subroutine dsd(Q,Re,Np,D,N,nsizes,dtype,rho_a,tk, & dmin,dmax,apm,bpm,rho_c,p1,p2,p3) use array_lib use math_lib implicit none ! Purpose: ! Create a discrete drop size distribution ! ! Starting with Quickbeam V3, this routine now allows input of ! both effective radius (Re) and total number concentration (Nt) ! Roj Marchand July 2010 ! ! The version in Quickbeam v.104 was modified to allow Re but not Nt ! This is a significantly modified form for the version ! ! Originally Part of QuickBeam v1.03 by John Haynes ! http://reef.atmos.colostate.edu/haynes/radarsim ! ! Inputs: ! ! [Q] hydrometeor mixing ratio (g/kg) ! [Re] Optional Effective Radius (microns). 0 = use defaults (p1, p2, p3) ! ! [D] array of discrete drop sizes (um) where we desire to know the number concentraiton n(D). ! [nsizes] number of elements of [D] ! ! [dtype] distribution type ! [rho_a] ambient air density (kg m^-3) ! [tk] temperature (K) ! [dmin] minimum size cutoff (um) ! [dmax] maximum size cutoff (um) ! [rho_c] alternate constant density (kg m^-3) ! [p1],[p2],[p3] distribution parameters ! ! Input/Output: ! [apm] a parameter for mass (kg m^[-bpm]) ! [bmp] b params for mass ! ! Outputs: ! [N] discrete concentrations (cm^-3 um^-1) ! or, for monodisperse, a constant (1/cm^3) ! ! Requires: ! function infind ! ! Created: ! 11/28/05 John Haynes (haynes@atmos.colostate.edu) ! Modified: ! 01/31/06 Port from IDL to Fortran 90 ! 07/07/06 Rewritten for variable DSD's ! 10/02/06 Rewritten using scaling factors (Roger Marchand and JMH), Re added V1.04 ! July 2020 "N Scale factors" (variable fc) removed (Roj Marchand). ! ----- INPUTS ----- integer, intent(in) :: nsizes integer, intent(in) :: dtype real*8, intent(in) :: Q,Re,Np,D(nsizes) real*8, intent(in) :: rho_a,tk,dmin,dmax,rho_c,p1,p2,p3 real*8, intent(inout) :: apm,bpm ! ----- OUTPUTS ----- real*8, intent(out) :: N(nsizes) ! ----- INTERNAL ----- real*8 :: fc(nsizes) real*8 :: & N0,D0,vu,local_np,dm,ld, & ! gamma, exponential variables dmin_mm,dmax_mm,ahp,bhp, & ! power law variables rg,log_sigma_g, & ! lognormal variables rho_e ! particle density (kg m^-3) real*8 :: tmp1, tmp2 real*8 :: pi,rc,tc integer k,lidx,uidx tc = tk - 273.15 pi = acos(-1.0) ! // if density is constant, store equivalent values for apm and bpm if ((rho_c > 0) .and. (apm < 0)) then apm = (pi/6)*rho_c bpm = 3. endif ! will preferentially use Re input over Np. ! if only Np given then calculate Re ! if neigher than use other defaults (p1,p2,p3) following quickbeam documentation if(Re==0 .and. Np>0) then call calc_Re(Q,Np,rho_a, & dtype,dmin,dmax,apm,bpm,rho_c,p1,p2,p3, & Re) endif select case(dtype) ! ---------------------------------------------------------! ! // modified gamma ! ! ---------------------------------------------------------! ! :: np = total number concentration ! :: D0 = characteristic diameter (um) ! :: dm = mean diameter (um) - first moment over zeroth moment ! :: vu = distribution width parameter case(1) if( abs(p3+2) < 1E-8) then if( Np>1E-30) then ! Morrison scheme with Martin 1994 shape parameter (NOTE: vu = pc +1) ! fixed Roj. Dec. 2010 -- after comment by S. Mcfarlane vu = (1/(0.2714 + 0.00057145*Np*rho_a*1E-6))**2.0 ! units of Nt = Np*rhoa = #/cm^3 else print *, 'Error: Must specify a value for Np in each volume', & ' with Morrison/Martin Scheme.' stop endif elseif (abs(p3+1) > 1E-8) then ! vu is fixed in hp structure vu = p3 else ! vu isn't specified print *, 'Error: Must specify a value for vu for Modified Gamma distribution' stop endif if(Re>0) then D0 = 2.0*Re*gamma(vu+2)/gamma(vu+3) fc = ( & ((D*1E-6)**(vu-1)*exp(-1*D/D0)) / & (apm*((D0*1E-6)**(vu+bpm))*gamma(vu+bpm)) & ) * 1E-12 N = fc*rho_a*(Q*1E-3) elseif( p2+1 > 1E-8) then ! use default value for MEAN diameter dm = p2 D0 = gamma(vu)/gamma(vu+1)*dm fc = ( & ((D*1E-6)**(vu-1)*exp(-1*D/D0)) / & (apm*((D0*1E-6)**(vu+bpm))*gamma(vu+bpm)) & ) * 1E-12 N = fc*rho_a*(Q*1E-3) elseif(abs(p3+1) > 1E-8) then! use default number concentration local_np = p1 ! total number concentration / pa check tmp1 = (Q*1E-3)**(1./bpm) fc = (D*1E-6 / (gamma(vu)/(apm*local_np*gamma(vu+bpm)))** & (1./bpm))**vu N = ( & (rho_a*local_np*fc*(D*1E-6)**(-1.))/(gamma(vu)*tmp1**vu) * & exp(-1.*fc**(1./vu)/tmp1) & ) * 1E-12 else print *, 'Error: No default value for Dm or Np provided! ' stop endif ! ---------------------------------------------------------! ! // exponential ! ! ---------------------------------------------------------! ! :: N0 = intercept parameter (m^-4) ! :: ld = slope parameter (um) case(2) if(Re>0) then ld = 1.5/Re ! units 1/um fc = (ld*1E6)**(1.+bpm)/(apm*gamma(1+bpm))* & exp(-1.*(ld*1E6)*(D*1E-6))*1E-12 N = fc*rho_a*(Q*1E-3) elseif (abs(p1+1) > 1E-8) then ! use N0 default value N0 = p1 tmp1 = 1./(1.+bpm) fc = ((apm*gamma(1.+bpm)*N0)**tmp1)*(D*1E-6) N = ( & N0*exp(-1.*fc*(1./(rho_a*Q*1E-3))**tmp1) & ) * 1E-12 elseif (abs(p2+1) > 1E-8) then ! used default value for lambda ld = p2 fc = (ld*1E6)**(1.+bpm)/(apm*gamma(1+bpm))* & exp(-1.*(ld*1E6)*(D*1E-6))*1E-12 N = fc*rho_a*(Q*1E-3) else ! ld "parameterized" from temperature (carry over from original Quickbeam). ld = 1220*10.**(-0.0245*tc)*1E-6 N0 = ((ld*1E6)**(1+bpm)*Q*1E-3*rho_a)/(apm*gamma(1+bpm)) N = ( & N0*exp(-1*ld*D) & ) * 1E-12 endif ! ---------------------------------------------------------! ! // power law ! ! ---------------------------------------------------------! ! :: ahp = Ar parameter (m^-4 mm^-bhp) ! :: bhp = br parameter ! :: dmin_mm = lower bound (mm) ! :: dmax_mm = upper bound (mm) case(3) if(Re>0) then print *, 'Variable Re not supported for ', & 'Power-Law distribution' stop elseif(Np>0) then print *, 'Variable Np not supported for ', & 'Power-Law distribution' stop endif ! :: br parameter if (abs(p1+2) < 1E-8) then ! :: if p1=-2, bhp is parameterized according to Ryan (2000), ! :: applicatable to cirrus clouds if (tc < -30) then bhp = -1.75+0.09*((tc+273)-243.16) elseif ((tc >= -30) .and. (tc < -9)) then bhp = -3.25-0.06*((tc+273)-265.66) else bhp = -2.15 endif elseif (abs(p1+3) < 1E-8) then ! :: if p1=-3, bhp is parameterized according to Ryan (2000), ! :: applicable to frontal clouds if (tc < -35) then bhp = -1.75+0.09*((tc+273)-243.16) elseif ((tc >= -35) .and. (tc < -17.5)) then bhp = -2.65+0.09*((tc+273)-255.66) elseif ((tc >= -17.5) .and. (tc < -9)) then bhp = -3.25-0.06*((tc+273)-265.66) else bhp = -2.15 endif else ! :: otherwise the specified value is used bhp = p1 endif ! :: Ar parameter dmin_mm = dmin*1E-3 dmax_mm = dmax*1E-3 ! :: commented lines are original method with constant density ! rc = 500. ! (kg/m^3) ! tmp1 = 6*rho_a*(bhp+4) ! tmp2 = pi*rc*(dmax_mm**(bhp+4))*(1-(dmin_mm/dmax_mm)**(bhp+4)) ! ahp = (Q*1E-3)*1E12*tmp1/tmp2 ! :: new method is more consistent with the rest of the distributions ! :: and allows density to vary with particle size tmp1 = rho_a*(Q*1E-3)*(bhp+bpm+1) tmp2 = apm*(dmax_mm**bhp*dmax**(bpm+1)-dmin_mm**bhp*dmin**(bpm+1)) ahp = tmp1/tmp2 * 1E24 ! ahp = tmp1/tmp2 lidx = infind(D,dmin) uidx = infind(D,dmax) do k=lidx,uidx N(k) = ( & ahp*(D(k)*1E-3)**bhp & ) * 1E-12 enddo ! print *,'test=',ahp,bhp,ahp/(rho_a*Q),D(100),N(100),bpm,dmin_mm,dmax_mm ! ---------------------------------------------------------! ! // monodisperse ! ! ---------------------------------------------------------! ! :: D0 = particle diameter (um) case(4) if (Re>0) then D0 = Re else D0 = p1 endif rho_e = (6/pi)*apm*(D0*1E-6)**(bpm-3) fc(1) = (6./(pi*D0**3*rho_e))*1E12 N(1) = fc(1)*rho_a*(Q*1E-3) ! ---------------------------------------------------------! ! // lognormal ! ! ---------------------------------------------------------! ! :: N0 = total number concentration (m^-3) ! :: np = fixed number concentration (kg^-1) ! :: rg = mean radius (um) ! :: log_sigma_g = ln(geometric standard deviation) case(5) if (abs(p1+1) < 1E-8 .or. Re>0 ) then ! // rg, log_sigma_g are given log_sigma_g = p3 tmp2 = (bpm*log_sigma_g)**2. if(Re.le.0) then rg = p2 else rg =Re*exp(-2.5*(log_sigma_g**2)) endif fc = 0.5 * ( & (1./((2.*rg*1E-6)**(bpm)*apm*(2.*pi)**(0.5) * & log_sigma_g*D*0.5*1E-6)) * & exp(-0.5*((log(0.5*D/rg)/log_sigma_g)**2.+tmp2)) & ) * 1E-12 N = fc*rho_a*(Q*1E-3) elseif (abs(p2+1) < 1E-8 .or. Np>0) then ! // Np, log_sigma_g are given if(Np>0) then local_Np=Np else local_Np = p1 endif log_sigma_g = p3 N0 = local_np*rho_a tmp1 = (rho_a*(Q*1E-3))/(2.**bpm*apm*N0) tmp2 = exp(0.5*bpm**2.*(log_sigma_g))**2. rg = ((tmp1/tmp2)**(1/bpm))*1E6 N = 0.5*( & N0 / ((2.*pi)**(0.5)*log_sigma_g*D*0.5*1E-6) * & exp((-0.5*(log(0.5*D/rg)/log_sigma_g)**2.)) & ) * 1E-12 else print *, 'Error: Must specify a value for sigma_g' stop endif end select end subroutine dsd