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p4zche.F90 @ 9125

Last change on this file since 9125 was 9125, checked in by timgraham, 6 years ago
Removed wrk_arrays from whole code. No change in SETTE results from this.
Property svn:keywords set to `Id`
File size: 37.1 KB

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1	MODULE p4zche
2	!!======================================================================
3	!! * MODULE p4zche *
4	!! TOP : PISCES Sea water chemistry computed following OCMIP protocol
5	!!======================================================================
6	!! History : OPA ! 1988 (E. Maier-Reimer) Original code
7	!! - ! 1998 (O. Aumont) addition
8	!! - ! 1999 (C. Le Quere) modification
9	!! NEMO 1.0 ! 2004 (O. Aumont) modification
10	!! - ! 2006 (R. Gangsto) modification
11	!! 2.0 ! 2007-12 (C. Ethe, G. Madec) F90
12	!! ! 2011-02 (J. Simeon, J.Orr ) update O2 solubility constants
13	!! 3.6 ! 2016-03 (O. Aumont) Change chemistry to MOCSY standards
14	!!----------------------------------------------------------------------
15	!! p4z_che : Sea water chemistry computed following OCMIP protocol
16	!!----------------------------------------------------------------------
17	USE oce_trc ! shared variables between ocean and passive tracers
18	USE trc ! passive tracers common variables
19	USE sms_pisces ! PISCES Source Minus Sink variables
20	USE lib_mpp ! MPP library
21	USE eosbn2, ONLY : neos
22
23	IMPLICIT NONE
24	PRIVATE
25
26	PUBLIC p4z_che !
27	PUBLIC p4z_che_alloc !
28	PUBLIC ahini_for_at !
29	PUBLIC solve_at_general !
30
31	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: sio3eq ! chemistry of Si
32	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: fekeq ! chemistry of Fe
33	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: chemc ! Solubilities of O2 and CO2
34	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: chemo2 ! Solubilities of O2 and CO2
35	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:,:) :: fesol ! solubility of Fe
36	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: salinprac ! Practical salinity
37	REAL(wp), PUBLIC, ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: tempis ! In situ temperature
38
39	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: akb3 !: ???
40	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: akw3 !: ???
41	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: akf3 !: ???
42	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: aks3 !: ???
43	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ak1p3 !: ???
44	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ak2p3 !: ???
45	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: ak3p3 !: ???
46	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: aksi3 !: ???
47	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: borat !: ???
48	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: fluorid !: ???
49	REAL(wp), ALLOCATABLE, SAVE, DIMENSION(:,:,:) :: sulfat !: ???
50
51	!!* Variable for chemistry of the CO2 cycle
52
53	REAL(wp), PUBLIC :: atcox = 0.20946 ! units atm
54
55	REAL(wp) :: o2atm = 1. / ( 1000. * 0.20946 )
56
57	REAL(wp) :: rgas = 83.14472 ! universal gas constants
58	REAL(wp) :: oxyco = 1. / 22.4144 ! converts from liters of an ideal gas to moles
59	! ! coeff. for seawater pressure correction : millero 95
60	! ! AGRIF doesn't like the DATA instruction
61	REAL(wp) :: devk10 = -25.5
62	REAL(wp) :: devk11 = -15.82
63	REAL(wp) :: devk12 = -29.48
64	REAL(wp) :: devk13 = -20.02
65	REAL(wp) :: devk14 = -18.03
66	REAL(wp) :: devk15 = -9.78
67	REAL(wp) :: devk16 = -48.76
68	REAL(wp) :: devk17 = -14.51
69	REAL(wp) :: devk18 = -23.12
70	REAL(wp) :: devk19 = -26.57
71	REAL(wp) :: devk110 = -29.48
72	!
73	REAL(wp) :: devk20 = 0.1271
74	REAL(wp) :: devk21 = -0.0219
75	REAL(wp) :: devk22 = 0.1622
76	REAL(wp) :: devk23 = 0.1119
77	REAL(wp) :: devk24 = 0.0466
78	REAL(wp) :: devk25 = -0.0090
79	REAL(wp) :: devk26 = 0.5304
80	REAL(wp) :: devk27 = 0.1211
81	REAL(wp) :: devk28 = 0.1758
82	REAL(wp) :: devk29 = 0.2020
83	REAL(wp) :: devk210 = 0.1622
84	!
85	REAL(wp) :: devk30 = 0.
86	REAL(wp) :: devk31 = 0.
87	REAL(wp) :: devk32 = 2.608E-3
88	REAL(wp) :: devk33 = -1.409e-3
89	REAL(wp) :: devk34 = 0.316e-3
90	REAL(wp) :: devk35 = -0.942e-3
91	REAL(wp) :: devk36 = 0.
92	REAL(wp) :: devk37 = -0.321e-3
93	REAL(wp) :: devk38 = -2.647e-3
94	REAL(wp) :: devk39 = -3.042e-3
95	REAL(wp) :: devk310 = -2.6080e-3
96	!
97	REAL(wp) :: devk40 = -3.08E-3
98	REAL(wp) :: devk41 = 1.13E-3
99	REAL(wp) :: devk42 = -2.84E-3
100	REAL(wp) :: devk43 = -5.13E-3
101	REAL(wp) :: devk44 = -4.53e-3
102	REAL(wp) :: devk45 = -3.91e-3
103	REAL(wp) :: devk46 = -11.76e-3
104	REAL(wp) :: devk47 = -2.67e-3
105	REAL(wp) :: devk48 = -5.15e-3
106	REAL(wp) :: devk49 = -4.08e-3
107	REAL(wp) :: devk410 = -2.84e-3
108	!
109	REAL(wp) :: devk50 = 0.0877E-3
110	REAL(wp) :: devk51 = -0.1475E-3
111	REAL(wp) :: devk52 = 0.
112	REAL(wp) :: devk53 = 0.0794E-3
113	REAL(wp) :: devk54 = 0.09e-3
114	REAL(wp) :: devk55 = 0.054e-3
115	REAL(wp) :: devk56 = 0.3692E-3
116	REAL(wp) :: devk57 = 0.0427e-3
117	REAL(wp) :: devk58 = 0.09e-3
118	REAL(wp) :: devk59 = 0.0714e-3
119	REAL(wp) :: devk510 = 0.0
120	!
121	! General parameters
122	REAL(wp), PARAMETER :: pp_rdel_ah_target = 1.E-4_wp
123	REAL(wp), PARAMETER :: pp_ln10 = 2.302585092994045684018_wp
124
125	! Maximum number of iterations for each method
126	INTEGER, PARAMETER :: jp_maxniter_atgen = 20
127
128	! Bookkeeping variables for each method
129	! - SOLVE_AT_GENERAL
130	INTEGER :: niter_atgen = jp_maxniter_atgen
131
132	!!----------------------------------------------------------------------
133	!! NEMO/TOP 3.3 , NEMO Consortium (2010)
134	!! $Id$
135	!! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt)
136	!!----------------------------------------------------------------------
137	CONTAINS
138
139	SUBROUTINE p4z_che
140	!!---------------------------------------------------------------------
141	!! * ROUTINE p4z_che *
142	!!
143	!! ** Purpose : Sea water chemistry computed following OCMIP protocol
144	!!
145	!! ** Method : - ...
146	!!---------------------------------------------------------------------
147	INTEGER :: ji, jj, jk
148	REAL(wp) :: ztkel, ztkel1, zt , zsal , zsal2 , zbuf1 , zbuf2
149	REAL(wp) :: ztgg , ztgg2, ztgg3 , ztgg4 , ztgg5
150	REAL(wp) :: zpres, ztc , zcl , zcpexp, zoxy , zcpexp2
151	REAL(wp) :: zsqrt, ztr , zlogt , zcek1, zc1, zplat
152	REAL(wp) :: zis , zis2 , zsal15, zisqrt, za1, za2
153	REAL(wp) :: zckb , zck1 , zck2 , zckw , zak1 , zak2 , zakb , zaksp0, zakw
154	REAL(wp) :: zck1p, zck2p, zck3p, zcksi, zak1p, zak2p, zak3p, zaksi
155	REAL(wp) :: zst , zft , zcks , zckf , zaksp1
156	REAL(wp) :: total2free, free2SWS, total2SWS, SWS2total
157	!!---------------------------------------------------------------------
158	!
159	IF( ln_timing ) CALL timing_start('p4z_che')
160	!
161	! Computation of chemical constants require practical salinity
162	! Thus, when TEOS08 is used, absolute salinity is converted to
163	! practical salinity
164	! -------------------------------------------------------------
165	IF (neos == -1) THEN
166	salinprac(:,:,:) = tsn(:,:,:,jp_sal) * 35.0 / 35.16504
167	ELSE
168	salinprac(:,:,:) = tsn(:,:,:,jp_sal)
169	ENDIF
170
171	!
172	! Computations of chemical constants require in situ temperature
173	! Here a quite simple formulation is used to convert
174	! potential temperature to in situ temperature. The errors is less than
175	! 0.04°C relative to an exact computation
176	! ---------------------------------------------------------------------
177	DO jk = 1, jpk
178	DO jj = 1, jpj
179	DO ji = 1, jpi
180	zpres = gdept_n(ji,jj,jk) / 1000.
181	za1 = 0.04 * ( 1.0 + 0.185 * tsn(ji,jj,jk,jp_tem) + 0.035 * (salinprac(ji,jj,jk) - 35.0) )
182	za2 = 0.0075 * ( 1.0 - tsn(ji,jj,jk,jp_tem) / 30.0 )
183	tempis(ji,jj,jk) = tsn(ji,jj,jk,jp_tem) - za1 * zpres + za2 * zpres**2
184	END DO
185	END DO
186	END DO
187	!
188	! CHEMICAL CONSTANTS - SURFACE LAYER
189	! ----------------------------------
190	!CDIR NOVERRCHK
191	DO jj = 1, jpj
192	!CDIR NOVERRCHK
193	DO ji = 1, jpi
194	! ! SET ABSOLUTE TEMPERATURE
195	ztkel = tempis(ji,jj,1) + 273.15
196	zt = ztkel * 0.01
197	zsal = salinprac(ji,jj,1) + ( 1.- tmask(ji,jj,1) ) * 35.
198	! ! LN(K0) OF SOLUBILITY OF CO2 (EQ. 12, WEISS, 1980)
199	! ! AND FOR THE ATMOSPHERE FOR NON IDEAL GAS
200	zcek1 = 9345.17/ztkel - 60.2409 + 23.3585 * LOG(zt) + zsal(0.023517 - 0.00023656ztkel &
201	& + 0.0047036e-4ztkel*2)
202	chemc(ji,jj,1) = EXP( zcek1 ) * 1E-6 * rhop(ji,jj,1) / 1000. ! mol/(L atm)
203	chemc(ji,jj,2) = -1636.75 + 12.0408ztkel - 0.0327957ztkel*2 + 0.0000316528ztkel**3
204	chemc(ji,jj,3) = 57.7 - 0.118*ztkel
205	!
206	END DO
207	END DO
208
209	! OXYGEN SOLUBILITY - DEEP OCEAN
210	! -------------------------------
211	!CDIR NOVERRCHK
212	DO jk = 1, jpk
213	!CDIR NOVERRCHK
214	DO jj = 1, jpj
215	!CDIR NOVERRCHK
216	DO ji = 1, jpi
217	ztkel = tempis(ji,jj,jk) + 273.15
218	zsal = salinprac(ji,jj,jk) + ( 1.- tmask(ji,jj,jk) ) * 35.
219	zsal2 = zsal * zsal
220	ztgg = LOG( ( 298.15 - tempis(ji,jj,jk) ) / ztkel ) ! Set the GORDON & GARCIA scaled temperature
221	ztgg2 = ztgg * ztgg
222	ztgg3 = ztgg2 * ztgg
223	ztgg4 = ztgg3 * ztgg
224	ztgg5 = ztgg4 * ztgg
225
226	zoxy = 2.00856 + 3.22400 * ztgg + 3.99063 * ztgg2 + 4.80299 * ztgg3 &
227	& + 9.78188e-1 * ztgg4 + 1.71069 * ztgg5 + zsal * ( -6.24097e-3 &
228	& - 6.93498e-3 * ztgg - 6.90358e-3 * ztgg2 - 4.29155e-3 * ztgg3 ) &
229	& - 3.11680e-7 * zsal2
230	chemo2(ji,jj,jk) = ( EXP( zoxy ) * o2atm ) * oxyco * atcox ! mol/(L atm)
231	END DO
232	END DO
233	END DO
234
235
236
237	! CHEMICAL CONSTANTS - DEEP OCEAN
238	! -------------------------------
239	!CDIR NOVERRCHK
240	DO jk = 1, jpk
241	!CDIR NOVERRCHK
242	DO jj = 1, jpj
243	!CDIR NOVERRCHK
244	DO ji = 1, jpi
245
246	! SET PRESSION ACCORDING TO SAUNDER (1980)
247	zplat = SIN ( ABS(gphit(ji,jj)*3.141592654/180.) )
248	zc1 = 5.92E-3 + zplat*2 5.25E-3
249	zpres = ((1-zc1)-SQRT(((1-zc1)*2)-(8.84E-6gdept_n(ji,jj,jk)))) / 4.42E-6
250	zpres = zpres / 10.0
251
252	! SET ABSOLUTE TEMPERATURE
253	ztkel = tempis(ji,jj,jk) + 273.15
254	zsal = salinprac(ji,jj,jk) + ( 1.-tmask(ji,jj,jk) ) * 35.
255	zsqrt = SQRT( zsal )
256	zsal15 = zsqrt * zsal
257	zlogt = LOG( ztkel )
258	ztr = 1. / ztkel
259	zis = 19.924 * zsal / ( 1000.- 1.005 * zsal )
260	zis2 = zis * zis
261	zisqrt = SQRT( zis )
262	ztc = tempis(ji,jj,jk) + ( 1.- tmask(ji,jj,jk) ) * 20.
263
264	! CHLORINITY (WOOSTER ET AL., 1969)
265	zcl = zsal / 1.80655
266
267	! TOTAL SULFATE CONCENTR. [MOLES/kg soln]
268	zst = 0.14 * zcl /96.062
269
270	! TOTAL FLUORIDE CONCENTR. [MOLES/kg soln]
271	zft = 0.000067 * zcl /18.9984
272
273	! DISSOCIATION CONSTANT FOR SULFATES on free H scale (Dickson 1990)
274	zcks = EXP(-4276.1 * ztr + 141.328 - 23.093 * zlogt &
275	& + (-13856. * ztr + 324.57 - 47.986 * zlogt) * zisqrt &
276	& + (35474. * ztr - 771.54 + 114.723 * zlogt) * zis &
277	& - 2698. * ztr * zis*1.5 + 1776. ztr * zis2 &
278	& + LOG(1.0 - 0.001005 * zsal))
279
280	! DISSOCIATION CONSTANT FOR FLUORIDES on free H scale (Dickson and Riley 79)
281	zckf = EXP( 1590.2ztr - 12.641 + 1.525zisqrt &
282	& + LOG(1.0d0 - 0.001005d0*zsal) &
283	& + LOG(1.0d0 + zst/zcks))
284
285	! DISSOCIATION CONSTANT FOR CARBONATE AND BORATE
286	zckb= (-8966.90 - 2890.53zsqrt - 77.942zsal &
287	& + 1.728zsal15 - 0.0996zsalzsal)ztr &
288	& + (148.0248 + 137.1942zsqrt + 1.62142zsal) &
289	& + (-24.4344 - 25.085zsqrt - 0.2474zsal) &
290	& * zlogt + 0.053105zsqrtztkel
291
292	! DISSOCIATION COEFFICIENT FOR CARBONATE ACCORDING TO
293	! MEHRBACH (1973) REFIT BY MILLERO (1995), seawater scale
294	zck1 = -1.0(3633.86ztr - 61.2172 + 9.6777*zlogt &
295	- 0.011555zsal + 0.0001152zsal*zsal)
296	zck2 = -1.0(471.78ztr + 25.9290 - 3.16967*zlogt &
297	- 0.01781zsal + 0.0001122zsal*zsal)
298
299	! PKW (H2O) (MILLERO, 1995) from composite data
300	zckw = -13847.26 * ztr + 148.9652 - 23.6521 * zlogt + ( 118.67 * ztr &
301	- 5.977 + 1.0495 * zlogt ) * zsqrt - 0.01615 * zsal
302
303	! CONSTANTS FOR PHOSPHATE (MILLERO, 1995)
304	zck1p = -4576.752ztr + 115.540 - 18.453zlogt &
305	& + (-106.736ztr + 0.69171) zsqrt &
306	& + (-0.65643ztr - 0.01844) zsal
307
308	zck2p = -8814.715ztr + 172.1033 - 27.927zlogt &
309	& + (-160.340ztr + 1.3566)zsqrt &
310	& + (0.37335ztr - 0.05778)zsal
311
312	zck3p = -3070.75*ztr - 18.126 &
313	& + (17.27039ztr + 2.81197) zsqrt &
314	& + (-44.99486ztr - 0.09984) zsal
315
316	! CONSTANT FOR SILICATE, MILLERO (1995)
317	zcksi = -8904.2ztr + 117.400 - 19.334zlogt &
318	& + (-458.79ztr + 3.5913) zisqrt &
319	& + (188.74ztr - 1.5998) zis &
320	& + (-12.1652ztr + 0.07871) zis2 &
321	& + LOG(1.0 - 0.001005*zsal)
322
323	! APPARENT SOLUBILITY PRODUCT K'SP OF CALCITE IN SEAWATER
324	! (S=27-43, T=2-25 DEG C) at pres =0 (atmos. pressure) (MUCCI 1983)
325	zaksp0 = -171.9065 -0.077993ztkel + 2839.319ztr + 71.595*LOG10( ztkel ) &
326	& + (-0.77712 + 0.00284263ztkel + 178.34ztr) * zsqrt &
327	& - 0.07711zsal + 0.0041249zsal15
328
329	! CONVERT FROM DIFFERENT PH SCALES
330	total2free = 1.0/(1.0 + zst/zcks)
331	free2SWS = 1. + zst/zcks + zft/(zckf*total2free)
332	total2SWS = total2free * free2SWS
333	SWS2total = 1.0 / total2SWS
334
335	! K1, K2 OF CARBONIC ACID, KB OF BORIC ACID, KW (H2O) (LIT.?)
336	zak1 = 10*(zck1) total2SWS
337	zak2 = 10*(zck2) total2SWS
338	zakb = EXP( zckb ) * total2SWS
339	zakw = EXP( zckw )
340	zaksp1 = 10**(zaksp0)
341	zak1p = exp( zck1p )
342	zak2p = exp( zck2p )
343	zak3p = exp( zck3p )
344	zaksi = exp( zcksi )
345	zckf = zckf * total2SWS
346
347	! FORMULA FOR CPEXP AFTER EDMOND & GIESKES (1970)
348	! (REFERENCE TO CULBERSON & PYTKOQICZ (1968) AS MADE
349	! IN BROECKER ET AL. (1982) IS INCORRECT; HERE RGAS IS
350	! TAKEN TENFOLD TO CORRECT FOR THE NOTATION OF pres IN
351	! DBAR INSTEAD OF BAR AND THE EXPRESSION FOR CPEXP IS
352	! MULTIPLIED BY LN(10.) TO ALLOW USE OF EXP-FUNCTION
353	! WITH BASIS E IN THE FORMULA FOR AKSPP (CF. EDMOND
354	! & GIESKES (1970), P. 1285-1286 (THE SMALL
355	! FORMULA ON P. 1286 IS RIGHT AND CONSISTENT WITH THE
356	! SIGN IN PARTIAL MOLAR VOLUME CHANGE AS SHOWN ON P. 1285))
357	zcpexp = zpres / (rgas*ztkel)
358	zcpexp2 = zpres * zcpexp
359
360	! KB OF BORIC ACID, K1,K2 OF CARBONIC ACID PRESSURE
361	! CORRECTION AFTER CULBERSON AND PYTKOWICZ (1968)
362	! (CF. BROECKER ET AL., 1982)
363
364	zbuf1 = - ( devk10 + devk20 * ztc + devk30 * ztc * ztc )
365	zbuf2 = 0.5 * ( devk40 + devk50 * ztc )
366	ak13(ji,jj,jk) = zak1 * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 )
367
368	zbuf1 = - ( devk11 + devk21 * ztc + devk31 * ztc * ztc )
369	zbuf2 = 0.5 * ( devk41 + devk51 * ztc )
370	ak23(ji,jj,jk) = zak2 * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 )
371
372	zbuf1 = - ( devk12 + devk22 * ztc + devk32 * ztc * ztc )
373	zbuf2 = 0.5 * ( devk42 + devk52 * ztc )
374	akb3(ji,jj,jk) = zakb * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 )
375
376	zbuf1 = - ( devk13 + devk23 * ztc + devk33 * ztc * ztc )
377	zbuf2 = 0.5 * ( devk43 + devk53 * ztc )
378	akw3(ji,jj,jk) = zakw * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 )
379
380	zbuf1 = - ( devk14 + devk24 * ztc + devk34 * ztc * ztc )
381	zbuf2 = 0.5 * ( devk44 + devk54 * ztc )
382	aks3(ji,jj,jk) = zcks * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 )
383
384	zbuf1 = - ( devk15 + devk25 * ztc + devk35 * ztc * ztc )
385	zbuf2 = 0.5 * ( devk45 + devk55 * ztc )
386	akf3(ji,jj,jk) = zckf * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 )
387
388	zbuf1 = - ( devk17 + devk27 * ztc + devk37 * ztc * ztc )
389	zbuf2 = 0.5 * ( devk47 + devk57 * ztc )
390	ak1p3(ji,jj,jk) = zak1p * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 )
391
392	zbuf1 = - ( devk18 + devk28 * ztc + devk38 * ztc * ztc )
393	zbuf2 = 0.5 * ( devk48 + devk58 * ztc )
394	ak2p3(ji,jj,jk) = zak2p * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 )
395
396	zbuf1 = - ( devk19 + devk29 * ztc + devk39 * ztc * ztc )
397	zbuf2 = 0.5 * ( devk49 + devk59 * ztc )
398	ak3p3(ji,jj,jk) = zak3p * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 )
399
400	zbuf1 = - ( devk110 + devk210 * ztc + devk310 * ztc * ztc )
401	zbuf2 = 0.5 * ( devk410 + devk510 * ztc )
402	aksi3(ji,jj,jk) = zaksi * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 )
403
404	! CONVERT FROM DIFFERENT PH SCALES
405	total2free = 1.0/(1.0 + zst/aks3(ji,jj,jk))
406	free2SWS = 1. + zst/aks3(ji,jj,jk) + zft/akf3(ji,jj,jk)
407	total2SWS = total2free * free2SWS
408	SWS2total = 1.0 / total2SWS
409
410	! Convert to total scale
411	ak13(ji,jj,jk) = ak13(ji,jj,jk) * SWS2total
412	ak23(ji,jj,jk) = ak23(ji,jj,jk) * SWS2total
413	akb3(ji,jj,jk) = akb3(ji,jj,jk) * SWS2total
414	akw3(ji,jj,jk) = akw3(ji,jj,jk) * SWS2total
415	ak1p3(ji,jj,jk) = ak1p3(ji,jj,jk) * SWS2total
416	ak2p3(ji,jj,jk) = ak2p3(ji,jj,jk) * SWS2total
417	ak3p3(ji,jj,jk) = ak3p3(ji,jj,jk) * SWS2total
418	aksi3(ji,jj,jk) = aksi3(ji,jj,jk) * SWS2total
419	akf3(ji,jj,jk) = akf3(ji,jj,jk) / total2free
420
421	! APPARENT SOLUBILITY PRODUCT K'SP OF CALCITE
422	! AS FUNCTION OF PRESSURE FOLLOWING MILLERO
423	! (P. 1285) AND BERNER (1976)
424	zbuf1 = - ( devk16 + devk26 * ztc + devk36 * ztc * ztc )
425	zbuf2 = 0.5 * ( devk46 + devk56 * ztc )
426	aksp(ji,jj,jk) = zaksp1 * EXP( zbuf1 * zcpexp + zbuf2 * zcpexp2 )
427
428	! TOTAL F, S, and BORATE CONCENTR. [MOLES/L]
429	borat(ji,jj,jk) = 0.0002414 * zcl / 10.811
430	sulfat(ji,jj,jk) = zst
431	fluorid(ji,jj,jk) = zft
432
433	! Iron and SIO3 saturation concentration from ...
434	sio3eq(ji,jj,jk) = EXP( LOG( 10.) * ( 6.44 - 968. / ztkel ) ) * 1.e-6
435	fekeq (ji,jj,jk) = 10**( 17.27 - 1565.7 / ztkel )
436
437	! Liu and Millero (1999) only valid 5 - 50 degC
438	ztkel1 = MAX( 5. , tempis(ji,jj,jk) ) + 273.16
439	fesol(ji,jj,jk,1) = 10*(-13.486 - 0.1856 zis*0.5 + 0.3073zis + 5254.0/ztkel1)
440	fesol(ji,jj,jk,2) = 10*(2.517 - 0.8885zis*0.5 + 0.2139 zis - 1320.0/ztkel1 )
441	fesol(ji,jj,jk,3) = 10*(0.4511 - 0.3305zis**0.5 - 1996.0/ztkel1 )
442	fesol(ji,jj,jk,4) = 10*(-0.2965 - 0.7881zis**0.5 - 4086.0/ztkel1 )
443	fesol(ji,jj,jk,5) = 10*(4.4466 - 0.8505zis**0.5 - 7980.0/ztkel1 )
444	END DO
445	END DO
446	END DO
447	!
448	IF( ln_timing ) CALL timing_stop('p4z_che')
449	!
450	END SUBROUTINE p4z_che
451
452
453	SUBROUTINE ahini_for_at(p_hini)
454	!!---------------------------------------------------------------------
455	!! * ROUTINE ahini_for_at *
456	!!
457	!! Subroutine returns the root for the 2nd order approximation of the
458	!! DIC -- B_T -- A_CB equation for [H+] (reformulated as a cubic
459	!! polynomial) around the local minimum, if it exists.
460	!! Returns * 1E-03_wp if p_alkcb <= 0
461	!! * 1E-10_wp if p_alkcb >= 2*p_dictot + p_bortot
462	!! * 1E-07_wp if 0 < p_alkcb < 2*p_dictot + p_bortot
463	!! and the 2nd order approximation does not have
464	!! a solution
465	!!---------------------------------------------------------------------
466	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(OUT) :: p_hini
467	INTEGER :: ji, jj, jk
468	REAL(wp) :: zca1, zba1
469	REAL(wp) :: zd, zsqrtd, zhmin
470	REAL(wp) :: za2, za1, za0
471	REAL(wp) :: p_dictot, p_bortot, p_alkcb
472	!!---------------------------------------------------------------------
473
474	IF( ln_timing ) CALL timing_start('ahini_for_at')
475	!
476	DO jk = 1, jpk
477	DO jj = 1, jpj
478	DO ji = 1, jpi
479	p_alkcb = trb(ji,jj,jk,jptal) * 1000. / (rhop(ji,jj,jk) + rtrn)
480	p_dictot = trb(ji,jj,jk,jpdic) * 1000. / (rhop(ji,jj,jk) + rtrn)
481	p_bortot = borat(ji,jj,jk)
482	IF (p_alkcb <= 0.) THEN
483	p_hini(ji,jj,jk) = 1.e-3
484	ELSEIF (p_alkcb >= (2.*p_dictot + p_bortot)) THEN
485	p_hini(ji,jj,jk) = 1.e-10_wp
486	ELSE
487	zca1 = p_dictot/( p_alkcb + rtrn )
488	zba1 = p_bortot/ (p_alkcb + rtrn )
489	! Coefficients of the cubic polynomial
490	za2 = aKb3(ji,jj,jk)(1. - zba1) + ak13(ji,jj,jk)(1.-zca1)
491	za1 = ak13(ji,jj,jk)akb3(ji,jj,jk)(1. - zba1 - zca1) &
492	& + ak13(ji,jj,jk)ak23(ji,jj,jk)(1. - (zca1+zca1))
493	za0 = ak13(ji,jj,jk)ak23(ji,jj,jk)akb3(ji,jj,jk)*(1. - zba1 - (zca1+zca1))
494	! Taylor expansion around the minimum
495	zd = za2za2 - 3.za1 ! Discriminant of the quadratic equation
496	! for the minimum close to the root
497
498	IF(zd > 0.) THEN ! If the discriminant is positive
499	zsqrtd = SQRT(zd)
500	IF(za2 < 0) THEN
501	zhmin = (-za2 + zsqrtd)/3.
502	ELSE
503	zhmin = -za1/(za2 + zsqrtd)
504	ENDIF
505	p_hini(ji,jj,jk) = zhmin + SQRT(-(za0 + zhmin(za1 + zhmin(za2 + zhmin)))/zsqrtd)
506	ELSE
507	p_hini(ji,jj,jk) = 1.e-7
508	ENDIF
509	!
510	ENDIF
511	END DO
512	END DO
513	END DO
514	!
515	IF( ln_timing ) CALL timing_stop('ahini_for_at')
516	!
517	END SUBROUTINE ahini_for_at
518
519	!===============================================================================
520
521	SUBROUTINE anw_infsup( p_alknw_inf, p_alknw_sup )
522
523	! Subroutine returns the lower and upper bounds of "non-water-selfionization"
524	! contributions to total alkalinity (the infimum and the supremum), i.e
525	! inf(TA - [OH-] + [H+]) and sup(TA - [OH-] + [H+])
526
527	! Argument variables
528	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(OUT) :: p_alknw_inf
529	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(OUT) :: p_alknw_sup
530
531	p_alknw_inf(:,:,:) = -trb(:,:,:,jppo4) * 1000. / (rhop(:,:,:) + rtrn) - sulfat(:,:,:) &
532	& - fluorid(:,:,:)
533	p_alknw_sup(:,:,:) = (2. * trb(:,:,:,jpdic) + 2. * trb(:,:,:,jppo4) + trb(:,:,:,jpsil) ) &
534	& * 1000. / (rhop(:,:,:) + rtrn) + borat(:,:,:)
535
536	END SUBROUTINE anw_infsup
537
538
539	SUBROUTINE solve_at_general( p_hini, zhi )
540
541	! Universal pH solver that converges from any given initial value,
542	! determines upper an lower bounds for the solution if required
543
544	! Argument variables
545	!--------------------
546	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(IN) :: p_hini
547	REAL(wp), DIMENSION(jpi,jpj,jpk), INTENT(OUT) :: zhi
548
549	! Local variables
550	!-----------------
551	INTEGER :: ji, jj, jk, jn
552	REAL(wp) :: zh_ini, zh, zh_prev, zh_lnfactor
553	REAL(wp) :: zdelta, zh_delta
554	REAL(wp) :: zeqn, zdeqndh, zalka
555	REAL(wp) :: aphscale
556	REAL(wp) :: znumer_dic, zdnumer_dic, zdenom_dic, zalk_dic, zdalk_dic
557	REAL(wp) :: znumer_bor, zdnumer_bor, zdenom_bor, zalk_bor, zdalk_bor
558	REAL(wp) :: znumer_po4, zdnumer_po4, zdenom_po4, zalk_po4, zdalk_po4
559	REAL(wp) :: znumer_sil, zdnumer_sil, zdenom_sil, zalk_sil, zdalk_sil
560	REAL(wp) :: znumer_so4, zdnumer_so4, zdenom_so4, zalk_so4, zdalk_so4
561	REAL(wp) :: znumer_flu, zdnumer_flu, zdenom_flu, zalk_flu, zdalk_flu
562	REAL(wp) :: zalk_wat, zdalk_wat
563	REAL(wp) :: zfact, p_alktot, zdic, zbot, zpt, zst, zft, zsit
564	LOGICAL :: l_exitnow
565	REAL(wp), PARAMETER :: pz_exp_threshold = 1.0
566	REAL(wp), DIMENSION(jpi,jpj,jpk) :: zalknw_inf, zalknw_sup, rmask, zh_min, zh_max, zeqn_absmin
567
568	IF( ln_timing ) CALL timing_start('solve_at_general')
569
570	CALL anw_infsup( zalknw_inf, zalknw_sup )
571
572	rmask(:,:,:) = tmask(:,:,:)
573	zhi(:,:,:) = 0.
574
575	! TOTAL H+ scale: conversion factor for Htot = aphscale * Hfree
576	DO jk = 1, jpk
577	DO jj = 1, jpj
578	DO ji = 1, jpi
579	IF (rmask(ji,jj,jk) == 1.) THEN
580	p_alktot = trb(ji,jj,jk,jptal) * 1000. / (rhop(ji,jj,jk) + rtrn)
581	aphscale = 1. + sulfat(ji,jj,jk)/aks3(ji,jj,jk)
582	zh_ini = p_hini(ji,jj,jk)
583
584	zdelta = (p_alktot-zalknw_inf(ji,jj,jk))*2 + 4.akw3(ji,jj,jk)/aphscale
585
586	IF(p_alktot >= zalknw_inf(ji,jj,jk)) THEN
587	zh_min(ji,jj,jk) = 2.*akw3(ji,jj,jk) /( p_alktot-zalknw_inf(ji,jj,jk) + SQRT(zdelta) )
588	ELSE
589	zh_min(ji,jj,jk) = aphscale*(-(p_alktot-zalknw_inf(ji,jj,jk)) + SQRT(zdelta) ) / 2.
590	ENDIF
591
592	zdelta = (p_alktot-zalknw_sup(ji,jj,jk))*2 + 4.akw3(ji,jj,jk)/aphscale
593
594	IF(p_alktot <= zalknw_sup(ji,jj,jk)) THEN
595	zh_max(ji,jj,jk) = aphscale*(-(p_alktot-zalknw_sup(ji,jj,jk)) + SQRT(zdelta) ) / 2.
596	ELSE
597	zh_max(ji,jj,jk) = 2.*akw3(ji,jj,jk) /( p_alktot-zalknw_sup(ji,jj,jk) + SQRT(zdelta) )
598	ENDIF
599
600	zhi(ji,jj,jk) = MAX(MIN(zh_max(ji,jj,jk), zh_ini), zh_min(ji,jj,jk))
601	ENDIF
602	END DO
603	END DO
604	END DO
605
606	zeqn_absmin(:,:,:) = HUGE(1._wp)
607
608	DO jn = 1, jp_maxniter_atgen
609	DO jk = 1, jpk
610	DO jj = 1, jpj
611	DO ji = 1, jpi
612	IF (rmask(ji,jj,jk) == 1.) THEN
613	zfact = rhop(ji,jj,jk) / 1000. + rtrn
614	p_alktot = trb(ji,jj,jk,jptal) / zfact
615	zdic = trb(ji,jj,jk,jpdic) / zfact
616	zbot = borat(ji,jj,jk)
617	zpt = trb(ji,jj,jk,jppo4) / zfact * po4r
618	zsit = trb(ji,jj,jk,jpsil) / zfact
619	zst = sulfat (ji,jj,jk)
620	zft = fluorid(ji,jj,jk)
621	aphscale = 1. + sulfat(ji,jj,jk)/aks3(ji,jj,jk)
622	zh = zhi(ji,jj,jk)
623	zh_prev = zh
624
625	! H2CO3 - HCO3 - CO3 : n=2, m=0
626	znumer_dic = 2.ak13(ji,jj,jk)ak23(ji,jj,jk) + zh*ak13(ji,jj,jk)
627	zdenom_dic = ak13(ji,jj,jk)ak23(ji,jj,jk) + zh(ak13(ji,jj,jk) + zh)
628	zalk_dic = zdic * (znumer_dic/zdenom_dic)
629	zdnumer_dic = ak13(ji,jj,jk)ak13(ji,jj,jk)ak23(ji,jj,jk) + zh &
630	(4.ak13(ji,jj,jk)ak23(ji,jj,jk) + zhak13(ji,jj,jk))
631	zdalk_dic = -zdic(zdnumer_dic/zdenom_dic*2)
632
633
634	! B(OH)3 - B(OH)4 : n=1, m=0
635	znumer_bor = akb3(ji,jj,jk)
636	zdenom_bor = akb3(ji,jj,jk) + zh
637	zalk_bor = zbot * (znumer_bor/zdenom_bor)
638	zdnumer_bor = akb3(ji,jj,jk)
639	zdalk_bor = -zbot(zdnumer_bor/zdenom_bor*2)
640
641
642	! H3PO4 - H2PO4 - HPO4 - PO4 : n=3, m=1
643	znumer_po4 = 3.ak1p3(ji,jj,jk)ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) &
644	& + zh(2.ak1p3(ji,jj,jk)ak2p3(ji,jj,jk) + zh ak1p3(ji,jj,jk))
645	zdenom_po4 = ak1p3(ji,jj,jk)ak2p3(ji,jj,jk)ak3p3(ji,jj,jk) &
646	& + zh( ak1p3(ji,jj,jk)ak2p3(ji,jj,jk) + zh*(ak1p3(ji,jj,jk) + zh))
647	zalk_po4 = zpt * (znumer_po4/zdenom_po4 - 1.) ! Zero level of H3PO4 = 1
648	zdnumer_po4 = ak1p3(ji,jj,jk)ak2p3(ji,jj,jk)ak1p3(ji,jj,jk)ak2p3(ji,jj,jk)ak3p3(ji,jj,jk) &
649	& + zh(4.ak1p3(ji,jj,jk)ak1p3(ji,jj,jk)ak2p3(ji,jj,jk)*ak3p3(ji,jj,jk) &
650	& + zh(9.ak1p3(ji,jj,jk)ak2p3(ji,jj,jk)ak3p3(ji,jj,jk) &
651	& + ak1p3(ji,jj,jk)ak1p3(ji,jj,jk)ak2p3(ji,jj,jk) &
652	& + zh(4.ak1p3(ji,jj,jk)ak2p3(ji,jj,jk) + zh ak1p3(ji,jj,jk) ) ) )
653	zdalk_po4 = -zpt * (zdnumer_po4/zdenom_po4**2)
654
655	! H4SiO4 - H3SiO4 : n=1, m=0
656	znumer_sil = aksi3(ji,jj,jk)
657	zdenom_sil = aksi3(ji,jj,jk) + zh
658	zalk_sil = zsit * (znumer_sil/zdenom_sil)
659	zdnumer_sil = aksi3(ji,jj,jk)
660	zdalk_sil = -zsit * (zdnumer_sil/zdenom_sil**2)
661
662	! HSO4 - SO4 : n=1, m=1
663	aphscale = 1.0 + zst/aks3(ji,jj,jk)
664	znumer_so4 = aks3(ji,jj,jk) * aphscale
665	zdenom_so4 = aks3(ji,jj,jk) * aphscale + zh
666	zalk_so4 = zst * (znumer_so4/zdenom_so4 - 1.)
667	zdnumer_so4 = aks3(ji,jj,jk)
668	zdalk_so4 = -zst * (zdnumer_so4/zdenom_so4**2)
669
670	! HF - F : n=1, m=1
671	znumer_flu = akf3(ji,jj,jk)
672	zdenom_flu = akf3(ji,jj,jk) + zh
673	zalk_flu = zft * (znumer_flu/zdenom_flu - 1.)
674	zdnumer_flu = akf3(ji,jj,jk)
675	zdalk_flu = -zft * (zdnumer_flu/zdenom_flu**2)
676
677	! H2O - OH
678	aphscale = 1.0 + zst/aks3(ji,jj,jk)
679	zalk_wat = akw3(ji,jj,jk)/zh - zh/aphscale
680	zdalk_wat = -akw3(ji,jj,jk)/zh**2 - 1./aphscale
681
682	! CALCULATE [ALK]([CO3--], [HCO3-])
683	zeqn = zalk_dic + zalk_bor + zalk_po4 + zalk_sil &
684	& + zalk_so4 + zalk_flu &
685	& + zalk_wat - p_alktot
686
687	zalka = p_alktot - (zalk_bor + zalk_po4 + zalk_sil &
688	& + zalk_so4 + zalk_flu + zalk_wat)
689
690	zdeqndh = zdalk_dic + zdalk_bor + zdalk_po4 + zdalk_sil &
691	& + zdalk_so4 + zdalk_flu + zdalk_wat
692
693	! Adapt bracketing interval
694	IF(zeqn > 0._wp) THEN
695	zh_min(ji,jj,jk) = zh_prev
696	ELSEIF(zeqn < 0._wp) THEN
697	zh_max(ji,jj,jk) = zh_prev
698	ENDIF
699
700	IF(ABS(zeqn) >= 0.5_wp*zeqn_absmin(ji,jj,jk)) THEN
701	! if the function evaluation at the current point is
702	! not decreasing faster than with a bisection step (at least linearly)
703	! in absolute value take one bisection step on [ph_min, ph_max]
704	! ph_new = (ph_min + ph_max)/2d0
705	!
706	! In terms of [H]_new:
707	! [H]_new = 10**(-ph_new)
708	! = 10**(-(ph_min + ph_max)/2d0)
709	! = SQRT(10**(-(ph_min + phmax)))
710	! = SQRT(zh_max * zh_min)
711	zh = SQRT(zh_max(ji,jj,jk) * zh_min(ji,jj,jk))
712	zh_lnfactor = (zh - zh_prev)/zh_prev ! Required to test convergence below
713	ELSE
714	! dzeqn/dpH = dzeqn/d[H] * d[H]/dpH
715	! = -zdeqndh * LOG(10) * [H]
716	! \Delta pH = -zeqn/(zdeqndhd[H]/dpH) = zeqn/(zdeqndh[H]*LOG(10))
717	!
718	! pH_new = pH_old + \deltapH
719	!
720	! [H]_new = 10**(-pH_new)
721	! = 10**(-pH_old - \Delta pH)
722	! = [H]_old * 10*(-zeqn/(zdeqndh[H]_old*LOG(10)))
723	! = [H]_old * EXP(-LOG(10)zeqn/(zdeqndh[H]_old*LOG(10)))
724	! = [H]_old * EXP(-zeqn/(zdeqndh*[H]_old))
725
726	zh_lnfactor = -zeqn/(zdeqndh*zh_prev)
727
728	IF(ABS(zh_lnfactor) > pz_exp_threshold) THEN
729	zh = zh_prev*EXP(zh_lnfactor)
730	ELSE
731	zh_delta = zh_lnfactor*zh_prev
732	zh = zh_prev + zh_delta
733	ENDIF
734
735	IF( zh < zh_min(ji,jj,jk) ) THEN
736	! if [H]_new < [H]_min
737	! i.e., if ph_new > ph_max then
738	! take one bisection step on [ph_prev, ph_max]
739	! ph_new = (ph_prev + ph_max)/2d0
740	! In terms of [H]_new:
741	! [H]_new = 10**(-ph_new)
742	! = 10**(-(ph_prev + ph_max)/2d0)
743	! = SQRT(10**(-(ph_prev + phmax)))
744	! = SQRT([H]_old10*(-ph_max))
745	! = SQRT([H]_old * zh_min)
746	zh = SQRT(zh_prev * zh_min(ji,jj,jk))
747	zh_lnfactor = (zh - zh_prev)/zh_prev ! Required to test convergence below
748	ENDIF
749
750	IF( zh > zh_max(ji,jj,jk) ) THEN
751	! if [H]_new > [H]_max
752	! i.e., if ph_new < ph_min, then
753	! take one bisection step on [ph_min, ph_prev]
754	! ph_new = (ph_prev + ph_min)/2d0
755	! In terms of [H]_new:
756	! [H]_new = 10**(-ph_new)
757	! = 10**(-(ph_prev + ph_min)/2d0)
758	! = SQRT(10**(-(ph_prev + ph_min)))
759	! = SQRT([H]_old10*(-ph_min))
760	! = SQRT([H]_old * zhmax)
761	zh = SQRT(zh_prev * zh_max(ji,jj,jk))
762	zh_lnfactor = (zh - zh_prev)/zh_prev ! Required to test convergence below
763	ENDIF
764	ENDIF
765
766	zeqn_absmin(ji,jj,jk) = MIN( ABS(zeqn), zeqn_absmin(ji,jj,jk))
767
768	! Stop iterations once \|\delta{[H]}/[H]\| < rdel
769	! <=> \|(zh - zh_prev)/zh_prev\| = \|EXP(-zeqn/(zdeqndh*zh_prev)) -1\| < rdel
770	! \|EXP(-zeqn/(zdeqndhzh_prev)) -1\| ~ \|zeqn/(zdeqndhzh_prev)\|
771
772	! Alternatively:
773	! \|\Delta pH\| = \|zeqn/(zdeqndhzh_prevLOG(10))\|
774	! ~ 1/LOG(10) * \|\Delta [H]\|/[H]
775	! < 1/LOG(10) * rdel
776
777	! Hence \|zeqn/(zdeqndh*zh)\| < rdel
778
779	! rdel <-- pp_rdel_ah_target
780	l_exitnow = (ABS(zh_lnfactor) < pp_rdel_ah_target)
781
782	IF(l_exitnow) THEN
783	rmask(ji,jj,jk) = 0.
784	ENDIF
785
786	zhi(ji,jj,jk) = zh
787
788	IF(jn >= jp_maxniter_atgen) THEN
789	zhi(ji,jj,jk) = -1._wp
790	ENDIF
791
792	ENDIF
793	END DO
794	END DO
795	END DO
796	END DO
797	!
798
799	IF( ln_timing ) CALL timing_stop('solve_at_general')
800	!
801	END SUBROUTINE solve_at_general
802
803
804	INTEGER FUNCTION p4z_che_alloc()
805	!!----------------------------------------------------------------------
806	!! * ROUTINE p4z_che_alloc *
807	!!----------------------------------------------------------------------
808	INTEGER :: ierr(3) ! Local variables
809	!!----------------------------------------------------------------------
810
811	ierr(:) = 0
812
813	ALLOCATE( sio3eq(jpi,jpj,jpk), fekeq(jpi,jpj,jpk), chemc(jpi,jpj,3), chemo2(jpi,jpj,jpk), STAT=ierr(1) )
814
815	ALLOCATE( akb3(jpi,jpj,jpk) , tempis(jpi, jpj, jpk), &
816	& akw3(jpi,jpj,jpk) , borat (jpi,jpj,jpk) , &
817	& aks3(jpi,jpj,jpk) , akf3(jpi,jpj,jpk) , &
818	& ak1p3(jpi,jpj,jpk) , ak2p3(jpi,jpj,jpk) , &
819	& ak3p3(jpi,jpj,jpk) , aksi3(jpi,jpj,jpk) , &
820	& fluorid(jpi,jpj,jpk) , sulfat(jpi,jpj,jpk) , &
821	& salinprac(jpi,jpj,jpk), STAT=ierr(2) )
822
823	ALLOCATE( fesol(jpi,jpj,jpk,5), STAT=ierr(3) )
824
825	!* Variable for chemistry of the CO2 cycle
826	p4z_che_alloc = MAXVAL( ierr )
827	!
828	IF( p4z_che_alloc /= 0 ) CALL ctl_warn('p4z_che_alloc : failed to allocate arrays.')
829	!
830	END FUNCTION p4z_che_alloc
831
832	!!======================================================================
833	END MODULE p4zche

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