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- Committer: Package Import Robot
- Author(s): Alastair McKinstry
- Date: 2013-07-18 07:26:49 UTC
- mfrom: (1.1.1)
- Revision ID: package-import@ubuntu.com-20130718072649-s2yct1q8we4z1w37
Tags: 3.0.2-1
* New upstream release.
* Move to DH 9.
* Move to DH 9.
- files added:
- .pc/python3.patch
- .pc/python3.patch/gsw
- .pc/python3.patch/gsw/gibbs
- .pc/python3.patch/gsw/test
- .pc/python3.patch/gsw/utilities
- files removed:
- .pc/remove-setuptools.patch
- gsw.egg-info
- files modified:
- .pc/applied-patches
added
removed
.pc/python3.patch/gsw/gibbs/basic_thermodynamic_t.py
1
# -*- coding: utf-8 -*-
2
3
from __future__ import division
4
5
import numpy as np
6
7
from library import gibbs
8
from absolute_salinity_sstar_ct import CT_from_t
9
from gsw.utilities import match_args_return, strip_mask
10
from conversions import pt_from_CT, pt_from_t, pt0_from_t
11
from constants import Kelvin, db2Pascal, P0, SSO, cp0, R, sfac, M_S
12
13
__all__ = [
14
'rho_t_exact',
15
'pot_rho_t_exact',
16
'sigma0_pt0_exact',
17
'alpha_wrt_CT_t_exact',
18
'alpha_wrt_pt_t_exact',
19
'alpha_wrt_t_exact',
20
'beta_const_CT_t_exact',
21
'beta_const_pt_t_exact',
22
'beta_const_t_exact',
23
'specvol_t_exact',
24
'specvol_anom_t_exact',
25
'sound_speed_t_exact',
26
'kappa_t_exact',
27
'kappa_const_t_exact',
28
'internal_energy_t_exact',
29
'enthalpy_t_exact',
30
'dynamic_enthalpy_t_exact',
31
'SA_from_rho_t_exact',
32
#'t_from_rho_exact',
33
't_maxdensity_exact',
34
'entropy_t_exact',
35
'cp_t_exact',
36
'isochoric_heat_cap_t_exact',
37
'chem_potential_relative_t_exact',
38
'chem_potential_water_t_exact',
39
'chem_potential_salt_t_exact',
40
'Helmholtz_energy_t_exact',
41
'adiabatic_lapse_rate_t_exact',
42
'osmotic_coefficient_t_exact',
43
'osmotic_pressure_t_exact'
44
]
45
46
n0, n1, n2 = 0, 1, 2
47
48
49
@match_args_return
50
def Helmholtz_energy_t_exact(SA, t, p):
51
r"""Calculates the Helmholtz energy of seawater.
52
53
The specific Helmholtz energy of seawater :math:`f` is given by:
54
55
.. math::
56
f(SA, t, p) = g - (p + P_0) \nu =
57
g - (p + P_0) \frac{\partial g}{\partial P}\Big|_{SA,T}
58
59
Parameters
60
----------
61
SA : array_like
62
Absolute salinity [g kg :sup:`-1`]
63
t : array_like
64
in situ temperature [:math:`^\circ` C (ITS-90)]
65
p : array_like
66
pressure [dbar]
67
68
Returns
69
-------
70
Helmholtz_energy : array_like
71
Helmholtz energy [J kg :sup:`-1`]
72
73
See Also
74
--------
75
TODO
76
77
Notes
78
-----
79
TODO
80
81
Examples
82
--------
83
>>> import gsw
84
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
85
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
86
>>> p = [10, 50, 125, 250, 600, 1000]
87
>>> gsw.Helmholtz_energy_t_exact(SA, t, p)
88
array([-5985.58288209, -5830.81845224, -3806.96617841, -877.66369421,
89
-462.17033905, -245.50407205])
90
91
References
92
----------
93
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
94
of seawater - 2010: Calculation and use of thermodynamic properties.
95
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
96
UNESCO (English), 196 pp. See section 2.13.
97
98
Modifications:
99
2011-03-29. Trevor McDougall
100
"""
101
102
return (gibbs(n0, n0, n0, SA, t, p) -
103
(db2Pascal * p + P0) * gibbs(n0, n0, n1, SA, t, p))
104
105
106
@match_args_return
107
def rho_t_exact(SA, t, p):
108
r"""Calculates in situ density of seawater from Absolute Salinity and in
109
situ temperature.
110
111
Parameters
112
----------
113
SA : array_like
114
Absolute salinity [g kg :sup:`-1`]
115
t : array_like
116
in situ temperature [:math:`^\circ` C (ITS-90)]
117
p : array_like
118
pressure [dbar]
119
120
Returns
121
-------
122
rho_t_exact : array_like
123
in situ density [kg m :sup:`-3`]
124
125
See Also
126
--------
127
TODO
128
129
Notes
130
-----
131
TODO
132
133
Examples
134
--------
135
>>> import gsw
136
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
137
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
138
>>> p = [10, 50, 125, 250, 600, 1000]
139
>>> gsw.rho(SA, t, p)
140
array([ 1021.84017319, 1022.26268993, 1024.42771594, 1027.79020181,
141
1029.83771473, 1032.00240412])
142
143
References
144
----------
145
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
146
of seawater - 2010: Calculation and use of thermodynamic properties.
147
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
148
UNESCO (English), 196 pp. See section 2.8.
149
150
Modifications:
151
2011-03-29. Paul Barker, David Jackett and Trevor McDougal
152
"""
153
154
return 1. / gibbs(n0, n0, n1, SA, t, p)
155
156
157
@match_args_return
158
def sigma0_pt0_exact(SA, pt0):
159
r"""Calculates potential density anomaly with reference sea pressure of
160
zero (0) dbar. The temperature input to this function is potential
161
temperature referenced to zero dbar.
162
163
Parameters
164
----------
165
SA : array_like
166
Absolute salinity [g kg :sup:`-1`]
167
pt0 : array_like
168
potential temperature [:math:`^\circ` C (ITS-90)]
169
with respect to a reference sea pressure of 0 dbar
170
171
Returns
172
-------
173
sigma0_pt0_exact : array_like
174
potential density anomaly [kg m :sup:`-3`]
175
respect to a reference pressure of 0 dbar
176
177
See Also
178
--------
179
TODO
180
181
Notes
182
-----
183
TODO
184
185
Examples
186
--------
187
>>> import gsw
188
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
189
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
190
>>> p = [10, 50, 125, 250, 600, 1000]
191
>>> gsw.rho(SA, t, p)
192
array([ 1021.84017319, 1022.26268993, 1024.42771594, 1027.79020181,
193
1029.83771473, 1032.00240412])
194
195
References
196
----------
197
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
198
of seawater - 2010: Calculation and use of thermodynamic properties.
199
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
200
UNESCO (English), 196 pp. See Eqn. (3.6.1).
201
202
Modifications:
203
2011-03-29. Trevor McDougal and Paul Barker.
204
"""
205
SA = np.maximum(SA, 0) # Ensure that SA is non-negative.
206
207
x2 = sfac * SA
208
x = np.sqrt(x2)
209
y = pt0 * 0.025
210
211
g03 = (100015.695367145 +
212
y * (-270.983805184062 +
213
y * (1455.0364540468 +
214
y * (-672.50778314507 +
215
y * (397.968445406972 +
216
y * (-194.618310617595 +
217
y * (63.5113936641785 -
218
y * 9.63108119393062)))))))
219
220
g08 = x2 * (-3310.49154044839 +
221
x * (199.459603073901 +
222
x * (-54.7919133532887 +
223
x * 36.0284195611086 -
224
y * 22.6683558512829) +
225
y * (-175.292041186547 +
226
y * (383.058066002476 +
227
y * (-460.319931801257 +
228
y * 234.565187611355)))) +
229
y * (729.116529735046 +
230
y * (-860.764303783977 +
231
y * (694.244814133268 +
232
y * (-297.728741987187)))))
233
234
"""The above code is exactly the same as the following two lines of code.
235
sigma0_pt_exact = rho_t_exact(SA, pt0, 0.) - 1000
236
"""
237
238
return 100000000. / (g03 + g08) - 1000.0
239
240
241
@match_args_return
242
def enthalpy_t_exact(SA, t, p):
243
r"""Calculates the specific enthalpy of seawater.
244
245
The specific enthalpy of seawater :math:`h` is given by:
246
247
.. math::
248
h(SA, t, p) = g + (T_0 + t)\eta =
249
g - (T_0 + t) \frac{\partial g}{\partial T}\Big|_{SA,p}
250
251
Parameters
252
----------
253
SA : array_like
254
Absolute salinity [g kg :sup:`-1`]
255
t : array_like
256
in situ temperature [:math:`^\circ` C (ITS-90)]
257
p : array_like
258
pressure [dbar]
259
260
Returns
261
-------
262
enthalpy : array_like
263
specific enthalpy [J kg :sup:`-1`]
264
265
See Also
266
--------
267
TODO
268
269
Notes
270
-----
271
TODO
272
273
Examples
274
--------
275
>>> import gsw
276
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
277
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
278
>>> p = [10, 50, 125, 250, 600, 1000]
279
>>> gsw.enthalpy(SA, t, p)
280
array([ 115103.26047838, 114014.8036012 , 92179.9209311 ,
281
43255.32838089, 33087.21597002, 26970.5880448 ])
282
283
References
284
----------
285
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
286
of seawater - 2010: Calculation and use of thermodynamic properties.
287
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
288
UNESCO (English), 196 pp. See appendix A.11.
289
290
Modifications:
291
2011-03-29. David Jackett, Trevor McDougall and Paul Barker.
292
"""
293
294
return (gibbs(n0, n0, n0, SA, t, p) -
295
(t + Kelvin) * gibbs(n0, n1, n0, SA, t, p))
296
297
298
@match_args_return
299
def specvol_t_exact(SA, t, p):
300
r"""Calculates the specific volume of seawater.
301
302
Parameters
303
----------
304
SA : array_like
305
Absolute salinity [g kg :sup:`-1`]
306
t : array_like
307
in situ temperature [:math:`^\circ` C (ITS-90)]
308
p : array_like
309
pressure [dbar]
310
311
Returns
312
-------
313
specvol : array_like
314
specific volume [m :sup:`3` kg :sup:`-1`]
315
316
See Also
317
--------
318
TODO
319
320
Notes
321
-----
322
TODO
323
324
Examples
325
--------
326
>>> import gsw
327
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
328
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
329
>>> p = [10, 50, 125, 250, 600, 1000]
330
>>> gsw.specvol(SA, t, p)
331
array([ 0.00097863, 0.00097822, 0.00097615, 0.00097296, 0.00097103,
332
0.00096899])
333
334
References
335
----------
336
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
337
of seawater - 2010: Calculation and use of thermodynamic properties.
338
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
339
UNESCO (English), 196 pp. See section 2.7.
340
341
Modifications:
342
2011-03-23. David Jackett and Paul Barker.
343
"""
344
345
return gibbs(n0, n0, n1, SA, t, p)
346
347
348
@match_args_return
349
def entropy_t_exact(SA, t, p):
350
r"""Calculates specific entropy of seawater.
351
352
The specific entropy of seawater :math:`\eta` is given by:
353
354
.. math::
355
\eta(SA, t, p) = -g_T = \frac{\partial g}{\partial T}\Big|_{SA,p}
356
357
When taking derivatives with respect to *in situ* temperature, the symbol
358
:math:`T` will be used for temperature in order that these derivatives not
359
be confused with time derivatives.
360
361
Parameters
362
----------
363
SA : array_like
364
Absolute salinity [g kg :sup:`-1`]
365
t : array_like
366
in situ temperature [:math:`^\circ` C (ITS-90)]
367
p : array_like
368
pressure [dbar]
369
370
Returns
371
-------
372
entropy : array_like
373
specific entropy [J kg :sup:`-1` K :sup:`-1`]
374
375
See Also
376
--------
377
TODO
378
379
Notes
380
-----
381
TODO
382
383
Examples
384
--------
385
>>> import gsw
386
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
387
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
388
>>> p = [10, 50, 125, 250, 600, 1000]
389
>>> gsw.entropy_t_exact(SA, t, p)
390
array([ 400.38942528, 395.43817843, 319.8664982 , 146.79088159,
391
98.64734087, 62.79150873])
392
393
References
394
----------
395
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
396
of seawater - 2010: Calculation and use of thermodynamic properties.
397
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
398
UNESCO (English), 196 pp.
399
400
Modifications:
401
2011-03-29. David Jackett, Trevor McDougall and Paul Barker.
402
"""
403
404
return -gibbs(n0, n1, n0, SA, t, p)
405
406
407
@match_args_return
408
def cp_t_exact(SA, t, p):
409
r"""Calculates the isobaric heat capacity of seawater.
410
411
Parameters
412
----------
413
SA : array_like
414
Absolute salinity [g kg :sup:`-1`]
415
t : array_like
416
in situ temperature [:math:`^\circ` C (ITS-90)]
417
p : array_like
418
pressure [dbar]
419
420
Returns
421
-------
422
cp_t_exact : array_like
423
heat capacity of seawater [J kg :sup:`-1` K :sup:`-1`]
424
425
See Also
426
--------
427
TODO
428
429
Notes
430
-----
431
TODO
432
433
Examples
434
--------
435
>>> import gsw
436
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
437
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
438
>>> p = [10, 50, 125, 250, 600, 1000]
439
>>> gsw.cp_t_exact(SA, t, p)
440
array([ 4002.88800396, 4000.98028393, 3995.54646889, 3985.07676902,
441
3973.59384348, 3960.18408479])
442
443
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
444
of seawater - 2010: Calculation and use of thermodynamic properties.
445
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
446
UNESCO (English), 196 pp.
447
448
Modifications:
449
2011-03-29. David Jackett, Trevor McDougall and Paul Barker
450
"""
451
452
return -(t + Kelvin) * gibbs(n0, n2, n0, SA, t, p)
453
454
455
@match_args_return
456
def sound_speed_t_exact(SA, t, p):
457
r"""Calculates the speed of sound in seawater.
458
459
The speed of sound in seawater :math:`c` is given by:
460
461
.. math::
462
c(SA, t, p) = \sqrt{ \partial P / \partial \rho |_{SA,\eta}} =
463
\sqrt{(\rho\kappa)^{-1}} =
464
g_P \sqrt{g_{TT}/(g^2_{TP} - g_{TT}g_{PP})}
465
466
Note that in these expressions, since sound speed is in m s :sup`-1` and
467
density has units of kg m :sup:`-3` it follows that the pressure of the
468
partial derivatives must be in Pa and the isentropic compressibility
469
:math:`kappa` must have units of Pa :sup:`-1`. The sound speed c produced
470
by both the SIA and the GSW software libraries (appendices M and N) has
471
units of m s :sup:`-1`.
472
473
Parameters
474
----------
475
SA : array_like
476
Absolute salinity [g kg :sup:`-1`]
477
t : array_like
478
in situ temperature [:math:`^\circ` C (ITS-90)]
479
p : array_like
480
pressure [dbar]
481
482
Returns
483
-------
484
sound_speed : array_like
485
speed of sound in seawater [m s :sup:`-1`]
486
487
See Also
488
--------
489
TODO
490
491
Notes
492
-----
493
TODO
494
495
Examples
496
--------
497
>>> import gsw
498
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
499
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
500
>>> p = [10, 50, 125, 250, 600, 1000]
501
>>> gsw.sound_speed_t_exact(SA, t, p)
502
array([ 1542.61580359, 1542.70353407, 1530.84497914, 1494.40999692,
503
1487.37710252, 1483.93460908])
504
505
References
506
----------
507
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
508
of seawater - 2010: Calculation and use of thermodynamic properties.
509
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
510
UNESCO (English), 196 pp. See Eqn. (2.17.1)
511
512
Modifications:
513
2011-03-29. David Jackett, Paul Barker and Trevor McDougall.
514
"""
515
516
return (gibbs(n0, n0, n1, SA, t, p) * np.sqrt(gibbs(n0, n2, n0, SA, t, p) /
517
(gibbs(n0, n1, n1, SA, t, p) ** 2 - gibbs(n0, n2, n0, SA, t, p) *
518
gibbs(n0, n0, n2, SA, t, p))))
519
520
521
@match_args_return
522
def specvol_anom_t_exact(SA, t, p):
523
r"""Calculates specific volume anomaly from Absolute Salinity, in situ
524
temperature and pressure, using the full TEOS-10 Gibbs function.
525
526
The reference value of Absolute Salinity is SSO and the reference value of
527
Conservative Temperature is equal to 0 :math:`^\circ` C.
528
529
Parameters
530
----------
531
SA : array_like
532
Absolute salinity [g kg :sup:`-1`]
533
t : array_like
534
in situ temperature [:math:`^\circ` C (ITS-90)]
535
p : array_like
536
pressure [dbar]
537
538
Returns
539
-------
540
specvol_anom_t_exact : array_like
541
specific volume anomaly [m :sup:`3` kg :sup:`-1`]
542
543
See Also
544
--------
545
TODO
546
547
Notes
548
-----
549
TODO
550
551
Examples
552
--------
553
>>> import gsw
554
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
555
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
556
>>> p = [10, 50, 125, 250, 600, 1000]
557
>>> gsw.specvol_anom_t_exact(SA, t, p)
558
array([ 6.01044463e-06, 5.78602432e-06, 4.05564999e-06,
559
1.42198662e-06, 1.04351837e-06, 7.63964850e-07])
560
561
References
562
----------
563
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
564
of seawater - 2010: Calculation and use of thermodynamic properties.
565
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
566
UNESCO (English), 196 pp. See Eqn. (3.7.3)
567
568
Modifications:
569
2011-03-23. Trevor McDougall and Paul Barker
570
"""
571
572
pt_zero = pt_from_CT(SSO, 0)
573
t_zero = pt_from_t(SSO, pt_zero, 0, p)
574
return (gibbs(n0, n0, n1, SA, t, p) -
575
gibbs(n0, n0, n1, SSO, t_zero, p))
576
577
578
@match_args_return
579
def chem_potential_relative_t_exact(SA, t, p):
580
r"""Calculates the adiabatic lapse rate of seawater.
581
582
Parameters
583
----------
584
SA : array_like
585
Absolute salinity [g kg :sup:`-1`]
586
t : array_like
587
in situ temperature [:math:`^\circ` C (ITS-90)]
588
p : array_like
589
pressure [dbar]
590
591
Returns
592
-------
593
chem_potential_relative : array_like
594
relative chemical potential [J kg :sup:`-1`]
595
596
See Also
597
--------
598
TODO
599
600
Notes
601
-----
602
TODO
603
604
Examples
605
--------
606
>>> import gsw
607
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
608
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
609
>>> p = [10, 50, 125, 250, 600, 1000]
610
>>> gsw.chem_potential_relative_t_exact(SA, t, p)
611
array([ 79.4254481 , 79.25989214, 74.69154859, 65.64063719,
612
61.22685656, 57.21298557])
613
614
References
615
----------
616
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
617
of seawater - 2010: Calculation and use of thermodynamic properties.
618
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
619
UNESCO (English), 196 pp.
620
621
Modifications:
622
2011-03-29. Trevor McDougall and Paul Barker
623
"""
624
625
return gibbs(n1, n0, n0, SA, t, p)
626
627
628
@match_args_return
629
def internal_energy_t_exact(SA, t, p):
630
r"""Calculates the Helmholtz energy of seawater.
631
632
The specific internal energy of seawater :math:`u` is given by:
633
634
.. math::
635
u(SA, t, p) = g + (T_0 + t)\eta - (p + P_0)\nu =
636
g - (T_0 + t)\frac{\partial g}{\partial T}\Big|_{SA,p} -
637
(p + P_0)\frac{\partial g}{\partial P}\Big|_{SA,T}
638
639
where :math:`T_0` is the Celsius zero point, 273.15 K and
640
:math:`P_0` = 101 325 Pa is the standard atmosphere pressure.
641
642
Parameters
643
----------
644
SA : array_like
645
Absolute salinity [g kg :sup:`-1`]
646
t : array_like
647
in situ temperature [:math:`^\circ` C (ITS-90)]
648
p : array_like
649
pressure [dbar]
650
651
Returns
652
-------
653
internal_energy (u) : array_like
654
specific internal energy [J kg :sup:`-1`]
655
656
See Also
657
--------
658
TODO
659
660
Notes
661
-----
662
TODO
663
664
Examples
665
--------
666
>>> import gsw
667
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
668
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
669
>>> p = [10, 50, 125, 250, 600, 1000]
670
>>> gsw.internal_energy_t_exact(SA, t, p)
671
array([ 114906.23847309, 113426.57417062, 90860.81858842,
672
40724.34005719, 27162.66600185, 17182.50522667])
673
674
References
675
----------
676
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
677
of seawater - 2010: Calculation and use of thermodynamic properties.
678
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
679
UNESCO (English), 196 pp. See Eqn. (2.11.1)
680
681
Modifications:
682
2011-03-29. Trevor McDougall
683
"""
684
685
return (gibbs(n0, n0, n0, SA, t, p) -
686
(Kelvin + t) * gibbs(n0, n1, n0, SA, t, p) -
687
(db2Pascal * p + P0) * gibbs(n0, n0, n1, SA, t, p))
688
689
690
@match_args_return
691
def kappa_const_t_exact(SA, t, p):
692
r"""Calculates isothermal compressibility of seawater at constant in situ
693
temperature.
694
695
.. math::
696
\kappa^t(SA, t, p) =
697
\rho^{-1}\frac{\partial \rho}{\partial P}\Big|_{SA,T} =
698
-\nu^{-1}\frac{\partial \nu}{\partial P}\Big|_{SA,T} =
699
-\frac{g_{PP}}{g_P}
700
701
Parameters
702
----------
703
SA : array_like
704
Absolute salinity [g kg :sup:`-1`]
705
t : array_like
706
in situ temperature [:math:`^\circ` C (ITS-90)]
707
p : array_like
708
pressure [dbar]
709
710
Returns
711
-------
712
kappa : array_like
713
Isothermal compressibility [Pa :sup:`-1`]
714
715
See Also
716
--------
717
TODO
718
719
Notes
720
-----
721
This is the compressibility of seawater at constant in situ temperature.
722
723
Examples
724
--------
725
>>> import gsw
726
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
727
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
728
>>> p = [10, 50, 125, 250, 600, 1000]
729
>>> gsw.kappa_const_t_exact(SA, t, p)
730
array([ 4.19071646e-10, 4.18743202e-10, 4.22265764e-10,
731
4.37735100e-10, 4.40373818e-10, 4.41156577e-10])
732
733
References
734
----------
735
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
736
of seawater - 2010: Calculation and use of thermodynamic properties.
737
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
738
UNESCO (English), 196 pp. See Eqn. (2.15.1)
739
740
Modifications:
741
2011-03-29. David Jackett, Trevor McDougall and Paul Barker
742
"""
743
744
return -gibbs(n0, n0, n2, SA, t, p) / gibbs(n0, n0, n1, SA, t, p)
745
746
747
@match_args_return
748
def alpha_wrt_t_exact(SA, t, p):
749
r"""Calculates the thermal expansion coefficient of seawater with respect
750
to in situ temperature.
751
752
Parameters
753
----------
754
SA : array_like
755
Absolute salinity [g kg :sup:`-1`]
756
t : array_like
757
in situ temperature [:math:`^\circ` C (ITS-90)]
758
p : array_like
759
pressure [dbar]
760
761
Returns
762
-------
763
alpha_wrt_t : array_like
764
thermal expansion coefficient [K :sup:`-1`]
765
766
See Also
767
--------
768
TODO
769
770
Notes
771
-----
772
TODO
773
774
Examples
775
--------
776
>>> import gsw
777
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
778
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
779
>>> p = [10, 50, 125, 250, 600, 1000]
780
>>> gsw.alpha_wrt_t_exact(SA, t, p)
781
array([ 0.0003256 , 0.00032345, 0.00028141, 0.00017283, 0.00014557,
782
0.00012836])
783
784
References
785
----------
786
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
787
of seawater - 2010: Calculation and use of thermodynamic properties.
788
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
789
UNESCO (English), 196 pp. See Eqn. (2.18.1)
790
791
.. [2] McDougall, T.J., D.R. Jackett and F.J. Millero, 2010: An algorithm
792
for estimating Absolute Salinity in the global ocean. Submitted to Ocean
793
Science. A preliminary version is available at Ocean Sci. Discuss.,
794
6, 215-242.
795
796
Modifications:
797
2011-03-29. David Jackett, Trevor McDougall and Paul Barker
798
"""
799
800
return gibbs(n0, n1, n1, SA, t, p) / gibbs(n0, n0, n1, SA, t, p)
801
802
803
@match_args_return
804
def isochoric_heat_cap_t_exact(SA, t, p):
805
r"""Calculates the isochoric heat capacity of seawater.
806
807
Parameters
808
----------
809
SA : array_like
810
Absolute salinity [g kg :sup:`-1`]
811
t : array_like
812
in situ temperature [:math:`^\circ` C (ITS-90)]
813
p : array_like
814
pressure [dbar]
815
816
Returns
817
-------
818
isochoric_heat_cap : array_like
819
isochoric heat capacity [J kg :sup:`-1` K :sup:`-1`]
820
821
See Also
822
--------
823
TODO
824
825
Notes
826
-----
827
TODO
828
829
Examples
830
--------
831
>>> import gsw
832
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
833
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
834
>>> p = [10, 50, 125, 250, 600, 1000]
835
>>> gsw.isochoric_heat_cap_t_exact(SA, t, p)
836
array([ 3928.13708702, 3927.27381633, 3941.36418525, 3966.26126146,
837
3960.50903222, 3950.13901342])
838
839
References
840
----------
841
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
842
of seawater - 2010: Calculation and use of thermodynamic properties.
843
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
844
UNESCO (English), 196 pp. See section 2.21.
845
846
Modifications:
847
2011-03-29. Trevor McDougall
848
"""
849
850
return (-(Kelvin + t) * (gibbs(n0, n2, n0, SA, t, p) -
851
gibbs(n0, n1, n1, SA, t, p) ** 2 / gibbs(n0, n0, n2, SA, t, p)))
852
853
854
@match_args_return
855
def kappa_t_exact(SA, t, p):
856
r"""Calculates the isentropic compressibility of seawater.
857
858
When the entropy and Absolute Salinity are held constant while the pressure
859
is changed, the isentropic and isohaline compressibility
860
:math:`kappa` is obtained:
861
862
.. math::
863
\kappa(SA, t, p) =
864
\rho^{-1}\frac{\partial \rho}{\partial P}\Big|_{SA,\eta} =
865
-\nu^{-1}\frac{\partial \nu}{\partial P}\Big|_{SA,\eta} =
866
\rho^{-1}\frac{\partial \rho}{\partial P}\Big|_{SA,\theta} =
867
-\nu^{-1}\frac{\partial \nu}{\partial P}\Big|_{SA,\theta} =
868
-\frac{ (g_{TP}^2 - g_{TT} g_{PP} ) }{g_P g_{TT}}
869
870
The isentropic and isohaline compressibility is sometimes called simply the
871
isentropic compressibility (or sometimes the "adiabatic compressibility"),
872
on the unstated understanding that there is also no transfer of salt during
873
the isentropic or adiabatic change in pressure.
874
875
Parameters
876
----------
877
SA : array_like
878
Absolute salinity [g kg :sup:`-1`]
879
t : array_like
880
in situ temperature [:math:`^\circ` C (ITS-90)]
881
p : array_like
882
pressure [dbar]
883
884
Returns
885
-------
886
kappa : array_like
887
Isentropic compressibility [Pa :sup:`-1`]
888
889
See Also
890
--------
891
TODO
892
893
Notes
894
-----
895
The output is Pascal and not dbar.
896
897
Examples
898
--------
899
>>> import gsw
900
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
901
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
902
>>> p = [10, 50, 125, 250, 600, 1000]
903
>>> gsw.kappa_t_exact(SA, t, p)
904
array([ 4.11245799e-10, 4.11029072e-10, 4.16539558e-10,
905
4.35668338e-10, 4.38923693e-10, 4.40037576e-10])
906
907
References
908
----------
909
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
910
of seawater - 2010: Calculation and use of thermodynamic properties.
911
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
912
UNESCO (English), 196 pp. See Eqns. (2.16.1) and the row for kappa in
913
Table P.1 of appendix P
914
915
Modifications:
916
2011-03-23. David Jackett, Trevor McDougall and Paul Barker
917
"""
918
919
return ((gibbs(n0, n1, n1, SA, t, p) ** 2 - gibbs(n0, n2, n0, SA, t, p) *
920
gibbs(n0, n0, n2, SA, t, p)) / (gibbs(n0, n0, n1, SA, t, p) *
921
gibbs(n0, n2, n0, SA, t, p)))
922
923
924
@match_args_return
925
def SA_from_rho_t_exact(rho, t, p):
926
r"""Calculates the Absolute Salinity of a seawater sample, for given values
927
of its density, in situ temperature and sea pressure (in dbar).
928
929
One use for this function is in the laboratory where a measured value of
930
the in situ density :math:`\rho` of a seawater sample may have been made at
931
the laboratory temperature :math:`t` and at atmospheric pressure :math:`p`.
932
The present function will return the Absolute Salinity SA of this seawater
933
sample.
934
935
Parameters
936
----------
937
rho : array_like
938
in situ density [kg m :sup:`-3`]
939
t : array_like
940
in situ temperature [:math:`^\circ` C (ITS-90)]
941
p : array_like
942
pressure [dbar]
943
944
Returns
945
-------
946
SA : array_like
947
Absolute salinity [g kg :sup:`-1`]
948
949
See Also
950
--------
951
TODO
952
953
Notes
954
-----
955
This is expressed on the Reference-Composition Salinity Scale of
956
Millero et al. (2008).
957
958
After two iterations of a modified Newton-Raphson iteration,
959
the error in SA is typically no larger than
960
2 :math:`^\times` 10 :sup:`-13` [g kg :sup:`-1`]
961
962
Examples
963
--------
964
>>> import gsw
965
>>> rho = [1021.839, 1022.262, 1024.426, 1027.792, 1029.839, 1032.002]
966
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
967
>>> p = [10, 50, 125, 250, 600, 1000]
968
>>> gsw.SA_from_rho_t_exact(rho, t, p)
969
array([ 34.71022966, 34.89057683, 35.02332421, 34.84952096,
970
34.73824809, 34.73188384])
971
972
References
973
----------
974
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
975
of seawater - 2010: Calculation and use of thermodynamic properties.
976
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
977
UNESCO (English), 196 pp. See section 2.5.
978
979
.. [2] Millero, F. J., R. Feistel, D. G. Wright, and T. J. McDougall, 2008:
980
The composition of Standard Seawater and the definition of the
981
Reference-Composition Salinity Scale, Deep-Sea Res. I, 55, 50-72.
982
983
Modifications:
984
2011-03-28. Trevor McDougall and Paul Barker.
985
"""
986
987
v_lab = np.ones_like(rho) / rho
988
v_0 = gibbs(n0, n0, n1, 0, t, p)
989
v_120 = gibbs(n0, n0, n1, 120, t, p)
990
991
# Initial estimate of SA.
992
SA = 120 * (v_lab - v_0) / (v_120 - v_0)
993
Ior = np.logical_or(SA < 0, SA > 120)
994
995
# Initial estimate of v_SA, SA derivative of v
996
v_SA = (v_120 - v_0) / 120
997
998
for k in range(0, 2):
999
SA_old = SA
1000
delta_v = gibbs(n0, n0, n1, SA_old, t, p) - v_lab
1001
# Half way the mod. N-R method (McDougall and Wotherspoon, 2012)
1002
SA = SA_old - delta_v / v_SA
1003
SA_mean = 0.5 * (SA + SA_old)
1004
v_SA = gibbs(n1, n0, n1, SA_mean, t, p)
1005
SA = SA_old - delta_v / v_SA
1006
1007
SA[Ior] = np.ma.masked
1008
1009
return SA
1010
1011
1012
@match_args_return
1013
def t_from_rho_exact(rho, SA, p):
1014
r"""Calculates the in-situ temperature of a seawater sample, for given
1015
values of its density, Absolute Salinity and sea pressure (in dbar).
1016
1017
1018
Parameters
1019
----------
1020
rho : array_like
1021
in situ density [kg m :sup:`-3`]
1022
SA : array_like
1023
Absolute salinity [g kg :sup:`-1`]
1024
p : array_like
1025
pressure [dbar]
1026
1027
Returns
1028
-------
1029
t : array_like
1030
in situ temperature [:math:`^\circ` C (ITS-90)]
1031
t_multiple : array_like
1032
in situ temperature [:math:`^\circ` C (ITS-90)]
1033
1034
See Also
1035
--------
1036
TODO
1037
1038
Notes
1039
-----
1040
At low salinities, in brackish water, there are two possible temperatures
1041
for a single density. This program will output both valid solutions
1042
(t, t_multiple), if there is only one possible solution the second variable
1043
will be set to NaN.
1044
1045
1046
Examples
1047
--------
1048
TODO
1049
1050
References
1051
----------
1052
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
1053
of seawater - 2010: Calculation and use of thermodynamic properties.
1054
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
1055
UNESCO (English), 196 pp.
1056
1057
Modifications:
1058
2011-04-21. Trevor McDougall and Paul Barker.
1059
"""
1060
1061
"""alpha_limit is the positive value of the thermal expansion coefficient
1062
which is used at the freezing temperature to distinguish between I_salty
1063
and I_fresh."""
1064
alpha_limit = 1e-5
1065
1066
"""rec_half_rho_TT is a constant representing the reciprocal of half the
1067
second derivative of density with respect to temperature near the
1068
temperature of maximum density."""
1069
rec_half_rho_TT = -110.0
1070
1071
t = np.zeros_like(SA) + np.NaN
1072
t_multiple = np.zeros_like(SA) + np.NaN
1073
1074
I_SA = np.logical_or(SA < 0, SA > 42)
1075
I_p = np.logical_or(p < -1.5, p > 12000)
1076
I_SA_p = np.logical_or(I_SA, I_p)
1077
1078
SA[I_SA_p] = np.ma.masked
1079
1080
rho_40 = rho_t_exact(SA, 40 * np.ones_like(SA), p)
1081
1082
I_rho_light = (rho - rho_40) < 0
1083
1084
SA[I_rho_light] = np.ma.masked
1085
1086
t_max_rho = t_maxdensity_exact(SA, p)
1087
rho_max = rho_t_exact(SA, t_max_rho, p)
1088
rho_extreme = rho_max
1089
t_freezing = t_freezing(SA, p) # Assumes seawater is saturated with air.
1090
rho_freezing = rho_t_exact(SA, t_freezing, p)
1091
1092
I_fr_gr_max = (t_freezing - t_max_rho) > 0
1093
rho_extreme[I_fr_gr_max] = rho_freezing[I_fr_gr_max]
1094
1095
I_rho_dense = rho > rho_extreme
1096
SA[I_rho_dense] = np.ma.masked
1097
1098
# FIXME: Is this needed?
1099
I_bad = np.isnan(SA * p * rho)
1100
SA[I_bad] = np.ma.masked
1101
1102
alpha_freezing = alpha_wrt_t_exact(SA, t_freezing, p)
1103
1104
I_salty = alpha_freezing > alpha_limit
1105
1106
t_diff = 40. * np.ones_like(I_salty) - t_freezing(I_salty)
1107
1108
top = (rho_40[I_salty] - rho_freezing[I_salty] +
1109
rho_freezing[I_salty] * alpha_freezing[I_salty] * t_diff)
1110
1111
a = top / (t_diff ** 2)
1112
b = -rho_freezing[I_salty] * alpha_freezing[I_salty]
1113
c = rho_freezing[I_salty] - rho[I_salty]
1114
sqrt_disc = np.sqrt(b ** 2 - 4 * a * c)
1115
# The value of t[I_salty] is the initial guess `t` in the range of I_salty.
1116
t[I_salty] = t_freezing[I_salty] + 0.5 * (-b - sqrt_disc) / a
1117
1118
I_fresh = alpha_freezing <= alpha_limit
1119
t_diff = 40 * np.ones_like[I_fresh] - t_max_rho[I_fresh]
1120
factor = ((rho_max[I_fresh] - rho[I_fresh]) /
1121
(rho_max[I_fresh] - rho_40[I_fresh]))
1122
delta_t = t_diff * np.sqrt(factor)
1123
1124
I_fresh_NR = delta_t > 5
1125
t[I_fresh[I_fresh_NR]] = (t_max_rho[I_fresh[I_fresh_NR]] +
1126
delta_t[I_fresh_NR])
1127
1128
I_quad = delta_t <= 5
1129
t_a = np.zeros_like(SA) + np.NaN
1130
# Set the initial value of the quadratic solution roots.
1131
t_a[I_fresh[I_quad]] = (t_max_rho[I_fresh[I_quad]] +
1132
np.sqrt(rec_half_rho_TT * (rho[I_fresh[I_quad]] -
1133
rho_max[I_fresh[I_quad]])))
1134
1135
for Number_of_iterations in range(0, 5):
1136
t_old = t_a
1137
rho_old = rho_t_exact(SA, t_old, p)
1138
factorqa = (rho_max - rho) / (rho_max - rho_old)
1139
t_a = t_max_rho + (t_old - t_max_rho) * np.sqrt(factorqa)
1140
1141
t_a[t_freezing - t_a < 0] = np.ma.masked
1142
1143
t_b = np.zeros_like(SA) + np.NaN
1144
# Set the initial value of the quadratic solution routes.
1145
t_b[I_fresh[I_quad]] = (t_max_rho[I_fresh[I_quad]] -
1146
np.sqrt(rec_half_rho_TT * (rho[I_fresh[I_quad]] -
1147
rho_max[I_fresh[I_quad]])))
1148
for Number_of_iterations in range(0, 6):
1149
t_old = t_b
1150
rho_old = rho_t_exact(SA, t_old, p)
1151
factorqb = (rho_max - rho) / (rho_max - rho_old)
1152
t_b = t_max_rho + (t_old - t_max_rho) * np.sqrt(factorqb)
1153
1154
# After seven iterations of this quadratic iterative procedure,
1155
# the error in rho is no larger than 4.6x10^-13 kg/m^3.
1156
t_b[t_freezing - t_b < 0] = np.ma.masked
1157
1158
# Begin the modified Newton-Raphson iterative method, which will only
1159
# operate on non-masked data.
1160
1161
v_lab = np.ones_like(rho) / rho
1162
v_t = gibbs(0, 1, 1, SA, t, p)
1163
for Number_of_iterations in range(0, 3):
1164
t_old = t
1165
delta_v = gibbs(0, 0, 1, SA, t_old, p) - v_lab
1166
t = t_old - delta_v / v_t # Half way through the modified N-R method.
1167
t_mean = 0.5 * (t + t_old)
1168
v_t = gibbs(0, 1, 1, SA, t_mean, p)
1169
t = t_old - delta_v / v_t
1170
1171
I_quad = ~np.isnan(t_a)
1172
t[I_quad] = t_a[I_quad]
1173
1174
I_quad = ~np.isnan(t_b)
1175
t_multiple[I_quad] = t_b[I_quad]
1176
1177
# After three iterations of this modified Newton-Raphson iteration,
1178
# the error in rho is no larger than 4.6x10^-13 kg/m^3.
1179
1180
return t, t_multiple
1181
1182
1183
@match_args_return
1184
def pot_rho_t_exact(SA, t, p, p_ref=0):
1185
r"""Calculates potential density of seawater.
1186
1187
Parameters
1188
----------
1189
SA : array_like
1190
Absolute salinity [g kg :sup:`-1`]
1191
t : array_like
1192
in situ temperature [:math:`^\circ` C (ITS-90)]
1193
p : array_like
1194
pressure [dbar]
1195
p_ref : int, float, optional
1196
reference pressure, default = 0
1197
1198
Returns
1199
-------
1200
pot_rho : array_like
1201
potential density [kg m :sup:`-3`]
1202
1203
See Also
1204
--------
1205
TODO
1206
1207
Notes
1208
-----
1209
TODO
1210
1211
Examples
1212
--------
1213
>>> import gsw
1214
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
1215
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
1216
>>> p = [10, 50, 125, 250, 600, 1000]
1217
>>> gsw.pot_rho_t_exact(SA, t, p)
1218
array([ 1021.79814581, 1022.05248442, 1023.89358365, 1026.66762112,
1219
1027.10723087, 1027.40963126])
1220
>>> gsw.pot_rho(SA, t, p, p_ref=1000)
1221
array([ 1025.95554512, 1026.21306986, 1028.12563226, 1031.1204547 ,
1222
1031.63768355, 1032.00240412])
1223
1224
References
1225
----------
1226
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
1227
of seawater - 2010: Calculation and use of thermodynamic properties.
1228
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
1229
UNESCO (English), 196 pp. See section 3.4.
1230
1231
Modifications:
1232
2011-03-29. David Jackett, Trevor McDougall and Paul Barker
1233
"""
1234
1235
pt = pt_from_t(SA, t, p, p_ref=p_ref)
1236
1237
return rho_t_exact(SA, pt, p_ref)
1238
1239
1240
@match_args_return
1241
def alpha_wrt_CT_t_exact(SA, t, p):
1242
r"""Calculates the thermal expansion coefficient of seawater with respect
1243
to Conservative Temperature.
1244
1245
Parameters
1246
----------
1247
SA : array_like
1248
Absolute salinity [g kg :sup:`-1`]
1249
t : array_like
1250
in situ temperature [:math:`^\circ` C (ITS-90)]
1251
p : array_like
1252
pressure [dbar]
1253
1254
Returns
1255
-------
1256
alpha_wrt_CT : array_like
1257
thermal expansion coefficient [K :sup:`-1`]
1258
1259
See Also
1260
--------
1261
TODO
1262
1263
Notes
1264
-----
1265
TODO
1266
1267
Examples
1268
--------
1269
>>> import gsw
1270
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
1271
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
1272
>>> p = [10, 50, 125, 250, 600, 1000]
1273
>>> gsw.alpha_wrt_CT_t_exact(SA, t, p)
1274
array([ 0.00032471, 0.00032272, 0.00028118, 0.00017314, 0.00014627,
1275
0.00012943])
1276
1277
References
1278
----------
1279
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
1280
of seawater - 2010: Calculation and use of thermodynamic properties.
1281
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
1282
UNESCO (English), 196 pp. See Eqn. (2.18.3).
1283
1284
Modifications:
1285
2011-03-29. Trevor McDougall and Paul Barker
1286
"""
1287
1288
pt0 = pt0_from_t(SA, t, p)
1289
factor = -cp0 / ((Kelvin + pt0) * gibbs(n0, n2, n0, SA, t, p))
1290
return factor * (gibbs(n0, n1, n1, SA, t, p) / gibbs(n0, n0, n1, SA, t, p))
1291
1292
1293
@match_args_return
1294
def alpha_wrt_pt_t_exact(SA, t, p):
1295
r"""Calculates the thermal expansion coefficient of seawater with respect
1296
to potential temperature, with a reference pressure of zero.
1297
1298
Parameters
1299
----------
1300
SA : array_like
1301
Absolute salinity [g kg :sup:`-1`]
1302
t : array_like
1303
in situ temperature [:math:`^\circ` C (ITS-90)]
1304
p : array_like
1305
pressure [dbar]
1306
1307
Returns
1308
-------
1309
alpha_wrt_pt : array_like
1310
thermal expansion coefficient [K :sup:`-1`]
1311
1312
See Also
1313
--------
1314
TODO
1315
1316
Notes
1317
-----
1318
TODO
1319
1320
Examples
1321
--------
1322
>>> import gsw
1323
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
1324
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
1325
>>> p = [10, 50, 125, 250, 600, 1000]
1326
>>> gsw.alpha_wrt_pt_t_exact(SA, t, p)
1327
array([ 0.00032562, 0.00032355, 0.00028164, 0.00017314, 0.00014623,
1328
0.00012936])
1329
1330
References
1331
----------
1332
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
1333
of seawater - 2010: Calculation and use of thermodynamic properties.
1334
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
1335
UNESCO (English), 196 pp. See Eqn. (2.18.2).
1336
1337
Modifications:
1338
2011-03-29. David Jackett, Trevor McDougall and Paul Barker
1339
"""
1340
1341
pt0 = pt0_from_t(SA, t, p)
1342
factor = gibbs(n0, n2, n0, SA, pt0, 0) / gibbs(n0, n2, n0, SA, t, p)
1343
return factor * (gibbs(n0, n1, n1, SA, t, p) / gibbs(n0, n0, n1, SA, t, p))
1344
1345
1346
@match_args_return
1347
def beta_const_CT_t_exact(SA, t, p):
1348
r"""Calculates the saline (i.e. haline) contraction coefficient of seawater
1349
at constant Conservative Temperature.
1350
1351
Parameters
1352
----------
1353
SA : array_like
1354
Absolute salinity [g kg :sup:`-1`]
1355
t : array_like
1356
in situ temperature [:math:`^\circ` C (ITS-90)]
1357
p : array_like
1358
pressure [dbar]
1359
1360
Returns
1361
-------
1362
beta_const_CT : array_like
1363
saline contraction coefficient [kg g :sup:`-1`]
1364
1365
See Also
1366
--------
1367
TODO
1368
1369
Notes
1370
-----
1371
TODO
1372
1373
Examples
1374
--------
1375
>>> import gsw
1376
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
1377
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
1378
>>> p = [10, 50, 125, 250, 600, 1000]
1379
>>> gsw.beta_const_CT_t_exact(SA, t, p)
1380
array([ 0.00071749, 0.00071765, 0.00072622, 0.00075051, 0.00075506,
1381
0.00075707])
1382
1383
References
1384
----------
1385
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
1386
of seawater - 2010: Calculation and use of thermodynamic properties.
1387
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
1388
UNESCO (English), 196 pp. See Eqn. (2.19.3)
1389
1390
Modifications:
1391
2010-07-23. David Jackett, Trevor McDougall and Paul Barker
1392
"""
1393
1394
# TODO: Original GSW-V3 re-implements gibbs, check what to do here!
1395
1396
pt0 = pt0_from_t(SA, t, p)
1397
1398
factora = (gibbs(n1, n1, n0, SA, t, p) - gibbs(n1, n0, n0, SA, pt0, 0) /
1399
(Kelvin + pt0))
1400
factor = (factora / (gibbs(n0, n0, n1, SA, t, p) *
1401
gibbs(n0, n2, n0, SA, t, p)))
1402
1403
return (gibbs(n0, n1, n1, SA, t, p) * factor -
1404
gibbs(n1, n0, n1, SA, t, p) / gibbs(n0, n0, n1, SA, t, p))
1405
1406
1407
@match_args_return
1408
def beta_const_pt_t_exact(SA, t, p):
1409
r"""Calculates the saline (i.e. haline) contraction coefficient of seawater
1410
at constant potential temperature with a reference pressure of 0 dbar.
1411
1412
Parameters
1413
----------
1414
SA : array_like
1415
Absolute salinity [g kg :sup:`-1`]
1416
t : array_like
1417
in situ temperature [:math:`^\circ` C (ITS-90)]
1418
p : array_like
1419
pressure [dbar]
1420
1421
Returns
1422
-------
1423
beta_const_pt : array_like
1424
saline contraction coefficient [kg g :sup:`-1`]
1425
1426
See Also
1427
--------
1428
TODO
1429
1430
Notes
1431
-----
1432
TODO
1433
1434
Examples
1435
--------
1436
>>> import gsw
1437
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
1438
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
1439
>>> p = [10, 50, 125, 250, 600, 1000]
1440
>>> gsw.beta_const_pt_t_exact(SA, t, p)
1441
array([ 0.00073112, 0.00073106, 0.00073599, 0.00075375, 0.00075712,
1442
0.00075843])
1443
1444
References
1445
----------
1446
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
1447
of seawater - 2010: Calculation and use of thermodynamic properties.
1448
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
1449
UNESCO (English), 196 pp. See Eqn. (2.19.2)
1450
1451
Modifications:
1452
2011-04-10. Trevor McDougall and Paul Barker
1453
"""
1454
# NOTE: The original Matlab toolbox re-implement some code here. Why?
1455
1456
pt0 = pt0_from_t(SA, t, p)
1457
1458
factora = gibbs(n1, n1, n0, SA, t, p) - gibbs(n1, n1, n0, SA, pt0, 0)
1459
1460
factor = (factora / (gibbs(n0, n0, n1, SA, t, p) *
1461
gibbs(n0, n2, n0, SA, t, p)))
1462
1463
return (gibbs(n0, n1, n1, SA, t, p) * factor -
1464
gibbs(n1, n0, n1, SA, t, p) / gibbs(n0, n0, n1, SA, t, p))
1465
1466
1467
@match_args_return
1468
def beta_const_t_exact(SA, t, p):
1469
r"""Calculates the saline (i.e. haline) contraction coefficient of seawater
1470
at constant in situ temperature.
1471
1472
Parameters
1473
----------
1474
SA : array_like
1475
Absolute salinity [g kg :sup:`-1`]
1476
t : array_like
1477
in situ temperature [:math:`^\circ` C (ITS-90)]
1478
p : array_like
1479
pressure [dbar]
1480
1481
Returns
1482
-------
1483
beta_const_t : array_like
1484
saline contraction coefficient [kg g :sup:`-1`]
1485
1486
See Also
1487
--------
1488
TODO
1489
1490
Notes
1491
-----
1492
TODO
1493
1494
Examples
1495
--------
1496
>>> import gsw
1497
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
1498
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
1499
>>> p = [10, 50, 125, 250, 600, 1000]
1500
>>> gsw.beta_const_t_exact(SA, t, p)
1501
array([ 0.00073112, 0.00073107, 0.00073602, 0.00075381, 0.00075726,
1502
0.00075865])
1503
1504
References
1505
----------
1506
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
1507
of seawater - 2010: Calculation and use of thermodynamic properties.
1508
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
1509
UNESCO (English), 196 pp. See Eqn. (2.19.1)
1510
1511
Modifications:
1512
2011-03-29. David Jackett, Trevor McDougall and Paul Barker
1513
"""
1514
1515
return -gibbs(n1, n0, n1, SA, t, p) / gibbs(n0, n0, n1, SA, t, p)
1516
1517
1518
@match_args_return
1519
def chem_potential_water_t_exact(SA, t, p):
1520
r"""Calculates the chemical potential of water in seawater.
1521
1522
Parameters
1523
----------
1524
SA : array_like
1525
Absolute salinity [g kg :sup:`-1`]
1526
t : array_like
1527
in situ temperature [:math:`^\circ` C (ITS-90)]
1528
p : array_like
1529
pressure [dbar]
1530
1531
Returns
1532
-------
1533
chem_potential_water : array_like
1534
chemical potential of water in seawater
1535
[J kg :sup:`-1`]
1536
1537
See Also
1538
--------
1539
TODO
1540
1541
Notes
1542
-----
1543
TODO
1544
1545
Examples
1546
--------
1547
>>> import gsw
1548
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
1549
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
1550
>>> p = [10, 50, 125, 250, 600, 1000]
1551
>>> gsw.chem_potential_water_t_exact(SA, t, p)
1552
array([-8545.56114628, -8008.08554834, -5103.98013987, -634.06778275,
1553
3335.56680347, 7555.43444597])
1554
1555
References
1556
----------
1557
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
1558
of seawater - 2010: Calculation and use of thermodynamic properties.
1559
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
1560
UNESCO (English), 196 pp.
1561
1562
Modifications:
1563
2011-03-29. Trevor McDougall and Paul Barker
1564
"""
1565
SA, t, p, mask = strip_mask(SA, t, p)
1566
1567
# FIXME: Ugly copy from gibbs, why?
1568
x2 = sfac * SA
1569
1570
x = np.sqrt(x2)
1571
y = t * 0.025
1572
z = p * 1e-4 # Pressure (p) is sea pressure in units of dbar.
1573
1574
g03_g = (101.342743139674 + z * (100015.695367145 +
1575
z * (-2544.5765420363 + z * (284.517778446287 +
1576
z * (-33.3146754253611 + (4.20263108803084 -
1577
0.546428511471039 * z) * z)))) +
1578
y * (5.90578347909402 + z * (-270.983805184062 +
1579
z * (776.153611613101 + z * (-196.51255088122 +
1580
(28.9796526294175 - 2.13290083518327 * z) * z))) +
1581
y * (-12357.785933039 + z * (1455.0364540468 +
1582
z * (-756.558385769359 + z * (273.479662323528 +
1583
z * (-55.5604063817218 + 4.34420671917197 * z)))) +
1584
y * (736.741204151612 + z * (-672.50778314507 +
1585
z * (499.360390819152 + z * (-239.545330654412 +
1586
(48.8012518593872 - 1.66307106208905 * z) * z))) +
1587
y * (-148.185936433658 + z * (397.968445406972 +
1588
z * (-301.815380621876 + (152.196371733841 -
1589
26.3748377232802 * z) * z)) +
1590
y * (58.0259125842571 + z * (-194.618310617595 +
1591
z * (120.520654902025 + z * (-55.2723052340152 +
1592
6.48190668077221 * z))) +
1593
y * (-18.9843846514172 + y * (3.05081646487967 -
1594
9.63108119393062 * z) +
1595
z * (63.5113936641785 + z * (-22.2897317140459 +
1596
8.17060541818112 * z)))))))))
1597
1598
g08_g = x2 * (1416.27648484197 +
1599
x * (-2432.14662381794 + x * (2025.80115603697 +
1600
y * (543.835333000098 + y * (-68.5572509204491 +
1601
y * (49.3667694856254 + y * (-17.1397577419788 +
1602
2.49697009569508 * y))) - 22.6683558512829 * z) +
1603
x * (-1091.66841042967 - 196.028306689776 * y +
1604
x * (374.60123787784 - 48.5891069025409 * x +
1605
36.7571622995805 * y) + 36.0284195611086 * z) +
1606
z * (-54.7919133532887 + (-4.08193978912261 -
1607
30.1755111971161 * z) * z)) +
1608
z * (199.459603073901 + z * (-52.2940909281335 +
1609
(68.0444942726459 - 3.41251932441282 * z) * z)) +
1610
y * (-493.407510141682 + z * (-175.292041186547 +
1611
(83.1923927801819 - 29.483064349429 * z) * z) +
1612
y * (-43.0664675978042 + z * (383.058066002476 +
1613
z * (-54.1917262517112 + 25.6398487389914 * z)) +
1614
y * (-10.0227370861875 - 460.319931801257 * z + y *
1615
(0.875600661808945 + 234.565187611355 * z))))) +
1616
y * (168.072408311545))
1617
1618
g_SA_part = (8645.36753595126 +
1619
x * (-7296.43987145382 + x * (8103.20462414788 +
1620
y * (2175.341332000392 + y * (-274.2290036817964 +
1621
y * (197.4670779425016 + y * (-68.5590309679152 +
1622
9.98788038278032 * y))) - 90.6734234051316 * z) +
1623
x * (-5458.34205214835 - 980.14153344888 * y +
1624
x * (2247.60742726704 - 340.1237483177863 * x +
1625
220.542973797483 * y) + 180.142097805543 * z) +
1626
z * (-219.1676534131548 + (-16.32775915649044 -
1627
120.7020447884644 * z) * z)) +
1628
z * (598.378809221703 + z * (-156.8822727844005 +
1629
(204.1334828179377 - 10.23755797323846 * z) * z)) +
1630
y * (-1480.222530425046 + z * (-525.876123559641 +
1631
(249.57717834054571 - 88.449193048287 * z) * z) +
1632
y * (-129.1994027934126 + z * (1149.174198007428 +
1633
z * (-162.5751787551336 + 76.9195462169742 * z)) +
1634
y * (-30.0682112585625 - 1380.9597954037708 * z + y *
1635
(2.626801985426835 + 703.695562834065 * z))))) +
1636
y * (1187.3715515697959))
1637
1638
chem_potential_water = g03_g + g08_g - 0.5 * sfac * SA * g_SA_part
1639
1640
return np.ma.array(chem_potential_water, mask=mask, copy=False)
1641
1642
1643
@match_args_return
1644
def chem_potential_salt_t_exact(SA, t, p):
1645
r"""Calculates the chemical potential of salt in seawater.
1646
1647
Parameters
1648
----------
1649
SA : array_like
1650
Absolute salinity [g kg :sup:`-1`]
1651
t : array_like
1652
in situ temperature [:math:`^\circ` C (ITS-90)]
1653
p : array_like
1654
pressure [dbar]
1655
1656
Returns
1657
-------
1658
chem_potential_salt : array_like
1659
chemical potential of salt in seawater [J kg :sup:`-1`]
1660
1661
See Also
1662
--------
1663
TODO
1664
1665
Notes
1666
-----
1667
TODO
1668
1669
Examples
1670
--------
1671
>>> import gsw
1672
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
1673
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
1674
>>> p = [10, 50, 125, 250, 600, 1000]
1675
>>> gsw.chem_potential_salt_t_exact(SA, t, p)
1676
array([-8466.13569818, -7928.8256562 , -5029.28859129, -568.42714556,
1677
3396.79366004, 7612.64743154])
1678
1679
References
1680
----------
1681
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
1682
of seawater - 2010: Calculation and use of thermodynamic properties.
1683
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
1684
UNESCO (English), 196 pp. See section 2.9.
1685
1686
Modifications:
1687
2010-03-29. Trevor McDougall and Paul Barker
1688
"""
1689
1690
return (chem_potential_relative_t_exact(SA, t, p) +
1691
chem_potential_water_t_exact(SA, t, p))
1692
1693
1694
@match_args_return
1695
def adiabatic_lapse_rate_t_exact(SA, t, p):
1696
r"""Calculates the adiabatic lapse rate of seawater.
1697
1698
Parameters
1699
----------
1700
SA : array_like
1701
Absolute salinity [g kg :sup:`-1`]
1702
t : array_like
1703
in situ temperature [:math:`^\circ` C (ITS-90)]
1704
p : array_like
1705
pressure [dbar]
1706
1707
Returns
1708
-------
1709
adiabatic_lapse_rate : array_like
1710
Adiabatic lapse rate [K Pa :sup:`-1`]
1711
1712
See Also
1713
--------
1714
TODO
1715
1716
Notes
1717
-----
1718
The output is in unit of degrees Celsius per Pa, (or equivalently K/Pa) not
1719
in units of K/dbar
1720
1721
Examples
1722
--------
1723
>>> import gsw
1724
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
1725
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
1726
>>> p = [10, 50, 125, 250, 600, 1000]
1727
>>> gsw.adiabatic_lapse_rate_t_exact(SA, t, p)
1728
array([ 2.40350282e-08, 2.38496700e-08, 2.03479880e-08,
1729
1.19586543e-08, 9.96170718e-09, 8.71747270e-09])
1730
1731
References
1732
----------
1733
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
1734
of seawater - 2010: Calculation and use of thermodynamic properties.
1735
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
1736
UNESCO (English), 196 pp. See Eqn. (2.22.1).
1737
1738
Modifications:
1739
2011-03-29. Trevor McDougall and Paul Barker
1740
"""
1741
1742
return -gibbs(n0, n1, n1, SA, t, p) / gibbs(n0, n2, n0, SA, t, p)
1743
1744
1745
@match_args_return
1746
def osmotic_coefficient_t_exact(SA, t, p):
1747
r"""Calculates the osmotic coefficient of seawater.
1748
1749
Parameters
1750
----------
1751
SA : array_like
1752
Absolute salinity [g kg :sup:`-1`]
1753
t : array_like
1754
in situ temperature [:math:`^\circ` C (ITS-90)]
1755
p : array_like
1756
pressure [dbar]
1757
1758
Returns
1759
-------
1760
osmotic_coefficient : array_like
1761
osmotic coefficient of seawater [unitless]
1762
1763
See Also
1764
--------
1765
TODO
1766
1767
Notes
1768
-----
1769
TODO
1770
1771
Examples
1772
--------
1773
>>> import gsw
1774
>>> SA = [34.7118, 34.8915, 35.0256, 34.8472, 34.7366, 34.7324]
1775
>>> t = [28.7856, 28.4329, 22.8103, 10.2600, 6.8863, 4.4036]
1776
>>> p = [10, 50, 125, 250, 600, 1000]
1777
>>> gsw.osmotic_coefficient_t_exact(SA,t , p)
1778
array([ 0.90284718, 0.90298624, 0.90238866, 0.89880927, 0.89801054,
1779
0.89767912])
1780
1781
References
1782
----------
1783
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
1784
of seawater - 2010: Calculation and use of thermodynamic properties.
1785
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
1786
UNESCO (English), 196 pp.
1787
1788
Modifications:
1789
2011-04-01. Trevor McDougall and Paul Barker.
1790
2012-11-15. Trevor McDougall and Paul Barker.
1791
"""
1792
1793
SA = np.maximum(SA, 0)
1794
k = M_S / R
1795
part = k * (1000 - SA) / (Kelvin + t)
1796
1797
x2 = sfac * SA
1798
x = np.sqrt(x2)
1799
y = t * 0.025
1800
# Note that the input pressure (p) is sea pressure in units of dbar.
1801
z = p / db2Pascal
1802
1803
oc = (7.231916621570606e1, 1.059039593127674e1, -3.025914794694813e1,
1804
5.040733670521486e1, -4.074543321119333e1, 1.864215613820487e1,
1805
-3.022566485046178, -6.138647522851840, 1.353207379758663e1,
1806
-7.316560781114737, 1.829232499785750, -5.358042980767074e-1,
1807
-1.705887283375562, -1.246962174707332e-1, 1.228376913546017,
1808
1.089364009088042e-2, -4.264828939262248e-1, 6.213127679460041e-2,
1809
2.481543497315280, -1.363368964861909, -5.640491627443773e-1,
1810
1.344724779893754, -2.180866793244492, 4.765753255963401,
1811
-5.726993916772165, 2.918303792060746, -6.506082399183509e-1,
1812
-1.015695507663942e-1, 1.035024326471108, -6.742173543702397e-1,
1813
8.465642650849419e-1, -7.508472135244717e-1, -3.668086444057845e-1,
1814
3.189939162107803e-1, -4.245629194309487e-2)
1815
1816
tl = (oc[0] + oc[1] * y + x * (oc[2] + x * (oc[3] + x * (oc[4] + x *
1817
(oc[5] + oc[6] * x))) + y * (oc[7] + x * (oc[8] + x *
1818
(oc[9] + oc[10] * x)) + y * (oc[11] + oc[12] * x + y * (oc[13] +
1819
oc[14] * x + y * (oc[15] + x * (oc[16] + oc[17] * y))))) + z *
1820
(oc[18] + x * (oc[19] + oc[20] * y + oc[21] * x) + y * (oc[22] + y *
1821
(oc[23] + y * (oc[24] + oc[25] * y))) + z * (oc[26] + oc[27] * x + y *
1822
(oc[28] + oc[29] * y) + z * (oc[30] + oc[31] * x + y * (oc[32] +
1823
oc[33] * y) + oc[34] * z)))))
1824
1825
return tl * part
1826
1827
1828
@match_args_return
1829
def dynamic_enthalpy_t_exact(SA, t, p):
1830
r"""Calculates the dynamic enthalpy of seawater from Absolute Salinity, in
1831
situ temperature and pressure. Dynamic enthalpy was defined by Young
1832
(2010) as the difference between enthalpy and potential enthalpy. Note that
1833
this function uses the full TEOS-10 Gibbs function (i.e. the sum of the
1834
IAPWS-09 and IAPWS-08 Gibbs functions, see the TEOS-10 Manual, IOC et al.
1835
(2010)).
1836
1837
Parameters
1838
----------
1839
SA : array_like
1840
Absolute salinity [g kg :sup:`-1`]
1841
t : array_like
1842
in situ temperature [:math:`^\circ` C (ITS-90)]
1843
p : array_like
1844
pressure [dbar]
1845
1846
Returns
1847
-------
1848
dynamic_enthalpy_t_exact : array_like
1849
dynamic enthalpy [J :sup:`-1`]
1850
1851
1852
See Also
1853
--------
1854
TODO
1855
1856
Notes
1857
-----
1858
TODO
1859
1860
Examples
1861
--------
1862
1863
References
1864
----------
1865
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
1866
of seawater - 2010: Calculation and use of thermodynamic properties.
1867
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
1868
UNESCO (English), 196 pp.
1869
1870
.. [2] Young, W.R., 2010: Dynamic enthalpy, Conservative Temperature, and
1871
the seawater. Boussinesq approximation. Journal of Physical Oceanography,
1872
40, 394-400.
1873
1874
Modifications:
1875
2011-04-11. Trevor McDougall and Paul Barker
1876
"""
1877
1878
CT = CT_from_t(SA, t, p)
1879
1880
return enthalpy_t_exact(SA, t, p) - cp0 * CT
1881
1882
1883
@match_args_return
1884
def t_maxdensity_exact(SA, p):
1885
r"""Calculates the in-situ temperature of maximum density of seawater.
1886
This function returns the in-situ temperature at which the density of
1887
seawater is a maximum, at given Absolute Salinity, SA, and sea pressure, p
1888
(in dbar).
1889
1890
Parameters
1891
----------
1892
SA : array_like
1893
Absolute salinity [g kg :sup:`-1`]
1894
p : array_like
1895
pressure [dbar]
1896
1897
Returns
1898
-------
1899
t_maxdensity_exact : array_like
1900
max in-situ temperature [:math:`^\circ` C]
1901
1902
1903
See Also
1904
--------
1905
TODO
1906
1907
Notes
1908
-----
1909
TODO
1910
1911
Examples
1912
--------
1913
1914
References
1915
----------
1916
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
1917
of seawater - 2010: Calculation and use of thermodynamic properties.
1918
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
1919
UNESCO (English), 196 pp. See section 3.42.
1920
1921
Modifications:
1922
2011-04-03. Trevor McDougall and Paul Barker
1923
"""
1924
1925
# The temperature increment for calculating the gibbs_PTT derivative.
1926
dt = 0.001
1927
t = 3.978 - 0.22072 * SA # The initial guess of t_maxden.
1928
gibbs_PTT = 1.1e-8 # The initial guess for g_PTT.
1929
1930
for Number_of_iterations in range(0, 3):
1931
t_old = t
1932
gibbs_PT = gibbs(n0, n1, n1, SA, t_old, p)
1933
# Half way through the mod. method (McDougall and Wotherspoon, 2012)
1934
t = t_old - gibbs_PT / gibbs_PTT
1935
t_mean = 0.5 * (t + t_old)
1936
gibbs_PTT = (gibbs(n0, n1, n1, SA, t_mean + dt, p) -
1937
gibbs(n0, n1, n1, SA, t_mean - dt, p)) / (dt + dt)
1938
t = t_old - gibbs_PT / gibbs_PTT
1939
1940
# After three iterations of this modified Newton-Raphson iteration, the
1941
# error in t_maxdensity_exact is typically no larger than 1x10^-15 deg C.
1942
1943
return t
1944
1945
1946
@match_args_return
1947
def osmotic_pressure_t_exact(SA, t, pw):
1948
r"""Calculates the osmotic pressure of seawater.
1949
1950
Parameters
1951
----------
1952
SA : array_like
1953
Absolute salinity [g kg :sup:`-1`]
1954
t : array_like
1955
in situ temperature [:math:`^\circ` C (ITS-90)]
1956
pw : array_like
1957
sea pressure of the pure water side [dbar]
1958
1959
Returns
1960
-------
1961
osmotic_pressure_t_exact : array_like
1962
dynamic osmotic pressure of seawater [dbar]
1963
1964
1965
See Also
1966
--------
1967
TODO
1968
1969
Notes
1970
-----
1971
TODO
1972
1973
Examples
1974
--------
1975
1976
References
1977
----------
1978
.. [1] IOC, SCOR and IAPSO, 2010: The international thermodynamic equation
1979
of seawater - 2010: Calculation and use of thermodynamic properties.
1980
Intergovernmental Oceanographic Commission, Manuals and Guides No. 56,
1981
UNESCO (English), 196 pp. See section 3.41.
1982
1983
Modifications:
1984
2011-05-26. Trevor McDougall and Paul Barker
1985
"""
1986
SA = np.maximum(SA, 0)
1987
gibbs_pure_water = gibbs(0, 0, 0, 0, t, pw)
1988
1989
# Initial guess of p, in dbar.
1990
p = pw + 235.4684
1991
1992
# Initial guess of df/dp.
1993
df_dp = -db2Pascal * (gibbs(n0, n0, n1, SA, t, p) -
1994
SA * gibbs(n1, n0, n1, SA, t, p))
1995
1996
for Number_of_iterations in range(0, 2):
1997
p_old = p
1998
f = gibbs_pure_water - chem_potential_water_t_exact(SA, t, p_old)
1999
# This is half way through the modified N-R method.
2000
p = p_old - f / df_dp
2001
p_mean = 0.5 * (p + p_old)
2002
df_dp = -db2Pascal * (gibbs(0, 0, 1, SA, t, p_mean) -
2003
SA * gibbs(1, 0, 1, SA, t, p_mean))
2004
p = p_old - f / df_dp
2005
2006
# After two iterations though the modified Newton-Raphson technique the
2007
# maximum error is 6x10^-12 dbar.
2008
2009
# Osmotic pressure of seawater in dbar.
2010
return p - pw
2011
2012
2013
if __name__ == '__main__':
2014
import doctest
2015
doctest.testmod()
Loggerhead is a web-based interface for Breezy
Version: 2.0.1