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eosbn2.F90 in NEMO/branches/2021/dev_r14116_HPC-10_mcastril_Mixed_Precision_implementation/src/OCE/TRA – NEMO

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source: NEMO/branches/2021/dev_r14116_HPC-10_mcastril_Mixed_Precision_implementation/src/OCE/TRA/eosbn2.F90 @ 15066

Last change on this file since 15066 was 15066, checked in by sparonuz, 3 years ago
Added interface in eosbn2.F90 to ease the weight of casts necessary in mixed precision + Removed unnecessary casts
Property svn:keywords set to `Id`
File size: 101.0 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_wp, eos_insitu_pot_wp, eos_insitu_2d, eos_insitu_pot_2d
59	MODULE PROCEDURE eos_insitu_mixed, eos_insitu_pot_mixed
60	END INTERFACE
61	!
62	INTERFACE eos_rab
63	MODULE PROCEDURE rab_3d_wp, rab_2d, rab_0d
64	MODULE PROCEDURE rab_3d_mixed
65	END INTERFACE
66	!
67	INTERFACE eos_fzp
68	MODULE PROCEDURE eos_fzp_2d, eos_fzp_0d
69	END INTERFACE
70	!
71	PUBLIC eos ! called by step, istate, tranpc and zpsgrd modules
72	PUBLIC bn2 ! called by step module
73	PUBLIC eos_rab ! called by ldfslp, zdfddm, trabbl
74	PUBLIC eos_pt_from_ct ! called by sbcssm
75	PUBLIC eos_fzp ! called by traadv_cen2 and sbcice_... modules
76	PUBLIC eos_pen ! used for pe diagnostics in trdpen module
77	PUBLIC eos_init ! called by istate module
78
79	! !! Namelist nameos
80	LOGICAL , PUBLIC :: ln_TEOS10
81	LOGICAL , PUBLIC :: ln_EOS80
82	LOGICAL , PUBLIC :: ln_SEOS
83
84	! Parameters
85	LOGICAL , PUBLIC :: l_useCT ! =T in ln_TEOS10=T (i.e. use eos_pt_from_ct to compute sst_m), =F otherwise
86	INTEGER , PUBLIC :: neos ! Identifier for equation of state used
87
88	INTEGER , PARAMETER :: np_teos10 = -1 ! parameter for using TEOS10
89	INTEGER , PARAMETER :: np_eos80 = 0 ! parameter for using EOS80
90	INTEGER , PARAMETER :: np_seos = 1 ! parameter for using Simplified Equation of state
91
92	! !!! simplified eos coefficients (default value: Vallis 2006)
93	REAL(wp), PUBLIC :: rn_a0 = 1.6550e-1_wp ! thermal expansion coeff.
94	REAL(wp), PUBLIC :: 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	# include "single_precision_substitute.h90"
187	!!----------------------------------------------------------------------
188	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
189	!! $Id$
190	!! Software governed by the CeCILL license (see ./LICENSE)
191	!!----------------------------------------------------------------------
192	CONTAINS
193
194	SUBROUTINE eos_insitu_wp( pts, prd, pdep )
195	!!
196	REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
197	! ! 2 : salinity [psu]
198	REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: prd ! in situ density [-]
199	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pdep ! depth [m]
200	!!
201	CALL eos_insitu_t_wp( pts, is_tile(pts), prd, is_tile(prd), pdep, is_tile(pdep) )
202	END SUBROUTINE eos_insitu_wp
203
204	SUBROUTINE eos_insitu_mixed( pts, prd, pdep )
205	!!
206	REAL(dp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
207	! ! 2 : salinity [psu]
208	REAL(sp), DIMENSION(:,:,:) , INTENT( out) :: prd ! in situ density [-]
209	REAL(sp), DIMENSION(:,:,:) , INTENT(in ) :: pdep ! depth [m]
210	!!
211	CALL eos_insitu_t_mixed( pts, is_tile(pts), prd, is_tile(prd), pdep, is_tile(pdep) )
212	END SUBROUTINE
213
214	SUBROUTINE eos_insitu_t_wp( pts, ktts, prd, ktrd, pdep, ktdep )
215	!!----------------------------------------------------------------------
216	!! *** ROUTINE
217	!!
218	!! ** Purpose : Compute the in situ density (ratio rho/rho0) from
219	!! potential temperature and salinity using an equation of state
220	!! selected in the nameos namelist
221	!!
222	!! ** Method : prd(t,s,z) = ( rho(t,s,z) - rho0 ) / rho0
223	!! with prd in situ density anomaly no units
224	!! t TEOS10: CT or EOS80: PT Celsius
225	!! s TEOS10: SA or EOS80: SP TEOS10: g/kg or EOS80: psu
226	!! z depth meters
227	!! rho in situ density kg/m^3
228	!! rho0 reference density kg/m^3
229	!!
230	!! ln_teos10 : polynomial TEOS-10 equation of state is used for rho(t,s,z).
231	!! Check value: rho = 1028.21993233072 kg/m^3 for z=3000 dbar, ct=3 Celsius, sa=35.5 g/kg
232	!!
233	!! ln_eos80 : polynomial EOS-80 equation of state is used for rho(t,s,z).
234	!! Check value: rho = 1028.35011066567 kg/m^3 for z=3000 dbar, pt=3 Celsius, sp=35.5 psu
235	!!
236	!! ln_seos : simplified equation of state
237	!! prd(t,s,z) = ( -a0(1+lambda/2(T-T0)+muz+nu(S-S0))(T-T0) + b0(S-S0) ) / rho0
238	!! linear case function of T only: rn_alpha<>0, other coefficients = 0
239	!! linear eos function of T and S: rn_alpha and rn_beta<>0, other coefficients=0
240	!! Vallis like equation: use default values of coefficients
241	!!
242	!! ** Action : compute prd , the in situ density (no units)
243	!!
244	!! References : Roquet et al, Ocean Modelling, in preparation (2014)
245	!! Vallis, Atmospheric and Oceanic Fluid Dynamics, 2006
246	!! TEOS-10 Manual, 2010
247	!!----------------------------------------------------------------------
248	INTEGER , INTENT(in ) :: ktts, ktrd, ktdep
249	REAL(wp), DIMENSION(A2D_T(ktts) ,JPK,JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
250	! ! 2 : salinity [psu]
251	REAL(wp), DIMENSION(A2D_T(ktrd) ,JPK ), INTENT( out) :: prd ! in situ density [-]
252	REAL(wp), DIMENSION(A2D_T(ktdep),JPK ), INTENT(in ) :: pdep ! depth [m]
253	!
254	INTEGER :: ji, jj, jk ! dummy loop indices
255	REAL(wp) :: zt , zh , zs , ztm ! local scalars
256	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
257	!!----------------------------------------------------------------------
258	!
259	IF( ln_timing ) CALL timing_start('eos-insitu')
260	!
261	SELECT CASE( neos )
262	!
263	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
264	!
265	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
266	!
267	zh = pdep(ji,jj,jk) * r1_Z0 ! depth
268	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
269	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
270	ztm = tmask(ji,jj,jk) ! tmask
271	!
272	zn3 = EOS013*zt &
273	& + EOS103*zs+EOS003
274	!
275	zn2 = (EOS022*zt &
276	& + EOS112zs+EOS012)zt &
277	& + (EOS202zs+EOS102)zs+EOS002
278	!
279	zn1 = (((EOS041*zt &
280	& + EOS131zs+EOS031)zt &
281	& + (EOS221zs+EOS121)zs+EOS021)*zt &
282	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
283	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
284	!
285	zn0 = (((((EOS060*zt &
286	& + EOS150zs+EOS050)zt &
287	& + (EOS240zs+EOS140)zs+EOS040)*zt &
288	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
289	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
290	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
291	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
292	!
293	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
294	!
295	prd(ji,jj,jk) = ( zn * r1_rho0 - 1._wp ) * ztm ! density anomaly (masked)
296	!
297	END_3D
298	!
299	CASE( np_seos ) !== simplified EOS ==!
300	!
301	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
302	zt = pts (ji,jj,jk,jp_tem) - 10._wp
303	zs = pts (ji,jj,jk,jp_sal) - 35._wp
304	zh = pdep (ji,jj,jk)
305	ztm = tmask(ji,jj,jk)
306	!
307	zn = - rn_a0 * ( 1._wp + 0.5_wprn_lambda1zt + rn_mu1zh ) zt &
308	& + rn_b0 * ( 1._wp - 0.5_wprn_lambda2zs - rn_mu2zh ) zs &
309	& - rn_nu * zt * zs
310	!
311	prd(ji,jj,jk) = zn * r1_rho0 * ztm ! density anomaly (masked)
312	END_3D
313	!
314	END SELECT
315	!
316	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-insitu : ', kdim=jpk )
317	!
318	IF( ln_timing ) CALL timing_stop('eos-insitu')
319	!
320	END SUBROUTINE eos_insitu_t_wp
321	SUBROUTINE eos_insitu_t_mixed( pts, ktts, prd, ktrd, pdep, ktdep )
322	!!----------------------------------------------------------------------
323	!! * ROUTINE eos_insitu *
324	!!
325	!! ** Purpose : Compute the in situ density (ratio rho/rho0) from
326	!! potential temperature and salinity using an equation of state
327	!! selected in the nameos namelist
328	!!
329	!! ** Method : prd(t,s,z) = ( rho(t,s,z) - rho0 ) / rho0
330	!! with prd in situ density anomaly no units
331	!! t TEOS10: CT or EOS80: PT Celsius
332	!! s TEOS10: SA or EOS80: SP TEOS10: g/kg or EOS80: psu
333	!! z depth meters
334	!! rho in situ density kg/m^3
335	!! rho0 reference density kg/m^3
336	!!
337	!! ln_teos10 : polynomial TEOS-10 equation of state is used for rho(t,s,z).
338	!! Check value: rho = 1028.21993233072 kg/m^3 for z=3000 dbar, ct=3 Celsius, sa=35.5 g/kg
339	!!
340	!! ln_eos80 : polynomial EOS-80 equation of state is used for rho(t,s,z).
341	!! Check value: rho = 1028.35011066567 kg/m^3 for z=3000 dbar, pt=3 Celsius, sp=35.5 psu
342	!!
343	!! ln_seos : simplified equation of state
344	!! prd(t,s,z) = ( -a0(1+lambda/2(T-T0)+muz+nu(S-S0))(T-T0) + b0(S-S0) ) / rho0
345	!! linear case function of T only: rn_alpha<>0, other coefficients = 0
346	!! linear eos function of T and S: rn_alpha and rn_beta<>0, other coefficients=0
347	!! Vallis like equation: use default values of coefficients
348	!!
349	!! ** Action : compute prd , the in situ density (no units)
350	!!
351	!! References : Roquet et al, Ocean Modelling, in preparation (2014)
352	!! Vallis, Atmospheric and Oceanic Fluid Dynamics, 2006
353	!! TEOS-10 Manual, 2010
354	!!----------------------------------------------------------------------
355	INTEGER , INTENT(in ) :: ktts, ktrd, ktdep
356	REAL(dp), DIMENSION(A2D_T(ktts) ,JPK,JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
357	! ! 2 : salinity [psu]
358	REAL(sp), DIMENSION(A2D_T(ktrd) ,JPK ), INTENT( out) :: prd ! in situ density [-]
359	REAL(sp), DIMENSION(A2D_T(ktdep),JPK ), INTENT(in ) :: pdep ! depth [m]
360	!
361	INTEGER :: ji, jj, jk ! dummy loop indices
362	REAL(sp) :: zt , zh , zs , ztm ! local scalars
363	REAL(sp) :: zn , zn0, zn1, zn2, zn3 ! - -
364	!!----------------------------------------------------------------------
365	!
366	IF( ln_timing ) CALL timing_start('eos-insitu')
367	!
368	SELECT CASE( neos )
369	!
370	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
371	!
372	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
373	!
374	zh = pdep(ji,jj,jk) * r1_Z0 ! depth
375	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
376	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
377	ztm = tmask(ji,jj,jk) ! tmask
378	!
379	zn3 = EOS013*zt &
380	& + EOS103*zs+EOS003
381	!
382	zn2 = (EOS022*zt &
383	& + EOS112zs+EOS012)zt &
384	& + (EOS202zs+EOS102)zs+EOS002
385	!
386	zn1 = (((EOS041*zt &
387	& + EOS131zs+EOS031)zt &
388	& + (EOS221zs+EOS121)zs+EOS021)*zt &
389	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
390	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
391	!
392	zn0 = (((((EOS060*zt &
393	& + EOS150zs+EOS050)zt &
394	& + (EOS240zs+EOS140)zs+EOS040)*zt &
395	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
396	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
397	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
398	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
399	!
400	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
401	!
402	prd(ji,jj,jk) = ( zn * r1_rho0 - 1._wp ) * ztm ! density anomaly (masked)
403	!
404	END_3D
405	!
406	CASE( np_seos ) !== simplified EOS ==!
407	!
408	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
409	zt = pts (ji,jj,jk,jp_tem) - 10._wp
410	zs = pts (ji,jj,jk,jp_sal) - 35._wp
411	zh = pdep (ji,jj,jk)
412	ztm = tmask(ji,jj,jk)
413	!
414	zn = - rn_a0 * ( 1._wp + 0.5_wprn_lambda1zt + rn_mu1zh ) zt &
415	& + rn_b0 * ( 1._wp - 0.5_wprn_lambda2zs - rn_mu2zh ) zs &
416	& - rn_nu * zt * zs
417	!
418	prd(ji,jj,jk) = zn * r1_rho0 * ztm ! density anomaly (masked)
419	END_3D
420	!
421	END SELECT
422	!
423	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=REAL(prd, wp), clinfo1=' eos-insitu : ', kdim=jpk )
424	!
425	IF( ln_timing ) CALL timing_stop('eos-insitu')
426	!
427	END SUBROUTINE eos_insitu_t_mixed
428
429
430	SUBROUTINE eos_insitu_pot_wp( pts, prd, prhop, pdep )
431	!!
432	REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
433	! ! 2 : salinity [psu]
434	REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: prd ! in situ density [-]
435	REAL(dp), DIMENSION(:,:,:) , INTENT( out) :: prhop ! potential density (surface referenced)
436	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pdep ! depth [m]
437	!!
438	CALL eos_insitu_pot_t_wp( pts, is_tile(pts), prd, is_tile(prd), prhop, is_tile(prhop), pdep, is_tile(pdep) )
439	END SUBROUTINE eos_insitu_pot_wp
440
441	SUBROUTINE eos_insitu_pot_mixed( pts, prd, prhop, pdep )
442	!!
443	REAL(dp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
444	! ! 2 : salinity [psu]
445	REAL(sp), DIMENSION(:,:,:) , INTENT( out) :: prd ! in situ density [-]
446	REAL(dp), DIMENSION(:,:,:) , INTENT( out) :: prhop ! potential density (surface referenced)
447	REAL(sp), DIMENSION(:,:,:) , INTENT(in ) :: pdep ! depth [m]
448	!!
449	CALL eos_insitu_pot_t_mixed( pts, is_tile(pts), prd, is_tile(prd), prhop, is_tile(prhop), pdep, is_tile(pdep) )
450	END SUBROUTINE eos_insitu_pot_mixed
451
452
453	SUBROUTINE eos_insitu_pot_t_wp( pts, ktts, prd, ktrd, prhop, ktrhop, pdep, ktdep )
454	!!----------------------------------------------------------------------
455	!! * ROUTINE eos_insitu_pot *
456	!!
457	!! ** Purpose : Compute the in situ density (ratio rho/rho0) and the
458	!! potential volumic mass (Kg/m3) from potential temperature and
459	!! salinity fields using an equation of state selected in the
460	!! namelist.
461	!!
462	!! ** Action : - prd , the in situ density (no units)
463	!! - prhop, the potential volumic mass (Kg/m3)
464	!!
465	!!----------------------------------------------------------------------
466	INTEGER , INTENT(in ) :: ktts, ktrd, ktrhop, ktdep
467	REAL(wp), DIMENSION(A2D_T(ktts) ,JPK,JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
468	! ! 2 : salinity [psu]
469	REAL(wp), DIMENSION(A2D_T(ktrd) ,JPK ), INTENT( out) :: prd ! in situ density [-]
470	REAL(dp), DIMENSION(A2D_T(ktrhop),JPK ), INTENT( out) :: prhop ! potential density (surface referenced)
471	REAL(wp), DIMENSION(A2D_T(ktdep) ,JPK ), INTENT(in ) :: pdep ! depth [m]
472	!
473	INTEGER :: ji, jj, jk, jsmp ! dummy loop indices
474	INTEGER :: jdof
475	REAL(wp) :: zt , zh , zstemp, zs , ztm ! local scalars
476	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
477	REAL(wp), DIMENSION(:), ALLOCATABLE :: zn0_sto, zn_sto, zsign ! local vectors
478	!!----------------------------------------------------------------------
479	!
480	IF( ln_timing ) CALL timing_start('eos-pot')
481	!
482	SELECT CASE ( neos )
483	!
484	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
485	!
486	! Stochastic equation of state
487	IF ( ln_sto_eos ) THEN
488	ALLOCATE(zn0_sto(1:2*nn_sto_eos))
489	ALLOCATE(zn_sto(1:2*nn_sto_eos))
490	ALLOCATE(zsign(1:2*nn_sto_eos))
491	DO jsmp = 1, 2*nn_sto_eos, 2
492	zsign(jsmp) = 1._wp
493	zsign(jsmp+1) = -1._wp
494	END DO
495	!
496	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
497	!
498	! compute density (2*nn_sto_eos) times:
499	! (1) for t+dt, s+ds (with the random TS fluctutation computed in sto_pts)
500	! (2) for t-dt, s-ds (with the opposite fluctuation)
501	DO jsmp = 1, nn_sto_eos*2
502	jdof = (jsmp + 1) / 2
503	zh = pdep(ji,jj,jk) * r1_Z0 ! depth
504	zt = (pts (ji,jj,jk,jp_tem) + pts_ran(ji,jj,jk,jp_tem,jdof) * zsign(jsmp)) * r1_T0 ! temperature
505	zstemp = pts (ji,jj,jk,jp_sal) + pts_ran(ji,jj,jk,jp_sal,jdof) * zsign(jsmp)
506	zs = SQRT( ABS( zstemp + rdeltaS ) * r1_S0 ) ! square root salinity
507	ztm = tmask(ji,jj,jk) ! tmask
508	!
509	zn3 = EOS013*zt &
510	& + EOS103*zs+EOS003
511	!
512	zn2 = (EOS022*zt &
513	& + EOS112zs+EOS012)zt &
514	& + (EOS202zs+EOS102)zs+EOS002
515	!
516	zn1 = (((EOS041*zt &
517	& + EOS131zs+EOS031)zt &
518	& + (EOS221zs+EOS121)zs+EOS021)*zt &
519	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
520	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
521	!
522	zn0_sto(jsmp) = (((((EOS060*zt &
523	& + EOS150zs+EOS050)zt &
524	& + (EOS240zs+EOS140)zs+EOS040)*zt &
525	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
526	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
527	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
528	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
529	!
530	zn_sto(jsmp) = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0_sto(jsmp)
531	END DO
532	!
533	! compute stochastic density as the mean of the (2*nn_sto_eos) densities
534	prhop(ji,jj,jk) = 0._wp ; prd(ji,jj,jk) = 0._wp
535	DO jsmp = 1, nn_sto_eos*2
536	prhop(ji,jj,jk) = prhop(ji,jj,jk) + zn0_sto(jsmp) ! potential density referenced at the surface
537	!
538	prd(ji,jj,jk) = prd(ji,jj,jk) + ( zn_sto(jsmp) * r1_rho0 - 1._wp ) ! density anomaly (masked)
539	END DO
540	prhop(ji,jj,jk) = 0.5_wp * prhop(ji,jj,jk) * ztm / nn_sto_eos
541	prd (ji,jj,jk) = 0.5_wp * prd (ji,jj,jk) * ztm / nn_sto_eos
542	END_3D
543	DEALLOCATE(zn0_sto,zn_sto,zsign)
544	! Non-stochastic equation of state
545	ELSE
546	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
547	!
548	zh = pdep(ji,jj,jk) * r1_Z0 ! depth
549	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
550	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
551	ztm = tmask(ji,jj,jk) ! tmask
552	!
553	zn3 = EOS013*zt &
554	& + EOS103*zs+EOS003
555	!
556	zn2 = (EOS022*zt &
557	& + EOS112zs+EOS012)zt &
558	& + (EOS202zs+EOS102)zs+EOS002
559	!
560	zn1 = (((EOS041*zt &
561	& + EOS131zs+EOS031)zt &
562	& + (EOS221zs+EOS121)zs+EOS021)*zt &
563	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
564	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
565	!
566	zn0 = (((((EOS060*zt &
567	& + EOS150zs+EOS050)zt &
568	& + (EOS240zs+EOS140)zs+EOS040)*zt &
569	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
570	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
571	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
572	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
573	!
574	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
575	!
576	prhop(ji,jj,jk) = zn0 * ztm ! potential density referenced at the surface
577	!
578	prd(ji,jj,jk) = ( zn * r1_rho0 - 1._wp ) * ztm ! density anomaly (masked)
579	END_3D
580	ENDIF
581
582	CASE( np_seos ) !== simplified EOS ==!
583	!
584	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
585	zt = pts (ji,jj,jk,jp_tem) - 10._wp
586	zs = pts (ji,jj,jk,jp_sal) - 35._wp
587	zh = pdep (ji,jj,jk)
588	ztm = tmask(ji,jj,jk)
589	! ! potential density referenced at the surface
590	zn = - rn_a0 * ( 1._wp + 0.5_wprn_lambda1zt ) * zt &
591	& + rn_b0 * ( 1._wp - 0.5_wprn_lambda2zs ) * zs &
592	& - rn_nu * zt * zs
593	prhop(ji,jj,jk) = ( rho0 + zn ) * ztm
594	! ! density anomaly (masked)
595	zn = zn - ( rn_a0 * rn_mu1 * zt + rn_b0 * rn_mu2 * zs ) * zh
596	prd(ji,jj,jk) = zn * r1_rho0 * ztm
597	!
598	END_3D
599	!
600	END SELECT
601	!
602	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-pot: ', &
603	& tab3d_2=CASTWP(prhop), clinfo2=' pot : ', kdim=jpk )
604	!
605	IF( ln_timing ) CALL timing_stop('eos-pot')
606	!
607	END SUBROUTINE eos_insitu_pot_t_wp
608
609	SUBROUTINE eos_insitu_pot_t_mixed( pts, ktts, prd, ktrd, prhop, ktrhop, pdep, ktdep )
610	!!----------------------------------------------------------------------
611	!! * ROUTINE eos_insitu_pot *
612	!!
613	!! ** Purpose : Compute the in situ density (ratio rho/rho0) and the
614	!! potential volumic mass (Kg/m3) from potential temperature and
615	!! salinity fields using an equation of state selected in the
616	!! namelist.
617	!!
618	!! ** Action : - prd , the in situ density (no units)
619	!! - prhop, the potential volumic mass (Kg/m3)
620	!!
621	!!----------------------------------------------------------------------
622	INTEGER , INTENT(in ) :: ktts, ktrd, ktrhop, ktdep
623	REAL(dp), DIMENSION(A2D_T(ktts) ,JPK,JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
624	! ! 2 : salinity [psu]
625	REAL(sp), DIMENSION(A2D_T(ktrd) ,JPK ), INTENT( out) :: prd ! in situ density [-]
626	REAL(dp), DIMENSION(A2D_T(ktrhop),JPK ), INTENT( out) :: prhop ! potential density (surface referenced)
627	REAL(sp), DIMENSION(A2D_T(ktdep) ,JPK ), INTENT(in ) :: pdep ! depth [m]
628	!
629	INTEGER :: ji, jj, jk, jsmp ! dummy loop indices
630	INTEGER :: jdof
631	REAL(wp) :: zt , zh , zstemp, zs , ztm ! local scalars
632	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
633	REAL(wp), DIMENSION(:), ALLOCATABLE :: zn0_sto, zn_sto, zsign ! local vectors
634	!!----------------------------------------------------------------------
635	!
636	IF( ln_timing ) CALL timing_start('eos-pot')
637	!
638	SELECT CASE ( neos )
639	!
640	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
641	!
642	! Stochastic equation of state
643	IF ( ln_sto_eos ) THEN
644	ALLOCATE(zn0_sto(1:2*nn_sto_eos))
645	ALLOCATE(zn_sto(1:2*nn_sto_eos))
646	ALLOCATE(zsign(1:2*nn_sto_eos))
647	DO jsmp = 1, 2*nn_sto_eos, 2
648	zsign(jsmp) = 1._wp
649	zsign(jsmp+1) = -1._wp
650	END DO
651	!
652	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
653	!
654	! compute density (2*nn_sto_eos) times:
655	! (1) for t+dt, s+ds (with the random TS fluctutation computed in sto_pts)
656	! (2) for t-dt, s-ds (with the opposite fluctuation)
657	DO jsmp = 1, nn_sto_eos*2
658	jdof = (jsmp + 1) / 2
659	zh = pdep(ji,jj,jk) * r1_Z0 ! depth
660	zt = (pts (ji,jj,jk,jp_tem) + pts_ran(ji,jj,jk,jp_tem,jdof) * zsign(jsmp)) * r1_T0 ! temperature
661	zstemp = pts (ji,jj,jk,jp_sal) + pts_ran(ji,jj,jk,jp_sal,jdof) * zsign(jsmp)
662	zs = SQRT( ABS( zstemp + rdeltaS ) * r1_S0 ) ! square root salinity
663	ztm = tmask(ji,jj,jk) ! tmask
664	!
665	zn3 = EOS013*zt &
666	& + EOS103*zs+EOS003
667	!
668	zn2 = (EOS022*zt &
669	& + EOS112zs+EOS012)zt &
670	& + (EOS202zs+EOS102)zs+EOS002
671	!
672	zn1 = (((EOS041*zt &
673	& + EOS131zs+EOS031)zt &
674	& + (EOS221zs+EOS121)zs+EOS021)*zt &
675	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
676	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
677	!
678	zn0_sto(jsmp) = (((((EOS060*zt &
679	& + EOS150zs+EOS050)zt &
680	& + (EOS240zs+EOS140)zs+EOS040)*zt &
681	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
682	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
683	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
684	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
685	!
686	zn_sto(jsmp) = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0_sto(jsmp)
687	END DO
688	!
689	! compute stochastic density as the mean of the (2*nn_sto_eos) densities
690	prhop(ji,jj,jk) = 0._wp ; prd(ji,jj,jk) = 0._wp
691	DO jsmp = 1, nn_sto_eos*2
692	prhop(ji,jj,jk) = prhop(ji,jj,jk) + zn0_sto(jsmp) ! potential density referenced at the surface
693	!
694	prd(ji,jj,jk) = prd(ji,jj,jk) + ( zn_sto(jsmp) * r1_rho0 - 1._wp ) ! density anomaly (masked)
695	END DO
696	prhop(ji,jj,jk) = 0.5_wp * prhop(ji,jj,jk) * ztm / nn_sto_eos
697	prd (ji,jj,jk) = 0.5_wp * prd (ji,jj,jk) * ztm / nn_sto_eos
698	END_3D
699	DEALLOCATE(zn0_sto,zn_sto,zsign)
700	! Non-stochastic equation of state
701	ELSE
702	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
703	!
704	zh = pdep(ji,jj,jk) * r1_Z0 ! depth
705	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
706	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
707	ztm = tmask(ji,jj,jk) ! tmask
708	!
709	zn3 = EOS013*zt &
710	& + EOS103*zs+EOS003
711	!
712	zn2 = (EOS022*zt &
713	& + EOS112zs+EOS012)zt &
714	& + (EOS202zs+EOS102)zs+EOS002
715	!
716	zn1 = (((EOS041*zt &
717	& + EOS131zs+EOS031)zt &
718	& + (EOS221zs+EOS121)zs+EOS021)*zt &
719	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
720	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
721	!
722	zn0 = (((((EOS060*zt &
723	& + EOS150zs+EOS050)zt &
724	& + (EOS240zs+EOS140)zs+EOS040)*zt &
725	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
726	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
727	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
728	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
729	!
730	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
731	!
732	prhop(ji,jj,jk) = zn0 * ztm ! potential density referenced at the surface
733	!
734	prd(ji,jj,jk) = ( zn * r1_rho0 - 1._wp ) * ztm ! density anomaly (masked)
735	END_3D
736	ENDIF
737
738	CASE( np_seos ) !== simplified EOS ==!
739	!
740	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
741	zt = pts (ji,jj,jk,jp_tem) - 10._wp
742	zs = pts (ji,jj,jk,jp_sal) - 35._wp
743	zh = pdep (ji,jj,jk)
744	ztm = tmask(ji,jj,jk)
745	! ! potential density referenced at the surface
746	zn = - rn_a0 * ( 1._wp + 0.5_wprn_lambda1zt ) * zt &
747	& + rn_b0 * ( 1._wp - 0.5_wprn_lambda2zs ) * zs &
748	& - rn_nu * zt * zs
749	prhop(ji,jj,jk) = ( rho0 + zn ) * ztm
750	! ! density anomaly (masked)
751	zn = zn - ( rn_a0 * rn_mu1 * zt + rn_b0 * rn_mu2 * zs ) * zh
752	prd(ji,jj,jk) = zn * r1_rho0 * ztm
753	!
754	END_3D
755	!
756	END SELECT
757	!
758	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=REAL(prd, wp), clinfo1=' eos-pot: ', &
759	& tab3d_2=REAL(prhop, wp), clinfo2=' pot : ', kdim=jpk )
760	!
761	IF( ln_timing ) CALL timing_stop('eos-pot')
762	!
763	END SUBROUTINE eos_insitu_pot_t_mixed
764
765
766	SUBROUTINE eos_insitu_2d( pts, pdep, prd )
767	!!
768	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
769	! ! 2 : salinity [psu]
770	REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pdep ! depth [m]
771	REAL(wp), DIMENSION(:,:) , INTENT( out) :: prd ! in situ density
772	!!
773	CALL eos_insitu_2d_t( pts, is_tile(pts), pdep, is_tile(pdep), prd, is_tile(prd) )
774	END SUBROUTINE eos_insitu_2d
775
776
777	SUBROUTINE eos_insitu_2d_t( pts, ktts, pdep, ktdep, prd, ktrd )
778	!!----------------------------------------------------------------------
779	!! * ROUTINE eos_insitu_2d *
780	!!
781	!! ** Purpose : Compute the in situ density (ratio rho/rho0) from
782	!! potential temperature and salinity using an equation of state
783	!! selected in the nameos namelist. * 2D field case
784	!!
785	!! ** Action : - prd , the in situ density (no units) (unmasked)
786	!!
787	!!----------------------------------------------------------------------
788	INTEGER , INTENT(in ) :: ktts, ktdep, ktrd
789	REAL(wp), DIMENSION(A2D_T(ktts),JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
790	! ! 2 : salinity [psu]
791	REAL(wp), DIMENSION(A2D_T(ktdep) ), INTENT(in ) :: pdep ! depth [m]
792	REAL(wp), DIMENSION(A2D_T(ktrd) ), INTENT( out) :: prd ! in situ density
793	!
794	INTEGER :: ji, jj, jk ! dummy loop indices
795	REAL(wp) :: zt , zh , zs ! local scalars
796	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
797	!!----------------------------------------------------------------------
798	!
799	IF( ln_timing ) CALL timing_start('eos2d')
800	!
801	prd(:,:) = 0._wp
802	!
803	SELECT CASE( neos )
804	!
805	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
806	!
807	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
808	!
809	zh = pdep(ji,jj) * r1_Z0 ! depth
810	zt = pts (ji,jj,jp_tem) * r1_T0 ! temperature
811	zs = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
812	!
813	zn3 = EOS013*zt &
814	& + EOS103*zs+EOS003
815	!
816	zn2 = (EOS022*zt &
817	& + EOS112zs+EOS012)zt &
818	& + (EOS202zs+EOS102)zs+EOS002
819	!
820	zn1 = (((EOS041*zt &
821	& + EOS131zs+EOS031)zt &
822	& + (EOS221zs+EOS121)zs+EOS021)*zt &
823	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
824	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
825	!
826	zn0 = (((((EOS060*zt &
827	& + EOS150zs+EOS050)zt &
828	& + (EOS240zs+EOS140)zs+EOS040)*zt &
829	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
830	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
831	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
832	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
833	!
834	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
835	!
836	prd(ji,jj) = zn * r1_rho0 - 1._wp ! unmasked in situ density anomaly
837	!
838	END_2D
839	!
840	CASE( np_seos ) !== simplified EOS ==!
841	!
842	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
843	!
844	zt = pts (ji,jj,jp_tem) - 10._wp
845	zs = pts (ji,jj,jp_sal) - 35._wp
846	zh = pdep (ji,jj) ! depth at the partial step level
847	!
848	zn = - rn_a0 * ( 1._wp + 0.5_wprn_lambda1zt + rn_mu1zh ) zt &
849	& + rn_b0 * ( 1._wp - 0.5_wprn_lambda2zs - rn_mu2zh ) zs &
850	& - rn_nu * zt * zs
851	!
852	prd(ji,jj) = zn * r1_rho0 ! unmasked in situ density anomaly
853	!
854	END_2D
855	!
856	END SELECT
857	!
858	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=prd, clinfo1=' eos2d: ' )
859	!
860	IF( ln_timing ) CALL timing_stop('eos2d')
861	!
862	END SUBROUTINE eos_insitu_2d_t
863
864
865	SUBROUTINE eos_insitu_pot_2d( pts, prhop )
866	!!
867	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
868	! ! 2 : salinity [psu]
869	REAL(dp), DIMENSION(:,:) , INTENT( out) :: prhop ! potential density (surface referenced)
870	!!
871	CALL eos_insitu_pot_2d_t( pts, is_tile(pts), prhop, is_tile(prhop) )
872	END SUBROUTINE eos_insitu_pot_2d
873
874
875	SUBROUTINE eos_insitu_pot_2d_t( pts, ktts, prhop, ktrhop )
876	!!----------------------------------------------------------------------
877	!! * ROUTINE eos_insitu_pot *
878	!!
879	!! ** Purpose : Compute the in situ density (ratio rho/rho0) and the
880	!! potential volumic mass (Kg/m3) from potential temperature and
881	!! salinity fields using an equation of state selected in the
882	!! namelist.
883	!!
884	!! ** Action :
885	!! - prhop, the potential volumic mass (Kg/m3)
886	!!
887	!!----------------------------------------------------------------------
888	INTEGER , INTENT(in ) :: ktts, ktrhop
889	REAL(wp), DIMENSION(A2D_T(ktts),JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
890	! ! 2 : salinity [psu]
891	REAL(dp), DIMENSION(A2D_T(ktrhop) ), INTENT( out) :: prhop ! potential density (surface referenced)
892	!
893	INTEGER :: ji, jj, jk, jsmp ! dummy loop indices
894	INTEGER :: jdof
895	REAL(wp) :: zt , zh , zstemp, zs , ztm ! local scalars
896	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
897	REAL(wp), DIMENSION(:), ALLOCATABLE :: zn0_sto, zn_sto, zsign ! local vectors
898	!!----------------------------------------------------------------------
899	!
900	IF( ln_timing ) CALL timing_start('eos-pot')
901	!
902	SELECT CASE ( neos )
903	!
904	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
905	!
906	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
907	!
908	zt = pts (ji,jj,jp_tem) * r1_T0 ! temperature
909	zs = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
910	ztm = tmask(ji,jj,1) ! tmask
911	!
912	zn0 = (((((EOS060*zt &
913	& + EOS150zs+EOS050)zt &
914	& + (EOS240zs+EOS140)zs+EOS040)*zt &
915	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
916	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
917	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
918	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
919	!
920	!
921	prhop(ji,jj) = zn0 * ztm ! potential density referenced at the surface
922	!
923	END_2D
924
925	CASE( np_seos ) !== simplified EOS ==!
926	!
927	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
928	zt = pts (ji,jj,jp_tem) - 10._wp
929	zs = pts (ji,jj,jp_sal) - 35._wp
930	ztm = tmask(ji,jj,1)
931	! ! potential density referenced at the surface
932	zn = - rn_a0 * ( 1._wp + 0.5_wprn_lambda1zt ) * zt &
933	& + rn_b0 * ( 1._wp - 0.5_wprn_lambda2zs ) * zs &
934	& - rn_nu * zt * zs
935	prhop(ji,jj) = ( rho0 + zn ) * ztm
936	!
937	END_2D
938	!
939	END SELECT
940	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=CASTWP(prhop), clinfo1=' pot: ', kdim=1 )
941	!
942	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=CASTWP(prhop), clinfo1=' eos-pot: ' )
943	!
944	IF( ln_timing ) CALL timing_stop('eos-pot')
945	!
946	END SUBROUTINE eos_insitu_pot_2d_t
947
948
949	SUBROUTINE rab_3d_wp( pts, pab, Kmm )
950	!!
951	INTEGER , INTENT(in ) :: Kmm ! time level index
952	REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! pot. temperature & salinity
953	REAL(wp), DIMENSION(:,:,:,:), INTENT( out) :: pab ! thermal/haline expansion ratio
954	!!
955	CALL rab_3d_t_wp( pts, is_tile(pts), pab, is_tile(pab), Kmm )
956	END SUBROUTINE rab_3d_wp
957
958	SUBROUTINE rab_3d_mixed( pts, pab, Kmm )
959	!!
960	INTEGER , INTENT(in ) :: Kmm ! time level index
961	REAL(dp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! pot. temperature & salinity
962	REAL(sp), DIMENSION(:,:,:,:), INTENT( out) :: pab ! thermal/haline expansion ratio
963	!!
964	CALL rab_3d_t_mixed( pts, is_tile(pts), pab, is_tile(pab), Kmm )
965	END SUBROUTINE rab_3d_mixed
966
967
968	SUBROUTINE rab_3d_t_wp( pts, ktts, pab, ktab, Kmm )
969	!!----------------------------------------------------------------------
970	!! * ROUTINE rab_3d *
971	!!
972	!! ** Purpose : Calculates thermal/haline expansion ratio at T-points
973	!!
974	!! ** Method : calculates alpha / beta at T-points
975	!!
976	!! ** Action : - pab : thermal/haline expansion ratio at T-points
977	!!----------------------------------------------------------------------
978	INTEGER , INTENT(in ) :: Kmm ! time level index
979	INTEGER , INTENT(in ) :: ktts, ktab
980	REAL(wp), DIMENSION(A2D_T(ktts),JPK,JPTS), INTENT(in ) :: pts ! pot. temperature & salinity
981	REAL(wp), DIMENSION(A2D_T(ktab),JPK,JPTS), INTENT( out) :: pab ! thermal/haline expansion ratio
982	!
983	INTEGER :: ji, jj, jk ! dummy loop indices
984	REAL(wp) :: zt , zh , zs , ztm ! local scalars
985	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
986	!!----------------------------------------------------------------------
987	!
988	IF( ln_timing ) CALL timing_start('rab_3d')
989	!
990	SELECT CASE ( neos )
991	!
992	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
993	!
994	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
995	!
996	zh = gdept(ji,jj,jk,Kmm) * r1_Z0 ! depth
997	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
998	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
999	ztm = tmask(ji,jj,jk) ! tmask
1000	!
1001	! alpha
1002	zn3 = ALP003
1003	!
1004	zn2 = ALP012zt + ALP102zs+ALP002
1005	!
1006	zn1 = ((ALP031*zt &
1007	& + ALP121zs+ALP021)zt &
1008	& + (ALP211zs+ALP111)zs+ALP011)*zt &
1009	& + ((ALP301zs+ALP201)zs+ALP101)*zs+ALP001
1010	!
1011	zn0 = ((((ALP050*zt &
1012	& + ALP140zs+ALP040)zt &
1013	& + (ALP230zs+ALP130)zs+ALP030)*zt &
1014	& + ((ALP320zs+ALP220)zs+ALP120)zs+ALP020)zt &
1015	& + (((ALP410zs+ALP310)zs+ALP210)zs+ALP110)zs+ALP010)*zt &
1016	& + ((((ALP500zs+ALP400)zs+ALP300)zs+ALP200)zs+ALP100)*zs+ALP000
1017	!
1018	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
1019	!
1020	pab(ji,jj,jk,jp_tem) = zn * r1_rho0 * ztm
1021	!
1022	! beta
1023	zn3 = BET003
1024	!
1025	zn2 = BET012zt + BET102zs+BET002
1026	!
1027	zn1 = ((BET031*zt &
1028	& + BET121zs+BET021)zt &
1029	& + (BET211zs+BET111)zs+BET011)*zt &
1030	& + ((BET301zs+BET201)zs+BET101)*zs+BET001
1031	!
1032	zn0 = ((((BET050*zt &
1033	& + BET140zs+BET040)zt &
1034	& + (BET230zs+BET130)zs+BET030)*zt &
1035	& + ((BET320zs+BET220)zs+BET120)zs+BET020)zt &
1036	& + (((BET410zs+BET310)zs+BET210)zs+BET110)zs+BET010)*zt &
1037	& + ((((BET500zs+BET400)zs+BET300)zs+BET200)zs+BET100)*zs+BET000
1038	!
1039	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
1040	!
1041	pab(ji,jj,jk,jp_sal) = zn / zs * r1_rho0 * ztm
1042	!
1043	END_3D
1044	!
1045	CASE( np_seos ) !== simplified EOS ==!
1046	!
1047	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
1048	zt = pts (ji,jj,jk,jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
1049	zs = pts (ji,jj,jk,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
1050	zh = gdept(ji,jj,jk,Kmm) ! depth in meters at t-point
1051	ztm = tmask(ji,jj,jk) ! land/sea bottom mask = surf. mask
1052	!
1053	zn = rn_a0 * ( 1._wp + rn_lambda1zt + rn_mu1zh ) + rn_nu*zs
1054	pab(ji,jj,jk,jp_tem) = zn * r1_rho0 * ztm ! alpha
1055	!
1056	zn = rn_b0 * ( 1._wp - rn_lambda2zs - rn_mu2zh ) - rn_nu*zt
1057	pab(ji,jj,jk,jp_sal) = zn * r1_rho0 * ztm ! beta
1058	!
1059	END_3D
1060	!
1061	CASE DEFAULT
1062	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1063	CALL ctl_stop( 'rab_3d:', ctmp1 )
1064	!
1065	END SELECT
1066	!
1067	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=pab(:,:,:,jp_tem), clinfo1=' rab_3d_t: ', &
1068	& tab3d_2=pab(:,:,:,jp_sal), clinfo2=' rab_3d_s : ', kdim=jpk )
1069	!
1070	IF( ln_timing ) CALL timing_stop('rab_3d')
1071	!
1072	END SUBROUTINE rab_3d_t_wp
1073
1074	SUBROUTINE rab_3d_t_mixed( pts, ktts, pab, ktab, Kmm )
1075	!!----------------------------------------------------------------------
1076	!! * ROUTINE rab_3d *
1077	!!
1078	!! ** Purpose : Calculates thermal/haline expansion ratio at T-points
1079	!!
1080	!! ** Method : calculates alpha / beta at T-points
1081	!!
1082	!! ** Action : - pab : thermal/haline expansion ratio at T-points
1083	!!----------------------------------------------------------------------
1084	INTEGER , INTENT(in ) :: Kmm ! time level index
1085	INTEGER , INTENT(in ) :: ktts, ktab
1086	REAL(dp), DIMENSION(A2D_T(ktts),JPK,JPTS), INTENT(in ) :: pts ! pot. temperature & salinity
1087	REAL(sp), DIMENSION(A2D_T(ktab),JPK,JPTS), INTENT( out) :: pab ! thermal/haline expansion ratio
1088	!
1089	INTEGER :: ji, jj, jk ! dummy loop indices
1090	REAL(wp) :: zt , zh , zs , ztm ! local scalars
1091	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
1092	!!----------------------------------------------------------------------
1093	!
1094	IF( ln_timing ) CALL timing_start('rab_3d')
1095	!
1096	SELECT CASE ( neos )
1097	!
1098	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
1099	!
1100	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
1101	!
1102	zh = gdept(ji,jj,jk,Kmm) * r1_Z0 ! depth
1103	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
1104	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
1105	ztm = tmask(ji,jj,jk) ! tmask
1106	!
1107	! alpha
1108	zn3 = ALP003
1109	!
1110	zn2 = ALP012zt + ALP102zs+ALP002
1111	!
1112	zn1 = ((ALP031*zt &
1113	& + ALP121zs+ALP021)zt &
1114	& + (ALP211zs+ALP111)zs+ALP011)*zt &
1115	& + ((ALP301zs+ALP201)zs+ALP101)*zs+ALP001
1116	!
1117	zn0 = ((((ALP050*zt &
1118	& + ALP140zs+ALP040)zt &
1119	& + (ALP230zs+ALP130)zs+ALP030)*zt &
1120	& + ((ALP320zs+ALP220)zs+ALP120)zs+ALP020)zt &
1121	& + (((ALP410zs+ALP310)zs+ALP210)zs+ALP110)zs+ALP010)*zt &
1122	& + ((((ALP500zs+ALP400)zs+ALP300)zs+ALP200)zs+ALP100)*zs+ALP000
1123	!
1124	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
1125	!
1126	pab(ji,jj,jk,jp_tem) = zn * r1_rho0 * ztm
1127	!
1128	! beta
1129	zn3 = BET003
1130	!
1131	zn2 = BET012zt + BET102zs+BET002
1132	!
1133	zn1 = ((BET031*zt &
1134	& + BET121zs+BET021)zt &
1135	& + (BET211zs+BET111)zs+BET011)*zt &
1136	& + ((BET301zs+BET201)zs+BET101)*zs+BET001
1137	!
1138	zn0 = ((((BET050*zt &
1139	& + BET140zs+BET040)zt &
1140	& + (BET230zs+BET130)zs+BET030)*zt &
1141	& + ((BET320zs+BET220)zs+BET120)zs+BET020)zt &
1142	& + (((BET410zs+BET310)zs+BET210)zs+BET110)zs+BET010)*zt &
1143	& + ((((BET500zs+BET400)zs+BET300)zs+BET200)zs+BET100)*zs+BET000
1144	!
1145	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
1146	!
1147	pab(ji,jj,jk,jp_sal) = zn / zs * r1_rho0 * ztm
1148	!
1149	END_3D
1150	!
1151	CASE( np_seos ) !== simplified EOS ==!
1152	!
1153	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
1154	zt = pts (ji,jj,jk,jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
1155	zs = pts (ji,jj,jk,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
1156	zh = gdept(ji,jj,jk,Kmm) ! depth in meters at t-point
1157	ztm = tmask(ji,jj,jk) ! land/sea bottom mask = surf. mask
1158	!
1159	zn = rn_a0 * ( 1._wp + rn_lambda1zt + rn_mu1zh ) + rn_nu*zs
1160	pab(ji,jj,jk,jp_tem) = zn * r1_rho0 * ztm ! alpha
1161	!
1162	zn = rn_b0 * ( 1._wp - rn_lambda2zs - rn_mu2zh ) - rn_nu*zt
1163	pab(ji,jj,jk,jp_sal) = zn * r1_rho0 * ztm ! beta
1164	!
1165	END_3D
1166	!
1167	CASE DEFAULT
1168	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1169	CALL ctl_stop( 'rab_3d:', ctmp1 )
1170	!
1171	END SELECT
1172	!
1173	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=REAL(pab(:,:,:,jp_tem), wp), clinfo1=' rab_3d_t: ', &
1174	& tab3d_2=REAL(pab(:,:,:,jp_sal), wp), clinfo2=' rab_3d_s : ', kdim=jpk )
1175	!
1176	IF( ln_timing ) CALL timing_stop('rab_3d')
1177	!
1178	END SUBROUTINE rab_3d_t_mixed
1179
1180
1181	SUBROUTINE rab_2d( pts, pdep, pab, Kmm )
1182	!!
1183	INTEGER , INTENT(in ) :: Kmm ! time level index
1184	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pts ! pot. temperature & salinity
1185	REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pdep ! depth [m]
1186	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: pab ! thermal/haline expansion ratio
1187	!!
1188	CALL rab_2d_t(pts, is_tile(pts), pdep, is_tile(pdep), pab, is_tile(pab), Kmm)
1189	END SUBROUTINE rab_2d
1190
1191
1192	SUBROUTINE rab_2d_t( pts, ktts, pdep, ktdep, pab, ktab, Kmm )
1193	!!----------------------------------------------------------------------
1194	!! * ROUTINE rab_2d *
1195	!!
1196	!! ** Purpose : Calculates thermal/haline expansion ratio for a 2d field (unmasked)
1197	!!
1198	!! ** Action : - pab : thermal/haline expansion ratio at T-points
1199	!!----------------------------------------------------------------------
1200	INTEGER , INTENT(in ) :: Kmm ! time level index
1201	INTEGER , INTENT(in ) :: ktts, ktdep, ktab
1202	REAL(wp), DIMENSION(A2D_T(ktts),JPTS), INTENT(in ) :: pts ! pot. temperature & salinity
1203	REAL(wp), DIMENSION(A2D_T(ktdep) ), INTENT(in ) :: pdep ! depth [m]
1204	REAL(wp), DIMENSION(A2D_T(ktab),JPTS), INTENT( out) :: pab ! thermal/haline expansion ratio
1205	!
1206	INTEGER :: ji, jj, jk ! dummy loop indices
1207	REAL(wp) :: zt , zh , zs ! local scalars
1208	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
1209	!!----------------------------------------------------------------------
1210	!
1211	IF( ln_timing ) CALL timing_start('rab_2d')
1212	!
1213	pab(:,:,:) = 0._wp
1214	!
1215	SELECT CASE ( neos )
1216	!
1217	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
1218	!
1219	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
1220	!
1221	zh = pdep(ji,jj) * r1_Z0 ! depth
1222	zt = pts (ji,jj,jp_tem) * r1_T0 ! temperature
1223	zs = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
1224	!
1225	! alpha
1226	zn3 = ALP003
1227	!
1228	zn2 = ALP012zt + ALP102zs+ALP002
1229	!
1230	zn1 = ((ALP031*zt &
1231	& + ALP121zs+ALP021)zt &
1232	& + (ALP211zs+ALP111)zs+ALP011)*zt &
1233	& + ((ALP301zs+ALP201)zs+ALP101)*zs+ALP001
1234	!
1235	zn0 = ((((ALP050*zt &
1236	& + ALP140zs+ALP040)zt &
1237	& + (ALP230zs+ALP130)zs+ALP030)*zt &
1238	& + ((ALP320zs+ALP220)zs+ALP120)zs+ALP020)zt &
1239	& + (((ALP410zs+ALP310)zs+ALP210)zs+ALP110)zs+ALP010)*zt &
1240	& + ((((ALP500zs+ALP400)zs+ALP300)zs+ALP200)zs+ALP100)*zs+ALP000
1241	!
1242	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
1243	!
1244	pab(ji,jj,jp_tem) = zn * r1_rho0
1245	!
1246	! beta
1247	zn3 = BET003
1248	!
1249	zn2 = BET012zt + BET102zs+BET002
1250	!
1251	zn1 = ((BET031*zt &
1252	& + BET121zs+BET021)zt &
1253	& + (BET211zs+BET111)zs+BET011)*zt &
1254	& + ((BET301zs+BET201)zs+BET101)*zs+BET001
1255	!
1256	zn0 = ((((BET050*zt &
1257	& + BET140zs+BET040)zt &
1258	& + (BET230zs+BET130)zs+BET030)*zt &
1259	& + ((BET320zs+BET220)zs+BET120)zs+BET020)zt &
1260	& + (((BET410zs+BET310)zs+BET210)zs+BET110)zs+BET010)*zt &
1261	& + ((((BET500zs+BET400)zs+BET300)zs+BET200)zs+BET100)*zs+BET000
1262	!
1263	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
1264	!
1265	pab(ji,jj,jp_sal) = zn / zs * r1_rho0
1266	!
1267	!
1268	END_2D
1269	!
1270	CASE( np_seos ) !== simplified EOS ==!
1271	!
1272	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
1273	!
1274	zt = pts (ji,jj,jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
1275	zs = pts (ji,jj,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
1276	zh = pdep (ji,jj) ! depth at the partial step level
1277	!
1278	zn = rn_a0 * ( 1._wp + rn_lambda1zt + rn_mu1zh ) + rn_nu*zs
1279	pab(ji,jj,jp_tem) = zn * r1_rho0 ! alpha
1280	!
1281	zn = rn_b0 * ( 1._wp - rn_lambda2zs - rn_mu2zh ) - rn_nu*zt
1282	pab(ji,jj,jp_sal) = zn * r1_rho0 ! beta
1283	!
1284	END_2D
1285	!
1286	CASE DEFAULT
1287	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1288	CALL ctl_stop( 'rab_2d:', ctmp1 )
1289	!
1290	END SELECT
1291	!
1292	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=pab(:,:,jp_tem), clinfo1=' rab_2d_t: ', &
1293	& tab2d_2=pab(:,:,jp_sal), clinfo2=' rab_2d_s : ' )
1294	!
1295	IF( ln_timing ) CALL timing_stop('rab_2d')
1296	!
1297	END SUBROUTINE rab_2d_t
1298
1299
1300	SUBROUTINE rab_0d( pts, pdep, pab, Kmm )
1301	!!----------------------------------------------------------------------
1302	!! * ROUTINE rab_0d *
1303	!!
1304	!! ** Purpose : Calculates thermal/haline expansion ratio for a 2d field (unmasked)
1305	!!
1306	!! ** Action : - pab : thermal/haline expansion ratio at T-points
1307	!!----------------------------------------------------------------------
1308	INTEGER , INTENT(in ) :: Kmm ! time level index
1309	REAL(wp), DIMENSION(jpts) , INTENT(in ) :: pts ! pot. temperature & salinity
1310	REAL(wp), INTENT(in ) :: pdep ! depth [m]
1311	REAL(wp), DIMENSION(jpts) , INTENT( out) :: pab ! thermal/haline expansion ratio
1312	!
1313	REAL(wp) :: zt , zh , zs ! local scalars
1314	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
1315	!!----------------------------------------------------------------------
1316	!
1317	IF( ln_timing ) CALL timing_start('rab_0d')
1318	!
1319	pab(:) = 0._wp
1320	!
1321	SELECT CASE ( neos )
1322	!
1323	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
1324	!
1325	!
1326	zh = pdep * r1_Z0 ! depth
1327	zt = pts (jp_tem) * r1_T0 ! temperature
1328	zs = SQRT( ABS( pts(jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
1329	!
1330	! alpha
1331	zn3 = ALP003
1332	!
1333	zn2 = ALP012zt + ALP102zs+ALP002
1334	!
1335	zn1 = ((ALP031*zt &
1336	& + ALP121zs+ALP021)zt &
1337	& + (ALP211zs+ALP111)zs+ALP011)*zt &
1338	& + ((ALP301zs+ALP201)zs+ALP101)*zs+ALP001
1339	!
1340	zn0 = ((((ALP050*zt &
1341	& + ALP140zs+ALP040)zt &
1342	& + (ALP230zs+ALP130)zs+ALP030)*zt &
1343	& + ((ALP320zs+ALP220)zs+ALP120)zs+ALP020)zt &
1344	& + (((ALP410zs+ALP310)zs+ALP210)zs+ALP110)zs+ALP010)*zt &
1345	& + ((((ALP500zs+ALP400)zs+ALP300)zs+ALP200)zs+ALP100)*zs+ALP000
1346	!
1347	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
1348	!
1349	pab(jp_tem) = zn * r1_rho0
1350	!
1351	! beta
1352	zn3 = BET003
1353	!
1354	zn2 = BET012zt + BET102zs+BET002
1355	!
1356	zn1 = ((BET031*zt &
1357	& + BET121zs+BET021)zt &
1358	& + (BET211zs+BET111)zs+BET011)*zt &
1359	& + ((BET301zs+BET201)zs+BET101)*zs+BET001
1360	!
1361	zn0 = ((((BET050*zt &
1362	& + BET140zs+BET040)zt &
1363	& + (BET230zs+BET130)zs+BET030)*zt &
1364	& + ((BET320zs+BET220)zs+BET120)zs+BET020)zt &
1365	& + (((BET410zs+BET310)zs+BET210)zs+BET110)zs+BET010)*zt &
1366	& + ((((BET500zs+BET400)zs+BET300)zs+BET200)zs+BET100)*zs+BET000
1367	!
1368	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
1369	!
1370	pab(jp_sal) = zn / zs * r1_rho0
1371	!
1372	!
1373	!
1374	CASE( np_seos ) !== simplified EOS ==!
1375	!
1376	zt = pts(jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
1377	zs = pts(jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
1378	zh = pdep ! depth at the partial step level
1379	!
1380	zn = rn_a0 * ( 1._wp + rn_lambda1zt + rn_mu1zh ) + rn_nu*zs
1381	pab(jp_tem) = zn * r1_rho0 ! alpha
1382	!
1383	zn = rn_b0 * ( 1._wp - rn_lambda2zs - rn_mu2zh ) - rn_nu*zt
1384	pab(jp_sal) = zn * r1_rho0 ! beta
1385	!
1386	CASE DEFAULT
1387	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1388	CALL ctl_stop( 'rab_0d:', ctmp1 )
1389	!
1390	END SELECT
1391	!
1392	IF( ln_timing ) CALL timing_stop('rab_0d')
1393	!
1394	END SUBROUTINE rab_0d
1395
1396
1397	SUBROUTINE bn2( pts, pab, pn2, Kmm )
1398	!!
1399	INTEGER , INTENT(in ) :: Kmm ! time level index
1400	REAL(dp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature and salinity [Celsius,psu]
1401	REAL(wp), DIMENSION(:,:,:,:) , INTENT(in ) :: pab ! thermal/haline expansion coef. [Celsius-1,psu-1]
1402	REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: pn2 ! Brunt-Vaisala frequency squared [1/s^2]
1403	!!
1404	CALL bn2_t( pts, pab, is_tile(pab), pn2, is_tile(pn2), Kmm )
1405	END SUBROUTINE bn2
1406
1407
1408	SUBROUTINE bn2_t( pts, pab, ktab, pn2, ktn2, Kmm )
1409	!!----------------------------------------------------------------------
1410	!! * ROUTINE bn2 *
1411	!!
1412	!! ** Purpose : Compute the local Brunt-Vaisala frequency at the
1413	!! time-step of the input arguments
1414	!!
1415	!! ** Method : pn2 = grav * (alpha dk[T] + beta dk[S] ) / e3w
1416	!! where alpha and beta are given in pab, and computed on T-points.
1417	!! N.B. N^2 is set one for all to zero at jk=1 in istate module.
1418	!!
1419	!! ** Action : pn2 : square of the brunt-vaisala frequency at w-point
1420	!!
1421	!!----------------------------------------------------------------------
1422	INTEGER , INTENT(in ) :: Kmm ! time level index
1423	INTEGER , INTENT(in ) :: ktab, ktn2
1424	REAL(dp), DIMENSION(jpi,jpj, jpk,jpts), INTENT(in ) :: pts ! pot. temperature and salinity [Celsius,psu]
1425	REAL(wp), DIMENSION(A2D_T(ktab),JPK,JPTS), INTENT(in ) :: pab ! thermal/haline expansion coef. [Celsius-1,psu-1]
1426	REAL(wp), DIMENSION(A2D_T(ktn2),JPK ), INTENT( out) :: pn2 ! Brunt-Vaisala frequency squared [1/s^2]
1427	!
1428	INTEGER :: ji, jj, jk ! dummy loop indices
1429	REAL(wp) :: zaw, zbw, zrw ! local scalars
1430	!!----------------------------------------------------------------------
1431	!
1432	IF( ln_timing ) CALL timing_start('bn2')
1433	!
1434	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 2, jpkm1 ) ! interior points only (2=< jk =< jpkm1 ); surface and bottom value set to zero one for all in istate.F90
1435	zrw = ( gdepw(ji,jj,jk ,Kmm) - gdept(ji,jj,jk,Kmm) ) &
1436	& / ( gdept(ji,jj,jk-1,Kmm) - gdept(ji,jj,jk,Kmm) )
1437	!
1438	zaw = pab(ji,jj,jk,jp_tem) * (1. - zrw) + pab(ji,jj,jk-1,jp_tem) * zrw
1439	zbw = pab(ji,jj,jk,jp_sal) * (1. - zrw) + pab(ji,jj,jk-1,jp_sal) * zrw
1440	!
1441	pn2(ji,jj,jk) = grav * ( zaw * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) &
1442	& - zbw * ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) ) &
1443	& / e3w(ji,jj,jk,Kmm) * wmask(ji,jj,jk)
1444	END_3D
1445	!
1446	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=pn2, clinfo1=' bn2 : ', kdim=jpk )
1447	!
1448	IF( ln_timing ) CALL timing_stop('bn2')
1449	!
1450	END SUBROUTINE bn2_t
1451
1452
1453	FUNCTION eos_pt_from_ct( ctmp, psal ) RESULT( ptmp )
1454	!!----------------------------------------------------------------------
1455	!! * ROUTINE eos_pt_from_ct *
1456	!!
1457	!! ** Purpose : Compute pot.temp. from cons. temp. [Celsius]
1458	!!
1459	!! ** Method : rational approximation (5/3th order) of TEOS-10 algorithm
1460	!! checkvalue: pt=20.02391895 Celsius for sa=35.7g/kg, ct=20degC
1461	!!
1462	!! Reference : TEOS-10, UNESCO
1463	!! Rational approximation to TEOS10 algorithm (rms error on WOA13 values: 4.0e-5 degC)
1464	!!----------------------------------------------------------------------
1465	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: ctmp ! Cons. Temp [Celsius]
1466	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu]
1467	! Leave result array automatic rather than making explicitly allocated
1468	REAL(wp), DIMENSION(jpi,jpj) :: ptmp ! potential temperature [Celsius]
1469	!
1470	INTEGER :: ji, jj ! dummy loop indices
1471	REAL(wp) :: zt , zs , ztm ! local scalars
1472	REAL(wp) :: zn , zd ! local scalars
1473	REAL(wp) :: zdeltaS , z1_S0 , z1_T0
1474	!!----------------------------------------------------------------------
1475	!
1476	IF( ln_timing ) CALL timing_start('eos_pt_from_ct')
1477	!
1478	zdeltaS = 5._wp
1479	z1_S0 = 0.875_wp/35.16504_wp
1480	z1_T0 = 1._wp/40._wp
1481	!
1482	DO_2D( 1, 1, 1, 1 )
1483	!
1484	zt = ctmp (ji,jj) * z1_T0
1485	zs = SQRT( ABS( psal(ji,jj) + zdeltaS ) * r1_S0 )
1486	ztm = tmask(ji,jj,1)
1487	!
1488	zn = ((((-2.1385727895e-01_wp*zt &
1489	& - 2.7674419971e-01_wpzs+1.0728094330_wp)zt &
1490	& + (2.6366564313_wpzs+3.3546960647_wp)zs-7.8012209473_wp)*zt &
1491	& + ((1.8835586562_wpzs+7.3949191679_wp)zs-3.3937395875_wp)zs-5.6414948432_wp)zt &
1492	& + (((3.5737370589_wpzs-1.5512427389e+01_wp)zs+2.4625741105e+01_wp)*zs &
1493	& +1.9912291000e+01_wp)zs-3.2191146312e+01_wp)zt &
1494	& + ((((5.7153204649e-01_wpzs-3.0943149543_wp)zs+9.3052495181_wp)*zs &
1495	& -9.4528934807_wp)zs+3.1066408996_wp)zs-4.3504021262e-01_wp
1496	!
1497	zd = (2.0035003456_wp*zt &
1498	& -3.4570358592e-01_wpzs+5.6471810638_wp)zt &
1499	& + (1.5393993508_wpzs-6.9394762624_wp)zs+1.2750522650e+01_wp
1500	!
1501	ptmp(ji,jj) = ( zt / z1_T0 + zn / zd ) * ztm
1502	!
1503	END_2D
1504	!
1505	IF( ln_timing ) CALL timing_stop('eos_pt_from_ct')
1506	!
1507	END FUNCTION eos_pt_from_ct
1508
1509
1510	SUBROUTINE eos_fzp_2d( psal, ptf, pdep )
1511	!!
1512	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu]
1513	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ), OPTIONAL :: pdep ! depth [m]
1514	REAL(wp), DIMENSION(:,:) , INTENT(out ) :: ptf ! freezing temperature [Celsius]
1515	!!
1516	CALL eos_fzp_2d_t( psal, ptf, is_tile(ptf), pdep )
1517	END SUBROUTINE eos_fzp_2d
1518
1519
1520	SUBROUTINE eos_fzp_2d_t( psal, ptf, kttf, pdep )
1521	!!----------------------------------------------------------------------
1522	!! * ROUTINE eos_fzp *
1523	!!
1524	!! ** Purpose : Compute the freezing point temperature [Celsius]
1525	!!
1526	!! ** Method : UNESCO freezing point (ptf) in Celsius is given by
1527	!! ptf(t,z) = (-.0575+1.710523e-3sqrt(abs(s))-2.154996e-4s)s - 7.53e-4z
1528	!! checkvalue: tf=-2.588567 Celsius for s=40psu, z=500m
1529	!!
1530	!! Reference : UNESCO tech. papers in the marine science no. 28. 1978
1531	!!----------------------------------------------------------------------
1532	INTEGER , INTENT(in ) :: kttf
1533	REAL(wp), DIMENSION(jpi,jpj) , INTENT(in ) :: psal ! salinity [psu]
1534	REAL(wp), DIMENSION(jpi,jpj) , INTENT(in ), OPTIONAL :: pdep ! depth [m]
1535	REAL(wp), DIMENSION(A2D_T(kttf)), INTENT(out ) :: ptf ! freezing temperature [Celsius]
1536	!
1537	INTEGER :: ji, jj ! dummy loop indices
1538	REAL(wp) :: zt, zs, z1_S0 ! local scalars
1539	!!----------------------------------------------------------------------
1540	!
1541	SELECT CASE ( neos )
1542	!
1543	CASE ( np_teos10, np_seos ) !== CT,SA (TEOS-10 and S-EOS formulations) ==!
1544	!
1545	z1_S0 = 1._wp / 35.16504_wp
1546	DO_2D( 1, 1, 1, 1 )
1547	zs= SQRT( ABS( psal(ji,jj) ) * z1_S0 ) ! square root salinity
1548	ptf(ji,jj) = ((((1.46873e-03_wpzs-9.64972e-03_wp)zs+2.28348e-02_wp)*zs &
1549	& - 3.12775e-02_wp)zs+2.07679e-02_wp)zs-5.87701e-02_wp
1550	END_2D
1551	ptf(:,:) = ptf(:,:) * psal(:,:)
1552	!
1553	IF( PRESENT( pdep ) ) ptf(:,:) = ptf(:,:) - 7.53e-4 * pdep(:,:)
1554	!
1555	CASE ( np_eos80 ) !== PT,SP (UNESCO formulation) ==!
1556	!
1557	ptf(:,:) = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal(:,:) ) &
1558	& - 2.154996e-4_wp * psal(:,:) ) * psal(:,:)
1559	!
1560	IF( PRESENT( pdep ) ) ptf(:,:) = ptf(:,:) - 7.53e-4 * pdep(:,:)
1561	!
1562	CASE DEFAULT
1563	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1564	CALL ctl_stop( 'eos_fzp_2d:', ctmp1 )
1565	!
1566	END SELECT
1567	!
1568	END SUBROUTINE eos_fzp_2d_t
1569
1570
1571	SUBROUTINE eos_fzp_0d( psal, ptf, pdep )
1572	!!----------------------------------------------------------------------
1573	!! * ROUTINE eos_fzp *
1574	!!
1575	!! ** Purpose : Compute the freezing point temperature [Celsius]
1576	!!
1577	!! ** Method : UNESCO freezing point (ptf) in Celsius is given by
1578	!! ptf(t,z) = (-.0575+1.710523e-3sqrt(abs(s))-2.154996e-4s)s - 7.53e-4z
1579	!! checkvalue: tf=-2.588567 Celsius for s=40psu, z=500m
1580	!!
1581	!! Reference : UNESCO tech. papers in the marine science no. 28. 1978
1582	!!----------------------------------------------------------------------
1583	REAL(wp), INTENT(in ) :: psal ! salinity [psu]
1584	REAL(wp), INTENT(in ), OPTIONAL :: pdep ! depth [m]
1585	REAL(wp), INTENT(out) :: ptf ! freezing temperature [Celsius]
1586	!
1587	REAL(wp) :: zs ! local scalars
1588	!!----------------------------------------------------------------------
1589	!
1590	SELECT CASE ( neos )
1591	!
1592	CASE ( np_teos10, np_seos ) !== CT,SA (TEOS-10 and S-EOS formulations) ==!
1593	!
1594	zs = SQRT( ABS( psal ) / 35.16504_wp ) ! square root salinity
1595	ptf = ((((1.46873e-03_wpzs-9.64972e-03_wp)zs+2.28348e-02_wp)*zs &
1596	& - 3.12775e-02_wp)zs+2.07679e-02_wp)zs-5.87701e-02_wp
1597	ptf = ptf * psal
1598	!
1599	IF( PRESENT( pdep ) ) ptf = ptf - 7.53e-4 * pdep
1600	!
1601	CASE ( np_eos80 ) !== PT,SP (UNESCO formulation) ==!
1602	!
1603	ptf = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal ) &
1604	& - 2.154996e-4_wp * psal ) * psal
1605	!
1606	IF( PRESENT( pdep ) ) ptf = ptf - 7.53e-4 * pdep
1607	!
1608	CASE DEFAULT
1609	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1610	CALL ctl_stop( 'eos_fzp_0d:', ctmp1 )
1611	!
1612	END SELECT
1613	!
1614	END SUBROUTINE eos_fzp_0d
1615
1616
1617	SUBROUTINE eos_pen( pts, pab_pe, ppen, Kmm )
1618	!!----------------------------------------------------------------------
1619	!! * ROUTINE eos_pen *
1620	!!
1621	!! ** Purpose : Calculates nonlinear anomalies of alpha_PE, beta_PE and PE at T-points
1622	!!
1623	!! ** Method : PE is defined analytically as the vertical
1624	!! primitive of EOS times -g integrated between 0 and z>0.
1625	!! pen is the nonlinear bsq-PE anomaly: pen = ( PE - rho0 gz ) / rho0 gz - rd
1626	!! = 1/z * /int_0^z rd dz - rd
1627	!! where rd is the density anomaly (see eos_rhd function)
1628	!! ab_pe are partial derivatives of PE anomaly with respect to T and S:
1629	!! ab_pe(1) = - 1/(rho0 gz) * dPE/dT + drd/dT = - d(pen)/dT
1630	!! ab_pe(2) = 1/(rho0 gz) * dPE/dS + drd/dS = d(pen)/dS
1631	!!
1632	!! ** Action : - pen : PE anomaly given at T-points
1633	!! : - pab_pe : given at T-points
1634	!! pab_pe(:,:,:,jp_tem) is alpha_pe
1635	!! pab_pe(:,:,:,jp_sal) is beta_pe
1636	!!----------------------------------------------------------------------
1637	INTEGER , INTENT(in ) :: Kmm ! time level index
1638	REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature & salinity
1639	REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT( out) :: pab_pe ! alpha_pe and beta_pe
1640	REAL(wp), DIMENSION(jpi,jpj,jpk) , INTENT( out) :: ppen ! potential energy anomaly
1641	!
1642	INTEGER :: ji, jj, jk ! dummy loop indices
1643	REAL(wp) :: zt , zh , zs , ztm ! local scalars
1644	REAL(wp) :: zn , zn0, zn1, zn2 ! - -
1645	!!----------------------------------------------------------------------
1646	!
1647	IF( ln_timing ) CALL timing_start('eos_pen')
1648	!
1649	SELECT CASE ( neos )
1650	!
1651	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
1652	!
1653	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
1654	!
1655	zh = gdept(ji,jj,jk,Kmm) * r1_Z0 ! depth
1656	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
1657	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
1658	ztm = tmask(ji,jj,jk) ! tmask
1659	!
1660	! potential energy non-linear anomaly
1661	zn2 = (PEN012)*zt &
1662	& + PEN102*zs+PEN002
1663	!
1664	zn1 = ((PEN021)*zt &
1665	& + PEN111zs+PEN011)zt &
1666	& + (PEN201zs+PEN101)zs+PEN001
1667	!
1668	zn0 = ((((PEN040)*zt &
1669	& + PEN130zs+PEN030)zt &
1670	& + (PEN220zs+PEN120)zs+PEN020)*zt &
1671	& + ((PEN310zs+PEN210)zs+PEN110)zs+PEN010)zt &
1672	& + (((PEN400zs+PEN300)zs+PEN200)zs+PEN100)zs+PEN000
1673	!
1674	zn = ( zn2 * zh + zn1 ) * zh + zn0
1675	!
1676	ppen(ji,jj,jk) = zn * zh * r1_rho0 * ztm
1677	!
1678	! alphaPE non-linear anomaly
1679	zn2 = APE002
1680	!
1681	zn1 = (APE011)*zt &
1682	& + APE101*zs+APE001
1683	!
1684	zn0 = (((APE030)*zt &
1685	& + APE120zs+APE020)zt &
1686	& + (APE210zs+APE110)zs+APE010)*zt &
1687	& + ((APE300zs+APE200)zs+APE100)*zs+APE000
1688	!
1689	zn = ( zn2 * zh + zn1 ) * zh + zn0
1690	!
1691	pab_pe(ji,jj,jk,jp_tem) = zn * zh * r1_rho0 * ztm
1692	!
1693	! betaPE non-linear anomaly
1694	zn2 = BPE002
1695	!
1696	zn1 = (BPE011)*zt &
1697	& + BPE101*zs+BPE001
1698	!
1699	zn0 = (((BPE030)*zt &
1700	& + BPE120zs+BPE020)zt &
1701	& + (BPE210zs+BPE110)zs+BPE010)*zt &
1702	& + ((BPE300zs+BPE200)zs+BPE100)*zs+BPE000
1703	!
1704	zn = ( zn2 * zh + zn1 ) * zh + zn0
1705	!
1706	pab_pe(ji,jj,jk,jp_sal) = zn / zs * zh * r1_rho0 * ztm
1707	!
1708	END_3D
1709	!
1710	CASE( np_seos ) !== Vallis (2006) simplified EOS ==!
1711	!
1712	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
1713	zt = pts(ji,jj,jk,jp_tem) - 10._wp ! temperature anomaly (t-T0)
1714	zs = pts (ji,jj,jk,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
1715	zh = gdept(ji,jj,jk,Kmm) ! depth in meters at t-point
1716	ztm = tmask(ji,jj,jk) ! tmask
1717	zn = 0.5_wp * zh * r1_rho0 * ztm
1718	! ! Potential Energy
1719	ppen(ji,jj,jk) = ( rn_a0 * rn_mu1 * zt + rn_b0 * rn_mu2 * zs ) * zn
1720	! ! alphaPE
1721	pab_pe(ji,jj,jk,jp_tem) = - rn_a0 * rn_mu1 * zn
1722	pab_pe(ji,jj,jk,jp_sal) = rn_b0 * rn_mu2 * zn
1723	!
1724	END_3D
1725	!
1726	CASE DEFAULT
1727	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1728	CALL ctl_stop( 'eos_pen:', ctmp1 )
1729	!
1730	END SELECT
1731	!
1732	IF( ln_timing ) CALL timing_stop('eos_pen')
1733	!
1734	END SUBROUTINE eos_pen
1735
1736
1737	SUBROUTINE eos_init
1738	!!----------------------------------------------------------------------
1739	!! * ROUTINE eos_init *
1740	!!
1741	!! ** Purpose : initializations for the equation of state
1742	!!
1743	!! ** Method : Read the namelist nameos and control the parameters
1744	!!----------------------------------------------------------------------
1745	INTEGER :: ios ! local integer
1746	INTEGER :: ioptio ! local integer
1747	!!
1748	NAMELIST/nameos/ ln_TEOS10, ln_EOS80, ln_SEOS, rn_a0, rn_b0, rn_lambda1, rn_mu1, &
1749	& rn_lambda2, rn_mu2, rn_nu
1750	!!----------------------------------------------------------------------
1751	!
1752	READ ( numnam_ref, nameos, IOSTAT = ios, ERR = 901 )
1753	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'nameos in reference namelist' )
1754	!
1755	READ ( numnam_cfg, nameos, IOSTAT = ios, ERR = 902 )
1756	902 IF( ios > 0 ) CALL ctl_nam ( ios , 'nameos in configuration namelist' )
1757	IF(lwm) WRITE( numond, nameos )
1758	!
1759	rho0 = 1026._wp !: volumic mass of reference [kg/m3]
1760	rcp = 3991.86795711963_wp !: heat capacity [J/K]
1761	!
1762	IF(lwp) THEN ! Control print
1763	WRITE(numout,*)
1764	WRITE(numout,*) 'eos_init : equation of state'
1765	WRITE(numout,*) '~~~~~~~~'
1766	WRITE(numout,*) ' Namelist nameos : Chosen the Equation Of Seawater (EOS)'
1767	WRITE(numout,*) ' TEOS-10 : rho=F(Conservative Temperature, Absolute Salinity, depth) ln_TEOS10 = ', ln_TEOS10
1768	WRITE(numout,*) ' EOS-80 : rho=F(Potential Temperature, Practical Salinity, depth) ln_EOS80 = ', ln_EOS80
1769	WRITE(numout,*) ' S-EOS : rho=F(Conservative Temperature, Absolute Salinity, depth) ln_SEOS = ', ln_SEOS
1770	ENDIF
1771
1772	! Check options for equation of state & set neos based on logical flags
1773	ioptio = 0
1774	IF( ln_TEOS10 ) THEN ; ioptio = ioptio+1 ; neos = np_teos10 ; ENDIF
1775	IF( ln_EOS80 ) THEN ; ioptio = ioptio+1 ; neos = np_eos80 ; ENDIF
1776	IF( ln_SEOS ) THEN ; ioptio = ioptio+1 ; neos = np_seos ; ENDIF
1777	IF( ioptio /= 1 ) CALL ctl_stop("Exactly one equation of state option must be selected")
1778	!
1779	SELECT CASE( neos ) ! check option
1780	!
1781	CASE( np_teos10 ) !== polynomial TEOS-10 ==!
1782	IF(lwp) WRITE(numout,*)
1783	IF(lwp) WRITE(numout,*) ' ==>>> use of TEOS-10 equation of state (cons. temp. and abs. salinity)'
1784	!
1785	l_useCT = .TRUE. ! model temperature is Conservative temperature
1786	!
1787	rdeltaS = 32._wp
1788	r1_S0 = 0.875_wp/35.16504_wp
1789	r1_T0 = 1._wp/40._wp
1790	r1_Z0 = 1.e-4_wp
1791	!
1792	EOS000 = 8.0189615746e+02_wp
1793	EOS100 = 8.6672408165e+02_wp
1794	EOS200 = -1.7864682637e+03_wp
1795	EOS300 = 2.0375295546e+03_wp
1796	EOS400 = -1.2849161071e+03_wp
1797	EOS500 = 4.3227585684e+02_wp
1798	EOS600 = -6.0579916612e+01_wp
1799	EOS010 = 2.6010145068e+01_wp
1800	EOS110 = -6.5281885265e+01_wp
1801	EOS210 = 8.1770425108e+01_wp
1802	EOS310 = -5.6888046321e+01_wp
1803	EOS410 = 1.7681814114e+01_wp
1804	EOS510 = -1.9193502195_wp
1805	EOS020 = -3.7074170417e+01_wp
1806	EOS120 = 6.1548258127e+01_wp
1807	EOS220 = -6.0362551501e+01_wp
1808	EOS320 = 2.9130021253e+01_wp
1809	EOS420 = -5.4723692739_wp
1810	EOS030 = 2.1661789529e+01_wp
1811	EOS130 = -3.3449108469e+01_wp
1812	EOS230 = 1.9717078466e+01_wp
1813	EOS330 = -3.1742946532_wp
1814	EOS040 = -8.3627885467_wp
1815	EOS140 = 1.1311538584e+01_wp
1816	EOS240 = -5.3563304045_wp
1817	EOS050 = 5.4048723791e-01_wp
1818	EOS150 = 4.8169980163e-01_wp
1819	EOS060 = -1.9083568888e-01_wp
1820	EOS001 = 1.9681925209e+01_wp
1821	EOS101 = -4.2549998214e+01_wp
1822	EOS201 = 5.0774768218e+01_wp
1823	EOS301 = -3.0938076334e+01_wp
1824	EOS401 = 6.6051753097_wp
1825	EOS011 = -1.3336301113e+01_wp
1826	EOS111 = -4.4870114575_wp
1827	EOS211 = 5.0042598061_wp
1828	EOS311 = -6.5399043664e-01_wp
1829	EOS021 = 6.7080479603_wp
1830	EOS121 = 3.5063081279_wp
1831	EOS221 = -1.8795372996_wp
1832	EOS031 = -2.4649669534_wp
1833	EOS131 = -5.5077101279e-01_wp
1834	EOS041 = 5.5927935970e-01_wp
1835	EOS002 = 2.0660924175_wp
1836	EOS102 = -4.9527603989_wp
1837	EOS202 = 2.5019633244_wp
1838	EOS012 = 2.0564311499_wp
1839	EOS112 = -2.1311365518e-01_wp
1840	EOS022 = -1.2419983026_wp
1841	EOS003 = -2.3342758797e-02_wp
1842	EOS103 = -1.8507636718e-02_wp
1843	EOS013 = 3.7969820455e-01_wp
1844	!
1845	ALP000 = -6.5025362670e-01_wp
1846	ALP100 = 1.6320471316_wp
1847	ALP200 = -2.0442606277_wp
1848	ALP300 = 1.4222011580_wp
1849	ALP400 = -4.4204535284e-01_wp
1850	ALP500 = 4.7983755487e-02_wp
1851	ALP010 = 1.8537085209_wp
1852	ALP110 = -3.0774129064_wp
1853	ALP210 = 3.0181275751_wp
1854	ALP310 = -1.4565010626_wp
1855	ALP410 = 2.7361846370e-01_wp
1856	ALP020 = -1.6246342147_wp
1857	ALP120 = 2.5086831352_wp
1858	ALP220 = -1.4787808849_wp
1859	ALP320 = 2.3807209899e-01_wp
1860	ALP030 = 8.3627885467e-01_wp
1861	ALP130 = -1.1311538584_wp
1862	ALP230 = 5.3563304045e-01_wp
1863	ALP040 = -6.7560904739e-02_wp
1864	ALP140 = -6.0212475204e-02_wp
1865	ALP050 = 2.8625353333e-02_wp
1866	ALP001 = 3.3340752782e-01_wp
1867	ALP101 = 1.1217528644e-01_wp
1868	ALP201 = -1.2510649515e-01_wp
1869	ALP301 = 1.6349760916e-02_wp
1870	ALP011 = -3.3540239802e-01_wp
1871	ALP111 = -1.7531540640e-01_wp
1872	ALP211 = 9.3976864981e-02_wp
1873	ALP021 = 1.8487252150e-01_wp
1874	ALP121 = 4.1307825959e-02_wp
1875	ALP031 = -5.5927935970e-02_wp
1876	ALP002 = -5.1410778748e-02_wp
1877	ALP102 = 5.3278413794e-03_wp
1878	ALP012 = 6.2099915132e-02_wp
1879	ALP003 = -9.4924551138e-03_wp
1880	!
1881	BET000 = 1.0783203594e+01_wp
1882	BET100 = -4.4452095908e+01_wp
1883	BET200 = 7.6048755820e+01_wp
1884	BET300 = -6.3944280668e+01_wp
1885	BET400 = 2.6890441098e+01_wp
1886	BET500 = -4.5221697773_wp
1887	BET010 = -8.1219372432e-01_wp
1888	BET110 = 2.0346663041_wp
1889	BET210 = -2.1232895170_wp
1890	BET310 = 8.7994140485e-01_wp
1891	BET410 = -1.1939638360e-01_wp
1892	BET020 = 7.6574242289e-01_wp
1893	BET120 = -1.5019813020_wp
1894	BET220 = 1.0872489522_wp
1895	BET320 = -2.7233429080e-01_wp
1896	BET030 = -4.1615152308e-01_wp
1897	BET130 = 4.9061350869e-01_wp
1898	BET230 = -1.1847737788e-01_wp
1899	BET040 = 1.4073062708e-01_wp
1900	BET140 = -1.3327978879e-01_wp
1901	BET050 = 5.9929880134e-03_wp
1902	BET001 = -5.2937873009e-01_wp
1903	BET101 = 1.2634116779_wp
1904	BET201 = -1.1547328025_wp
1905	BET301 = 3.2870876279e-01_wp
1906	BET011 = -5.5824407214e-02_wp
1907	BET111 = 1.2451933313e-01_wp
1908	BET211 = -2.4409539932e-02_wp
1909	BET021 = 4.3623149752e-02_wp
1910	BET121 = -4.6767901790e-02_wp
1911	BET031 = -6.8523260060e-03_wp
1912	BET002 = -6.1618945251e-02_wp
1913	BET102 = 6.2255521644e-02_wp
1914	BET012 = -2.6514181169e-03_wp
1915	BET003 = -2.3025968587e-04_wp
1916	!
1917	PEN000 = -9.8409626043_wp
1918	PEN100 = 2.1274999107e+01_wp
1919	PEN200 = -2.5387384109e+01_wp
1920	PEN300 = 1.5469038167e+01_wp
1921	PEN400 = -3.3025876549_wp
1922	PEN010 = 6.6681505563_wp
1923	PEN110 = 2.2435057288_wp
1924	PEN210 = -2.5021299030_wp
1925	PEN310 = 3.2699521832e-01_wp
1926	PEN020 = -3.3540239802_wp
1927	PEN120 = -1.7531540640_wp
1928	PEN220 = 9.3976864981e-01_wp
1929	PEN030 = 1.2324834767_wp
1930	PEN130 = 2.7538550639e-01_wp
1931	PEN040 = -2.7963967985e-01_wp
1932	PEN001 = -1.3773949450_wp
1933	PEN101 = 3.3018402659_wp
1934	PEN201 = -1.6679755496_wp
1935	PEN011 = -1.3709540999_wp
1936	PEN111 = 1.4207577012e-01_wp
1937	PEN021 = 8.2799886843e-01_wp
1938	PEN002 = 1.7507069098e-02_wp
1939	PEN102 = 1.3880727538e-02_wp
1940	PEN012 = -2.8477365341e-01_wp
1941	!
1942	APE000 = -1.6670376391e-01_wp
1943	APE100 = -5.6087643219e-02_wp
1944	APE200 = 6.2553247576e-02_wp
1945	APE300 = -8.1748804580e-03_wp
1946	APE010 = 1.6770119901e-01_wp
1947	APE110 = 8.7657703198e-02_wp
1948	APE210 = -4.6988432490e-02_wp
1949	APE020 = -9.2436260751e-02_wp
1950	APE120 = -2.0653912979e-02_wp
1951	APE030 = 2.7963967985e-02_wp
1952	APE001 = 3.4273852498e-02_wp
1953	APE101 = -3.5518942529e-03_wp
1954	APE011 = -4.1399943421e-02_wp
1955	APE002 = 7.1193413354e-03_wp
1956	!
1957	BPE000 = 2.6468936504e-01_wp
1958	BPE100 = -6.3170583896e-01_wp
1959	BPE200 = 5.7736640125e-01_wp
1960	BPE300 = -1.6435438140e-01_wp
1961	BPE010 = 2.7912203607e-02_wp
1962	BPE110 = -6.2259666565e-02_wp
1963	BPE210 = 1.2204769966e-02_wp
1964	BPE020 = -2.1811574876e-02_wp
1965	BPE120 = 2.3383950895e-02_wp
1966	BPE030 = 3.4261630030e-03_wp
1967	BPE001 = 4.1079296834e-02_wp
1968	BPE101 = -4.1503681096e-02_wp
1969	BPE011 = 1.7676120780e-03_wp
1970	BPE002 = 1.7269476440e-04_wp
1971	!
1972	CASE( np_eos80 ) !== polynomial EOS-80 formulation ==!
1973	!
1974	IF(lwp) WRITE(numout,*)
1975	IF(lwp) WRITE(numout,*) ' ==>>> use of EOS-80 equation of state (pot. temp. and pract. salinity)'
1976	!
1977	l_useCT = .FALSE. ! model temperature is Potential temperature
1978	rdeltaS = 20._wp
1979	r1_S0 = 1._wp/40._wp
1980	r1_T0 = 1._wp/40._wp
1981	r1_Z0 = 1.e-4_wp
1982	!
1983	EOS000 = 9.5356891948e+02_wp
1984	EOS100 = 1.7136499189e+02_wp
1985	EOS200 = -3.7501039454e+02_wp
1986	EOS300 = 5.1856810420e+02_wp
1987	EOS400 = -3.7264470465e+02_wp
1988	EOS500 = 1.4302533998e+02_wp
1989	EOS600 = -2.2856621162e+01_wp
1990	EOS010 = 1.0087518651e+01_wp
1991	EOS110 = -1.3647741861e+01_wp
1992	EOS210 = 8.8478359933_wp
1993	EOS310 = -7.2329388377_wp
1994	EOS410 = 1.4774410611_wp
1995	EOS510 = 2.0036720553e-01_wp
1996	EOS020 = -2.5579830599e+01_wp
1997	EOS120 = 2.4043512327e+01_wp
1998	EOS220 = -1.6807503990e+01_wp
1999	EOS320 = 8.3811577084_wp
2000	EOS420 = -1.9771060192_wp
2001	EOS030 = 1.6846451198e+01_wp
2002	EOS130 = -2.1482926901e+01_wp
2003	EOS230 = 1.0108954054e+01_wp
2004	EOS330 = -6.2675951440e-01_wp
2005	EOS040 = -8.0812310102_wp
2006	EOS140 = 1.0102374985e+01_wp
2007	EOS240 = -4.8340368631_wp
2008	EOS050 = 1.2079167803_wp
2009	EOS150 = 1.1515380987e-01_wp
2010	EOS060 = -2.4520288837e-01_wp
2011	EOS001 = 1.0748601068e+01_wp
2012	EOS101 = -1.7817043500e+01_wp
2013	EOS201 = 2.2181366768e+01_wp
2014	EOS301 = -1.6750916338e+01_wp
2015	EOS401 = 4.1202230403_wp
2016	EOS011 = -1.5852644587e+01_wp
2017	EOS111 = -7.6639383522e-01_wp
2018	EOS211 = 4.1144627302_wp
2019	EOS311 = -6.6955877448e-01_wp
2020	EOS021 = 9.9994861860_wp
2021	EOS121 = -1.9467067787e-01_wp
2022	EOS221 = -1.2177554330_wp
2023	EOS031 = -3.4866102017_wp
2024	EOS131 = 2.2229155620e-01_wp
2025	EOS041 = 5.9503008642e-01_wp
2026	EOS002 = 1.0375676547_wp
2027	EOS102 = -3.4249470629_wp
2028	EOS202 = 2.0542026429_wp
2029	EOS012 = 2.1836324814_wp
2030	EOS112 = -3.4453674320e-01_wp
2031	EOS022 = -1.2548163097_wp
2032	EOS003 = 1.8729078427e-02_wp
2033	EOS103 = -5.7238495240e-02_wp
2034	EOS013 = 3.8306136687e-01_wp
2035	!
2036	ALP000 = -2.5218796628e-01_wp
2037	ALP100 = 3.4119354654e-01_wp
2038	ALP200 = -2.2119589983e-01_wp
2039	ALP300 = 1.8082347094e-01_wp
2040	ALP400 = -3.6936026529e-02_wp
2041	ALP500 = -5.0091801383e-03_wp
2042	ALP010 = 1.2789915300_wp
2043	ALP110 = -1.2021756164_wp
2044	ALP210 = 8.4037519952e-01_wp
2045	ALP310 = -4.1905788542e-01_wp
2046	ALP410 = 9.8855300959e-02_wp
2047	ALP020 = -1.2634838399_wp
2048	ALP120 = 1.6112195176_wp
2049	ALP220 = -7.5817155402e-01_wp
2050	ALP320 = 4.7006963580e-02_wp
2051	ALP030 = 8.0812310102e-01_wp
2052	ALP130 = -1.0102374985_wp
2053	ALP230 = 4.8340368631e-01_wp
2054	ALP040 = -1.5098959754e-01_wp
2055	ALP140 = -1.4394226233e-02_wp
2056	ALP050 = 3.6780433255e-02_wp
2057	ALP001 = 3.9631611467e-01_wp
2058	ALP101 = 1.9159845880e-02_wp
2059	ALP201 = -1.0286156825e-01_wp
2060	ALP301 = 1.6738969362e-02_wp
2061	ALP011 = -4.9997430930e-01_wp
2062	ALP111 = 9.7335338937e-03_wp
2063	ALP211 = 6.0887771651e-02_wp
2064	ALP021 = 2.6149576513e-01_wp
2065	ALP121 = -1.6671866715e-02_wp
2066	ALP031 = -5.9503008642e-02_wp
2067	ALP002 = -5.4590812035e-02_wp
2068	ALP102 = 8.6134185799e-03_wp
2069	ALP012 = 6.2740815484e-02_wp
2070	ALP003 = -9.5765341718e-03_wp
2071	!
2072	BET000 = 2.1420623987_wp
2073	BET100 = -9.3752598635_wp
2074	BET200 = 1.9446303907e+01_wp
2075	BET300 = -1.8632235232e+01_wp
2076	BET400 = 8.9390837485_wp
2077	BET500 = -1.7142465871_wp
2078	BET010 = -1.7059677327e-01_wp
2079	BET110 = 2.2119589983e-01_wp
2080	BET210 = -2.7123520642e-01_wp
2081	BET310 = 7.3872053057e-02_wp
2082	BET410 = 1.2522950346e-02_wp
2083	BET020 = 3.0054390409e-01_wp
2084	BET120 = -4.2018759976e-01_wp
2085	BET220 = 3.1429341406e-01_wp
2086	BET320 = -9.8855300959e-02_wp
2087	BET030 = -2.6853658626e-01_wp
2088	BET130 = 2.5272385134e-01_wp
2089	BET230 = -2.3503481790e-02_wp
2090	BET040 = 1.2627968731e-01_wp
2091	BET140 = -1.2085092158e-01_wp
2092	BET050 = 1.4394226233e-03_wp
2093	BET001 = -2.2271304375e-01_wp
2094	BET101 = 5.5453416919e-01_wp
2095	BET201 = -6.2815936268e-01_wp
2096	BET301 = 2.0601115202e-01_wp
2097	BET011 = -9.5799229402e-03_wp
2098	BET111 = 1.0286156825e-01_wp
2099	BET211 = -2.5108454043e-02_wp
2100	BET021 = -2.4333834734e-03_wp
2101	BET121 = -3.0443885826e-02_wp
2102	BET031 = 2.7786444526e-03_wp
2103	BET002 = -4.2811838287e-02_wp
2104	BET102 = 5.1355066072e-02_wp
2105	BET012 = -4.3067092900e-03_wp
2106	BET003 = -7.1548119050e-04_wp
2107	!
2108	PEN000 = -5.3743005340_wp
2109	PEN100 = 8.9085217499_wp
2110	PEN200 = -1.1090683384e+01_wp
2111	PEN300 = 8.3754581690_wp
2112	PEN400 = -2.0601115202_wp
2113	PEN010 = 7.9263222935_wp
2114	PEN110 = 3.8319691761e-01_wp
2115	PEN210 = -2.0572313651_wp
2116	PEN310 = 3.3477938724e-01_wp
2117	PEN020 = -4.9997430930_wp
2118	PEN120 = 9.7335338937e-02_wp
2119	PEN220 = 6.0887771651e-01_wp
2120	PEN030 = 1.7433051009_wp
2121	PEN130 = -1.1114577810e-01_wp
2122	PEN040 = -2.9751504321e-01_wp
2123	PEN001 = -6.9171176978e-01_wp
2124	PEN101 = 2.2832980419_wp
2125	PEN201 = -1.3694684286_wp
2126	PEN011 = -1.4557549876_wp
2127	PEN111 = 2.2969116213e-01_wp
2128	PEN021 = 8.3654420645e-01_wp
2129	PEN002 = -1.4046808820e-02_wp
2130	PEN102 = 4.2928871430e-02_wp
2131	PEN012 = -2.8729602515e-01_wp
2132	!
2133	APE000 = -1.9815805734e-01_wp
2134	APE100 = -9.5799229402e-03_wp
2135	APE200 = 5.1430784127e-02_wp
2136	APE300 = -8.3694846809e-03_wp
2137	APE010 = 2.4998715465e-01_wp
2138	APE110 = -4.8667669469e-03_wp
2139	APE210 = -3.0443885826e-02_wp
2140	APE020 = -1.3074788257e-01_wp
2141	APE120 = 8.3359333577e-03_wp
2142	APE030 = 2.9751504321e-02_wp
2143	APE001 = 3.6393874690e-02_wp
2144	APE101 = -5.7422790533e-03_wp
2145	APE011 = -4.1827210323e-02_wp
2146	APE002 = 7.1824006288e-03_wp
2147	!
2148	BPE000 = 1.1135652187e-01_wp
2149	BPE100 = -2.7726708459e-01_wp
2150	BPE200 = 3.1407968134e-01_wp
2151	BPE300 = -1.0300557601e-01_wp
2152	BPE010 = 4.7899614701e-03_wp
2153	BPE110 = -5.1430784127e-02_wp
2154	BPE210 = 1.2554227021e-02_wp
2155	BPE020 = 1.2166917367e-03_wp
2156	BPE120 = 1.5221942913e-02_wp
2157	BPE030 = -1.3893222263e-03_wp
2158	BPE001 = 2.8541225524e-02_wp
2159	BPE101 = -3.4236710714e-02_wp
2160	BPE011 = 2.8711395266e-03_wp
2161	BPE002 = 5.3661089288e-04_wp
2162	!
2163	CASE( np_seos ) !== Simplified EOS ==!
2164
2165	r1_S0 = 0.875_wp/35.16504_wp ! Used to convert CT in potential temperature when using bulk formulae (eos_pt_from_ct)
2166
2167	IF(lwp) THEN
2168	WRITE(numout,*)
2169	WRITE(numout,*) ' ==>>> use of simplified eos: '
2170	WRITE(numout,) ' rhd(dT=T-10,dS=S-35,Z) = [-a0(1+lambda1/2dT+mu1Z)*dT '
2171	WRITE(numout,) ' + b0(1+lambda2/2dT+mu2Z)dS - nudT*dS] / rho0'
2172	WRITE(numout,*) ' with the following coefficients :'
2173	WRITE(numout,*) ' thermal exp. coef. rn_a0 = ', rn_a0
2174	WRITE(numout,*) ' saline cont. coef. rn_b0 = ', rn_b0
2175	WRITE(numout,*) ' cabbeling coef. rn_lambda1 = ', rn_lambda1
2176	WRITE(numout,*) ' cabbeling coef. rn_lambda2 = ', rn_lambda2
2177	WRITE(numout,*) ' thermobar. coef. rn_mu1 = ', rn_mu1
2178	WRITE(numout,*) ' thermobar. coef. rn_mu2 = ', rn_mu2
2179	WRITE(numout,*) ' 2nd cabbel. coef. rn_nu = ', rn_nu
2180	WRITE(numout,*) ' Caution: rn_beta0=0 incompatible with ddm parameterization '
2181	ENDIF
2182	l_useCT = .TRUE. ! Use conservative temperature
2183	!
2184	CASE DEFAULT !== ERROR in neos ==!
2185	WRITE(ctmp1,*) ' bad flag value for neos = ', neos, '. You should never see this error'
2186	CALL ctl_stop( ctmp1 )
2187	!
2188	END SELECT
2189	!
2190	rho0_rcp = rho0 * rcp
2191	r1_rho0 = 1._wp / rho0
2192	r1_rcp = 1._wp / rcp
2193	r1_rho0_rcp = 1._wp / rho0_rcp
2194	!
2195	IF(lwp) THEN
2196	IF( l_useCT ) THEN
2197	WRITE(numout,*)
2198	WRITE(numout,*) ' ==>>> model uses Conservative Temperature'
2199	WRITE(numout,*) ' Important: model must be initialized with CT and SA fields'
2200	ELSE
2201	WRITE(numout,*)
2202	WRITE(numout,*) ' ==>>> model does not use Conservative Temperature'
2203	ENDIF
2204	ENDIF
2205	!
2206	IF(lwp) WRITE(numout,*)
2207	IF(lwp) WRITE(numout,*) ' Associated physical constant'
2208	IF(lwp) WRITE(numout,*) ' volumic mass of reference rho0 = ', rho0 , ' kg/m^3'
2209	IF(lwp) WRITE(numout,*) ' 1. / rho0 r1_rho0 = ', r1_rho0, ' m^3/kg'
2210	IF(lwp) WRITE(numout,*) ' ocean specific heat rcp = ', rcp , ' J/Kelvin'
2211	IF(lwp) WRITE(numout,) ' rho0 rcp rho0_rcp = ', rho0_rcp
2212	IF(lwp) WRITE(numout,) ' 1. / ( rho0 rcp ) r1_rho0_rcp = ', r1_rho0_rcp
2213	!
2214	END SUBROUTINE eos_init
2215
2216	!!======================================================================
2217	END MODULE eosbn2

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