-
Notifications
You must be signed in to change notification settings - Fork 1
/
Copy pathgsw_SP_from_R.m
181 lines (155 loc) · 5.65 KB
/
gsw_SP_from_R.m
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
function SP = gsw_SP_from_R(R,t,p)
% gsw_SP_from_R Practical Salinity from conductivity ratio
%==========================================================================
%
% USAGE:
% SP = gsw_SP_from_R(R,t,p)
%
% DESCRIPTION:
% Calculates Practical Salinity, SP, from the conductivity ratio, R,
% primarily using the PSS-78 algorithm. Note that the PSS-78 algorithm
% for Practical Salinity is only valid in the range 2 < SP < 42. If the
% PSS-78 algorithm produces a Practical Salinity that is less than 2 then
% the Practical Salinity is recalculated with a modified form of the
% Hill et al. (1986) formula. The modification of the Hill et al. (1986)
% expression are to ensure that it is exactly consistent with PSS-78
% at SP = 2.
%
% INPUT:
% R = conductivity ratio [ unitless ]
% t = in-situ temperature (ITS-90) [ deg C ]
% p = sea pressure [ dbar ]
% ( i.e. absolute pressure - 10.1325 dbar )
%
% t & p may have dimensions 1x1 or Mx1 or 1xN or MxN, where R is MxN.
%
% OUTPUT:
% SP = Practical Salinity on the PSS-78 scale [ unitless ]
%
% AUTHOR:
% Paul Barker, Trevor McDougall and Rich Pawlowicz [ [email protected] ]
%
% VERSION NUMBER: 3.05 (27th January 2015)
%
% REFERENCES:
% Hill, K.D., T.M. Dauphinee & D.J. Woods, 1986: The extension of the
% Practical Salinity Scale 1978 to low salinities. IEEE J. Oceanic Eng.,
% OE-11, 1, 109 - 112.
%
% 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 appendix E of this TEOS-10 Manual.
%
% Unesco, 1983: Algorithms for computation of fundamental properties of
% seawater. Unesco Technical Papers in Marine Science, 44, 53 pp.
%
% The software is available from http://www.TEOS-10.org
%
%==========================================================================
%--------------------------------------------------------------------------
% Check variables and resize if necessary
%--------------------------------------------------------------------------
if ~(nargin == 3)
error('gsw_SP_from_R: Requires three input arguments')
end %if
[mc,nc] = size(R);
[mt,nt] = size(t);
[mp,np] = size(p);
if (mt == 1) & (nt == 1) % t scalar - fill to size of R
t = t*ones(size(R));
elseif (nc == nt) & (mt == 1) % t is row vector,
t = t(ones(1,mc), :); % copy down each column.
elseif (mc == mt) & (nt == 1) % t is column vector,
t = t(:,ones(1,nc)); % copy across each row.
elseif (nc == mt) & (nt == 1) % t is a transposed row vector,
t = t.'; % transposed then
t = t(ones(1,mc), :); % copy down each column.
elseif (mc == mt) & (nc == nt)
% ok
else
error('gsw_SP_from_R: Inputs array dimensions arguments do not agree')
end %if
if (mp == 1) & (np == 1) % p scalar - fill to size of R
p = p*ones(size(R));
elseif (nc == np) & (mp == 1) % p is row vector,
p = p(ones(1,mc), :); % copy down each column.
elseif (mc == mp) & (np == 1) % p is column vector,
p = p(:,ones(1,nc)); % copy across each row.
elseif (nc == mp) & (np == 1) % p is a transposed row vector,
p = p.'; % transposed then
p = p(ones(1,mc), :); % copy down each column.
elseif (mc == mp) & (nc == np)
% ok
else
error('gsw_SP_from_R: Inputs array dimensions arguments do not agree')
end
if mc == 1
R = R.';
t = t.';
p = p.';
transposed = 1;
else
transposed = 0;
end
%--------------------------------------------------------------------------
% Start of the calculation
%--------------------------------------------------------------------------
a0 = 0.0080;
a1 = -0.1692;
a2 = 25.3851;
a3 = 14.0941;
a4 = -7.0261;
a5 = 2.7081;
b0 = 0.0005;
b1 = -0.0056;
b2 = -0.0066;
b3 = -0.0375;
b4 = 0.0636;
b5 = -0.0144;
c0 = 0.6766097;
c1 = 2.00564e-2;
c2 = 1.104259e-4;
c3 = -6.9698e-7;
c4 = 1.0031e-9;
d1 = 3.426e-2;
d2 = 4.464e-4;
d3 = 4.215e-1;
d4 = -3.107e-3;
e1 = 2.070e-5;
e2 = -6.370e-10;
e3 = 3.989e-15;
k = 0.0162;
[Iocean] = find(~isnan(R + t + p));
t68 = t(Iocean).*1.00024;
ft68 = (t68 - 15)./(1 + k*(t68 - 15));
% rt_lc corresponds to rt as defined in the UNESCO 44 (1983) routines.
rt_lc = c0 + (c1 + (c2 + (c3 + c4.*t68).*t68).*t68).*t68;
Rp = 1 + (p(Iocean).*(e1 + p(Iocean).*(e2 + e3.*p(Iocean))))./ ...
(1 + d1.*t68 + d2.*t68.*t68 + (d3 + d4.*t68).*R(Iocean));
Rt = R(Iocean)./(Rp.*rt_lc);
Rt(Rt < 0) = NaN;
Rtx = sqrt(Rt);
SP = NaN(size(R));
SP(Iocean) = a0 + (a1 + (a2 + (a3 + (a4 + a5.*Rtx).*Rtx).*Rtx).*Rtx).*Rtx + ...
ft68.*(b0 + (b1 + (b2+ (b3 + (b4 + b5.*Rtx).*Rtx).*Rtx).*Rtx).*Rtx);
% The following section of the code is designed for SP < 2 based on the
% Hill et al. (1986) algorithm. This algorithm is adjusted so that it is
% exactly equal to the PSS-78 algorithm at SP = 2.
if any(SP(Iocean) < 2)
[I2] = find(SP(Iocean) < 2);
Hill_ratio = gsw_Hill_ratio_at_SP2(t(Iocean(I2)));
x = 400*Rt(I2);
sqrty = 10*Rtx(I2);
part1 = 1 + x.*(1.5 + x);
part2 = 1 + sqrty.*(1 + sqrty.*(1 + sqrty));
SP_Hill_raw = SP(I2) - a0./part1 - b0.*ft68(I2)./part2;
SP(Iocean(I2)) = Hill_ratio.*SP_Hill_raw;
end
% This line ensures that SP is non-negative.
SP(SP < 0) = 0;
if transposed
SP = SP.';
end
end