source: LMDZ6/branches/LMDZ_ECRad/libf/phylmd/nonlocal.F90 @ 5376

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    Name of program: LMDZ
    Creation date: 1984
    Version: LMDZ5
    License: CeCILL version 2
    Holder: Laboratoire de m\'et\'eorologie dynamique, CNRS, UMR 8539
    See the license file in the root directory
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1
2! $Header$
3
4! ======================================================================
5SUBROUTINE nonlocal(knon, paprs, pplay, tsol, beta, u, v, t, q, cd_h, cd_m, &
6    pcfh, pcfm, cgh, cgq)
7  USE dimphy
8  IMPLICIT NONE
9  ! ======================================================================
10  ! Laurent Li (LMD/CNRS), le 30 septembre 1998
11  ! Couche limite non-locale. Adaptation du code du CCM3.
12  ! Code non teste, donc a ne pas utiliser.
13  ! ======================================================================
14  ! Nonlocal scheme that determines eddy diffusivities based on a
15  ! diagnosed boundary layer height and a turbulent velocity scale.
16  ! Also countergradient effects for heat and moisture are included.
17
18  ! For more information, see Holtslag, A.A.M., and B.A. Boville, 1993:
19  ! Local versus nonlocal boundary-layer diffusion in a global climate
20  ! model. J. of Climate, vol. 6, 1825-1842.
21  ! ======================================================================
22  include "YOMCST.h"
23
24  ! Arguments:
25
26  INTEGER knon ! nombre de points a calculer
27  REAL tsol(klon) ! temperature du sol (K)
28  REAL beta(klon) ! efficacite d'evaporation (entre 0 et 1)
29  REAL paprs(klon, klev+1) ! pression a inter-couche (Pa)
30  REAL pplay(klon, klev) ! pression au milieu de couche (Pa)
31  REAL u(klon, klev) ! vitesse U (m/s)
32  REAL v(klon, klev) ! vitesse V (m/s)
33  REAL t(klon, klev) ! temperature (K)
34  REAL q(klon, klev) ! vapeur d'eau (kg/kg)
35  REAL cd_h(klon) ! coefficient de friction au sol pour chaleur
36  REAL cd_m(klon) ! coefficient de friction au sol pour vitesse
37
38  INTEGER isommet
39  REAL vk
40  PARAMETER (vk=0.40)
41  REAL ricr
42  PARAMETER (ricr=0.4)
43  REAL fak
44  PARAMETER (fak=8.5)
45  REAL fakn
46  PARAMETER (fakn=7.2)
47  REAL onet
48  PARAMETER (onet=1.0/3.0)
49  REAL t_coup
50  PARAMETER (t_coup=273.15)
51  REAL zkmin
52  PARAMETER (zkmin=0.01)
53  REAL betam
54  PARAMETER (betam=15.0)
55  REAL betah
56  PARAMETER (betah=15.0)
57  REAL betas
58  PARAMETER (betas=5.0)
59  REAL sffrac
60  PARAMETER (sffrac=0.1)
61  REAL binm
62  PARAMETER (binm=betam*sffrac)
63  REAL binh
64  PARAMETER (binh=betah*sffrac)
65  REAL ccon
66  PARAMETER (ccon=fak*sffrac*vk)
67
68  REAL z(klon, klev)
69  REAL pcfm(klon, klev), pcfh(klon, klev)
70
71  INTEGER i, k
72  REAL zxt, zxq, zxu, zxv, zxmod, taux, tauy
73  REAL zx_alf1, zx_alf2 ! parametres pour extrapolation
74  REAL khfs(klon) ! surface kinematic heat flux [mK/s]
75  REAL kqfs(klon) ! sfc kinematic constituent flux [m/s]
76  REAL heatv(klon) ! surface virtual heat flux
77  REAL ustar(klon)
78  REAL rino(klon, klev) ! bulk Richardon no. from level to ref lev
79  LOGICAL unstbl(klon) ! pts w/unstbl pbl (positive virtual ht flx)
80  LOGICAL stblev(klon) ! stable pbl with levels within pbl
81  LOGICAL unslev(klon) ! unstbl pbl with levels within pbl
82  LOGICAL unssrf(klon) ! unstb pbl w/lvls within srf pbl lyr
83  LOGICAL unsout(klon) ! unstb pbl w/lvls in outer pbl lyr
84  LOGICAL check(klon) ! True=>chk if Richardson no.>critcal
85  REAL pblh(klon)
86  REAL cgh(klon, 2:klev) ! counter-gradient term for heat [K/m]
87  REAL cgq(klon, 2:klev) ! counter-gradient term for constituents
88  REAL cgs(klon, 2:klev) ! counter-gradient star (cg/flux)
89  REAL obklen(klon)
90  REAL ztvd, ztvu, zdu2
91  REAL therm(klon) ! thermal virtual temperature excess
92  REAL phiminv(klon) ! inverse phi function for momentum
93  REAL phihinv(klon) ! inverse phi function for heat
94  REAL wm(klon) ! turbulent velocity scale for momentum
95  REAL fak1(klon) ! k*ustar*pblh
96  REAL fak2(klon) ! k*wm*pblh
97  REAL fak3(klon) ! fakn*wstr/wm
98  REAL pblk(klon) ! level eddy diffusivity for momentum
99  REAL pr(klon) ! Prandtl number for eddy diffusivities
100  REAL zl(klon) ! zmzp / Obukhov length
101  REAL zh(klon) ! zmzp / pblh
102  REAL zzh(klon) ! (1-(zmzp/pblh))**2
103  REAL wstr(klon) ! w*, convective velocity scale
104  REAL zm(klon) ! current level height
105  REAL zp(klon) ! current level height + one level up
106  REAL zcor, zdelta, zcvm5, zxqs
107  REAL fac, pblmin, zmzp, term
108
109  include "YOETHF.h"
110  include "FCTTRE.h"
111
112  ! Initialisation
113
114  isommet = klev
115
116  DO i = 1, klon
117    pcfh(i, 1) = cd_h(i)
118    pcfm(i, 1) = cd_m(i)
119  END DO
120  DO k = 2, klev
121    DO i = 1, klon
122      pcfh(i, k) = zkmin
123      pcfm(i, k) = zkmin
124      cgs(i, k) = 0.0
125      cgh(i, k) = 0.0
126      cgq(i, k) = 0.0
127    END DO
128  END DO
129
130  ! Calculer les hauteurs de chaque couche
131
132  DO i = 1, knon
133    z(i, 1) = rd*t(i, 1)/(0.5*(paprs(i,1)+pplay(i,1)))*(paprs(i,1)-pplay(i,1) &
134      )/rg
135  END DO
136  DO k = 2, klev
137    DO i = 1, knon
138      z(i, k) = z(i, k-1) + rd*0.5*(t(i,k-1)+t(i,k))/paprs(i, k)*(pplay(i,k-1 &
139        )-pplay(i,k))/rg
140    END DO
141  END DO
142
143  DO i = 1, knon
144    IF (thermcep) THEN
145      zdelta = max(0., sign(1.,rtt-tsol(i)))
146      zcvm5 = r5les*rlvtt*(1.-zdelta) + r5ies*rlstt*zdelta
147      zcvm5 = zcvm5/rcpd/(1.0+rvtmp2*q(i,1))
148      zxqs = r2es*foeew(tsol(i), zdelta)/paprs(i, 1)
149      zxqs = min(0.5, zxqs)
150      zcor = 1./(1.-retv*zxqs)
151      zxqs = zxqs*zcor
152    ELSE
153      IF (tsol(i)<t_coup) THEN
154        zxqs = qsats(tsol(i))/paprs(i, 1)
155      ELSE
156        zxqs = qsatl(tsol(i))/paprs(i, 1)
157      END IF
158    END IF
159    zx_alf1 = 1.0
160    zx_alf2 = 1.0 - zx_alf1
161    zxt = (t(i,1)+z(i,1)*rg/rcpd/(1.+rvtmp2*q(i,1)))*(1.+retv*q(i,1))*zx_alf1 &
162      + (t(i,2)+z(i,2)*rg/rcpd/(1.+rvtmp2*q(i,2)))*(1.+retv*q(i,2))*zx_alf2
163    zxu = u(i, 1)*zx_alf1 + u(i, 2)*zx_alf2
164    zxv = v(i, 1)*zx_alf1 + v(i, 2)*zx_alf2
165    zxq = q(i, 1)*zx_alf1 + q(i, 2)*zx_alf2
166    zxmod = 1.0 + sqrt(zxu**2+zxv**2)
167    khfs(i) = (tsol(i)*(1.+retv*q(i,1))-zxt)*zxmod*cd_h(i)
168    kqfs(i) = (zxqs-zxq)*zxmod*cd_h(i)*beta(i)
169    heatv(i) = khfs(i) + 0.61*zxt*kqfs(i)
170    taux = zxu*zxmod*cd_m(i)
171    tauy = zxv*zxmod*cd_m(i)
172    ustar(i) = sqrt(taux**2+tauy**2)
173    ustar(i) = max(sqrt(ustar(i)), 0.01)
174  END DO
175
176  DO i = 1, knon
177    rino(i, 1) = 0.0
178    check(i) = .TRUE.
179    pblh(i) = z(i, 1)
180    obklen(i) = -t(i, 1)*ustar(i)**3/(rg*vk*heatv(i))
181  END DO
182
183
184  ! PBL height calculation:
185  ! Search for level of pbl. Scan upward until the Richardson number between
186  ! the first level and the current level exceeds the "critical" value.
187
188  fac = 100.0
189  DO k = 1, isommet
190    DO i = 1, knon
191      IF (check(i)) THEN
192        zdu2 = (u(i,k)-u(i,1))**2 + (v(i,k)-v(i,1))**2 + fac*ustar(i)**2
193        zdu2 = max(zdu2, 1.0E-20)
194        ztvd = (t(i,k)+z(i,k)*0.5*rg/rcpd/(1.+rvtmp2*q(i, &
195          k)))*(1.+retv*q(i,k))
196        ztvu = (t(i,1)-z(i,k)*0.5*rg/rcpd/(1.+rvtmp2*q(i, &
197          1)))*(1.+retv*q(i,1))
198        rino(i, k) = (z(i,k)-z(i,1))*rg*(ztvd-ztvu)/(zdu2*0.5*(ztvd+ztvu))
199        IF (rino(i,k)>=ricr) THEN
200          pblh(i) = z(i, k-1) + (z(i,k-1)-z(i,k))*(ricr-rino(i,k-1))/(rino(i, &
201            k-1)-rino(i,k))
202          check(i) = .FALSE.
203        END IF
204      END IF
205    END DO
206  END DO
207
208
209  ! Set pbl height to maximum value where computation exceeds number of
210  ! layers allowed
211
212  DO i = 1, knon
213    IF (check(i)) pblh(i) = z(i, isommet)
214  END DO
215
216  ! Improve estimate of pbl height for the unstable points.
217  ! Find unstable points (sensible heat flux is upward):
218
219  DO i = 1, knon
220    IF (heatv(i)>0.) THEN
221      unstbl(i) = .TRUE.
222      check(i) = .TRUE.
223    ELSE
224      unstbl(i) = .FALSE.
225      check(i) = .FALSE.
226    END IF
227  END DO
228
229  ! For the unstable case, compute velocity scale and the
230  ! convective temperature excess:
231
232  DO i = 1, knon
233    IF (check(i)) THEN
234      phiminv(i) = (1.-binm*pblh(i)/obklen(i))**onet
235      wm(i) = ustar(i)*phiminv(i)
236      therm(i) = heatv(i)*fak/wm(i)
237      rino(i, 1) = 0.0
238    END IF
239  END DO
240
241  ! Improve pblh estimate for unstable conditions using the
242  ! convective temperature excess:
243
244  DO k = 1, isommet
245    DO i = 1, knon
246      IF (check(i)) THEN
247        zdu2 = (u(i,k)-u(i,1))**2 + (v(i,k)-v(i,1))**2 + fac*ustar(i)**2
248        zdu2 = max(zdu2, 1.0E-20)
249        ztvd = (t(i,k)+z(i,k)*0.5*rg/rcpd/(1.+rvtmp2*q(i, &
250          k)))*(1.+retv*q(i,k))
251        ztvu = (t(i,1)+therm(i)-z(i,k)*0.5*rg/rcpd/(1.+rvtmp2*q(i, &
252          1)))*(1.+retv*q(i,1))
253        rino(i, k) = (z(i,k)-z(i,1))*rg*(ztvd-ztvu)/(zdu2*0.5*(ztvd+ztvu))
254        IF (rino(i,k)>=ricr) THEN
255          pblh(i) = z(i, k-1) + (z(i,k-1)-z(i,k))*(ricr-rino(i,k-1))/(rino(i, &
256            k-1)-rino(i,k))
257          check(i) = .FALSE.
258        END IF
259      END IF
260    END DO
261  END DO
262
263  ! Set pbl height to maximum value where computation exceeds number of
264  ! layers allowed
265
266  DO i = 1, knon
267    IF (check(i)) pblh(i) = z(i, isommet)
268  END DO
269
270  ! Points for which pblh exceeds number of pbl layers allowed;
271  ! set to maximum
272
273  DO i = 1, knon
274    IF (check(i)) pblh(i) = z(i, isommet)
275  END DO
276
277  ! PBL height must be greater than some minimum mechanical mixing depth
278  ! Several investigators have proposed minimum mechanical mixing depth
279  ! relationships as a function of the local friction velocity, u*.  We
280  ! make use of a linear relationship of the form h = c u* where c=700.
281  ! The scaling arguments that give rise to this relationship most often
282  ! represent the coefficient c as some constant over the local coriolis
283  ! parameter.  Here we make use of the experimental results of Koracin
284  ! and Berkowicz (1988) [BLM, Vol 43] for wich they recommend 0.07/f
285  ! where f was evaluated at 39.5 N and 52 N.  Thus we use a typical mid
286  ! latitude value for f so that c = 0.07/f = 700.
287
288  DO i = 1, knon
289    pblmin = 700.0*ustar(i)
290    pblh(i) = max(pblh(i), pblmin)
291  END DO
292
293  ! pblh is now available; do preparation for diffusivity calculation:
294
295  DO i = 1, knon
296    pblk(i) = 0.0
297    fak1(i) = ustar(i)*pblh(i)*vk
298
299    ! Do additional preparation for unstable cases only, set temperature
300    ! and moisture perturbations depending on stability.
301
302    IF (unstbl(i)) THEN
303      zxt = (t(i,1)-z(i,1)*0.5*rg/rcpd/(1.+rvtmp2*q(i,1)))*(1.+retv*q(i,1))
304      phiminv(i) = (1.-binm*pblh(i)/obklen(i))**onet
305      phihinv(i) = sqrt(1.-binh*pblh(i)/obklen(i))
306      wm(i) = ustar(i)*phiminv(i)
307      fak2(i) = wm(i)*pblh(i)*vk
308      wstr(i) = (heatv(i)*rg*pblh(i)/zxt)**onet
309      fak3(i) = fakn*wstr(i)/wm(i)
310    END IF
311  END DO
312
313  ! Main level loop to compute the diffusivities and
314  ! counter-gradient terms:
315
316  DO k = 2, isommet
317
318    ! Find levels within boundary layer:
319
320    DO i = 1, knon
321      unslev(i) = .FALSE.
322      stblev(i) = .FALSE.
323      zm(i) = z(i, k-1)
324      zp(i) = z(i, k)
325      IF (zkmin==0.0 .AND. zp(i)>pblh(i)) zp(i) = pblh(i)
326      IF (zm(i)<pblh(i)) THEN
327        zmzp = 0.5*(zm(i)+zp(i))
328        zh(i) = zmzp/pblh(i)
329        zl(i) = zmzp/obklen(i)
330        zzh(i) = 0.
331        IF (zh(i)<=1.0) zzh(i) = (1.-zh(i))**2
332
333        ! stblev for points zm < plbh and stable and neutral
334        ! unslev for points zm < plbh and unstable
335
336        IF (unstbl(i)) THEN
337          unslev(i) = .TRUE.
338        ELSE
339          stblev(i) = .TRUE.
340        END IF
341      END IF
342    END DO
343
344    ! Stable and neutral points; set diffusivities; counter-gradient
345    ! terms zero for stable case:
346
347    DO i = 1, knon
348      IF (stblev(i)) THEN
349        IF (zl(i)<=1.) THEN
350          pblk(i) = fak1(i)*zh(i)*zzh(i)/(1.+betas*zl(i))
351        ELSE
352          pblk(i) = fak1(i)*zh(i)*zzh(i)/(betas+zl(i))
353        END IF
354        pcfm(i, k) = pblk(i)
355        pcfh(i, k) = pcfm(i, k)
356      END IF
357    END DO
358
359    ! unssrf, unstable within surface layer of pbl
360    ! unsout, unstable within outer   layer of pbl
361
362    DO i = 1, knon
363      unssrf(i) = .FALSE.
364      unsout(i) = .FALSE.
365      IF (unslev(i)) THEN
366        IF (zh(i)<sffrac) THEN
367          unssrf(i) = .TRUE.
368        ELSE
369          unsout(i) = .TRUE.
370        END IF
371      END IF
372    END DO
373
374    ! Unstable for surface layer; counter-gradient terms zero
375
376    DO i = 1, knon
377      IF (unssrf(i)) THEN
378        term = (1.-betam*zl(i))**onet
379        pblk(i) = fak1(i)*zh(i)*zzh(i)*term
380        pr(i) = term/sqrt(1.-betah*zl(i))
381      END IF
382    END DO
383
384    ! Unstable for outer layer; counter-gradient terms non-zero:
385
386    DO i = 1, knon
387      IF (unsout(i)) THEN
388        pblk(i) = fak2(i)*zh(i)*zzh(i)
389        cgs(i, k) = fak3(i)/(pblh(i)*wm(i))
390        cgh(i, k) = khfs(i)*cgs(i, k)
391        pr(i) = phiminv(i)/phihinv(i) + ccon*fak3(i)/fak
392        cgq(i, k) = kqfs(i)*cgs(i, k)
393      END IF
394    END DO
395
396    ! For all unstable layers, set diffusivities
397
398    DO i = 1, knon
399      IF (unslev(i)) THEN
400        pcfm(i, k) = pblk(i)
401        pcfh(i, k) = pblk(i)/pr(i)
402      END IF
403    END DO
404  END DO ! end of level loop
405
406  RETURN
407END SUBROUTINE nonlocal
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