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pbl_parameters.F @ 1242

Last change on this file since 1242 was 1226, checked in by aslmd, 11 years ago
LMDZ.MARS : Replaced comcstfi and planete includes by modules.
File size: 16.8 KB

Rev	Line
[529]	1	SUBROUTINE pbl_parameters(ngrid,nlay,ps,pplay,pz0,
[566]	2	& pg,zzlay,zzlev,pu,pv,wstar_in,hfmax,zmax,pts,ph,z_out,n_out,
[605]	3	& T_out,u_out,ustar,tstar,L_mo,vhf,vvv)
[1226]	4	USE comcstfi_h
[496]	5	IMPLICIT NONE
	6	!=======================================================================
	7	!
	8	! Anlysis of the PBL from input temperature, wind field and thermals outputs.
	9	!
	10	! -------
	11	!
	12	! Author: Arnaud Colaitis 09/01/12
	13	! -------
	14	!
	15	! Arguments:
	16	! ----------
	17	!
	18	! inputs:
	19	! ------
	20	! ngrid size of the horizontal grid
	21	! nlay size of the vertical grid
	22	! pz0(ngrid) surface roughness length
	23	! pg gravity (m s -2)
[529]	24	! zzlay(ngrid,nlay) height of mid-layers
	25	! zzlev(ngrid,nlay+1) height of layers interfaces
[496]	26	! pu(ngrid,nlay) u component of the wind
	27	! pv(ngrid,nlay) v component of the wind
[662]	28	! wstar_in(ngrid) free convection velocity in PBL
[496]	29	! hfmax(ngrid) maximum vertical turbulent heat flux in thermals
	30	! zmax(ngrid) height reached by the thermals (pbl height)
	31	! pts(ngrid) surface temperature
	32	! ph(ngrid,nlay) potential temperature T*(p/ps)^kappa
[566]	33	! z_out(n_out) heights of interpolation
	34	! n_out number of points for interpolation
[496]	35	!
	36	! outputs:
	37	! ------
	38	!
[566]	39	! Teta_out(ngrid,n_out) interpolated teta
	40	! u_out(ngrid,n_out) interpolated u
[496]	41	! ustar(ngrid) friction velocity
	42	! tstar(ngrid) friction temperature
	43	! L_mo(ngrid) monin_obukhov length
	44	!
	45	!
	46	!=======================================================================
	47	!
	48	!-----------------------------------------------------------------------
	49	! Declarations:
	50	! -------------
	51
	52	#include "callkeys.h"
	53
	54	! Arguments:
	55	! ----------
	56
[566]	57	INTEGER, INTENT(IN) :: ngrid,nlay,n_out
[529]	58	REAL, INTENT(IN) :: pz0(ngrid),ps(ngrid),pplay(ngrid,nlay)
	59	REAL, INTENT(IN) :: pg,zzlay(ngrid,nlay),zzlev(ngrid,nlay)
[496]	60	REAL, INTENT(IN) :: pu(ngrid,nlay),pv(ngrid,nlay)
[529]	61	REAL, INTENT(IN) :: wstar_in(ngrid),hfmax(ngrid),zmax(ngrid)
[496]	62	REAL, INTENT(IN) :: pts(ngrid),ph(ngrid,nlay)
[566]	63	REAL, INTENT(IN) :: z_out(n_out)
[529]	64
	65	! Outputs:
	66	! --------
	67
[605]	68	REAL, INTENT(OUT) :: T_out(ngrid,n_out),u_out(ngrid,n_out)
	69	REAL Teta_out(ngrid,n_out)
[529]	70	REAL, INTENT(OUT) :: ustar(ngrid), tstar(ngrid)
[496]	71	REAL, INTENT(OUT) :: L_mo(ngrid)
	72
	73	! Local:
	74	! ------
	75
[566]	76	INTEGER ig,k,n
[496]	77	REAL karman,nu
	78	DATA karman,nu/.41,0.001/
	79	SAVE karman,nu
	80
	81	! Local(2):
	82	! ---------
	83
	84	REAL zout
	85	REAL rib(ngrid) ! Bulk Richardson number
	86	REAL fm(ngrid) ! stability function for momentum
	87	REAL fh(ngrid) ! stability function for heat
	88	REAL z1z0,z1z0t ! ratios z1/z0 and z1/z0T
	89	! phim = 1+betamzeta or (1-bmzeta)**am
	90	! phih = alphah + betahzeta or alphah(1.-bhzeta)**ah
	91	REAL betam, betah, alphah, bm, bh, lambda
	92	! ah and am are assumed to be -0.25 and -0.5 respectively
	93	REAL cdn(ngrid),chn(ngrid) ! neutral momentum and heat drag coefficient
	94	REAL pz0t ! initial thermal roughness length. (local)
	95	REAL ric ! critical richardson number
	96	REAL reynolds(ngrid) ! reynolds number for UBL
	97	REAL prandtl(ngrid) ! prandtl number for UBL
	98	REAL pz0tcomp(ngrid) ! computed z0t
	99	REAL ite
	100	REAL residual,zcd0,z1
	101	REAL pcdv(ngrid),pcdh(ngrid)
	102	REAL zu2(ngrid) ! Large-scale wind at first layer
	103	REAL pbl_teta(ngrid) ! mixed-layer potential temperature
	104	INTEGER pbl_height_index(ngrid) ! index of nearest vertical grid point for zmax
	105	REAL dteta(ngrid,nlay),x(ngrid) ! potential temperature gradient and z/zi
	106	REAL dvhf(ngrid),dvvv(ngrid) ! dimensionless vertical heat flux and
	107	! dimensionless vertical velocity variance
	108	REAL vhf(ngrid),vvv(ngrid) ! vertical heat flux and vertical velocity variance
	109	INTEGER ii(1)
	110	! temporary
	111	INTEGER dimout
	112
	113	!------------------------------------------------------------------------
	114	!------------------------------------------------------------------------
	115	! PART I : RICHARDSON/REYNOLDS/THERMAL_ROUGHNESS/STABILITY_COEFFICIENTS
	116	!------------------------------------------------------------------------
	117	!------------------------------------------------------------------------
	118
[566]	119	DO n=1,n_out
	120
[496]	121	c Initialisation :
	122
	123	L_mo(:)=0.
	124	ustar(:)=0.
	125	tstar(:)=0.
[566]	126	zout=z_out(n)
[496]	127	reynolds(:)=0.
	128	pz0t = 0.
	129	pz0tcomp(:) = 0.1*pz0(:)
	130	rib(:)=0.
	131	pcdv(:)=0.
	132	pcdh(:)=0.
	133
	134	! this formulation assumes alphah=1., implying betah=betam
	135	! We use Dyer et al. parameters, as they cover a broad range of Richardson numbers :
	136
	137	bm=16. !UBL
	138	bh=16. !UBL
	139	alphah=1.
	140	betam=5. !SBL
	141	betah=5. !SBL
	142	lambda=(sqrt(bh/bm))/alphah
	143	ric=betah/(betam**2)
	144	DO ig=1,ngrid
	145	ite=0.
	146	residual=abs(pz0tcomp(ig)-pz0t)
[636]	147	! zu2(ig)=MAX(pu(ig,1)pu(ig,1)+pv(ig,1)pv(ig,1)
	148	! & ,(0.3wstar_in(ig))*2)
[648]	149	zu2(ig)=pu(ig,1)pu(ig,1)+pv(ig,1)pv(ig,1)
[636]	150	& + (log(1.+0.7wstar_in(ig) + 2.3wstar_in(ig)2))2
[496]	151
	152	DO WHILE((residual .gt. 0.01*pz0(ig)) .and. (ite .lt. 10.))
	153
	154	pz0t=pz0tcomp(ig)
	155	IF (zu2(ig) .ne. 0.) THEN
	156	! Richardson number formulation proposed by D.E. England et al. (1995)
[605]	157	rib(ig) = (pg/pts(ig))
[636]	158	& sqrt(zzlay(ig,1)pz0(ig))
	159	& (((log(zzlay(ig,1)/pz0(ig)))*2)/(log(zzlay(ig,1)/pz0t)))
[496]	160	& *(ph(ig,1)-pts(ig))/zu2(ig)
	161	ELSE
	162	print*,'warning, infinite Richardson at surface'
	163	print*,pu(ig,1),pv(ig,1)
	164	rib(ig) = ric
	165	ENDIF
	166
[636]	167	z1z0=zzlay(ig,1)/pz0(ig)
	168	z1z0t=zzlay(ig,1)/pz0t
[496]	169
	170	cdn(ig)=karman/log(z1z0)
	171	cdn(ig)=cdn(ig)*cdn(ig)
	172	chn(ig)=cdn(ig)*log(z1z0)/log(z1z0t)
	173
	174	! STABLE BOUNDARY LAYER :
	175	IF (rib(ig) .gt. 0.) THEN
	176	! From D.E. England et al. (95)
	177	prandtl(ig)=1.
	178	if(rib(ig) .lt. ric) then
	179	! Assuming alphah=1. and bh=bm for stable conditions :
	180	fm(ig)=((ric-rib(ig))/ric)**2
	181	fh(ig)=((ric-rib(ig))/ric)**2
	182	else
	183	! For Ri>Ric, we consider Ri->Infinity => no turbulent mixing at surface
	184	fm(ig)=0.
	185	fh(ig)=0.
	186	endif
	187	! UNSTABLE BOUNDARY LAYER :
	188	ELSE
	189	! From D.E. England et al. (95)
	190	fm(ig)=sqrt(1.-lambdabmrib(ig))
	191	fh(ig)=(1./alphah)((1.-lambdabhrib(ig))0.5)
	192	& (1.-lambdabmrib(ig))**0.25
	193	prandtl(ig)=alphah((1.-lambdabmrib(ig))*0.25)/
	194	& ((1.-lambdabhrib(ig))**0.5)
	195	ENDIF
	196
	197	reynolds(ig)=karman*sqrt(fm(ig))
	198	& *sqrt(zu2(ig))
	199	& pz0(ig)/(log(z1z0)nu)
	200	pz0tcomp(ig)=pz0(ig)exp(-karman7.3*
	201	& (reynolds(ig)*0.25)(prandtl(ig)**0.5))
	202	residual = abs(pz0t-pz0tcomp(ig))
	203	ite = ite+1
[605]	204
[496]	205	ENDDO ! of while
	206	pz0t=0.
	207
	208	! Drag computation:
	209
	210	pcdv(ig)=cdn(ig)*fm(ig)
	211	pcdh(ig)=chn(ig)*fh(ig)
	212
	213	ENDDO ! of ngrid
	214
	215	!------------------------------------------------------------------------
	216	!------------------------------------------------------------------------
	217	! PART II : USTAR/TSTAR/U_OUT/TETA_OUT COMPUTATIONS
	218	!------------------------------------------------------------------------
	219	!------------------------------------------------------------------------
	220
	221
	222	! u* theta* computation
[636]	223	! and Monin Obukhov length:
[496]	224
	225	DO ig=1,ngrid
	226	IF (rib(ig) .ge. ric) THEN
	227	ustar(ig)=0.
	228	tstar(ig)=0.
[636]	229	L_mo(ig)=0.
[496]	230	ELSE
	231	ustar(ig)=sqrt(pcdv(ig))
	232	& sqrt(pu(ig,1)pu(ig,1)+pv(ig,1)*pv(ig,1))
	233	tstar(ig)=-pcdh(ig)*(pts(ig)-ph(ig,1))
	234	& /sqrt(pcdv(ig))
[636]	235	L_mo(ig)=pts(ig)(ustar(ig)2)/(pgkarman*tstar(ig)) !as defined here, L is positive for SBL, negative for UBL
[496]	236	ENDIF
	237	ENDDO
	238
	239	! Monin Obukhov length:
	240
[636]	241	! DO ig=1,ngrid
	242	! IF (rib(ig) .ge. ric) THEN
	243	! L_mo(ig)=0.
	244	! ELSE
	245	! L_mo(ig)=pts(ig)(ustar(ig)2)/(pgkarman*tstar(ig)) !as defined here, L is positive for SBL, negative for UBL
	246	! ENDIF
	247	! ENDDO
[496]	248
	249	! Interpolation:
	250
	251	DO ig=1,ngrid
	252	IF(zout .lt. pz0tcomp(ig)) THEN
[566]	253	u_out(ig,n)=0.
	254	Teta_out(ig,n)=pts(ig)
[496]	255	ELSEIF (L_mo(ig) .gt. 0.) THEN
[636]	256	! u_out(ig,n)=(ustar(ig)/karman)*log(zout/pz0(ig)) +
	257	! & 5.(ustar(ig)/(karmanL_mo(ig)))*(zout-pz0(ig))
	258	! Teta_out(ig,n)=pts(ig)+(tstar(ig)/(prandtl(ig)*karman))
	259	! & *log(zout/pz0tcomp(ig)) +
	260	! & 5.(tstar(ig)/(prandtl(ig)karman*L_mo(ig)))
	261	! & *(zout-pz0tcomp(ig))
	262	IF ((zout/L_mo(ig).lt.ric).and.(pz0(ig).lt.ric)) THEN
	263	! & ((zout/L_mo(ig).gt.ric).and.(pz0(ig).gt.ric)) ) THEN
	264
	265	u_out(ig,n)=(ustar(ig)/karman)*(
	266	& log((ric-pz0(ig)/L_mo(ig))/(ric-zout/L_mo(ig)))
	267	& +log(zout/pz0(ig))
	268	& )
	269	ELSEIF ((zout/L_mo(ig).gt.ric).and.(pz0(ig).gt.ric)) THEN
	270
	271	u_out(ig,n)=(ustar(ig)/karman)*(
	272	& log((zout-ricL_mo(ig))/(pz0(ig)-ricL_mo(ig)))
	273	& +log(pz0(ig)/zout)
	274	& )
	275
	276	ELSEIF ((zout/L_mo(ig).gt.ric).and.(pz0(ig).lt.ric)) THEN
	277	!integral of the stability function does not converge
	278
	279
	280	u_out(ig,n)=sqrt(pu(ig,1)2 + pv(ig,1)2)
	281
	282
	283	ENDIF
	284	IF((zout/L_mo(ig).lt.ric).and.(pz0tcomp(ig).lt.ric)) THEN
	285	! & ((zout/L_mo(ig).gt.ric).and.(pz0tcomp(ig).gt.ric)) ) THEN
	286
	287	Teta_out(ig,n)=pts(ig)+(tstar(ig)/(prandtl(ig)karman))(
	288	& log((ric-pz0tcomp(ig)/L_mo(ig))/(ric-zout/L_mo(ig)))
	289	& +log(zout/pz0tcomp(ig))
	290	& )
	291	ELSEIF ((zout/L_mo(ig).gt.ric).and.(pz0tcomp(ig).gt.ric)) THEN
	292
	293	Teta_out(ig,n)=pts(ig)+(tstar(ig)/(prandtl(ig)karman))(
	294	& log((zout-ricL_mo(ig))/(pz0tcomp(ig)-ricL_mo(ig)))
	295	& +log(pz0tcomp(ig)/zout)
	296	& )
	297
	298	ELSEIF ((zout/L_mo(ig).gt.ric).and.(pz0tcomp(ig).lt.ric)) THEN
	299	!integral of the stability function does not converge
	300
	301	Teta_out(ig,n)=ph(ig,1)
	302
	303	ENDIF
	304
[496]	305	ELSEIF (L_mo(ig) .lt. 0.) THEN
	306
	307	IF(L_mo(ig) .gt. -1000.) THEN
	308
[566]	309	u_out(ig,n)=(ustar(ig)/karman)*(
[496]	310	& 2.atan((1.-16.zout/L_mo(ig))**0.25)
	311	& -2.atan((1.-16.pz0(ig)/L_mo(ig))**0.25)
	312	& -2.log(1.+(1.-16.zout/L_mo(ig))**0.25)
	313	& +2.log(1.+(1.-16.pz0(ig)/L_mo(ig))**0.25)
	314	& - log(1.+sqrt(1.-16.*zout/L_mo(ig)))
	315	& + log(1.+sqrt(1.-16.*pz0(ig)/L_mo(ig)))
	316	& + log(zout/pz0(ig))
	317	& )
	318
[605]	319	Teta_out(ig,n)=MAX(pts(ig)+(tstar(ig)/(prandtl(ig)karman))(
[496]	320	& 2.log(1.+sqrt(1.-16.pz0tcomp(ig)/L_mo(ig)))
	321	& -2.log(1.+sqrt(1.-16.zout/L_mo(ig)))
	322	& + log(zout/pz0tcomp(ig))
[605]	323	& ),ph(ig,1))
[496]	324
	325	ELSE
	326
	327	! We have to treat the case where L is very large and negative,
	328	! corresponding to a very nearly stable atmosphere (but not quite !)
	329	! i.e. teta* <0 and almost zero. We choose the cutoff
	330	! corresponding to L_mo < -1000 and use a 3rd order taylor expansion. The difference
	331	! between the two expression for z/L = -1/1000 is -1.54324*10^-9
	332	! (we do that to avoid using r*4 precision, otherwise, we get -inf values)
	333
[566]	334	u_out(ig,n)=(ustar(ig)/karman)*(
[496]	335	& (4./L_mo(ig))*(zout-pz0(ig))
	336	& + (20./(L_mo(ig))*2)(zout2-pz0(ig)2)
	337	& + (160./(L_mo(ig))*3)(zout3-pz0(ig)3)
	338	& + log(zout/pz0(ig))
	339	& )
	340
[605]	341	Teta_out(ig,n)=MAX(pts(ig)+(tstar(ig)/(prandtl(ig)karman))(
[496]	342	& (8./L_mo(ig))*(zout-pz0tcomp(ig))
	343	& + (48./(L_mo(ig))*2)(zout2-pz0tcomp(ig)2)
	344	& + (1280./(3.(L_mo(ig))3))(zout3-pz0tcomp(ig)3)
	345	& + log(zout/pz0tcomp(ig))
[605]	346	& ),ph(ig,1))
[496]	347
	348	ENDIF
	349	ELSE
[636]	350	u_out(ig,n)=sqrt(pu(ig,1)2 + pv(ig,1)2)
	351	Teta_out(ig,n)=ph(ig,1)
[496]	352	ENDIF
	353	IF(zout .lt. pz0(ig)) THEN
[566]	354	u_out(ig,n)=0.
[496]	355	ENDIF
[636]	356
	357	! Final check
	358	IF (L_mo(ig) .gt. 0) THEN
	359	IF (Teta_out(ig,n) .gt. ph(ig,1)) THEN
	360	Teta_out(ig,n)=ph(ig,1)
	361	ELSEIF (Teta_out(ig,n) .lt. pts(ig)) THEN
	362	Teta_out(ig,n)=pts(ig)
	363	ENDIF
	364	ELSEIF (L_mo(ig) .lt. 0) THEN
	365	IF (Teta_out(ig,n) .lt. ph(ig,1)) THEN
	366	Teta_out(ig,n)=ph(ig,1)
	367	ELSEIF (Teta_out(ig,n) .gt. pts(ig)) THEN
	368	Teta_out(ig,n)=pts(ig)
	369	ENDIF
	370	ENDIF
	371
	372	IF (u_out(ig,n) .gt. sqrt(pu(ig,1)2 + pv(ig,1)2)) THEN
	373	u_out(ig,n)=sqrt(pu(ig,1)2 + pv(ig,1)2)
	374	ENDIF
	375
[496]	376	ENDDO
	377
	378	! when using convective adjustment without thermals, a vertical potential temperature
	379	! profile is assumed up to the thermal roughness length. Hence, theoretically, theta
	380	! interpolated at any height in the surface layer is theta at the first level.
	381
	382	IF ((.not.calltherm).and.(calladj)) THEN
[605]	383	Teta_out(:,n)=ph(:,1)
	384	u_out(:,n)=(sqrt(cdn(:))sqrt(pu(:,1)pu(:,1)+pv(:,1)*pv(:,1))
	385	& /karman)*log(zout/pz0(:))
[496]	386	ENDIF
[566]	387	T_out(:,n) = Teta_out(:,n)*(exp(
[529]	388	& (zout/zzlay(:,1))*(log(pplay(:,1)/ps))
	389	& )
	390	& )**rcp
	391
[566]	392	ENDDO !of n=1,n_out
[529]	393
[496]	394	!------------------------------------------------------------------------
	395	!------------------------------------------------------------------------
	396	! PART III : WSTAR COMPUTATION
	397	!------------------------------------------------------------------------
	398	!------------------------------------------------------------------------
	399
	400	! Detection of the mixed-layer potential temperature
	401	! ------------
	402
	403	! Nearest index for the pbl height
	404
[566]	405	IF (calltherm) THEN
	406
[496]	407	pbl_height_index(:)=1
	408
	409	DO k=1,nlay-1
	410	DO ig=1, ngrid
[529]	411	IF (abs(zmax(ig)-zzlay(ig,k)) .lt.
	412	& abs(zmax(ig)-zzlay(ig,pbl_height_index(ig)))) THEN
[496]	413	pbl_height_index(ig)=k
	414	ENDIF
	415	ENDDO
	416	ENDDO
	417
	418	! Potential temperature gradient
	419
	420	dteta(:,nlay)=0.
	421	DO k=1,nlay-1
	422	DO ig=1, ngrid
[529]	423	dteta(ig,k) = (ph(ig,k+1)-ph(ig,k))/(zzlay(ig,k+1)-zzlay(ig,k))
[496]	424	ENDDO
	425	ENDDO
	426
	427	! Computation of the pbl mixed layer temperature
	428
	429	DO ig=1, ngrid
	430	ii=MINLOC(abs(dteta(ig,1:pbl_height_index(ig))))
	431	pbl_teta(ig) = ph(ig,ii(1))
	432	ENDDO
	433
	434	!------------------------------------------------------------------------
	435	!------------------------------------------------------------------------
	436	! PART IV : VERTICAL_VELOCITY_VARIANCE/VERTICAL_TURBULENT_FLUX PROFILES
	437	!------------------------------------------------------------------------
	438	!------------------------------------------------------------------------
	439
	440	! We follow Spiga et. al 2010 (QJRMS)
	441	! ------------
	442
	443	DO ig=1, ngrid
	444	IF (zmax(ig) .gt. 0.) THEN
	445	x(ig) = zout/zmax(ig)
	446	ELSE
	447	x(ig) = 999.
	448	ENDIF
	449	ENDDO
	450
	451	DO ig=1, ngrid
	452	! dimensionless vertical heat flux
	453	IF (x(ig) .le. 0.3) THEN
	454	dvhf(ig) = ((-3.85/log(x(ig)))+0.07*log(x(ig)))
	455	& exp(-4.61x(ig))
	456	ELSEIF (x(ig) .le. 1.) THEN
	457	dvhf(ig) = -1.52*x(ig) + 1.24
	458	ELSE
	459	dvhf(ig) = 0.
	460	ENDIF
	461	! dimensionless vertical velocity variance
	462	IF (x(ig) .le. 1.) THEN
	463	dvvv(ig) = 2.05(x(ig)(2./3.))(1.-0.64x(ig))*2
	464	ELSE
	465	dvvv(ig) = 0.
	466	ENDIF
	467	ENDDO
	468
	469	vhf(:) = dvhf(:)*hfmax(:)
[662]	470	vvv(:) = dvvv(:)(wstar_in(:))*2
[496]	471
[566]	472	ENDIF ! of if calltherm
[496]	473
[1212]	474	#ifndef MESOSCALE
[636]	475	call WRITEDIAGFI(ngrid,'rib_pbl',
	476	& 'Richardson in pbl parameter','m/s',2,rib)
	477	call WRITEDIAGFI(ngrid,'cdn_pbl',
	478	& 'neutral momentum coef','m/s',2,cdn)
	479	call WRITEDIAGFI(ngrid,'fm_pbl',
	480	& 'momentum stab function','m/s',2,fm)
	481	call WRITEDIAGFI(ngrid,'uv',
	482	& 'wind norm first layer','m/s',2,sqrt(zu2))
	483	call WRITEDIAGFI(ngrid,'uvtrue',
	484	& 'wind norm first layer','m/s',2,sqrt(pu(:,1)2+pv(:,1)2))
	485	call WRITEDIAGFI(ngrid,'chn_pbl',
	486	& 'neutral momentum coef','m/s',2,chn)
	487	call WRITEDIAGFI(ngrid,'fh_pbl',
	488	& 'momentum stab function','m/s',2,fh)
	489	call WRITEDIAGFI(ngrid,'B_pbl',
	490	& 'flottabilité','m/',2,(ph(:,1)-pts(:))/pts(:))
	491	call WRITEDIAGFI(ngrid,'zot_pbl',
	492	& 'flottabilité','ms',2,pz0tcomp)
	493	call WRITEDIAGFI(ngrid,'zz1','flottabilité','m',2,zzlay(:,1))
[1212]	494	#endif
[636]	495
[496]	496	RETURN
	497	END

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