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eosbn2.F90 in NEMO/branches/UKMO/dev_r12866_HPC-02_Daley_Tiling_trial_extra_halo/src/OCE/TRA – NEMO

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source: NEMO/branches/UKMO/dev_r12866_HPC-02_Daley_Tiling_trial_extra_halo/src/OCE/TRA/eosbn2.F90 @ 13409

Last change on this file since 13409 was 13409, checked in by hadcv, 3 years ago
Remaining changes prior to trunk merge
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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
53	IMPLICIT NONE
54	PRIVATE
55
56	! !! * Interface
57	INTERFACE eos
58	MODULE PROCEDURE eos_insitu, eos_insitu_pot, eos_insitu_2d
59	END INTERFACE
60	!
61	INTERFACE eos_rab
62	MODULE PROCEDURE rab_3d, rab_2d, rab_0d
63	END INTERFACE
64	!
65	INTERFACE eos_fzp
66	MODULE PROCEDURE eos_fzp_2d, eos_fzp_0d
67	END INTERFACE
68	!
69	PUBLIC eos ! called by step, istate, tranpc and zpsgrd modules
70	PUBLIC bn2 ! called by step module
71	PUBLIC eos_rab ! called by ldfslp, zdfddm, trabbl
72	PUBLIC eos_pt_from_ct ! called by sbcssm
73	PUBLIC eos_fzp ! called by traadv_cen2 and sbcice_... modules
74	PUBLIC eos_pen ! used for pe diagnostics in trdpen module
75	PUBLIC eos_init ! called by istate module
76
77	! !! Namelist nameos
78	LOGICAL , PUBLIC :: ln_TEOS10
79	LOGICAL , PUBLIC :: ln_EOS80
80	LOGICAL , PUBLIC :: ln_SEOS
81
82	! Parameters
83	LOGICAL , PUBLIC :: l_useCT ! =T in ln_TEOS10=T (i.e. use eos_pt_from_ct to compute sst_m), =F otherwise
84	INTEGER , PUBLIC :: neos ! Identifier for equation of state used
85
86	INTEGER , PARAMETER :: np_teos10 = -1 ! parameter for using TEOS10
87	INTEGER , PARAMETER :: np_eos80 = 0 ! parameter for using EOS80
88	INTEGER , PARAMETER :: np_seos = 1 ! parameter for using Simplified Equation of state
89
90	! !!! simplified eos coefficients (default value: Vallis 2006)
91	REAL(wp) :: rn_a0 = 1.6550e-1_wp ! thermal expansion coeff.
92	REAL(wp) :: rn_b0 = 7.6554e-1_wp ! saline expansion coeff.
93	REAL(wp) :: rn_lambda1 = 5.9520e-2_wp ! cabbeling coeff. in T^2
94	REAL(wp) :: rn_lambda2 = 5.4914e-4_wp ! cabbeling coeff. in S^2
95	REAL(wp) :: rn_mu1 = 1.4970e-4_wp ! thermobaric coeff. in T
96	REAL(wp) :: rn_mu2 = 1.1090e-5_wp ! thermobaric coeff. in S
97	REAL(wp) :: rn_nu = 2.4341e-3_wp ! cabbeling coeff. in theta*salt
98
99	! TEOS10/EOS80 parameters
100	REAL(wp) :: r1_S0, r1_T0, r1_Z0, rdeltaS
101
102	! EOS parameters
103	REAL(wp) :: EOS000 , EOS100 , EOS200 , EOS300 , EOS400 , EOS500 , EOS600
104	REAL(wp) :: EOS010 , EOS110 , EOS210 , EOS310 , EOS410 , EOS510
105	REAL(wp) :: EOS020 , EOS120 , EOS220 , EOS320 , EOS420
106	REAL(wp) :: EOS030 , EOS130 , EOS230 , EOS330
107	REAL(wp) :: EOS040 , EOS140 , EOS240
108	REAL(wp) :: EOS050 , EOS150
109	REAL(wp) :: EOS060
110	REAL(wp) :: EOS001 , EOS101 , EOS201 , EOS301 , EOS401
111	REAL(wp) :: EOS011 , EOS111 , EOS211 , EOS311
112	REAL(wp) :: EOS021 , EOS121 , EOS221
113	REAL(wp) :: EOS031 , EOS131
114	REAL(wp) :: EOS041
115	REAL(wp) :: EOS002 , EOS102 , EOS202
116	REAL(wp) :: EOS012 , EOS112
117	REAL(wp) :: EOS022
118	REAL(wp) :: EOS003 , EOS103
119	REAL(wp) :: EOS013
120
121	! ALPHA parameters
122	REAL(wp) :: ALP000 , ALP100 , ALP200 , ALP300 , ALP400 , ALP500
123	REAL(wp) :: ALP010 , ALP110 , ALP210 , ALP310 , ALP410
124	REAL(wp) :: ALP020 , ALP120 , ALP220 , ALP320
125	REAL(wp) :: ALP030 , ALP130 , ALP230
126	REAL(wp) :: ALP040 , ALP140
127	REAL(wp) :: ALP050
128	REAL(wp) :: ALP001 , ALP101 , ALP201 , ALP301
129	REAL(wp) :: ALP011 , ALP111 , ALP211
130	REAL(wp) :: ALP021 , ALP121
131	REAL(wp) :: ALP031
132	REAL(wp) :: ALP002 , ALP102
133	REAL(wp) :: ALP012
134	REAL(wp) :: ALP003
135
136	! BETA parameters
137	REAL(wp) :: BET000 , BET100 , BET200 , BET300 , BET400 , BET500
138	REAL(wp) :: BET010 , BET110 , BET210 , BET310 , BET410
139	REAL(wp) :: BET020 , BET120 , BET220 , BET320
140	REAL(wp) :: BET030 , BET130 , BET230
141	REAL(wp) :: BET040 , BET140
142	REAL(wp) :: BET050
143	REAL(wp) :: BET001 , BET101 , BET201 , BET301
144	REAL(wp) :: BET011 , BET111 , BET211
145	REAL(wp) :: BET021 , BET121
146	REAL(wp) :: BET031
147	REAL(wp) :: BET002 , BET102
148	REAL(wp) :: BET012
149	REAL(wp) :: BET003
150
151	! PEN parameters
152	REAL(wp) :: PEN000 , PEN100 , PEN200 , PEN300 , PEN400
153	REAL(wp) :: PEN010 , PEN110 , PEN210 , PEN310
154	REAL(wp) :: PEN020 , PEN120 , PEN220
155	REAL(wp) :: PEN030 , PEN130
156	REAL(wp) :: PEN040
157	REAL(wp) :: PEN001 , PEN101 , PEN201
158	REAL(wp) :: PEN011 , PEN111
159	REAL(wp) :: PEN021
160	REAL(wp) :: PEN002 , PEN102
161	REAL(wp) :: PEN012
162
163	! ALPHA_PEN parameters
164	REAL(wp) :: APE000 , APE100 , APE200 , APE300
165	REAL(wp) :: APE010 , APE110 , APE210
166	REAL(wp) :: APE020 , APE120
167	REAL(wp) :: APE030
168	REAL(wp) :: APE001 , APE101
169	REAL(wp) :: APE011
170	REAL(wp) :: APE002
171
172	! BETA_PEN parameters
173	REAL(wp) :: BPE000 , BPE100 , BPE200 , BPE300
174	REAL(wp) :: BPE010 , BPE110 , BPE210
175	REAL(wp) :: BPE020 , BPE120
176	REAL(wp) :: BPE030
177	REAL(wp) :: BPE001 , BPE101
178	REAL(wp) :: BPE011
179	REAL(wp) :: BPE002
180
181	!! * Substitutions
182	# include "do_loop_substitute.h90"
183	!!----------------------------------------------------------------------
184	!! NEMO/OCE 4.0 , NEMO Consortium (2018)
185	!! $Id$
186	!! Software governed by the CeCILL license (see ./LICENSE)
187	!!----------------------------------------------------------------------
188	CONTAINS
189	SUBROUTINE eos_insitu( pts, prd, pdep )
190	!!
191	REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
192	! ! 2 : salinity [psu]
193	REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: prd ! in situ density [-]
194	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pdep ! depth [m]
195	!!
196	CALL eos_insitu_t( pts, is_tile(pts), prd, is_tile(prd), pdep, is_tile(pdep) )
197	END SUBROUTINE eos_insitu
198
199	SUBROUTINE eos_insitu_t( pts, ktts, prd, ktrd, pdep, ktdep )
200	!!----------------------------------------------------------------------
201	!! * ROUTINE eos_insitu *
202	!!
203	!! ** Purpose : Compute the in situ density (ratio rho/rho0) from
204	!! potential temperature and salinity using an equation of state
205	!! selected in the nameos namelist
206	!!
207	!! ** Method : prd(t,s,z) = ( rho(t,s,z) - rho0 ) / rho0
208	!! with prd in situ density anomaly no units
209	!! t TEOS10: CT or EOS80: PT Celsius
210	!! s TEOS10: SA or EOS80: SP TEOS10: g/kg or EOS80: psu
211	!! z depth meters
212	!! rho in situ density kg/m^3
213	!! rho0 reference density kg/m^3
214	!!
215	!! ln_teos10 : polynomial TEOS-10 equation of state is used for rho(t,s,z).
216	!! Check value: rho = 1028.21993233072 kg/m^3 for z=3000 dbar, ct=3 Celsius, sa=35.5 g/kg
217	!!
218	!! ln_eos80 : polynomial EOS-80 equation of state is used for rho(t,s,z).
219	!! Check value: rho = 1028.35011066567 kg/m^3 for z=3000 dbar, pt=3 Celsius, sp=35.5 psu
220	!!
221	!! ln_seos : simplified equation of state
222	!! prd(t,s,z) = ( -a0(1+lambda/2(T-T0)+muz+nu(S-S0))(T-T0) + b0(S-S0) ) / rho0
223	!! linear case function of T only: rn_alpha<>0, other coefficients = 0
224	!! linear eos function of T and S: rn_alpha and rn_beta<>0, other coefficients=0
225	!! Vallis like equation: use default values of coefficients
226	!!
227	!! ** Action : compute prd , the in situ density (no units)
228	!!
229	!! References : Roquet et al, Ocean Modelling, in preparation (2014)
230	!! Vallis, Atmospheric and Oceanic Fluid Dynamics, 2006
231	!! TEOS-10 Manual, 2010
232	!!----------------------------------------------------------------------
233	INTEGER , INTENT(in ) :: ktts, ktrd, ktdep
234	REAL(wp), DIMENSION(T2D(ktts) ,jpk,jpts), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
235	! ! 2 : salinity [psu]
236	REAL(wp), DIMENSION(T2D(ktrd) ,jpk ), INTENT( out) :: prd ! in situ density [-]
237	REAL(wp), DIMENSION(T2D(ktdep),jpk ), INTENT(in ) :: pdep ! depth [m]
238	!
239	INTEGER :: ji, jj, jk ! dummy loop indices
240	REAL(wp) :: zt , zh , zs , ztm ! local scalars
241	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
242	REAL(wp), SAVE :: zsum1
243	!!----------------------------------------------------------------------
244	!
245	IF( ln_timing ) CALL timing_start('eos-insitu')
246	!
247	SELECT CASE( neos )
248	!
249	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
250	!
251	DO_3D_11_11( 1, jpkm1 )
252	!
253	zh = pdep(ji,jj,jk) * r1_Z0 ! depth
254	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
255	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
256	ztm = tmask(ji,jj,jk) ! tmask
257	!
258	zn3 = EOS013*zt &
259	& + EOS103*zs+EOS003
260	!
261	zn2 = (EOS022*zt &
262	& + EOS112zs+EOS012)zt &
263	& + (EOS202zs+EOS102)zs+EOS002
264	!
265	zn1 = (((EOS041*zt &
266	& + EOS131zs+EOS031)zt &
267	& + (EOS221zs+EOS121)zs+EOS021)*zt &
268	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
269	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
270	!
271	zn0 = (((((EOS060*zt &
272	& + EOS150zs+EOS050)zt &
273	& + (EOS240zs+EOS140)zs+EOS040)*zt &
274	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
275	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
276	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
277	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
278	!
279	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
280	!
281	prd(ji,jj,jk) = ( zn * r1_rho0 - 1._wp ) * ztm ! density anomaly (masked)
282	!
283	END_3D
284	!
285	CASE( np_seos ) !== simplified EOS ==!
286	!
287	DO_3D_11_11( 1, jpkm1 )
288	zt = pts (ji,jj,jk,jp_tem) - 10._wp
289	zs = pts (ji,jj,jk,jp_sal) - 35._wp
290	zh = pdep (ji,jj,jk)
291	ztm = tmask(ji,jj,jk)
292	!
293	zn = - rn_a0 * ( 1._wp + 0.5_wprn_lambda1zt + rn_mu1zh ) zt &
294	& + rn_b0 * ( 1._wp - 0.5_wprn_lambda2zs - rn_mu2zh ) zs &
295	& - rn_nu * zt * zs
296	!
297	prd(ji,jj,jk) = zn * r1_rho0 * ztm ! density anomaly (masked)
298	END_3D
299	!
300	END SELECT
301	!
302	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-insitu : ', kdim=jpk, psum1=zsum1 )
303	!
304	IF( ln_timing ) CALL timing_stop('eos-insitu')
305	!
306	END SUBROUTINE eos_insitu_t
307
308
309	SUBROUTINE eos_insitu_pot( pts, prd, prhop, pdep )
310	!!
311	REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
312	! ! 2 : salinity [psu]
313	REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: prd ! in situ density [-]
314	REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: prhop ! potential density (surface referenced)
315	REAL(wp), DIMENSION(:,:,:) , INTENT(in ) :: pdep ! depth [m]
316	!!
317	CALL eos_insitu_pot_t( pts, is_tile(pts), prd, is_tile(prd), prhop, is_tile(prhop), pdep, is_tile(pdep) )
318	END SUBROUTINE eos_insitu_pot
319
320
321	SUBROUTINE eos_insitu_pot_t( pts, ktts, prd, ktrd, prhop, ktrhop, pdep, ktdep )
322	!!----------------------------------------------------------------------
323	!! * ROUTINE eos_insitu_pot *
324	!!
325	!! ** Purpose : Compute the in situ density (ratio rho/rho0) and the
326	!! potential volumic mass (Kg/m3) from potential temperature and
327	!! salinity fields using an equation of state selected in the
328	!! namelist.
329	!!
330	!! ** Action : - prd , the in situ density (no units)
331	!! - prhop, the potential volumic mass (Kg/m3)
332	!!
333	!!----------------------------------------------------------------------
334	INTEGER , INTENT(in ) :: ktts, ktrd, ktrhop, ktdep
335	REAL(wp), DIMENSION(T2D(ktts) ,jpk,jpts), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
336	! ! 2 : salinity [psu]
337	REAL(wp), DIMENSION(T2D(ktrd) ,jpk ), INTENT( out) :: prd ! in situ density [-]
338	REAL(wp), DIMENSION(T2D(ktrhop),jpk ), INTENT( out) :: prhop ! potential density (surface referenced)
339	REAL(wp), DIMENSION(T2D(ktdep) ,jpk ), INTENT(in ) :: pdep ! depth [m]
340	!
341	INTEGER :: ji, jj, jk, jsmp ! dummy loop indices
342	INTEGER :: jdof
343	REAL(wp) :: zt , zh , zstemp, zs , ztm ! local scalars
344	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
345	REAL(wp), SAVE :: zsum1, zsum2
346	REAL(wp), DIMENSION(:), ALLOCATABLE :: zn0_sto, zn_sto, zsign ! local vectors
347	!!----------------------------------------------------------------------
348	!
349	IF( ln_timing ) CALL timing_start('eos-pot')
350	!
351	SELECT CASE ( neos )
352	!
353	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
354	!
355	! Stochastic equation of state
356	IF ( ln_sto_eos ) THEN
357	ALLOCATE(zn0_sto(1:2*nn_sto_eos))
358	ALLOCATE(zn_sto(1:2*nn_sto_eos))
359	ALLOCATE(zsign(1:2*nn_sto_eos))
360	DO jsmp = 1, 2*nn_sto_eos, 2
361	zsign(jsmp) = 1._wp
362	zsign(jsmp+1) = -1._wp
363	END DO
364	!
365	DO_3D_11_11( 1, jpkm1 )
366	!
367	! compute density (2*nn_sto_eos) times:
368	! (1) for t+dt, s+ds (with the random TS fluctutation computed in sto_pts)
369	! (2) for t-dt, s-ds (with the opposite fluctuation)
370	DO jsmp = 1, nn_sto_eos*2
371	jdof = (jsmp + 1) / 2
372	zh = pdep(ji,jj,jk) * r1_Z0 ! depth
373	zt = (pts (ji,jj,jk,jp_tem) + pts_ran(ji,jj,jk,jp_tem,jdof) * zsign(jsmp)) * r1_T0 ! temperature
374	zstemp = pts (ji,jj,jk,jp_sal) + pts_ran(ji,jj,jk,jp_sal,jdof) * zsign(jsmp)
375	zs = SQRT( ABS( zstemp + rdeltaS ) * r1_S0 ) ! square root salinity
376	ztm = tmask(ji,jj,jk) ! tmask
377	!
378	zn3 = EOS013*zt &
379	& + EOS103*zs+EOS003
380	!
381	zn2 = (EOS022*zt &
382	& + EOS112zs+EOS012)zt &
383	& + (EOS202zs+EOS102)zs+EOS002
384	!
385	zn1 = (((EOS041*zt &
386	& + EOS131zs+EOS031)zt &
387	& + (EOS221zs+EOS121)zs+EOS021)*zt &
388	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
389	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
390	!
391	zn0_sto(jsmp) = (((((EOS060*zt &
392	& + EOS150zs+EOS050)zt &
393	& + (EOS240zs+EOS140)zs+EOS040)*zt &
394	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
395	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
396	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
397	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
398	!
399	zn_sto(jsmp) = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0_sto(jsmp)
400	END DO
401	!
402	! compute stochastic density as the mean of the (2*nn_sto_eos) densities
403	prhop(ji,jj,jk) = 0._wp ; prd(ji,jj,jk) = 0._wp
404	DO jsmp = 1, nn_sto_eos*2
405	prhop(ji,jj,jk) = prhop(ji,jj,jk) + zn0_sto(jsmp) ! potential density referenced at the surface
406	!
407	prd(ji,jj,jk) = prd(ji,jj,jk) + ( zn_sto(jsmp) * r1_rho0 - 1._wp ) ! density anomaly (masked)
408	END DO
409	prhop(ji,jj,jk) = 0.5_wp * prhop(ji,jj,jk) * ztm / nn_sto_eos
410	prd (ji,jj,jk) = 0.5_wp * prd (ji,jj,jk) * ztm / nn_sto_eos
411	END_3D
412	DEALLOCATE(zn0_sto,zn_sto,zsign)
413	! Non-stochastic equation of state
414	ELSE
415	DO_3D_11_11( 1, jpkm1 )
416	!
417	zh = pdep(ji,jj,jk) * r1_Z0 ! depth
418	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
419	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
420	ztm = tmask(ji,jj,jk) ! tmask
421	!
422	zn3 = EOS013*zt &
423	& + EOS103*zs+EOS003
424	!
425	zn2 = (EOS022*zt &
426	& + EOS112zs+EOS012)zt &
427	& + (EOS202zs+EOS102)zs+EOS002
428	!
429	zn1 = (((EOS041*zt &
430	& + EOS131zs+EOS031)zt &
431	& + (EOS221zs+EOS121)zs+EOS021)*zt &
432	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
433	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
434	!
435	zn0 = (((((EOS060*zt &
436	& + EOS150zs+EOS050)zt &
437	& + (EOS240zs+EOS140)zs+EOS040)*zt &
438	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
439	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
440	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
441	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
442	!
443	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
444	!
445	prhop(ji,jj,jk) = zn0 * ztm ! potential density referenced at the surface
446	!
447	prd(ji,jj,jk) = ( zn * r1_rho0 - 1._wp ) * ztm ! density anomaly (masked)
448	END_3D
449	ENDIF
450
451	CASE( np_seos ) !== simplified EOS ==!
452	!
453	DO_3D_11_11( 1, jpkm1 )
454	zt = pts (ji,jj,jk,jp_tem) - 10._wp
455	zs = pts (ji,jj,jk,jp_sal) - 35._wp
456	zh = pdep (ji,jj,jk)
457	ztm = tmask(ji,jj,jk)
458	! ! potential density referenced at the surface
459	zn = - rn_a0 * ( 1._wp + 0.5_wprn_lambda1zt ) * zt &
460	& + rn_b0 * ( 1._wp - 0.5_wprn_lambda2zs ) * zs &
461	& - rn_nu * zt * zs
462	prhop(ji,jj,jk) = ( rho0 + zn ) * ztm
463	! ! density anomaly (masked)
464	zn = zn - ( rn_a0 * rn_mu1 * zt + rn_b0 * rn_mu2 * zs ) * zh
465	prd(ji,jj,jk) = zn * r1_rho0 * ztm
466	!
467	END_3D
468	!
469	END SELECT
470	!
471	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=prd, clinfo1=' eos-pot: ', psum1=zsum1, &
472	& tab3d_2=prhop, clinfo2=' pot : ', psum2=zsum2, kdim=jpk )
473	!
474	IF( ln_timing ) CALL timing_stop('eos-pot')
475	!
476	END SUBROUTINE eos_insitu_pot_t
477
478
479	SUBROUTINE eos_insitu_2d( pts, pdep, prd )
480	!!
481	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
482	! ! 2 : salinity [psu]
483	REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pdep ! depth [m]
484	REAL(wp), DIMENSION(:,:) , INTENT( out) :: prd ! in situ density
485	!!
486	CALL eos_insitu_2d_t( pts, is_tile(pts), pdep, is_tile(pdep), prd, is_tile(prd) )
487	END SUBROUTINE eos_insitu_2d
488
489
490	SUBROUTINE eos_insitu_2d_t( pts, ktts, pdep, ktdep, prd, ktrd )
491	!!----------------------------------------------------------------------
492	!! * ROUTINE eos_insitu_2d *
493	!!
494	!! ** Purpose : Compute the in situ density (ratio rho/rho0) from
495	!! potential temperature and salinity using an equation of state
496	!! selected in the nameos namelist. * 2D field case
497	!!
498	!! ** Action : - prd , the in situ density (no units) (unmasked)
499	!!
500	!!----------------------------------------------------------------------
501	INTEGER , INTENT(in ) :: ktts, ktdep, ktrd
502	REAL(wp), DIMENSION(T2D(ktts),jpts), INTENT(in ) :: pts ! 1 : potential temperature [Celsius]
503	! ! 2 : salinity [psu]
504	REAL(wp), DIMENSION(T2D(ktdep) ), INTENT(in ) :: pdep ! depth [m]
505	REAL(wp), DIMENSION(T2D(ktrd) ), INTENT( out) :: prd ! in situ density
506	!
507	INTEGER :: ji, jj, jk ! dummy loop indices
508	REAL(wp) :: zt , zh , zs ! local scalars
509	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
510	REAL(wp), SAVE :: zsum1
511	!!----------------------------------------------------------------------
512	!
513	IF( ln_timing ) CALL timing_start('eos2d')
514	!
515	prd(:,:) = 0._wp
516	!
517	SELECT CASE( neos )
518	!
519	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
520	!
521	DO_2D_11_11
522	!
523	zh = pdep(ji,jj) * r1_Z0 ! depth
524	zt = pts (ji,jj,jp_tem) * r1_T0 ! temperature
525	zs = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
526	!
527	zn3 = EOS013*zt &
528	& + EOS103*zs+EOS003
529	!
530	zn2 = (EOS022*zt &
531	& + EOS112zs+EOS012)zt &
532	& + (EOS202zs+EOS102)zs+EOS002
533	!
534	zn1 = (((EOS041*zt &
535	& + EOS131zs+EOS031)zt &
536	& + (EOS221zs+EOS121)zs+EOS021)*zt &
537	& + ((EOS311zs+EOS211)zs+EOS111)zs+EOS011)zt &
538	& + (((EOS401zs+EOS301)zs+EOS201)zs+EOS101)zs+EOS001
539	!
540	zn0 = (((((EOS060*zt &
541	& + EOS150zs+EOS050)zt &
542	& + (EOS240zs+EOS140)zs+EOS040)*zt &
543	& + ((EOS330zs+EOS230)zs+EOS130)zs+EOS030)zt &
544	& + (((EOS420zs+EOS320)zs+EOS220)zs+EOS120)zs+EOS020)*zt &
545	& + ((((EOS510zs+EOS410)zs+EOS310)zs+EOS210)zs+EOS110)zs+EOS010)zt &
546	& + (((((EOS600zs+EOS500)zs+EOS400)zs+EOS300)zs+EOS200)zs+EOS100)zs+EOS000
547	!
548	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
549	!
550	prd(ji,jj) = zn * r1_rho0 - 1._wp ! unmasked in situ density anomaly
551	!
552	END_2D
553	!
554	CASE( np_seos ) !== simplified EOS ==!
555	!
556	DO_2D_11_11
557	!
558	zt = pts (ji,jj,jp_tem) - 10._wp
559	zs = pts (ji,jj,jp_sal) - 35._wp
560	zh = pdep (ji,jj) ! depth at the partial step level
561	!
562	zn = - rn_a0 * ( 1._wp + 0.5_wprn_lambda1zt + rn_mu1zh ) zt &
563	& + rn_b0 * ( 1._wp - 0.5_wprn_lambda2zs - rn_mu2zh ) zs &
564	& - rn_nu * zt * zs
565	!
566	prd(ji,jj) = zn * r1_rho0 ! unmasked in situ density anomaly
567	!
568	END_2D
569	!
570	END SELECT
571	!
572	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=prd, clinfo1=' eos2d: ', psum1=zsum1 )
573	!
574	IF( ln_timing ) CALL timing_stop('eos2d')
575	!
576	END SUBROUTINE eos_insitu_2d_t
577
578
579	SUBROUTINE rab_3d( pts, pab, Kmm )
580	!!
581	INTEGER , INTENT(in ) :: Kmm ! time level index
582	REAL(wp), DIMENSION(:,:,:,:), INTENT(in ) :: pts ! pot. temperature & salinity
583	REAL(wp), DIMENSION(:,:,:,:), INTENT( out) :: pab ! thermal/haline expansion ratio
584	!!
585	CALL rab_3d_t( pts, is_tile(pts), pab, is_tile(pab), Kmm )
586	END SUBROUTINE rab_3d
587
588
589	SUBROUTINE rab_3d_t( pts, ktts, pab, ktab, Kmm )
590	!!----------------------------------------------------------------------
591	!! * ROUTINE rab_3d *
592	!!
593	!! ** Purpose : Calculates thermal/haline expansion ratio at T-points
594	!!
595	!! ** Method : calculates alpha / beta at T-points
596	!!
597	!! ** Action : - pab : thermal/haline expansion ratio at T-points
598	!!----------------------------------------------------------------------
599	INTEGER , INTENT(in ) :: Kmm ! time level index
600	INTEGER , INTENT(in ) :: ktts, ktab
601	REAL(wp), DIMENSION(T2D(ktts),jpk,jpts), INTENT(in ) :: pts ! pot. temperature & salinity
602	REAL(wp), DIMENSION(T2D(ktab),jpk,jpts), INTENT( out) :: pab ! thermal/haline expansion ratio
603	!
604	INTEGER :: ji, jj, jk ! dummy loop indices
605	REAL(wp) :: zt , zh , zs , ztm ! local scalars
606	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
607	REAL(wp), SAVE :: zsum1, zsum2
608	!!----------------------------------------------------------------------
609	!
610	IF( ln_timing ) CALL timing_start('rab_3d')
611	!
612	SELECT CASE ( neos )
613	!
614	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
615	!
616	DO_3D_11_11( 1, jpkm1 )
617	!
618	zh = gdept(ji,jj,jk,Kmm) * r1_Z0 ! depth
619	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
620	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
621	ztm = tmask(ji,jj,jk) ! tmask
622	!
623	! alpha
624	zn3 = ALP003
625	!
626	zn2 = ALP012zt + ALP102zs+ALP002
627	!
628	zn1 = ((ALP031*zt &
629	& + ALP121zs+ALP021)zt &
630	& + (ALP211zs+ALP111)zs+ALP011)*zt &
631	& + ((ALP301zs+ALP201)zs+ALP101)*zs+ALP001
632	!
633	zn0 = ((((ALP050*zt &
634	& + ALP140zs+ALP040)zt &
635	& + (ALP230zs+ALP130)zs+ALP030)*zt &
636	& + ((ALP320zs+ALP220)zs+ALP120)zs+ALP020)zt &
637	& + (((ALP410zs+ALP310)zs+ALP210)zs+ALP110)zs+ALP010)*zt &
638	& + ((((ALP500zs+ALP400)zs+ALP300)zs+ALP200)zs+ALP100)*zs+ALP000
639	!
640	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
641	!
642	pab(ji,jj,jk,jp_tem) = zn * r1_rho0 * ztm
643	!
644	! beta
645	zn3 = BET003
646	!
647	zn2 = BET012zt + BET102zs+BET002
648	!
649	zn1 = ((BET031*zt &
650	& + BET121zs+BET021)zt &
651	& + (BET211zs+BET111)zs+BET011)*zt &
652	& + ((BET301zs+BET201)zs+BET101)*zs+BET001
653	!
654	zn0 = ((((BET050*zt &
655	& + BET140zs+BET040)zt &
656	& + (BET230zs+BET130)zs+BET030)*zt &
657	& + ((BET320zs+BET220)zs+BET120)zs+BET020)zt &
658	& + (((BET410zs+BET310)zs+BET210)zs+BET110)zs+BET010)*zt &
659	& + ((((BET500zs+BET400)zs+BET300)zs+BET200)zs+BET100)*zs+BET000
660	!
661	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
662	!
663	pab(ji,jj,jk,jp_sal) = zn / zs * r1_rho0 * ztm
664	!
665	END_3D
666	!
667	CASE( np_seos ) !== simplified EOS ==!
668	!
669	DO_3D_11_11( 1, jpkm1 )
670	zt = pts (ji,jj,jk,jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
671	zs = pts (ji,jj,jk,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
672	zh = gdept(ji,jj,jk,Kmm) ! depth in meters at t-point
673	ztm = tmask(ji,jj,jk) ! land/sea bottom mask = surf. mask
674	!
675	zn = rn_a0 * ( 1._wp + rn_lambda1zt + rn_mu1zh ) + rn_nu*zs
676	pab(ji,jj,jk,jp_tem) = zn * r1_rho0 * ztm ! alpha
677	!
678	zn = rn_b0 * ( 1._wp - rn_lambda2zs - rn_mu2zh ) - rn_nu*zt
679	pab(ji,jj,jk,jp_sal) = zn * r1_rho0 * ztm ! beta
680	!
681	END_3D
682	!
683	CASE DEFAULT
684	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
685	CALL ctl_stop( 'rab_3d:', ctmp1 )
686	!
687	END SELECT
688	!
689	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=pab(:,:,:,jp_tem), clinfo1=' rab_3d_t: ', psum1=zsum1, &
690	& tab3d_2=pab(:,:,:,jp_sal), clinfo2=' rab_3d_s : ', psum2=zsum2, kdim=jpk )
691	!
692	IF( ln_timing ) CALL timing_stop('rab_3d')
693	!
694	END SUBROUTINE rab_3d_t
695
696
697	SUBROUTINE rab_2d( pts, pdep, pab, Kmm )
698	!!
699	INTEGER , INTENT(in ) :: Kmm ! time level index
700	REAL(wp), DIMENSION(:,:,:), INTENT(in ) :: pts ! pot. temperature & salinity
701	REAL(wp), DIMENSION(:,:) , INTENT(in ) :: pdep ! depth [m]
702	REAL(wp), DIMENSION(:,:,:), INTENT( out) :: pab ! thermal/haline expansion ratio
703	!!
704	CALL rab_2d_t(pts, is_tile(pts), pdep, is_tile(pdep), pab, is_tile(pab), Kmm)
705	END SUBROUTINE rab_2d
706
707
708	SUBROUTINE rab_2d_t( pts, ktts, pdep, ktdep, pab, ktab, Kmm )
709	!!----------------------------------------------------------------------
710	!! * ROUTINE rab_2d *
711	!!
712	!! ** Purpose : Calculates thermal/haline expansion ratio for a 2d field (unmasked)
713	!!
714	!! ** Action : - pab : thermal/haline expansion ratio at T-points
715	!!----------------------------------------------------------------------
716	INTEGER , INTENT(in ) :: Kmm ! time level index
717	INTEGER , INTENT(in ) :: ktts, ktdep, ktab
718	REAL(wp), DIMENSION(T2D(ktts),jpts), INTENT(in ) :: pts ! pot. temperature & salinity
719	REAL(wp), DIMENSION(T2D(ktdep) ), INTENT(in ) :: pdep ! depth [m]
720	REAL(wp), DIMENSION(T2D(ktab),jpts), INTENT( out) :: pab ! thermal/haline expansion ratio
721	!
722	INTEGER :: ji, jj, jk ! dummy loop indices
723	REAL(wp) :: zt , zh , zs ! local scalars
724	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
725	REAL(wp), SAVE :: zsum1, zsum2
726	!!----------------------------------------------------------------------
727	!
728	IF( ln_timing ) CALL timing_start('rab_2d')
729	!
730	pab(:,:,:) = 0._wp
731	!
732	SELECT CASE ( neos )
733	!
734	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
735	!
736	DO_2D_11_11
737	!
738	zh = pdep(ji,jj) * r1_Z0 ! depth
739	zt = pts (ji,jj,jp_tem) * r1_T0 ! temperature
740	zs = SQRT( ABS( pts(ji,jj,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
741	!
742	! alpha
743	zn3 = ALP003
744	!
745	zn2 = ALP012zt + ALP102zs+ALP002
746	!
747	zn1 = ((ALP031*zt &
748	& + ALP121zs+ALP021)zt &
749	& + (ALP211zs+ALP111)zs+ALP011)*zt &
750	& + ((ALP301zs+ALP201)zs+ALP101)*zs+ALP001
751	!
752	zn0 = ((((ALP050*zt &
753	& + ALP140zs+ALP040)zt &
754	& + (ALP230zs+ALP130)zs+ALP030)*zt &
755	& + ((ALP320zs+ALP220)zs+ALP120)zs+ALP020)zt &
756	& + (((ALP410zs+ALP310)zs+ALP210)zs+ALP110)zs+ALP010)*zt &
757	& + ((((ALP500zs+ALP400)zs+ALP300)zs+ALP200)zs+ALP100)*zs+ALP000
758	!
759	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
760	!
761	pab(ji,jj,jp_tem) = zn * r1_rho0
762	!
763	! beta
764	zn3 = BET003
765	!
766	zn2 = BET012zt + BET102zs+BET002
767	!
768	zn1 = ((BET031*zt &
769	& + BET121zs+BET021)zt &
770	& + (BET211zs+BET111)zs+BET011)*zt &
771	& + ((BET301zs+BET201)zs+BET101)*zs+BET001
772	!
773	zn0 = ((((BET050*zt &
774	& + BET140zs+BET040)zt &
775	& + (BET230zs+BET130)zs+BET030)*zt &
776	& + ((BET320zs+BET220)zs+BET120)zs+BET020)zt &
777	& + (((BET410zs+BET310)zs+BET210)zs+BET110)zs+BET010)*zt &
778	& + ((((BET500zs+BET400)zs+BET300)zs+BET200)zs+BET100)*zs+BET000
779	!
780	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
781	!
782	pab(ji,jj,jp_sal) = zn / zs * r1_rho0
783	!
784	!
785	END_2D
786	!
787	CASE( np_seos ) !== simplified EOS ==!
788	!
789	DO_2D_11_11
790	!
791	zt = pts (ji,jj,jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
792	zs = pts (ji,jj,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
793	zh = pdep (ji,jj) ! depth at the partial step level
794	!
795	zn = rn_a0 * ( 1._wp + rn_lambda1zt + rn_mu1zh ) + rn_nu*zs
796	pab(ji,jj,jp_tem) = zn * r1_rho0 ! alpha
797	!
798	zn = rn_b0 * ( 1._wp - rn_lambda2zs - rn_mu2zh ) - rn_nu*zt
799	pab(ji,jj,jp_sal) = zn * r1_rho0 ! beta
800	!
801	END_2D
802	!
803	CASE DEFAULT
804	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
805	CALL ctl_stop( 'rab_2d:', ctmp1 )
806	!
807	END SELECT
808	!
809	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab2d_1=pab(:,:,jp_tem), clinfo1=' rab_2d_t: ', psum1=zsum1, &
810	& tab2d_2=pab(:,:,jp_sal), clinfo2=' rab_2d_s : ', psum2=zsum2 )
811	!
812	IF( ln_timing ) CALL timing_stop('rab_2d')
813	!
814	END SUBROUTINE rab_2d_t
815
816
817	SUBROUTINE rab_0d( pts, pdep, pab, Kmm )
818	!!----------------------------------------------------------------------
819	!! * ROUTINE rab_0d *
820	!!
821	!! ** Purpose : Calculates thermal/haline expansion ratio for a 2d field (unmasked)
822	!!
823	!! ** Action : - pab : thermal/haline expansion ratio at T-points
824	!!----------------------------------------------------------------------
825	INTEGER , INTENT(in ) :: Kmm ! time level index
826	REAL(wp), DIMENSION(jpts) , INTENT(in ) :: pts ! pot. temperature & salinity
827	REAL(wp), INTENT(in ) :: pdep ! depth [m]
828	REAL(wp), DIMENSION(jpts) , INTENT( out) :: pab ! thermal/haline expansion ratio
829	!
830	REAL(wp) :: zt , zh , zs ! local scalars
831	REAL(wp) :: zn , zn0, zn1, zn2, zn3 ! - -
832	!!----------------------------------------------------------------------
833	!
834	IF( ln_timing ) CALL timing_start('rab_0d')
835	!
836	pab(:) = 0._wp
837	!
838	SELECT CASE ( neos )
839	!
840	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
841	!
842	!
843	zh = pdep * r1_Z0 ! depth
844	zt = pts (jp_tem) * r1_T0 ! temperature
845	zs = SQRT( ABS( pts(jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
846	!
847	! alpha
848	zn3 = ALP003
849	!
850	zn2 = ALP012zt + ALP102zs+ALP002
851	!
852	zn1 = ((ALP031*zt &
853	& + ALP121zs+ALP021)zt &
854	& + (ALP211zs+ALP111)zs+ALP011)*zt &
855	& + ((ALP301zs+ALP201)zs+ALP101)*zs+ALP001
856	!
857	zn0 = ((((ALP050*zt &
858	& + ALP140zs+ALP040)zt &
859	& + (ALP230zs+ALP130)zs+ALP030)*zt &
860	& + ((ALP320zs+ALP220)zs+ALP120)zs+ALP020)zt &
861	& + (((ALP410zs+ALP310)zs+ALP210)zs+ALP110)zs+ALP010)*zt &
862	& + ((((ALP500zs+ALP400)zs+ALP300)zs+ALP200)zs+ALP100)*zs+ALP000
863	!
864	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
865	!
866	pab(jp_tem) = zn * r1_rho0
867	!
868	! beta
869	zn3 = BET003
870	!
871	zn2 = BET012zt + BET102zs+BET002
872	!
873	zn1 = ((BET031*zt &
874	& + BET121zs+BET021)zt &
875	& + (BET211zs+BET111)zs+BET011)*zt &
876	& + ((BET301zs+BET201)zs+BET101)*zs+BET001
877	!
878	zn0 = ((((BET050*zt &
879	& + BET140zs+BET040)zt &
880	& + (BET230zs+BET130)zs+BET030)*zt &
881	& + ((BET320zs+BET220)zs+BET120)zs+BET020)zt &
882	& + (((BET410zs+BET310)zs+BET210)zs+BET110)zs+BET010)*zt &
883	& + ((((BET500zs+BET400)zs+BET300)zs+BET200)zs+BET100)*zs+BET000
884	!
885	zn = ( ( zn3 * zh + zn2 ) * zh + zn1 ) * zh + zn0
886	!
887	pab(jp_sal) = zn / zs * r1_rho0
888	!
889	!
890	!
891	CASE( np_seos ) !== simplified EOS ==!
892	!
893	zt = pts(jp_tem) - 10._wp ! pot. temperature anomaly (t-T0)
894	zs = pts(jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
895	zh = pdep ! depth at the partial step level
896	!
897	zn = rn_a0 * ( 1._wp + rn_lambda1zt + rn_mu1zh ) + rn_nu*zs
898	pab(jp_tem) = zn * r1_rho0 ! alpha
899	!
900	zn = rn_b0 * ( 1._wp - rn_lambda2zs - rn_mu2zh ) - rn_nu*zt
901	pab(jp_sal) = zn * r1_rho0 ! beta
902	!
903	CASE DEFAULT
904	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
905	CALL ctl_stop( 'rab_0d:', ctmp1 )
906	!
907	END SELECT
908	!
909	IF( ln_timing ) CALL timing_stop('rab_0d')
910	!
911	END SUBROUTINE rab_0d
912
913
914	SUBROUTINE bn2( pts, pab, pn2, Kmm )
915	!!
916	INTEGER , INTENT(in ) :: Kmm ! time level index
917	REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature and salinity [Celsius,psu]
918	REAL(wp), DIMENSION(:,:,:,:) , INTENT(in ) :: pab ! thermal/haline expansion coef. [Celsius-1,psu-1]
919	REAL(wp), DIMENSION(:,:,:) , INTENT( out) :: pn2 ! Brunt-Vaisala frequency squared [1/s^2]
920	!!
921	CALL bn2_t( pts, pab, is_tile(pab), pn2, is_tile(pn2), Kmm )
922	END SUBROUTINE bn2
923
924
925	SUBROUTINE bn2_t( pts, pab, ktab, pn2, ktn2, Kmm )
926	!!----------------------------------------------------------------------
927	!! * ROUTINE bn2 *
928	!!
929	!! ** Purpose : Compute the local Brunt-Vaisala frequency at the
930	!! time-step of the input arguments
931	!!
932	!! ** Method : pn2 = grav * (alpha dk[T] + beta dk[S] ) / e3w
933	!! where alpha and beta are given in pab, and computed on T-points.
934	!! N.B. N^2 is set one for all to zero at jk=1 in istate module.
935	!!
936	!! ** Action : pn2 : square of the brunt-vaisala frequency at w-point
937	!!
938	!!----------------------------------------------------------------------
939	INTEGER , INTENT(in ) :: Kmm ! time level index
940	INTEGER , INTENT(in ) :: ktab, ktn2
941	REAL(wp), DIMENSION(jpi,jpj, jpk,jpts), INTENT(in ) :: pts ! pot. temperature and salinity [Celsius,psu]
942	REAL(wp), DIMENSION(T2D(ktab),jpk,jpts), INTENT(in ) :: pab ! thermal/haline expansion coef. [Celsius-1,psu-1]
943	REAL(wp), DIMENSION(T2D(ktn2),jpk ), INTENT( out) :: pn2 ! Brunt-Vaisala frequency squared [1/s^2]
944	!
945	INTEGER :: ji, jj, jk ! dummy loop indices
946	REAL(wp) :: zaw, zbw, zrw ! local scalars
947	REAL(wp), SAVE :: zsum1
948	!!----------------------------------------------------------------------
949	!
950	IF( ln_timing ) CALL timing_start('bn2')
951	!
952	DO_3D_11_11( 2, jpkm1 )
953	zrw = ( gdepw(ji,jj,jk ,Kmm) - gdept(ji,jj,jk,Kmm) ) &
954	& / ( gdept(ji,jj,jk-1,Kmm) - gdept(ji,jj,jk,Kmm) )
955	!
956	zaw = pab(ji,jj,jk,jp_tem) * (1. - zrw) + pab(ji,jj,jk-1,jp_tem) * zrw
957	zbw = pab(ji,jj,jk,jp_sal) * (1. - zrw) + pab(ji,jj,jk-1,jp_sal) * zrw
958	!
959	pn2(ji,jj,jk) = grav * ( zaw * ( pts(ji,jj,jk-1,jp_tem) - pts(ji,jj,jk,jp_tem) ) &
960	& - zbw * ( pts(ji,jj,jk-1,jp_sal) - pts(ji,jj,jk,jp_sal) ) ) &
961	& / e3w(ji,jj,jk,Kmm) * wmask(ji,jj,jk)
962	END_3D
963	!
964	IF(sn_cfctl%l_prtctl) CALL prt_ctl( tab3d_1=pn2, clinfo1=' bn2 : ', kdim=jpk, psum1=zsum1 )
965	!
966	IF( ln_timing ) CALL timing_stop('bn2')
967	!
968	END SUBROUTINE bn2_t
969
970
971	FUNCTION eos_pt_from_ct( ctmp, psal ) RESULT( ptmp )
972	!!----------------------------------------------------------------------
973	!! * ROUTINE eos_pt_from_ct *
974	!!
975	!! ** Purpose : Compute pot.temp. from cons. temp. [Celsius]
976	!!
977	!! ** Method : rational approximation (5/3th order) of TEOS-10 algorithm
978	!! checkvalue: pt=20.02391895 Celsius for sa=35.7g/kg, ct=20degC
979	!!
980	!! Reference : TEOS-10, UNESCO
981	!! Rational approximation to TEOS10 algorithm (rms error on WOA13 values: 4.0e-5 degC)
982	!!----------------------------------------------------------------------
983	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: ctmp ! Cons. Temp [Celsius]
984	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu]
985	! Leave result array automatic rather than making explicitly allocated
986	REAL(wp), DIMENSION(jpi,jpj) :: ptmp ! potential temperature [Celsius]
987	!
988	INTEGER :: ji, jj ! dummy loop indices
989	REAL(wp) :: zt , zs , ztm ! local scalars
990	REAL(wp) :: zn , zd ! local scalars
991	REAL(wp) :: zdeltaS , z1_S0 , z1_T0
992	!!----------------------------------------------------------------------
993	!
994	IF( ln_timing ) CALL timing_start('eos_pt_from_ct')
995	!
996	zdeltaS = 5._wp
997	z1_S0 = 0.875_wp/35.16504_wp
998	z1_T0 = 1._wp/40._wp
999	!
1000	DO_2D_11_11
1001	!
1002	zt = ctmp (ji,jj) * z1_T0
1003	zs = SQRT( ABS( psal(ji,jj) + zdeltaS ) * r1_S0 )
1004	ztm = tmask(ji,jj,1)
1005	!
1006	zn = ((((-2.1385727895e-01_wp*zt &
1007	& - 2.7674419971e-01_wpzs+1.0728094330_wp)zt &
1008	& + (2.6366564313_wpzs+3.3546960647_wp)zs-7.8012209473_wp)*zt &
1009	& + ((1.8835586562_wpzs+7.3949191679_wp)zs-3.3937395875_wp)zs-5.6414948432_wp)zt &
1010	& + (((3.5737370589_wpzs-1.5512427389e+01_wp)zs+2.4625741105e+01_wp)*zs &
1011	& +1.9912291000e+01_wp)zs-3.2191146312e+01_wp)zt &
1012	& + ((((5.7153204649e-01_wpzs-3.0943149543_wp)zs+9.3052495181_wp)*zs &
1013	& -9.4528934807_wp)zs+3.1066408996_wp)zs-4.3504021262e-01_wp
1014	!
1015	zd = (2.0035003456_wp*zt &
1016	& -3.4570358592e-01_wpzs+5.6471810638_wp)zt &
1017	& + (1.5393993508_wpzs-6.9394762624_wp)zs+1.2750522650e+01_wp
1018	!
1019	ptmp(ji,jj) = ( zt / z1_T0 + zn / zd ) * ztm
1020	!
1021	END_2D
1022	!
1023	IF( ln_timing ) CALL timing_stop('eos_pt_from_ct')
1024	!
1025	END FUNCTION eos_pt_from_ct
1026
1027
1028	SUBROUTINE eos_fzp_2d( psal, ptf, pdep )
1029	!!
1030	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ) :: psal ! salinity [psu]
1031	REAL(wp), DIMENSION(jpi,jpj), INTENT(in ), OPTIONAL :: pdep ! depth [m]
1032	REAL(wp), DIMENSION(:,:) , INTENT(out ) :: ptf ! freezing temperature [Celsius]
1033	!!
1034	CALL eos_fzp_2d_t( psal, ptf, is_tile(ptf), pdep )
1035	END SUBROUTINE eos_fzp_2d
1036
1037
1038	SUBROUTINE eos_fzp_2d_t( psal, ptf, kttf, pdep )
1039	!!----------------------------------------------------------------------
1040	!! * ROUTINE eos_fzp *
1041	!!
1042	!! ** Purpose : Compute the freezing point temperature [Celsius]
1043	!!
1044	!! ** Method : UNESCO freezing point (ptf) in Celsius is given by
1045	!! ptf(t,z) = (-.0575+1.710523e-3sqrt(abs(s))-2.154996e-4s)s - 7.53e-4z
1046	!! checkvalue: tf=-2.588567 Celsius for s=40psu, z=500m
1047	!!
1048	!! Reference : UNESCO tech. papers in the marine science no. 28. 1978
1049	!!----------------------------------------------------------------------
1050	INTEGER , INTENT(in ) :: kttf
1051	REAL(wp), DIMENSION(jpi,jpj) , INTENT(in ) :: psal ! salinity [psu]
1052	REAL(wp), DIMENSION(jpi,jpj) , INTENT(in ), OPTIONAL :: pdep ! depth [m]
1053	REAL(wp), DIMENSION(T2D(kttf)), INTENT(out ) :: ptf ! freezing temperature [Celsius]
1054	!
1055	INTEGER :: ji, jj ! dummy loop indices
1056	REAL(wp) :: zt, zs, z1_S0 ! local scalars
1057	!!----------------------------------------------------------------------
1058	!
1059	SELECT CASE ( neos )
1060	!
1061	CASE ( np_teos10, np_seos ) !== CT,SA (TEOS-10 and S-EOS formulations) ==!
1062	!
1063	z1_S0 = 1._wp / 35.16504_wp
1064	DO_2D_11_11
1065	zs= SQRT( ABS( psal(ji,jj) ) * z1_S0 ) ! square root salinity
1066	ptf(ji,jj) = ((((1.46873e-03_wpzs-9.64972e-03_wp)zs+2.28348e-02_wp)*zs &
1067	& - 3.12775e-02_wp)zs+2.07679e-02_wp)zs-5.87701e-02_wp
1068	END_2D
1069	ptf(:,:) = ptf(:,:) * psal(:,:)
1070	!
1071	IF( PRESENT( pdep ) ) ptf(:,:) = ptf(:,:) - 7.53e-4 * pdep(:,:)
1072	!
1073	CASE ( np_eos80 ) !== PT,SP (UNESCO formulation) ==!
1074	!
1075	ptf(:,:) = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal(:,:) ) &
1076	& - 2.154996e-4_wp * psal(:,:) ) * psal(:,:)
1077	!
1078	IF( PRESENT( pdep ) ) ptf(:,:) = ptf(:,:) - 7.53e-4 * pdep(:,:)
1079	!
1080	CASE DEFAULT
1081	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1082	CALL ctl_stop( 'eos_fzp_2d:', ctmp1 )
1083	!
1084	END SELECT
1085	!
1086	END SUBROUTINE eos_fzp_2d_t
1087
1088
1089	SUBROUTINE eos_fzp_0d( psal, ptf, pdep )
1090	!!----------------------------------------------------------------------
1091	!! * ROUTINE eos_fzp *
1092	!!
1093	!! ** Purpose : Compute the freezing point temperature [Celsius]
1094	!!
1095	!! ** Method : UNESCO freezing point (ptf) in Celsius is given by
1096	!! ptf(t,z) = (-.0575+1.710523e-3sqrt(abs(s))-2.154996e-4s)s - 7.53e-4z
1097	!! checkvalue: tf=-2.588567 Celsius for s=40psu, z=500m
1098	!!
1099	!! Reference : UNESCO tech. papers in the marine science no. 28. 1978
1100	!!----------------------------------------------------------------------
1101	REAL(wp), INTENT(in ) :: psal ! salinity [psu]
1102	REAL(wp), INTENT(in ), OPTIONAL :: pdep ! depth [m]
1103	REAL(wp), INTENT(out) :: ptf ! freezing temperature [Celsius]
1104	!
1105	REAL(wp) :: zs ! local scalars
1106	!!----------------------------------------------------------------------
1107	!
1108	SELECT CASE ( neos )
1109	!
1110	CASE ( np_teos10, np_seos ) !== CT,SA (TEOS-10 and S-EOS formulations) ==!
1111	!
1112	zs = SQRT( ABS( psal ) / 35.16504_wp ) ! square root salinity
1113	ptf = ((((1.46873e-03_wpzs-9.64972e-03_wp)zs+2.28348e-02_wp)*zs &
1114	& - 3.12775e-02_wp)zs+2.07679e-02_wp)zs-5.87701e-02_wp
1115	ptf = ptf * psal
1116	!
1117	IF( PRESENT( pdep ) ) ptf = ptf - 7.53e-4 * pdep
1118	!
1119	CASE ( np_eos80 ) !== PT,SP (UNESCO formulation) ==!
1120	!
1121	ptf = ( - 0.0575_wp + 1.710523e-3_wp * SQRT( psal ) &
1122	& - 2.154996e-4_wp * psal ) * psal
1123	!
1124	IF( PRESENT( pdep ) ) ptf = ptf - 7.53e-4 * pdep
1125	!
1126	CASE DEFAULT
1127	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1128	CALL ctl_stop( 'eos_fzp_0d:', ctmp1 )
1129	!
1130	END SELECT
1131	!
1132	END SUBROUTINE eos_fzp_0d
1133
1134
1135	SUBROUTINE eos_pen( pts, pab_pe, ppen, Kmm )
1136	!!----------------------------------------------------------------------
1137	!! * ROUTINE eos_pen *
1138	!!
1139	!! ** Purpose : Calculates nonlinear anomalies of alpha_PE, beta_PE and PE at T-points
1140	!!
1141	!! ** Method : PE is defined analytically as the vertical
1142	!! primitive of EOS times -g integrated between 0 and z>0.
1143	!! pen is the nonlinear bsq-PE anomaly: pen = ( PE - rho0 gz ) / rho0 gz - rd
1144	!! = 1/z * /int_0^z rd dz - rd
1145	!! where rd is the density anomaly (see eos_rhd function)
1146	!! ab_pe are partial derivatives of PE anomaly with respect to T and S:
1147	!! ab_pe(1) = - 1/(rho0 gz) * dPE/dT + drd/dT = - d(pen)/dT
1148	!! ab_pe(2) = 1/(rho0 gz) * dPE/dS + drd/dS = d(pen)/dS
1149	!!
1150	!! ** Action : - pen : PE anomaly given at T-points
1151	!! : - pab_pe : given at T-points
1152	!! pab_pe(:,:,:,jp_tem) is alpha_pe
1153	!! pab_pe(:,:,:,jp_sal) is beta_pe
1154	!!----------------------------------------------------------------------
1155	INTEGER , INTENT(in ) :: Kmm ! time level index
1156	REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT(in ) :: pts ! pot. temperature & salinity
1157	REAL(wp), DIMENSION(jpi,jpj,jpk,jpts), INTENT( out) :: pab_pe ! alpha_pe and beta_pe
1158	REAL(wp), DIMENSION(jpi,jpj,jpk) , INTENT( out) :: ppen ! potential energy anomaly
1159	!
1160	INTEGER :: ji, jj, jk ! dummy loop indices
1161	REAL(wp) :: zt , zh , zs , ztm ! local scalars
1162	REAL(wp) :: zn , zn0, zn1, zn2 ! - -
1163	!!----------------------------------------------------------------------
1164	!
1165	IF( ln_timing ) CALL timing_start('eos_pen')
1166	!
1167	SELECT CASE ( neos )
1168	!
1169	CASE( np_teos10, np_eos80 ) !== polynomial TEOS-10 / EOS-80 ==!
1170	!
1171	DO_3D_11_11( 1, jpkm1 )
1172	!
1173	zh = gdept(ji,jj,jk,Kmm) * r1_Z0 ! depth
1174	zt = pts (ji,jj,jk,jp_tem) * r1_T0 ! temperature
1175	zs = SQRT( ABS( pts(ji,jj,jk,jp_sal) + rdeltaS ) * r1_S0 ) ! square root salinity
1176	ztm = tmask(ji,jj,jk) ! tmask
1177	!
1178	! potential energy non-linear anomaly
1179	zn2 = (PEN012)*zt &
1180	& + PEN102*zs+PEN002
1181	!
1182	zn1 = ((PEN021)*zt &
1183	& + PEN111zs+PEN011)zt &
1184	& + (PEN201zs+PEN101)zs+PEN001
1185	!
1186	zn0 = ((((PEN040)*zt &
1187	& + PEN130zs+PEN030)zt &
1188	& + (PEN220zs+PEN120)zs+PEN020)*zt &
1189	& + ((PEN310zs+PEN210)zs+PEN110)zs+PEN010)zt &
1190	& + (((PEN400zs+PEN300)zs+PEN200)zs+PEN100)zs+PEN000
1191	!
1192	zn = ( zn2 * zh + zn1 ) * zh + zn0
1193	!
1194	ppen(ji,jj,jk) = zn * zh * r1_rho0 * ztm
1195	!
1196	! alphaPE non-linear anomaly
1197	zn2 = APE002
1198	!
1199	zn1 = (APE011)*zt &
1200	& + APE101*zs+APE001
1201	!
1202	zn0 = (((APE030)*zt &
1203	& + APE120zs+APE020)zt &
1204	& + (APE210zs+APE110)zs+APE010)*zt &
1205	& + ((APE300zs+APE200)zs+APE100)*zs+APE000
1206	!
1207	zn = ( zn2 * zh + zn1 ) * zh + zn0
1208	!
1209	pab_pe(ji,jj,jk,jp_tem) = zn * zh * r1_rho0 * ztm
1210	!
1211	! betaPE non-linear anomaly
1212	zn2 = BPE002
1213	!
1214	zn1 = (BPE011)*zt &
1215	& + BPE101*zs+BPE001
1216	!
1217	zn0 = (((BPE030)*zt &
1218	& + BPE120zs+BPE020)zt &
1219	& + (BPE210zs+BPE110)zs+BPE010)*zt &
1220	& + ((BPE300zs+BPE200)zs+BPE100)*zs+BPE000
1221	!
1222	zn = ( zn2 * zh + zn1 ) * zh + zn0
1223	!
1224	pab_pe(ji,jj,jk,jp_sal) = zn / zs * zh * r1_rho0 * ztm
1225	!
1226	END_3D
1227	!
1228	CASE( np_seos ) !== Vallis (2006) simplified EOS ==!
1229	!
1230	DO_3D_11_11( 1, jpkm1 )
1231	zt = pts(ji,jj,jk,jp_tem) - 10._wp ! temperature anomaly (t-T0)
1232	zs = pts (ji,jj,jk,jp_sal) - 35._wp ! abs. salinity anomaly (s-S0)
1233	zh = gdept(ji,jj,jk,Kmm) ! depth in meters at t-point
1234	ztm = tmask(ji,jj,jk) ! tmask
1235	zn = 0.5_wp * zh * r1_rho0 * ztm
1236	! ! Potential Energy
1237	ppen(ji,jj,jk) = ( rn_a0 * rn_mu1 * zt + rn_b0 * rn_mu2 * zs ) * zn
1238	! ! alphaPE
1239	pab_pe(ji,jj,jk,jp_tem) = - rn_a0 * rn_mu1 * zn
1240	pab_pe(ji,jj,jk,jp_sal) = rn_b0 * rn_mu2 * zn
1241	!
1242	END_3D
1243	!
1244	CASE DEFAULT
1245	WRITE(ctmp1,*) ' bad flag value for neos = ', neos
1246	CALL ctl_stop( 'eos_pen:', ctmp1 )
1247	!
1248	END SELECT
1249	!
1250	IF( ln_timing ) CALL timing_stop('eos_pen')
1251	!
1252	END SUBROUTINE eos_pen
1253
1254
1255	SUBROUTINE eos_init
1256	!!----------------------------------------------------------------------
1257	!! * ROUTINE eos_init *
1258	!!
1259	!! ** Purpose : initializations for the equation of state
1260	!!
1261	!! ** Method : Read the namelist nameos and control the parameters
1262	!!----------------------------------------------------------------------
1263	INTEGER :: ios ! local integer
1264	INTEGER :: ioptio ! local integer
1265	!!
1266	NAMELIST/nameos/ ln_TEOS10, ln_EOS80, ln_SEOS, rn_a0, rn_b0, rn_lambda1, rn_mu1, &
1267	& rn_lambda2, rn_mu2, rn_nu
1268	!!----------------------------------------------------------------------
1269	!
1270	READ ( numnam_ref, nameos, IOSTAT = ios, ERR = 901 )
1271	901 IF( ios /= 0 ) CALL ctl_nam ( ios , 'nameos in reference namelist' )
1272	!
1273	READ ( numnam_cfg, nameos, IOSTAT = ios, ERR = 902 )
1274	902 IF( ios > 0 ) CALL ctl_nam ( ios , 'nameos in configuration namelist' )
1275	IF(lwm) WRITE( numond, nameos )
1276	!
1277	rho0 = 1026._wp !: volumic mass of reference [kg/m3]
1278	rcp = 3991.86795711963_wp !: heat capacity [J/K]
1279	!
1280	IF(lwp) THEN ! Control print
1281	WRITE(numout,*)
1282	WRITE(numout,*) 'eos_init : equation of state'
1283	WRITE(numout,*) '~~~~~~~~'
1284	WRITE(numout,*) ' Namelist nameos : Chosen the Equation Of Seawater (EOS)'
1285	WRITE(numout,*) ' TEOS-10 : rho=F(Conservative Temperature, Absolute Salinity, depth) ln_TEOS10 = ', ln_TEOS10
1286	WRITE(numout,*) ' EOS-80 : rho=F(Potential Temperature, Practical Salinity, depth) ln_EOS80 = ', ln_EOS80
1287	WRITE(numout,*) ' S-EOS : rho=F(Conservative Temperature, Absolute Salinity, depth) ln_SEOS = ', ln_SEOS
1288	ENDIF
1289
1290	! Check options for equation of state & set neos based on logical flags
1291	ioptio = 0
1292	IF( ln_TEOS10 ) THEN ; ioptio = ioptio+1 ; neos = np_teos10 ; ENDIF
1293	IF( ln_EOS80 ) THEN ; ioptio = ioptio+1 ; neos = np_eos80 ; ENDIF
1294	IF( ln_SEOS ) THEN ; ioptio = ioptio+1 ; neos = np_seos ; ENDIF
1295	IF( ioptio /= 1 ) CALL ctl_stop("Exactly one equation of state option must be selected")
1296	!
1297	SELECT CASE( neos ) ! check option
1298	!
1299	CASE( np_teos10 ) !== polynomial TEOS-10 ==!
1300	IF(lwp) WRITE(numout,*)
1301	IF(lwp) WRITE(numout,*) ' ==>>> use of TEOS-10 equation of state (cons. temp. and abs. salinity)'
1302	!
1303	l_useCT = .TRUE. ! model temperature is Conservative temperature
1304	!
1305	rdeltaS = 32._wp
1306	r1_S0 = 0.875_wp/35.16504_wp
1307	r1_T0 = 1._wp/40._wp
1308	r1_Z0 = 1.e-4_wp
1309	!
1310	EOS000 = 8.0189615746e+02_wp
1311	EOS100 = 8.6672408165e+02_wp
1312	EOS200 = -1.7864682637e+03_wp
1313	EOS300 = 2.0375295546e+03_wp
1314	EOS400 = -1.2849161071e+03_wp
1315	EOS500 = 4.3227585684e+02_wp
1316	EOS600 = -6.0579916612e+01_wp
1317	EOS010 = 2.6010145068e+01_wp
1318	EOS110 = -6.5281885265e+01_wp
1319	EOS210 = 8.1770425108e+01_wp
1320	EOS310 = -5.6888046321e+01_wp
1321	EOS410 = 1.7681814114e+01_wp
1322	EOS510 = -1.9193502195_wp
1323	EOS020 = -3.7074170417e+01_wp
1324	EOS120 = 6.1548258127e+01_wp
1325	EOS220 = -6.0362551501e+01_wp
1326	EOS320 = 2.9130021253e+01_wp
1327	EOS420 = -5.4723692739_wp
1328	EOS030 = 2.1661789529e+01_wp
1329	EOS130 = -3.3449108469e+01_wp
1330	EOS230 = 1.9717078466e+01_wp
1331	EOS330 = -3.1742946532_wp
1332	EOS040 = -8.3627885467_wp
1333	EOS140 = 1.1311538584e+01_wp
1334	EOS240 = -5.3563304045_wp
1335	EOS050 = 5.4048723791e-01_wp
1336	EOS150 = 4.8169980163e-01_wp
1337	EOS060 = -1.9083568888e-01_wp
1338	EOS001 = 1.9681925209e+01_wp
1339	EOS101 = -4.2549998214e+01_wp
1340	EOS201 = 5.0774768218e+01_wp
1341	EOS301 = -3.0938076334e+01_wp
1342	EOS401 = 6.6051753097_wp
1343	EOS011 = -1.3336301113e+01_wp
1344	EOS111 = -4.4870114575_wp
1345	EOS211 = 5.0042598061_wp
1346	EOS311 = -6.5399043664e-01_wp
1347	EOS021 = 6.7080479603_wp
1348	EOS121 = 3.5063081279_wp
1349	EOS221 = -1.8795372996_wp
1350	EOS031 = -2.4649669534_wp
1351	EOS131 = -5.5077101279e-01_wp
1352	EOS041 = 5.5927935970e-01_wp
1353	EOS002 = 2.0660924175_wp
1354	EOS102 = -4.9527603989_wp
1355	EOS202 = 2.5019633244_wp
1356	EOS012 = 2.0564311499_wp
1357	EOS112 = -2.1311365518e-01_wp
1358	EOS022 = -1.2419983026_wp
1359	EOS003 = -2.3342758797e-02_wp
1360	EOS103 = -1.8507636718e-02_wp
1361	EOS013 = 3.7969820455e-01_wp
1362	!
1363	ALP000 = -6.5025362670e-01_wp
1364	ALP100 = 1.6320471316_wp
1365	ALP200 = -2.0442606277_wp
1366	ALP300 = 1.4222011580_wp
1367	ALP400 = -4.4204535284e-01_wp
1368	ALP500 = 4.7983755487e-02_wp
1369	ALP010 = 1.8537085209_wp
1370	ALP110 = -3.0774129064_wp
1371	ALP210 = 3.0181275751_wp
1372	ALP310 = -1.4565010626_wp
1373	ALP410 = 2.7361846370e-01_wp
1374	ALP020 = -1.6246342147_wp
1375	ALP120 = 2.5086831352_wp
1376	ALP220 = -1.4787808849_wp
1377	ALP320 = 2.3807209899e-01_wp
1378	ALP030 = 8.3627885467e-01_wp
1379	ALP130 = -1.1311538584_wp
1380	ALP230 = 5.3563304045e-01_wp
1381	ALP040 = -6.7560904739e-02_wp
1382	ALP140 = -6.0212475204e-02_wp
1383	ALP050 = 2.8625353333e-02_wp
1384	ALP001 = 3.3340752782e-01_wp
1385	ALP101 = 1.1217528644e-01_wp
1386	ALP201 = -1.2510649515e-01_wp
1387	ALP301 = 1.6349760916e-02_wp
1388	ALP011 = -3.3540239802e-01_wp
1389	ALP111 = -1.7531540640e-01_wp
1390	ALP211 = 9.3976864981e-02_wp
1391	ALP021 = 1.8487252150e-01_wp
1392	ALP121 = 4.1307825959e-02_wp
1393	ALP031 = -5.5927935970e-02_wp
1394	ALP002 = -5.1410778748e-02_wp
1395	ALP102 = 5.3278413794e-03_wp
1396	ALP012 = 6.2099915132e-02_wp
1397	ALP003 = -9.4924551138e-03_wp
1398	!
1399	BET000 = 1.0783203594e+01_wp
1400	BET100 = -4.4452095908e+01_wp
1401	BET200 = 7.6048755820e+01_wp
1402	BET300 = -6.3944280668e+01_wp
1403	BET400 = 2.6890441098e+01_wp
1404	BET500 = -4.5221697773_wp
1405	BET010 = -8.1219372432e-01_wp
1406	BET110 = 2.0346663041_wp
1407	BET210 = -2.1232895170_wp
1408	BET310 = 8.7994140485e-01_wp
1409	BET410 = -1.1939638360e-01_wp
1410	BET020 = 7.6574242289e-01_wp
1411	BET120 = -1.5019813020_wp
1412	BET220 = 1.0872489522_wp
1413	BET320 = -2.7233429080e-01_wp
1414	BET030 = -4.1615152308e-01_wp
1415	BET130 = 4.9061350869e-01_wp
1416	BET230 = -1.1847737788e-01_wp
1417	BET040 = 1.4073062708e-01_wp
1418	BET140 = -1.3327978879e-01_wp
1419	BET050 = 5.9929880134e-03_wp
1420	BET001 = -5.2937873009e-01_wp
1421	BET101 = 1.2634116779_wp
1422	BET201 = -1.1547328025_wp
1423	BET301 = 3.2870876279e-01_wp
1424	BET011 = -5.5824407214e-02_wp
1425	BET111 = 1.2451933313e-01_wp
1426	BET211 = -2.4409539932e-02_wp
1427	BET021 = 4.3623149752e-02_wp
1428	BET121 = -4.6767901790e-02_wp
1429	BET031 = -6.8523260060e-03_wp
1430	BET002 = -6.1618945251e-02_wp
1431	BET102 = 6.2255521644e-02_wp
1432	BET012 = -2.6514181169e-03_wp
1433	BET003 = -2.3025968587e-04_wp
1434	!
1435	PEN000 = -9.8409626043_wp
1436	PEN100 = 2.1274999107e+01_wp
1437	PEN200 = -2.5387384109e+01_wp
1438	PEN300 = 1.5469038167e+01_wp
1439	PEN400 = -3.3025876549_wp
1440	PEN010 = 6.6681505563_wp
1441	PEN110 = 2.2435057288_wp
1442	PEN210 = -2.5021299030_wp
1443	PEN310 = 3.2699521832e-01_wp
1444	PEN020 = -3.3540239802_wp
1445	PEN120 = -1.7531540640_wp
1446	PEN220 = 9.3976864981e-01_wp
1447	PEN030 = 1.2324834767_wp
1448	PEN130 = 2.7538550639e-01_wp
1449	PEN040 = -2.7963967985e-01_wp
1450	PEN001 = -1.3773949450_wp
1451	PEN101 = 3.3018402659_wp
1452	PEN201 = -1.6679755496_wp
1453	PEN011 = -1.3709540999_wp
1454	PEN111 = 1.4207577012e-01_wp
1455	PEN021 = 8.2799886843e-01_wp
1456	PEN002 = 1.7507069098e-02_wp
1457	PEN102 = 1.3880727538e-02_wp
1458	PEN012 = -2.8477365341e-01_wp
1459	!
1460	APE000 = -1.6670376391e-01_wp
1461	APE100 = -5.6087643219e-02_wp
1462	APE200 = 6.2553247576e-02_wp
1463	APE300 = -8.1748804580e-03_wp
1464	APE010 = 1.6770119901e-01_wp
1465	APE110 = 8.7657703198e-02_wp
1466	APE210 = -4.6988432490e-02_wp
1467	APE020 = -9.2436260751e-02_wp
1468	APE120 = -2.0653912979e-02_wp
1469	APE030 = 2.7963967985e-02_wp
1470	APE001 = 3.4273852498e-02_wp
1471	APE101 = -3.5518942529e-03_wp
1472	APE011 = -4.1399943421e-02_wp
1473	APE002 = 7.1193413354e-03_wp
1474	!
1475	BPE000 = 2.6468936504e-01_wp
1476	BPE100 = -6.3170583896e-01_wp
1477	BPE200 = 5.7736640125e-01_wp
1478	BPE300 = -1.6435438140e-01_wp
1479	BPE010 = 2.7912203607e-02_wp
1480	BPE110 = -6.2259666565e-02_wp
1481	BPE210 = 1.2204769966e-02_wp
1482	BPE020 = -2.1811574876e-02_wp
1483	BPE120 = 2.3383950895e-02_wp
1484	BPE030 = 3.4261630030e-03_wp
1485	BPE001 = 4.1079296834e-02_wp
1486	BPE101 = -4.1503681096e-02_wp
1487	BPE011 = 1.7676120780e-03_wp
1488	BPE002 = 1.7269476440e-04_wp
1489	!
1490	CASE( np_eos80 ) !== polynomial EOS-80 formulation ==!
1491	!
1492	IF(lwp) WRITE(numout,*)
1493	IF(lwp) WRITE(numout,*) ' ==>>> use of EOS-80 equation of state (pot. temp. and pract. salinity)'
1494	!
1495	l_useCT = .FALSE. ! model temperature is Potential temperature
1496	rdeltaS = 20._wp
1497	r1_S0 = 1._wp/40._wp
1498	r1_T0 = 1._wp/40._wp
1499	r1_Z0 = 1.e-4_wp
1500	!
1501	EOS000 = 9.5356891948e+02_wp
1502	EOS100 = 1.7136499189e+02_wp
1503	EOS200 = -3.7501039454e+02_wp
1504	EOS300 = 5.1856810420e+02_wp
1505	EOS400 = -3.7264470465e+02_wp
1506	EOS500 = 1.4302533998e+02_wp
1507	EOS600 = -2.2856621162e+01_wp
1508	EOS010 = 1.0087518651e+01_wp
1509	EOS110 = -1.3647741861e+01_wp
1510	EOS210 = 8.8478359933_wp
1511	EOS310 = -7.2329388377_wp
1512	EOS410 = 1.4774410611_wp
1513	EOS510 = 2.0036720553e-01_wp
1514	EOS020 = -2.5579830599e+01_wp
1515	EOS120 = 2.4043512327e+01_wp
1516	EOS220 = -1.6807503990e+01_wp
1517	EOS320 = 8.3811577084_wp
1518	EOS420 = -1.9771060192_wp
1519	EOS030 = 1.6846451198e+01_wp
1520	EOS130 = -2.1482926901e+01_wp
1521	EOS230 = 1.0108954054e+01_wp
1522	EOS330 = -6.2675951440e-01_wp
1523	EOS040 = -8.0812310102_wp
1524	EOS140 = 1.0102374985e+01_wp
1525	EOS240 = -4.8340368631_wp
1526	EOS050 = 1.2079167803_wp
1527	EOS150 = 1.1515380987e-01_wp
1528	EOS060 = -2.4520288837e-01_wp
1529	EOS001 = 1.0748601068e+01_wp
1530	EOS101 = -1.7817043500e+01_wp
1531	EOS201 = 2.2181366768e+01_wp
1532	EOS301 = -1.6750916338e+01_wp
1533	EOS401 = 4.1202230403_wp
1534	EOS011 = -1.5852644587e+01_wp
1535	EOS111 = -7.6639383522e-01_wp
1536	EOS211 = 4.1144627302_wp
1537	EOS311 = -6.6955877448e-01_wp
1538	EOS021 = 9.9994861860_wp
1539	EOS121 = -1.9467067787e-01_wp
1540	EOS221 = -1.2177554330_wp
1541	EOS031 = -3.4866102017_wp
1542	EOS131 = 2.2229155620e-01_wp
1543	EOS041 = 5.9503008642e-01_wp
1544	EOS002 = 1.0375676547_wp
1545	EOS102 = -3.4249470629_wp
1546	EOS202 = 2.0542026429_wp
1547	EOS012 = 2.1836324814_wp
1548	EOS112 = -3.4453674320e-01_wp
1549	EOS022 = -1.2548163097_wp
1550	EOS003 = 1.8729078427e-02_wp
1551	EOS103 = -5.7238495240e-02_wp
1552	EOS013 = 3.8306136687e-01_wp
1553	!
1554	ALP000 = -2.5218796628e-01_wp
1555	ALP100 = 3.4119354654e-01_wp
1556	ALP200 = -2.2119589983e-01_wp
1557	ALP300 = 1.8082347094e-01_wp
1558	ALP400 = -3.6936026529e-02_wp
1559	ALP500 = -5.0091801383e-03_wp
1560	ALP010 = 1.2789915300_wp
1561	ALP110 = -1.2021756164_wp
1562	ALP210 = 8.4037519952e-01_wp
1563	ALP310 = -4.1905788542e-01_wp
1564	ALP410 = 9.8855300959e-02_wp
1565	ALP020 = -1.2634838399_wp
1566	ALP120 = 1.6112195176_wp
1567	ALP220 = -7.5817155402e-01_wp
1568	ALP320 = 4.7006963580e-02_wp
1569	ALP030 = 8.0812310102e-01_wp
1570	ALP130 = -1.0102374985_wp
1571	ALP230 = 4.8340368631e-01_wp
1572	ALP040 = -1.5098959754e-01_wp
1573	ALP140 = -1.4394226233e-02_wp
1574	ALP050 = 3.6780433255e-02_wp
1575	ALP001 = 3.9631611467e-01_wp
1576	ALP101 = 1.9159845880e-02_wp
1577	ALP201 = -1.0286156825e-01_wp
1578	ALP301 = 1.6738969362e-02_wp
1579	ALP011 = -4.9997430930e-01_wp
1580	ALP111 = 9.7335338937e-03_wp
1581	ALP211 = 6.0887771651e-02_wp
1582	ALP021 = 2.6149576513e-01_wp
1583	ALP121 = -1.6671866715e-02_wp
1584	ALP031 = -5.9503008642e-02_wp
1585	ALP002 = -5.4590812035e-02_wp
1586	ALP102 = 8.6134185799e-03_wp
1587	ALP012 = 6.2740815484e-02_wp
1588	ALP003 = -9.5765341718e-03_wp
1589	!
1590	BET000 = 2.1420623987_wp
1591	BET100 = -9.3752598635_wp
1592	BET200 = 1.9446303907e+01_wp
1593	BET300 = -1.8632235232e+01_wp
1594	BET400 = 8.9390837485_wp
1595	BET500 = -1.7142465871_wp
1596	BET010 = -1.7059677327e-01_wp
1597	BET110 = 2.2119589983e-01_wp
1598	BET210 = -2.7123520642e-01_wp
1599	BET310 = 7.3872053057e-02_wp
1600	BET410 = 1.2522950346e-02_wp
1601	BET020 = 3.0054390409e-01_wp
1602	BET120 = -4.2018759976e-01_wp
1603	BET220 = 3.1429341406e-01_wp
1604	BET320 = -9.8855300959e-02_wp
1605	BET030 = -2.6853658626e-01_wp
1606	BET130 = 2.5272385134e-01_wp
1607	BET230 = -2.3503481790e-02_wp
1608	BET040 = 1.2627968731e-01_wp
1609	BET140 = -1.2085092158e-01_wp
1610	BET050 = 1.4394226233e-03_wp
1611	BET001 = -2.2271304375e-01_wp
1612	BET101 = 5.5453416919e-01_wp
1613	BET201 = -6.2815936268e-01_wp
1614	BET301 = 2.0601115202e-01_wp
1615	BET011 = -9.5799229402e-03_wp
1616	BET111 = 1.0286156825e-01_wp
1617	BET211 = -2.5108454043e-02_wp
1618	BET021 = -2.4333834734e-03_wp
1619	BET121 = -3.0443885826e-02_wp
1620	BET031 = 2.7786444526e-03_wp
1621	BET002 = -4.2811838287e-02_wp
1622	BET102 = 5.1355066072e-02_wp
1623	BET012 = -4.3067092900e-03_wp
1624	BET003 = -7.1548119050e-04_wp
1625	!
1626	PEN000 = -5.3743005340_wp
1627	PEN100 = 8.9085217499_wp
1628	PEN200 = -1.1090683384e+01_wp
1629	PEN300 = 8.3754581690_wp
1630	PEN400 = -2.0601115202_wp
1631	PEN010 = 7.9263222935_wp
1632	PEN110 = 3.8319691761e-01_wp
1633	PEN210 = -2.0572313651_wp
1634	PEN310 = 3.3477938724e-01_wp
1635	PEN020 = -4.9997430930_wp
1636	PEN120 = 9.7335338937e-02_wp
1637	PEN220 = 6.0887771651e-01_wp
1638	PEN030 = 1.7433051009_wp
1639	PEN130 = -1.1114577810e-01_wp
1640	PEN040 = -2.9751504321e-01_wp
1641	PEN001 = -6.9171176978e-01_wp
1642	PEN101 = 2.2832980419_wp
1643	PEN201 = -1.3694684286_wp
1644	PEN011 = -1.4557549876_wp
1645	PEN111 = 2.2969116213e-01_wp
1646	PEN021 = 8.3654420645e-01_wp
1647	PEN002 = -1.4046808820e-02_wp
1648	PEN102 = 4.2928871430e-02_wp
1649	PEN012 = -2.8729602515e-01_wp
1650	!
1651	APE000 = -1.9815805734e-01_wp
1652	APE100 = -9.5799229402e-03_wp
1653	APE200 = 5.1430784127e-02_wp
1654	APE300 = -8.3694846809e-03_wp
1655	APE010 = 2.4998715465e-01_wp
1656	APE110 = -4.8667669469e-03_wp
1657	APE210 = -3.0443885826e-02_wp
1658	APE020 = -1.3074788257e-01_wp
1659	APE120 = 8.3359333577e-03_wp
1660	APE030 = 2.9751504321e-02_wp
1661	APE001 = 3.6393874690e-02_wp
1662	APE101 = -5.7422790533e-03_wp
1663	APE011 = -4.1827210323e-02_wp
1664	APE002 = 7.1824006288e-03_wp
1665	!
1666	BPE000 = 1.1135652187e-01_wp
1667	BPE100 = -2.7726708459e-01_wp
1668	BPE200 = 3.1407968134e-01_wp
1669	BPE300 = -1.0300557601e-01_wp
1670	BPE010 = 4.7899614701e-03_wp
1671	BPE110 = -5.1430784127e-02_wp
1672	BPE210 = 1.2554227021e-02_wp
1673	BPE020 = 1.2166917367e-03_wp
1674	BPE120 = 1.5221942913e-02_wp
1675	BPE030 = -1.3893222263e-03_wp
1676	BPE001 = 2.8541225524e-02_wp
1677	BPE101 = -3.4236710714e-02_wp
1678	BPE011 = 2.8711395266e-03_wp
1679	BPE002 = 5.3661089288e-04_wp
1680	!
1681	CASE( np_seos ) !== Simplified EOS ==!
1682
1683	r1_S0 = 0.875_wp/35.16504_wp ! Used to convert CT in potential temperature when using bulk formulae (eos_pt_from_ct)
1684
1685	IF(lwp) THEN
1686	WRITE(numout,*)
1687	WRITE(numout,*) ' ==>>> use of simplified eos: '
1688	WRITE(numout,) ' rhd(dT=T-10,dS=S-35,Z) = [-a0(1+lambda1/2dT+mu1Z)*dT '
1689	WRITE(numout,) ' + b0(1+lambda2/2dT+mu2Z)dS - nudT*dS] / rho0'
1690	WRITE(numout,*) ' with the following coefficients :'
1691	WRITE(numout,*) ' thermal exp. coef. rn_a0 = ', rn_a0
1692	WRITE(numout,*) ' saline cont. coef. rn_b0 = ', rn_b0
1693	WRITE(numout,*) ' cabbeling coef. rn_lambda1 = ', rn_lambda1
1694	WRITE(numout,*) ' cabbeling coef. rn_lambda2 = ', rn_lambda2
1695	WRITE(numout,*) ' thermobar. coef. rn_mu1 = ', rn_mu1
1696	WRITE(numout,*) ' thermobar. coef. rn_mu2 = ', rn_mu2
1697	WRITE(numout,*) ' 2nd cabbel. coef. rn_nu = ', rn_nu
1698	WRITE(numout,*) ' Caution: rn_beta0=0 incompatible with ddm parameterization '
1699	ENDIF
1700	l_useCT = .TRUE. ! Use conservative temperature
1701	!
1702	CASE DEFAULT !== ERROR in neos ==!
1703	WRITE(ctmp1,*) ' bad flag value for neos = ', neos, '. You should never see this error'
1704	CALL ctl_stop( ctmp1 )
1705	!
1706	END SELECT
1707	!
1708	rho0_rcp = rho0 * rcp
1709	r1_rho0 = 1._wp / rho0
1710	r1_rcp = 1._wp / rcp
1711	r1_rho0_rcp = 1._wp / rho0_rcp
1712	!
1713	IF(lwp) THEN
1714	IF( l_useCT ) THEN
1715	WRITE(numout,*)
1716	WRITE(numout,*) ' ==>>> model uses Conservative Temperature'
1717	WRITE(numout,*) ' Important: model must be initialized with CT and SA fields'
1718	ELSE
1719	WRITE(numout,*)
1720	WRITE(numout,*) ' ==>>> model does not use Conservative Temperature'
1721	ENDIF
1722	ENDIF
1723	!
1724	IF(lwp) WRITE(numout,*)
1725	IF(lwp) WRITE(numout,*) ' Associated physical constant'
1726	IF(lwp) WRITE(numout,*) ' volumic mass of reference rho0 = ', rho0 , ' kg/m^3'
1727	IF(lwp) WRITE(numout,*) ' 1. / rho0 r1_rho0 = ', r1_rho0, ' m^3/kg'
1728	IF(lwp) WRITE(numout,*) ' ocean specific heat rcp = ', rcp , ' J/Kelvin'
1729	IF(lwp) WRITE(numout,) ' rho0 rcp rho0_rcp = ', rho0_rcp
1730	IF(lwp) WRITE(numout,) ' 1. / ( rho0 rcp ) r1_rho0_rcp = ', r1_rho0_rcp
1731	!
1732	END SUBROUTINE eos_init
1733
1734	!!======================================================================
1735	END MODULE eosbn2

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