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eosbn2.F90 in NEMO/branches/UKMO/NEMO_4.0-TRUNK_r14960_HPG/tests/SEAMOUNT/MY_SRC – NEMO

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source: NEMO/branches/UKMO/NEMO_4.0-TRUNK_r14960_HPG/tests/SEAMOUNT/MY_SRC/eosbn2.F90 @ 15719

Last change on this file since 15719 was 15719, checked in by dbruciaferri, 2 years ago
updating tests from git repo
File size: 85.2 KB

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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	USE usrdef_nam
53
54	IMPLICIT NONE
55	PRIVATE
56
57	! !! * Interface
58	INTERFACE eos
59	MODULE PROCEDURE eos_insitu, eos_insitu_pot, eos_insitu_2d, eos_insitu_pot_2d
60	END INTERFACE
61	!
62	INTERFACE eos_rab
63	MODULE PROCEDURE rab_3d, rab_2d, rab_0d
64	END INTERFACE
65	!
66	INTERFACE eos_fzp
67	MODULE PROCEDURE eos_fzp_2d, eos_fzp_0d
68	END INTERFACE
69	!
70	PUBLIC eos ! called by step, istate, tranpc and zpsgrd modules
71	PUBLIC bn2 ! called by step module
72	PUBLIC eos_rab ! called by ldfslp, zdfddm, trabbl
73	PUBLIC eos_pt_from_ct ! called by sbcssm
74	PUBLIC eos_fzp ! called by traadv_cen2 and sbcice_... modules
75	PUBLIC eos_pen ! used for pe diagnostics in trdpen module
76	PUBLIC eos_init ! called by istate module
77
78	! !! Namelist nameos
79	LOGICAL , PUBLIC :: ln_TEOS10
80	LOGICAL , PUBLIC :: ln_EOS80
81	LOGICAL , PUBLIC :: ln_SEOS
82	LOGICAL , PUBLIC :: ln_EEOS ! determine if exponential eos is used
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	INTEGER , PARAMETER :: np_eeos = 2 ! parameter for using exponential equation of state (SEAMOUNT)
92
93	! !!! simplified eos coefficients (default value: Vallis 2006)
94	REAL(wp), PUBLIC :: rn_a0 = 1.6550e-1_wp ! thermal expansion coeff.
95	REAL(wp), PUBLIC :: rn_b0 = 7.6554e-1_wp ! saline expansion coeff.
96	REAL(wp) :: rn_lambda1 = 5.9520e-2_wp ! cabbeling coeff. in T^2
97	REAL(wp) :: rn_lambda2 = 5.4914e-4_wp ! cabbeling coeff. in S^2
98	REAL(wp) :: rn_mu1 = 1.4970e-4_wp ! thermobaric coeff. in T
99	REAL(wp) :: rn_mu2 = 1.1090e-5_wp ! thermobaric coeff. in S
100	REAL(wp) :: rn_nu = 2.4341e-3_wp ! cabbeling coeff. in theta*salt
101
102	! TEOS10/EOS80 parameters
103	REAL(wp) :: r1_S0, r1_T0, r1_Z0, rdeltaS
104
105	! EOS parameters
106	REAL(wp) :: EOS000 , EOS100 , EOS200 , EOS300 , EOS400 , EOS500 , EOS600
107	REAL(wp) :: EOS010 , EOS110 , EOS210 , EOS310 , EOS410 , EOS510
108	REAL(wp) :: EOS020 , EOS120 , EOS220 , EOS320 , EOS420
109	REAL(wp) :: EOS030 , EOS130 , EOS230 , EOS330
110	REAL(wp) :: EOS040 , EOS140 , EOS240
111	REAL(wp) :: EOS050 , EOS150
112	REAL(wp) :: EOS060
113	REAL(wp) :: EOS001 , EOS101 , EOS201 , EOS301 , EOS401
114	REAL(wp) :: EOS011 , EOS111 , EOS211 , EOS311
115	REAL(wp) :: EOS021 , EOS121 , EOS221
116	REAL(wp) :: EOS031 , EOS131
117	REAL(wp) :: EOS041
118	REAL(wp) :: EOS002 , EOS102 , EOS202
119	REAL(wp) :: EOS012 , EOS112
120	REAL(wp) :: EOS022
121	REAL(wp) :: EOS003 , EOS103
122	REAL(wp) :: EOS013
123
124	! ALPHA parameters
125	REAL(wp) :: ALP000 , ALP100 , ALP200 , ALP300 , ALP400 , ALP500
126	REAL(wp) :: ALP010 , ALP110 , ALP210 , ALP310 , ALP410
127	REAL(wp) :: ALP020 , ALP120 , ALP220 , ALP320
128	REAL(wp) :: ALP030 , ALP130 , ALP230
129	REAL(wp) :: ALP040 , ALP140
130	REAL(wp) :: ALP050
131	REAL(wp) :: ALP001 , ALP101 , ALP201 , ALP301
132	REAL(wp) :: ALP011 , ALP111 , ALP211
133	REAL(wp) :: ALP021 , ALP121
134	REAL(wp) :: ALP031
135	REAL(wp) :: ALP002 , ALP102
136	REAL(wp) :: ALP012
137	REAL(wp) :: ALP003
138
139	! BETA parameters
140	REAL(wp) :: BET000 , BET100 , BET200 , BET300 , BET400 , BET500
141	REAL(wp) :: BET010 , BET110 , BET210 , BET310 , BET410
142	REAL(wp) :: BET020 , BET120 , BET220 , BET320
143	REAL(wp) :: BET030 , BET130 , BET230
144	REAL(wp) :: BET040 , BET140
145	REAL(wp) :: BET050
146	REAL(wp) :: BET001 , BET101 , BET201 , BET301
147	REAL(wp) :: BET011 , BET111 , BET211
148	REAL(wp) :: BET021 , BET121
149	REAL(wp) :: BET031
150	REAL(wp) :: BET002 , BET102
151	REAL(wp) :: BET012
152	REAL(wp) :: BET003
153
154	! PEN parameters
155	REAL(wp) :: PEN000 , PEN100 , PEN200 , PEN300 , PEN400
156	REAL(wp) :: PEN010 , PEN110 , PEN210 , PEN310
157	REAL(wp) :: PEN020 , PEN120 , PEN220
158	REAL(wp) :: PEN030 , PEN130
159	REAL(wp) :: PEN040
160	REAL(wp) :: PEN001 , PEN101 , PEN201
161	REAL(wp) :: PEN011 , PEN111
162	REAL(wp) :: PEN021
163	REAL(wp) :: PEN002 , PEN102
164	REAL(wp) :: PEN012
165
166	! ALPHA_PEN parameters
167	REAL(wp) :: APE000 , APE100 , APE200 , APE300
168	REAL(wp) :: APE010 , APE110 , APE210
169	REAL(wp) :: APE020 , APE120
170	REAL(wp) :: APE030
171	REAL(wp) :: APE001 , APE101
172	REAL(wp) :: APE011
173	REAL(wp) :: APE002
174
175	! BETA_PEN parameters
176	REAL(wp) :: BPE000 , BPE100 , BPE200 , BPE300
177	REAL(wp) :: BPE010 , BPE110 , BPE210
178	REAL(wp) :: BPE020 , BPE120
179	REAL(wp) :: BPE030
180	REAL(wp) :: BPE001 , BPE101
181	REAL(wp) :: BPE011
182	REAL(wp) :: BPE002
183
184	!! * Substitutions
185	# include "do_loop_substitute.h90"
186	# include "domzgr_substitute.h90"
187	!!----------------------------------------------------------------------
188	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
189	!! $Id: eosbn2.F90 14131 2020-12-08 12:09:14Z jchanut $
190	!! Software governed by the CeCILL license (see ./LICENSE)
191	!!----------------------------------------------------------------------
192	CONTAINS
193
194	SUBROUTINE eos_insitu( 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( pts, is_tile(pts), prd, is_tile(prd), pdep, is_tile(pdep) )
202	END SUBROUTINE eos_insitu
203
204	SUBROUTINE eos_insitu_t( pts, ktts, prd, ktrd, pdep, ktdep )
205	!!----------------------------------------------------------------------
206	!! * ROUTINE eos_insitu *
207	!!
208	!! ** Purpose : Compute the in situ density (ratio rho/rho0) from
209	!! potential temperature and salinity using an equation of state
210	!! selected in the nameos namelist
211	!!
212	!! ** Method : prd(t,s,z) = ( rho(t,s,z) - rho0 ) / rho0
213	!! with prd in situ density anomaly no units
214	!! t TEOS10: CT or EOS80: PT Celsius
215	!! s TEOS10: SA or EOS80: SP TEOS10: g/kg or EOS80: psu
216	!! z depth meters
217	!! rho in situ density kg/m^3
218	!! rho0 reference density kg/m^3
219	!!
220	!! ln_teos10 : polynomial TEOS-10 equation of state is used for rho(t,s,z).
221	!! Check value: rho = 1028.21993233072 kg/m^3 for z=3000 dbar, ct=3 Celsius, sa=35.5 g/kg
222	!!
223	!! ln_eos80 : polynomial EOS-80 equation of state is used for rho(t,s,z).
224	!! Check value: rho = 1028.35011066567 kg/m^3 for z=3000 dbar, pt=3 Celsius, sp=35.5 psu
225	!!
226	!! ln_seos : simplified equation of state
227	!! prd(t,s,z) = ( -a0(1+lambda/2(T-T0)+muz+nu(S-S0))(T-T0) + b0(S-S0) ) / rho0
228	!! linear case function of T only: rn_alpha<>0, other coefficients = 0
229	!! linear eos function of T and S: rn_alpha and rn_beta<>0, other coefficients=0
230	!! Vallis like equation: use default values of coefficients
231	!! ln_eosano : exponential SEAMOUNT equation of state returning density anomaly only
232	!! prd(t,s,z) = ( -a0(T-T0) + b0(S-S0) ) / rho0
233	!! setup for SEAMOUNT exponential 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( nn_hls, nn_hls, nn_hls, nn_hls, 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( nn_hls, nn_hls, nn_hls, nn_hls, 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_eeos ) !== exponential SEAMOUNT EOS ==!
308	!
309	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
310	zt = pts (ji,jj,jk,jp_tem) + ( 28 - rn_drho * EXP(- pdep (ji,jj,jk) / 1000._wp) ) / rn_a0
311	ztm = tmask(ji,jj,jk)
312	!
313	zn = - rn_a0 * zt
314	!
315	prd(ji,jj,jk) = zn * r1_rho0 * ztm ! density anomaly (masked)
316	END_3D
317	END SELECT
318	!
319	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-insitu : ', kdim=jpk )
320	!
321	IF( ln_timing ) CALL timing_stop('eos-insitu')
322	!
323	END SUBROUTINE eos_insitu_t
324
325
326	SUBROUTINE eos_insitu_pot( pts, prd, prhop, pdep )
327	!!
328	REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
329	! ! 2 : salinity [psu]
330	REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: prd ! in situ density [-]
331	REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: prhop ! potential density (surface referenced)
332	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pdep ! depth [m]
333	!!
334	CALL eos_insitu_pot_t( pts, is_tile(pts), prd, is_tile(prd), prhop, is_tile(prhop), pdep, is_tile(pdep) )
335	END SUBROUTINE eos_insitu_pot
336
337
338	SUBROUTINE eos_insitu_pot_t( pts, ktts, prd, ktrd, prhop, ktrhop, pdep, ktdep )
339	!!----------------------------------------------------------------------
340	!! * ROUTINE eos_insitu_pot *
341	!!
342	!! ** Purpose : Compute the in situ density (ratio rho/rho0) and the
343	!! potential volumic mass (Kg/m3) from potential temperature and
344	!! salinity fields using an equation of state selected in the
345	!! namelist.
346	!!
347	!! ** Action : - prd , the in situ density (no units)
348	!! - prhop, the potential volumic mass (Kg/m3)
349	!!
350	!!----------------------------------------------------------------------
351	INTEGER , INTENT(in ) :: ktts, ktrd, ktrhop, ktdep
352	REAL(wp), DIMENSION(A2D_T(ktts) ,JPK,JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
353	! ! 2 : salinity [psu]
354	REAL(wp), DIMENSION(A2D_T(ktrd) ,JPK ), INTENT( out) :: prd ! in situ density [-]
355	REAL(wp), DIMENSION(A2D_T(ktrhop),JPK ), INTENT( out) :: prhop ! potential density (surface referenced)
356	REAL(wp), DIMENSION(A2D_T(ktdep) ,JPK ), INTENT(in ) :: pdep ! depth [m]
357	!
358	INTEGER :: ji, jj, jk, jsmp ! dummy loop indices
359	INTEGER :: jdof
360	REAL(wp) :: zt , zh , zstemp, zs , ztm ! local scalars
361	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
362	REAL(wp), DIMENSION(:), ALLOCATABLE :: zn0_sto, zn_sto, zsign ! local vectors
363	!!----------------------------------------------------------------------
364	!
365	IF( ln_timing ) CALL timing_start('eos-pot')
366	!
367	SELECT CASE ( neos )
368	!
369	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
370	!
371	! Stochastic equation of state
372	IF ( ln_sto_eos ) THEN
373	ALLOCATE(zn0_sto(1:2*nn_sto_eos))
374	ALLOCATE(zn_sto(1:2*nn_sto_eos))
375	ALLOCATE(zsign(1:2*nn_sto_eos))
376	DO jsmp = 1, 2*nn_sto_eos, 2
377	zsign(jsmp) = 1._wp
378	zsign(jsmp+1) = -1._wp
379	END DO
380	!
381	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
382	!
383	! compute density (2*nn_sto_eos) times:
384	! (1) for t+dt, s+ds (with the random TS fluctutation computed in sto_pts)
385	! (2) for t-dt, s-ds (with the opposite fluctuation)
386	DO jsmp = 1, nn_sto_eos*2
387	jdof = (jsmp + 1) / 2
388	zh = pdep(ji,jj,jk) * r1_Z0 ! depth
389	zt = (pts (ji,jj,jk,jp_tem) + pts_ran(ji,jj,jk,jp_tem,jdof) * zsign(jsmp)) * r1_T0 ! temperature
390	zstemp = pts (ji,jj,jk,jp_sal) + pts_ran(ji,jj,jk,jp_sal,jdof) * zsign(jsmp)
391	zs = SQRT( ABS( zstemp + rdeltaS ) * r1_S0 ) ! square root salinity
392	ztm = tmask(ji,jj,jk) ! tmask
393	!
394	zn3 = EOS013*zt &
395	& + EOS103*zs+EOS003
396	!
397	zn2 = (EOS022*zt &
398	& + EOS112zs+EOS012)zt &
399	& + (EOS202zs+EOS102)zs+EOS002
400	!
401	zn1 = (((EOS041*zt &
402	& + EOS131zs+EOS031)zt &
403	& + (EOS221zs+EOS121)zs+EOS021)*zt &
404	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
405	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
406	!
407	zn0_sto(jsmp) = (((((EOS060*zt &
408	& + EOS150zs+EOS050)zt &
409	& + (EOS240zs+EOS140)zs+EOS040)*zt &
410	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
411	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
412	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
413	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
414	!
415	zn_sto(jsmp) = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0_sto(jsmp)
416	END DO
417	!
418	! compute stochastic density as the mean of the (2*nn_sto_eos) densities
419	prhop(ji,jj,jk) = 0._wp ; prd(ji,jj,jk) = 0._wp
420	DO jsmp = 1, nn_sto_eos*2
421	prhop(ji,jj,jk) = prhop(ji,jj,jk) + zn0_sto(jsmp) ! potential density referenced at the surface
422	!
423	prd(ji,jj,jk) = prd(ji,jj,jk) + ( zn_sto(jsmp) * r1_rho0 - 1._wp ) ! density anomaly (masked)
424	END DO
425	prhop(ji,jj,jk) = 0.5_wp * prhop(ji,jj,jk) * ztm / nn_sto_eos
426	prd (ji,jj,jk) = 0.5_wp * prd (ji,jj,jk) * ztm / nn_sto_eos
427	END_3D
428	DEALLOCATE(zn0_sto,zn_sto,zsign)
429	! Non-stochastic equation of state
430	ELSE
431	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
432	!
433	zh = pdep(ji,jj,jk) * r1_Z0 ! depth
434	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
435	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
436	ztm = tmask(ji,jj,jk) ! tmask
437	!
438	zn3 = EOS013*zt &
439	& + EOS103*zs+EOS003
440	!
441	zn2 = (EOS022*zt &
442	& + EOS112zs+EOS012)zt &
443	& + (EOS202zs+EOS102)zs+EOS002
444	!
445	zn1 = (((EOS041*zt &
446	& + EOS131zs+EOS031)zt &
447	& + (EOS221zs+EOS121)zs+EOS021)*zt &
448	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
449	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
450	!
451	zn0 = (((((EOS060*zt &
452	& + EOS150zs+EOS050)zt &
453	& + (EOS240zs+EOS140)zs+EOS040)*zt &
454	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
455	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
456	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
457	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
458	!
459	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
460	!
461	prhop(ji,jj,jk) = zn0 * ztm ! potential density referenced at the surface
462	!
463	prd(ji,jj,jk) = ( zn * r1_rho0 - 1._wp ) * ztm ! density anomaly (masked)
464	END_3D
465	ENDIF
466
467	CASE( np_seos ) !== simplified EOS ==!
468	!
469	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
470	zt = pts (ji,jj,jk,jp_tem) - 10._wp
471	zs = pts (ji,jj,jk,jp_sal) - 35._wp
472	zh = pdep (ji,jj,jk)
473	ztm = tmask(ji,jj,jk)
474	! ! potential density referenced at the surface
475	zn = - rn_a0 * ( 1._wp + 0.5_wprn_lambda1zt ) * zt &
476	& + rn_b0 * ( 1._wp - 0.5_wprn_lambda2zs ) * zs &
477	& - rn_nu * zt * zs
478	prhop(ji,jj,jk) = ( rho0 + zn ) * ztm
479	! ! density anomaly (masked)
480	zn = zn - ( rn_a0 * rn_mu1 * zt + rn_b0 * rn_mu2 * zs ) * zh
481	prd(ji,jj,jk) = zn * r1_rho0 * ztm
482	!
483	END_3D
484	!
485	CASE( np_eeos ) !== exponential SEAMOUNT EOS ==!
486	!
487	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
488	zt = pts (ji,jj,jk,jp_tem) + ( 28 - rn_drho * EXP(- pdep (ji,jj,jk) / 1000._wp) ) / rn_a0
489	ztm = tmask(ji,jj,jk)
490	!
491	zn = - rn_a0 * zt
492	! ! potential density referenced at the surface
493	prhop(ji,jj,jk) = ( rho0 + zn ) * ztm
494	prd(ji,jj,jk) = zn * r1_rho0 * ztm ! density anomaly (masked)
495	END_3D
496	!
497	END SELECT
498	!
499	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-pot: ', &
500	& tab3d_2=prhop, clinfo2=' pot : ', kdim=jpk )
501	!
502	IF( ln_timing ) CALL timing_stop('eos-pot')
503	!
504	END SUBROUTINE eos_insitu_pot_t
505
506
507	SUBROUTINE eos_insitu_2d( pts, pdep, prd )
508	!!
509	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
510	! ! 2 : salinity [psu]
511	REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pdep ! depth [m]
512	REAL(wp), DIMENSION(:,:) , INTENT( out) :: prd ! in situ density
513	!!
514	CALL eos_insitu_2d_t( pts, is_tile(pts), pdep, is_tile(pdep), prd, is_tile(prd) )
515	END SUBROUTINE eos_insitu_2d
516
517
518	SUBROUTINE eos_insitu_2d_t( pts, ktts, pdep, ktdep, prd, ktrd )
519	!!----------------------------------------------------------------------
520	!! * ROUTINE eos_insitu_2d *
521	!!
522	!! ** Purpose : Compute the in situ density (ratio rho/rho0) from
523	!! potential temperature and salinity using an equation of state
524	!! selected in the nameos namelist. * 2D field case
525	!!
526	!! ** Action : - prd , the in situ density (no units) (unmasked)
527	!!
528	!!----------------------------------------------------------------------
529	INTEGER , INTENT(in ) :: ktts, ktdep, ktrd
530	REAL(wp), DIMENSION(A2D_T(ktts),JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
531	! ! 2 : salinity [psu]
532	REAL(wp), DIMENSION(A2D_T(ktdep) ), INTENT(in ) :: pdep ! depth [m]
533	REAL(wp), DIMENSION(A2D_T(ktrd) ), INTENT( out) :: prd ! in situ density
534	!
535	INTEGER :: ji, jj, jk ! dummy loop indices
536	REAL(wp) :: zt , zh , zs ! local scalars
537	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
538	!!----------------------------------------------------------------------
539	!
540	IF( ln_timing ) CALL timing_start('eos2d')
541	!
542	prd(:,:) = 0._wp
543	!
544	SELECT CASE( neos )
545	!
546	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
547	!
548	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
549	!
550	zh = pdep(ji,jj) * r1_Z0 ! depth
551	zt = pts (ji,jj,jp_tem) * r1_T0 ! temperature
552	zs = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
553	!
554	zn3 = EOS013*zt &
555	& + EOS103*zs+EOS003
556	!
557	zn2 = (EOS022*zt &
558	& + EOS112zs+EOS012)zt &
559	& + (EOS202zs+EOS102)zs+EOS002
560	!
561	zn1 = (((EOS041*zt &
562	& + EOS131zs+EOS031)zt &
563	& + (EOS221zs+EOS121)zs+EOS021)*zt &
564	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
565	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
566	!
567	zn0 = (((((EOS060*zt &
568	& + EOS150zs+EOS050)zt &
569	& + (EOS240zs+EOS140)zs+EOS040)*zt &
570	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
571	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
572	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
573	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
574	!
575	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
576	!
577	prd(ji,jj) = zn * r1_rho0 - 1._wp ! unmasked in situ density anomaly
578	!
579	END_2D
580	!
581	CASE( np_seos ) !== simplified EOS ==!
582	!
583	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
584	!
585	zt = pts (ji,jj,jp_tem) - 10._wp
586	zs = pts (ji,jj,jp_sal) - 35._wp
587	zh = pdep (ji,jj) ! depth at the partial step level
588	!
589	zn = - rn_a0 * ( 1._wp + 0.5_wprn_lambda1zt + rn_mu1zh ) zt &
590	& + rn_b0 * ( 1._wp - 0.5_wprn_lambda2zs - rn_mu2zh ) zs &
591	& - rn_nu * zt * zs
592	!
593	prd(ji,jj) = zn * r1_rho0 ! unmasked in situ density anomaly
594	!
595	END_2D
596	!
597	CASE( np_eeos ) !== exponential SEAMOUNT EOS ==!
598	!
599	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
600	zt = pts (ji,jj,jp_tem) + ( 28 - rn_drho * EXP(- pdep (ji,jj) / 1000._wp) ) / rn_a0
601	!
602	zn = - rn_a0 * zt
603	!
604	prd(ji,jj) = zn * r1_rho0 ! density anomaly (masked)
605	END_2D
606	!
607	END SELECT
608	!
609	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=prd, clinfo1=' eos2d: ' )
610	!
611	IF( ln_timing ) CALL timing_stop('eos2d')
612	!
613	END SUBROUTINE eos_insitu_2d_t
614
615
616	SUBROUTINE eos_insitu_pot_2d( pts, prhop )
617	!!
618	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
619	! ! 2 : salinity [psu]
620	REAL(wp), DIMENSION(:,:) , INTENT( out) :: prhop ! potential density (surface referenced)
621	!!
622	CALL eos_insitu_pot_2d_t( pts, is_tile(pts), prhop, is_tile(prhop) )
623	END SUBROUTINE eos_insitu_pot_2d
624
625	SUBROUTINE eos_insitu_pot_2d_t( pts, ktts, prhop, ktrhop )
626	!!----------------------------------------------------------------------
627	!! * ROUTINE eos_insitu_pot *
628	!!
629	!! ** Purpose : Compute the in situ density (ratio rho/rho0) and the
630	!! potential volumic mass (Kg/m3) from potential temperature and
631	!! salinity fields using an equation of state selected in the
632	!! namelist.
633	!!
634	!! ** Action :
635	!! - prhop, the potential volumic mass (Kg/m3)
636	!!
637	!!----------------------------------------------------------------------
638	INTEGER , INTENT(in ) :: ktts, ktrhop
639	REAL(wp), DIMENSION(A2D_T(ktts),JPTS), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
640	! ! 2 : salinity [psu]
641	REAL(wp), DIMENSION(A2D_T(ktrhop) ), 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( nn_hls, nn_hls, nn_hls, nn_hls )
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( nn_hls, nn_hls, nn_hls, nn_hls )
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	CASE( np_eeos ) !== exponential SEAMOUNT EOS ==!
689	!
690	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
691	zt = pts (ji,jj,jp_tem) + ( 28 ) / rn_a0
692	ztm = tmask(ji,jj,1)
693	!
694	zn = - rn_a0 * zt
695	!
696	prhop(ji,jj) = ( rho0 + zn ) * ztm
697	END_2D
698	!
699	END SELECT
700	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=prhop, clinfo1=' pot: ', kdim=1 )
701	!
702	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=prhop, clinfo1=' eos-pot: ' )
703	!
704	IF( ln_timing ) CALL timing_stop('eos-pot')
705	!
706	END SUBROUTINE eos_insitu_pot_2d_t
707
708
709	SUBROUTINE rab_3d( pts, pab, Kmm )
710	!!
711	INTEGER , INTENT(in ) :: Kmm ! time level index
712	REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! pot. temperature & salinity
713	REAL(wp), DIMENSION(:,:,:,:), INTENT( out) :: pab ! thermal/haline expansion ratio
714	!!
715	CALL rab_3d_t( pts, is_tile(pts), pab, is_tile(pab), Kmm )
716	END SUBROUTINE rab_3d
717
718
719	SUBROUTINE rab_3d_t( pts, ktts, pab, ktab, Kmm )
720	!!----------------------------------------------------------------------
721	!! * ROUTINE rab_3d *
722	!!
723	!! ** Purpose : Calculates thermal/haline expansion ratio at T-points
724	!!
725	!! ** Method : calculates alpha / beta at T-points
726	!!
727	!! ** Action : - pab : thermal/haline expansion ratio at T-points
728	!!----------------------------------------------------------------------
729	INTEGER , INTENT(in ) :: Kmm ! time level index
730	INTEGER , INTENT(in ) :: ktts, ktab
731	REAL(wp), DIMENSION(A2D_T(ktts),JPK,JPTS), INTENT(in ) :: pts ! pot. temperature & salinity
732	REAL(wp), DIMENSION(A2D_T(ktab),JPK,JPTS), INTENT( out) :: pab ! thermal/haline expansion ratio
733	!
734	INTEGER :: ji, jj, jk ! dummy loop indices
735	REAL(wp) :: zt , zh , zs , ztm ! local scalars
736	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
737	!!----------------------------------------------------------------------
738	!
739	IF( ln_timing ) CALL timing_start('rab_3d')
740	!
741	SELECT CASE ( neos )
742	!
743	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
744	!
745	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
746	!
747	zh = gdept(ji,jj,jk,Kmm) * r1_Z0 ! depth
748	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
749	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
750	ztm = tmask(ji,jj,jk) ! tmask
751	!
752	! alpha
753	zn3 = ALP003
754	!
755	zn2 = ALP012zt + ALP102zs+ALP002
756	!
757	zn1 = ((ALP031*zt &
758	& + ALP121zs+ALP021)zt &
759	& + (ALP211zs+ALP111)zs+ALP011)*zt &
760	& + ((ALP301zs+ALP201)zs+ALP101)*zs+ALP001
761	!
762	zn0 = ((((ALP050*zt &
763	& + ALP140zs+ALP040)zt &
764	& + (ALP230zs+ALP130)zs+ALP030)*zt &
765	& + ((ALP320zs+ALP220)zs+ALP120)zs+ALP020)zt &
766	& + (((ALP410zs+ALP310)zs+ALP210)zs+ALP110)zs+ALP010)*zt &
767	& + ((((ALP500zs+ALP400)zs+ALP300)zs+ALP200)zs+ALP100)*zs+ALP000
768	!
769	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
770	!
771	pab(ji,jj,jk,jp_tem) = zn * r1_rho0 * ztm
772	!
773	! beta
774	zn3 = BET003
775	!
776	zn2 = BET012zt + BET102zs+BET002
777	!
778	zn1 = ((BET031*zt &
779	& + BET121zs+BET021)zt &
780	& + (BET211zs+BET111)zs+BET011)*zt &
781	& + ((BET301zs+BET201)zs+BET101)*zs+BET001
782	!
783	zn0 = ((((BET050*zt &
784	& + BET140zs+BET040)zt &
785	& + (BET230zs+BET130)zs+BET030)*zt &
786	& + ((BET320zs+BET220)zs+BET120)zs+BET020)zt &
787	& + (((BET410zs+BET310)zs+BET210)zs+BET110)zs+BET010)*zt &
788	& + ((((BET500zs+BET400)zs+BET300)zs+BET200)zs+BET100)*zs+BET000
789	!
790	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
791	!
792	pab(ji,jj,jk,jp_sal) = zn / zs * r1_rho0 * ztm
793	!
794	END_3D
795	!
796	CASE( np_seos ) !== simplified EOS ==!
797	!
798	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
799	zt = pts (ji,jj,jk,jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
800	zs = pts (ji,jj,jk,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
801	zh = gdept(ji,jj,jk,Kmm) ! depth in meters at t-point
802	ztm = tmask(ji,jj,jk) ! land/sea bottom mask = surf. mask
803	!
804	zn = rn_a0 * ( 1._wp + rn_lambda1zt + rn_mu1zh ) + rn_nu*zs
805	pab(ji,jj,jk,jp_tem) = zn * r1_rho0 * ztm ! alpha
806	!
807	zn = rn_b0 * ( 1._wp - rn_lambda2zs - rn_mu2zh ) - rn_nu*zt
808	pab(ji,jj,jk,jp_sal) = zn * r1_rho0 * ztm ! beta
809	!
810	END_3D
811	!
812	CASE( np_eeos ) !== exponential SEAMOUNT EOS ==!
813	!
814	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
815	zt = pts (ji,jj,jk,jp_tem) + ( 28 - rn_drho * EXP(- gdept (ji,jj,jk,Kmm) / 1000._wp) ) / rn_a0
816	ztm = tmask(ji,jj,jk)
817	!
818	zn = rn_a0
819	!
820	pab(ji,jj,jk,jp_tem) = zn * r1_rho0 * ztm ! alpha
821	pab(ji,jj,jk,jp_sal) = 0
822	!
823	END_3D
824	CASE DEFAULT
825	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
826	CALL ctl_stop( 'rab_3d:', ctmp1 )
827	!
828	END SELECT
829	!
830	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=pab(:,:,:,jp_tem), clinfo1=' rab_3d_t: ', &
831	& tab3d_2=pab(:,:,:,jp_sal), clinfo2=' rab_3d_s : ', kdim=jpk )
832	!
833	IF( ln_timing ) CALL timing_stop('rab_3d')
834	!
835	END SUBROUTINE rab_3d_t
836
837
838	SUBROUTINE rab_2d( pts, pdep, pab, Kmm )
839	!!
840	INTEGER , INTENT(in ) :: Kmm ! time level index
841	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pts ! pot. temperature & salinity
842	REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pdep ! depth [m]
843	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: pab ! thermal/haline expansion ratio
844	!!
845	CALL rab_2d_t(pts, is_tile(pts), pdep, is_tile(pdep), pab, is_tile(pab), Kmm)
846	END SUBROUTINE rab_2d
847
848
849	SUBROUTINE rab_2d_t( pts, ktts, pdep, ktdep, pab, ktab, Kmm )
850	!!----------------------------------------------------------------------
851	!! * ROUTINE rab_2d *
852	!!
853	!! ** Purpose : Calculates thermal/haline expansion ratio for a 2d field (unmasked)
854	!!
855	!! ** Action : - pab : thermal/haline expansion ratio at T-points
856	!!----------------------------------------------------------------------
857	INTEGER , INTENT(in ) :: Kmm ! time level index
858	INTEGER , INTENT(in ) :: ktts, ktdep, ktab
859	REAL(wp), DIMENSION(A2D_T(ktts),JPTS), INTENT(in ) :: pts ! pot. temperature & salinity
860	REAL(wp), DIMENSION(A2D_T(ktdep) ), INTENT(in ) :: pdep ! depth [m]
861	REAL(wp), DIMENSION(A2D_T(ktab),JPTS), INTENT( out) :: pab ! thermal/haline expansion ratio
862	!
863	INTEGER :: ji, jj, jk ! dummy loop indices
864	REAL(wp) :: zt , zh , zs ! local scalars
865	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
866	!!----------------------------------------------------------------------
867	!
868	IF( ln_timing ) CALL timing_start('rab_2d')
869	!
870	pab(:,:,:) = 0._wp
871	!
872	SELECT CASE ( neos )
873	!
874	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
875	!
876	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
877	!
878	zh = pdep(ji,jj) * r1_Z0 ! depth
879	zt = pts (ji,jj,jp_tem) * r1_T0 ! temperature
880	zs = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
881	!
882	! alpha
883	zn3 = ALP003
884	!
885	zn2 = ALP012zt + ALP102zs+ALP002
886	!
887	zn1 = ((ALP031*zt &
888	& + ALP121zs+ALP021)zt &
889	& + (ALP211zs+ALP111)zs+ALP011)*zt &
890	& + ((ALP301zs+ALP201)zs+ALP101)*zs+ALP001
891	!
892	zn0 = ((((ALP050*zt &
893	& + ALP140zs+ALP040)zt &
894	& + (ALP230zs+ALP130)zs+ALP030)*zt &
895	& + ((ALP320zs+ALP220)zs+ALP120)zs+ALP020)zt &
896	& + (((ALP410zs+ALP310)zs+ALP210)zs+ALP110)zs+ALP010)*zt &
897	& + ((((ALP500zs+ALP400)zs+ALP300)zs+ALP200)zs+ALP100)*zs+ALP000
898	!
899	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
900	!
901	pab(ji,jj,jp_tem) = zn * r1_rho0
902	!
903	! beta
904	zn3 = BET003
905	!
906	zn2 = BET012zt + BET102zs+BET002
907	!
908	zn1 = ((BET031*zt &
909	& + BET121zs+BET021)zt &
910	& + (BET211zs+BET111)zs+BET011)*zt &
911	& + ((BET301zs+BET201)zs+BET101)*zs+BET001
912	!
913	zn0 = ((((BET050*zt &
914	& + BET140zs+BET040)zt &
915	& + (BET230zs+BET130)zs+BET030)*zt &
916	& + ((BET320zs+BET220)zs+BET120)zs+BET020)zt &
917	& + (((BET410zs+BET310)zs+BET210)zs+BET110)zs+BET010)*zt &
918	& + ((((BET500zs+BET400)zs+BET300)zs+BET200)zs+BET100)*zs+BET000
919	!
920	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
921	!
922	pab(ji,jj,jp_sal) = zn / zs * r1_rho0
923	!
924	!
925	END_2D
926	!
927	CASE( np_seos ) !== simplified EOS ==!
928	!
929	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
930	!
931	zt = pts (ji,jj,jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
932	zs = pts (ji,jj,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
933	zh = pdep (ji,jj) ! depth at the partial step level
934	!
935	zn = rn_a0 * ( 1._wp + rn_lambda1zt + rn_mu1zh ) + rn_nu*zs
936	pab(ji,jj,jp_tem) = zn * r1_rho0 ! alpha
937	!
938	zn = rn_b0 * ( 1._wp - rn_lambda2zs - rn_mu2zh ) - rn_nu*zt
939	pab(ji,jj,jp_sal) = zn * r1_rho0 ! beta
940	!
941	END_2D
942	!
943	CASE( np_eeos ) !== exponential SEAMOUNT EOS ==!
944	!
945	DO_2D( nn_hls, nn_hls, nn_hls, nn_hls )
946	zt = pts (ji,jj,jp_tem) + ( 28 - rn_drho * EXP(- pdep (ji,jj) / 1000._wp) ) / rn_a0
947	!
948	zn = rn_a0
949	!
950	pab(ji,jj,jp_tem) = zn * r1_rho0 ! alpha
951	pab(ji,jj,jp_sal) = 0.0_wp
952	END_2D
953	CASE DEFAULT
954	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
955	CALL ctl_stop( 'rab_2d:', ctmp1 )
956	!
957	END SELECT
958	!
959	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=pab(:,:,jp_tem), clinfo1=' rab_2d_t: ', &
960	& tab2d_2=pab(:,:,jp_sal), clinfo2=' rab_2d_s : ' )
961	!
962	IF( ln_timing ) CALL timing_stop('rab_2d')
963	!
964	END SUBROUTINE rab_2d_t
965
966
967	SUBROUTINE rab_0d( pts, pdep, pab, Kmm )
968	!!----------------------------------------------------------------------
969	!! * ROUTINE rab_0d *
970	!!
971	!! ** Purpose : Calculates thermal/haline expansion ratio for a 2d field (unmasked)
972	!!
973	!! ** Action : - pab : thermal/haline expansion ratio at T-points
974	!!----------------------------------------------------------------------
975	INTEGER , INTENT(in ) :: Kmm ! time level index
976	REAL(wp), DIMENSION(jpts) , INTENT(in ) :: pts ! pot. temperature & salinity
977	REAL(wp), INTENT(in ) :: pdep ! depth [m]
978	REAL(wp), DIMENSION(jpts) , INTENT( out) :: pab ! thermal/haline expansion ratio
979	!
980	REAL(wp) :: zt , zh , zs ! local scalars
981	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
982	!!----------------------------------------------------------------------
983	!
984	IF( ln_timing ) CALL timing_start('rab_0d')
985	!
986	pab(:) = 0._wp
987	!
988	SELECT CASE ( neos )
989	!
990	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
991	!
992	!
993	zh = pdep * r1_Z0 ! depth
994	zt = pts (jp_tem) * r1_T0 ! temperature
995	zs = SQRT( ABS( pts(jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
996	!
997	! alpha
998	zn3 = ALP003
999	!
1000	zn2 = ALP012zt + ALP102zs+ALP002
1001	!
1002	zn1 = ((ALP031*zt &
1003	& + ALP121zs+ALP021)zt &
1004	& + (ALP211zs+ALP111)zs+ALP011)*zt &
1005	& + ((ALP301zs+ALP201)zs+ALP101)*zs+ALP001
1006	!
1007	zn0 = ((((ALP050*zt &
1008	& + ALP140zs+ALP040)zt &
1009	& + (ALP230zs+ALP130)zs+ALP030)*zt &
1010	& + ((ALP320zs+ALP220)zs+ALP120)zs+ALP020)zt &
1011	& + (((ALP410zs+ALP310)zs+ALP210)zs+ALP110)zs+ALP010)*zt &
1012	& + ((((ALP500zs+ALP400)zs+ALP300)zs+ALP200)zs+ALP100)*zs+ALP000
1013	!
1014	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
1015	!
1016	pab(jp_tem) = zn * r1_rho0
1017	!
1018	! beta
1019	zn3 = BET003
1020	!
1021	zn2 = BET012zt + BET102zs+BET002
1022	!
1023	zn1 = ((BET031*zt &
1024	& + BET121zs+BET021)zt &
1025	& + (BET211zs+BET111)zs+BET011)*zt &
1026	& + ((BET301zs+BET201)zs+BET101)*zs+BET001
1027	!
1028	zn0 = ((((BET050*zt &
1029	& + BET140zs+BET040)zt &
1030	& + (BET230zs+BET130)zs+BET030)*zt &
1031	& + ((BET320zs+BET220)zs+BET120)zs+BET020)zt &
1032	& + (((BET410zs+BET310)zs+BET210)zs+BET110)zs+BET010)*zt &
1033	& + ((((BET500zs+BET400)zs+BET300)zs+BET200)zs+BET100)*zs+BET000
1034	!
1035	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
1036	!
1037	pab(jp_sal) = zn / zs * r1_rho0
1038	!
1039	!
1040	!
1041	CASE( np_seos ) !== simplified EOS ==!
1042	!
1043	zt = pts(jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
1044	zs = pts(jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
1045	zh = pdep ! depth at the partial step level
1046	!
1047	zn = rn_a0 * ( 1._wp + rn_lambda1zt + rn_mu1zh ) + rn_nu*zs
1048	pab(jp_tem) = zn * r1_rho0 ! alpha
1049	!
1050	zn = rn_b0 * ( 1._wp - rn_lambda2zs - rn_mu2zh ) - rn_nu*zt
1051	pab(jp_sal) = zn * r1_rho0 ! beta
1052	!
1053	CASE( np_eeos ) !== exponential SEAMOUNT EOS ==!
1054	!
1055	zt = pts (jp_tem) + ( 28 - rn_drho * EXP(- pdep / 1000._wp) ) / rn_a0
1056	!
1057	zn = rn_a0
1058	!
1059	pab(jp_tem) = zn * r1_rho0 ! alpha
1060	pab(jp_sal) = zn * r1_rho0 ! beta
1061	!
1062	CASE DEFAULT
1063	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1064	CALL ctl_stop( 'rab_0d:', ctmp1 )
1065	!
1066	END SELECT
1067	!
1068	IF( ln_timing ) CALL timing_stop('rab_0d')
1069	!
1070	END SUBROUTINE rab_0d
1071
1072
1073	SUBROUTINE bn2( pts, pab, pn2, Kmm )
1074	!!
1075	INTEGER , INTENT(in ) :: Kmm ! time level index
1076	REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature and salinity [Celsius,psu]
1077	REAL(wp), DIMENSION(:,:,:,:) , INTENT(in ) :: pab ! thermal/haline expansion coef. [Celsius-1,psu-1]
1078	REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: pn2 ! Brunt-Vaisala frequency squared [1/s^2]
1079	!!
1080	CALL bn2_t( pts, pab, is_tile(pab), pn2, is_tile(pn2), Kmm )
1081	END SUBROUTINE bn2
1082
1083
1084	SUBROUTINE bn2_t( pts, pab, ktab, pn2, ktn2, Kmm )
1085	!!----------------------------------------------------------------------
1086	!! * ROUTINE bn2 *
1087	!!
1088	!! ** Purpose : Compute the local Brunt-Vaisala frequency at the
1089	!! time-step of the input arguments
1090	!!
1091	!! ** Method : pn2 = grav * (alpha dk[T] + beta dk[S] ) / e3w
1092	!! where alpha and beta are given in pab, and computed on T-points.
1093	!! N.B. N^2 is set one for all to zero at jk=1 in istate module.
1094	!!
1095	!! ** Action : pn2 : square of the brunt-vaisala frequency at w-point
1096	!!
1097	!!----------------------------------------------------------------------
1098	INTEGER , INTENT(in ) :: Kmm ! time level index
1099	INTEGER , INTENT(in ) :: ktab, ktn2
1100	REAL(wp), DIMENSION(jpi,jpj, jpk,jpts), INTENT(in ) :: pts ! pot. temperature and salinity [Celsius,psu]
1101	REAL(wp), DIMENSION(A2D_T(ktab),JPK,JPTS), INTENT(in ) :: pab ! thermal/haline expansion coef. [Celsius-1,psu-1]
1102	REAL(wp), DIMENSION(A2D_T(ktn2),JPK ), INTENT( out) :: pn2 ! Brunt-Vaisala frequency squared [1/s^2]
1103	!
1104	INTEGER :: ji, jj, jk ! dummy loop indices
1105	REAL(wp) :: zaw, zbw, zrw ! local scalars
1106	!!----------------------------------------------------------------------
1107	!
1108	IF( ln_timing ) CALL timing_start('bn2')
1109	!
1110	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
1111	zrw = ( gdepw(ji,jj,jk ,Kmm) - gdept(ji,jj,jk,Kmm) ) &
1112	& / ( gdept(ji,jj,jk-1,Kmm) - gdept(ji,jj,jk,Kmm) )
1113	!
1114	zaw = pab(ji,jj,jk,jp_tem) * (1. - zrw) + pab(ji,jj,jk-1,jp_tem) * zrw
1115	zbw = pab(ji,jj,jk,jp_sal) * (1. - zrw) + pab(ji,jj,jk-1,jp_sal) * zrw
1116	!
1117	pn2(ji,jj,jk) = grav * ( zaw * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) &
1118	& - zbw * ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) ) &
1119	& / e3w(ji,jj,jk,Kmm) * wmask(ji,jj,jk)
1120	END_3D
1121	!
1122	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=pn2, clinfo1=' bn2 : ', kdim=jpk )
1123	!
1124	IF( ln_timing ) CALL timing_stop('bn2')
1125	!
1126	END SUBROUTINE bn2_t
1127
1128
1129	FUNCTION eos_pt_from_ct( ctmp, psal ) RESULT( ptmp )
1130	!!----------------------------------------------------------------------
1131	!! * ROUTINE eos_pt_from_ct *
1132	!!
1133	!! ** Purpose : Compute pot.temp. from cons. temp. [Celsius]
1134	!!
1135	!! ** Method : rational approximation (5/3th order) of TEOS-10 algorithm
1136	!! checkvalue: pt=20.02391895 Celsius for sa=35.7g/kg, ct=20degC
1137	!!
1138	!! Reference : TEOS-10, UNESCO
1139	!! Rational approximation to TEOS10 algorithm (rms error on WOA13 values: 4.0e-5 degC)
1140	!!----------------------------------------------------------------------
1141	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: ctmp ! Cons. Temp [Celsius]
1142	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu]
1143	! Leave result array automatic rather than making explicitly allocated
1144	REAL(wp), DIMENSION(jpi,jpj) :: ptmp ! potential temperature [Celsius]
1145	!
1146	INTEGER :: ji, jj ! dummy loop indices
1147	REAL(wp) :: zt , zs , ztm ! local scalars
1148	REAL(wp) :: zn , zd ! local scalars
1149	REAL(wp) :: zdeltaS , z1_S0 , z1_T0
1150	!!----------------------------------------------------------------------
1151	!
1152	IF( ln_timing ) CALL timing_start('eos_pt_from_ct')
1153	!
1154	zdeltaS = 5._wp
1155	z1_S0 = 0.875_wp/35.16504_wp
1156	z1_T0 = 1._wp/40._wp
1157	!
1158	DO_2D( 1, 1, 1, 1 )
1159	!
1160	zt = ctmp (ji,jj) * z1_T0
1161	zs = SQRT( ABS( psal(ji,jj) + zdeltaS ) * r1_S0 )
1162	ztm = tmask(ji,jj,1)
1163	!
1164	zn = ((((-2.1385727895e-01_wp*zt &
1165	& - 2.7674419971e-01_wpzs+1.0728094330_wp)zt &
1166	& + (2.6366564313_wpzs+3.3546960647_wp)zs-7.8012209473_wp)*zt &
1167	& + ((1.8835586562_wpzs+7.3949191679_wp)zs-3.3937395875_wp)zs-5.6414948432_wp)zt &
1168	& + (((3.5737370589_wpzs-1.5512427389e+01_wp)zs+2.4625741105e+01_wp)*zs &
1169	& +1.9912291000e+01_wp)zs-3.2191146312e+01_wp)zt &
1170	& + ((((5.7153204649e-01_wpzs-3.0943149543_wp)zs+9.3052495181_wp)*zs &
1171	& -9.4528934807_wp)zs+3.1066408996_wp)zs-4.3504021262e-01_wp
1172	!
1173	zd = (2.0035003456_wp*zt &
1174	& -3.4570358592e-01_wpzs+5.6471810638_wp)zt &
1175	& + (1.5393993508_wpzs-6.9394762624_wp)zs+1.2750522650e+01_wp
1176	!
1177	ptmp(ji,jj) = ( zt / z1_T0 + zn / zd ) * ztm
1178	!
1179	END_2D
1180	!
1181	IF( ln_timing ) CALL timing_stop('eos_pt_from_ct')
1182	!
1183	END FUNCTION eos_pt_from_ct
1184
1185
1186	SUBROUTINE eos_fzp_2d( psal, ptf, pdep )
1187	!!
1188	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu]
1189	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ), OPTIONAL :: pdep ! depth [m]
1190	REAL(wp), DIMENSION(:,:) , INTENT(out ) :: ptf ! freezing temperature [Celsius]
1191	!!
1192	CALL eos_fzp_2d_t( psal, ptf, is_tile(ptf), pdep )
1193	END SUBROUTINE eos_fzp_2d
1194
1195
1196	SUBROUTINE eos_fzp_2d_t( psal, ptf, kttf, pdep )
1197	!!----------------------------------------------------------------------
1198	!! * ROUTINE eos_fzp *
1199	!!
1200	!! ** Purpose : Compute the freezing point temperature [Celsius]
1201	!!
1202	!! ** Method : UNESCO freezing point (ptf) in Celsius is given by
1203	!! ptf(t,z) = (-.0575+1.710523e-3sqrt(abs(s))-2.154996e-4s)s - 7.53e-4z
1204	!! checkvalue: tf=-2.588567 Celsius for s=40psu, z=500m
1205	!!
1206	!! Reference : UNESCO tech. papers in the marine science no. 28. 1978
1207	!!----------------------------------------------------------------------
1208	INTEGER , INTENT(in ) :: kttf
1209	REAL(wp), DIMENSION(jpi,jpj) , INTENT(in ) :: psal ! salinity [psu]
1210	REAL(wp), DIMENSION(jpi,jpj) , INTENT(in ), OPTIONAL :: pdep ! depth [m]
1211	REAL(wp), DIMENSION(A2D_T(kttf)), INTENT(out ) :: ptf ! freezing temperature [Celsius]
1212	!
1213	INTEGER :: ji, jj ! dummy loop indices
1214	REAL(wp) :: zt, zs, z1_S0 ! local scalars
1215	!!----------------------------------------------------------------------
1216	!
1217	SELECT CASE ( neos )
1218	!
1219	CASE ( np_teos10, np_seos ) !== CT,SA (TEOS-10 and S-EOS formulations) ==!
1220	!
1221	z1_S0 = 1._wp / 35.16504_wp
1222	DO_2D( 1, 1, 1, 1 )
1223	zs= SQRT( ABS( psal(ji,jj) ) * z1_S0 ) ! square root salinity
1224	ptf(ji,jj) = ((((1.46873e-03_wpzs-9.64972e-03_wp)zs+2.28348e-02_wp)*zs &
1225	& - 3.12775e-02_wp)zs+2.07679e-02_wp)zs-5.87701e-02_wp
1226	END_2D
1227	ptf(:,:) = ptf(:,:) * psal(:,:)
1228	!
1229	IF( PRESENT( pdep ) ) ptf(:,:) = ptf(:,:) - 7.53e-4 * pdep(:,:)
1230	!
1231	CASE ( np_eos80 ) !== PT,SP (UNESCO formulation) ==!
1232	!
1233	ptf(:,:) = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal(:,:) ) &
1234	& - 2.154996e-4_wp * psal(:,:) ) * psal(:,:)
1235	!
1236	IF( PRESENT( pdep ) ) ptf(:,:) = ptf(:,:) - 7.53e-4 * pdep(:,:)
1237	!
1238	CASE DEFAULT
1239	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1240	CALL ctl_stop( 'eos_fzp_2d:', ctmp1 )
1241	!
1242	END SELECT
1243	!
1244	END SUBROUTINE eos_fzp_2d_t
1245
1246
1247	SUBROUTINE eos_fzp_0d( psal, ptf, pdep )
1248	!!----------------------------------------------------------------------
1249	!! * ROUTINE eos_fzp *
1250	!!
1251	!! ** Purpose : Compute the freezing point temperature [Celsius]
1252	!!
1253	!! ** Method : UNESCO freezing point (ptf) in Celsius is given by
1254	!! ptf(t,z) = (-.0575+1.710523e-3sqrt(abs(s))-2.154996e-4s)s - 7.53e-4z
1255	!! checkvalue: tf=-2.588567 Celsius for s=40psu, z=500m
1256	!!
1257	!! Reference : UNESCO tech. papers in the marine science no. 28. 1978
1258	!!----------------------------------------------------------------------
1259	REAL(wp), INTENT(in ) :: psal ! salinity [psu]
1260	REAL(wp), INTENT(in ), OPTIONAL :: pdep ! depth [m]
1261	REAL(wp), INTENT(out) :: ptf ! freezing temperature [Celsius]
1262	!
1263	REAL(wp) :: zs ! local scalars
1264	!!----------------------------------------------------------------------
1265	!
1266	SELECT CASE ( neos )
1267	!
1268	CASE ( np_teos10, np_seos ) !== CT,SA (TEOS-10 and S-EOS formulations) ==!
1269	!
1270	zs = SQRT( ABS( psal ) / 35.16504_wp ) ! square root salinity
1271	ptf = ((((1.46873e-03_wpzs-9.64972e-03_wp)zs+2.28348e-02_wp)*zs &
1272	& - 3.12775e-02_wp)zs+2.07679e-02_wp)zs-5.87701e-02_wp
1273	ptf = ptf * psal
1274	!
1275	IF( PRESENT( pdep ) ) ptf = ptf - 7.53e-4 * pdep
1276	!
1277	CASE ( np_eos80 ) !== PT,SP (UNESCO formulation) ==!
1278	!
1279	ptf = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal ) &
1280	& - 2.154996e-4_wp * psal ) * psal
1281	!
1282	IF( PRESENT( pdep ) ) ptf = ptf - 7.53e-4 * pdep
1283	!
1284	CASE DEFAULT
1285	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1286	CALL ctl_stop( 'eos_fzp_0d:', ctmp1 )
1287	!
1288	END SELECT
1289	!
1290	END SUBROUTINE eos_fzp_0d
1291
1292
1293	SUBROUTINE eos_pen( pts, pab_pe, ppen, Kmm )
1294	!!----------------------------------------------------------------------
1295	!! * ROUTINE eos_pen *
1296	!!
1297	!! ** Purpose : Calculates nonlinear anomalies of alpha_PE, beta_PE and PE at T-points
1298	!!
1299	!! ** Method : PE is defined analytically as the vertical
1300	!! primitive of EOS times -g integrated between 0 and z>0.
1301	!! pen is the nonlinear bsq-PE anomaly: pen = ( PE - rho0 gz ) / rho0 gz - rd
1302	!! = 1/z * /int_0^z rd dz - rd
1303	!! where rd is the density anomaly (see eos_rhd function)
1304	!! ab_pe are partial derivatives of PE anomaly with respect to T and S:
1305	!! ab_pe(1) = - 1/(rho0 gz) * dPE/dT + drd/dT = - d(pen)/dT
1306	!! ab_pe(2) = 1/(rho0 gz) * dPE/dS + drd/dS = d(pen)/dS
1307	!!
1308	!! ** Action : - pen : PE anomaly given at T-points
1309	!! : - pab_pe : given at T-points
1310	!! pab_pe(:,:,:,jp_tem) is alpha_pe
1311	!! pab_pe(:,:,:,jp_sal) is beta_pe
1312	!!----------------------------------------------------------------------
1313	INTEGER , INTENT(in ) :: Kmm ! time level index
1314	REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature & salinity
1315	REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT( out) :: pab_pe ! alpha_pe and beta_pe
1316	REAL(wp), DIMENSION(jpi,jpj,jpk) , INTENT( out) :: ppen ! potential energy anomaly
1317	!
1318	INTEGER :: ji, jj, jk ! dummy loop indices
1319	REAL(wp) :: zt , zh , zs , ztm ! local scalars
1320	REAL(wp) :: zn , zn0, zn1, zn2 ! - -
1321	!!----------------------------------------------------------------------
1322	!
1323	IF( ln_timing ) CALL timing_start('eos_pen')
1324	!
1325	SELECT CASE ( neos )
1326	!
1327	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
1328	!
1329	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
1330	!
1331	zh = gdept(ji,jj,jk,Kmm) * r1_Z0 ! depth
1332	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
1333	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
1334	ztm = tmask(ji,jj,jk) ! tmask
1335	!
1336	! potential energy non-linear anomaly
1337	zn2 = (PEN012)*zt &
1338	& + PEN102*zs+PEN002
1339	!
1340	zn1 = ((PEN021)*zt &
1341	& + PEN111zs+PEN011)zt &
1342	& + (PEN201zs+PEN101)zs+PEN001
1343	!
1344	zn0 = ((((PEN040)*zt &
1345	& + PEN130zs+PEN030)zt &
1346	& + (PEN220zs+PEN120)zs+PEN020)*zt &
1347	& + ((PEN310zs+PEN210)zs+PEN110)zs+PEN010)zt &
1348	& + (((PEN400zs+PEN300)zs+PEN200)zs+PEN100)zs+PEN000
1349	!
1350	zn = ( zn2 * zh + zn1 ) * zh + zn0
1351	!
1352	ppen(ji,jj,jk) = zn * zh * r1_rho0 * ztm
1353	!
1354	! alphaPE non-linear anomaly
1355	zn2 = APE002
1356	!
1357	zn1 = (APE011)*zt &
1358	& + APE101*zs+APE001
1359	!
1360	zn0 = (((APE030)*zt &
1361	& + APE120zs+APE020)zt &
1362	& + (APE210zs+APE110)zs+APE010)*zt &
1363	& + ((APE300zs+APE200)zs+APE100)*zs+APE000
1364	!
1365	zn = ( zn2 * zh + zn1 ) * zh + zn0
1366	!
1367	pab_pe(ji,jj,jk,jp_tem) = zn * zh * r1_rho0 * ztm
1368	!
1369	! betaPE non-linear anomaly
1370	zn2 = BPE002
1371	!
1372	zn1 = (BPE011)*zt &
1373	& + BPE101*zs+BPE001
1374	!
1375	zn0 = (((BPE030)*zt &
1376	& + BPE120zs+BPE020)zt &
1377	& + (BPE210zs+BPE110)zs+BPE010)*zt &
1378	& + ((BPE300zs+BPE200)zs+BPE100)*zs+BPE000
1379	!
1380	zn = ( zn2 * zh + zn1 ) * zh + zn0
1381	!
1382	pab_pe(ji,jj,jk,jp_sal) = zn / zs * zh * r1_rho0 * ztm
1383	!
1384	END_3D
1385	!
1386	CASE( np_seos ) !== Vallis (2006) simplified EOS ==!
1387	!
1388	DO_3D( 1, 1, 1, 1, 1, jpkm1 )
1389	zt = pts(ji,jj,jk,jp_tem) - 10._wp ! temperature anomaly (t-T0)
1390	zs = pts (ji,jj,jk,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
1391	zh = gdept(ji,jj,jk,Kmm) ! depth in meters at t-point
1392	ztm = tmask(ji,jj,jk) ! tmask
1393	zn = 0.5_wp * zh * r1_rho0 * ztm
1394	! ! Potential Energy
1395	ppen(ji,jj,jk) = ( rn_a0 * rn_mu1 * zt + rn_b0 * rn_mu2 * zs ) * zn
1396	! ! alphaPE
1397	pab_pe(ji,jj,jk,jp_tem) = - rn_a0 * rn_mu1 * zn
1398	pab_pe(ji,jj,jk,jp_sal) = rn_b0 * rn_mu2 * zn
1399	!
1400	END_3D
1401	!
1402	CASE( np_eeos ) !== exponential SEAMOUNT EOS ==!
1403	!
1404	DO_3D( nn_hls, nn_hls, nn_hls, nn_hls, 1, jpkm1 )
1405	ppen(ji,jk,jk) = 0.
1406	!
1407	pab_pe(ji,jj,jk,jp_tem) = 0.
1408	pab_pe(ji,jj,jk,jp_sal) = 0.
1409	END_3D
1410	!
1411	CASE DEFAULT
1412	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1413	CALL ctl_stop( 'eos_pen:', ctmp1 )
1414	!
1415	END SELECT
1416	!
1417	IF( ln_timing ) CALL timing_stop('eos_pen')
1418	!
1419	END SUBROUTINE eos_pen
1420
1421
1422	SUBROUTINE eos_init
1423	!!----------------------------------------------------------------------
1424	!! * ROUTINE eos_init *
1425	!!
1426	!! ** Purpose : initializations for the equation of state
1427	!!
1428	!! ** Method : Read the namelist nameos and control the parameters
1429	!!----------------------------------------------------------------------
1430	INTEGER :: ios ! local integer
1431	INTEGER :: ioptio ! local integer
1432	!!
1433	NAMELIST/nameos/ ln_TEOS10, ln_EOS80, ln_SEOS, ln_EEOS, rn_a0, rn_b0, rn_lambda1, rn_mu1, &
1434	& rn_lambda2, rn_mu2, rn_nu
1435	!!----------------------------------------------------------------------
1436	!
1437	READ ( numnam_ref, nameos, IOSTAT = ios, ERR = 901 )
1438	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'nameos in reference namelist' )
1439	!
1440	READ ( numnam_cfg, nameos, IOSTAT = ios, ERR = 902 )
1441	902 IF( ios > 0 ) CALL ctl_nam ( ios , 'nameos in configuration namelist' )
1442	IF(lwm) WRITE( numond, nameos )
1443	!
1444	rho0 = 1000._wp !: volumic mass of reference [kg/m3]
1445	rcp = 3991.86795711963_wp !: heat capacity [J/K]
1446	!
1447	IF(lwp) THEN ! Control print
1448	WRITE(numout,*)
1449	WRITE(numout,*) 'eos_init : equation of state'
1450	WRITE(numout,*) '~~~~~~~~'
1451	WRITE(numout,*) ' Namelist nameos : Chosen the Equation Of Seawater (EOS)'
1452	WRITE(numout,*) ' TEOS-10 : rho=F(Conservative Temperature, Absolute Salinity, depth) ln_TEOS10 = ', ln_TEOS10
1453	WRITE(numout,*) ' EOS-80 : rho=F(Potential Temperature, Practical Salinity, depth) ln_EOS80 = ', ln_EOS80
1454	WRITE(numout,*) ' S-EOS : rho=F(Conservative Temperature, Absolute Salinity, depth) ln_SEOS = ', ln_SEOS
1455	WRITE(numout,*) ' E-EOS : rho=F(Conservative Temperature, depth) ln_EEOS = ', ln_EEOS
1456	ENDIF
1457
1458	! Check options for equation of state & set neos based on logical flags
1459	ioptio = 0
1460	IF( ln_TEOS10 ) THEN ; ioptio = ioptio+1 ; neos = np_teos10 ; ENDIF
1461	IF( ln_EOS80 ) THEN ; ioptio = ioptio+1 ; neos = np_eos80 ; ENDIF
1462	IF( ln_SEOS ) THEN ; ioptio = ioptio+1 ; neos = np_seos ; ENDIF
1463	IF( ln_EEOS ) THEN ; ioptio = ioptio+1 ; neos = np_eeos ; ENDIF
1464	IF( ioptio /= 1 ) CALL ctl_stop("Exactly one equation of state option must be selected")
1465	!
1466	SELECT CASE( neos ) ! check option
1467	!
1468	CASE( np_teos10 ) !== polynomial TEOS-10 ==!
1469	IF(lwp) WRITE(numout,*)
1470	IF(lwp) WRITE(numout,*) ' ==>>> use of TEOS-10 equation of state (cons. temp. and abs. salinity)'
1471	!
1472	l_useCT = .TRUE. ! model temperature is Conservative temperature
1473	!
1474	rdeltaS = 32._wp
1475	r1_S0 = 0.875_wp/35.16504_wp
1476	r1_T0 = 1._wp/40._wp
1477	r1_Z0 = 1.e-4_wp
1478	!
1479	EOS000 = 8.0189615746e+02_wp
1480	EOS100 = 8.6672408165e+02_wp
1481	EOS200 = -1.7864682637e+03_wp
1482	EOS300 = 2.0375295546e+03_wp
1483	EOS400 = -1.2849161071e+03_wp
1484	EOS500 = 4.3227585684e+02_wp
1485	EOS600 = -6.0579916612e+01_wp
1486	EOS010 = 2.6010145068e+01_wp
1487	EOS110 = -6.5281885265e+01_wp
1488	EOS210 = 8.1770425108e+01_wp
1489	EOS310 = -5.6888046321e+01_wp
1490	EOS410 = 1.7681814114e+01_wp
1491	EOS510 = -1.9193502195_wp
1492	EOS020 = -3.7074170417e+01_wp
1493	EOS120 = 6.1548258127e+01_wp
1494	EOS220 = -6.0362551501e+01_wp
1495	EOS320 = 2.9130021253e+01_wp
1496	EOS420 = -5.4723692739_wp
1497	EOS030 = 2.1661789529e+01_wp
1498	EOS130 = -3.3449108469e+01_wp
1499	EOS230 = 1.9717078466e+01_wp
1500	EOS330 = -3.1742946532_wp
1501	EOS040 = -8.3627885467_wp
1502	EOS140 = 1.1311538584e+01_wp
1503	EOS240 = -5.3563304045_wp
1504	EOS050 = 5.4048723791e-01_wp
1505	EOS150 = 4.8169980163e-01_wp
1506	EOS060 = -1.9083568888e-01_wp
1507	EOS001 = 1.9681925209e+01_wp
1508	EOS101 = -4.2549998214e+01_wp
1509	EOS201 = 5.0774768218e+01_wp
1510	EOS301 = -3.0938076334e+01_wp
1511	EOS401 = 6.6051753097_wp
1512	EOS011 = -1.3336301113e+01_wp
1513	EOS111 = -4.4870114575_wp
1514	EOS211 = 5.0042598061_wp
1515	EOS311 = -6.5399043664e-01_wp
1516	EOS021 = 6.7080479603_wp
1517	EOS121 = 3.5063081279_wp
1518	EOS221 = -1.8795372996_wp
1519	EOS031 = -2.4649669534_wp
1520	EOS131 = -5.5077101279e-01_wp
1521	EOS041 = 5.5927935970e-01_wp
1522	EOS002 = 2.0660924175_wp
1523	EOS102 = -4.9527603989_wp
1524	EOS202 = 2.5019633244_wp
1525	EOS012 = 2.0564311499_wp
1526	EOS112 = -2.1311365518e-01_wp
1527	EOS022 = -1.2419983026_wp
1528	EOS003 = -2.3342758797e-02_wp
1529	EOS103 = -1.8507636718e-02_wp
1530	EOS013 = 3.7969820455e-01_wp
1531	!
1532	ALP000 = -6.5025362670e-01_wp
1533	ALP100 = 1.6320471316_wp
1534	ALP200 = -2.0442606277_wp
1535	ALP300 = 1.4222011580_wp
1536	ALP400 = -4.4204535284e-01_wp
1537	ALP500 = 4.7983755487e-02_wp
1538	ALP010 = 1.8537085209_wp
1539	ALP110 = -3.0774129064_wp
1540	ALP210 = 3.0181275751_wp
1541	ALP310 = -1.4565010626_wp
1542	ALP410 = 2.7361846370e-01_wp
1543	ALP020 = -1.6246342147_wp
1544	ALP120 = 2.5086831352_wp
1545	ALP220 = -1.4787808849_wp
1546	ALP320 = 2.3807209899e-01_wp
1547	ALP030 = 8.3627885467e-01_wp
1548	ALP130 = -1.1311538584_wp
1549	ALP230 = 5.3563304045e-01_wp
1550	ALP040 = -6.7560904739e-02_wp
1551	ALP140 = -6.0212475204e-02_wp
1552	ALP050 = 2.8625353333e-02_wp
1553	ALP001 = 3.3340752782e-01_wp
1554	ALP101 = 1.1217528644e-01_wp
1555	ALP201 = -1.2510649515e-01_wp
1556	ALP301 = 1.6349760916e-02_wp
1557	ALP011 = -3.3540239802e-01_wp
1558	ALP111 = -1.7531540640e-01_wp
1559	ALP211 = 9.3976864981e-02_wp
1560	ALP021 = 1.8487252150e-01_wp
1561	ALP121 = 4.1307825959e-02_wp
1562	ALP031 = -5.5927935970e-02_wp
1563	ALP002 = -5.1410778748e-02_wp
1564	ALP102 = 5.3278413794e-03_wp
1565	ALP012 = 6.2099915132e-02_wp
1566	ALP003 = -9.4924551138e-03_wp
1567	!
1568	BET000 = 1.0783203594e+01_wp
1569	BET100 = -4.4452095908e+01_wp
1570	BET200 = 7.6048755820e+01_wp
1571	BET300 = -6.3944280668e+01_wp
1572	BET400 = 2.6890441098e+01_wp
1573	BET500 = -4.5221697773_wp
1574	BET010 = -8.1219372432e-01_wp
1575	BET110 = 2.0346663041_wp
1576	BET210 = -2.1232895170_wp
1577	BET310 = 8.7994140485e-01_wp
1578	BET410 = -1.1939638360e-01_wp
1579	BET020 = 7.6574242289e-01_wp
1580	BET120 = -1.5019813020_wp
1581	BET220 = 1.0872489522_wp
1582	BET320 = -2.7233429080e-01_wp
1583	BET030 = -4.1615152308e-01_wp
1584	BET130 = 4.9061350869e-01_wp
1585	BET230 = -1.1847737788e-01_wp
1586	BET040 = 1.4073062708e-01_wp
1587	BET140 = -1.3327978879e-01_wp
1588	BET050 = 5.9929880134e-03_wp
1589	BET001 = -5.2937873009e-01_wp
1590	BET101 = 1.2634116779_wp
1591	BET201 = -1.1547328025_wp
1592	BET301 = 3.2870876279e-01_wp
1593	BET011 = -5.5824407214e-02_wp
1594	BET111 = 1.2451933313e-01_wp
1595	BET211 = -2.4409539932e-02_wp
1596	BET021 = 4.3623149752e-02_wp
1597	BET121 = -4.6767901790e-02_wp
1598	BET031 = -6.8523260060e-03_wp
1599	BET002 = -6.1618945251e-02_wp
1600	BET102 = 6.2255521644e-02_wp
1601	BET012 = -2.6514181169e-03_wp
1602	BET003 = -2.3025968587e-04_wp
1603	!
1604	PEN000 = -9.8409626043_wp
1605	PEN100 = 2.1274999107e+01_wp
1606	PEN200 = -2.5387384109e+01_wp
1607	PEN300 = 1.5469038167e+01_wp
1608	PEN400 = -3.3025876549_wp
1609	PEN010 = 6.6681505563_wp
1610	PEN110 = 2.2435057288_wp
1611	PEN210 = -2.5021299030_wp
1612	PEN310 = 3.2699521832e-01_wp
1613	PEN020 = -3.3540239802_wp
1614	PEN120 = -1.7531540640_wp
1615	PEN220 = 9.3976864981e-01_wp
1616	PEN030 = 1.2324834767_wp
1617	PEN130 = 2.7538550639e-01_wp
1618	PEN040 = -2.7963967985e-01_wp
1619	PEN001 = -1.3773949450_wp
1620	PEN101 = 3.3018402659_wp
1621	PEN201 = -1.6679755496_wp
1622	PEN011 = -1.3709540999_wp
1623	PEN111 = 1.4207577012e-01_wp
1624	PEN021 = 8.2799886843e-01_wp
1625	PEN002 = 1.7507069098e-02_wp
1626	PEN102 = 1.3880727538e-02_wp
1627	PEN012 = -2.8477365341e-01_wp
1628	!
1629	APE000 = -1.6670376391e-01_wp
1630	APE100 = -5.6087643219e-02_wp
1631	APE200 = 6.2553247576e-02_wp
1632	APE300 = -8.1748804580e-03_wp
1633	APE010 = 1.6770119901e-01_wp
1634	APE110 = 8.7657703198e-02_wp
1635	APE210 = -4.6988432490e-02_wp
1636	APE020 = -9.2436260751e-02_wp
1637	APE120 = -2.0653912979e-02_wp
1638	APE030 = 2.7963967985e-02_wp
1639	APE001 = 3.4273852498e-02_wp
1640	APE101 = -3.5518942529e-03_wp
1641	APE011 = -4.1399943421e-02_wp
1642	APE002 = 7.1193413354e-03_wp
1643	!
1644	BPE000 = 2.6468936504e-01_wp
1645	BPE100 = -6.3170583896e-01_wp
1646	BPE200 = 5.7736640125e-01_wp
1647	BPE300 = -1.6435438140e-01_wp
1648	BPE010 = 2.7912203607e-02_wp
1649	BPE110 = -6.2259666565e-02_wp
1650	BPE210 = 1.2204769966e-02_wp
1651	BPE020 = -2.1811574876e-02_wp
1652	BPE120 = 2.3383950895e-02_wp
1653	BPE030 = 3.4261630030e-03_wp
1654	BPE001 = 4.1079296834e-02_wp
1655	BPE101 = -4.1503681096e-02_wp
1656	BPE011 = 1.7676120780e-03_wp
1657	BPE002 = 1.7269476440e-04_wp
1658	!
1659	CASE( np_eos80 ) !== polynomial EOS-80 formulation ==!
1660	!
1661	IF(lwp) WRITE(numout,*)
1662	IF(lwp) WRITE(numout,*) ' ==>>> use of EOS-80 equation of state (pot. temp. and pract. salinity)'
1663	!
1664	l_useCT = .FALSE. ! model temperature is Potential temperature
1665	rdeltaS = 20._wp
1666	r1_S0 = 1._wp/40._wp
1667	r1_T0 = 1._wp/40._wp
1668	r1_Z0 = 1.e-4_wp
1669	!
1670	EOS000 = 9.5356891948e+02_wp
1671	EOS100 = 1.7136499189e+02_wp
1672	EOS200 = -3.7501039454e+02_wp
1673	EOS300 = 5.1856810420e+02_wp
1674	EOS400 = -3.7264470465e+02_wp
1675	EOS500 = 1.4302533998e+02_wp
1676	EOS600 = -2.2856621162e+01_wp
1677	EOS010 = 1.0087518651e+01_wp
1678	EOS110 = -1.3647741861e+01_wp
1679	EOS210 = 8.8478359933_wp
1680	EOS310 = -7.2329388377_wp
1681	EOS410 = 1.4774410611_wp
1682	EOS510 = 2.0036720553e-01_wp
1683	EOS020 = -2.5579830599e+01_wp
1684	EOS120 = 2.4043512327e+01_wp
1685	EOS220 = -1.6807503990e+01_wp
1686	EOS320 = 8.3811577084_wp
1687	EOS420 = -1.9771060192_wp
1688	EOS030 = 1.6846451198e+01_wp
1689	EOS130 = -2.1482926901e+01_wp
1690	EOS230 = 1.0108954054e+01_wp
1691	EOS330 = -6.2675951440e-01_wp
1692	EOS040 = -8.0812310102_wp
1693	EOS140 = 1.0102374985e+01_wp
1694	EOS240 = -4.8340368631_wp
1695	EOS050 = 1.2079167803_wp
1696	EOS150 = 1.1515380987e-01_wp
1697	EOS060 = -2.4520288837e-01_wp
1698	EOS001 = 1.0748601068e+01_wp
1699	EOS101 = -1.7817043500e+01_wp
1700	EOS201 = 2.2181366768e+01_wp
1701	EOS301 = -1.6750916338e+01_wp
1702	EOS401 = 4.1202230403_wp
1703	EOS011 = -1.5852644587e+01_wp
1704	EOS111 = -7.6639383522e-01_wp
1705	EOS211 = 4.1144627302_wp
1706	EOS311 = -6.6955877448e-01_wp
1707	EOS021 = 9.9994861860_wp
1708	EOS121 = -1.9467067787e-01_wp
1709	EOS221 = -1.2177554330_wp
1710	EOS031 = -3.4866102017_wp
1711	EOS131 = 2.2229155620e-01_wp
1712	EOS041 = 5.9503008642e-01_wp
1713	EOS002 = 1.0375676547_wp
1714	EOS102 = -3.4249470629_wp
1715	EOS202 = 2.0542026429_wp
1716	EOS012 = 2.1836324814_wp
1717	EOS112 = -3.4453674320e-01_wp
1718	EOS022 = -1.2548163097_wp
1719	EOS003 = 1.8729078427e-02_wp
1720	EOS103 = -5.7238495240e-02_wp
1721	EOS013 = 3.8306136687e-01_wp
1722	!
1723	ALP000 = -2.5218796628e-01_wp
1724	ALP100 = 3.4119354654e-01_wp
1725	ALP200 = -2.2119589983e-01_wp
1726	ALP300 = 1.8082347094e-01_wp
1727	ALP400 = -3.6936026529e-02_wp
1728	ALP500 = -5.0091801383e-03_wp
1729	ALP010 = 1.2789915300_wp
1730	ALP110 = -1.2021756164_wp
1731	ALP210 = 8.4037519952e-01_wp
1732	ALP310 = -4.1905788542e-01_wp
1733	ALP410 = 9.8855300959e-02_wp
1734	ALP020 = -1.2634838399_wp
1735	ALP120 = 1.6112195176_wp
1736	ALP220 = -7.5817155402e-01_wp
1737	ALP320 = 4.7006963580e-02_wp
1738	ALP030 = 8.0812310102e-01_wp
1739	ALP130 = -1.0102374985_wp
1740	ALP230 = 4.8340368631e-01_wp
1741	ALP040 = -1.5098959754e-01_wp
1742	ALP140 = -1.4394226233e-02_wp
1743	ALP050 = 3.6780433255e-02_wp
1744	ALP001 = 3.9631611467e-01_wp
1745	ALP101 = 1.9159845880e-02_wp
1746	ALP201 = -1.0286156825e-01_wp
1747	ALP301 = 1.6738969362e-02_wp
1748	ALP011 = -4.9997430930e-01_wp
1749	ALP111 = 9.7335338937e-03_wp
1750	ALP211 = 6.0887771651e-02_wp
1751	ALP021 = 2.6149576513e-01_wp
1752	ALP121 = -1.6671866715e-02_wp
1753	ALP031 = -5.9503008642e-02_wp
1754	ALP002 = -5.4590812035e-02_wp
1755	ALP102 = 8.6134185799e-03_wp
1756	ALP012 = 6.2740815484e-02_wp
1757	ALP003 = -9.5765341718e-03_wp
1758	!
1759	BET000 = 2.1420623987_wp
1760	BET100 = -9.3752598635_wp
1761	BET200 = 1.9446303907e+01_wp
1762	BET300 = -1.8632235232e+01_wp
1763	BET400 = 8.9390837485_wp
1764	BET500 = -1.7142465871_wp
1765	BET010 = -1.7059677327e-01_wp
1766	BET110 = 2.2119589983e-01_wp
1767	BET210 = -2.7123520642e-01_wp
1768	BET310 = 7.3872053057e-02_wp
1769	BET410 = 1.2522950346e-02_wp
1770	BET020 = 3.0054390409e-01_wp
1771	BET120 = -4.2018759976e-01_wp
1772	BET220 = 3.1429341406e-01_wp
1773	BET320 = -9.8855300959e-02_wp
1774	BET030 = -2.6853658626e-01_wp
1775	BET130 = 2.5272385134e-01_wp
1776	BET230 = -2.3503481790e-02_wp
1777	BET040 = 1.2627968731e-01_wp
1778	BET140 = -1.2085092158e-01_wp
1779	BET050 = 1.4394226233e-03_wp
1780	BET001 = -2.2271304375e-01_wp
1781	BET101 = 5.5453416919e-01_wp
1782	BET201 = -6.2815936268e-01_wp
1783	BET301 = 2.0601115202e-01_wp
1784	BET011 = -9.5799229402e-03_wp
1785	BET111 = 1.0286156825e-01_wp
1786	BET211 = -2.5108454043e-02_wp
1787	BET021 = -2.4333834734e-03_wp
1788	BET121 = -3.0443885826e-02_wp
1789	BET031 = 2.7786444526e-03_wp
1790	BET002 = -4.2811838287e-02_wp
1791	BET102 = 5.1355066072e-02_wp
1792	BET012 = -4.3067092900e-03_wp
1793	BET003 = -7.1548119050e-04_wp
1794	!
1795	PEN000 = -5.3743005340_wp
1796	PEN100 = 8.9085217499_wp
1797	PEN200 = -1.1090683384e+01_wp
1798	PEN300 = 8.3754581690_wp
1799	PEN400 = -2.0601115202_wp
1800	PEN010 = 7.9263222935_wp
1801	PEN110 = 3.8319691761e-01_wp
1802	PEN210 = -2.0572313651_wp
1803	PEN310 = 3.3477938724e-01_wp
1804	PEN020 = -4.9997430930_wp
1805	PEN120 = 9.7335338937e-02_wp
1806	PEN220 = 6.0887771651e-01_wp
1807	PEN030 = 1.7433051009_wp
1808	PEN130 = -1.1114577810e-01_wp
1809	PEN040 = -2.9751504321e-01_wp
1810	PEN001 = -6.9171176978e-01_wp
1811	PEN101 = 2.2832980419_wp
1812	PEN201 = -1.3694684286_wp
1813	PEN011 = -1.4557549876_wp
1814	PEN111 = 2.2969116213e-01_wp
1815	PEN021 = 8.3654420645e-01_wp
1816	PEN002 = -1.4046808820e-02_wp
1817	PEN102 = 4.2928871430e-02_wp
1818	PEN012 = -2.8729602515e-01_wp
1819	!
1820	APE000 = -1.9815805734e-01_wp
1821	APE100 = -9.5799229402e-03_wp
1822	APE200 = 5.1430784127e-02_wp
1823	APE300 = -8.3694846809e-03_wp
1824	APE010 = 2.4998715465e-01_wp
1825	APE110 = -4.8667669469e-03_wp
1826	APE210 = -3.0443885826e-02_wp
1827	APE020 = -1.3074788257e-01_wp
1828	APE120 = 8.3359333577e-03_wp
1829	APE030 = 2.9751504321e-02_wp
1830	APE001 = 3.6393874690e-02_wp
1831	APE101 = -5.7422790533e-03_wp
1832	APE011 = -4.1827210323e-02_wp
1833	APE002 = 7.1824006288e-03_wp
1834	!
1835	BPE000 = 1.1135652187e-01_wp
1836	BPE100 = -2.7726708459e-01_wp
1837	BPE200 = 3.1407968134e-01_wp
1838	BPE300 = -1.0300557601e-01_wp
1839	BPE010 = 4.7899614701e-03_wp
1840	BPE110 = -5.1430784127e-02_wp
1841	BPE210 = 1.2554227021e-02_wp
1842	BPE020 = 1.2166917367e-03_wp
1843	BPE120 = 1.5221942913e-02_wp
1844	BPE030 = -1.3893222263e-03_wp
1845	BPE001 = 2.8541225524e-02_wp
1846	BPE101 = -3.4236710714e-02_wp
1847	BPE011 = 2.8711395266e-03_wp
1848	BPE002 = 5.3661089288e-04_wp
1849	!
1850	CASE( np_seos ) !== Simplified EOS ==!
1851
1852	r1_S0 = 0.875_wp/35.16504_wp ! Used to convert CT in potential temperature when using bulk formulae (eos_pt_from_ct)
1853
1854	IF(lwp) THEN
1855	WRITE(numout,*)
1856	WRITE(numout,*) ' ==>>> use of simplified eos: '
1857	WRITE(numout,) ' rhd(dT=T-10,dS=S-35,Z) = [-a0(1+lambda1/2dT+mu1Z)*dT '
1858	WRITE(numout,) ' + b0(1+lambda2/2dT+mu2Z)dS - nudT*dS] / rho0'
1859	WRITE(numout,*) ' with the following coefficients :'
1860	WRITE(numout,*) ' thermal exp. coef. rn_a0 = ', rn_a0
1861	WRITE(numout,*) ' saline cont. coef. rn_b0 = ', rn_b0
1862	WRITE(numout,*) ' cabbeling coef. rn_lambda1 = ', rn_lambda1
1863	WRITE(numout,*) ' cabbeling coef. rn_lambda2 = ', rn_lambda2
1864	WRITE(numout,*) ' thermobar. coef. rn_mu1 = ', rn_mu1
1865	WRITE(numout,*) ' thermobar. coef. rn_mu2 = ', rn_mu2
1866	WRITE(numout,*) ' 2nd cabbel. coef. rn_nu = ', rn_nu
1867	WRITE(numout,*) ' Caution: rn_beta0=0 incompatible with ddm parameterization '
1868	ENDIF
1869	l_useCT = .TRUE. ! Use conservative temperature
1870	!
1871	CASE( np_eeos ) !== Exponential SEAMOUNT EOS ==!
1872
1873	r1_S0 = 0.875_wp/35.16504_wp ! Used to convert CT in potential temperature when using bulk formulae (eos_pt_from_ct)
1874
1875	IF(lwp) THEN
1876	WRITE(numout,*)
1877	WRITE(numout,*) ' use of exponential SEAMOUNT eos: rhd(dT=T-(exp_profile), Z) = '
1878	WRITE(numout,) ' [ -a0dT ]/rho0'
1879	WRITE(numout,*)
1880	WRITE(numout,*) ' thermal exp. coef. rn_a0 = ', rn_a0
1881	ENDIF
1882	l_useCT = .TRUE. ! Use conservative temperature
1883	!
1884	CASE DEFAULT !== ERROR in neos ==!
1885	WRITE(ctmp1,*) ' bad flag value for neos = ', neos, '. You should never see this error'
1886	CALL ctl_stop( ctmp1 )
1887	!
1888	END SELECT
1889	!
1890	rho0_rcp = rho0 * rcp
1891	r1_rho0 = 1._wp / rho0
1892	r1_rcp = 1._wp / rcp
1893	r1_rho0_rcp = 1._wp / rho0_rcp
1894	!
1895	IF(lwp) THEN
1896	IF( l_useCT ) THEN
1897	WRITE(numout,*)
1898	WRITE(numout,*) ' ==>>> model uses Conservative Temperature'
1899	WRITE(numout,*) ' Important: model must be initialized with CT and SA fields'
1900	ELSE
1901	WRITE(numout,*)
1902	WRITE(numout,*) ' ==>>> model does not use Conservative Temperature'
1903	ENDIF
1904	ENDIF
1905	!
1906	IF(lwp) WRITE(numout,*)
1907	IF(lwp) WRITE(numout,*) ' Associated physical constant'
1908	IF(lwp) WRITE(numout,*) ' volumic mass of reference rho0 = ', rho0 , ' kg/m^3'
1909	IF(lwp) WRITE(numout,*) ' 1. / rho0 r1_rho0 = ', r1_rho0, ' m^3/kg'
1910	IF(lwp) WRITE(numout,*) ' ocean specific heat rcp = ', rcp , ' J/Kelvin'
1911	IF(lwp) WRITE(numout,) ' rho0 rcp rho0_rcp = ', rho0_rcp
1912	IF(lwp) WRITE(numout,) ' 1. / ( rho0 rcp ) r1_rho0_rcp = ', r1_rho0_rcp
1913	!
1914	END SUBROUTINE eos_init
1915
1916	!!======================================================================
1917	END MODULE eosbn2

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