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module_sf_slab.F @ 354

Last change on this file since 354 was 1, checked in by lfita, 10 years ago

-- --- Opening of the WRF+LMDZ coupling repository --- -- -

WRF: version v3.3
LMDZ: version v1818

More details in:

File size: 27.2 KB

Line
1	!WRF:MODEL_LAYER:PHYSICS
2	!
3	MODULE module_sf_slab
4
5	!---SPECIFY CONSTANTS AND LAYERS FOR SOIL MODEL
6	!---SOIL DIFFUSION CONSTANT SET (M^2/S)
7
8	REAL, PARAMETER :: DIFSL=5.e-7
9
10	!---FACTOR TO MAKE SOIL STEP MORE CONSERVATIVE
11
12	REAL , PARAMETER :: SOILFAC=1.25
13
14	CONTAINS
15
16	!----------------------------------------------------------------
17	SUBROUTINE SLAB(T3D,QV3D,P3D,FLHC,FLQC, &
18	PSFC,XLAND,TMN,HFX,QFX,LH,TSK,QSFC,CHKLOWQ, &
19	GSW,GLW,CAPG,THC,SNOWC,EMISS,MAVAIL, &
20	DELTSM,ROVCP,XLV,DTMIN,IFSNOW, &
21	SVP1,SVP2,SVP3,SVPT0,EP2, &
22	KARMAN,EOMEG,STBOLT, &
23	TSLB,ZS,DZS,num_soil_layers,radiation, &
24	P1000mb, &
25	ids,ide, jds,jde, kds,kde, &
26	ims,ime, jms,jme, kms,kme, &
27	its,ite, jts,jte, kts,kte )
28	!----------------------------------------------------------------
29	IMPLICIT NONE
30	!----------------------------------------------------------------
31	!
32	! SUBROUTINE SLAB CALCULATES THE GROUND TEMPERATURE TENDENCY
33	! ACCORDING TO THE RESIDUAL OF THE SURFACE ENERGY BUDGET
34	! (BLACKADAR, 1978B).
35	!
36	! CHANGES:
37	! FOR SOIL SUB-TIMESTEPS UPDATE SURFACE HFX AND QFX AS TG
38	! CHANGES TO PREVENT POSSIBLE INSTABILITY FOR LONG MODEL
39	! STEPS (DT > ~200 SEC).
40	!
41	! PUT SNOW COVER CHECK ON SOIL SUB-TIMESTEPS
42	!
43	! MAKE UPPER LIMIT ON SOIL SUB-STEP LENGTH MORE CONSERVATIVE
44	!
45	!----------------------------------------------------------------
46	!-- T3D temperature (K)
47	!-- QV3D 3D water vapor mixing ratio (Kg/Kg)
48	!-- P3D 3D pressure (Pa)
49	!-- FLHC exchange coefficient for heat (m/s)
50	!-- FLQC exchange coefficient for moisture (m/s)
51	!-- PSFC surface pressure (Pa)
52	!-- XLAND land mask (1 for land, 2 for water)
53	!-- TMN soil temperature at lower boundary (K)
54	!-- HFX upward heat flux at the surface (W/m^2)
55	!-- QFX upward moisture flux at the surface (kg/m^2/s)
56	!-- LH latent heat flux at the surface (W/m^2)
57	!-- TSK surface temperature (K)
58	!-- GSW downward short wave flux at ground surface (W/m^2)
59	!-- GLW downward long wave flux at ground surface (W/m^2)
60	!-- CAPG heat capacity for soil (J/K/m^3)
61	!-- THC thermal inertia (Cal/cm/K/s^0.5)
62	!-- SNOWC flag indicating snow coverage (1 for snow cover)
63	!-- EMISS surface emissivity (between 0 and 1)
64	!-- DELTSM time step (second)
65	!-- ROVCP R/CP
66	!-- XLV latent heat of melting (J/kg)
67	!-- DTMIN time step (minute)
68	!-- IFSNOW ifsnow=1 for snow-cover effects
69	!-- SVP1 constant for saturation vapor pressure (kPa)
70	!-- SVP2 constant for saturation vapor pressure (dimensionless)
71	!-- SVP3 constant for saturation vapor pressure (K)
72	!-- SVPT0 constant for saturation vapor pressure (K)
73	!-- EP1 constant for virtual temperature (R_v/R_d - 1) (dimensionless)
74	!-- EP2 constant for specific humidity calculation
75	! (R_d/R_v) (dimensionless)
76	!-- KARMAN Von Karman constant
77	!-- EOMEG angular velocity of earth's rotation (rad/s)
78	!-- STBOLT Stefan-Boltzmann constant (W/m^2/K^4)
79	!-- TSLB soil temperature in 5-layer model
80	!-- ZS depths of centers of soil layers
81	!-- DZS thicknesses of soil layers
82	!-- num_soil_layers the number of soil layers
83	!-- ids start index for i in domain
84	!-- ide end index for i in domain
85	!-- jds start index for j in domain
86	!-- jde end index for j in domain
87	!-- kds start index for k in domain
88	!-- kde end index for k in domain
89	!-- ims start index for i in memory
90	!-- ime end index for i in memory
91	!-- jms start index for j in memory
92	!-- jme end index for j in memory
93	!-- kms start index for k in memory
94	!-- kme end index for k in memory
95	!-- its start index for i in tile
96	!-- ite end index for i in tile
97	!-- jts start index for j in tile
98	!-- jte end index for j in tile
99	!-- kts start index for k in tile
100	!-- kte end index for k in tile
101	!----------------------------------------------------------------
102	INTEGER, INTENT(IN ) :: ids,ide, jds,jde, kds,kde, &
103	ims,ime, jms,jme, kms,kme, &
104	its,ite, jts,jte, kts,kte
105
106	INTEGER, INTENT(IN) :: num_soil_layers
107	LOGICAL, INTENT(IN) :: radiation
108
109	INTEGER, INTENT(IN ) :: IFSNOW
110
111	!
112	REAL, INTENT(IN ) :: DTMIN,XLV,ROVCP,DELTSM
113
114	REAL, INTENT(IN ) :: SVP1,SVP2,SVP3,SVPT0
115	REAL, INTENT(IN ) :: EP2,KARMAN,EOMEG,STBOLT
116	REAL, INTENT(IN ) :: P1000mb
117
118	REAL, DIMENSION( ims:ime , 1:num_soil_layers, jms:jme ), &
119	INTENT(INOUT) :: TSLB
120
121	REAL, DIMENSION(1:num_soil_layers), INTENT(IN)::ZS,DZS
122
123	REAL, DIMENSION( ims:ime, kms:kme, jms:jme ) , &
124	INTENT(IN ) :: QV3D, &
125	P3D, &
126	T3D
127	!
128	REAL, DIMENSION( ims:ime, jms:jme ) , &
129	INTENT(IN ) :: SNOWC, &
130	XLAND, &
131	EMISS, &
132	MAVAIL, &
133	TMN, &
134	GSW, &
135	GLW, &
136	THC
137
138	!CHKLOWQ is declared as memory size
139	!
140	REAL, DIMENSION( ims:ime, jms:jme ) , &
141	INTENT(INOUT) :: HFX, &
142	QFX, &
143	LH, &
144	CAPG, &
145	TSK, &
146	QSFC, &
147	CHKLOWQ
148
149	REAL, DIMENSION( ims:ime, jms:jme ) , &
150	INTENT(IN ) :: PSFC
151	!
152	REAL, DIMENSION( ims:ime, jms:jme ), INTENT(INOUT) :: &
153	FLHC, &
154	FLQC
155
156	! LOCAL VARS
157
158	REAL, DIMENSION( its:ite ) :: QV1D, &
159	P1D, &
160	T1D
161	INTEGER :: I,J
162
163	DO J=jts,jte
164
165	DO i=its,ite
166	T1D(i) =T3D(i,1,j)
167	QV1D(i)=QV3D(i,1,j)
168	P1D(i) =P3D(i,1,j)
169	ENDDO
170
171	! the indices to the PSFC argument in the following call look
172	! wrong; however, it is correct to call with its (and not ims)
173	! because of the way PSFC is defined in SLAB1D. Whether that
174	! is a good idea or not, this commenter cannot comment. JM
175
176	CALL SLAB1D(J,T1D,QV1D,P1D,FLHC(ims,j),FLQC(ims,j), &
177	PSFC(its,j),XLAND(ims,j),TMN(ims,j),HFX(ims,j), &
178	QFX(ims,j),TSK(ims,j),QSFC(ims,j),CHKLOWQ(ims,j), &
179	LH(ims,j),GSW(ims,j),GLW(ims,j), &
180	CAPG(ims,j),THC(ims,j),SNOWC(ims,j),EMISS(ims,j), &
181	MAVAIL(ims,j),DELTSM,ROVCP,XLV,DTMIN,IFSNOW, &
182	SVP1,SVP2,SVP3,SVPT0,EP2,KARMAN,EOMEG,STBOLT, &
183	TSLB(ims,1,j),ZS,DZS,num_soil_layers,radiation, &
184	P1000mb, &
185	ids,ide, jds,jde, kds,kde, &
186	ims,ime, jms,jme, kms,kme, &
187	its,ite, jts,jte, kts,kte )
188
189	ENDDO
190
191	END SUBROUTINE SLAB
192
193	!----------------------------------------------------------------
194	SUBROUTINE SLAB1D(J,T1D,QV1D,P1D,FLHC,FLQC, &
195	PSFCPA,XLAND,TMN,HFX,QFX,TSK,QSFC,CHKLOWQ, &
196	LH,GSW,GLW,CAPG,THC,SNOWC,EMISS,MAVAIL, &
197	DELTSM,ROVCP,XLV,DTMIN,IFSNOW, &
198	SVP1,SVP2,SVP3,SVPT0,EP2, &
199	KARMAN,EOMEG,STBOLT, &
200	TSLB2D,ZS,DZS,num_soil_layers,radiation, &
201	P1000mb, &
202	ids,ide, jds,jde, kds,kde, &
203	ims,ime, jms,jme, kms,kme, &
204	its,ite, jts,jte, kts,kte )
205	!----------------------------------------------------------------
206	IMPLICIT NONE
207	!----------------------------------------------------------------
208	!
209	! SUBROUTINE SLAB CALCULATES THE GROUND TEMPERATURE TENDENCY
210	! ACCORDING TO THE RESIDUAL OF THE SURFACE ENERGY BUDGET
211	! (BLACKADAR, 1978B).
212	!
213	! CHANGES:
214	! FOR SOIL SUB-TIMESTEPS UPDATE SURFACE HFX AND QFX AS TG
215	! CHANGES TO PREVENT POSSIBLE INSTABILITY FOR LONG MODEL
216	! STEPS (DT > ~200 SEC).
217	!
218	! PUT SNOW COVER CHECK ON SOIL SUB-TIMESTEPS
219	!
220	! MAKE UPPER LIMIT ON SOIL SUB-STEP LENGTH MORE CONSERVATIVE
221	!
222	!----------------------------------------------------------------
223
224	INTEGER, INTENT(IN ) :: ids,ide, jds,jde, kds,kde, &
225	ims,ime, jms,jme, kms,kme, &
226	its,ite, jts,jte, kts,kte,J
227
228	INTEGER , INTENT(IN) :: num_soil_layers
229	LOGICAL, INTENT(IN ) :: radiation
230
231	INTEGER, INTENT(IN ) :: IFSNOW
232	!
233	REAL, INTENT(IN ) :: DTMIN,XLV,ROVCP,DELTSM
234
235	REAL, INTENT(IN ) :: SVP1,SVP2,SVP3,SVPT0
236	REAL, INTENT(IN ) :: EP2,KARMAN,EOMEG,STBOLT
237	REAL, INTENT(IN ) :: P1000mb
238
239	REAL, DIMENSION( ims:ime , 1:num_soil_layers ), &
240	INTENT(INOUT) :: TSLB2D
241
242	REAL, DIMENSION(1:num_soil_layers), INTENT(IN)::ZS,DZS
243
244	!
245	REAL, DIMENSION( ims:ime ) , &
246	INTENT(INOUT) :: HFX, &
247	QFX, &
248	LH, &
249	CAPG, &
250	TSK, &
251	QSFC, &
252	CHKLOWQ
253	!
254	REAL, DIMENSION( ims:ime ) , &
255	INTENT(IN ) :: SNOWC, &
256	XLAND, &
257	EMISS, &
258	MAVAIL, &
259	TMN, &
260	GSW, &
261	GLW, &
262	THC
263	!
264	REAL, DIMENSION( its:ite ) , &
265	INTENT(IN ) :: QV1D, &
266	P1D, &
267	T1D
268	!
269	REAL, DIMENSION( its:ite ) , &
270	INTENT(IN ) :: PSFCPA
271
272	!
273	REAL, DIMENSION( ims:ime ), INTENT(INOUT) :: &
274	FLHC, &
275	FLQC
276	! LOCAL VARS
277
278	REAL, DIMENSION( its:ite ) :: PSFC
279
280	REAL, DIMENSION( its:ite ) :: &
281	THX, &
282	QX, &
283	SCR3
284
285	REAL, DIMENSION( its:ite ) :: DTHGDT, &
286	TG0, &
287	THTMN, &
288	XLD1, &
289	TSCVN, &
290	OLTG, &
291	UPFLUX, &
292	HM, &
293	RNET, &
294	XINET, &
295	QS, &
296	DTSDT
297	!
298	REAL, DIMENSION( its:ite, num_soil_layers ) :: FLUX
299	!
300	INTEGER :: I,K,NSOIL,ITSOIL,L,NK,RADSWTCH
301	REAL :: PS,PS1,XLDCOL,TSKX,RNSOIL,RHOG1,RHOG2,RHOG3,LAMDAG
302	REAL :: THG,ESG,QSG,HFXT,QFXT,CS,CSW,LAMG(4),THCON,PL
303
304	!----------------------------------------------------------------------
305	!-----DETERMINE IF ANY POINTS IN COLUMN ARE LAND (RATHER THAN OCEAN)
306	! POINTS. IF NOT, SKIP DOWN TO THE PRINT STATEMENTS SINCE OCEAN
307	! SURFACE TEMPERATURES ARE NOT ALLOWED TO CHANGE.
308	!
309	! from sfcrad
310	!----------------------------------------------------------------------
311	DATA CSW/4.183E6/
312	DATA LAMG/1.407E-8, -1.455E-5, 6.290E-3, 0.16857/
313
314	DO i=its,ite
315	! in cmb
316	PSFC(I)=PSFCPA(I)/1000.
317	ENDDO
318
319
320	DO I=its,ite
321	! PL cmb
322	PL=P1D(I)/1000.
323	SCR3(I)=T1D(I)
324	! THCON=(100./PL)**ROVCP
325	THCON=(P1000mb0.001/PL)*ROVCP
326	THX(I)=SCR3(I)*THCON
327	QX(I)=0.
328	ENDDO
329
330	! IF(IDRY.EQ.1) GOTO 81
331	DO I=its,ite
332	QX(I)=QV1D(I)
333	ENDDO
334	81 CONTINUE
335
336	!
337	!-----THE SLAB THERMAL CAPACITY CAPG(I) ARE DEPENDENT ON:
338	! THC(I) - SOIL THERMAL INERTIAL, ONLY.
339	!
340	DO I=its,ite
341	CAPG(I)=3.298E6*THC(I)
342	IF(num_soil_layers .gt. 1)THEN
343
344	! CAPG REPRESENTS SOIL HEAT CAPACITY (J/K/M^3) WHEN DIFSL=5.E-7 (M^2/S)
345	! TO GIVE A CORRECT THERMAL INERTIA (=CAPG*DIFSL^0.5)
346
347	CAPG(I)=5.9114E7*THC(I)
348	ENDIF
349	ENDDO
350	!
351	XLDCOL=2.0
352	DO 10 I=its,ite
353	XLDCOL=AMIN1(XLDCOL,XLAND(I))
354	10 CONTINUE
355	!
356	IF(XLDCOL.GT.1.5)GOTO 90
357	!
358	!
359	!-----CONVERT SLAB TEMPERATURE TO POTENTIAL TEMPERATURE AND
360	! SET XLD1(I) = 0. FOR OCEAN POINTS:
361	!
362	!
363	DO 20 I=its,ite
364	IF((XLAND(I)-1.5).GE.0)THEN
365	XLD1(I)=0.
366	ELSE
367	XLD1(I)=1.
368	ENDIF
369	20 CONTINUE
370	!
371	!-----CONVERT 'TSK(THETAG)' TO 'TG' FOR 'IUP' CALCULATION ....
372	! IF WE ARE USING THE BLACKADAR MULTI-LEVEL (HIGH-RESOLUTION)
373	! PBL MODEL
374	!
375	DO 50 I=its,ite
376	IF(XLD1(I).LT.0.5)GOTO 50
377
378	! PS cmb
379	PS=PSFC(I)
380
381	! TSK is Temperature at gound sfc
382	! TG0(I)=TSK(I)(PS0.01)**ROVCP
383	TG0(I)=TSK(I)
384	50 CONTINUE
385	!
386	!-----COMPUTE THE SURFACE ENERGY BUDGET:
387	!
388	! IF(ISOIL.EQ.1)NSOIL=1
389	IF(num_soil_layers .gt. 1)NSOIL=1
390
391
392	IF (radiation) then
393	RADSWTCH=1
394	ELSE
395	RADSWTCH=0
396	ENDIF
397
398	DO 70 I=its,ite
399	IF(XLD1(I).LT.0.5)GOTO 70
400	! OLTG(I)=TSK(I)(100./PSFC(I))*ROVCP
401	OLTG(I)=TSK(I)(P1000mb0.001/PSFC(I))**ROVCP
402	UPFLUX(I)=RADSWTCHSTBOLTTG0(I)**4
403	XINET(I)=EMISS(I)*(GLW(I)-UPFLUX(I))
404	RNET(I)=GSW(I)+XINET(I)
405	HM(I)=1.18EOMEG(TG0(I)-TMN(I))
406	! MOISTURE FLUX CALCULATED HERE (OVERWRITES SFC LAYER VALUE FOR LAND)
407	ESG=SVP1EXP(SVP2(TG0(I)-SVPT0)/(TG0(I)-SVP3))
408	QSG=EP2*ESG/(PSFC(I)-ESG)
409	THG=TSK(I)(100./PSFC(I))*ROVCP
410	HFX(I)=FLHC(I)*(THG-THX(I))
411	QFX(I)=FLQC(I)*(QSG-QX(I))
412	LH(I)=QFX(I)*XLV
413	QS(I)=HFX(I)+QFX(I)*XLV
414	! IF(ISOIL.EQ.0)THEN
415	IF(num_soil_layers .EQ. 1)THEN
416	DTHGDT(I)=(RNET(I)-QS(I))/CAPG(I)-HM(I)
417	ELSE
418	DTHGDT(I)=0.
419	ENDIF
420	70 CONTINUE
421	! IF(ISOIL.EQ.1)THEN
422	IF(num_soil_layers .gt. 1)THEN
423	NSOIL=1+IFIX(SOILFAC4DIFSL/DZS(1)*DELTSM/DZS(1))
424	RNSOIL=1./FLOAT(NSOIL)
425	!
426	! SOIL SUB-TIMESTEP
427	!
428	DO ITSOIL=1,NSOIL
429	DO I=its,ite
430	DO L=1,num_soil_layers-1
431	IF(XLD1(I).LT.0.5)GOTO 75
432	IF(L.EQ.1.AND.ITSOIL.GT.1)THEN
433	! PS1=(PSFC(I)0.01)*ROVCP
434	PS1=(PSFCPA(I)/P1000mb)**ROVCP
435
436	! for rk scheme A and B are the same
437	PS=PSFC(I)
438	THG=TSLB2D(I,1)/PS1
439	ESG=SVP1EXP(SVP2(TSLB2D(I,1)-SVPT0)/(TSLB2D(I,1) &
440	-SVP3))
441	QSG=EP2*ESG/(PS-ESG)
442	! UPDATE FLUXES FOR NEW GROUND TEMPERATURE
443	HFXT=FLHC(I)*(THG-THX(I))
444	QFXT=FLQC(I)*(QSG-QX(I))
445	QS(I)=HFXT+QFXT*XLV
446	! SUM HFX AND QFX OVER SOIL TIMESTEPS
447	HFX(I)=HFX(I)+HFXT
448	QFX(I)=QFX(I)+QFXT
449	ENDIF
450	FLUX(I,1)=RNET(I)-QS(I)
451	FLUX(I,L+1)=-DIFSLCAPG(I)(TSLB2D(I,L+1)-TSLB2D(I,L))/( &
452	ZS(L+1)-ZS(L))
453	DTSDT(I)=-(FLUX(I,L+1)-FLUX(I,L))/(DZS(L)*CAPG(I))
454	TSLB2D(I,L)=TSLB2D(I,L)+DTSDT(I)DELTSMRNSOIL
455	IF(IFSNOW.EQ.1.AND.L.EQ.1)THEN
456	IF((SNOWC(I).GT.0..AND.TSLB2D(I,1).GT.273.16))THEN
457	TSLB2D(I,1)=273.16
458	ENDIF
459	ENDIF
460	IF(L.EQ.1)DTHGDT(I)=DTHGDT(I)+RNSOIL*DTSDT(I)
461	IF(ITSOIL.EQ.NSOIL.AND.L.EQ.1)THEN
462	! AVERAGE HFX AND QFX OVER SOIL TIMESTEPS FOR OUTPUT TO PBL
463	HFX(I)=HFX(I)*RNSOIL
464	QFX(I)=QFX(I)*RNSOIL
465	LH(I)=QFX(I)*XLV
466	ENDIF
467	75 CONTINUE
468	ENDDO
469	ENDDO
470	ENDDO
471	ENDIF
472	!
473	DO 80 I=its,ite
474	IF(XLD1(I).LT.0.5) GOTO 80
475	TSKX=TG0(I)+DELTSM*DTHGDT(I)
476
477	! TSK is temperature
478	! TSK(I)=TSKX(100./PS1)*ROVCP
479	TSK(I)=TSKX
480	80 CONTINUE
481
482	!
483	!-----MODIFY THE THE GROUND TEMPERATURE IF THE SNOW COVER EFFECTS ARE
484	! CONSIDERED: LIMIT THE GROUND TEMPERATURE UNDER 0 C.
485	!
486	IF(IFSNOW.EQ.0)GOTO 90
487	DO 85 I=its,ite
488	IF(XLD1(I).LT.0.5)GOTO 85
489	! PS1=(PSFC(I)0.01)*ROVCP
490	! TSCVN(I)=TSK(I)*PS1
491	TSCVN(I)=TSK(I)
492	IF((SNOWC(I).GT.0..AND.TSCVN(I).GT.273.16))THEN
493	TSCVN(I)=273.16
494	ELSE
495	TSCVN(I)=TSCVN(I)
496	ENDIF
497	! TSK(I)=TSCVN(I)/PS1
498	TSK(I)=TSCVN(I)
499	85 CONTINUE
500	!
501	90 CONTINUE
502	DO I=its,ite
503	! QSFC and CHKLOWQ needed by Eta PBL
504	! WA added check for flqc = 0 to accomodate TEMF (and others?)
505	if ( FLQC(I) .ne. 0.) then
506	QSFC(I)=QX(I)+QFX(I)/FLQC(I)
507	else
508	QSFC(I) = QX(I)
509	end if
510	CHKLOWQ(I)=MAVAIL(I)
511	ENDDO
512	!
513	140 CONTINUE
514
515	END SUBROUTINE SLAB1D
516
517	!================================================================
518	SUBROUTINE slabinit(TSK,TMN, &
519	TSLB,ZS,DZS,num_soil_layers, &
520	allowed_to_read, start_of_simulation, &
521	ids,ide, jds,jde, kds,kde, &
522	ims,ime, jms,jme, kms,kme, &
523	its,ite, jts,jte, kts,kte )
524	!----------------------------------------------------------------
525	IMPLICIT NONE
526	!----------------------------------------------------------------
527	LOGICAL , INTENT(IN) :: allowed_to_read
528	LOGICAL , INTENT(IN) :: start_of_simulation
529	INTEGER, INTENT(IN ) :: ids,ide, jds,jde, kds,kde, &
530	ims,ime, jms,jme, kms,kme, &
531	its,ite, jts,jte, kts,kte
532
533	INTEGER, INTENT(IN ) :: num_soil_layers
534	!
535	REAL, DIMENSION( ims:ime , 1:num_soil_layers , jms:jme ), INTENT(INOUT) :: TSLB
536
537	REAL, DIMENSION(1:num_soil_layers), INTENT(IN) :: ZS,DZS
538
539	REAL, DIMENSION( ims:ime, jms:jme ) , &
540	INTENT(IN) :: TSK, &
541	TMN
542
543	! LOCAR VAR
544
545	INTEGER :: L,J,I,itf,jtf
546	CHARACTER*1024 message
547
548	!----------------------------------------------------------------
549
550	itf=min0(ite,ide-1)
551	jtf=min0(jte,jde-1)
552
553	END SUBROUTINE slabinit
554	!-------------------------------------------------------------------
555
556	END MODULE module_sf_slab

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