source: LMDZ6/trunk/libf/phylmd/cospv2/quickbeam_optics.f90 @ 5408

Last change on this file since 5408 was 5268, checked in by abarral, 8 weeks ago

.f90 <-> .F90 depending on cpp key use
File size: 64.3 KB
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1! %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2! Copyright (c) 2015, Regents of the University of Colorado
3! All rights reserved.
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6! permitted provided that the following conditions are met:
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19! THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY
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24! OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
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28!
29! History:
30! May 2015:  Dustin Swales - Initial version
31!
32! %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
33module mod_quickbeam_optics
34  USE COSP_KINDS,          ONLY: wp,dp
35  USE array_lib,           ONLY: infind
36  USE math_lib,            ONLY: path_integral,avint,gamma
37  USE optics_lib,          ONLY: m_wat,m_ice,MieInt
38  USE cosp_math_constants, ONLY: pi
39  USE cosp_phys_constants, ONLY: rhoice 
40  use quickbeam,           ONLY: radar_cfg,dmin,dmax,Re_BIN_LENGTH,  &
41                                 Re_MAX_BIN,nRe_types,nd,maxhclass
42  use mod_cosp_config,     ONLY: N_HYDRO
43  use mod_cosp_error,      ONLY: errorMessage
44  implicit none
45
46  ! Derived type for particle size distribution
47  TYPE size_distribution
48     real(wp),dimension(maxhclass) :: p1,p2,p3,dmin,dmax,apm,bpm,rho
49     integer, dimension(maxhclass) :: dtype,phase
50  END TYPE size_distribution
51 
52  ! Parameters
53  integer,parameter ::   & !
54       cnt_liq       = 19, & ! Liquid temperature count
55       cnt_ice       = 20    ! Lce temperature count
56 
57  ! Initialization variables
58  real(wp),dimension(cnt_ice) :: mt_tti
59  real(wp),dimension(cnt_liq) :: mt_ttl
60  real(wp),dimension(nd)      :: D
61  !logical :: lQuickbeamInit
62 
63contains
64  ! ######################################################################################
65  ! SUBROUTINE quickbeam_optics_init
66  ! ######################################################################################
67  subroutine quickbeam_optics_init()
68    integer :: j
69   
70    mt_tti = (/ ((j-1)*5-90 + 273.15, j = 1, cnt_ice) /)
71    mt_ttl = (/ ((j-1)*5-60 + 273.15, j = 1, cnt_liq) /)
72    D(1) = dmin
73    do j=2,nd
74       D(j) = D(j-1)*exp((log(dmax)-log(dmin))/(nd-1))
75    enddo
76    !lQuickbeamInit = .true.
77  end subroutine quickbeam_optics_init
78 
79  ! ######################################################################################
80  ! SUBROUTINE QUICKBEAM_OPTICS
81  ! ######################################################################################
82  subroutine quickbeam_optics(sd, rcfg, nprof, ngate, undef, hm_matrix, re_matrix,       &
83       Np_matrix, p_matrix, t_matrix, sh_matrix,z_vol,kr_vol)
84   
85    ! INPUTS
86    type(size_distribution),intent(inout) :: &
87         sd               !
88    type(radar_cfg),intent(inout) :: &
89         rcfg             !
90    integer,intent(in) :: &
91         nprof,         & ! Number of hydrometeor profiles
92         ngate            ! Number of vertical layers
93    real(wp),intent(in) :: &
94         undef            ! Missing data value
95    real(wp),intent(in),dimension(nprof,ngate) :: &
96         p_matrix,      & ! Pressure profile (hPa)
97         t_matrix,      & ! Temperature profile (K)
98         sh_matrix        ! Specific humidity profile (%) -- only needed if gaseous aborption calculated.
99    real(wp),intent(in),dimension(nprof,ngate,rcfg%nhclass) :: &
100         re_matrix,     & ! Table of hydrometeor effective radii.       0 ==> use defaults. (units=microns)
101         hm_matrix        ! Table of hydrometeor mixing ratios (g/kg)
102    real(wp),intent(inout),dimension(nprof,ngate,rcfg%nhclass) :: &
103         Np_matrix        ! Table of hydrometeor number concentration.  0 ==> use defaults. (units = 1/kg)
104
105    ! OUTPUTS
106    real(wp),intent(out), dimension(nprof, ngate) :: &
107         z_vol,         & ! Effective reflectivity factor (mm^6/m^3)
108         kr_vol           ! Attenuation coefficient hydro (dB/km)
109
110    ! INTERNAL VARIABLES   
111    integer :: &
112         phase, ns,tp,j,k,pr,itt,iRe_type,n
113    logical :: &
114         hydro
115    real(wp) :: &
116         t_kelvin,Re_internal
117    real(wp) :: &
118         rho_a,kr,ze,zr,scale_factor,Re,Np,base,step
119
120    real(wp),dimension(:),allocatable :: &
121         Deq,     & ! Discrete drop sizes (um)
122         Ni,      & ! Discrete concentrations (cm^-3 um^-1)
123         rhoi,    & ! Discrete densities (kg m^-3)
124         xxa,     & !
125         Di         ! Discrete drop sizes (um)
126   
127    real(wp), dimension(nprof, ngate) :: &
128         z_ray      ! Reflectivity factor, Rayleigh only (mm^6/m^3)
129   
130    ! PARAMETERS   
131    logical, parameter ::       & !
132         DO_LUT_TEST = .false., & !
133         DO_NP_TEST  = .false.    !
134    real(wp), parameter :: &
135         one_third   = 1._wp/3._wp    !
136
137    ! Initialization
138    z_vol    = 0._wp
139    z_ray    = 0._wp
140    kr_vol   = 0._wp
141
142    do k=1,ngate       ! Loop over each profile (nprof)
143       do pr=1,nprof
144          ! Determine if hydrometeor(s) present in volume
145          hydro = .false.
146          do j=1,rcfg%nhclass
147             if ((hm_matrix(pr,k,j) > 1E-12) .and. (sd%dtype(j) > 0)) then
148                hydro = .true.
149                exit
150             endif
151          enddo
152
153          t_kelvin = t_matrix(pr,k)
154          ! If there is hydrometeor in the volume
155          if (hydro) then
156             rho_a = (p_matrix(pr,k))/(287._wp*(t_kelvin))
157             
158             ! Loop over hydrometeor type
159             do tp=1,rcfg%nhclass
160                Re_internal = re_matrix(pr,k,tp)
161
162                if (hm_matrix(pr,k,tp) <= 1E-12) cycle
163               
164                ! Index into temperature dimension of scaling tables
165                !   These tables have regular steps -- exploit this and abandon infind
166                phase = sd%phase(tp)
167                if (phase==0) then
168                   itt = infind(mt_ttl,t_kelvin)
169                else
170                   itt = infind(mt_tti,t_kelvin)
171                endif
172               
173                ! Compute effective radius from number concentration and distribution parameters
174                if (Re_internal .eq. 0) then
175                   call calc_Re(hm_matrix(pr,k,tp),Np_matrix(pr,k,tp),rho_a, &
176                        sd%dtype(tp),sd%apm(tp),sd%bpm(tp),sd%rho(tp),sd%p1(tp),sd%p2(tp),sd%p3(tp),Re)
177                   Re_internal=Re
178                   !re_matrix(pr,k,tp)=Re
179                else
180                   if (Np_matrix(pr,k,tp) > 0) then
181                      call errorMessage('WARNING(optics/quickbeam_optics.f90): Re and Np set for the same volume & hydrometeor type.  Np is being ignored.')
182                   endif
183                   Re = Re_internal
184                   !Re = re_matrix(pr,k,tp)
185                endif
186               
187                ! Index into particle size dimension of scaling tables
188                iRe_type=1
189                if(Re.gt.0) then
190                   ! Determine index in to scale LUT
191                   ! Distance between Re points (defined by "base" and "step") for
192                   ! each interval of size Re_BIN_LENGTH
193                   ! Integer asignment, avoids calling floor intrinsic
194                   n=Re/Re_BIN_LENGTH
195                   if (n>=Re_MAX_BIN) n=Re_MAX_BIN-1
196                   step = rcfg%step_list(n+1)
197                   base = rcfg%base_list(n+1)
198                   iRe_type=Re/step
199                   if (iRe_type.lt.1) iRe_type=1
200                   Re=step*(iRe_type+0.5_wp)    ! set value of Re to closest value allowed in LUT.
201                   iRe_type=iRe_type+base-int(n*Re_BIN_LENGTH/step)
202                   
203                   ! Make sure iRe_type is within bounds
204                   if (iRe_type.ge.nRe_types) then
205                      !write(*,*) 'Warning: size of Re exceed value permitted ', &
206                      !            'in Look-Up Table (LUT).  Will calculate. '
207                      ! No scaling allowed
208                      iRe_type=nRe_types
209                      rcfg%Z_scale_flag(tp,itt,iRe_type)=.false.
210                   else
211                      ! Set value in re_matrix to closest values in LUT
212                      if (.not. DO_LUT_TEST) re_internal=Re
213                      !if (.not. DO_LUT_TEST) re_matrix(pr,k,tp)=Re
214                   endif
215                endif
216               
217                ! Use Ze_scaled, Zr_scaled, and kr_scaled ... if know them
218                ! if not we will calculate Ze, Zr, and Kr from the distribution parameters
219!                if( rcfg%Z_scale_flag(tp,itt,iRe_type) .and. .not. DO_LUT_TEST)  then
220!                   ! can use z scaling
221!                   scale_factor=rho_a*hm_matrix(pr,k,tp)
222!                   zr = rcfg%Zr_scaled(tp,itt,iRe_type) * scale_factor
223!                   ze = rcfg%Ze_scaled(tp,itt,iRe_type) * scale_factor
224!                   kr = rcfg%kr_scaled(tp,itt,iRe_type) * scale_factor
225!                else
226                if( (.not. rcfg%Z_scale_flag(tp,itt,iRe_type)) .or. DO_LUT_TEST)  then
227                   ! Create a discrete distribution of hydrometeors within volume
228                   select case(sd%dtype(tp))
229                   case(4)
230                      ns = 1
231                      allocate(Di(ns),Ni(ns),rhoi(ns),xxa(ns),Deq(ns))
232                      Di = sd%p1(tp)
233                      Ni = 0._wp
234                   case default
235                      ns = nd   ! constant defined in simulator/quickbeam.f90
236                      allocate(Di(ns),Ni(ns),rhoi(ns),xxa(ns),Deq(ns))
237                      Di = D
238                      Ni = 0._wp
239                   end select
240                   call dsd(hm_matrix(pr,k,tp),re_internal,Np_matrix(pr,k,tp), &
241                        Di,Ni,ns,sd%dtype(tp),rho_a,t_kelvin, &
242                        sd%dmin(tp),sd%dmax(tp),sd%apm(tp),sd%bpm(tp), &
243                        sd%rho(tp),sd%p1(tp),sd%p2(tp),sd%p3(tp))
244                   
245                   ! Calculate particle density
246                   if (phase == 1) then
247                      if (sd%rho(tp) < 0) then
248                         ! Use equivalent volume spheres.
249                         rcfg%rho_eff(tp,1:ns,iRe_type) = rhoice ! solid ice == equivalent volume approach
250                         Deq = ( ( 6/pi*sd%apm(tp)/rhoice) ** one_third ) * ( (Di*1E-6) ** (sd%bpm(tp)/3._wp) )  * 1E6
251                         ! alternative is to comment out above two lines and use the following block
252                         ! MG Mie approach - adjust density of sphere with D = D_characteristic to match particle density
253                         !
254                         ! rcfg%rho_eff(tp,1:ns,iRe_type) = (6/pi)*sd%apm(tp)*(Di*1E-6)**(sd%bpm(tp)-3)   !MG Mie approach
255                         
256                         ! as the particle size gets small it is possible that the mass to size relationship of
257                         ! (given by power law in hclass.data) can produce impossible results
258                         ! where the mass is larger than a solid sphere of ice. 
259                         ! This loop ensures that no ice particle can have more mass/density larger than an ice sphere.
260                         ! do i=1,ns
261                         ! if(rcfg%rho_eff(tp,i,iRe_type) > 917 ) then
262                         ! rcfg%rho_eff(tp,i,iRe_type) = 917
263                         ! endif
264                         ! enddo
265                      else
266                         ! Equivalent volume sphere (solid ice rhoice=917 kg/m^3).
267                         rcfg%rho_eff(tp,1:ns,iRe_type) = rhoice
268                         Deq=Di * ((sd%rho(tp)/rhoice)**one_third)
269                         ! alternative ... coment out above two lines and use the following for MG-Mie
270                         ! rcfg%rho_eff(tp,1:ns,iRe_type) = sd%rho(tp)   !MG Mie approach
271                      endif
272                   else
273                      ! I assume here that water phase droplets are spheres.
274                      ! sd%rho should be ~ 1000  or sd%apm=524 .and. sd%bpm=3
275                      Deq = Di
276                   endif
277
278                   ! Calculate effective reflectivity factor of volume
279                   ! xxa are unused (Mie scattering and extinction efficiencies)
280                   xxa(1:ns) = -9.9_wp
281                   rhoi = rcfg%rho_eff(tp,1:ns,iRe_type)
282                   call zeff(rcfg%freq,Deq,Ni,ns,rcfg%k2,t_kelvin,phase,rcfg%do_ray, &
283                        ze,zr,kr,xxa,xxa,rhoi)
284
285                   ! Test compares total number concentration with sum of discrete samples
286                   ! The second test, below, compares ab initio and "scaled" computations
287                   !    of reflectivity
288                   !  These should get broken out as a unit test that gets called on
289                   !    data. That routine could write to std out.
290                   
291                   ! Test code ... compare Np value input to routine with sum of DSD
292                   ! NOTE: if .not. DO_LUT_TEST, then you are checking the LUT approximation
293                   ! not just the DSD representation given by Ni
294                   if(Np_matrix(pr,k,tp)>0 .and. DO_NP_TEST ) then
295                      Np = path_integral(Ni,Di,1,ns-1)/rho_a*1.E6_wp
296                      ! Note: Representation is not great or small Re < 2
297                      if( (Np_matrix(pr,k,tp)-Np)/Np_matrix(pr,k,tp)>0.1 ) then
298                         call errorMessage('ERROR(optics/quickbeam_optics.f90): Error: Np input does not match sum(N)')
299                      endif
300                   endif
301
302                   ! Clean up space
303                   deallocate(Di,Ni,rhoi,xxa,Deq)
304
305                   ! LUT test code
306                   ! This segment of code compares full calculation to scaling result
307                   if ( rcfg%Z_scale_flag(tp,itt,iRe_type) .and. DO_LUT_TEST )  then
308                      scale_factor=rho_a*hm_matrix(pr,k,tp)
309                      ! if more than 2 dBZe difference print error message/parameters.
310                      if ( abs(10*log10(ze) - 10*log10(rcfg%Ze_scaled(tp,itt,iRe_type) * &
311                           scale_factor)) > 2 ) then
312                         call errorMessage('ERROR(optics/quickbeam_optics.f90): ERROR: Roj Error?')
313                      endif
314                   endif
315                else
316                   ! Use z scaling
317                   scale_factor=rho_a*hm_matrix(pr,k,tp)
318                   zr = rcfg%Zr_scaled(tp,itt,iRe_type) * scale_factor
319                   ze = rcfg%Ze_scaled(tp,itt,iRe_type) * scale_factor
320                   kr = rcfg%kr_scaled(tp,itt,iRe_type) * scale_factor
321                endif  ! end z_scaling
322               
323                kr_vol(pr,k) = kr_vol(pr,k) + kr
324                z_vol(pr,k)  = z_vol(pr,k)  + ze
325                z_ray(pr,k)  = z_ray(pr,k)  + zr
326               
327                ! Construct Ze_scaled, Zr_scaled, and kr_scaled ... if we can
328                if ( .not. rcfg%Z_scale_flag(tp,itt,iRe_type) ) then
329                   if (iRe_type>1) then
330                      scale_factor=rho_a*hm_matrix(pr,k,tp)
331                      rcfg%Ze_scaled(tp,itt,iRe_type) = ze/ scale_factor
332                      rcfg%Zr_scaled(tp,itt,iRe_type) = zr/ scale_factor
333                      rcfg%kr_scaled(tp,itt,iRe_type) = kr/ scale_factor
334                      rcfg%Z_scale_flag(tp,itt,iRe_type) = .true.
335                      rcfg%Z_scale_added_flag(tp,itt,iRe_type)=.true.
336                   endif
337                endif
338             enddo   ! end loop of tp (hydrometeor type)
339          endif
340       enddo
341    enddo
342   
343    where(kr_vol(:,:) <= EPSILON(kr_vol))
344       ! Volume is hydrometeor-free     
345       !z_vol(:,:)  = undef
346       z_ray(:,:)  = undef
347    end where
348
349  end subroutine quickbeam_optics
350  ! ##############################################################################################
351  ! ##############################################################################################
352  subroutine calc_Re(Q,Np,rho_a,dtype,apm,bpm,rho_c,p1,p2,p3,Re) 
353    ! ##############################################################################################
354    ! Purpose:
355    !   Calculates Effective Radius (1/2 distribution 3rd moment / 2nd moment).
356    !
357    !   For some distribution types, the total number concentration (per kg), Np
358    !   may be optionally specified.   Should be set to zero, otherwise.
359    !
360    !   Roj Marchand July 2010
361    !
362    ! Inputs:
363    !
364    !   [Q]        hydrometeor mixing ratio (g/kg)  ! not needed for some distribution types
365    !   [Np]       Optional Total number concentration (per kg).  0 = use defaults (p1, p2, p3)
366    !   [rho_a]    ambient air density (kg m^-3)   
367    !
368    !   Distribution parameters as per quickbeam documentation.
369    !   [dtype]    distribution type
370    !   [apm]      a parameter for mass (kg m^[-bpm])
371    !   [bmp]      b params for mass
372    !   [p1],[p2],[p3]  distribution parameters
373    !
374    ! Outputs:
375    !   [Re]       Effective radius, 1/2 the 3rd moment/2nd moment (um)
376    !
377    ! Created:
378    !   July 2010  Roj Marchand
379    ! Modified:
380    !   12/18/14  Dustin Swales: Define type REALs as double precision (dustin.swales@noaa.gov)
381    !
382    ! ##############################################################################################
383    ! ##############################################################################################
384   
385    ! Inputs
386    real(wp), intent(in)    :: Q,Np,rho_a,rho_c,p1,p2,p3
387    integer,  intent(in)    :: dtype
388    real(wp), intent(inout) :: apm,bpm 
389   
390    ! Outputs
391    real(wp), intent(out) :: Re
392   
393    ! Internal
394    integer  :: local_dtype
395    real(wp) :: local_p3,local_Np,tmp1,tmp2
396    real(wp) :: N0,D0,vu,dm,ld,rg,log_sigma_g        ! gamma, exponential variables
397   
398   
399    ! If density is constant, set equivalent values for apm and bpm
400    if ((rho_c > 0) .and. (apm < 0)) then
401       apm = (pi/6)*rho_c
402       bpm = 3._wp
403    endif
404   
405    ! Exponential is same as modified gamma with vu =1
406    ! if Np is specified then we will just treat as modified gamma
407    if(dtype .eq. 2 .and. Np .gt. 0) then
408       local_dtype = 1
409       local_p3    = 1
410    else
411       local_dtype = dtype
412       local_p3    = p3
413    endif
414    select case(local_dtype)
415       
416       ! ---------------------------------------------------------!
417       ! Modified gamma                                           !
418       ! Np = total number concentration (1/kg) = Nt / rho_a      !
419       ! D0 = characteristic diameter (um)                        !
420       ! dm = mean diameter (um) - first moment over zeroth moment!
421       ! vu = distribution width parameter                        !
422       ! ---------------------------------------------------------!
423    case(1) 
424       
425       if( abs(local_p3+2) < 1E-8) then
426          if(Np>1E-30) then
427             ! Morrison scheme with Martin 1994 shape parameter (NOTE: vu = pc +1)
428             ! fixed Roj. Dec. 2010 -- after comment by S. Mcfarlane
429             vu = (1/(0.2714_wp + 0.00057145_wp*Np*rho_a*1E-6))**2 ! units of Nt = Np*rhoa = #/cm^3
430          else
431             call errorMessage('FATAL ERROR(optics/quickbeam_optics.f90:Calc_Re): Must specify a value for Np in each volume with Morrison/Martin Scheme.')
432             return
433          endif
434       elseif (abs(local_p3+1) > 1E-8) then
435          ! vu is fixed in hp structure 
436          vu = local_p3
437       else
438          ! vu isn't specified
439          call errorMessage('FATAL ERROR(optics/quickbeam_optics.f90:Calc_Re): Must specify a value for vu for Modified Gamma distribution')
440          return
441       endif
442       
443       if( Np.eq.0 .and. p2+1 > 1E-8) then     ! use default value for MEAN diameter as first default 
444          dm = p2             ! by definition, should have units of microns
445          D0 = gamma(vu)/gamma(vu+1)*dm
446       else   ! use value of Np
447          if(Np.eq.0) then
448             if( abs(p1+1) > 1E-8 ) then  !   use default number concentration   
449                local_Np = p1 ! total number concentration / pa --- units kg^-1
450             else
451                call errorMessage('FATAL ERROR(optics/quickbeam_optics.f90:Calc_Re): Must specify Np or default value (p1=Dm [um] or p2=Np [1/kg]) for Modified Gamma distribution')
452                return
453             endif
454          else
455             local_Np=Np;   
456          endif
457          D0 = 1E6 * ( Q*1E-3*gamma(vu)/(apm*local_Np*gamma(vu+bpm)) )**(1/bpm)  ! units = microns
458       endif
459       Re = 0.5_wp*D0*gamma(vu+3)/gamma(vu+2)
460       
461       ! ---------------------------------------------------------!
462       ! Exponential                                              !
463       ! N0 = intercept parameter (m^-4)                          !
464       ! ld = slope parameter (um)                                !
465       ! ---------------------------------------------------------!
466    case(2)
467       
468       ! Np not specified (see if statement above)
469       if((abs(p1+1) > 1E-8) ) then   ! N0 has been specified, determine ld
470          N0   = p1
471          tmp1 = 1._wp/(1._wp+bpm)
472          ld   = ((apm*gamma(1.+bpm)*N0)/(rho_a*Q*1E-3))**tmp1
473          ld   = ld/1E6                     ! set units to microns^-1
474       elseif (abs(p2+1) > 1E-8) then  ! lambda=ld has been specified as default
475          ld = p2     ! should have units of microns^-1
476       else
477          call errorMessage('FATAL ERROR(optics/quickbeam_optics.f90:Calc_Re): Must specify Np or default value (p1=No or p2=lambda) for Exponential distribution')
478          return
479       endif
480       Re = 1.5_wp/ld
481       
482       ! ---------------------------------------------------------!
483       ! Power law                                                !
484       ! ahp = Ar parameter (m^-4 mm^-bhp)                        !
485       ! bhp = br parameter                                       !
486       ! dmin_mm = lower bound (mm)                               !
487       ! dmax_mm = upper bound (mm)                               !
488       ! ---------------------------------------------------------!
489    case(3)
490       
491       Re=0._wp  ! Not supporting LUT approach for power-law ...
492       if(Np>0) then
493          call errorMessage('FATAL ERROR(optics/quickbeam_optics.f90:Calc_Re): Variable Np not supported for Power Law distribution')
494          return
495       endif
496       
497       ! ---------------------------------------------------------!
498       ! Monodisperse                                             !
499       ! D0 = particle diameter (um) == Re                        !
500       ! ---------------------------------------------------------!
501    case(4)
502       
503       Re = p1
504       if(Np>0) then
505          call errorMessage('FATAL ERROR(optics/quickbeam_optics.f90:Calc_Re): Variable Np not supported for Monodispersed distribution')
506          return
507       endif
508       
509       ! ---------------------------------------------------------!
510       ! Lognormal                                                !
511       ! N0 = total number concentration (m^-3)                   !
512       ! np = fixed number concentration (kg^-1)                  !
513       ! rg = mean radius (um)                                    !
514       ! log_sigma_g = ln(geometric standard deviation)           !
515       ! ---------------------------------------------------------!
516    case(5)
517       
518       if( abs(local_p3+1) > 1E-8 ) then
519          !set natural log width
520          log_sigma_g = local_p3
521       else
522          call errorMessage('FATAL ERROR(optics/quickbeam_optics.f90:Calc_Re): Must specify a value for sigma_g when using a Log-Normal distribution')
523          return
524       endif
525       
526       ! get rg ...
527       if( Np.eq.0 .and. (abs(p2+1) > 1E-8) ) then ! use default value of rg
528          rg = p2     
529       else
530          if(Np>0) then
531             local_Np=Np; 
532          elseif(abs(p2+1) < 1E-8) then
533             local_Np=p1
534          else
535             call errorMessage('ERROR(optics/quickbeam_optics.f90:Calc_Re): Must specify Np or default value (p2=Rg or p1=Np) for Log-Normal distribution')
536          endif
537          log_sigma_g = p3
538          tmp1        = (Q*1E-3)/(2._wp**bpm*apm*local_Np)
539          tmp2        = exp(0.5_wp*bpm*bpm*(log_sigma_g))*exp(0.5_wp*bpm*bpm*(log_sigma_g))   
540          rg          = ((tmp1/tmp2)**(1._wp/bpm))*1E6
541       endif
542       Re = rg*exp(2.5_wp*(log_sigma_g*log_sigma_g))   
543    end select
544  end subroutine calc_Re
545  ! ##############################################################################################
546  ! ##############################################################################################
547  subroutine dsd(Q,Re,Np,D,N,nsizes,dtype,rho_a,tk,dmin,dmax,apm,bpm,rho_c,p1,p2,p3)
548    ! ##############################################################################################
549    ! Purpose:
550    !   Create a discrete drop size distribution
551    !
552    !   Starting with Quickbeam V3, this routine now allows input of
553    !   both effective radius (Re) and total number concentration (Nt)
554    !   Roj Marchand July 2010
555    !
556    !   The version in Quickbeam v.104 was modified to allow Re but not Nt
557    !   This is a significantly modified form for the version     
558    !
559    !   Originally Part of QuickBeam v1.03 by John Haynes
560    !   http://reef.atmos.colostate.edu/haynes/radarsim
561    !
562    ! Inputs:
563    !
564    !   [Q]        hydrometeor mixing ratio (g/kg)
565    !   [Re]       Optional Effective Radius (microns).  0 = use defaults (p1, p2, p3)
566    !
567    !   [D]        array of discrete drop sizes (um) where we desire to know the number concentraiton n(D).
568    !   [nsizes]   number of elements of [D]
569    !
570    !   [dtype]    distribution type
571    !   [rho_a]    ambient air density (kg m^-3)
572    !   [tk]       temperature (K)
573    !   [dmin]     minimum size cutoff (um)
574    !   [dmax]     maximum size cutoff (um)
575    !   [rho_c]    alternate constant density (kg m^-3)
576    !   [p1],[p2],[p3]  distribution parameters
577    !
578    ! Input/Output:
579    !   [apm]      a parameter for mass (kg m^[-bpm])
580    !   [bmp]      b params for mass
581    !
582    ! Outputs:
583    !   [N]        discrete concentrations (cm^-3 um^-1)
584    !              or, for monodisperse, a constant (1/cm^3)
585    !
586    ! Requires:
587    !   function infind
588    !
589    ! Created:
590    !   11/28/05  John Haynes (haynes@atmos.colostate.edu)
591    ! Modified:
592    !   01/31/06  Port from IDL to Fortran 90
593    !   07/07/06  Rewritten for variable DSD's
594    !   10/02/06  Rewritten using scaling factors (Roger Marchand and JMH), Re added V1.04
595    !   July 2020 "N Scale factors" (variable fc) removed (Roj Marchand).
596    !   12/18/14  Define type REALs as double precision (dustin.swales@noaa.gov)
597    ! ##############################################################################################
598   
599    ! Inputs
600    integer, intent(in)                   :: &
601         nsizes,& ! Number of elements of [D]
602         dtype    !  distribution type
603    real(wp),intent(in),dimension(nsizes) :: &
604         D        ! Array of discrete drop sizes (um) where we desire to know the number concentraiton n(D).
605    real(wp),intent(in) :: &
606         Q,     & ! Hydrometeor mixing ratio (g/kg)
607         Np,    & !
608         rho_a, & ! Ambient air density (kg m^-3)
609         tk,    & ! Temperature (K)
610         dmin,  & ! Minimum size cutoff (um)
611         dmax,  & ! Maximum size cutoff (um)
612         rho_c, & ! Alternate constant density (kg m^-3)
613         p1,    & ! Distribution parameter 1
614         p2,    & ! Distribution parameter 2
615         p3       ! Distribution parameter 3
616    real(wp),intent(inout) :: &
617         apm,   & ! a parameter for mass (kg m^[-bpm])
618         bpm,   & ! b params for mass
619         Re       ! Optional Effective Radius (microns)
620   
621    ! Outputs
622    real(wp),intent(out),dimension(nsizes) :: &
623         N        ! Discrete concentrations (cm^-3 um^-1)
624                  ! or, for monodisperse, a constant (1/cm^3)
625   
626    ! Internal Variables
627    real(wp),dimension(nsizes) :: &
628         fc
629    real(wp)                   :: &
630         N0,D0,vu,local_np,dm,ld, & ! gamma, exponential variables
631         dmin_mm,dmax_mm,ahp,bhp, & ! power law variables
632         rg,log_sigma_g,          & ! lognormal variables
633         rho_e,                   & ! particle density (kg m^-3)
634         tmp1,tmp2,tc
635    integer :: &
636         k,lidx,uidx
637   
638    ! Convert temperature from Kelvin to Celsius
639    tc = tk - 273.15_wp
640   
641    ! If density is constant, store equivalent values for apm and bpm
642    if ((rho_c > 0) .and. (apm < 0)) then
643       apm = (pi/6)*rho_c
644       bpm = 3._wp
645    endif
646   
647    ! Will preferentially use Re input over Np.
648    ! if only Np given then calculate Re
649    ! if neigher than use other defaults (p1,p2,p3) following quickbeam documentation
650    if(Re==0 .and. Np>0) then
651       call calc_Re(Q,Np,rho_a,dtype,apm,bpm,rho_c,p1,p2,p3,Re)
652    endif
653    select case(dtype)
654       
655       ! ---------------------------------------------------------!
656       ! Modified gamma                                           !
657       ! np = total number concentration                          !
658       ! D0 = characteristic diameter (um)                        !
659       ! dm = mean diameter (um) - first moment over zeroth moment!
660       ! vu = distribution width parameter                        !
661       ! ---------------------------------------------------------!
662    case(1) 
663       
664       if( abs(p3+2) < 1E-8) then
665          if( Np>1E-30) then
666             ! Morrison scheme with Martin 1994 shape parameter (NOTE: vu = pc +1)
667             ! fixed Roj. Dec. 2010 -- after comment by S. Mcfarlane
668             vu = (1/(0.2714_wp + 0.00057145_wp*Np*rho_a*1E-6))**2._wp ! units of Nt = Np*rhoa = #/cm^3
669          else
670             call errorMessage('FATAL ERROR(optics/quickbeam_optics.f90:dsd): Must specify a value for Np in each volume with Morrison/Martin Scheme.')
671             return
672          endif
673       elseif (abs(p3+1) > 1E-8) then
674          ! vu is fixed in hp structure 
675          vu = p3
676       else
677          ! vu isn't specified
678          call errorMessage('FATAL ERROR(optics/quickbeam_optics.f90:dsd): Must specify a value for vu for Modified Gamma distribution')
679          return
680       endif
681       
682       if(Re>0) then
683          D0 = 2._wp*Re*gamma(vu+2)/gamma(vu+3)
684          fc = (((D*1E-6)**(vu-1)*exp(-1*D/D0)) / &
685               (apm*((D0*1E-6)**(vu+bpm))*gamma(vu+bpm))) * 1E-12
686          N  = fc*rho_a*(Q*1E-3)
687       elseif( p2+1 > 1E-8) then     ! use default value for MEAN diameter
688          dm = p2
689          D0 = gamma(vu)/gamma(vu+1)*dm
690          fc = (((D*1E-6)**(vu-1)*exp(-1*D/D0)) / &
691               (apm*((D0*1E-6)**(vu+bpm))*gamma(vu+bpm))) * 1E-12
692          N  = fc*rho_a*(Q*1E-3)
693       elseif(abs(p3+1) > 1E-8)  then! use default number concentration
694          local_np = p1 ! total number concentration / pa check
695          tmp1     = (Q*1E-3)**(1./bpm)
696          fc       = (D*1E-6 / (gamma(vu)/(apm*local_np*gamma(vu+bpm)))**(1._wp/bpm))**vu
697          N        = ((rho_a*local_np*fc*(D*1E-6)**(-1._wp))/(gamma(vu)*tmp1**vu) * &
698               exp(-1._wp*fc**(1._wp/vu)/tmp1)) * 1E-12
699       else
700          call errorMessage('FATAL ERROR(optics/quickbeam_optics.f90:dsd): No default value for Dm or Np provided!')
701          return
702       endif
703       
704       ! ---------------------------------------------------------!
705       ! Exponential                                              !
706       ! N0 = intercept parameter (m^-4)                          !
707       ! ld = slope parameter (um)                                !
708       ! ---------------------------------------------------------!
709    case(2)
710       
711       if(Re>0) then
712          ld = 1.5_wp/Re   ! units 1/um
713          fc = (ld*1E6)**(1.+bpm)/(apm*gamma(1+bpm))*exp(-1._wp*(ld*1E6)*(D*1E-6))*1E-12
714          N  = fc*rho_a*(Q*1E-3)
715       elseif (abs(p1+1) > 1E-8) then
716          ! Use N0 default value
717          N0   = p1
718          tmp1 = 1._wp/(1._wp+bpm)
719          fc   = ((apm*gamma(1.+bpm)*N0)**tmp1)*(D*1E-6)
720          N    = (N0*exp(-1._wp*fc*(1._wp/(rho_a*Q*1E-3))**tmp1)) * 1E-12
721       elseif (abs(p2+1) > 1E-8) then
722          ! Use default value for lambda
723          ld = p2
724          fc = (ld*1E6)**(1._wp+bpm)/(apm*gamma(1+bpm))*exp(-1._wp*(ld*1E6)*(D*1E-6))*1E-12
725          N  = fc*rho_a*(Q*1E-3)
726       else
727          ! ld "parameterized" from temperature (carry over from original Quickbeam).
728          ld = 1220._wp*10._wp**(-0.0245_wp*tc)*1E-6
729          N0 = ((ld*1E6)**(1._wp+bpm)*Q*1E-3*rho_a)/(apm*gamma(1+bpm))
730          N  = (N0*exp(-ld*D)) * 1E-12
731       endif
732       
733       ! ---------------------------------------------------------!
734       ! Power law                                                !
735       ! ahp = Ar parameter (m^-4 mm^-bhp)                        !
736       ! bhp = br parameter                                       !
737       ! dmin_mm = lower bound (mm)                               !
738       ! dmax_mm = upper bound (mm)                               !
739       ! ---------------------------------------------------------!
740    case(3)
741       
742       if(Re>0) then
743          call errorMessage('FATAL ERROR(optics/quickbeam_optics.f90:dsd): Variable Re not supported for Power-Law distribution')
744          return
745       elseif(Np>0) then
746          call errorMessage('FATAL ERROR(optics/quickbeam_optics.f90:dsd): Variable Np not supported for Power-Law distribution')
747          return
748       endif
749       
750       ! br parameter
751       if (abs(p1+2) < 1E-8) then
752          ! if p1=-2, bhp is parameterized according to Ryan (2000),
753          ! applicatable to cirrus clouds
754          if (tc < -30) then
755             bhp = -1.75_wp+0.09_wp*((tc+273._wp)-243.16_wp)
756          elseif ((tc >= -30) .and. (tc < -9)) then
757             bhp = -3.25_wp-0.06_wp*((tc+273._wp)-265.66_wp)
758          else
759             bhp = -2.15_wp
760          endif
761       elseif (abs(p1+3) < 1E-8) then     
762          ! if p1=-3, bhp is parameterized according to Ryan (2000),
763          ! applicable to frontal clouds
764          if (tc < -35) then
765             bhp = -1.75_wp+0.09_wp*((tc+273._wp)-243.16_wp)
766          elseif ((tc >= -35) .and. (tc < -17.5)) then
767             bhp = -2.65_wp+0.09_wp*((tc+273._wp)-255.66_wp)
768          elseif ((tc >= -17.5) .and. (tc < -9)) then
769             bhp = -3.25_wp-0.06_wp*((tc+273._wp)-265.66_wp)
770          else
771             bhp = -2.15_wp
772          endif
773       else
774          ! Otherwise the specified value is used
775          bhp = p1
776       endif
777       
778       ! Ar parameter
779       dmin_mm = dmin*1E-3
780       dmax_mm = dmax*1E-3
781       
782       ! Commented lines are original method with constant density
783       ! rc = 500.       ! (kg/m^3)
784       ! tmp1 = 6*rho_a*(bhp+4)
785       ! tmp2 = pi*rc*(dmax_mm**(bhp+4))*(1-(dmin_mm/dmax_mm)**(bhp+4))
786       ! ahp = (Q*1E-3)*1E12*tmp1/tmp2
787       
788       ! New method is more consistent with the rest of the distributions
789       ! and allows density to vary with particle size
790       tmp1 = rho_a*(Q*1E-3)*(bhp+bpm+1)
791       tmp2 = apm*(dmax_mm**bhp*dmax**(bpm+1)-dmin_mm**bhp*dmin**(bpm+1))
792       ahp  = tmp1/tmp2 * 1E24
793       ! ahp = tmp1/tmp2
794       lidx = infind(D,dmin)
795       uidx = infind(D,dmax)   
796       do k=lidx,uidx
797          N(k) = (ahp*(D(k)*1E-3)**bhp) * 1E-12   
798       enddo
799       
800       ! ---------------------------------------------------------!
801       ! Monodisperse                                             !
802       ! D0 = particle diameter (um)                              !
803       ! ---------------------------------------------------------!
804    case(4)
805       
806       if (Re>0) then
807          D0 = Re
808       else
809          D0 = p1
810       endif
811       
812       rho_e = (6._wp/pi)*apm*(D0*1E-6)**(bpm-3)
813       fc(1) = (6._wp/(pi*D0*D0*D0*rho_e))*1E12
814       N(1)  = fc(1)*rho_a*(Q*1E-3)
815       
816       ! ---------------------------------------------------------!
817       ! Lognormal                                                !
818       ! N0 = total number concentration (m^-3)                   !
819       ! np = fixed number concentration (kg^-1)                  !
820       ! rg = mean radius (um)                                    !
821       ! og_sigma_g = ln(geometric standard deviation)            !
822       ! ---------------------------------------------------------!
823    case(5)
824       if (abs(p1+1) < 1E-8 .or. Re>0 ) then
825          ! rg, log_sigma_g are given
826          log_sigma_g = p3
827          tmp2 = (bpm*log_sigma_g)*(bpm*log_sigma_g)
828          if(Re.le.0) then
829             rg = p2
830          else
831             !rg = Re*exp(-2.5*(log_sigma_g*log_sigma_g))
832             rg =Re*exp(-2.5_wp*(log_sigma_g**2))
833             
834          endif
835         
836          fc = 0.5_wp*((1._wp/((2._wp*rg*1E-6)**(bpm)*apm*(2._wp*pi)**(0.5_wp) * &
837               log_sigma_g*D*0.5_wp*1E-6))*exp(-0.5_wp*((log(0.5_wp*D/rg)/log_sigma_g)**2._wp+tmp2)))*1E-12
838          N = fc*rho_a*(Q*1E-3)
839         
840       elseif (abs(p2+1) < 1E-8 .or. Np>0) then
841          ! Np, log_sigma_g are given   
842          if(Np>0) then
843             local_Np = Np
844          else
845             local_Np = p1
846          endif
847         
848          log_sigma_g = p3
849          N0   = local_np*rho_a
850          tmp1 = (rho_a*(Q*1E-3))/(2._wp**bpm*apm*N0)
851          tmp2 = exp(0.5_wp*bpm*bpm*(log_sigma_g))*exp(0.5_wp*bpm*bpm*(log_sigma_g))
852          rg   = ((tmp1/tmp2)**(1/bpm))*1E6
853         
854          N = 0.5_wp*(N0 / ((2._wp*pi)**(0.5_wp)*log_sigma_g*D*0.5_wp*1E-6) * &
855               exp((-0.5_wp*(log(0.5_wp*D/rg)/log_sigma_g)**2._wp)))*1E-12     
856       else
857          call errorMessage('FATAL ERROR(optics/quickbeam_optics.f90:dsd): Must specify a value for sigma_g')
858          return
859       endif
860    end select
861  end subroutine dsd
862  ! ##############################################################################################
863  ! ##############################################################################################
864  subroutine zeff(freq,D,N,nsizes,k2,tt,ice,xr,z_eff,z_ray,kr,qe,qs,rho_e)
865    ! ##############################################################################################
866    ! Purpose:
867    !   Simulates radar return of a volume given DSD of spheres
868    !   Part of QuickBeam v1.03 by John Haynes
869    !   http://reef.atmos.colostate.edu/haynes/radarsim
870    !
871    ! Inputs:
872    !   [freq]      radar frequency (GHz)
873    !   [D]         discrete drop sizes (um)
874    !   [N]         discrete concentrations (cm^-3 um^-1)
875    !   [nsizes]    number of discrete drop sizes
876    !   [k2]        |K|^2, -1=use frequency dependent default
877    !   [tt]        hydrometeor temperature (K)
878    !   [ice]       indicates volume consists of ice
879    !   [xr]        perform Rayleigh calculations?
880    !   [qe]        if using a mie table, these contain ext/sca ...
881    !   [qs]        ... efficiencies; otherwise set to -1
882    !   [rho_e]     medium effective density (kg m^-3) (-1 = pure)
883    !
884    ! Outputs:
885    !   [z_eff]     unattenuated effective reflectivity factor (mm^6/m^3)
886    !   [z_ray]     reflectivity factor, Rayleigh only (mm^6/m^3)
887    !   [kr]        attenuation coefficient (db km^-1)
888    !
889    ! Created:
890    !   11/28/05  John Haynes (haynes@atmos.colostate.edu)
891    ! Modified:
892    !   12/18/14  Dustin Swales: Define type REALs as double precision (dustin.swales@noaa.gov)
893    ! ##############################################################################################
894    ! Inputs
895    integer,  intent(in) :: &
896         ice,        & ! Indicates volume consists of ice
897         xr,         & ! Perform Rayleigh calculations?
898         nsizes        ! Number of discrete drop sizes
899    real(wp), intent(in),dimension(nsizes) :: &
900         D,     & ! Discrete drop sizes (um)
901         N,     & ! Discrete concentrations (cm^-3 um^-1)
902         rho_e, & ! Medium effective density (kg m^-3) (-1 = pure)
903         qe,    & ! Extinction efficiency, when using Mie tables
904         qs       ! Scatering efficiency, when using Mie tables
905    real(wp),intent(in) :: &
906         freq,  & ! Radar frequency (GHz)
907         tt       ! Hydrometeor temperature (K)
908    real(wp), intent(inout) :: &
909         k2            ! |K|^2, -1=use frequency dependent default
910   
911    ! Outputs
912    real(wp), intent(out) :: &
913         z_eff,      & ! Unattenuated effective reflectivity factor (mm^6/m^3)
914         z_ray,      & ! Reflectivity factor, Rayleigh only (mm^6/m^3)
915         kr            ! Attenuation coefficient (db km^-1)
916   
917    ! Internal Variables
918    integer                     :: correct_for_rho ! Correct for density flag
919    real(wp), dimension(nsizes) :: &
920         D0,        &    ! D in (m)
921         N0,        &    ! N in m^-3 m^-1
922         sizep,     &    ! Size parameter
923         qext,      &    ! Extinction efficiency
924         qbsca,     &    ! Backscatter efficiency
925         f,         &    ! Ice fraction
926         xtemp           !
927    real(wp) :: &
928         wl, cr,eta_sum,eta_mie,const,z0_eff,z0_ray,k_sum,n_r,n_i,dqv(1),dqsc,dg,dph(1)
929    complex(wp)         :: &
930         m,                  &    ! Complex index of refraction of bulk form
931         Xs1(1), Xs2(1)           !
932    integer          :: &
933         i, err                   !
934    integer, parameter :: &
935         one=1                    !
936    real(wp),parameter :: &
937         conv_d  = 1e-6,     &    ! Conversion factor for drop sizes (to m)
938         conv_n  = 1e12,     &    ! Conversion factor for drop concentrations (to m^-3)
939         conv_f  = 0.299792458    ! Conversion for radar frequency (to m)
940    complex(wp),dimension(nsizes) ::&
941         m0             ! Complex index of refraction
942   
943    ! Initialize
944    z0_ray = 0._wp
945   
946    ! Conversions
947    D0 = d*conv_d
948    N0 = n*conv_n
949    wl = conv_f/freq
950   
951    ! // dielectric constant |k^2| defaults
952    if (k2 < 0) then
953       k2 = 0.933_wp
954       if (abs(94.-freq) < 3.) k2=0.75_wp
955       if (abs(35.-freq) < 3.) k2=0.88_wp
956       if (abs(13.8-freq) < 3.) k2=0.925_wp
957    endif
958   
959    if (qe(1) < -9) then
960       
961       ! Get the refractive index of the bulk hydrometeors
962       if (ice == 0) then
963          call m_wat(freq,tt,n_r,n_i)
964       else
965          call m_ice(freq,tt,n_r,n_i)
966       endif
967       m = cmplx(n_r,-n_i)
968       m0(1:nsizes) = m
969       
970       correct_for_rho = 0
971       if ((ice == 1) .and. (minval(rho_e) >= 0)) correct_for_rho = 1
972       
973       ! Correct refractive index for ice density if needed
974       if (correct_for_rho == 1) then
975          f  = rho_e/rhoice
976          m0 = sqrt((2+(m0*m0)+2*f*((m0*m0)-1))/(2+(m0*m0)+f*(1-(m0*m0))))
977       endif
978       
979       ! Mie calculations
980       sizep = (pi*D0)/wl
981       dqv(1) = 0._wp
982       do i=1,nsizes
983          call mieint(sizep(i), m0(i), one, dqv, qext(i), dqsc, qbsca(i), &
984               dg, xs1, xs2, dph, err)
985       end do
986
987    else
988       ! Mie table used
989       qext  = qe
990       qbsca = qs
991    endif
992   
993    ! eta_mie = 0.25*sum[qbsca*pi*D^2*N(D)*deltaD]
994    ! <--------- eta_sum --------->
995    ! z0_eff = (wl^4/!pi^5)*(1./k2)*eta_mie
996    eta_sum = 0._wp
997    if (size(D0) == 1) then
998       eta_sum = qbsca(1)*(n(1)*1E6)*D0(1)*D0(1)
999    else
1000       xtemp = qbsca*N0*D0*D0
1001       call avint(xtemp,D0,nsizes,D0(1),D0(size(D0,1)),eta_sum)
1002    endif
1003   
1004    eta_mie = eta_sum*0.25_wp*pi
1005    const   = ((wl*wl*wl*wl)/(pi*pi*pi*pi*pi))*(1._wp/k2)
1006   
1007    z0_eff  = const*eta_mie
1008   
1009    ! kr = 0.25*cr*sum[qext*pi*D^2*N(D)*deltaD]
1010    ! <---------- k_sum ---------> 
1011    k_sum = 0._wp
1012    if (size(D0) == 1) then
1013       k_sum = qext(1)*(n(1)*1E6)*D0(1)*D0(1)
1014    else
1015       xtemp = qext*N0*D0*D0
1016       call avint(xtemp,D0,nsizes,D0(1),D0(size(D0,1)),k_sum)
1017    endif
1018    ! DS2014 START: Making this calculation in double precision results in a small
1019    !               amount of very small errors in the COSP output field,dBZE94,
1020    !               so it will be left as is.
1021    !cr = 10._wp/log(10._wp)
1022    cr = 10./log(10.)
1023    ! DS2014 STOP
1024    kr = k_sum*0.25_wp*pi*(1000._wp*cr)
1025   
1026    ! z_ray = sum[D^6*N(D)*deltaD]
1027    if (xr == 1) then
1028       z0_ray = 0._wp
1029       if (size(D0) == 1) then
1030          z0_ray = (n(1)*1E6)*D0(1)*D0(1)*D0(1)*D0(1)*D0(1)*D0(1)
1031       else
1032          xtemp = N0*D0*D0*D0*D0*D0*D0
1033          call avint(xtemp,D0,nsizes,D0(1),D0(size(D0)),z0_ray)
1034       endif
1035    endif
1036   
1037    ! Convert to mm^6/m^3
1038    z_eff = z0_eff*1E18 !  10.*alog10(z0_eff*1E18)
1039    z_ray = z0_ray*1E18 !  10.*alog10(z0_ray*1E18)
1040   
1041  end subroutine zeff
1042  ! ##############################################################################################
1043  ! ##############################################################################################
1044  function gases(PRES_mb,T,SH,f)
1045    ! ##############################################################################################
1046    ! Purpose:
1047    !   Compute 2-way gaseous attenuation through a volume in microwave
1048    !
1049    ! Inputs:
1050    !   [PRES_mb]   pressure (mb) (hPa)
1051    !   [T]         temperature (K)
1052    !   [RH]        relative humidity (%)
1053    !   [f]         frequency (GHz), < 300 GHz
1054    !
1055    ! Returns:
1056    !   2-way gaseous attenuation (dB/km)
1057    !
1058    ! Reference:
1059    !   Uses method of Liebe (1985)
1060    !
1061    ! Created:
1062    !   12/09/05  John Haynes (haynes@atmos.colostate.edu)
1063    ! Modified:
1064    !   01/31/06  Port from IDL to Fortran 90
1065    !   12/19/14  Dustin Swales: Define type REALs as double precision (dustin.swales@noaa.gov)
1066    ! ##############################################################################################
1067   
1068    ! INPUTS
1069    real(wp), intent(in) :: & !
1070         PRES_mb,           & ! Pressure (mb) (hPa)
1071         T,                 & ! Temperature (K)
1072         SH,                & ! Specific humidity
1073         f                    ! Frequency (GHz), < 300 GHz
1074   
1075    ! PARAMETERS
1076    integer, parameter   :: & !
1077         nbands_o2  = 48,   & ! Number of O2 bands
1078         nbands_h2o = 30      ! Number of h2o bands
1079    ! LOCAL VARIABLES
1080    real(wp) :: &
1081         gases, th, e, p, sumo, gm0, a0, ap, term1,    &
1082         term2, term3, bf, be, term4, npp,e_th,one_th, &
1083         pth3,eth35,aux1,aux2,aux3, aux4,gm,delt,x,y,  &
1084         gm2,fpp_o2,fpp_h2o,s_o2,s_h2o
1085    integer :: i
1086
1087    ! Table1 parameters  v0, a1, a2, a3, a4, a5, a6 
1088    real(wp),dimension(nbands_o2),parameter ::                                          &
1089         v0 = (/49.4523790,49.9622570,50.4742380,50.9877480,51.5033500,                 &
1090                52.0214090,52.5423930,53.0669060,53.5957480,54.1299999,54.6711570,      &
1091                55.2213650,55.7838000,56.2647770,56.3378700,56.9681000,57.6124810,      &
1092                58.3238740,58.4465890,59.1642040,59.5909820,60.3060570,60.4347750,      &
1093                61.1505580,61.8001520,62.4112120,62.4862530,62.9979740,63.5685150,      &
1094                64.1277640,64.6789000,65.2240670,65.7647690,66.3020880,66.8368270,      &
1095                67.3695950,67.9008620,68.4310010,68.9603060,69.4890210,70.0173420,      &
1096                118.7503410,368.4983500,424.7631200,487.2493700,715.3931500,            &
1097                773.8387300, 834.1453300/),                                             &
1098         a1 = (/0.0000001,0.0000003,0.0000009,0.0000025,0.0000061,0.0000141,            &
1099                0.0000310,0.0000641,0.0001247,0.0002280,0.0003918,0.0006316,0.0009535,  &
1100                0.0005489,0.0013440,0.0017630,0.0000213,0.0000239,0.0000146,0.0000240,  &
1101                0.0000211,0.0000212,0.0000246,0.0000250,0.0000230,0.0000193,0.0000152,  &
1102                0.0000150,0.0000109,0.0007335,0.0004635,0.0002748,0.0001530,0.0000801,  &
1103                0.0000395,0.0000183,0.0000080,0.0000033,0.0000013,0.0000005,0.0000002,  &
1104                0.0000094,0.0000679,0.0006380,0.0002350,0.0000996,0.0006710,0.0001800/),&
1105         a2 = (/11.8300000,10.7200000,9.6900000,8.8900000,7.7400000,6.8400000,          &
1106                6.0000000,5.2200000,4.4800000,3.8100000,3.1900000,2.6200000,2.1150000,  &
1107                0.0100000,1.6550000,1.2550000,0.9100000,0.6210000,0.0790000,0.3860000,  &
1108                0.2070000,0.2070000,0.3860000,0.6210000,0.9100000,1.2550000,0.0780000,  &
1109                1.6600000,2.1100000,2.6200000,3.1900000,3.8100000,4.4800000,5.2200000,  &
1110                6.0000000,6.8400000,7.7400000,8.6900000,9.6900000,10.7200000,11.8300000,&
1111                0.0000000,0.0200000,0.0110000,0.0110000,0.0890000,0.0790000,0.0790000/),&
1112         a3 = (/0.0083000,0.0085000,0.0086000,0.0087000,0.0089000,0.0092000,            &
1113                0.0094000,0.0097000,0.0100000,0.0102000,0.0105000,0.0107900,0.0111000,  &
1114                0.0164600,0.0114400,0.0118100,0.0122100,0.0126600,0.0144900,0.0131900,  &
1115                0.0136000,0.0138200,0.0129700,0.0124800,0.0120700,0.0117100,0.0146800,  &
1116                0.0113900,0.0110800,0.0107800,0.0105000,0.0102000,0.0100000,0.0097000,  &
1117                0.0094000,0.0092000,0.0089000,0.0087000,0.0086000,0.0085000,0.0084000,  &
1118                0.0159200,0.0192000,0.0191600,0.0192000,0.0181000,0.0181000,0.0181000/),&
1119         a4 = (/0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,            &
1120                0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,  &
1121                0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,  &
1122                0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,  &
1123                0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,  &
1124                0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,0.0000000,  &
1125                0.0000000,0.6000000,0.6000000,0.6000000,0.6000000,0.6000000,0.6000000/),&
1126         a5 = (/0.0056000,0.0056000,0.0056000,0.0055000,0.0056000,0.0055000,            &
1127                0.0057000,0.0053000,0.0054000,0.0048000,0.0048000,0.0041700,0.0037500,  &
1128                0.0077400,0.0029700,0.0021200,0.0009400,-0.0005500,0.0059700,-0.0024400,&
1129                0.0034400,-0.0041300,0.0013200,-0.0003600,-0.0015900,-0.0026600,        &
1130                -0.0047700,-0.0033400,-0.0041700,-0.0044800,-0.0051000,-0.0051000,      &
1131                -0.0057000,-0.0055000,-0.0059000,-0.0056000,-0.0058000,-0.0057000,      &
1132                -0.0056000,-0.0056000,-0.0056000,-0.0004400,0.0000000,0.0000000,        &
1133                0.0000000,0.0000000,0.0000000,0.0000000/),                              &
1134         a6 = (/1.7000000,1.7000000,1.7000000,1.7000000,1.8000000,1.8000000,            &
1135                1.8000000,1.9000000,1.8000000,2.0000000,1.9000000,2.1000000,2.1000000,  &
1136                0.9000000,2.3000000,2.5000000,3.7000000,-3.1000000,0.8000000,0.1000000, &
1137                0.5000000,0.7000000,-1.0000000,5.8000000,2.9000000,2.3000000,0.9000000, &
1138                2.2000000,2.0000000,2.0000000,1.8000000,1.9000000,1.8000000,1.8000000,  &
1139                1.7000000,1.8000000,1.7000000,1.7000000,1.7000000,1.7000000,1.7000000,  &
1140                0.9000000,1.0000000,1.0000000,1.0000000,1.0000000,1.0000000,1.0000000/)
1141   
1142    ! Table2 parameters  v1, b1, b2, b3
1143    real(wp),dimension(nbands_h2o),parameter ::                                          &
1144         v1 = (/22.2350800,67.8139600,119.9959400,183.3101170,321.2256440,               &
1145                325.1529190,336.1870000,380.1973720,390.1345080,437.3466670,439.1508120, &
1146                443.0182950,448.0010750,470.8889740,474.6891270,488.4911330,503.5685320, &
1147                504.4826920,556.9360020,620.7008070,658.0065000,752.0332270,841.0735950, &
1148                859.8650000,899.4070000,902.5550000,906.2055240,916.1715820,970.3150220, &
1149                987.9267640/),                                                           &
1150         b1 = (/0.1090000,0.0011000,0.0007000,2.3000000,0.0464000,1.5400000,             &
1151                0.0010000,11.9000000,0.0044000,0.0637000,0.9210000,0.1940000,10.6000000, &
1152                0.3300000,1.2800000,0.2530000,0.0374000,0.0125000,510.0000000,5.0900000, &
1153                0.2740000,250.0000000,0.0130000,0.1330000,0.0550000,0.0380000,0.1830000, &
1154                8.5600000,9.1600000,138.0000000/),                                       &
1155         b2 = (/2.1430000,8.7300000,8.3470000,0.6530000,6.1560000,1.5150000,             &
1156                9.8020000,1.0180000,7.3180000,5.0150000,3.5610000,5.0150000,1.3700000,   &
1157                3.5610000,2.3420000,2.8140000,6.6930000,6.6930000,0.1140000,2.1500000,   &
1158                7.7670000,0.3360000,8.1130000,7.9890000,7.8450000,8.3600000,5.0390000,   &
1159                1.3690000,1.8420000,0.1780000/),                                         &
1160         b3 = (/0.0278400,0.0276000,0.0270000,0.0283500,0.0214000,0.0270000,             &
1161                0.0265000,0.0276000,0.0190000,0.0137000,0.0164000,0.0144000,0.0238000,   &
1162                0.0182000,0.0198000,0.0249000,0.0115000,0.0119000,0.0300000,0.0223000,   &
1163                0.0300000,0.0286000,0.0141000,0.0286000,0.0286000,0.0264000,0.0234000,   &
1164                0.0253000,0.0240000,0.0286000/)
1165
1166    ! Conversions
1167    th     = 300._wp/T                                             ! unitless
1168
1169    ! DS2014 START: Using _wp for the exponential in the denominator results in slight errors
1170    !               for dBze94. 0.01 % of values differ, relative range: 1.03e-05 to  1.78e-04
1171    !e      = (RH*th*th*th*th*th)/(41.45_wp*10**(9.834_wp*th-10))   ! kPa
1172    !e = (RH*th*th*th*th*th)/(41.45_wp*10**(9.834_wp*th-10))   ! kPa
1173    e = SH*PRES_mb/(SH+0.622_wp)/1000._wp !kPa
1174    ! DS2014 END
1175
1176    p      = PRES_mb/1000._wp-e                                      ! kPa
1177    e_th   = e*th
1178    one_th = 1 - th
1179    pth3   = p*th*th*th
1180    eth35  = e*th**(3.5)
1181   
1182    ! Term1
1183    sumo = 0._wp
1184    aux1 = 1.1_wp*e_th
1185    do i=1,nbands_o2
1186       aux2   = f/v0(i)
1187       aux3   = v0(i)-f
1188       aux4   = v0(i)+f
1189       gm     = a3(i)*(p*th**(0.8_wp-a4(i))+aux1)
1190       gm2    = gm*gm
1191       delt   = a5(i)*p*th**a6(i)
1192       x      = aux3*aux3+gm2
1193       y      = aux4*aux4+gm2
1194       fpp_o2 = (((1._wp/x)+(1._wp/y))*(gm*aux2) - (delt*aux2)*((aux3/(x))-(aux4/(x))))
1195       s_o2   = a1(i)*pth3*exp(a2(i)*one_th)
1196       sumo   = sumo + fpp_o2 * s_o2
1197    enddo
1198    term1 = sumo
1199
1200    ! Term2
1201    gm0   = 5.6E-3_wp*(p+1.1_wp*e)*th**(0.8_wp)
1202    a0    = 3.07E-4_wp
1203    ap    = 1.4_wp*(1-1.2_wp*f**(1.5_wp)*1E-5)*1E-10
1204    term2 = (2*a0*(gm0*(1+(f/gm0)*(f/gm0))*(1+(f/60._wp)**2))**(-1) + ap*p*th**(2.5_wp))*f*p*th*th
1205
1206    ! Term3
1207    sumo = 0._wp
1208    aux1 = 4.8_wp*e_th
1209    do i=1,nbands_h2o
1210       aux2    = f/v1(i)
1211       aux3    = v1(i)-f
1212       aux4    = v1(i)+f
1213       gm      = b3(i)*(p*th**(0.8)+aux1)
1214       gm2     = gm*gm
1215       x       = aux3*aux3+gm2
1216       y       = aux4*aux4+gm2
1217       fpp_h2o = ((1._wp/x)+(1._wp/y))*(gm*aux2) ! - (delt*aux2)*((aux3/(x))-(aux4/(x)))
1218       s_h2o   = b1(i)*eth35*exp(b2(i)*one_th)
1219       sumo    = sumo + fpp_h2o * s_h2o
1220    enddo
1221    term3 = sumo
1222
1223    ! Term4
1224    bf    = 1.4E-6_wp
1225    be    = 5.41E-5_wp
1226    term4 = (bf*p+be*e*th*th*th)*f*e*th**(2.5_wp)
1227
1228    ! Summation and result
1229    npp   = term1 + term2 + term3 + term4
1230    gases = 0.182_wp*f*npp
1231   
1232  end function gases
1233 subroutine hydro_class_init(lsingle,ldouble,sd)
1234    ! ##############################################################################################
1235    ! Purpose:
1236    !
1237    !   Initialize variables used by the radar simulator.
1238    !   Part of QuickBeam v3.0 by John Haynes and Roj Marchand
1239    !   
1240    ! Inputs: 
1241    !   NAME            SIZE        DESCRIPTION
1242    !   [lsingle]       (1)         Logical flag to use single moment
1243    !   [ldouble]       (1)         Logical flag to use two moment
1244    ! Outputs:
1245    !   [sd]                        Structure that define hydrometeor types
1246    !
1247    ! Local variables:
1248    !   [n_hydro]       (1)         Number of hydrometeor types
1249    !   [hclass_type]   (nhclass)   Type of distribution (see quickbeam documentation)
1250    !   [hclass_phase]  (nhclass)   1==ice, 0=liquid
1251    !   [hclass_dmin]   (nhclass)   Minimum diameter allowed is drop size distribution N(D<Dmin)=0
1252    !   [hclass_dmax]   (nhclass)   Maximum diameter allowed is drop size distribution N(D>Dmax)=0
1253    !   [hclass_apm]    (nhclass)   Density of partical apm*D^bpm or constant = rho
1254    !   [hclass_bpm]    (nhclass)   Density of partical apm*D^bpm or constant = rho
1255    !   [hclass_rho]    (nhclass)   Density of partical apm*D^bpm or constant = rho
1256    !   [hclass_p1]     (nhclass)   Default values of DSD parameters (see quickbeam documentation)
1257    !   [hclass_p2]     (nhclass)   Default values of DSD parameters (see quickbeam documentation)
1258    !   [hclass_p3]     (nhclass)   Default values of DSD parameters (see quickbeam documentation)   
1259    ! Modified:
1260    !   08/23/2006  placed into subroutine form (Roger Marchand)
1261    !   June 2010   New interface to support "radar_simulator_params" structure
1262    !   12/22/2014  Moved radar simulator (CLOUDSAT) configuration initialization to cloudsat_init
1263    ! ##############################################################################################
1264
1265    ! ####################################################################################
1266    ! NOTES on HCLASS variables
1267    !
1268    ! TYPE - Set to
1269    ! 1 for modified gamma distribution,
1270    ! 2 for exponential distribution,
1271    ! 3 for power law distribution,
1272    ! 4 for monodisperse distribution,
1273    ! 5 for lognormal distribution.
1274        !
1275    ! PHASE - Set to 0 for liquid, 1 for ice.
1276    ! DMIN  - The minimum drop size for this class (micron), ignored for monodisperse.
1277    ! DMAX  - The maximum drop size for this class (micron), ignored for monodisperse.
1278    ! Important note: The settings for DMIN and DMAX are
1279    ! ignored in the current version for all distributions except for power
1280    ! law. Except when the power law distribution is used, particle size
1281    ! is fixed to vary from zero to infinity, a restriction that is expected
1282    ! to be lifted in future versions. A placeholder must still be specified
1283    ! for each.
1284    ! Density of particles is given by apm*D^bpm or a fixed value rho. ONLY specify ONE of these two!!
1285    ! APM - The alpha_m coefficient in equation (1) (kg m**-beta_m )
1286    ! BPM - The beta_m coefficient in equation (1), see section 4.1.
1287    ! RHO - Hydrometeor density (kg m-3 ).
1288    !
1289    ! P1, P2, P3 - are default distribution parameters that depend on the type
1290    ! of distribution (see quickmbeam documentation for more information)
1291    !
1292    ! Modified Gamma (must set P3 and one of P1 or P2)
1293    ! P1 - Set to the total particle number concentration Nt /rho_a (kg-1 ), where
1294    ! rho_a is the density of air in the radar volume.
1295    ! P2 - Set to the particle mean diameter D (micron).
1296    ! P3 - Set to the distribution width nu.
1297    !
1298    ! Exponetial (set one of)
1299    ! P1 - Set to a constant intercept parameter N0 (m-4).
1300    ! P2 - Set to a constant lambda (micron-1).
1301    !
1302    ! Power Law
1303    ! P1 - Set this to the value of a constant power law parameter br
1304    !
1305    ! Monodisperse
1306    ! P1 - Set to a constant diameter D0 (micron) = Re.
1307    !
1308    ! Log-normal (must set P3 and one of P1 or P2)
1309    ! P1 - Set to the total particle number concentration Nt /rho_a (kg-1 )
1310    ! P2 - Set to the geometric mean particle radius rg (micron).
1311    ! P3 - Set to the natural logarithm of the geometric standard deviation.
1312    ! ####################################################################################
1313    ! INPUTS
1314    logical,intent(in) :: &
1315       lsingle, & ! True -> use single moment
1316       ldouble    ! True -> use two moment
1317                     
1318    ! OUTPUTS
1319    type(size_distribution),intent(out) ::&
1320         sd              !
1321
1322   ! SINGLE MOMENT PARAMETERS
1323   integer,parameter,dimension(N_HYDRO) :: &
1324                    ! LSL  LSI  LSR  LSS  CVL  CVI  CVR  CVS  LSG   
1325       HCLASS1_TYPE  = (/5,   1,   2,   2,   5,   1,   2,   2,   2/), & !
1326       HCLASS1_PHASE = (/0,   1,   0,   1,   0,   1,   0,   1,   1/)    !
1327   real(wp),parameter,dimension(N_HYDRO) ::&
1328                      ! LSL   LSI    LSR    LSS    CVL   CVI    CVR    CVS    LSG   
1329       HCLASS1_DMIN = (/ -1.,  -1.,   -1.,   -1.,   -1.,  -1.,   -1.,   -1.,   -1.  /),  &
1330       HCLASS1_DMAX = (/ -1.,  -1.,   -1.,   -1.,   -1.,  -1.,   -1.,   -1.,   -1.  /),  &
1331       HCLASS1_APM  = (/524., 110.8, 524.,   -1.,  524., 110.8, 524.,   -1.,   -1.  /),  &
1332       HCLASS1_BPM  = (/  3.,   2.91,  3.,   -1.,    3.,   2.91,  3.,   -1.,   -1.  /),  &
1333       HCLASS1_RHO  = (/ -1.,  -1.,   -1.,  100.,   -1.,  -1.,   -1.,  100.,  400.  /),  &
1334       HCLASS1_P1   = (/ -1.,  -1.,    8.e6,  3.e6, -1.,  -1.,    8.e6,  3.e6,  4.e6/),  &
1335       HCLASS1_P2   = (/  6.,  40.,   -1.,   -1.,    6.,  40.,   -1.,   -1.,   -1.   /), &
1336       HCLASS1_P3   = (/  0.3,  2.,   -1.,   -1.,    0.3,  2.,   -1.,   -1.,   -1.   /)
1337
1338    ! TWO MOMENT PARAMETERS
1339    integer,parameter,dimension(N_HYDRO) :: &
1340                      ! LSL  LSI  LSR  LSS  CVL  CVI  CVR  CVS  LSG
1341       HCLASS2_TYPE  = (/ 1,   1,   1,   1,   1,   1,   1,   1,   1/), &
1342       HCLASS2_PHASE = (/ 0,   1,   0,   1,   0,   1,   0,   1,   1/)
1343
1344    real(wp),parameter,dimension(N_HYDRO) :: &
1345                      ! LSL    LSI      LSR     LSS   CVL    CVI   CVR     CVS    LSG
1346       HCLASS2_DMIN = (/ -1,     -1,     -1,     -1,    -1,    -1,   -1,     -1,   -1/), &
1347       HCLASS2_DMAX = (/ -1,     -1,     -1,     -1,    -1,    -1,   -1,     -1,   -1/), &       
1348       HCLASS2_APM  = (/524,     -1,    524,     -1,   524,    -1,  524,     -1,   -1/), &
1349       HCLASS2_BPM  = (/  3,     -1,      3,     -1,     3,    -1,    3,     -1,   -1/), &
1350       HCLASS2_RHO  = (/ -1,    500,     -1,    100,    -1,   500,   -1,    100,  900/), &
1351       HCLASS2_P1   = (/ -1,     -1,     -1,     -1,    -1,    -1,   -1,     -1,   -1/), &
1352       HCLASS2_P2   = (/ -1,     -1,     -1,     -1,    -1,    -1,   -1,     -1,   -1/), &
1353       HCLASS2_P3   = (/ -2,      1,      1,      1,    -2,     1,    1,      1,    1/)
1354   
1355    if (lsingle) then   
1356       sd%dtype(1:N_HYDRO) = HCLASS1_TYPE(1:N_HYDRO)
1357       sd%phase(1:N_HYDRO) = HCLASS1_PHASE(1:N_HYDRO)
1358       sd%dmin(1:N_HYDRO)  = HCLASS1_DMIN(1:N_HYDRO)
1359       sd%dmax(1:N_HYDRO)  = HCLASS1_DMAX(1:N_HYDRO)
1360       sd%apm(1:N_HYDRO)   = HCLASS1_APM(1:N_HYDRO)
1361       sd%bpm(1:N_HYDRO)   = HCLASS1_BPM(1:N_HYDRO)
1362       sd%rho(1:N_HYDRO)   = HCLASS1_RHO(1:N_HYDRO)
1363       sd%p1(1:N_HYDRO)    = HCLASS1_P1(1:N_HYDRO)
1364       sd%p2(1:N_HYDRO)    = HCLASS1_P2(1:N_HYDRO)
1365       sd%p3(1:N_HYDRO)    = HCLASS1_P3(1:N_HYDRO)
1366    endif
1367    if (ldouble) then   
1368       sd%dtype(1:N_HYDRO) = HCLASS2_TYPE(1:N_HYDRO)
1369       sd%phase(1:N_HYDRO) = HCLASS2_PHASE(1:N_HYDRO)
1370       sd%dmin(1:N_HYDRO)  = HCLASS2_DMIN(1:N_HYDRO)
1371       sd%dmax(1:N_HYDRO)  = HCLASS2_DMAX(1:N_HYDRO)
1372       sd%apm(1:N_HYDRO)   = HCLASS2_APM(1:N_HYDRO)
1373       sd%bpm(1:N_HYDRO)   = HCLASS2_BPM(1:N_HYDRO)
1374       sd%rho(1:N_HYDRO)   = HCLASS2_RHO(1:N_HYDRO)
1375       sd%p1(1:N_HYDRO)    = HCLASS2_P1(1:N_HYDRO)
1376       sd%p2(1:N_HYDRO)    = HCLASS2_P2(1:N_HYDRO)
1377       sd%p3(1:N_HYDRO)    = HCLASS2_P3(1:N_HYDRO)
1378    endif   
1379  end subroutine hydro_class_init   
1380end module mod_quickbeam_optics
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