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eosbn2.F90 in NEMO/trunk/tests/ISOMIP+/MY_SRC – NEMO

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source: NEMO/trunk/tests/ISOMIP+/MY_SRC/eosbn2.F90 @ 14010

Last change on this file since 14010 was 14010, checked in by gsamson, 3 years ago
merge dev_r2052_ENHANCE-09_rbourdal_massfluxconvection into trunk
File size: 85.8 KB

Line
1	MODULE eosbn2
2	!!==============================================================================
3	!! * MODULE eosbn2 *
4	!! Equation Of Seawater : in situ density - Brunt-Vaisala frequency
5	!!==============================================================================
6	!! History : OPA ! 1989-03 (O. Marti) Original code
7	!! 6.0 ! 1994-07 (G. Madec, M. Imbard) add bn2
8	!! 6.0 ! 1994-08 (G. Madec) Add Jackett & McDougall eos
9	!! 7.0 ! 1996-01 (G. Madec) statement function for e3
10	!! 8.1 ! 1997-07 (G. Madec) density instead of volumic mass
11	!! - ! 1999-02 (G. Madec, N. Grima) semi-implicit pressure gradient
12	!! 8.2 ! 2001-09 (M. Ben Jelloul) bugfix on linear eos
13	!! NEMO 1.0 ! 2002-10 (G. Madec) add eos_init
14	!! - ! 2002-11 (G. Madec, A. Bozec) partial step, eos_insitu_2d
15	!! - ! 2003-08 (G. Madec) F90, free form
16	!! 3.0 ! 2006-08 (G. Madec) add tfreez function (now eos_fzp function)
17	!! 3.3 ! 2010-05 (C. Ethe, G. Madec) merge TRC-TRA
18	!! - ! 2010-10 (G. Nurser, G. Madec) add alpha/beta used in ldfslp
19	!! 3.7 ! 2012-03 (F. Roquet, G. Madec) add primitive of alpha and beta used in PE computation
20	!! - ! 2012-05 (F. Roquet) add Vallis and original JM95 equation of state
21	!! - ! 2013-04 (F. Roquet, G. Madec) add eos_rab, change bn2 computation and reorganize the module
22	!! - ! 2014-09 (F. Roquet) add TEOS-10, S-EOS, and modify EOS-80
23	!! - ! 2015-06 (P.A. Bouttier) eos_fzp functions changed to subroutines for AGRIF
24	!!----------------------------------------------------------------------
25
26	!!----------------------------------------------------------------------
27	!! eos : generic interface of the equation of state
28	!! eos_insitu : Compute the in situ density
29	!! eos_insitu_pot: Compute the insitu and surface referenced potential volumic mass
30	!! eos_insitu_2d : Compute the in situ density for 2d fields
31	!! bn2 : compute the Brunt-Vaisala frequency
32	!! eos_pt_from_ct: compute the potential temperature from the Conservative Temperature
33	!! eos_rab : generic interface of in situ thermal/haline expansion ratio
34	!! eos_rab_3d : compute in situ thermal/haline expansion ratio
35	!! eos_rab_2d : compute in situ thermal/haline expansion ratio for 2d fields
36	!! eos_fzp_2d : freezing temperature for 2d fields
37	!! eos_fzp_0d : freezing temperature for scalar
38	!! eos_init : set eos parameters (namelist)
39	!!----------------------------------------------------------------------
40	USE dom_oce ! ocean space and time domain
41	USE domutl, ONLY : is_tile
42	USE phycst ! physical constants
43	USE stopar ! Stochastic T/S fluctuations
44	USE stopts ! Stochastic T/S fluctuations
45	!
46	USE in_out_manager ! I/O manager
47	USE lib_mpp ! MPP library
48	USE lib_fortran ! Fortran utilities (allows no signed zero when 'key_nosignedzero' defined)
49	USE prtctl ! Print control
50	USE lbclnk ! ocean lateral boundary conditions
51	USE timing ! Timing
52
53	IMPLICIT NONE
54	PRIVATE
55
56	! !! * Interface
57	INTERFACE eos
58	MODULE PROCEDURE eos_insitu, eos_insitu_pot, eos_insitu_2d, eos_insitu_pot_2d
59	END INTERFACE
60	!
61	INTERFACE eos_rab
62	MODULE PROCEDURE rab_3d, rab_2d, rab_0d
63	END INTERFACE
64	!
65	INTERFACE eos_fzp
66	MODULE PROCEDURE eos_fzp_2d, eos_fzp_0d
67	END INTERFACE
68	!
69	PUBLIC eos ! called by step, istate, tranpc and zpsgrd modules
70	PUBLIC bn2 ! called by step module
71	PUBLIC eos_rab ! called by ldfslp, zdfddm, trabbl
72	PUBLIC eos_pt_from_ct ! called by sbcssm
73	PUBLIC eos_fzp ! called by traadv_cen2 and sbcice_... modules
74	PUBLIC eos_pen ! used for pe diagnostics in trdpen module
75	PUBLIC eos_init ! called by istate module
76
77	! !! Namelist nameos
78	LOGICAL , PUBLIC :: ln_TEOS10
79	LOGICAL , PUBLIC :: ln_EOS80
80	LOGICAL , PUBLIC :: ln_SEOS
81	LOGICAL , PUBLIC :: ln_LEOS ! determine if linear eos is used
82
83	! Parameters
84	LOGICAL , PUBLIC :: l_useCT ! =T in ln_TEOS10=T (i.e. use eos_pt_from_ct to compute sst_m), =F otherwise
85	INTEGER , PUBLIC :: neos ! Identifier for equation of state used
86
87	INTEGER , PARAMETER :: np_teos10 = -1 ! parameter for using TEOS10
88	INTEGER , PARAMETER :: np_eos80 = 0 ! parameter for using EOS80
89	INTEGER , PARAMETER :: np_seos = 1 ! parameter for using Simplified Equation of state
90	INTEGER , PARAMETER :: np_leos = 2 ! parameter for using linear equation of state (ISOMIP+)
91
92	! !!! simplified eos coefficients (default value: Vallis 2006)
93	REAL(wp) :: rn_a0 = 1.6550e-1_wp ! thermal expansion coeff.
94	REAL(wp) :: rn_b0 = 7.6554e-1_wp ! saline expansion coeff.
95	REAL(wp) :: rn_lambda1 = 5.9520e-2_wp ! cabbeling coeff. in T^2
96	REAL(wp) :: rn_lambda2 = 5.4914e-4_wp ! cabbeling coeff. in S^2
97	REAL(wp) :: rn_mu1 = 1.4970e-4_wp ! thermobaric coeff. in T
98	REAL(wp) :: rn_mu2 = 1.1090e-5_wp ! thermobaric coeff. in S
99	REAL(wp) :: rn_nu = 2.4341e-3_wp ! cabbeling coeff. in theta*salt
100
101	! TEOS10/EOS80 parameters
102	REAL(wp) :: r1_S0, r1_T0, r1_Z0, rdeltaS
103
104	! EOS parameters
105	REAL(wp) :: EOS000 , EOS100 , EOS200 , EOS300 , EOS400 , EOS500 , EOS600
106	REAL(wp) :: EOS010 , EOS110 , EOS210 , EOS310 , EOS410 , EOS510
107	REAL(wp) :: EOS020 , EOS120 , EOS220 , EOS320 , EOS420
108	REAL(wp) :: EOS030 , EOS130 , EOS230 , EOS330
109	REAL(wp) :: EOS040 , EOS140 , EOS240
110	REAL(wp) :: EOS050 , EOS150
111	REAL(wp) :: EOS060
112	REAL(wp) :: EOS001 , EOS101 , EOS201 , EOS301 , EOS401
113	REAL(wp) :: EOS011 , EOS111 , EOS211 , EOS311
114	REAL(wp) :: EOS021 , EOS121 , EOS221
115	REAL(wp) :: EOS031 , EOS131
116	REAL(wp) :: EOS041
117	REAL(wp) :: EOS002 , EOS102 , EOS202
118	REAL(wp) :: EOS012 , EOS112
119	REAL(wp) :: EOS022
120	REAL(wp) :: EOS003 , EOS103
121	REAL(wp) :: EOS013
122
123	! ALPHA parameters
124	REAL(wp) :: ALP000 , ALP100 , ALP200 , ALP300 , ALP400 , ALP500
125	REAL(wp) :: ALP010 , ALP110 , ALP210 , ALP310 , ALP410
126	REAL(wp) :: ALP020 , ALP120 , ALP220 , ALP320
127	REAL(wp) :: ALP030 , ALP130 , ALP230
128	REAL(wp) :: ALP040 , ALP140
129	REAL(wp) :: ALP050
130	REAL(wp) :: ALP001 , ALP101 , ALP201 , ALP301
131	REAL(wp) :: ALP011 , ALP111 , ALP211
132	REAL(wp) :: ALP021 , ALP121
133	REAL(wp) :: ALP031
134	REAL(wp) :: ALP002 , ALP102
135	REAL(wp) :: ALP012
136	REAL(wp) :: ALP003
137
138	! BETA parameters
139	REAL(wp) :: BET000 , BET100 , BET200 , BET300 , BET400 , BET500
140	REAL(wp) :: BET010 , BET110 , BET210 , BET310 , BET410
141	REAL(wp) :: BET020 , BET120 , BET220 , BET320
142	REAL(wp) :: BET030 , BET130 , BET230
143	REAL(wp) :: BET040 , BET140
144	REAL(wp) :: BET050
145	REAL(wp) :: BET001 , BET101 , BET201 , BET301
146	REAL(wp) :: BET011 , BET111 , BET211
147	REAL(wp) :: BET021 , BET121
148	REAL(wp) :: BET031
149	REAL(wp) :: BET002 , BET102
150	REAL(wp) :: BET012
151	REAL(wp) :: BET003
152
153	! PEN parameters
154	REAL(wp) :: PEN000 , PEN100 , PEN200 , PEN300 , PEN400
155	REAL(wp) :: PEN010 , PEN110 , PEN210 , PEN310
156	REAL(wp) :: PEN020 , PEN120 , PEN220
157	REAL(wp) :: PEN030 , PEN130
158	REAL(wp) :: PEN040
159	REAL(wp) :: PEN001 , PEN101 , PEN201
160	REAL(wp) :: PEN011 , PEN111
161	REAL(wp) :: PEN021
162	REAL(wp) :: PEN002 , PEN102
163	REAL(wp) :: PEN012
164
165	! ALPHA_PEN parameters
166	REAL(wp) :: APE000 , APE100 , APE200 , APE300
167	REAL(wp) :: APE010 , APE110 , APE210
168	REAL(wp) :: APE020 , APE120
169	REAL(wp) :: APE030
170	REAL(wp) :: APE001 , APE101
171	REAL(wp) :: APE011
172	REAL(wp) :: APE002
173
174	! BETA_PEN parameters
175	REAL(wp) :: BPE000 , BPE100 , BPE200 , BPE300
176	REAL(wp) :: BPE010 , BPE110 , BPE210
177	REAL(wp) :: BPE020 , BPE120
178	REAL(wp) :: BPE030
179	REAL(wp) :: BPE001 , BPE101
180	REAL(wp) :: BPE011
181	REAL(wp) :: BPE002
182
183	!! * Substitutions
184	# include "do_loop_substitute.h90"
185	# include "domzgr_substitute.h90"
186	!!----------------------------------------------------------------------
187	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
188	!! $Id: eosbn2.F90 10425 2018-12-19 21:54:16Z smasson $
189	!! Software governed by the CeCILL license (see ./LICENSE)
190	!!----------------------------------------------------------------------
191	CONTAINS
192
193	SUBROUTINE eos_insitu( pts, prd, pdep )
194	!!
195	REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
196	! ! 2 : salinity [psu]
197	REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: prd ! in situ density [-]
198	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pdep ! depth [m]
199	!!
200	CALL eos_insitu_t( pts, is_tile(pts), prd, is_tile(prd), pdep, is_tile(pdep) )
201	END SUBROUTINE eos_insitu
202
203	SUBROUTINE eos_insitu_t( pts, ktts, prd, ktrd, pdep, ktdep )
204	!!----------------------------------------------------------------------
205	!! * ROUTINE eos_insitu *
206	!!
207	!! ** Purpose : Compute the in situ density (ratio rho/rho0) from
208	!! potential temperature and salinity using an equation of state
209	!! selected in the nameos namelist
210	!!
211	!! ** Method : prd(t,s,z) = ( rho(t,s,z) - rho0 ) / rho0
212	!! with prd in situ density anomaly no units
213	!! t TEOS10: CT or EOS80: PT Celsius
214	!! s TEOS10: SA or EOS80: SP TEOS10: g/kg or EOS80: psu
215	!! z depth meters
216	!! rho in situ density kg/m^3
217	!! rho0 reference density kg/m^3
218	!!
219	!! ln_teos10 : polynomial TEOS-10 equation of state is used for rho(t,s,z).
220	!! Check value: rho = 1028.21993233072 kg/m^3 for z=3000 dbar, ct=3 Celsius, sa=35.5 g/kg
221	!!
222	!! ln_eos80 : polynomial EOS-80 equation of state is used for rho(t,s,z).
223	!! Check value: rho = 1028.35011066567 kg/m^3 for z=3000 dbar, pt=3 Celsius, sp=35.5 psu
224	!!
225	!! ln_seos : simplified equation of state
226	!! prd(t,s,z) = ( -a0(1+lambda/2(T-T0)+muz+nu(S-S0))(T-T0) + b0(S-S0) ) / rho0
227	!! linear case function of T only: rn_alpha<>0, other coefficients = 0
228	!! linear eos function of T and S: rn_alpha and rn_beta<>0, other coefficients=0
229	!! Vallis like equation: use default values of coefficients
230	!!
231	!! ln_leos : linear ISOMIP equation of state
232	!! prd(t,s,z) = ( -a0(T-T0) + b0(S-S0) ) / rho0
233	!! setup for ISOMIP linear eos
234	!!
235	!! ** Action : compute prd , the in situ density (no units)
236	!!
237	!! References : Roquet et al, Ocean Modelling, in preparation (2014)
238	!! Vallis, Atmospheric and Oceanic Fluid Dynamics, 2006
239	!! TEOS-10 Manual, 2010
240	!!----------------------------------------------------------------------
241	INTEGER , INTENT(in ) :: ktts, ktrd, ktdep
242	REAL(wp), DIMENSION(A2D_T(ktts) ,JPK,JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
243	! ! 2 : salinity [psu]
244	REAL(wp), DIMENSION(A2D_T(ktrd) ,JPK ), INTENT( out) :: prd ! in situ density [-]
245	REAL(wp), DIMENSION(A2D_T(ktdep),JPK ), INTENT(in ) :: pdep ! depth [m]
246	!
247	INTEGER :: ji, jj, jk ! dummy loop indices
248	REAL(wp) :: zt , zh , zs , ztm ! local scalars
249	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
250	!!----------------------------------------------------------------------
251	!
252	IF( ln_timing ) CALL timing_start('eos-insitu')
253	!
254	SELECT CASE( neos )
255	!
256	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
257	!
258	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
259	!
260	zh = pdep(ji,jj,jk) * r1_Z0 ! depth
261	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
262	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
263	ztm = tmask(ji,jj,jk) ! tmask
264	!
265	zn3 = EOS013*zt &
266	& + EOS103*zs+EOS003
267	!
268	zn2 = (EOS022*zt &
269	& + EOS112zs+EOS012)zt &
270	& + (EOS202zs+EOS102)zs+EOS002
271	!
272	zn1 = (((EOS041*zt &
273	& + EOS131zs+EOS031)zt &
274	& + (EOS221zs+EOS121)zs+EOS021)*zt &
275	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
276	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
277	!
278	zn0 = (((((EOS060*zt &
279	& + EOS150zs+EOS050)zt &
280	& + (EOS240zs+EOS140)zs+EOS040)*zt &
281	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
282	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
283	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
284	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
285	!
286	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
287	!
288	prd(ji,jj,jk) = ( zn * r1_rho0 - 1._wp ) * ztm ! density anomaly (masked)
289	!
290	END_3D
291	!
292	CASE( np_seos ) !== simplified EOS ==!
293	!
294	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
295	zt = pts (ji,jj,jk,jp_tem) - 10._wp
296	zs = pts (ji,jj,jk,jp_sal) - 35._wp
297	zh = pdep (ji,jj,jk)
298	ztm = tmask(ji,jj,jk)
299	!
300	zn = - rn_a0 * ( 1._wp + 0.5_wprn_lambda1zt + rn_mu1zh ) zt &
301	& + rn_b0 * ( 1._wp - 0.5_wprn_lambda2zs - rn_mu2zh ) zs &
302	& - rn_nu * zt * zs
303	!
304	prd(ji,jj,jk) = zn * r1_rho0 * ztm ! density anomaly (masked)
305	END_3D
306	!
307	CASE( np_leos ) !== linear ISOMIP EOS ==!
308	!
309	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
310	zt = pts (ji,jj,jk,jp_tem) - (-1._wp)
311	zs = pts (ji,jj,jk,jp_sal) - 34.2_wp
312	zh = pdep (ji,jj,jk)
313	ztm = tmask(ji,jj,jk)
314	!
315	zn = rho0 * ( - rn_a0 * zt + rn_b0 * zs )
316	!
317	prd(ji,jj,jk) = zn * r1_rho0 * ztm ! density anomaly (masked)
318	END_3D
319	!
320	END SELECT
321	!
322	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-insitu : ', kdim=jpk )
323	!
324	IF( ln_timing ) CALL timing_stop('eos-insitu')
325	!
326	END SUBROUTINE eos_insitu_t
327
328
329	SUBROUTINE eos_insitu_pot( pts, prd, prhop, pdep )
330	!!
331	REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
332	! ! 2 : salinity [psu]
333	REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: prd ! in situ density [-]
334	REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: prhop ! potential density (surface referenced)
335	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pdep ! depth [m]
336	!!
337	CALL eos_insitu_pot_t( pts, is_tile(pts), prd, is_tile(prd), prhop, is_tile(prhop), pdep, is_tile(pdep) )
338	END SUBROUTINE eos_insitu_pot
339
340
341	SUBROUTINE eos_insitu_pot_t( pts, ktts, prd, ktrd, prhop, ktrhop, pdep, ktdep )
342	!!----------------------------------------------------------------------
343	!! * ROUTINE eos_insitu_pot *
344	!!
345	!! ** Purpose : Compute the in situ density (ratio rho/rho0) and the
346	!! potential volumic mass (Kg/m3) from potential temperature and
347	!! salinity fields using an equation of state selected in the
348	!! namelist.
349	!!
350	!! ** Action : - prd , the in situ density (no units)
351	!! - prhop, the potential volumic mass (Kg/m3)
352	!!
353	!!----------------------------------------------------------------------
354	INTEGER , INTENT(in ) :: ktts, ktrd, ktrhop, ktdep
355	REAL(wp), DIMENSION(A2D_T(ktts) ,JPK,JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
356	! ! 2 : salinity [psu]
357	REAL(wp), DIMENSION(A2D_T(ktrd) ,JPK ), INTENT( out) :: prd ! in situ density [-]
358	REAL(wp), DIMENSION(A2D_T(ktrhop),JPK ), INTENT( out) :: prhop ! potential density (surface referenced)
359	REAL(wp), DIMENSION(A2D_T(ktdep) ,JPK ), INTENT(in ) :: pdep ! depth [m]
360	!
361	INTEGER :: ji, jj, jk, jsmp ! dummy loop indices
362	INTEGER :: jdof
363	REAL(wp) :: zt , zh , zstemp, zs , ztm ! local scalars
364	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
365	REAL(wp), DIMENSION(:), ALLOCATABLE :: zn0_sto, zn_sto, zsign ! local vectors
366	!!----------------------------------------------------------------------
367	!
368	IF( ln_timing ) CALL timing_start('eos-pot')
369	!
370	SELECT CASE ( neos )
371	!
372	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
373	!
374	! Stochastic equation of state
375	IF ( ln_sto_eos ) THEN
376	ALLOCATE(zn0_sto(1:2*nn_sto_eos))
377	ALLOCATE(zn_sto(1:2*nn_sto_eos))
378	ALLOCATE(zsign(1:2*nn_sto_eos))
379	DO jsmp = 1, 2*nn_sto_eos, 2
380	zsign(jsmp) = 1._wp
381	zsign(jsmp+1) = -1._wp
382	END DO
383	!
384	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
385	!
386	! compute density (2*nn_sto_eos) times:
387	! (1) for t+dt, s+ds (with the random TS fluctutation computed in sto_pts)
388	! (2) for t-dt, s-ds (with the opposite fluctuation)
389	DO jsmp = 1, nn_sto_eos*2
390	jdof = (jsmp + 1) / 2
391	zh = pdep(ji,jj,jk) * r1_Z0 ! depth
392	zt = (pts (ji,jj,jk,jp_tem) + pts_ran(ji,jj,jk,jp_tem,jdof) * zsign(jsmp)) * r1_T0 ! temperature
393	zstemp = pts (ji,jj,jk,jp_sal) + pts_ran(ji,jj,jk,jp_sal,jdof) * zsign(jsmp)
394	zs = SQRT( ABS( zstemp + rdeltaS ) * r1_S0 ) ! square root salinity
395	ztm = tmask(ji,jj,jk) ! tmask
396	!
397	zn3 = EOS013*zt &
398	& + EOS103*zs+EOS003
399	!
400	zn2 = (EOS022*zt &
401	& + EOS112zs+EOS012)zt &
402	& + (EOS202zs+EOS102)zs+EOS002
403	!
404	zn1 = (((EOS041*zt &
405	& + EOS131zs+EOS031)zt &
406	& + (EOS221zs+EOS121)zs+EOS021)*zt &
407	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
408	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
409	!
410	zn0_sto(jsmp) = (((((EOS060*zt &
411	& + EOS150zs+EOS050)zt &
412	& + (EOS240zs+EOS140)zs+EOS040)*zt &
413	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
414	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
415	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
416	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
417	!
418	zn_sto(jsmp) = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0_sto(jsmp)
419	END DO
420	!
421	! compute stochastic density as the mean of the (2*nn_sto_eos) densities
422	prhop(ji,jj,jk) = 0._wp ; prd(ji,jj,jk) = 0._wp
423	DO jsmp = 1, nn_sto_eos*2
424	prhop(ji,jj,jk) = prhop(ji,jj,jk) + zn0_sto(jsmp) ! potential density referenced at the surface
425	!
426	prd(ji,jj,jk) = prd(ji,jj,jk) + ( zn_sto(jsmp) * r1_rho0 - 1._wp ) ! density anomaly (masked)
427	END DO
428	prhop(ji,jj,jk) = 0.5_wp * prhop(ji,jj,jk) * ztm / nn_sto_eos
429	prd (ji,jj,jk) = 0.5_wp * prd (ji,jj,jk) * ztm / nn_sto_eos
430	END_3D
431	DEALLOCATE(zn0_sto,zn_sto,zsign)
432	! Non-stochastic equation of state
433	ELSE
434	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
435	!
436	zh = pdep(ji,jj,jk) * r1_Z0 ! depth
437	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
438	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
439	ztm = tmask(ji,jj,jk) ! tmask
440	!
441	zn3 = EOS013*zt &
442	& + EOS103*zs+EOS003
443	!
444	zn2 = (EOS022*zt &
445	& + EOS112zs+EOS012)zt &
446	& + (EOS202zs+EOS102)zs+EOS002
447	!
448	zn1 = (((EOS041*zt &
449	& + EOS131zs+EOS031)zt &
450	& + (EOS221zs+EOS121)zs+EOS021)*zt &
451	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
452	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
453	!
454	zn0 = (((((EOS060*zt &
455	& + EOS150zs+EOS050)zt &
456	& + (EOS240zs+EOS140)zs+EOS040)*zt &
457	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
458	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
459	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
460	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
461	!
462	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
463	!
464	prhop(ji,jj,jk) = zn0 * ztm ! potential density referenced at the surface
465	!
466	prd(ji,jj,jk) = ( zn * r1_rho0 - 1._wp ) * ztm ! density anomaly (masked)
467	END_3D
468	ENDIF
469
470	CASE( np_seos ) !== simplified EOS ==!
471	!
472	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
473	zt = pts (ji,jj,jk,jp_tem) - 10._wp
474	zs = pts (ji,jj,jk,jp_sal) - 35._wp
475	zh = pdep (ji,jj,jk)
476	ztm = tmask(ji,jj,jk)
477	! ! potential density referenced at the surface
478	zn = - rn_a0 * ( 1._wp + 0.5_wprn_lambda1zt ) * zt &
479	& + rn_b0 * ( 1._wp - 0.5_wprn_lambda2zs ) * zs &
480	& - rn_nu * zt * zs
481	prhop(ji,jj,jk) = ( rho0 + zn ) * ztm
482	! ! density anomaly (masked)
483	zn = zn - ( rn_a0 * rn_mu1 * zt + rn_b0 * rn_mu2 * zs ) * zh
484	prd(ji,jj,jk) = zn * r1_rho0 * ztm
485	!
486	END_3D
487	!
488	CASE( np_leos ) !== linear ISOMIP EOS ==!
489	!
490	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
491	zt = pts (ji,jj,jk,jp_tem) - (-1._wp)
492	zs = pts (ji,jj,jk,jp_sal) - 34.2_wp
493	zh = pdep (ji,jj,jk)
494	ztm = tmask(ji,jj,jk)
495	! ! potential density referenced at the surface
496	zn = rho0 * ( - rn_a0 * zt + rn_b0 * zs )
497	prhop(ji,jj,jk) = ( rho0 + zn ) * ztm
498	! ! density anomaly (masked)
499	prd(ji,jj,jk) = zn * r1_rho0 * ztm
500	!
501	END_3D
502	!
503	END SELECT
504	!
505	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-pot: ', tab3d_2=prhop, clinfo2=' pot : ', kdim=jpk )
506	!
507	IF( ln_timing ) CALL timing_stop('eos-pot')
508	!
509	END SUBROUTINE eos_insitu_pot_t
510
511
512	SUBROUTINE eos_insitu_2d( pts, pdep, prd )
513	!!
514	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
515	! ! 2 : salinity [psu]
516	REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pdep ! depth [m]
517	REAL(wp), DIMENSION(:,:) , INTENT( out) :: prd ! in situ density
518	!!
519	CALL eos_insitu_2d_t( pts, is_tile(pts), pdep, is_tile(pdep), prd, is_tile(prd) )
520	END SUBROUTINE eos_insitu_2d
521
522
523	SUBROUTINE eos_insitu_2d_t( pts, ktts, pdep, ktdep, prd, ktrd )
524	!!----------------------------------------------------------------------
525	!! * ROUTINE eos_insitu_2d *
526	!!
527	!! ** Purpose : Compute the in situ density (ratio rho/rho0) from
528	!! potential temperature and salinity using an equation of state
529	!! selected in the nameos namelist. * 2D field case
530	!!
531	!! ** Action : - prd , the in situ density (no units) (unmasked)
532	!!
533	!!----------------------------------------------------------------------
534	INTEGER , INTENT(in ) :: ktts, ktdep, ktrd
535	REAL(wp), DIMENSION(A2D_T(ktts),JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
536	! ! 2 : salinity [psu]
537	REAL(wp), DIMENSION(A2D_T(ktdep) ), INTENT(in ) :: pdep ! depth [m]
538	REAL(wp), DIMENSION(A2D_T(ktrd) ), INTENT( out) :: prd ! in situ density
539	!
540	INTEGER :: ji, jj, jk ! dummy loop indices
541	REAL(wp) :: zt , zh , zs ! local scalars
542	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
543	!!----------------------------------------------------------------------
544	!
545	IF( ln_timing ) CALL timing_start('eos2d')
546	!
547	prd(:,:) = 0._wp
548	!
549	SELECT CASE( neos )
550	!
551	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
552	!
553	DO_2D( 1, 1, 1, 1 )
554	!
555	zh = pdep(ji,jj) * r1_Z0 ! depth
556	zt = pts (ji,jj,jp_tem) * r1_T0 ! temperature
557	zs = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
558	!
559	zn3 = EOS013*zt &
560	& + EOS103*zs+EOS003
561	!
562	zn2 = (EOS022*zt &
563	& + EOS112zs+EOS012)zt &
564	& + (EOS202zs+EOS102)zs+EOS002
565	!
566	zn1 = (((EOS041*zt &
567	& + EOS131zs+EOS031)zt &
568	& + (EOS221zs+EOS121)zs+EOS021)*zt &
569	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
570	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
571	!
572	zn0 = (((((EOS060*zt &
573	& + EOS150zs+EOS050)zt &
574	& + (EOS240zs+EOS140)zs+EOS040)*zt &
575	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
576	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
577	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
578	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
579	!
580	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
581	!
582	prd(ji,jj) = zn * r1_rho0 - 1._wp ! unmasked in situ density anomaly
583	!
584	END_2D
585	!
586	CASE( np_seos ) !== simplified EOS ==!
587	!
588	DO_2D( 1, 1, 1, 1 )
589	!
590	zt = pts (ji,jj,jp_tem) - 10._wp
591	zs = pts (ji,jj,jp_sal) - 35._wp
592	zh = pdep (ji,jj) ! depth at the partial step level
593	!
594	zn = - rn_a0 * ( 1._wp + 0.5_wprn_lambda1zt + rn_mu1zh ) zt &
595	& + rn_b0 * ( 1._wp - 0.5_wprn_lambda2zs - rn_mu2zh ) zs &
596	& - rn_nu * zt * zs
597	!
598	prd(ji,jj) = zn * r1_rho0 ! unmasked in situ density anomaly
599	!
600	END_2D
601	!
602	CASE( np_leos ) !== ISOMIP EOS ==!
603	!
604	DO_2D( 1, 1, 1, 1 )
605	!
606	zt = pts (ji,jj,jp_tem) - (-1._wp)
607	zs = pts (ji,jj,jp_sal) - 34.2_wp
608	zh = pdep (ji,jj) ! depth at the partial step level
609	!
610	zn = rho0 * ( - rn_a0 * zt + rn_b0 * zs )
611	!
612	prd(ji,jj) = zn * r1_rho0 ! unmasked in situ density anomaly
613	!
614	END_2D
615	!
616	!
617	END SELECT
618	!
619	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=prd, clinfo1=' eos2d: ' )
620	!
621	IF( ln_timing ) CALL timing_stop('eos2d')
622	!
623	END SUBROUTINE eos_insitu_2d_t
624
625
626	SUBROUTINE eos_insitu_pot_2d( pts, prhop )
627	!!----------------------------------------------------------------------
628	!! * ROUTINE eos_insitu_pot *
629	!!
630	!! ** Purpose : Compute the in situ density (ratio rho/rho0) and the
631	!! potential volumic mass (Kg/m3) from potential temperature and
632	!! salinity fields using an equation of state selected in the
633	!! namelist.
634	!!
635	!! ** Action :
636	!! - prhop, the potential volumic mass (Kg/m3)
637	!!
638	!!----------------------------------------------------------------------
639	REAL(wp), DIMENSION(jpi,jpj,jpts), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
640	! ! 2 : salinity [psu]
641	REAL(wp), DIMENSION(jpi,jpj ), INTENT( out) :: prhop ! potential density (surface referenced)
642	!
643	INTEGER :: ji, jj, jk, jsmp ! dummy loop indices
644	INTEGER :: jdof
645	REAL(wp) :: zt , zh , zstemp, zs , ztm ! local scalars
646	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
647	REAL(wp), DIMENSION(:), ALLOCATABLE :: zn0_sto, zn_sto, zsign ! local vectors
648	!!----------------------------------------------------------------------
649	!
650	IF( ln_timing ) CALL timing_start('eos-pot')
651	!
652	SELECT CASE ( neos )
653	!
654	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
655	!
656	DO_2D( 1, 1, 1, 1 )
657	!
658	zt = pts (ji,jj,jp_tem) * r1_T0 ! temperature
659	zs = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
660	ztm = tmask(ji,jj,1) ! tmask
661	!
662	zn0 = (((((EOS060*zt &
663	& + EOS150zs+EOS050)zt &
664	& + (EOS240zs+EOS140)zs+EOS040)*zt &
665	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
666	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
667	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
668	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
669	!
670	!
671	prhop(ji,jj) = zn0 * ztm ! potential density referenced at the surface
672	!
673	END_2D
674
675	CASE( np_seos ) !== simplified EOS ==!
676	!
677	DO_2D( 1, 1, 1, 1 )
678	zt = pts (ji,jj,jp_tem) - 10._wp
679	zs = pts (ji,jj,jp_sal) - 35._wp
680	ztm = tmask(ji,jj,1)
681	! ! potential density referenced at the surface
682	zn = - rn_a0 * ( 1._wp + 0.5_wprn_lambda1zt ) * zt &
683	& + rn_b0 * ( 1._wp - 0.5_wprn_lambda2zs ) * zs &
684	& - rn_nu * zt * zs
685	prhop(ji,jj) = ( rho0 + zn ) * ztm
686	!
687	END_2D
688	!
689	CASE( np_leos ) !== ISOMIP EOS ==!
690	!
691	DO_2D( 1, 1, 1, 1 )
692	!
693	zt = pts (ji,jj,jp_tem) - (-1._wp)
694	zs = pts (ji,jj,jp_sal) - 34.2_wp
695	!zh = pdep (ji,jj) ! depth at the partial step level
696	!
697	zn = rho0 * ( - rn_a0 * zt + rn_b0 * zs )
698	!
699	prhop(ji,jj) = zn * r1_rho0 ! unmasked in situ density anomaly
700	!
701	END_2D
702	!
703	END SELECT
704	!
705	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=prhop, clinfo1=' eos-pot: ' )
706	!
707	IF( ln_timing ) CALL timing_stop('eos-pot')
708	!
709	END SUBROUTINE eos_insitu_pot_2d
710
711
712	SUBROUTINE rab_3d( pts, pab, Kmm )
713	!!
714	INTEGER , INTENT(in ) :: Kmm ! time level index
715	REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! pot. temperature & salinity
716	REAL(wp), DIMENSION(:,:,:,:), INTENT( out) :: pab ! thermal/haline expansion ratio
717	!!
718	CALL rab_3d_t( pts, is_tile(pts), pab, is_tile(pab), Kmm )
719	END SUBROUTINE rab_3d
720
721
722	SUBROUTINE rab_3d_t( pts, ktts, pab, ktab, Kmm )
723	!!----------------------------------------------------------------------
724	!! * ROUTINE rab_3d *
725	!!
726	!! ** Purpose : Calculates thermal/haline expansion ratio at T-points
727	!!
728	!! ** Method : calculates alpha / beta at T-points
729	!!
730	!! ** Action : - pab : thermal/haline expansion ratio at T-points
731	!!----------------------------------------------------------------------
732	INTEGER , INTENT(in ) :: Kmm ! time level index
733	INTEGER , INTENT(in ) :: ktts, ktab
734	REAL(wp), DIMENSION(A2D_T(ktts),JPK,JPTS), INTENT(in ) :: pts ! pot. temperature & salinity
735	REAL(wp), DIMENSION(A2D_T(ktab),JPK,JPTS), INTENT( out) :: pab ! thermal/haline expansion ratio
736	!
737	INTEGER :: ji, jj, jk ! dummy loop indices
738	REAL(wp) :: zt , zh , zs , ztm ! local scalars
739	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
740	!!----------------------------------------------------------------------
741	!
742	IF( ln_timing ) CALL timing_start('rab_3d')
743	!
744	SELECT CASE ( neos )
745	!
746	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
747	!
748	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
749	!
750	zh = gdept(ji,jj,jk,Kmm) * r1_Z0 ! depth
751	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
752	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
753	ztm = tmask(ji,jj,jk) ! tmask
754	!
755	! alpha
756	zn3 = ALP003
757	!
758	zn2 = ALP012zt + ALP102zs+ALP002
759	!
760	zn1 = ((ALP031*zt &
761	& + ALP121zs+ALP021)zt &
762	& + (ALP211zs+ALP111)zs+ALP011)*zt &
763	& + ((ALP301zs+ALP201)zs+ALP101)*zs+ALP001
764	!
765	zn0 = ((((ALP050*zt &
766	& + ALP140zs+ALP040)zt &
767	& + (ALP230zs+ALP130)zs+ALP030)*zt &
768	& + ((ALP320zs+ALP220)zs+ALP120)zs+ALP020)zt &
769	& + (((ALP410zs+ALP310)zs+ALP210)zs+ALP110)zs+ALP010)*zt &
770	& + ((((ALP500zs+ALP400)zs+ALP300)zs+ALP200)zs+ALP100)*zs+ALP000
771	!
772	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
773	!
774	pab(ji,jj,jk,jp_tem) = zn * r1_rho0 * ztm
775	!
776	! beta
777	zn3 = BET003
778	!
779	zn2 = BET012zt + BET102zs+BET002
780	!
781	zn1 = ((BET031*zt &
782	& + BET121zs+BET021)zt &
783	& + (BET211zs+BET111)zs+BET011)*zt &
784	& + ((BET301zs+BET201)zs+BET101)*zs+BET001
785	!
786	zn0 = ((((BET050*zt &
787	& + BET140zs+BET040)zt &
788	& + (BET230zs+BET130)zs+BET030)*zt &
789	& + ((BET320zs+BET220)zs+BET120)zs+BET020)zt &
790	& + (((BET410zs+BET310)zs+BET210)zs+BET110)zs+BET010)*zt &
791	& + ((((BET500zs+BET400)zs+BET300)zs+BET200)zs+BET100)*zs+BET000
792	!
793	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
794	!
795	pab(ji,jj,jk,jp_sal) = zn / zs * r1_rho0 * ztm
796	!
797	END_3D
798	!
799	CASE( np_seos ) !== simplified EOS ==!
800	!
801	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
802	zt = pts (ji,jj,jk,jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
803	zs = pts (ji,jj,jk,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
804	zh = gdept(ji,jj,jk,Kmm) ! depth in meters at t-point
805	ztm = tmask(ji,jj,jk) ! land/sea bottom mask = surf. mask
806	!
807	zn = rn_a0 * ( 1._wp + rn_lambda1zt + rn_mu1zh ) + rn_nu*zs
808	pab(ji,jj,jk,jp_tem) = zn * r1_rho0 * ztm ! alpha
809	!
810	zn = rn_b0 * ( 1._wp - rn_lambda2zs - rn_mu2zh ) - rn_nu*zt
811	pab(ji,jj,jk,jp_sal) = zn * r1_rho0 * ztm ! beta
812	!
813	END_3D
814	!
815	CASE( np_leos ) !== linear ISOMIP EOS ==!
816	!
817	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
818	zt = pts (ji,jj,jk,jp_tem) - (-1._wp)
819	zs = pts (ji,jj,jk,jp_sal) - 34.2_wp ! abs. salinity anomaly (s-S0)
820	zh = gdept(ji,jj,jk,Kmm) ! depth in meters at t-point
821	ztm = tmask(ji,jj,jk) ! land/sea bottom mask = surf. mask
822	!
823	zn = rn_a0 * rho0
824	pab(ji,jj,jk,jp_tem) = zn * r1_rho0 * ztm ! alpha
825	!
826	zn = rn_b0 * rho0
827	pab(ji,jj,jk,jp_sal) = zn * r1_rho0 * ztm ! beta
828	!
829	END_3D
830	!
831	CASE DEFAULT
832	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
833	CALL ctl_stop( 'rab_3d:', ctmp1 )
834	!
835	END SELECT
836	!
837	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=pab(:,:,:,jp_tem), clinfo1=' rab_3d_t: ', &
838	& tab3d_2=pab(:,:,:,jp_sal), clinfo2=' rab_3d_s : ', kdim=jpk )
839	!
840	IF( ln_timing ) CALL timing_stop('rab_3d')
841	!
842	END SUBROUTINE rab_3d_t
843
844
845	SUBROUTINE rab_2d( pts, pdep, pab, Kmm )
846	!!
847	INTEGER , INTENT(in ) :: Kmm ! time level index
848	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pts ! pot. temperature & salinity
849	REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pdep ! depth [m]
850	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: pab ! thermal/haline expansion ratio
851	!!
852	CALL rab_2d_t(pts, is_tile(pts), pdep, is_tile(pdep), pab, is_tile(pab), Kmm)
853	END SUBROUTINE rab_2d
854
855
856	SUBROUTINE rab_2d_t( pts, ktts, pdep, ktdep, pab, ktab, Kmm )
857	!!----------------------------------------------------------------------
858	!! * ROUTINE rab_2d *
859	!!
860	!! ** Purpose : Calculates thermal/haline expansion ratio for a 2d field (unmasked)
861	!!
862	!! ** Action : - pab : thermal/haline expansion ratio at T-points
863	!!----------------------------------------------------------------------
864	INTEGER , INTENT(in ) :: Kmm ! time level index
865	INTEGER , INTENT(in ) :: ktts, ktdep, ktab
866	REAL(wp), DIMENSION(A2D_T(ktts),JPTS), INTENT(in ) :: pts ! pot. temperature & salinity
867	REAL(wp), DIMENSION(A2D_T(ktdep) ), INTENT(in ) :: pdep ! depth [m]
868	REAL(wp), DIMENSION(A2D_T(ktab),JPTS), INTENT( out) :: pab ! thermal/haline expansion ratio
869	!
870	INTEGER :: ji, jj, jk ! dummy loop indices
871	REAL(wp) :: zt , zh , zs ! local scalars
872	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
873	!!----------------------------------------------------------------------
874	!
875	IF( ln_timing ) CALL timing_start('rab_2d')
876	!
877	pab(:,:,:) = 0._wp
878	!
879	SELECT CASE ( neos )
880	!
881	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
882	!
883	DO_2D( 1, 1, 1, 1 )
884	!
885	zh = pdep(ji,jj) * r1_Z0 ! depth
886	zt = pts (ji,jj,jp_tem) * r1_T0 ! temperature
887	zs = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
888	!
889	! alpha
890	zn3 = ALP003
891	!
892	zn2 = ALP012zt + ALP102zs+ALP002
893	!
894	zn1 = ((ALP031*zt &
895	& + ALP121zs+ALP021)zt &
896	& + (ALP211zs+ALP111)zs+ALP011)*zt &
897	& + ((ALP301zs+ALP201)zs+ALP101)*zs+ALP001
898	!
899	zn0 = ((((ALP050*zt &
900	& + ALP140zs+ALP040)zt &
901	& + (ALP230zs+ALP130)zs+ALP030)*zt &
902	& + ((ALP320zs+ALP220)zs+ALP120)zs+ALP020)zt &
903	& + (((ALP410zs+ALP310)zs+ALP210)zs+ALP110)zs+ALP010)*zt &
904	& + ((((ALP500zs+ALP400)zs+ALP300)zs+ALP200)zs+ALP100)*zs+ALP000
905	!
906	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
907	!
908	pab(ji,jj,jp_tem) = zn * r1_rho0
909	!
910	! beta
911	zn3 = BET003
912	!
913	zn2 = BET012zt + BET102zs+BET002
914	!
915	zn1 = ((BET031*zt &
916	& + BET121zs+BET021)zt &
917	& + (BET211zs+BET111)zs+BET011)*zt &
918	& + ((BET301zs+BET201)zs+BET101)*zs+BET001
919	!
920	zn0 = ((((BET050*zt &
921	& + BET140zs+BET040)zt &
922	& + (BET230zs+BET130)zs+BET030)*zt &
923	& + ((BET320zs+BET220)zs+BET120)zs+BET020)zt &
924	& + (((BET410zs+BET310)zs+BET210)zs+BET110)zs+BET010)*zt &
925	& + ((((BET500zs+BET400)zs+BET300)zs+BET200)zs+BET100)*zs+BET000
926	!
927	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
928	!
929	pab(ji,jj,jp_sal) = zn / zs * r1_rho0
930	!
931	!
932	END_2D
933	!
934	CASE( np_seos ) !== simplified EOS ==!
935	!
936	DO_2D( 1, 1, 1, 1 )
937	!
938	zt = pts (ji,jj,jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
939	zs = pts (ji,jj,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
940	zh = pdep (ji,jj) ! depth at the partial step level
941	!
942	zn = rn_a0 * ( 1._wp + rn_lambda1zt + rn_mu1zh ) + rn_nu*zs
943	pab(ji,jj,jp_tem) = zn * r1_rho0 ! alpha
944	!
945	zn = rn_b0 * ( 1._wp - rn_lambda2zs - rn_mu2zh ) - rn_nu*zt
946	pab(ji,jj,jp_sal) = zn * r1_rho0 ! beta
947	!
948	END_2D
949	!
950	CASE( np_leos ) !== linear ISOMIP EOS ==!
951	!
952	DO_2D( 1, 1, 1, 1 )
953	!
954	zt = pts (ji,jj,jp_tem) - (-1._wp) ! pot. temperature anomaly (t-T0)
955	zs = pts (ji,jj,jp_sal) - 34.2_wp ! abs. salinity anomaly (s-S0)
956	zh = pdep (ji,jj) ! depth at the partial step level
957	!
958	zn = rn_a0 * rho0
959	pab(ji,jj,jp_tem) = zn * r1_rho0 ! alpha
960	!
961	zn = rn_b0 * rho0
962	pab(ji,jj,jp_sal) = zn * r1_rho0 ! beta
963	!
964	END_2D
965	!
966	CASE DEFAULT
967	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
968	CALL ctl_stop( 'rab_2d:', ctmp1 )
969	!
970	END SELECT
971	!
972	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=pab(:,:,jp_tem), clinfo1=' rab_2d_t: ', &
973	& tab2d_2=pab(:,:,jp_sal), clinfo2=' rab_2d_s : ' )
974	!
975	IF( ln_timing ) CALL timing_stop('rab_2d')
976	!
977	END SUBROUTINE rab_2d_t
978
979
980	SUBROUTINE rab_0d( pts, pdep, pab, Kmm )
981	!!----------------------------------------------------------------------
982	!! * ROUTINE rab_0d *
983	!!
984	!! ** Purpose : Calculates thermal/haline expansion ratio for a 2d field (unmasked)
985	!!
986	!! ** Action : - pab : thermal/haline expansion ratio at T-points
987	!!----------------------------------------------------------------------
988	INTEGER , INTENT(in ) :: Kmm ! time level index
989	REAL(wp), DIMENSION(jpts) , INTENT(in ) :: pts ! pot. temperature & salinity
990	REAL(wp), INTENT(in ) :: pdep ! depth [m]
991	REAL(wp), DIMENSION(jpts) , INTENT( out) :: pab ! thermal/haline expansion ratio
992	!
993	REAL(wp) :: zt , zh , zs ! local scalars
994	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
995	!!----------------------------------------------------------------------
996	!
997	IF( ln_timing ) CALL timing_start('rab_0d')
998	!
999	pab(:) = 0._wp
1000	!
1001	SELECT CASE ( neos )
1002	!
1003	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
1004	!
1005	!
1006	zh = pdep * r1_Z0 ! depth
1007	zt = pts (jp_tem) * r1_T0 ! temperature
1008	zs = SQRT( ABS( pts(jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
1009	!
1010	! alpha
1011	zn3 = ALP003
1012	!
1013	zn2 = ALP012zt + ALP102zs+ALP002
1014	!
1015	zn1 = ((ALP031*zt &
1016	& + ALP121zs+ALP021)zt &
1017	& + (ALP211zs+ALP111)zs+ALP011)*zt &
1018	& + ((ALP301zs+ALP201)zs+ALP101)*zs+ALP001
1019	!
1020	zn0 = ((((ALP050*zt &
1021	& + ALP140zs+ALP040)zt &
1022	& + (ALP230zs+ALP130)zs+ALP030)*zt &
1023	& + ((ALP320zs+ALP220)zs+ALP120)zs+ALP020)zt &
1024	& + (((ALP410zs+ALP310)zs+ALP210)zs+ALP110)zs+ALP010)*zt &
1025	& + ((((ALP500zs+ALP400)zs+ALP300)zs+ALP200)zs+ALP100)*zs+ALP000
1026	!
1027	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
1028	!
1029	pab(jp_tem) = zn * r1_rho0
1030	!
1031	! beta
1032	zn3 = BET003
1033	!
1034	zn2 = BET012zt + BET102zs+BET002
1035	!
1036	zn1 = ((BET031*zt &
1037	& + BET121zs+BET021)zt &
1038	& + (BET211zs+BET111)zs+BET011)*zt &
1039	& + ((BET301zs+BET201)zs+BET101)*zs+BET001
1040	!
1041	zn0 = ((((BET050*zt &
1042	& + BET140zs+BET040)zt &
1043	& + (BET230zs+BET130)zs+BET030)*zt &
1044	& + ((BET320zs+BET220)zs+BET120)zs+BET020)zt &
1045	& + (((BET410zs+BET310)zs+BET210)zs+BET110)zs+BET010)*zt &
1046	& + ((((BET500zs+BET400)zs+BET300)zs+BET200)zs+BET100)*zs+BET000
1047	!
1048	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
1049	!
1050	pab(jp_sal) = zn / zs * r1_rho0
1051	!
1052	!
1053	!
1054	CASE( np_seos ) !== simplified EOS ==!
1055	!
1056	zt = pts(jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
1057	zs = pts(jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
1058	zh = pdep ! depth at the partial step level
1059	!
1060	zn = rn_a0 * ( 1._wp + rn_lambda1zt + rn_mu1zh ) + rn_nu*zs
1061	pab(jp_tem) = zn * r1_rho0 ! alpha
1062	!
1063	zn = rn_b0 * ( 1._wp - rn_lambda2zs - rn_mu2zh ) - rn_nu*zt
1064	pab(jp_sal) = zn * r1_rho0 ! beta
1065	!
1066	CASE( np_leos ) !== linear ISOMIP EOS ==!
1067	!
1068	zt = pts(jp_tem) - (-1._wp) ! pot. temperature anomaly (t-T0)
1069	zs = pts(jp_sal) - 34.2_wp ! abs. salinity anomaly (s-S0)
1070	zh = pdep ! depth at the partial step level
1071	!
1072	zn = rn_a0 * rho0
1073	pab(jp_tem) = zn * r1_rho0 ! alpha
1074	!
1075	zn = rn_b0 * rho0
1076	pab(jp_sal) = zn * r1_rho0 ! beta
1077	!
1078	CASE DEFAULT
1079	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1080	CALL ctl_stop( 'rab_0d:', ctmp1 )
1081	!
1082	END SELECT
1083	!
1084	IF( ln_timing ) CALL timing_stop('rab_0d')
1085	!
1086	END SUBROUTINE rab_0d
1087
1088
1089	SUBROUTINE bn2( pts, pab, pn2, Kmm )
1090	!!
1091	INTEGER , INTENT(in ) :: Kmm ! time level index
1092	REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature and salinity [Celsius,psu]
1093	REAL(wp), DIMENSION(:,:,:,:) , INTENT(in ) :: pab ! thermal/haline expansion coef. [Celsius-1,psu-1]
1094	REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: pn2 ! Brunt-Vaisala frequency squared [1/s^2]
1095	!!
1096	CALL bn2_t( pts, pab, is_tile(pab), pn2, is_tile(pn2), Kmm )
1097	END SUBROUTINE bn2
1098
1099
1100	SUBROUTINE bn2_t( pts, pab, ktab, pn2, ktn2, Kmm )
1101	!!----------------------------------------------------------------------
1102	!! * ROUTINE bn2 *
1103	!!
1104	!! ** Purpose : Compute the local Brunt-Vaisala frequency at the
1105	!! time-step of the input arguments
1106	!!
1107	!! ** Method : pn2 = grav * (alpha dk[T] + beta dk[S] ) / e3w
1108	!! where alpha and beta are given in pab, and computed on T-points.
1109	!! N.B. N^2 is set one for all to zero at jk=1 in istate module.
1110	!!
1111	!! ** Action : pn2 : square of the brunt-vaisala frequency at w-point
1112	!!
1113	!!----------------------------------------------------------------------
1114	INTEGER , INTENT(in ) :: Kmm ! time level index
1115	INTEGER , INTENT(in ) :: ktab, ktn2
1116	REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature and salinity [Celsius,psu]
1117	REAL(wp), DIMENSION(A2D_T(ktab),JPK,JPTS), INTENT(in ) :: pab ! thermal/haline expansion coef. [Celsius-1,psu-1]
1118	REAL(wp), DIMENSION(A2D_T(ktn2),JPK ), INTENT( out) :: pn2 ! Brunt-Vaisala frequency squared [1/s^2]
1119	!
1120	INTEGER :: ji, jj, jk ! dummy loop indices
1121	REAL(wp) :: zaw, zbw, zrw ! local scalars
1122	!!----------------------------------------------------------------------
1123	!
1124	IF( ln_timing ) CALL timing_start('bn2')
1125	!
1126	DO_3D( 1, 1, 1, 1, 2, jpkm1 ) ! interior points only (2=< jk =< jpkm1 ); surface and bottom value set to zero one for all in istate.F90
1127	zrw = ( gdepw(ji,jj,jk ,Kmm) - gdept(ji,jj,jk,Kmm) ) &
1128	& / ( gdept(ji,jj,jk-1,Kmm) - gdept(ji,jj,jk,Kmm) )
1129	!
1130	zaw = pab(ji,jj,jk,jp_tem) * (1. - zrw) + pab(ji,jj,jk-1,jp_tem) * zrw
1131	zbw = pab(ji,jj,jk,jp_sal) * (1. - zrw) + pab(ji,jj,jk-1,jp_sal) * zrw
1132	!
1133	pn2(ji,jj,jk) = grav * ( zaw * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) &
1134	& - zbw * ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) ) &
1135	& / e3w(ji,jj,jk,Kmm) * wmask(ji,jj,jk)
1136	END_3D
1137	!
1138	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=pn2, clinfo1=' bn2 : ', kdim=jpk )
1139	!
1140	IF( ln_timing ) CALL timing_stop('bn2')
1141	!
1142	END SUBROUTINE bn2_t
1143
1144
1145	FUNCTION eos_pt_from_ct( ctmp, psal ) RESULT( ptmp )
1146	!!----------------------------------------------------------------------
1147	!! * ROUTINE eos_pt_from_ct *
1148	!!
1149	!! ** Purpose : Compute pot.temp. from cons. temp. [Celsius]
1150	!!
1151	!! ** Method : rational approximation (5/3th order) of TEOS-10 algorithm
1152	!! checkvalue: pt=20.02391895 Celsius for sa=35.7g/kg, ct=20degC
1153	!!
1154	!! Reference : TEOS-10, UNESCO
1155	!! Rational approximation to TEOS10 algorithm (rms error on WOA13 values: 4.0e-5 degC)
1156	!!----------------------------------------------------------------------
1157	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: ctmp ! Cons. Temp [Celsius]
1158	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu]
1159	! Leave result array automatic rather than making explicitly allocated
1160	REAL(wp), DIMENSION(jpi,jpj) :: ptmp ! potential temperature [Celsius]
1161	!
1162	INTEGER :: ji, jj ! dummy loop indices
1163	REAL(wp) :: zt , zs , ztm ! local scalars
1164	REAL(wp) :: zn , zd ! local scalars
1165	REAL(wp) :: zdeltaS , z1_S0 , z1_T0
1166	!!----------------------------------------------------------------------
1167	!
1168	IF( ln_timing ) CALL timing_start('eos_pt_from_ct')
1169	!
1170	zdeltaS = 5._wp
1171	z1_S0 = 0.875_wp/35.16504_wp
1172	z1_T0 = 1._wp/40._wp
1173	!
1174	DO_2D( 1, 1, 1, 1 )
1175	!
1176	zt = ctmp (ji,jj) * z1_T0
1177	zs = SQRT( ABS( psal(ji,jj) + zdeltaS ) * r1_S0 )
1178	ztm = tmask(ji,jj,1)
1179	!
1180	zn = ((((-2.1385727895e-01_wp*zt &
1181	& - 2.7674419971e-01_wpzs+1.0728094330_wp)zt &
1182	& + (2.6366564313_wpzs+3.3546960647_wp)zs-7.8012209473_wp)*zt &
1183	& + ((1.8835586562_wpzs+7.3949191679_wp)zs-3.3937395875_wp)zs-5.6414948432_wp)zt &
1184	& + (((3.5737370589_wpzs-1.5512427389e+01_wp)zs+2.4625741105e+01_wp)*zs &
1185	& +1.9912291000e+01_wp)zs-3.2191146312e+01_wp)zt &
1186	& + ((((5.7153204649e-01_wpzs-3.0943149543_wp)zs+9.3052495181_wp)*zs &
1187	& -9.4528934807_wp)zs+3.1066408996_wp)zs-4.3504021262e-01_wp
1188	!
1189	zd = (2.0035003456_wp*zt &
1190	& -3.4570358592e-01_wpzs+5.6471810638_wp)zt &
1191	& + (1.5393993508_wpzs-6.9394762624_wp)zs+1.2750522650e+01_wp
1192	!
1193	ptmp(ji,jj) = ( zt / z1_T0 + zn / zd ) * ztm
1194	!
1195	END_2D
1196	!
1197	IF( ln_timing ) CALL timing_stop('eos_pt_from_ct')
1198	!
1199	END FUNCTION eos_pt_from_ct
1200
1201
1202	SUBROUTINE eos_fzp_2d( psal, ptf, pdep )
1203	!!
1204	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu]
1205	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ), OPTIONAL :: pdep ! depth [m]
1206	REAL(wp), DIMENSION(:,:) , INTENT(out ) :: ptf ! freezing temperature [Celsius]
1207	!!
1208	CALL eos_fzp_2d_t( psal, ptf, is_tile(ptf), pdep )
1209	END SUBROUTINE eos_fzp_2d
1210
1211
1212	SUBROUTINE eos_fzp_2d_t( psal, ptf, kttf, pdep )
1213	!!----------------------------------------------------------------------
1214	!! * ROUTINE eos_fzp *
1215	!!
1216	!! ** Purpose : Compute the freezing point temperature [Celsius]
1217	!!
1218	!! ** Method : UNESCO freezing point (ptf) in Celsius is given by
1219	!! ptf(t,z) = (-.0575+1.710523e-3sqrt(abs(s))-2.154996e-4s)s - 7.53e-4z
1220	!! checkvalue: tf=-2.588567 Celsius for s=40psu, z=500m
1221	!!
1222	!! Reference : UNESCO tech. papers in the marine science no. 28. 1978
1223	!!----------------------------------------------------------------------
1224	INTEGER , INTENT(in ) :: kttf
1225	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu]
1226	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ), OPTIONAL :: pdep ! depth [m]
1227	REAL(wp), DIMENSION(A2D_T(kttf)), INTENT(out ) :: ptf ! freezing temperature [Celsius]
1228	!
1229	INTEGER :: ji, jj ! dummy loop indices
1230	REAL(wp) :: zt, zs, z1_S0 ! local scalars
1231	!!----------------------------------------------------------------------
1232	!
1233	SELECT CASE ( neos )
1234	!
1235	CASE ( np_teos10, np_seos ) !== CT,SA (TEOS-10 and S-EOS formulations) ==!
1236	!
1237	z1_S0 = 1._wp / 35.16504_wp
1238	DO_2D( 1, 1, 1, 1 )
1239	zs= SQRT( ABS( psal(ji,jj) ) * z1_S0 ) ! square root salinity
1240	ptf(ji,jj) = ((((1.46873e-03_wpzs-9.64972e-03_wp)zs+2.28348e-02_wp)*zs &
1241	& - 3.12775e-02_wp)zs+2.07679e-02_wp)zs-5.87701e-02_wp
1242	END_2D
1243	ptf(:,:) = ptf(:,:) * psal(:,:)
1244	!
1245	IF( PRESENT( pdep ) ) ptf(:,:) = ptf(:,:) - 7.53e-4 * pdep(:,:)
1246	!
1247	CASE ( np_eos80 ) !== PT,SP (UNESCO formulation) ==!
1248	!
1249	ptf(:,:) = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal(:,:) ) &
1250	& - 2.154996e-4_wp * psal(:,:) ) * psal(:,:)
1251	!
1252	IF( PRESENT( pdep ) ) ptf(:,:) = ptf(:,:) - 7.53e-4 * pdep(:,:)
1253	!
1254	CASE DEFAULT
1255	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1256	CALL ctl_stop( 'eos_fzp_2d:', ctmp1 )
1257	!
1258	END SELECT
1259	!
1260	END SUBROUTINE eos_fzp_2d_t
1261
1262
1263	SUBROUTINE eos_fzp_0d( psal, ptf, pdep )
1264	!!----------------------------------------------------------------------
1265	!! * ROUTINE eos_fzp *
1266	!!
1267	!! ** Purpose : Compute the freezing point temperature [Celsius]
1268	!!
1269	!! ** Method : UNESCO freezing point (ptf) in Celsius is given by
1270	!! ptf(t,z) = (-.0575+1.710523e-3sqrt(abs(s))-2.154996e-4s)s - 7.53e-4z
1271	!! checkvalue: tf=-2.588567 Celsius for s=40psu, z=500m
1272	!!
1273	!! Reference : UNESCO tech. papers in the marine science no. 28. 1978
1274	!!----------------------------------------------------------------------
1275	REAL(wp), INTENT(in ) :: psal ! salinity [psu]
1276	REAL(wp), INTENT(in ), OPTIONAL :: pdep ! depth [m]
1277	REAL(wp), INTENT(out) :: ptf ! freezing temperature [Celsius]
1278	!
1279	REAL(wp) :: zs ! local scalars
1280	!!----------------------------------------------------------------------
1281	!
1282	SELECT CASE ( neos )
1283	!
1284	CASE ( np_teos10, np_seos ) !== CT,SA (TEOS-10 and S-EOS formulations) ==!
1285	!
1286	zs = SQRT( ABS( psal ) / 35.16504_wp ) ! square root salinity
1287	ptf = ((((1.46873e-03_wpzs-9.64972e-03_wp)zs+2.28348e-02_wp)*zs &
1288	& - 3.12775e-02_wp)zs+2.07679e-02_wp)zs-5.87701e-02_wp
1289	ptf = ptf * psal
1290	!
1291	IF( PRESENT( pdep ) ) ptf = ptf - 7.53e-4 * pdep
1292	!
1293	CASE ( np_eos80 ) !== PT,SP (UNESCO formulation) ==!
1294	!
1295	ptf = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal ) &
1296	& - 2.154996e-4_wp * psal ) * psal
1297	!
1298	IF( PRESENT( pdep ) ) ptf = ptf - 7.53e-4 * pdep
1299	!
1300	CASE DEFAULT
1301	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1302	CALL ctl_stop( 'eos_fzp_0d:', ctmp1 )
1303	!
1304	END SELECT
1305	!
1306	END SUBROUTINE eos_fzp_0d
1307
1308
1309	SUBROUTINE eos_pen( pts, pab_pe, ppen, Kmm )
1310	!!----------------------------------------------------------------------
1311	!! * ROUTINE eos_pen *
1312	!!
1313	!! ** Purpose : Calculates nonlinear anomalies of alpha_PE, beta_PE and PE at T-points
1314	!!
1315	!! ** Method : PE is defined analytically as the vertical
1316	!! primitive of EOS times -g integrated between 0 and z>0.
1317	!! pen is the nonlinear bsq-PE anomaly: pen = ( PE - rho0 gz ) / rho0 gz - rd
1318	!! = 1/z * /int_0^z rd dz - rd
1319	!! where rd is the density anomaly (see eos_rhd function)
1320	!! ab_pe are partial derivatives of PE anomaly with respect to T and S:
1321	!! ab_pe(1) = - 1/(rho0 gz) * dPE/dT + drd/dT = - d(pen)/dT
1322	!! ab_pe(2) = 1/(rho0 gz) * dPE/dS + drd/dS = d(pen)/dS
1323	!!
1324	!! ** Action : - pen : PE anomaly given at T-points
1325	!! : - pab_pe : given at T-points
1326	!! pab_pe(:,:,:,jp_tem) is alpha_pe
1327	!! pab_pe(:,:,:,jp_sal) is beta_pe
1328	!!----------------------------------------------------------------------
1329	INTEGER , INTENT(in ) :: Kmm ! time level index
1330	REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature & salinity
1331	REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT( out) :: pab_pe ! alpha_pe and beta_pe
1332	REAL(wp), DIMENSION(jpi,jpj,jpk) , INTENT( out) :: ppen ! potential energy anomaly
1333	!
1334	INTEGER :: ji, jj, jk ! dummy loop indices
1335	REAL(wp) :: zt , zh , zs , ztm ! local scalars
1336	REAL(wp) :: zn , zn0, zn1, zn2 ! - -
1337	!!----------------------------------------------------------------------
1338	!
1339	IF( ln_timing ) CALL timing_start('eos_pen')
1340	!
1341	SELECT CASE ( neos )
1342	!
1343	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
1344	!
1345	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
1346	!
1347	zh = gdept(ji,jj,jk,Kmm) * r1_Z0 ! depth
1348	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
1349	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
1350	ztm = tmask(ji,jj,jk) ! tmask
1351	!
1352	! potential energy non-linear anomaly
1353	zn2 = (PEN012)*zt &
1354	& + PEN102*zs+PEN002
1355	!
1356	zn1 = ((PEN021)*zt &
1357	& + PEN111zs+PEN011)zt &
1358	& + (PEN201zs+PEN101)zs+PEN001
1359	!
1360	zn0 = ((((PEN040)*zt &
1361	& + PEN130zs+PEN030)zt &
1362	& + (PEN220zs+PEN120)zs+PEN020)*zt &
1363	& + ((PEN310zs+PEN210)zs+PEN110)zs+PEN010)zt &
1364	& + (((PEN400zs+PEN300)zs+PEN200)zs+PEN100)zs+PEN000
1365	!
1366	zn = ( zn2 * zh + zn1 ) * zh + zn0
1367	!
1368	ppen(ji,jj,jk) = zn * zh * r1_rho0 * ztm
1369	!
1370	! alphaPE non-linear anomaly
1371	zn2 = APE002
1372	!
1373	zn1 = (APE011)*zt &
1374	& + APE101*zs+APE001
1375	!
1376	zn0 = (((APE030)*zt &
1377	& + APE120zs+APE020)zt &
1378	& + (APE210zs+APE110)zs+APE010)*zt &
1379	& + ((APE300zs+APE200)zs+APE100)*zs+APE000
1380	!
1381	zn = ( zn2 * zh + zn1 ) * zh + zn0
1382	!
1383	pab_pe(ji,jj,jk,jp_tem) = zn * zh * r1_rho0 * ztm
1384	!
1385	! betaPE non-linear anomaly
1386	zn2 = BPE002
1387	!
1388	zn1 = (BPE011)*zt &
1389	& + BPE101*zs+BPE001
1390	!
1391	zn0 = (((BPE030)*zt &
1392	& + BPE120zs+BPE020)zt &
1393	& + (BPE210zs+BPE110)zs+BPE010)*zt &
1394	& + ((BPE300zs+BPE200)zs+BPE100)*zs+BPE000
1395	!
1396	zn = ( zn2 * zh + zn1 ) * zh + zn0
1397	!
1398	pab_pe(ji,jj,jk,jp_sal) = zn / zs * zh * r1_rho0 * ztm
1399	!
1400	END_3D
1401	!
1402	CASE( np_seos ) !== Vallis (2006) simplified EOS ==!
1403	!
1404	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
1405	zt = pts(ji,jj,jk,jp_tem) - 10._wp ! temperature anomaly (t-T0)
1406	zs = pts (ji,jj,jk,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
1407	zh = gdept(ji,jj,jk,Kmm) ! depth in meters at t-point
1408	ztm = tmask(ji,jj,jk) ! tmask
1409	zn = 0.5_wp * zh * r1_rho0 * ztm
1410	! ! Potential Energy
1411	ppen(ji,jj,jk) = ( rn_a0 * rn_mu1 * zt + rn_b0 * rn_mu2 * zs ) * zn
1412	! ! alphaPE
1413	pab_pe(ji,jj,jk,jp_tem) = - rn_a0 * rn_mu1 * zn
1414	pab_pe(ji,jj,jk,jp_sal) = rn_b0 * rn_mu2 * zn
1415	!
1416	END_3D
1417	!
1418	CASE( np_leos ) !== linear ISOMIP EOS ==!
1419	!
1420	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
1421	zt = pts(ji,jj,jk,jp_tem) - (-1._wp) ! temperature anomaly (t-T0)
1422	zs = pts (ji,jj,jk,jp_sal) - 34.2_wp ! abs. salinity anomaly (s-S0)
1423	zh = gdept(ji,jj,jk,Kmm) ! depth in meters at t-point
1424	ztm = tmask(ji,jj,jk) ! tmask
1425	zn = 0.5_wp * zh * r1_rho0 * ztm
1426	! ! Potential Energy
1427	ppen(ji,jj,jk) = 0.
1428	! ! alphaPE
1429	pab_pe(ji,jj,jk,jp_tem) = 0.
1430	pab_pe(ji,jj,jk,jp_sal) = 0.
1431	!
1432	END_3D
1433	!
1434	CASE DEFAULT
1435	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1436	CALL ctl_stop( 'eos_pen:', ctmp1 )
1437	!
1438	END SELECT
1439	!
1440	IF( ln_timing ) CALL timing_stop('eos_pen')
1441	!
1442	END SUBROUTINE eos_pen
1443
1444
1445	SUBROUTINE eos_init
1446	!!----------------------------------------------------------------------
1447	!! * ROUTINE eos_init *
1448	!!
1449	!! ** Purpose : initializations for the equation of state
1450	!!
1451	!! ** Method : Read the namelist nameos and control the parameters
1452	!!----------------------------------------------------------------------
1453	INTEGER :: ios ! local integer
1454	INTEGER :: ioptio ! local integer
1455	!!
1456	NAMELIST/nameos/ ln_TEOS10, ln_EOS80, ln_SEOS, ln_LEOS, rn_a0, rn_b0, &
1457	& rn_lambda1, rn_mu1, rn_lambda2, rn_mu2, rn_nu
1458	!!----------------------------------------------------------------------
1459	!
1460	READ ( numnam_ref, nameos, IOSTAT = ios, ERR = 901 )
1461	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'nameos in reference namelist' )
1462	!
1463	READ ( numnam_cfg, nameos, IOSTAT = ios, ERR = 902 )
1464	902 IF( ios > 0 ) CALL ctl_nam ( ios , 'nameos in configuration namelist' )
1465	IF(lwm) WRITE( numond, nameos )
1466	!
1467	rho0 = 1027.51_wp !: volumic mass of reference [kg/m3]
1468	rcp = 3974.00_wp !: heat capacity [J/K]
1469	!
1470	IF(lwp) THEN ! Control print
1471	WRITE(numout,*)
1472	WRITE(numout,*) 'eos_init : equation of state'
1473	WRITE(numout,*) '~~~~~~~~'
1474	WRITE(numout,*) ' Namelist nameos : Chosen the Equation Of Seawater (EOS)'
1475	WRITE(numout,*) ' TEOS-10 : rho=F(Conservative Temperature, Absolute Salinity, depth) ln_TEOS10 = ', ln_TEOS10
1476	WRITE(numout,*) ' EOS-80 : rho=F(Potential Temperature, Practical Salinity, depth) ln_EOS80 = ', ln_EOS80
1477	WRITE(numout,*) ' S-EOS : rho=F(Conservative Temperature, Absolute Salinity, depth) ln_SEOS = ', ln_SEOS
1478	WRITE(numout,*) ' L-EOS : rho=F(Potential Temperature, Practical Salinity, depth) ln_LEOS = ', ln_LEOS
1479	ENDIF
1480
1481	! Check options for equation of state & set neos based on logical flags
1482	ioptio = 0
1483	IF( ln_TEOS10 ) THEN ; ioptio = ioptio+1 ; neos = np_teos10 ; ENDIF
1484	IF( ln_EOS80 ) THEN ; ioptio = ioptio+1 ; neos = np_eos80 ; ENDIF
1485	IF( ln_SEOS ) THEN ; ioptio = ioptio+1 ; neos = np_seos ; ENDIF
1486	IF( ln_LEOS ) THEN ; ioptio = ioptio+1 ; neos = np_leos ; ENDIF
1487	IF( ioptio /= 1 ) CALL ctl_stop("Exactly one equation of state option must be selected")
1488	!
1489	SELECT CASE( neos ) ! check option
1490	!
1491	CASE( np_teos10 ) !== polynomial TEOS-10 ==!
1492	IF(lwp) WRITE(numout,*)
1493	IF(lwp) WRITE(numout,*) ' ==>>> use of TEOS-10 equation of state (cons. temp. and abs. salinity)'
1494	!
1495	l_useCT = .TRUE. ! model temperature is Conservative temperature
1496	!
1497	rdeltaS = 32._wp
1498	r1_S0 = 0.875_wp/35.16504_wp
1499	r1_T0 = 1._wp/40._wp
1500	r1_Z0 = 1.e-4_wp
1501	!
1502	EOS000 = 8.0189615746e+02_wp
1503	EOS100 = 8.6672408165e+02_wp
1504	EOS200 = -1.7864682637e+03_wp
1505	EOS300 = 2.0375295546e+03_wp
1506	EOS400 = -1.2849161071e+03_wp
1507	EOS500 = 4.3227585684e+02_wp
1508	EOS600 = -6.0579916612e+01_wp
1509	EOS010 = 2.6010145068e+01_wp
1510	EOS110 = -6.5281885265e+01_wp
1511	EOS210 = 8.1770425108e+01_wp
1512	EOS310 = -5.6888046321e+01_wp
1513	EOS410 = 1.7681814114e+01_wp
1514	EOS510 = -1.9193502195_wp
1515	EOS020 = -3.7074170417e+01_wp
1516	EOS120 = 6.1548258127e+01_wp
1517	EOS220 = -6.0362551501e+01_wp
1518	EOS320 = 2.9130021253e+01_wp
1519	EOS420 = -5.4723692739_wp
1520	EOS030 = 2.1661789529e+01_wp
1521	EOS130 = -3.3449108469e+01_wp
1522	EOS230 = 1.9717078466e+01_wp
1523	EOS330 = -3.1742946532_wp
1524	EOS040 = -8.3627885467_wp
1525	EOS140 = 1.1311538584e+01_wp
1526	EOS240 = -5.3563304045_wp
1527	EOS050 = 5.4048723791e-01_wp
1528	EOS150 = 4.8169980163e-01_wp
1529	EOS060 = -1.9083568888e-01_wp
1530	EOS001 = 1.9681925209e+01_wp
1531	EOS101 = -4.2549998214e+01_wp
1532	EOS201 = 5.0774768218e+01_wp
1533	EOS301 = -3.0938076334e+01_wp
1534	EOS401 = 6.6051753097_wp
1535	EOS011 = -1.3336301113e+01_wp
1536	EOS111 = -4.4870114575_wp
1537	EOS211 = 5.0042598061_wp
1538	EOS311 = -6.5399043664e-01_wp
1539	EOS021 = 6.7080479603_wp
1540	EOS121 = 3.5063081279_wp
1541	EOS221 = -1.8795372996_wp
1542	EOS031 = -2.4649669534_wp
1543	EOS131 = -5.5077101279e-01_wp
1544	EOS041 = 5.5927935970e-01_wp
1545	EOS002 = 2.0660924175_wp
1546	EOS102 = -4.9527603989_wp
1547	EOS202 = 2.5019633244_wp
1548	EOS012 = 2.0564311499_wp
1549	EOS112 = -2.1311365518e-01_wp
1550	EOS022 = -1.2419983026_wp
1551	EOS003 = -2.3342758797e-02_wp
1552	EOS103 = -1.8507636718e-02_wp
1553	EOS013 = 3.7969820455e-01_wp
1554	!
1555	ALP000 = -6.5025362670e-01_wp
1556	ALP100 = 1.6320471316_wp
1557	ALP200 = -2.0442606277_wp
1558	ALP300 = 1.4222011580_wp
1559	ALP400 = -4.4204535284e-01_wp
1560	ALP500 = 4.7983755487e-02_wp
1561	ALP010 = 1.8537085209_wp
1562	ALP110 = -3.0774129064_wp
1563	ALP210 = 3.0181275751_wp
1564	ALP310 = -1.4565010626_wp
1565	ALP410 = 2.7361846370e-01_wp
1566	ALP020 = -1.6246342147_wp
1567	ALP120 = 2.5086831352_wp
1568	ALP220 = -1.4787808849_wp
1569	ALP320 = 2.3807209899e-01_wp
1570	ALP030 = 8.3627885467e-01_wp
1571	ALP130 = -1.1311538584_wp
1572	ALP230 = 5.3563304045e-01_wp
1573	ALP040 = -6.7560904739e-02_wp
1574	ALP140 = -6.0212475204e-02_wp
1575	ALP050 = 2.8625353333e-02_wp
1576	ALP001 = 3.3340752782e-01_wp
1577	ALP101 = 1.1217528644e-01_wp
1578	ALP201 = -1.2510649515e-01_wp
1579	ALP301 = 1.6349760916e-02_wp
1580	ALP011 = -3.3540239802e-01_wp
1581	ALP111 = -1.7531540640e-01_wp
1582	ALP211 = 9.3976864981e-02_wp
1583	ALP021 = 1.8487252150e-01_wp
1584	ALP121 = 4.1307825959e-02_wp
1585	ALP031 = -5.5927935970e-02_wp
1586	ALP002 = -5.1410778748e-02_wp
1587	ALP102 = 5.3278413794e-03_wp
1588	ALP012 = 6.2099915132e-02_wp
1589	ALP003 = -9.4924551138e-03_wp
1590	!
1591	BET000 = 1.0783203594e+01_wp
1592	BET100 = -4.4452095908e+01_wp
1593	BET200 = 7.6048755820e+01_wp
1594	BET300 = -6.3944280668e+01_wp
1595	BET400 = 2.6890441098e+01_wp
1596	BET500 = -4.5221697773_wp
1597	BET010 = -8.1219372432e-01_wp
1598	BET110 = 2.0346663041_wp
1599	BET210 = -2.1232895170_wp
1600	BET310 = 8.7994140485e-01_wp
1601	BET410 = -1.1939638360e-01_wp
1602	BET020 = 7.6574242289e-01_wp
1603	BET120 = -1.5019813020_wp
1604	BET220 = 1.0872489522_wp
1605	BET320 = -2.7233429080e-01_wp
1606	BET030 = -4.1615152308e-01_wp
1607	BET130 = 4.9061350869e-01_wp
1608	BET230 = -1.1847737788e-01_wp
1609	BET040 = 1.4073062708e-01_wp
1610	BET140 = -1.3327978879e-01_wp
1611	BET050 = 5.9929880134e-03_wp
1612	BET001 = -5.2937873009e-01_wp
1613	BET101 = 1.2634116779_wp
1614	BET201 = -1.1547328025_wp
1615	BET301 = 3.2870876279e-01_wp
1616	BET011 = -5.5824407214e-02_wp
1617	BET111 = 1.2451933313e-01_wp
1618	BET211 = -2.4409539932e-02_wp
1619	BET021 = 4.3623149752e-02_wp
1620	BET121 = -4.6767901790e-02_wp
1621	BET031 = -6.8523260060e-03_wp
1622	BET002 = -6.1618945251e-02_wp
1623	BET102 = 6.2255521644e-02_wp
1624	BET012 = -2.6514181169e-03_wp
1625	BET003 = -2.3025968587e-04_wp
1626	!
1627	PEN000 = -9.8409626043_wp
1628	PEN100 = 2.1274999107e+01_wp
1629	PEN200 = -2.5387384109e+01_wp
1630	PEN300 = 1.5469038167e+01_wp
1631	PEN400 = -3.3025876549_wp
1632	PEN010 = 6.6681505563_wp
1633	PEN110 = 2.2435057288_wp
1634	PEN210 = -2.5021299030_wp
1635	PEN310 = 3.2699521832e-01_wp
1636	PEN020 = -3.3540239802_wp
1637	PEN120 = -1.7531540640_wp
1638	PEN220 = 9.3976864981e-01_wp
1639	PEN030 = 1.2324834767_wp
1640	PEN130 = 2.7538550639e-01_wp
1641	PEN040 = -2.7963967985e-01_wp
1642	PEN001 = -1.3773949450_wp
1643	PEN101 = 3.3018402659_wp
1644	PEN201 = -1.6679755496_wp
1645	PEN011 = -1.3709540999_wp
1646	PEN111 = 1.4207577012e-01_wp
1647	PEN021 = 8.2799886843e-01_wp
1648	PEN002 = 1.7507069098e-02_wp
1649	PEN102 = 1.3880727538e-02_wp
1650	PEN012 = -2.8477365341e-01_wp
1651	!
1652	APE000 = -1.6670376391e-01_wp
1653	APE100 = -5.6087643219e-02_wp
1654	APE200 = 6.2553247576e-02_wp
1655	APE300 = -8.1748804580e-03_wp
1656	APE010 = 1.6770119901e-01_wp
1657	APE110 = 8.7657703198e-02_wp
1658	APE210 = -4.6988432490e-02_wp
1659	APE020 = -9.2436260751e-02_wp
1660	APE120 = -2.0653912979e-02_wp
1661	APE030 = 2.7963967985e-02_wp
1662	APE001 = 3.4273852498e-02_wp
1663	APE101 = -3.5518942529e-03_wp
1664	APE011 = -4.1399943421e-02_wp
1665	APE002 = 7.1193413354e-03_wp
1666	!
1667	BPE000 = 2.6468936504e-01_wp
1668	BPE100 = -6.3170583896e-01_wp
1669	BPE200 = 5.7736640125e-01_wp
1670	BPE300 = -1.6435438140e-01_wp
1671	BPE010 = 2.7912203607e-02_wp
1672	BPE110 = -6.2259666565e-02_wp
1673	BPE210 = 1.2204769966e-02_wp
1674	BPE020 = -2.1811574876e-02_wp
1675	BPE120 = 2.3383950895e-02_wp
1676	BPE030 = 3.4261630030e-03_wp
1677	BPE001 = 4.1079296834e-02_wp
1678	BPE101 = -4.1503681096e-02_wp
1679	BPE011 = 1.7676120780e-03_wp
1680	BPE002 = 1.7269476440e-04_wp
1681	!
1682	CASE( np_eos80 ) !== polynomial EOS-80 formulation ==!
1683	!
1684	IF(lwp) WRITE(numout,*)
1685	IF(lwp) WRITE(numout,*) ' ==>>> use of EOS-80 equation of state (pot. temp. and pract. salinity)'
1686	!
1687	l_useCT = .FALSE. ! model temperature is Potential temperature
1688	rdeltaS = 20._wp
1689	r1_S0 = 1._wp/40._wp
1690	r1_T0 = 1._wp/40._wp
1691	r1_Z0 = 1.e-4_wp
1692	!
1693	EOS000 = 9.5356891948e+02_wp
1694	EOS100 = 1.7136499189e+02_wp
1695	EOS200 = -3.7501039454e+02_wp
1696	EOS300 = 5.1856810420e+02_wp
1697	EOS400 = -3.7264470465e+02_wp
1698	EOS500 = 1.4302533998e+02_wp
1699	EOS600 = -2.2856621162e+01_wp
1700	EOS010 = 1.0087518651e+01_wp
1701	EOS110 = -1.3647741861e+01_wp
1702	EOS210 = 8.8478359933_wp
1703	EOS310 = -7.2329388377_wp
1704	EOS410 = 1.4774410611_wp
1705	EOS510 = 2.0036720553e-01_wp
1706	EOS020 = -2.5579830599e+01_wp
1707	EOS120 = 2.4043512327e+01_wp
1708	EOS220 = -1.6807503990e+01_wp
1709	EOS320 = 8.3811577084_wp
1710	EOS420 = -1.9771060192_wp
1711	EOS030 = 1.6846451198e+01_wp
1712	EOS130 = -2.1482926901e+01_wp
1713	EOS230 = 1.0108954054e+01_wp
1714	EOS330 = -6.2675951440e-01_wp
1715	EOS040 = -8.0812310102_wp
1716	EOS140 = 1.0102374985e+01_wp
1717	EOS240 = -4.8340368631_wp
1718	EOS050 = 1.2079167803_wp
1719	EOS150 = 1.1515380987e-01_wp
1720	EOS060 = -2.4520288837e-01_wp
1721	EOS001 = 1.0748601068e+01_wp
1722	EOS101 = -1.7817043500e+01_wp
1723	EOS201 = 2.2181366768e+01_wp
1724	EOS301 = -1.6750916338e+01_wp
1725	EOS401 = 4.1202230403_wp
1726	EOS011 = -1.5852644587e+01_wp
1727	EOS111 = -7.6639383522e-01_wp
1728	EOS211 = 4.1144627302_wp
1729	EOS311 = -6.6955877448e-01_wp
1730	EOS021 = 9.9994861860_wp
1731	EOS121 = -1.9467067787e-01_wp
1732	EOS221 = -1.2177554330_wp
1733	EOS031 = -3.4866102017_wp
1734	EOS131 = 2.2229155620e-01_wp
1735	EOS041 = 5.9503008642e-01_wp
1736	EOS002 = 1.0375676547_wp
1737	EOS102 = -3.4249470629_wp
1738	EOS202 = 2.0542026429_wp
1739	EOS012 = 2.1836324814_wp
1740	EOS112 = -3.4453674320e-01_wp
1741	EOS022 = -1.2548163097_wp
1742	EOS003 = 1.8729078427e-02_wp
1743	EOS103 = -5.7238495240e-02_wp
1744	EOS013 = 3.8306136687e-01_wp
1745	!
1746	ALP000 = -2.5218796628e-01_wp
1747	ALP100 = 3.4119354654e-01_wp
1748	ALP200 = -2.2119589983e-01_wp
1749	ALP300 = 1.8082347094e-01_wp
1750	ALP400 = -3.6936026529e-02_wp
1751	ALP500 = -5.0091801383e-03_wp
1752	ALP010 = 1.2789915300_wp
1753	ALP110 = -1.2021756164_wp
1754	ALP210 = 8.4037519952e-01_wp
1755	ALP310 = -4.1905788542e-01_wp
1756	ALP410 = 9.8855300959e-02_wp
1757	ALP020 = -1.2634838399_wp
1758	ALP120 = 1.6112195176_wp
1759	ALP220 = -7.5817155402e-01_wp
1760	ALP320 = 4.7006963580e-02_wp
1761	ALP030 = 8.0812310102e-01_wp
1762	ALP130 = -1.0102374985_wp
1763	ALP230 = 4.8340368631e-01_wp
1764	ALP040 = -1.5098959754e-01_wp
1765	ALP140 = -1.4394226233e-02_wp
1766	ALP050 = 3.6780433255e-02_wp
1767	ALP001 = 3.9631611467e-01_wp
1768	ALP101 = 1.9159845880e-02_wp
1769	ALP201 = -1.0286156825e-01_wp
1770	ALP301 = 1.6738969362e-02_wp
1771	ALP011 = -4.9997430930e-01_wp
1772	ALP111 = 9.7335338937e-03_wp
1773	ALP211 = 6.0887771651e-02_wp
1774	ALP021 = 2.6149576513e-01_wp
1775	ALP121 = -1.6671866715e-02_wp
1776	ALP031 = -5.9503008642e-02_wp
1777	ALP002 = -5.4590812035e-02_wp
1778	ALP102 = 8.6134185799e-03_wp
1779	ALP012 = 6.2740815484e-02_wp
1780	ALP003 = -9.5765341718e-03_wp
1781	!
1782	BET000 = 2.1420623987_wp
1783	BET100 = -9.3752598635_wp
1784	BET200 = 1.9446303907e+01_wp
1785	BET300 = -1.8632235232e+01_wp
1786	BET400 = 8.9390837485_wp
1787	BET500 = -1.7142465871_wp
1788	BET010 = -1.7059677327e-01_wp
1789	BET110 = 2.2119589983e-01_wp
1790	BET210 = -2.7123520642e-01_wp
1791	BET310 = 7.3872053057e-02_wp
1792	BET410 = 1.2522950346e-02_wp
1793	BET020 = 3.0054390409e-01_wp
1794	BET120 = -4.2018759976e-01_wp
1795	BET220 = 3.1429341406e-01_wp
1796	BET320 = -9.8855300959e-02_wp
1797	BET030 = -2.6853658626e-01_wp
1798	BET130 = 2.5272385134e-01_wp
1799	BET230 = -2.3503481790e-02_wp
1800	BET040 = 1.2627968731e-01_wp
1801	BET140 = -1.2085092158e-01_wp
1802	BET050 = 1.4394226233e-03_wp
1803	BET001 = -2.2271304375e-01_wp
1804	BET101 = 5.5453416919e-01_wp
1805	BET201 = -6.2815936268e-01_wp
1806	BET301 = 2.0601115202e-01_wp
1807	BET011 = -9.5799229402e-03_wp
1808	BET111 = 1.0286156825e-01_wp
1809	BET211 = -2.5108454043e-02_wp
1810	BET021 = -2.4333834734e-03_wp
1811	BET121 = -3.0443885826e-02_wp
1812	BET031 = 2.7786444526e-03_wp
1813	BET002 = -4.2811838287e-02_wp
1814	BET102 = 5.1355066072e-02_wp
1815	BET012 = -4.3067092900e-03_wp
1816	BET003 = -7.1548119050e-04_wp
1817	!
1818	PEN000 = -5.3743005340_wp
1819	PEN100 = 8.9085217499_wp
1820	PEN200 = -1.1090683384e+01_wp
1821	PEN300 = 8.3754581690_wp
1822	PEN400 = -2.0601115202_wp
1823	PEN010 = 7.9263222935_wp
1824	PEN110 = 3.8319691761e-01_wp
1825	PEN210 = -2.0572313651_wp
1826	PEN310 = 3.3477938724e-01_wp
1827	PEN020 = -4.9997430930_wp
1828	PEN120 = 9.7335338937e-02_wp
1829	PEN220 = 6.0887771651e-01_wp
1830	PEN030 = 1.7433051009_wp
1831	PEN130 = -1.1114577810e-01_wp
1832	PEN040 = -2.9751504321e-01_wp
1833	PEN001 = -6.9171176978e-01_wp
1834	PEN101 = 2.2832980419_wp
1835	PEN201 = -1.3694684286_wp
1836	PEN011 = -1.4557549876_wp
1837	PEN111 = 2.2969116213e-01_wp
1838	PEN021 = 8.3654420645e-01_wp
1839	PEN002 = -1.4046808820e-02_wp
1840	PEN102 = 4.2928871430e-02_wp
1841	PEN012 = -2.8729602515e-01_wp
1842	!
1843	APE000 = -1.9815805734e-01_wp
1844	APE100 = -9.5799229402e-03_wp
1845	APE200 = 5.1430784127e-02_wp
1846	APE300 = -8.3694846809e-03_wp
1847	APE010 = 2.4998715465e-01_wp
1848	APE110 = -4.8667669469e-03_wp
1849	APE210 = -3.0443885826e-02_wp
1850	APE020 = -1.3074788257e-01_wp
1851	APE120 = 8.3359333577e-03_wp
1852	APE030 = 2.9751504321e-02_wp
1853	APE001 = 3.6393874690e-02_wp
1854	APE101 = -5.7422790533e-03_wp
1855	APE011 = -4.1827210323e-02_wp
1856	APE002 = 7.1824006288e-03_wp
1857	!
1858	BPE000 = 1.1135652187e-01_wp
1859	BPE100 = -2.7726708459e-01_wp
1860	BPE200 = 3.1407968134e-01_wp
1861	BPE300 = -1.0300557601e-01_wp
1862	BPE010 = 4.7899614701e-03_wp
1863	BPE110 = -5.1430784127e-02_wp
1864	BPE210 = 1.2554227021e-02_wp
1865	BPE020 = 1.2166917367e-03_wp
1866	BPE120 = 1.5221942913e-02_wp
1867	BPE030 = -1.3893222263e-03_wp
1868	BPE001 = 2.8541225524e-02_wp
1869	BPE101 = -3.4236710714e-02_wp
1870	BPE011 = 2.8711395266e-03_wp
1871	BPE002 = 5.3661089288e-04_wp
1872	!
1873	CASE( np_seos ) !== Simplified EOS ==!
1874
1875	r1_S0 = 0.875_wp/35.16504_wp ! Used to convert CT in potential temperature when using bulk formulae (eos_pt_from_ct)
1876
1877	IF(lwp) THEN
1878	WRITE(numout,*)
1879	WRITE(numout,*) ' ==>>> use of simplified eos: '
1880	WRITE(numout,) ' rhd(dT=T-10,dS=S-35,Z) = [-a0(1+lambda1/2dT+mu1Z)*dT '
1881	WRITE(numout,) ' + b0(1+lambda2/2dT+mu2Z)dS - nudT*dS] / rho0'
1882	WRITE(numout,*) ' with the following coefficients :'
1883	WRITE(numout,*) ' thermal exp. coef. rn_a0 = ', rn_a0
1884	WRITE(numout,*) ' saline cont. coef. rn_b0 = ', rn_b0
1885	WRITE(numout,*) ' cabbeling coef. rn_lambda1 = ', rn_lambda1
1886	WRITE(numout,*) ' cabbeling coef. rn_lambda2 = ', rn_lambda2
1887	WRITE(numout,*) ' thermobar. coef. rn_mu1 = ', rn_mu1
1888	WRITE(numout,*) ' thermobar. coef. rn_mu2 = ', rn_mu2
1889	WRITE(numout,*) ' 2nd cabbel. coef. rn_nu = ', rn_nu
1890	WRITE(numout,*) ' Caution: rn_beta0=0 incompatible with ddm parameterization '
1891	ENDIF
1892	l_useCT = .TRUE. ! Use conservative temperature
1893	!
1894	CASE( np_leos ) !== Linear ISOMIP EOS ==!
1895
1896	r1_S0 = 0.875_wp/35.16504_wp ! Used to convert CT in potential temperature when using bulk formulae (eos_pt_from_ct)
1897
1898	IF(lwp) THEN
1899	WRITE(numout,*)
1900	WRITE(numout,*) ' use of linear ISOMIP eos: rhd(dT=T-(-1),dS=S-(34.2),Z) = '
1901	WRITE(numout,) ' [ -a0dT + b0*dS ]/rho0'
1902	WRITE(numout,*)
1903	WRITE(numout,*) ' thermal exp. coef. rn_a0 = ', rn_a0
1904	WRITE(numout,*) ' saline cont. coef. rn_b0 = ', rn_b0
1905	ENDIF
1906	l_useCT = .TRUE. ! Use conservative temperature
1907	!
1908	CASE DEFAULT !== ERROR in neos ==!
1909	WRITE(ctmp1,*) ' bad flag value for neos = ', neos, '. You should never see this error'
1910	CALL ctl_stop( ctmp1 )
1911	!
1912	END SELECT
1913	!
1914	rho0_rcp = rho0 * rcp
1915	r1_rho0 = 1._wp / rho0
1916	r1_rcp = 1._wp / rcp
1917	r1_rho0_rcp = 1._wp / rho0_rcp
1918	!
1919	IF(lwp) THEN
1920	IF( l_useCT ) THEN
1921	WRITE(numout,*)
1922	WRITE(numout,*) ' ==>>> model uses Conservative Temperature'
1923	WRITE(numout,*) ' Important: model must be initialized with CT and SA fields'
1924	ELSE
1925	WRITE(numout,*)
1926	WRITE(numout,*) ' ==>>> model does not use Conservative Temperature'
1927	ENDIF
1928	ENDIF
1929	!
1930	IF(lwp) WRITE(numout,*)
1931	IF(lwp) WRITE(numout,*) ' Associated physical constant'
1932	IF(lwp) WRITE(numout,*) ' volumic mass of reference rho0 = ', rho0 , ' kg/m^3'
1933	IF(lwp) WRITE(numout,*) ' 1. / rho0 r1_rho0 = ', r1_rho0, ' m^3/kg'
1934	IF(lwp) WRITE(numout,*) ' ocean specific heat rcp = ', rcp , ' J/Kelvin'
1935	IF(lwp) WRITE(numout,) ' rho0 rcp rho0_rcp = ', rho0_rcp
1936	IF(lwp) WRITE(numout,) ' 1. / ( rho0 rcp ) r1_rho0_rcp = ', r1_rho0_rcp
1937	!
1938	END SUBROUTINE eos_init
1939
1940	!!======================================================================
1941	END MODULE eosbn2

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