gsw_SAAR

`Absolute Salinity Anomaly Ratio`

USAGE:

`SAAR = gsw_SAAR(p,long,lat)`

DESCRIPTION:

`Calculates the Absolute Salinity Anomaly Ratio.`
 ```Click for a more detailed description of the Absolute Salinity Anomaly Ratio.```

INPUT:

```p     =  sea pressure                                           [ dbar ]
( i.e. absolute pressure - 10.1325 dbar )
long  =  longitude in decimal degrees                     [ 0 ... +360 ]
or [ -180 ... +180 ]
lat   =  latitude in decimal degrees north               [ -90 ... +90 ]```
`p, long & lat need to have the same dimensions.`

OUTPUT:

```SAAR      =  Absolute Salinity Anomaly Ratio                [ unitless ]
in_ocean  =  0, if long and lat are a long way from the ocean
=  1, if long and lat are in the ocean
Note. This flag is only set when the observation is well and truly on
dry land; often the warning flag is not set until one is several
hundred kilometres inland from the coast. ```

EXAMPLE:

```p =    [   10;   50;  125;  250;  600; 1000;]
lat =  [    4;    4;    4;    4;    4;    4;]
long = [  188;  188;  188;  188;  188;  188;]```
`[SAAR, in_ocean] = gsw_SAAR(p,long,lat)`
`SAAR = `
` 1.0e-003 *`
```   0.004794295602143
0.007668755837570
0.018919828449091
0.077293264028981
0.161974583039298
0.270652408428964```
`in_ocean =`
```     1
1
1
1
1
1```

AUTHOR:

`Paul Barker and Trevor McDougall                  [ help@teos-10.org ]`

VERSION NUMBER:

`3.05 (16th February, 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 section 2.5 of this TEOS-10 Manual.```
```McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and
P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity.
Ocean Science, 8, 1123-1134.
http://www.ocean-sci.net/8/1123/2012/os-8-1123-2012.pdf```
`The software is available from http://www.TEOS-10.org`
```function [SAAR, in_ocean] = gsw_SAAR(p,long,lat)

% gsw_SAAR       Absolute Salinity Anomaly Ratio (excluding the Baltic Sea)
%==========================================================================
%
% USAGE:
%  [SAAR, in_ocean] = gsw_SAAR(p,long,lat)
%
% DESCRIPTION:
%  Calculates the Absolute Salinity Anomaly Ratio, SAAR, in the open ocean
%  by spatially interpolating the global reference data set of SAAR to the
%  location of the seawater sample.
%
%  This function uses version 3.0 of the SAAR look up table (15th May 2011).
%
%  The Absolute Salinity Anomaly Ratio in the Baltic Sea is evaluated
%  separately, since it is a function of Practical Salinity, not of space.
%  The present function returns a SAAR of zero for data in the Baltic Sea.
%  The correct way of calculating Absolute Salinity in the Baltic Sea is by
%  calling gsw_SA_from_SP.
%
% INPUT:
%  p     =  sea pressure                                           [ dbar ]
%          ( i.e. absolute pressure - 10.1325 dbar )
%  long  =  Longitude in decimal degrees                     [ 0 ... +360 ]
%                                                      or [ -180 ... +180 ]
%  lat   =  Latitude in decimal degrees north               [ -90 ... +90 ]
%
%  p, long & lat need to be vectors and have the same dimensions.
%
% OUTPUT:
%  SAAR      =  Absolute Salinity Anomaly Ratio                [ unitless ]
%  in_ocean  =  0, if long and lat are a long way from the ocean
%            =  1, if long and lat are in or near the ocean
%  Note. This flag is only set when the observation is well and truly on
%    dry land; often the warning flag is not set until one is several
%    hundred kilometres inland from the coast.
%
% AUTHOR:
%  David Jackett                                       [ help@teos-10.org ]
%
% MODIFIED:
%  Paul Barker and Trevor McDougall
%  Acknowledgment. Matlab programming assisance from Sunke Schmidtko.
%
% 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
%
%  McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and
%   P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity.
%   Ocean Science, 8, 1123-1134.
%   http://www.ocean-sci.net/8/1123/2012/os-8-1123-2012.pdf
%
%  The software is available from http://www.TEOS-10.org
%
%==========================================================================

%--------------------------------------------------------------------------
% Check variables and resize if necessary
%--------------------------------------------------------------------------

if ~(nargin == 3)
error('gsw_SAAR:  Requires three inputs')
end %if

[mp,np] = size(p);
[mla,nla] = size(lat);
[mlo,nlo] = size(long);

if (mp ~= mla) | (mp ~=mlo) | (np ~= nla) | (np ~= nlo)
error('gsw_SAAR: Inputs need be of the same size')
end %if

if any(p < -1.5)
error('gsw_SAAR: pressure needs to be positive')
end

%set any pressures between 0 and -1.5 to be equal to 0 (i.e. the surface)
p(p < 0) = 0;

%--------------------------------------------------------------------------
% Start of the calculation (extracting from a look up table)
%--------------------------------------------------------------------------

persistent SAAR_ref lats_ref longs_ref p_ref ndepth_ref

if isempty(SAAR_ref)
gsw_data = 'gsw_data_v3_0.mat';

gsw_data_file = which(gsw_data);

'ndepth_ref');
end

% precalculate constants
nx = length(longs_ref);
ny = length(lats_ref);
nz = length(p_ref);
nyz = ny.*nz;

n0 = length(p);

dlongs_ref = longs_ref(2) - longs_ref(1);
dlats_ref = lats_ref(2) - lats_ref(1);

indsx0 = floor(1 + (nx-1)*(long - longs_ref(1))./(longs_ref(nx) - longs_ref(1)));
indsx0 = indsx0(:);
indsx0(indsx0 == nx) = nx - 1;

indsy0 = floor(1 + (ny-1)*(lat - lats_ref(1))./(lats_ref(ny) - lats_ref(1)));
indsy0 = indsy0(:);
indsy0(indsy0 == ny) = ny - 1;

% Assign a pressure bin for each bottle.
indsz0 = ones(n0,1);
for I = 2:nz
indsz0(p >= p_ref(I-1) & p < p_ref(I)) = I - 1;
end
indsz0(p >= p_ref(nz)) = nz-1;

indsy0_indsx0_ny = indsy0 + indsx0.*ny;
indsn1 = indsy0_indsx0_ny - ny;              %4 xy grid points surrounding the data
indsn2 = indsy0_indsx0_ny;
indsn3 = indsy0_indsx0_ny + 1;
indsn4 = indsy0_indsx0_ny + (1 - ny);

nmax = max([ndepth_ref(indsn1)';ndepth_ref(indsn2)';ndepth_ref(indsn3)';ndepth_ref(indsn4)']);

if any(indsz0(:)' > nmax)
inds1 = find(indsz0(:)' > nmax);                % casts deeper than GK maximum

p(inds1) = p_ref(nmax(inds1));                  % have reset p here so have to reset indsz0

indsz0(inds1) = nmax(inds1) - 1;
end

indsyx_tmp = indsy0_indsx0_ny.*nz;        % precalculate constants for loop
inds0 =  indsz0 + indsyx_tmp  - (nyz + nz);

data_indices = [indsx0,indsy0,indsz0,inds0];
data_inds = data_indices(:,3);

r1 = (long(:) - longs_ref(indsx0))./(longs_ref(indsx0+1) - longs_ref(indsx0));
s1 = (lat(:) - lats_ref(indsy0))./(lats_ref(indsy0+1) - lats_ref(indsy0));
t1 = (p(:) - p_ref(indsz0))./(p_ref(indsz0+1) - p_ref(indsz0));

sa_upper = NaN(size(data_inds));
sa_lower = sa_upper;
SAAR = sa_upper;
in_ocean = ones(size(SAAR));

indsyx_tmp = indsy0_indsx0_ny.*nz;        % precalculate constants for loop
saar_nan = nan(4,n0);

for k = 1:nz-1

inds_k = find(indsz0 == k);

if ~isempty(inds_k)

indsXYZ = k + indsyx_tmp(inds_k);

inds_di = find(data_inds == k);

% level k interpolation
saar = saar_nan;

saar(:,inds_k) = SAAR_ref([(indsXYZ-(nz+nyz))'; (indsXYZ - nz)'; (indsXYZ)'; (indsXYZ -nyz)']);

inds_pan = find(abs(long(inds_k)-277.6085)<=17.6085 & ...
abs(lat(inds_k)-9.775) <= 9.775);

if ~isempty(inds_pan)
inds = inds_k(inds_pan);
saar(:,inds) = gsw_saar_add_barrier(saar(:,inds),long(inds), ...
lat(inds),longs_ref(indsx0(inds)),lats_ref(indsy0(inds)),dlongs_ref,dlats_ref);
end

if any(isnan(sum(saar(:,inds_k))))
inds = inds_k(isnan(sum(saar(:,inds_k))));
end

sa_upper(inds_di) = (1-s1(inds_di)).*(saar(1,inds_k)' + ...
r1(inds_di).*(saar(2,inds_k)'-saar(1,inds_k)')) + ...
s1(inds_di).*(saar(4,inds_k)' + ...
r1(inds_di).*(saar(3,inds_k)'-saar(4,inds_k)'));  % level k+1 interpolation

saar = saar_nan;
saar(:,inds_k) = SAAR_ref([(indsXYZ+(1-nz-nyz))'; (indsXYZ+(1-nz))'; (indsXYZ+1)'; (indsXYZ+(1-nyz))';]);

if ~isempty(inds_pan)
inds = inds_k(inds_pan);
saar(:,inds) = gsw_saar_add_barrier(saar(:,inds),long(inds), ...
lat(inds),longs_ref(indsx0(inds)),lats_ref(indsy0(inds)),dlongs_ref,dlats_ref);
end

if any(isnan(sum(saar(:,inds_k))))
inds = inds_k(isnan(sum(saar(:,inds_k))));
end

sa_lower(inds_di) = (1-s1(inds_di)).*(saar(1,inds_k)' + ...
r1(inds_di).*(saar(2,inds_k)'-saar(1,inds_k)')) + ...
s1(inds_di).*(saar(4,inds_k)' + ...
r1(inds_di).*(saar(3,inds_k)'-saar(4,inds_k)'));

if any(isfinite(sa_upper(inds_di)) & isnan(sa_lower(inds_di)))
inds_different = find(isfinite(sa_upper(inds_di)) & isnan(sa_lower(inds_di)));
sa_lower(inds_di(inds_different)) = sa_upper(inds_di(inds_different));
end

SAAR(inds_di) = sa_upper(inds_di) + t1(inds_di).*(sa_lower(inds_di) - sa_upper(inds_di));

end
end

inds = find(~isfinite(SAAR));
SAAR(inds) = 0;

in_ocean(inds) = 0;

end

%##########################################################################

function SAAR = gsw_saar_add_mean(saar)

%==========================================================================
%
% USAGE:
%  SAAR = gsw_saar_add_mean(saar)
%
% DESCRIPTION:
%  Replaces NaN's with nanmean of the 4 adjacent neighbours
%
% INPUT:
%  saar  =  Absolute Salinity Anomaly Ratio of the 4 adjacent neighbours
%                                                              [ unitless ]
%
% OUTPUT:
%  SAAR  =  nanmean of the 4 adjacent neighbours               [ unitless ]
%
% AUTHOR:
%  David Jackett
%
% MODIFIED:
%  Paul Barker and Trevor McDougall
%  Acknowledgment. Matlab programming assisance from Sjoerd Groeskamp.
%
% 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
%
%  McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and
%   P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity.
%   Ocean Science, 8, 1123-1134.
%   http://www.ocean-sci.net/8/1123/2012/os-8-1123-2012.pdf
%
%  The software is available from http://www.TEOS-10.org
%
%==========================================================================

if exist('nanmean','file')
saar_nanmean = nanmean(saar);
saar_nanmean(2,:) = saar_nanmean;
saar_nanmean(3:4,:) = saar_nanmean;
nans = isnan(saar);
[Inans] = find(isnan(saar));
saar_mean_nans = nans(Inans).*saar_nanmean(Inans);
saar(Inans) = saar_mean_nans;
else
saar_mean = mean(saar);
inds_nan = find(isnan(saar_mean));
no_nan = length(inds_nan);
for kk = 1:no_nan
col = inds_nan(kk);
[Inn] = find(~isnan(saar(:,col)));
if ~isempty(Inn)
saar(isnan(saar(:,col)),col) = sum(saar(Inn,col))./numel(Inn);
end
end
end

SAAR = saar;

end

%##########################################################################

function SAAR = gsw_saar_add_barrier(saar,long,lat,longs_ref,lats_ref,dlongs_ref,dlats_ref)

%==========================================================================
%
% USAGE:
%  SAAR = gsw_saar_add_barrier(saar,long,lat,longs_ref,lats_ref,dlongs_ref,dlats_ref)
%
% DESCRIPTION:
%  Adds a barrier through Central America (Panama) and then averages
%  over the appropriate side of the barrier
%
% INPUT:
%  saar        =  Absolute Salinity Anomaly Ratio                          [ unitless ]
%  long        =  Longitudes of data in decimal degrees east               [ 0 ... +360 ]
%  lat         =  Latitudes of data in decimal degrees north               [ -90 ... +90 ]
%  longs_ref   =  Longitudes of regular grid in decimal degrees east       [ 0 ... +360 ]
%  lats_ref    =  Latitudes of regular grid in decimal degrees north       [ -90 ... +90 ]
%  dlongs_ref  =  Longitude difference of regular grid in decimal degrees  [ deg longitude ]
%  dlats_ref   =  Latitude difference of regular grid in decimal degrees   [ deg latitude ]
%
% OUTPUT:
%  SAAR        =  Absolute Salinity Anomaly Ratio                          [ unitless ]
%
% AUTHOR:
%  David Jackett
%
% MODIFIED:
%  Paul Barker and Trevor McDougall
%
% 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
%
%  McDougall, T.J., D.R. Jackett, F.J. Millero, R. Pawlowicz and
%   P.M. Barker, 2012: A global algorithm for estimating Absolute Salinity.
%   Ocean Science, 8, 1123-1134.
%   http://www.ocean-sci.net/8/1123/2012/os-8-1123-2012.pdf
%
%  The software is available from http://www.TEOS-10.org
%
%==========================================================================

longs_pan = [260.0000 272.5900 276.5000 278.6500 280.7300 295.2170];

lats_pan  = [ 19.5500  13.9700   9.6000   8.1000   9.3300   0];

lats_lines0 = interp1(longs_pan,lats_pan,long);

lats_lines1 = interp1(longs_pan,lats_pan,longs_ref);
lats_lines2 = interp1(longs_pan,lats_pan,(longs_ref+dlongs_ref));

for k0 = 1:length(long)
if lats_lines0(k0) <= lat(k0)
above_line0 = 1;
else
above_line0 = 0;
end
if lats_lines1(k0) <= lats_ref(k0)
above_line(1) = 1;
else
above_line(1) = 0;
end
if lats_lines1(k0) <= (lats_ref(k0) + dlats_ref)
above_line(4) = 1;
else
above_line(4) = 0;
end
if lats_lines2(k0) <= lats_ref(k0)
above_line(2) = 1;
else
above_line(2) = 0;
end
if lats_lines2(k0) <= (lats_ref(k0) + dlats_ref)
above_line(3) = 1;
else
above_line(3) = 0;
end
saar(above_line ~= above_line0,k0) = nan;     % indices of different sides of CA line
end

if any(isnan(saar))
end

SAAR = saar;

end
```