source: lmdz_wrf/trunk/tools/module_ForDiagnosticsVars.f90 @ 1776

Last change on this file since 1776 was 1776, checked in by lfita, 7 years ago

Adding `zwind': wind at a given height following power-law methodology

File size: 39.0 KB
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[772]1!! Fortran version of different diagnostics
2! L. Fita. LMD May 2016
3! gfortran module_generic.o -c module_ForDiagnostics.F90
4!
5! f2py -m module_ForDiagnostics --f90exec=/usr/bin/gfortran-4.7 -c module_generic.F90 module_ForDiagnostics.F90
6
7MODULE module_ForDiagnosticsVars
8
[1608]9  USE module_definitions
[772]10  USE module_generic
11
12  IMPLICIT NONE
13
14  CONTAINS
15
16!!!!!!! Variables
[1769]17! compute_psl_ptarget4d2: Compute sea level pressure using a target pressure. Similar to the Benjamin
18!   and Miller (1990). Method found in p_interp.F90
19! compute_tv4d: 4D calculation of virtual temperaure
20! SaturationMixingRatio: WRF's AFWA method to compute the saturation mixing ratio
21! The2T: WRF's AFWA method to compute the temperature at any pressure level along a saturation adiabat
22!   by iteratively solving for it from the parcel thetae.
23! Theta: WRF's AFWA method to compute potential temperature
24! Thetae: WRF's AFWA method to compute equivalent potential temperature
25! TLCL: WRF's AFWA method to compute the temperature of a parcel of air would have if lifed dry
26!   adiabatically to it's lifting condensation level (lcl)
27! var_cape_afwa1D: WRF's AFWA method to compute cape, cin, fclp, fclz and li
[772]28! var_cllmh: low, medium, high-cloud [0,1]
29! var_clt: total cloudiness [0,1]
[1773]30! var_zmla_generic: Subroutine to compute pbl-height following a generic method
[1776]31! var_zwind: Subroutine to extrapolate the wind at a given height following the 'power law' methodology
[1769]32! VirtualTemp1D: Function for 1D calculation of virtual temperaure
33! VirtualTemperature: WRF's AFWA method to compute virtual temperature
[772]34
35!!!!!!! Calculations
36! compute_clt: Computation of total cloudiness
37
38!!!
39! Variables
40!!!
41
42  FUNCTION var_cllmh(clfra, p, dz)
43! Function to compute cllmh on a 1D column 1: low-cloud; 2: medium-cloud; 3: high-cloud [1]
44
45    IMPLICIT NONE
46
47    INTEGER, INTENT(in)                                  :: dz
48    REAL(r_k), DIMENSION(dz), INTENT(in)                 :: clfra, p
49    REAL(r_k), DIMENSION(3)                              :: var_cllmh
50
51! Local
52    INTEGER                                              :: iz
53    REAL(r_k)                                            :: zclearl, zcloudl, zclearm, zcloudm,       &
54      zclearh, zcloudh
55
56!!!!!!! Variables
57! clfra: cloudfraction as 1D verical-column [1]
58! p: pressure values of the column
59    fname = 'var_cllmh'
60
[1608]61    zclearl = oneRK
62    zcloudl = zeroRK
63    zclearm = oneRK
64    zcloudm = zeroRK
65    zclearh = oneRK
66    zcloudh = zeroRK
[772]67
[1608]68    var_cllmh = oneRK
[772]69
70    DO iz=1, dz
71      IF (p(iz) < prmhc) THEN
[1608]72        var_cllmh(3) = var_cllmh(3)*(oneRK-MAX(clfra(iz),zcloudh))/(oneRK-MIN(zcloudh,oneRK-ZEPSEC))
[772]73        zcloudh = clfra(iz)
74      ELSE IF ( (p(iz) >= prmhc) .AND. (p(iz) < prmlc) ) THEN
[1608]75        var_cllmh(2) = var_cllmh(2)*(oneRK-MAX(clfra(iz),zcloudm))/(oneRK-MIN(zcloudm,oneRK-ZEPSEC))
[772]76        zcloudm = clfra(iz)
77      ELSE IF (p(iz) >= prmlc) THEN
[1608]78        var_cllmh(1) = var_cllmh(1)*(oneRK-MAX(clfra(iz),zcloudl))/(oneRK-MIN(zcloudl,oneRK-ZEPSEC))
[772]79        zcloudl = clfra(iz)
80      ELSE
81        PRINT *,'  ' // TRIM(fname) // ': This is weird, pressure:', p(iz), ' Pa fails out!!'
82        PRINT *,'    from high, low cloud pressures:', prmhc, ' ,', prmlc,' Pa at z-level:', iz
83        PRINT *,'    p_high > p:', prmhc,'> ',p(iz),' Pa'
84        PRINT *,'    p_low > p >= p_high:', prmlc,'> ',p(iz),' >=', prmhc,' Pa'
85        PRINT *,'    p_low >= p:', prmlc,'>= ',p(iz),' Pa'
86        STOP
87      END IF
88    END DO
89
[1608]90    var_cllmh = oneRK - var_cllmh
[772]91
92    RETURN
93
94  END FUNCTION var_cllmh
95
96  REAL(r_k) FUNCTION var_clt(clfra, dz)
97! Function to compute the total cloud following 'newmicro.F90' from LMDZ using 1D vertical
98!   column values
99
100    IMPLICIT NONE
101
[1141]102    INTEGER, INTENT(in)                                  :: dz
[772]103    REAL(r_k), DIMENSION(dz), INTENT(in)                 :: clfra
104! Local
105    INTEGER                                              :: iz
106    REAL(r_k)                                            :: zclear, zcloud
[1608]107
[772]108!!!!!!! Variables
109! cfra: 1-column cloud fraction values
110
111    fname = 'var_clt'
112
[1608]113    zclear = oneRK
114    zcloud = zeroRK
[772]115
116    DO iz=1,dz
[1608]117      zclear = zclear*(oneRK-MAX(clfra(iz),zcloud))/(oneRK-MIN(zcloud,1.-ZEPSEC))
118      var_clt = oneRK - zclear
[772]119      zcloud = clfra(iz)
120    END DO
121
122    RETURN
123
124  END FUNCTION var_clt
125
[1769]126
127  SUBROUTINE compute_psl_ptarget4d2(press, ps, hgt, ta, qv, ptarget, psl, d1, d2, d3, d4)
128    ! Subroutine to compute sea level pressure using a target pressure. Similar to the Benjamin
129    !   and Miller (1990). Method found in p_interp.F90
130
131    IMPLICIT NONE
132
133    INTEGER, INTENT(in)                                  :: d1, d2, d3, d4
134    REAL(r_k), DIMENSION(d1,d2,d3,d4), INTENT(in)        :: press, ta, qv
135    REAL(r_k), DIMENSION(d1,d2,d4), INTENT(in)           :: ps
136    REAL(r_k), DIMENSION(d1,d2), INTENT(in)              :: hgt
137    REAL(r_k), INTENT(in)                                :: ptarget
138    REAL(r_k), DIMENSION(d1,d2,d4), INTENT(out)          :: psl
139
140! Local
141    INTEGER                                              :: i, j, it
142    INTEGER                                              :: kin
143    INTEGER                                              :: kupper
144    REAL(r_k)                                            :: dpmin, dp, tbotextrap,   &
145      tvbotextrap, virtual
146    ! Exponential related to standard atmosphere lapse rate r_d*gammav/g
147    REAL(r_k), PARAMETER                                 :: expon=r_d*gammav/grav
148
149!!!!!!! Variables
150! press: Atmospheric pressure [Pa]
151! ps: surface pressure [Pa]
152! hgt: surface height
153! ta: temperature [K]
154! qv: water vapor mixing ratio
155! dz: number of vertical levels
156! psl: sea-level pressure
157
158    fname = 'compute_psl_ptarget4d2'
159
160    ! Minimal distance between pressures [Pa]
161    dpmin=1.e4
162    psl=0.
163
164    DO i=1,d1
165      DO j=1,d2
166        IF (hgt(i,j) /= 0.) THEN
167          DO it=1,d4
168
169            ! target pressure to be used for the extrapolation [Pa] (defined in namelist.input)
170            !   ptarget = 70000. default value
171
172            ! We are below both the ground and the lowest data level.
173
174            !      First, find the model level that is closest to a "target" pressure
175            !        level, where the "target" pressure is delta-p less that the local
176            !        value of a horizontally smoothed surface pressure field.  We use
177            !        delta-p = 150 hPa here. A standard lapse rate temperature profile
178            !        passing through the temperature at this model level will be used
179            !        to define the temperature profile below ground.  This is similar
180            !        to the Benjamin and Miller (1990) method, using 
181            !        700 hPa everywhere for the "target" pressure.
182
183            kupper = 0
184            loop_kIN: DO kin=d3,1,-1
185              kupper = kin
186              dp=abs( press(i,j,kin,it) - ptarget )
187              IF (dp .GT. dpmin) EXIT loop_kIN
188              dpmin=min(dpmin,dp)
189            ENDDO loop_kIN
190
191            tbotextrap=ta(i,j,kupper,it)*(ps(i,j,it)/ptarget)**expon
192            tvbotextrap=virtualTemp1D(tbotextrap,qv(i,j,kupper,it))
193
194            psl(i,j,it) = ps(i,j,it)*((tvbotextrap+gammav*hgt(i,j))/tvbotextrap)**(1/expon)
195          END DO
196        ELSE
197          psl(i,j,:) = ps(i,j,:)
198        END IF
199      END DO
200    END DO
201
202    RETURN
203
204  END SUBROUTINE compute_psl_ptarget4d2
205
206  SUBROUTINE compute_tv4d(ta,qv,tv,d1,d2,d3,d4)
207! 4D calculation of virtual temperaure
208
209    IMPLICIT NONE
210
211    INTEGER, INTENT(in)                                  :: d1, d2, d3, d4
212    REAL(r_k), DIMENSION(d1,d2,d3,d4), INTENT(in)        :: ta, qv
213    REAL(r_k), DIMENSION(d1,d2,d3,d4), INTENT(out)       :: tv
214
215! Variables
216! ta: temperature [K]
217! qv: mixing ratio [kgkg-1]
218! tv: virtual temperature
219
220    tv = ta*(oneRK+(qv/epsilonv))/(oneRK+qv)
221
222  END SUBROUTINE compute_tv4d
223
224  FUNCTION VirtualTemp1D (ta,qv) result (tv)
225! 1D calculation of virtual temperaure
226
227    IMPLICIT NONE
228
229    REAL(r_k), INTENT(in)                                :: ta, qv
230    REAL(r_k)                                            :: tv
231
232! Variables
233! ta: temperature [K]
234! qv: mixing ratio [kgkg-1]
235
236    tv = ta*(oneRK+(qv/epsilonv))/(oneRK+qv)
237
238  END FUNCTION VirtualTemp1D
239
240! ---- BEGIN modified from module_diag_afwa.F ---- !
241
242  !!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
243  !~
244  !~ Name:
245  !~    Theta
246  !~
247  !~ Description:
248  !~    This function calculates potential temperature as defined by
249  !~    Poisson's equation, given temperature and pressure ( hPa ).
250  !~
251  !!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
252  FUNCTION Theta ( t, p )
253
254    IMPLICIT NONE
255
256     !~ Variable declaration
257     !  --------------------
258     REAL(r_k), INTENT ( IN )                            :: t
259     REAL(r_k), INTENT ( IN )                            :: p
260     REAL(r_k)                                           :: theta
261
262     ! Using WRF values
263     !REAL :: Rd ! Dry gas constant
264     !REAL :: Cp ! Specific heat of dry air at constant pressure
265     !REAL :: p00 ! Standard pressure ( 1000 hPa )
266     REAL(r_k)                                           :: Rd, p00
267 
268     !Rd =  287.04
269     !Cp = 1004.67
270     !p00 = 1000.00
271
272     Rd = r_d
273     p00 = p1000mb/100.
274
275     !~ Poisson's equation
276     !  ------------------
277     theta = t * ( (p00/p)**(Rd/Cp) )
278 
279  END FUNCTION Theta
280
281  !!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
282  !~
283  !~ Name:
284  !~    Thetae
285  !~
286  !~ Description:
287  !~    This function returns equivalent potential temperature using the
288  !~    method described in Bolton 1980, Monthly Weather Review, equation 43.
289  !~
290  !!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
291  FUNCTION Thetae ( tK, p, rh, mixr )
292
293    IMPLICIT NONE
294
295     !~ Variable Declarations
296     !  ---------------------
297     REAL(r_k) :: tK        ! Temperature ( K )
298     REAL(r_k) :: p         ! Pressure ( hPa )
299     REAL(r_k) :: rh        ! Relative humidity
300     REAL(r_k) :: mixr      ! Mixing Ratio ( kg kg^-1)
301     REAL(r_k) :: te        ! Equivalent temperature ( K )
302     REAL(r_k) :: thetae    ! Equivalent potential temperature
303 
304     ! Using WRF values
305     !REAL, PARAMETER :: R  = 287.04         ! Universal gas constant (J/deg kg)
306     !REAL, PARAMETER :: P0 = 1000.0         ! Standard pressure at surface (hPa)
307     REAL(r_k)                                                :: R, p00, Lv
308     !REAL, PARAMETER :: lv = 2.54*(10**6)   ! Latent heat of vaporization
309                                            ! (J kg^-1)
310     !REAL, PARAMETER :: cp = 1004.67        ! Specific heat of dry air constant
311                                            ! at pressure (J/deg kg)
312     REAL(r_k) :: tlc                            ! LCL temperature
313 
314     R = r_d
315     p00 = p1000mb/100.
316     lv = XLV
317
318     !~ Calculate the temperature of the LCL
319     !  ------------------------------------
320     tlc = TLCL ( tK, rh )
321 
322     !~ Calculate theta-e
323     !  -----------------
324     thetae = (tK * (p00/p)**( (R/Cp)*(1.- ( (.28E-3)*mixr*1000.) ) ) )* &
325                 exp( (((3.376/tlc)-.00254))*&
326                    (mixr*1000.*(1.+(.81E-3)*mixr*1000.)) )
327 
328  END FUNCTION Thetae
329
330  !!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
331  !~
332  !~ Name:
333  !~    The2T.f90
334  !~
335  !~ Description:
336  !~    This function returns the temperature at any pressure level along a
337  !~    saturation adiabat by iteratively solving for it from the parcel
338  !~    thetae.
339  !~
340  !~ Dependencies:
341  !~    function thetae.f90
342  !~
343  !!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
344  FUNCTION The2T ( thetaeK, pres, flag ) result ( tparcel )
345
346    IMPLICIT NONE
347 
348     !~ Variable Declaration
349     !  --------------------
350     REAL(r_k),    INTENT     ( IN ) :: thetaeK
351     REAL(r_k),    INTENT     ( IN ) :: pres
352     LOGICAL, INTENT ( INOUT )  :: flag
353     REAL(r_k)                       :: tparcel
354 
355     REAL(r_k) :: thetaK
356     REAL(r_k) :: tovtheta
357     REAL(r_k) :: tcheck
358     REAL(r_k) :: svpr, svpr2
359     REAL(r_k) :: smixr, smixr2
360     REAL(r_k) :: thetae_check, thetae_check2
361     REAL(r_k) :: tguess_2, correction
362 
363     LOGICAL :: found
364     INTEGER :: iter
365 
366     ! Using WRF values
367     !REAL :: R     ! Dry gas constant
368     !REAL :: Cp    ! Specific heat for dry air
369     !REAL :: kappa ! Rd / Cp
370     !REAL :: Lv    ! Latent heat of vaporization at 0 deg. C
371     REAL(r_k)                                                :: R, kappa, Lv
372
373     R = r_d
374     Lv = XLV
375     !R     = 287.04
376     !Cp    = 1004.67
377     Kappa = R/Cp
378     !Lv    = 2.500E+6
379
380     !~ Make initial guess for temperature of the parcel
381     !  ------------------------------------------------
382     tovtheta = (pres/100000.0)**(r/cp)
383     tparcel  = thetaeK/exp(lv*.012/(cp*295.))*tovtheta
384
385     iter = 1
386     found = .false.
387     flag = .false.
388
389     DO
390        IF ( iter > 105 ) EXIT
391
392        tguess_2 = tparcel + REAL ( 1 )
393
394        svpr   = 6.122 * exp ( (17.67*(tparcel-273.15)) / (tparcel-29.66) )
395        smixr  = ( 0.622*svpr ) / ( (pres/100.0)-svpr )
396        svpr2  = 6.122 * exp ( (17.67*(tguess_2-273.15)) / (tguess_2-29.66) )
397        smixr2 = ( 0.622*svpr2 ) / ( (pres/100.0)-svpr2 )
398
399        !  ------------------------------------------------------------------ ~!
400        !~ When this function was orinially written, the final parcel         ~!
401        !~ temperature check was based off of the parcel temperature and      ~!
402        !~ not the theta-e it produced.  As there are multiple temperature-   ~!
403        !~ mixing ratio combinations that can produce a single theta-e value, ~!
404        !~ we change the check to be based off of the resultant theta-e       ~!
405        !~ value.  This seems to be the most accurate way of backing out      ~!
406        !~ temperature from theta-e.                                          ~!
407        !~                                                                    ~!
408        !~ Rentschler, April 2010                                             ~!
409        !  ------------------------------------------------------------------  !
410
411        !~ Old way...
412        !thetaK = thetaeK / EXP (lv * smixr  /(cp*tparcel) )
413        !tcheck = thetaK * tovtheta
414
415        !~ New way
416        thetae_check  = Thetae ( tparcel,  pres/100., 100., smixr  )
417        thetae_check2 = Thetae ( tguess_2, pres/100., 100., smixr2 )
418
419        !~ Whew doggies - that there is some accuracy...
420        !IF ( ABS (tparcel-tcheck) < .05) THEN
421        IF ( ABS (thetaeK-thetae_check) < .001) THEN
422           found = .true.
423           flag  = .true.
424           EXIT
425        END IF
426
427        !~ Old
428        !tparcel = tparcel + (tcheck - tparcel)*.3
429
430        !~ New
431        correction = ( thetaeK-thetae_check ) / ( thetae_check2-thetae_check )
432        tparcel = tparcel + correction
433
434        iter = iter + 1
435     END DO
436
437     !IF ( .not. found ) THEN
438     !   print*, "Warning! Thetae to temperature calculation did not converge!"
439     !   print*, "Thetae ", thetaeK, "Pressure ", pres
440     !END IF
441
442  END FUNCTION The2T
443
444  !!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
445  !~
446  !~ Name:
447  !~    VirtualTemperature
448  !~
449  !~ Description:
450  !~    This function returns virtual temperature given temperature ( K )
451  !~    and mixing ratio.
452  !~
453  !!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
454  FUNCTION VirtualTemperature ( tK, w ) result ( Tv )
455
456    IMPLICIT NONE
457
458     !~ Variable declaration
459     real(r_k), intent ( in ) :: tK !~ Temperature
460     real(r_k), intent ( in ) :: w  !~ Mixing ratio ( kg kg^-1 )
461     real(r_k)                :: Tv !~ Virtual temperature
462
463     Tv = tK * ( 1.0 + (w/0.622) ) / ( 1.0 + w )
464
465  END FUNCTION VirtualTemperature
466
467  !!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
468  !~
469  !~ Name:
470  !~    SaturationMixingRatio
471  !~
472  !~ Description:
473  !~    This function calculates saturation mixing ratio given the
474  !~    temperature ( K ) and the ambient pressure ( Pa ).  Uses
475  !~    approximation of saturation vapor pressure.
476  !~
477  !~ References:
478  !~    Bolton (1980), Monthly Weather Review, pg. 1047, Eq. 10
479  !~
480  !!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
481  FUNCTION SaturationMixingRatio ( tK, p ) result ( ws )
482
483    IMPLICIT NONE
484
485    REAL(r_k), INTENT ( IN ) :: tK
486    REAL(r_k), INTENT ( IN ) :: p
487    REAL(r_k)                :: ws
488
489    REAL(r_k) :: es
490
491    es = 6.122 * exp ( (17.67*(tK-273.15))/ (tK-29.66) )
492    ws = ( 0.622*es ) / ( (p/100.0)-es )
493
494  END FUNCTION SaturationMixingRatio
495
496  !!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
497  !~                                                                     
498  !~ Name:                                                               
499  !~    tlcl                                                               
500  !~                                                                       
501  !~ Description:                                                           
502  !~    This function calculates the temperature of a parcel of air would have
503  !~    if lifed dry adiabatically to it's lifting condensation level (lcl). 
504  !~                                                                         
505  !~ References:                                                             
506  !~    Bolton (1980), Monthly Weather Review, pg. 1048, Eq. 22
507  !~                                                                         
508  !!!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!!!
509  FUNCTION TLCL ( tk, rh )
510   
511    IMPLICIT NONE
512 
513    REAL(r_k), INTENT ( IN ) :: tK   !~ Temperature ( K )
514    REAL(r_k), INTENT ( IN ) :: rh   !~ Relative Humidity ( % )
515    REAL(r_k)                :: tlcl
516   
517    REAL(r_k) :: denom, term1, term2
518
519    term1 = 1.0 / ( tK - 55.0 )
520!! Lluis
521!    IF ( rh > REAL (0) ) THEN
522    IF ( rh > zeroRK ) THEN
523      term2 = ( LOG (rh/100.0)  / 2840.0 )
524    ELSE
525      term2 = ( LOG (0.001/oneRK) / 2840.0 )
526    END IF
527    denom = term1 - term2
528!! Lluis
529!    tlcl = ( 1.0 / denom ) + REAL ( 55 )
530    tlcl = ( oneRK / denom ) + 55*oneRK
531
532  END FUNCTION TLCL
533
534  FUNCTION var_cape_afwa1D(nz, tk, rhv, p, hgt, sfc, cape, cin, zlfc, plfc, lidx, parcel) RESULT (ostat)
535! Function to compute cape on a 1D column following implementation in phys/module_diag_afwa.F
536
537    IMPLICIT NONE
538
539    INTEGER, INTENT(in)                                  :: nz, sfc
540    REAL(r_k), DIMENSION(nz), INTENT(in)                 :: tk, rhv, p, hgt
541    REAL(r_k), INTENT(out)                               :: cape, cin, zlfc, plfc, lidx
542    INTEGER                                              :: ostat
543    INTEGER, INTENT(in)                                  :: parcel
544 
545    ! Local
546    !~ Derived profile variables
547    !  -------------------------
548    REAL(r_k), DIMENSION(nz)                             :: rh, ws, w, dTvK, buoy
549    REAL(r_k)                                            :: tlclK, plcl, nbuoy, pbuoy
550 
551    !~ Source parcel information
552    !  -------------------------
553    REAL(r_k)                                            :: srctK, srcrh, srcws, srcw, srcp,          &
554      srctheta, srcthetaeK
555    INTEGER                                              :: srclev
556    REAL(r_k)                                            :: spdiff
557   
558    !~ Parcel variables
559    !  ----------------
560    REAL(r_k)                                            :: ptK, ptvK, tvK, pw
561 
562    !~ Other utility variables
563    !  -----------------------
564    INTEGER                                              :: i, j, k
565    INTEGER                                              :: lfclev
566    INTEGER                                              :: prcl
567    INTEGER                                              :: mlev
568    INTEGER                                              :: lyrcnt
569    LOGICAL                                              :: flag
570    LOGICAL                                              :: wflag
571    REAL(r_k)                                            :: freeze
572    REAL(r_k)                                            :: pdiff
573    REAL(r_k)                                            :: pm, pu, pd
574    REAL(r_k)                                            :: lidxu
575    REAL(r_k)                                            :: lidxd
576 
577    REAL(r_k), PARAMETER                                 :: Rd = r_d
578    REAL(r_k), PARAMETER                                 :: RUNDEF = -9.999E30
579
580!!!!!!! Variables
581! nz: Number of vertical levels
582! sfc: Surface level in the profile
583! tk: Temperature profile [K]
584! rhv: Relative Humidity profile [1]
585! rh: Relative Humidity profile [%]
586! p: Pressure profile [Pa]
587! hgt: Geopotential height profile [gpm]
588! cape: CAPE [Jkg-1]
589! cin: CIN [Jkg-1]
590! zlfc: LFC Height [gpm]
591! plfc: LFC Pressure [Pa]
592! lidx: Lifted index
593!   FROM: https://en.wikipedia.org/wiki/Lifted_index
594!     lidx >= 6: Very Stable Conditions
595!     6 > lidx > 1: Stable Conditions, Thunderstorms Not Likely
596!     0 > lidx > -2: Slightly Unstable, Thunderstorms Possible, With Lifting Mechanism (i.e., cold front, daytime heating, ...)
597!     -2 > lidx > -6: Unstable, Thunderstorms Likely, Some Severe With Lifting Mechanism
598!     -6 > lidx: Very Unstable, Severe Thunderstorms Likely With Lifting Mechanism
599! ostat: Function return status (Nonzero is bad)
600! parcel:
601!   Most Unstable = 1 (default)
602!   Mean layer = 2
603!   Surface based = 3
604!~ Derived profile variables
605!  -------------------------
606! ws: Saturation mixing ratio
607! w: Mixing ratio
608! dTvK: Parcel / ambient Tv difference
609! buoy: Buoyancy
610! tlclK: LCL temperature [K]
611! plcl: LCL pressure [Pa]
612! nbuoy: Negative buoyancy
613! pbuoy: Positive buoyancy
614 
615!~ Source parcel information
616!  -------------------------
617! srctK: Source parcel temperature [K]
618! srcrh: Source parcel rh [%]
619! srcws: Source parcel sat. mixing ratio
620! srcw: Source parcel mixing ratio
621! srcp: Source parcel pressure [Pa]
622! srctheta: Source parcel theta [K]
623! srcthetaeK: Source parcel theta-e [K]
624! srclev: Level of the source parcel
625! spdiff: Pressure difference
626   
627!~ Parcel variables
628!  ----------------
629! ptK: Parcel temperature [K]
630! ptvK: Parcel virtual temperature [K]
631! tvK: Ambient virtual temperature [K]
632! pw: Parcel mixing ratio
633 
634!~ Other utility variables
635!  -----------------------
636! lfclev: Level of LFC
637! prcl: Internal parcel type indicator
638! mlev: Level for ML calculation
639! lyrcnt: Number of layers in mean layer
640! flag: Dummy flag
641! wflag: Saturation flag
642! freeze: Water loading multiplier
643! pdiff: Pressure difference between levs
644! pm, pu, pd: Middle, upper, lower pressures
645! lidxu: Lifted index at upper level
646! lidxd: Lifted index at lower level
647
648    fname = 'var_cape_afwa' 
649
650    !~ Initialize variables
651    !  --------------------
652    rh = rhv*100.
653    ostat = 0
654    CAPE = zeroRK
655    CIN = zeroRK
656    ZLFC = RUNDEF
657    PLFC = RUNDEF
658 
659    !~ Look for submitted parcel definition
660    !~ 1 = Most unstable
661    !~ 2 = Mean layer
662    !~ 3 = Surface based
663    !  -------------------------------------
664    IF ( parcel > 3 .or. parcel < 1 ) THEN
665       prcl = 1
666    ELSE
667       prcl =  parcel
668    END IF
669 
670    !~ Initalize our parcel to be (sort of) surface based.  Because of
671    !~ issues we've been observing in the WRF model, specifically with
672    !~ excessive surface moisture values at the surface, using a true
673    !~ surface based parcel is resulting a more unstable environment
674    !~ than is actually occuring.  To address this, our surface parcel
675    !~ is now going to be defined as the parcel between 25-50 hPa
676    !~ above the surface. UPDATE - now that this routine is in WRF,
677    !~ going to trust surface info. GAC 20140415
678    !  ----------------------------------------------------------------
679 
680    !~ Compute mixing ratio values for the layer
681    !  -----------------------------------------
682    DO k = sfc, nz
683      ws  ( k )   = SaturationMixingRatio ( tK(k), p(k) )
684      w   ( k )   = ( rh(k)/100.0 ) * ws ( k )
685    END DO
686 
687    srclev      = sfc
688    srctK       = tK    ( sfc )
689    srcrh       = rh    ( sfc )
690    srcp        = p     ( sfc )
691    srcws       = ws    ( sfc )
692    srcw        = w     ( sfc )
693    srctheta    = Theta ( tK(sfc), p(sfc)/100.0 )
694   
695      !~ Compute the profile mixing ratio.  If the parcel is the MU parcel,
696      !~ define our parcel to be the most unstable parcel within the lowest
697      !~ 180 mb.
698      !  -------------------------------------------------------------------
699      mlev = sfc + 1
700      DO k = sfc + 1, nz
701   
702         !~ Identify the last layer within 100 hPa of the surface
703         !  -----------------------------------------------------
704         pdiff = ( p (sfc) - p (k) ) / REAL ( 100 )
705         IF ( pdiff <= REAL (100) ) mlev = k
706
707         !~ If we've made it past the lowest 180 hPa, exit the loop
708         !  -------------------------------------------------------
709         IF ( pdiff >= REAL (180) ) EXIT
710
711         IF ( prcl == 1 ) THEN
712            !IF ( (p(k) > 70000.0) .and. (w(k) > srcw) ) THEN
713            IF ( (w(k) > srcw) ) THEN
714               srctheta = Theta ( tK(k), p(k)/100.0 )
715               srcw = w ( k )
716               srclev  = k
717               srctK   = tK ( k )
718               srcrh   = rh ( k )
719               srcp    = p  ( k )
720            END IF
721         END IF
722   
723      END DO
724   
725      !~ If we want the mean layer parcel, compute the mean values in the
726      !~ lowest 100 hPa.
727      !  ----------------------------------------------------------------
728      lyrcnt =  mlev - sfc + 1
729      IF ( prcl == 2 ) THEN
730   
731         srclev   = sfc
732         srctK    = SUM ( tK (sfc:mlev) ) / REAL ( lyrcnt )
733         srcw     = SUM ( w  (sfc:mlev) ) / REAL ( lyrcnt )
734         srcrh    = SUM ( rh (sfc:mlev) ) / REAL ( lyrcnt )
735         srcp     = SUM ( p  (sfc:mlev) ) / REAL ( lyrcnt )
736         srctheta = Theta ( srctK, srcp/100. )
737   
738      END IF
739   
740      srcthetaeK = Thetae ( srctK, srcp/100.0, srcrh, srcw )
741   
742      !~ Calculate temperature and pressure of the LCL
743      !  ---------------------------------------------
744      tlclK = TLCL ( tK(srclev), rh(srclev) )
745      plcl  = p(srclev) * ( (tlclK/tK(srclev))**(Cp/Rd) )
746   
747      !~ Now lift the parcel
748      !  -------------------
749   
750      buoy  = REAL ( 0 )
751      pw    = srcw
752      wflag = .false.
753      DO k  = srclev, nz
754         IF ( p (k) <= plcl ) THEN
755   
756            !~ The first level after we pass the LCL, we're still going to
757            !~ lift the parcel dry adiabatically, as we haven't added the
758            !~ the required code to switch between the dry adiabatic and moist
759            !~ adiabatic cooling.  Since the dry version results in a greater
760            !~ temperature loss, doing that for the first step so we don't over
761            !~ guesstimate the instability.
762            !  ----------------------------------------------------------------
763   
764            IF ( wflag ) THEN
765               flag  = .false.
766   
767               !~ Above the LCL, our parcel is now undergoing moist adiabatic
768               !~ cooling.  Because of the latent heating being undergone as
769               !~ the parcel rises above the LFC, must iterative solve for the
770               !~ parcel temperature using equivalant potential temperature,
771               !~ which is conserved during both dry adiabatic and
772               !~ pseudoadiabatic displacements.
773               !  --------------------------------------------------------------
774               ptK   = The2T ( srcthetaeK, p(k), flag )
775   
776               !~ Calculate the parcel mixing ratio, which is now changing
777               !~ as we condense moisture out of the parcel, and is equivalent
778               !~ to the saturation mixing ratio, since we are, in theory, at
779               !~ saturation.
780               !  ------------------------------------------------------------
781               pw = SaturationMixingRatio ( ptK, p(k) )
782   
783               !~ Now we can calculate the virtual temperature of the parcel
784               !~ and the surrounding environment to assess the buoyancy.
785               !  ----------------------------------------------------------
786               ptvK  = VirtualTemperature ( ptK, pw )
787               tvK   = VirtualTemperature ( tK (k), w (k) )
788   
789               !~ Modification to account for water loading
790               !  -----------------------------------------
791               freeze = 0.033 * ( 263.15 - pTvK )
792               IF ( freeze > 1.0 ) freeze = 1.0
793               IF ( freeze < 0.0 ) freeze = 0.0
794   
795               !~ Approximate how much of the water vapor has condensed out
796               !~ of the parcel at this level
797               !  ---------------------------------------------------------
798               freeze = freeze * 333700.0 * ( srcw - pw ) / 1005.7
799   
800               pTvK = pTvK - pTvK * ( srcw - pw ) + freeze
801               dTvK ( k ) = ptvK - tvK
802               buoy ( k ) = g * ( dTvK ( k ) / tvK )
803   
804            ELSE
805   
806               !~ Since the theta remains constant whilst undergoing dry
807               !~ adiabatic processes, can back out the parcel temperature
808               !~ from potential temperature below the LCL
809               !  --------------------------------------------------------
810               ptK   = srctheta / ( 100000.0/p(k) )**(Rd/Cp)
811   
812               !~ Grab the parcel virtual temperture, can use the source
813               !~ mixing ratio since we are undergoing dry adiabatic cooling
814               !  ----------------------------------------------------------
815               ptvK  = VirtualTemperature ( ptK, srcw )
816   
817               !~ Virtual temperature of the environment
818               !  --------------------------------------
819               tvK   = VirtualTemperature ( tK (k), w (k) )
820   
821               !~ Buoyancy at this level
822               !  ----------------------
823               dTvK ( k ) = ptvK - tvK
824               buoy ( k ) = g * ( dtvK ( k ) / tvK )
825   
826               wflag = .true.
827   
828            END IF
829   
830         ELSE
831   
832            !~ Since the theta remains constant whilst undergoing dry
833            !~ adiabatic processes, can back out the parcel temperature
834            !~ from potential temperature below the LCL
835            !  --------------------------------------------------------
836            ptK   = srctheta / ( 100000.0/p(k) )**(Rd/Cp)
837   
838            !~ Grab the parcel virtual temperture, can use the source
839            !~ mixing ratio since we are undergoing dry adiabatic cooling
840            !  ----------------------------------------------------------
841            ptvK  = VirtualTemperature ( ptK, srcw )
842   
843            !~ Virtual temperature of the environment
844            !  --------------------------------------
845            tvK   = VirtualTemperature ( tK (k), w (k) )
846   
847            !~ Buoyancy at this level
848            !  ---------------------
849            dTvK ( k ) = ptvK - tvK
850            buoy ( k ) = g * ( dtvK ( k ) / tvK )
851   
852         END IF
853
854         !~ Chirp
855         !  -----
856  !          WRITE ( *,'(I15,6F15.3)' )k,p(k)/100.,ptK,pw*1000.,ptvK,tvK,buoy(k)
857   
858      END DO
859   
860      !~ Add up the buoyancies, find the LFC
861      !  -----------------------------------
862      flag   = .false.
863      lfclev = -1
864      nbuoy  = REAL ( 0 )
865      pbuoy = REAL ( 0 )
866      DO k = sfc + 1, nz
867         IF ( tK (k) < 253.15 ) EXIT
868         CAPE = CAPE + MAX ( buoy (k), 0.0 ) * ( hgt (k) - hgt (k-1) )
869         CIN  = CIN  + MIN ( buoy (k), 0.0 ) * ( hgt (k) - hgt (k-1) )
870   
871         !~ If we've already passed the LFC
872         !  -------------------------------
873         IF ( flag .and. buoy (k) > REAL (0) ) THEN
874            pbuoy = pbuoy + buoy (k)
875         END IF
876   
877         !~ We are buoyant now - passed the LFC
878         !  -----------------------------------
879         IF ( .not. flag .and. buoy (k) > REAL (0) .and. p (k) < plcl ) THEN
880            flag = .true.
881            pbuoy = pbuoy + buoy (k)
882            lfclev = k
883         END IF
884   
885         !~ If we think we've passed the LFC, but encounter a negative layer
886         !~ start adding it up.
887         !  ----------------------------------------------------------------
888         IF ( flag .and. buoy (k) < REAL (0) ) THEN
889            nbuoy = nbuoy + buoy (k)
890
891            !~ If the accumulated negative buoyancy is greater than the
892            !~ positive buoyancy, then we are capped off.  Got to go higher
893            !~ to find the LFC. Reset positive and negative buoyancy summations
894            !  ----------------------------------------------------------------
895            IF ( ABS (nbuoy) > pbuoy ) THEN
896               flag   = .false.
897               nbuoy  = REAL ( 0 )
898               pbuoy  = REAL ( 0 )
899               lfclev = -1
900            END IF
901         END IF
902
903      END DO
904
905      !~ Calculate lifted index by interpolating difference between
906      !~ parcel and ambient Tv to 500mb.
907      !  ----------------------------------------------------------
908      DO k = sfc + 1, nz
909
910         pm = 50000.
911         pu = p ( k )
912         pd = p ( k - 1 )
913
914         !~ If we're already above 500mb just set lifted index to 0.
915         !~ --------------------------------------------------------
916         IF ( pd .le. pm ) THEN
917            lidx = zeroRK
918            EXIT
919   
920         ELSEIF ( pu .le. pm .and. pd .gt. pm) THEN
921
922            !~ Found trapping pressure: up, middle, down.
923            !~ We are doing first order interpolation. 
924            !  ------------------------------------------
925            lidxu = -dTvK ( k ) * ( pu / 100000. ) ** (Rd/Cp)
926            lidxd = -dTvK ( k-1 ) * ( pd / 100000. ) ** (Rd/Cp)
927            lidx = ( lidxu * (pm-pd) + lidxd * (pu-pm) ) / (pu-pd)
928            EXIT
929
930         ENDIF
931
932      END DO
933   
934      !~ Assuming the the LFC is at a pressure level for now
935      !  ---------------------------------------------------
936      IF ( lfclev > zeroRK ) THEN
937         PLFC = p   ( lfclev )
938         ZLFC = hgt ( lfclev )
939      END IF
940   
941      IF ( PLFC /= PLFC .OR. PLFC < zeroRK ) THEN
942         PLFC = -oneRK
943         ZLFC = -oneRK
944      END IF
945   
946      IF ( CAPE /= CAPE ) cape = zeroRK
947   
948      IF ( CIN  /= CIN  ) cin  = zeroRK
949
950      !~ Chirp
951      !  -----
952  !       WRITE ( *,* ) ' CAPE: ', cape, ' CIN:  ', cin
953  !       WRITE ( *,* ) ' LFC:  ', ZLFC, ' PLFC: ', PLFC
954  !       WRITE ( *,* ) ''
955  !       WRITE ( *,* ) ' Exiting buoyancy.'
956  !       WRITE ( *,* ) ' ==================================== '
957  !       WRITE ( *,* ) ''
958   
959    RETURN
960
961  END FUNCTION var_cape_afwa1D
962
963! ---- END modified from module_diag_afwa.F ---- !
964
[1773]965  SUBROUTINE var_zmla_generic(dz, qv, tpot, z, topo, zmla)
966!  Subroutine to compute pbl-height following a generic method
967!    from Nielsen-Gammon et al., 2008 J. Appl. Meteor. Clim.
968!    applied also in Garcia-Diez et al., 2013, QJRMS
969!   where
970!     "The technique identifies the ML height as a threshold increase of potential temperature from
971!       its minimum value within the boundary layer."
972!   here applied similarly to Garcia-Diez et al. where
973!      zmla = "...first level where potential temperature exceeds the minimum potential temperature
974!        reached in the mixed layer by more than 1.5 K"
[1769]975
[1773]976    IMPLICIT NONE
977
978    INTEGER, INTENT(in)                                  :: dz
979    REAL(r_k), DIMENSION(dz), INTENT(in)                 :: qv, tpot, z
980    REAL(r_k), INTENT(in)                                :: topo
981    REAL(r_k), INTENT(out)                               :: zmla
982
983! Local
984    INTEGER                                              :: i
985    INTEGER                                              :: mldlev, bllev
986    REAL(r_k)                                            :: dqvar, tpotmin, refdt
987
988!!!!!!! Variables
989! qv: water vapour mixing ratio
990! tpot: potential temperature [K]
991! z: height above sea level [m]
992! topo: topographic height [m]
993! zmla: boundary layer height [m]
994
995    fname = 'var_zmla_generic'
996
997    ! Pecentage of difference of mixing ratio used to determine Mixed layer depth
998    dqvar = 0.1
999
1000    ! MLD = Mixed layer with no substantial variation of mixing ratio /\qv < 10% ?
1001    !PRINT *,'  Mixed layer mixing ratios qv[1] lev qv[lev] dqvar% _______'
1002    DO mldlev = 2, dz
1003      IF (ABS(qv(mldlev)-qv(1))/qv(1) > dqvar ) EXIT
1004    !  PRINT *,qv(1), mldlev, qv(mldlev), ABS(qv(mldlev)-qv(1))/qv(1)
1005    END DO
1006
1007    ! Looking for the minimum potential temperature within the MLD [tpotmin = min(tpot)_0^MLD]
1008    tpotmin = MINVAL(tpot(1:mldlev))
1009
1010    ! Change in temperature to determine boundary layer height
1011    refdt = 1.5
1012
1013    ! Determine the first level where tpot > tpotmin + 1.5 K
1014    !PRINT *,'  Mixed layer tpotmin lev tpotmin[lev] dtpot _______'
1015    DO bllev = 1, dz
1016      IF (ABS(tpot(bllev)-tpotmin) > refdt ) EXIT
1017    !  PRINT *,tpotmin, bllev, tpot(bllev), ABS(tpot(bllev)-tpotmin)
1018    END DO
1019   
1020    !PRINT *,'   height end MLD:', z(mldlev)
1021    !PRINT *,'   pbl height:', z(bllev)
1022
1023    zmla = z(bllev) - topo
1024
1025    RETURN
1026
1027  END SUBROUTINE var_zmla_generic
1028
[1776]1029  SUBROUTINE var_zwind(d1, u, v, z, u10, v10, sa, ca, topo, newz, unewz, vnewz)
1030! Subroutine to extrapolate the wind at a given height following the 'power law' methodology
1031!    wss[newz] = wss[z1]*(newz/z1)**alpha
1032!    alpha = (ln(wss[z2])-ln(wss[z1]))/(ln(z2)-ln(z1))
1033! AFTER: Phd Thesis:
1034!   Benedicte Jourdier. Ressource eolienne en France metropolitaine : methodes d’evaluation du
1035!   potentiel, variabilite et tendances. Climatologie. Ecole Doctorale Polytechnique, 2015. French
1036!
1037    IMPLICIT NONE
1038
1039    INTEGER, INTENT(in)                                  :: d1
1040    REAL(r_k), DIMENSION(d1), INTENT(in)                 :: u,v,z
1041    REAL(r_k), INTENT(in)                                :: u10, v10, topo, sa, ca, newz
1042    REAL(r_k), INTENT(out)                               :: unewz, vnewz
1043
1044! Local
1045    INTEGER                                              :: inear
1046    REAL(r_k)                                            :: zaground
1047    REAL(r_k), DIMENSION(2)                              :: v1, v2, zz, alpha, uvnewz
1048
1049!!!!!!! Variables
1050! u,v: vertical wind components [ms-1]
1051! z: height above surface [m]
1052! u10,v10: 10-m wind components [ms-1]
1053! topo: topographical height [m]
1054! sa, ca: local sine and cosine of map rotation [1.]
1055! newz: desired height above grpund of extrapolation
1056! unewz,vnewz: Wind compoonents at the given height [ms-1]
1057
1058    fname = 'var_zwind'
1059
1060    PRINT *,' ilev zaground newz z[ilev+1] z[ilev+2] _______'
1061    IF (z(1) < newz ) THEN
1062      DO inear = 1,d1-2
1063        zaground = z(inear+2)
1064        PRINT *, inear, z(inear), newz, z(inear+1), z(inear+2)
1065        IF ( zaground >= newz) EXIT
1066      END DO
1067    ELSE
1068      PRINT *, 1, z(1), newz, z(2), z(3), ' z(1) > newz'
1069      inear = d1 - 2
1070    END IF
1071
1072    IF (inear == d1-2) THEN
1073    ! No vertical pair of levels is below newz, using 10m wind as first value and the first level as the second
1074       v1(1) = u10
1075       v1(2) = v10
1076       v2(1) = u(1)
1077       v2(2) = v(1)
1078       zz(1) = 10.
1079       zz(2) = z(1)
1080    ELSE
1081       v1(1) = u(inear)
1082       v1(2) = v(inear)
1083       v2(1) = u(inear+1)
1084       v2(2) = v(inear+1)
1085       zz(1) = z(inear) - topo
1086       zz(2) = z(inear+1) - topo
1087    END IF
1088
1089    ! Computing for each component
1090    alpha = (LOG(ABS(v2))-LOG(ABS(v1)))/(LOG(zz(2))-LOG(zz(1)))
1091    PRINT *,' Computing with v1:', v1, ' ms-1 v2:', v2, ' ms-1'
1092    PRINT *,' z1:', zz(1), 'm z2:', zz(2), ' m'
1093    PRINT *,' alhpa u:', alpha(1), ' alpha 2:', alpha(2)
1094   
1095    uvnewz = v1*(newz/zz(1))**alpha
1096    ! Earth-rotation
1097    unewz = uvnewz(1)*ca - uvnewz(2)*sa
1098    vnewz = uvnewz(1)*sa + uvnewz(2)*ca
1099
1100    PRINT *,'  result vz:', uvnewz
1101
1102    !STOP
1103
1104    RETURN
1105
1106  END SUBROUTINE var_zwind
1107
[772]1108END MODULE module_ForDiagnosticsVars
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