u18 = 6.797409608973845e-7, u19 = 3.345074990451475e-10,
u20 = 8.285687652694768e-13;
double t68, ft68, x, rtx=0.0, dsp_drtx, sqrty,
part1, part2, hill_ratio, sp_est,
rtx_old, rt, aa, bb, cc, dd, ee, ra,r, rt_lc, rtxm,
sp_hill_raw;
t68 = t*1.00024e0;
ft68 = (t68 - 15e0)/(1e0 + k*(t68 - 15e0));
x = sqrt(sp);
/*
|--------------------------------------------------------------------------
! Finding the starting value of Rtx, the square root of Rt, using four
! different polynomials of SP and t68.
!--------------------------------------------------------------------------
*/
if (sp >= 9.0) {
rtx = p0 + x*(p1 + p4*t68 + x*(p3 + p7*t68 + x*(p6
+ p11*t68 + x*(p10 + p16*t68 + x*p15))))
+ t68*(p2+ t68*(p5 + x*x*(p12 + x*p17) + p8*x
+ t68*(p9 + x*(p13 + x*p18)+ t68*(p14 + p19*x + p20*t68))));
} else if (sp >= 0.25 && sp < 9.0) {
rtx = q0 + x*(q1 + q4*t68 + x*(q3 + q7*t68 + x*(q6
+ q11*t68 + x*(q10 + q16*t68 + x*q15))))
+ t68*(q2+ t68*(q5 + x*x*(q12 + x*q17) + q8*x
+ t68*(q9 + x*(q13 + x*q18)+ t68*(q14 + q19*x + q20*t68))));
} else if (sp >= 0.003 && sp < 0.25) {
rtx = s0 + x*(s1 + s4*t68 + x*(s3 + s7*t68 + x*(s6
+ s11*t68 + x*(s10 + s16*t68 + x*s15))))
+ t68*(s2+ t68*(s5 + x*x*(s12 + x*s17) + s8*x
+ t68*(s9 + x*(s13 + x*s18)+ t68*(s14 + s19*x + s20*t68))));
} else if (sp < 0.003) {
rtx = u0 + x*(u1 + u4*t68 + x*(u3 + u7*t68 + x*(u6
+ u11*t68 + x*(u10 + u16*t68 + x*u15))))
+ t68*(u2+ t68*(u5 + x*x*(u12 + x*u17) + u8*x
+ t68*(u9 + x*(u13 + x*u18)+ t68*(u14 + u19*x + u20*t68))));
}
/*
!--------------------------------------------------------------------------
! Finding the starting value of dSP_dRtx, the derivative of SP with respect
! to Rtx.
!--------------------------------------------------------------------------
*/
dsp_drtx = a1 + (2e0*a2 + (3e0*a3 +
(4e0*a4 + 5e0*a5*rtx)*rtx)*rtx)*rtx
+ ft68*(b1 + (2e0*b2 + (3e0*b3 + (4e0*b4 +
5e0*b5*rtx)*rtx)*rtx)*rtx);
if (sp < 2.0) {
x = 400e0*(rtx*rtx);
sqrty = 10.0*rtx;
part1 = 1e0 + x*(1.5e0 + x);
part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty));
hill_ratio = gsw_hill_ratio_at_sp2(t);
dsp_drtx = dsp_drtx
+ a0*800e0*rtx*(1.5e0 + 2e0*x)/(part1*part1)
+ b0*ft68*(10e0 + sqrty*(20e0 + 30e0*sqrty))/
(part2*part2);
dsp_drtx = hill_ratio*dsp_drtx;
}
/*
!--------------------------------------------------------------------------
! One iteration through the modified Newton-Raphson method (McDougall and
! Wotherspoon, 2012) achieves an error in Practical Salinity of about
! 10^-12 for all combinations of the inputs. One and a half iterations of
! the modified Newton-Raphson method achevies a maximum error in terms of
! Practical Salinity of better than 2x10^-14 everywhere.
!
! We recommend one and a half iterations of the modified Newton-Raphson
! method.
!
! Begin the modified Newton-Raphson method.
!--------------------------------------------------------------------------
*/
sp_est = a0 + (a1 + (a2 + (a3 + (a4 + a5*rtx)*rtx)*rtx)*rtx)*rtx
+ ft68*(b0 + (b1 + (b2+ (b3 + (b4 + b5*rtx)*rtx)*rtx)*rtx)*rtx);
if (sp_est < 2.0) {
x = 400e0*(rtx*rtx);
sqrty = 10e0*rtx;
part1 = 1e0 + x*(1.5e0 + x);
part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty));
sp_hill_raw = sp_est - a0/part1 - b0*ft68/part2;
hill_ratio = gsw_hill_ratio_at_sp2(t);
sp_est = hill_ratio*sp_hill_raw;
}
rtx_old = rtx;
rtx = rtx_old - (sp_est - sp)/dsp_drtx;
rtxm = 0.5e0*(rtx + rtx_old); /*This mean value of Rtx, Rtxm, is the
value of Rtx at which the derivative dSP_dRtx is evaluated.*/
dsp_drtx= a1 + (2e0*a2 + (3e0*a3 + (4e0*a4 +
5e0*a5*rtxm)*rtxm)*rtxm)*rtxm
+ ft68*(b1 + (2e0*b2 + (3e0*b3 + (4e0*b4 +
5e0*b5*rtxm)*rtxm)*rtxm)*rtxm);
if (sp_est < 2.0) {
x = 400e0*(rtxm*rtxm);
sqrty = 10e0*rtxm;
part1 = 1e0 + x*(1.5e0 + x);
part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty));
dsp_drtx = dsp_drtx
+ a0*800e0*rtxm*(1.5e0 + 2e0*x)/(part1*part1)
+ b0*ft68*(10e0 + sqrty*(20e0 + 30e0*sqrty))/
(part2*part2);
hill_ratio = gsw_hill_ratio_at_sp2(t);
dsp_drtx = hill_ratio*dsp_drtx;
}
/*
!--------------------------------------------------------------------------
! The line below is where Rtx is updated at the end of the one full
! iteration of the modified Newton-Raphson technique.
!--------------------------------------------------------------------------
*/
rtx = rtx_old - (sp_est - sp)/dsp_drtx;
/*
!--------------------------------------------------------------------------
! Now we do another half iteration of the modified Newton-Raphson
! technique, making a total of one and a half modified N-R iterations.
!--------------------------------------------------------------------------
*/
sp_est = a0 + (a1 + (a2 + (a3 + (a4 + a5*rtx)*rtx)*rtx)*rtx)*rtx
+ ft68*(b0 + (b1 + (b2+ (b3 + (b4 + b5*rtx)*rtx)*rtx)*rtx)*rtx);
if (sp_est < 2.0) {
x = 400e0*(rtx*rtx);
sqrty = 10e0*rtx;
part1 = 1e0 + x*(1.5e0 + x);
part2 = 1e0 + sqrty*(1e0 + sqrty*(1e0 + sqrty));
sp_hill_raw = sp_est - a0/part1 - b0*ft68/part2;
hill_ratio = gsw_hill_ratio_at_sp2(t);
sp_est = hill_ratio*sp_hill_raw;
}
rtx = rtx - (sp_est - sp)/dsp_drtx;
/*
!--------------------------------------------------------------------------
! Now go from Rtx to Rt and then to the conductivity ratio R at pressure p.
!--------------------------------------------------------------------------
*/
rt = rtx*rtx;
aa = d3 + d4*t68;
bb = 1e0 + t68*(d1 + d2*t68);
cc = p*(e1 + p*(e2 + e3*p));
/* rt_lc (i.e. rt_lower_case) corresponds to rt as defined in
the UNESCO 44 (1983) routines. */
rt_lc = c0 + (c1 + (c2 + (c3 + c4*t68)*t68)*t68)*t68;
dd = bb - aa*rt_lc*rt;
ee = rt_lc*rt*aa*(bb + cc);
ra = sqrt(dd*dd + 4e0*ee) - dd;
r = 0.5e0*ra/aa;
/*
! 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^).
*/
return (gsw_c3515*r);
}
/*
!==========================================================================
function gsw_cabbeling(sa,ct,p)
!==========================================================================
! Calculates the cabbeling coefficient of seawater with respect to
! Conservative Temperature. This function uses the computationally-
! efficient expression for specific volume in terms of SA, CT and p
! (Roquet et al., 2014).
!
! sa : Absolute Salinity [g/kg]
! ct : Conservative Temperature (ITS-90) [deg C]
! p : sea pressure [dbar]
!
! cabbeling : cabbeling coefficient with respect to [1/K^2]
! Conservative Temperature.
*/
double
gsw_cabbeling(double sa, double ct, double p)
{
double alpha_ct, alpha_on_beta, alpha_sa, beta_sa, rho,
v_sa, v_ct, v_sa_sa, v_sa_ct, v_ct_ct;
gsw_specvol_first_derivatives(sa,ct,p,&v_sa,&v_ct, NULL);
gsw_specvol_second_derivatives(sa,ct,p,&v_sa_sa,&v_sa_ct,&v_ct_ct,
NULL, NULL);
rho = gsw_rho(sa,ct,p);
alpha_ct = rho*(v_ct_ct - rho*v_ct*v_ct);
alpha_sa = rho*(v_sa_ct - rho*v_sa*v_ct);
beta_sa = -rho*(v_sa_sa - rho*v_sa*v_sa);
alpha_on_beta = gsw_alpha_on_beta(sa,ct,p);
return (alpha_ct +
alpha_on_beta*(2.0*alpha_sa - alpha_on_beta*beta_sa));
}
/*
!==========================================================================
elemental function gsw_chem_potential_water_ice (t, p)
!==========================================================================
!
! Calculates the chemical potential of water in ice from in-situ
! temperature and pressure.
!
! t = in-situ temperature (ITS-90) [ deg C ]
! p = sea pressure [ dbar ]
! ( i.e. absolute pressure - 10.1325 dbar )
!
! chem_potential_water_ice = chemical potential of ice [ J/kg ]
!--------------------------------------------------------------------------
*/
double
gsw_chem_potential_water_ice(double t, double p)
{
return (gsw_gibbs_ice(0,0,t,p));
}
/*
!==========================================================================
elemental function gsw_chem_potential_water_t_exact (sa, t, p)
!==========================================================================
!
! Calculates the chemical potential of water in seawater.
!
! SA = Absolute Salinity [ g/kg ]
! t = in-situ temperature (ITS-90) [ deg C ]
! p = sea pressure [ dbar ]
! ( i.e. absolute pressure - 10.1325 dbar )
!
! chem_potential_water_t_exact = chemical potential of water in seawater
! [ J/g ]
!--------------------------------------------------------------------------
*/
double
gsw_chem_potential_water_t_exact(double sa, double t, double p)
{
GSW_TEOS10_CONSTANTS;
double g03_g, g08_g, g_sa_part, x, x2, y, z, kg2g = 1e-3;
x2 = gsw_sfac*sa;
x = sqrt(x2);
y = t*0.025;
z = p*1e-4;
g03_g = 101.342743139674 + z*(100015.695367145 +
z*(-2544.5765420363 + z*(284.517778446287 +
z*(-33.3146754253611 + (4.20263108803084 - 0.546428511471039*z)*z)))) +
y*(5.90578347909402 + z*(-270.983805184062 +
z*(776.153611613101 + z*(-196.51255088122 +
(28.9796526294175 - 2.13290083518327*z)*z))) +
y*(-12357.785933039 + z*(1455.0364540468 +
z*(-756.558385769359 + z*(273.479662323528 +
z*(-55.5604063817218 + 4.34420671917197*z)))) +
y*(736.741204151612 + z*(-672.50778314507 +
z*(499.360390819152 + z*(-239.545330654412 +
(48.8012518593872 - 1.66307106208905*z)*z))) +
y*(-148.185936433658 + z*(397.968445406972 +
z*(-301.815380621876 + (152.196371733841 - 26.3748377232802*z)*z)) +
y*(58.0259125842571 + z*(-194.618310617595 +
z*(120.520654902025 + z*(-55.2723052340152 + 6.48190668077221*z))) +
y*(-18.9843846514172 + y*(3.05081646487967 - 9.63108119393062*z) +
z*(63.5113936641785 + z*(-22.2897317140459 + 8.17060541818112*z))))))));
g08_g = x2*(1416.27648484197 +
x*(-2432.14662381794 + x*(2025.80115603697 +
y*(543.835333000098 + y*(-68.5572509204491 +
y*(49.3667694856254 + y*(-17.1397577419788 +
2.49697009569508*y))) - 22.6683558512829*z) +
x*(-1091.66841042967 - 196.028306689776*y +
x*(374.60123787784 - 48.5891069025409*x +
36.7571622995805*y) + 36.0284195611086*z) +
z*(-54.7919133532887 + (-4.08193978912261 -
30.1755111971161*z)*z)) +
z*(199.459603073901 + z*(-52.2940909281335 +
(68.0444942726459 - 3.41251932441282*z)*z)) +
y*(-493.407510141682 + z*(-175.292041186547 +
(83.1923927801819 - 29.483064349429*z)*z) +
y*(-43.0664675978042 + z*(383.058066002476 +
z*(-54.1917262517112 + 25.6398487389914*z)) +
y*(-10.0227370861875 - 460.319931801257*z +
y*(0.875600661808945 + 234.565187611355*z))))) +
y*(168.072408311545));
g_sa_part = 8645.36753595126 +
x*(-7296.43987145382 + x*(8103.20462414788 +
y*(2175.341332000392 + y*(-274.2290036817964 +
y*(197.4670779425016 + y*(-68.5590309679152 +
9.98788038278032*y))) - 90.6734234051316*z) +
x*(-5458.34205214835 - 980.14153344888*y +
x*(2247.60742726704 - 340.1237483177863*x +
220.542973797483*y) + 180.142097805543*z) +
z*(-219.1676534131548 + (-16.32775915649044 -
120.7020447884644*z)*z)) +
z*(598.378809221703 + z*(-156.8822727844005 +
(204.1334828179377 - 10.23755797323846*z)*z)) +
y*(-1480.222530425046 + z*(-525.876123559641 +
(249.57717834054571 - 88.449193048287*z)*z) +
y*(-129.1994027934126 + z*(1149.174198007428 +
z*(-162.5751787551336 + 76.9195462169742*z)) +
y*(-30.0682112585625 - 1380.9597954037708*z +
y*(2.626801985426835 + 703.695562834065*z))))) +
y*(1187.3715515697959);
return (kg2g*(g03_g + g08_g - 0.5*x2*g_sa_part));
}
/*
!==========================================================================
elemental function gsw_cp_ice (t, p)
!==========================================================================
!
! Calculates the isobaric heat capacity of seawater.
!
! t = in-situ temperature (ITS-90) [ deg C ]
! p = sea pressure [ dbar ]
! ( i.e. absolute pressure - 10.1325 dbar )
!
! gsw_cp_ice = heat capacity of ice [J kg^-1 K^-1]
!--------------------------------------------------------------------------
*/
double
gsw_cp_ice(double t, double p)
{
GSW_TEOS10_CONSTANTS;
return (-(t + gsw_t0)*gsw_gibbs_ice(2,0,t,p));
}
/*
!==========================================================================
function gsw_cp_t_exact(sa,t,p)
!==========================================================================
! Calculates isobaric heat capacity of seawater
!
! sa : Absolute Salinity [g/kg]
! t : in-situ temperature [deg C]
! p : sea pressure [dbar]
!
! gsw_cp_t_exact : heat capacity [J/(kg K)]
*/
double
gsw_cp_t_exact(double sa, double t, double p)
{
int n0, n2;
n0 = 0;
n2 = 2;
return (-(t+273.15e0)*gsw_gibbs(n0,n2,n0,sa,t,p));
}
/*
!==========================================================================
elemental subroutine gsw_ct_first_derivatives (sa, pt, ct_sa, ct_pt)
!==========================================================================
!
! Calculates the following two derivatives of Conservative Temperature
! (1) CT_SA, the derivative with respect to Absolute Salinity at
! constant potential temperature (with pr = 0 dbar), and
! 2) CT_pt, the derivative with respect to potential temperature
! (the regular potential temperature which is referenced to 0 dbar)
! at constant Absolute Salinity.
!
! SA = Absolute Salinity [ g/kg ]
! pt = potential temperature (ITS-90) [ deg C ]
! (whose reference pressure is 0 dbar)
!
! CT_SA = The derivative of Conservative Temperature with respect to
! Absolute Salinity at constant potential temperature
! (the regular potential temperature which has reference
! sea pressure of 0 dbar).
! The CT_SA output has units of: [ K/(g/kg)]
! CT_pt = The derivative of Conservative Temperature with respect to
! potential temperature (the regular one with pr = 0 dbar)
! at constant SA. CT_pt is dimensionless. [ unitless ]
!--------------------------------------------------------------------------
*/
void
gsw_ct_first_derivatives(double sa, double pt, double *ct_sa, double *ct_pt)
{
GSW_TEOS10_CONSTANTS;
double abs_pt, g_sa_mod, g_sa_t_mod, x, y_pt;
abs_pt = gsw_t0 + pt ;
if (ct_pt != NULL)
*ct_pt = -(abs_pt*gsw_gibbs_pt0_pt0(sa,pt))/gsw_cp0;
if (ct_sa == NULL)
return;
x = sqrt(gsw_sfac*sa);
y_pt = 0.025*pt;
g_sa_t_mod = 1187.3715515697959 + x*(-1480.222530425046
+ x*(2175.341332000392 + x*(-980.14153344888
+ 220.542973797483*x) + y_pt*(-548.4580073635929
+ y_pt*(592.4012338275047 + y_pt*(-274.2361238716608
+ 49.9394019139016*y_pt)))) + y_pt*(-258.3988055868252
+ y_pt*(-90.2046337756875 + y_pt*10.50720794170734)))
+ y_pt*(3520.125411988816 + y_pt*(-1351.605895580406
+ y_pt*(731.4083582010072 + y_pt*(-216.60324087531103
+ 25.56203650166196*y_pt))));
g_sa_t_mod = 0.5*gsw_sfac*0.025*g_sa_t_mod;
g_sa_mod = 8645.36753595126 + x*(-7296.43987145382
+ x*(8103.20462414788 + y_pt*(2175.341332000392
+ y_pt*(-274.2290036817964 + y_pt*(197.4670779425016
+ y_pt*(-68.5590309679152 + 9.98788038278032*y_pt))))
+ x*(-5458.34205214835 - 980.14153344888*y_pt
+ x*(2247.60742726704 - 340.1237483177863*x
+ 220.542973797483*y_pt))) + y_pt*(-1480.222530425046
+ y_pt*(-129.1994027934126 + y_pt*(-30.0682112585625
+ y_pt*(2.626801985426835 ))))) + y_pt*(1187.3715515697959
+ y_pt*(1760.062705994408 + y_pt*(-450.535298526802
+ y_pt*(182.8520895502518 + y_pt*(-43.3206481750622
+ 4.26033941694366*y_pt)))));
g_sa_mod = 0.5*gsw_sfac*g_sa_mod;
*ct_sa = (g_sa_mod - abs_pt*g_sa_t_mod)/gsw_cp0;
}
/*
!==========================================================================
elemental subroutine gsw_ct_first_derivatives_wrt_t_exact (sa, t, p, &
ct_sa_wrt_t, ct_t_wrt_t, ct_p_wrt_t)
!==========================================================================
!
! Calculates the following three derivatives of Conservative Temperature.
! These derivatives are done with respect to in-situ temperature t (in the
! case of CT_T_wrt_t) or at constant in-situ tempertature (in the cases of
! CT_SA_wrt_t and CT_P_wrt_t).
! (1) CT_SA_wrt_t, the derivative of CT with respect to Absolute Salinity
! at constant t and p, and
! (2) CT_T_wrt_t, derivative of CT with respect to in-situ temperature t
! at constant SA and p.
! (3) CT_P_wrt_t, derivative of CT with respect to pressure P (in Pa) at
! constant SA and t.
!
! This function uses the full Gibbs function. Note that this function
! avoids the NaN that would exist in CT_SA_wrt_t at SA = 0 if it were
! evaluated in the straightforward way from the derivatives of the Gibbs
! function function.
!
! SA = Absolute Salinity [ g/kg ]
! t = in-situ temperature (ITS-90) [ deg C ]
! p = sea pressure [ dbar ]
! ( i.e. absolute pressure - 10.1325 dbar)
!
! CT_SA_wrt_t = The first derivative of Conservative Temperature with