MODULE qf03
!
! Y. Shao, 29 Jan 2004
!
! JY Kang, 01 Dec 2008
! Modify the code for WRF_chem
!
! M. Klose, 2010-2015 Modifications
!-----------------------------------------------------------------------------------
! Calculate sediment flux for multi-particle size soils as a weighted average of Q(d)
! dust emission F(d) for covered and moisture soil
!
! Options for dust calculation:
! 1 Shao (2001)
! 2 Shao (2004)
! 3 Shao (2011): simplification of 2; added on 26 Sep 2009
!
!--------------------------------------------------------------------------------------
!
! input:
! n: number of particle size ranges.
! dm: median diameter of each particle size. [m]
! m_fract: Weight fraction of each particle range. Sum m_fract = 1
! ustar: Friciton velocity. [m/s]
! cf: fraction area covered by roughness elements/vegetation cover
! w: surface soil moisture content [m^3/m^3]
! wr: air-dry soil moisture [m^3/m^3] from SOILPARM.TBL
! c: Owen's coefficient
!
! output:
! ustart: Mean threshold velocity of each particle range.
! q: Sand flux from each size range.
! ffq: Weighted sand flux from each size range.
! qtotal: Total sand flux (weighted average).
! f: Weighted dust flux ejected by single sand size range for given d_d.
! fff: Weighted dust flux ejected by all sand size range from each dust size range.
! ftotal: Total dust flux (weighted average).
!--------------------------------------------------------------------------------------
!
CONTAINS
subroutine qf03_driver ( nmx, idst, g, rhop, rho, dt, &
ustar, w, cf, ust_min, imod, dz_lowest, &
soilc, tot_soilc, domsoilc, &
tc, bems, rough_cor_in, smois_cor_in, wr, &
d0, dd, psd_m, dpsd_m, ppsd_m, psd_f, dpsd_f, ppsd_f, imax, stype)
INTEGER, INTENT(IN ) :: nmx, imod, idst
REAL , INTENT(IN ) :: g, dt, rho, dz_lowest, ustar
REAL(8), INTENT(IN ) :: w
REAL(8), INTENT(INOUT) :: cf
REAL(8), INTENT( OUT) :: ust_min, rough_cor_in, smois_cor_in
REAL , INTENT(INOUT), DIMENSION(nmx) :: tc
REAL , INTENT( OUT), DIMENSION(nmx) :: bems
REAL , INTENT(IN ), DIMENSION(12) :: wr
!kang [2009/01/07] soil class type
REAL, INTENT(IN ) :: tot_soilc
REAL, DIMENSION(16), INTENT(IN) :: soilc
INTEGER, INTENT(IN ) :: domsoilc
integer :: imax, stype
real(8), dimension(0:imax), intent(in) :: d0
real(8), dimension(imax), intent(in) :: dd
real(8), dimension(imax,stype), intent(in) :: psd_m, dpsd_m, ppsd_m
real(8), dimension(imax,stype), intent(in) :: psd_f, dpsd_f, ppsd_f
!local variables
! particle-size distributions
real(8), dimension(imax) :: psdm, dpsdm, ppsdm ! minimally dispersed
real(8), dimension(imax) :: psdf, dpsdf, ppsdf ! fully dispersed
real(8), dimension(imax) :: psds, dpsds, ppsds ! sediment
real(8) :: smois_correc
integer :: i, j, n, kk, ij, ffile
real(8) :: total, qtotal, ftotal
real(8) :: ftotalb, ftotalp
!
real(8), dimension(imax) :: beta_d, beta_s ! beta1 and beta2 used by Shao et al. (1996) dust emission
real(8), dimension(imax) :: ustart, q, ffq, fff
real(8), dimension(imax,imax) :: f
!
real(8), parameter :: c_lambda=0.35
real(8) :: h, lambda
real(8) :: ghl, fc
real(8) :: phl
real(8) :: cys, u0, al0, rhos, smass, omega, rys
real(8) :: ddm, a1, a2, a3
real(8) :: zeta, sigma_m ! u*sqrt(rhos/p), bombardment coefficient
!
real(8) :: ustart0_out, qwhite_out, f_mb_out, f_hlys_out, pmass_out, vhlys_out
!
integer, parameter :: nbins = 5
real(8) :: sigma
real, dimension(nbins) :: dbin, fbin, cell_fbin
integer, dimension(nbins) :: ibin
data dbin/2.,3.6,6.,12.,20./ !size cut diameter (um) consistent with GOCART model
real(8), intent(in) :: rhop
real :: cell_ftotal
integer :: isl, cc
character :: msg, soil
!*******************************************************************************************
!
! initialization
cell_ftotal = 0.
do n = 1, nbins
cell_fbin(n) = 0.
enddo
!
DO cc = 1, 12 ! soil category
if (soilc(cc).eq.0.) then
go to 103
endif
!
psdm(:)=psd_m(:,cc)
psdf(:)=psd_f(:,cc)
dpsdm(:)=dpsd_m(:,cc)
dpsdf(:)=dpsd_f(:,cc)
ppsdm(:)=ppsd_m(:,cc)
ppsdf(:)=ppsd_f(:,cc)
! default settings:
rhos = 1000.d0 ! bulk density of soil [kg/m3]
phl = 30000. ! plastic pressure [N/m2]
cys = 0.00001 ! cys : parameter
sigma = rhop/rho ! particle-air density ratio
!
!-------------------
! frontal area index
!-------------------
if (cf .gt. 0.95) then
write(6,*) 'cover fraction too large, reset'
cf = 0.95
endif! as larger values lead to large lambda, which is problematic in Raupach scheme
lambda = - c_lambda*dlog( 1.d0 - cf )
call r_c(lambda, rough_cor_in)
! Matching WRF_soil class with Shao's class for moisture correction of Fecan (cc:WRF_soil class, isl:Shao's class)
! cc
! 1:sand, 2:loamy sand, 3:sandy loam, 4:silt loam, 5:silt, 6:loam, 7:sandy clay loam,
! 8:silty clay loam, 9:clay loam, 10:sandy clay, 11:silty clay, 12:clay
! isl
! 1:sand, 2:loamy sand, 3:sandy loam, 4:loam, 5:silt loam, 6: silt, 7:sandy clay loam,
! 8:clay loam, 9:silty clay loam, 10:sandy clay, 11:silty clay, 12:clay
if (cc.eq.1.or.cc.eq.2.or.cc.eq.3.or.cc.eq.7.or.cc.eq.10.or. &
& cc.eq.11.or.cc.eq.12) then
isl = cc
elseif (cc.eq.4) then
isl = 5
elseif (cc.eq.5) then
isl = 6
elseif (cc.eq.6) then
isl = 4
elseif (cc.eq.8) then
isl = 9
elseif (cc.eq.9) then
isl = 8
endif
call h_c(w, wr(cc), isl, smois_correc)
!----------------------------------------------
! for each particle size group, estimate ustart
!----------------------------------------------
!
ust_min = 999.0
do i = 1, imax
call ustart0(dd(i), sigma, g, rho, ustart0_out)
ustart(i) = ustart0_out
ustart(i) = rough_cor_in*smois_correc*ustart(i)
ust_min = dmin1(ust_min, ustart(i))
call qwhite(ustart(i), ustar, rho, g, qwhite_out)
q(i) = qwhite_out
q(i) = (1.d0-cf)*q(i)
enddo
if (cc.eq.domsoilc) then
smois_cor_in = smois_correc
endif
!
!
IF ( ustar .le. ust_min ) THEN ! no erosion goto 102
q = 0.d0
ffq = 0.d0
qtotal = 0.d0
fff = 0.d0
ftotal = 0.d0
fbin = 0.d0
goto 102
ELSE
ghl = dexp( -(ustar - ust_min)**3.d0 )
dpsds = ghl*dpsdm + (1.-ghl)*dpsdf
psds = ghl*psdm + (1.-ghl)*psdf
ppsds = ghl*ppsdm + (1.-ghl)*ppsdf
!
ffq = q*dpsds
qtotal = sum(ffq)
!--------------
! dust emission
!--------------
!
! size bin
do n=1,nbins
ibin(n)=0
do i=imax,1,-1
if(d0(i).ge.dbin(n)) ibin(n)=i
enddo
if(ibin(n).eq.0) stop 'wrong dust classes'
enddo
!
!
!
!--------------------------------
! Shao (2001) dust emission model
!--------------------------------
IF (imod .eq. 1) THEN
do i = idst+1, imax
ddm = dd(i)*1.d-6
call pmass(rhop, ddm, pmass_out) ! mass of saltating particles
smass = pmass_out
u0 = 10*ustar
al0 = 13.d0*3.14159d0/180.d0
call vhlys(phl, 2, smass, al0, u0, ddm, vhlys_out)
omega = vhlys_out ![m3]
!
do j = 1, idst
rys = psdm(j)/psdf(j)
if (rys.gt.1.) then
rys = 1.
endif
a1 = cys*( (1.-ghl) + ghl*rys )
a2 = ffq(i)*g/ustar**2/smass
if ( dpsdf(j) .lt. dpsdm(j) ) then
a3 = dpsdf(j)*rhos*omega
else
a3 = dpsdf(j)*rhos*omega + (dpsdf(j)-dpsdm(j))*smass
endif
f(i,j) = a1*a2*a3 ![kg/m2/s]
enddo
enddo
!
ftotal = 0.0
do j = 1, idst
fff(j) = 0.
do i = idst+1, imax
fff(j) = fff(j) + f(i,j)
enddo
fff(j) = (1.d0-cf)*fff(j)
ftotal = ftotal + fff(j)
enddo
!
do n=1,nbins
j0=1
if(n.gt.1) j0=ibin(n-1)+1
fbin(n)=0
do j=j0,ibin(n)
fbin(n)=fbin(n)+fff(j)
enddo
enddo
!
!--------------------------------
! Shao (2004) dust emission model
!--------------------------------
ELSEIF (imod .eq. 2) THEN
zeta = ustar*dsqrt( rhos/phl )
sigma_m = 12.d0*zeta*zeta*(1.d0+14.d0*zeta)
!
do i = idst+1, imax
do j = 1, idst
rys = psdm(j)/psdf(j)
if (rys .gt.1.) then
rys = 1.
endif
a1 = cys*dpsdf(j)*( (1.-ghl) + ghl*rys )
a2 = (1.+sigma_m)
a3 = ffq(i)*g/ustar**2
f(i,j) = a1*a2*a3
enddo
enddo
!
ftotal = 0.0
do j = 1, idst
fff(j) = 0.
do i = idst+1, imax
fff(j) = fff(j) + f(i,j)
enddo
fff(j) = (1.d0-cf)*fff(j)
ftotal = ftotal + fff(j)
enddo
!
do n=1,nbins
j0=1
if(n.gt.1) j0=ibin(n-1)+1
fbin(n)=0
do j=j0,ibin(n)
fbin(n)=fbin(n)+fff(j)
enddo
enddo
!
!
!--------------------------------------------------------------------------
! Shao (2011) minimal version, ghl = 1, Q independent of sand particle size
!
! See Eq. (34) in
! Shao, Y., M. Ishizuka, M. Mikami, J. Leys (2011): Parameterization of size-
! resolved dust emission and validation with measurements, JGR, 116, D08203,
! doi: 10.1029/2010JD014527
!--------------------------------------------------------------------------
ELSEIF (imod .eq. 3) THEN
zeta = ustar*dsqrt( rhos/phl )
sigma_m = 12.d0*zeta*zeta*(1.d0+14.d0*zeta)
!
ftotal = 0.0
!
do j = 1, idst
a1 = cys*dpsdm(j)
a2 = (1.+sigma_m)
a3 = qtotal*g/ustar**2
fff(j) = a1*a2*a3
fff(j) = (1.d0-cf)*fff(j)
ftotal = ftotal + fff(j)
enddo
!
do n=1,nbins
j0=1
if(n.gt.1) j0=ibin(n-1)+1
fbin(n)=0
do j=j0,ibin(n)
fbin(n)=fbin(n)+fff(j)
enddo
enddo
!
ENDIF ! dust scheme
ENDIF ! ust < ust_t
!
!
!
102 continue
do n = 1, nbins
cell_fbin(n) = cell_fbin(n) + (soilc(cc)/tot_soilc)*fbin(n)
enddo
103 continue
ENDDO ! cc, soil category
do n = 1, nbins
! fbin : [kg/m2/s], dz_lowest : [m], rho : [kg/m3], dt : [s] -> tc : [kg/kg-dryair]
tc(n) = tc(n) + cell_fbin(n)/dz_lowest/rho*dt ![kg/kg-dryair]
bems(n) = cell_fbin(n) ![kg/m2/s]
enddo
END subroutine qf03_driver
!*****************************************************************************
subroutine ustart0(dum, sigma, g, rho, ustart0_out)
!
! Y. Shao, 13 June 2000
!
! Calculate ustar0(d) using Shao and Lu (2000) for uncovered
! dry surface
!
! dum: particle diameter [um]
! ustar0: threshold friction velocity [m/s]
!
real, intent(in) :: g, rho
real(8), intent(in) :: dum, sigma
real(8), intent(out) :: ustart0_out
real(8) :: dm
real(8), parameter :: gamma = 1.65d-4 ! a constant
real(8), parameter :: f = 0.0123
dm = dum*1d-6
ustart0_out = f*(sigma*g*dm + gamma/(rho*dm) )
ustart0_out = dsqrt( ustart0_out )
! end function
end subroutine ustart0
!*****************************************************************************
subroutine qwhite(ust, ustar, rho, g, qwhite_out)
!
! Yaping Shao 17-07-99!
!
! White (1979) Sand Flux Equation
! Q = c*rho*u_*^3 over g (1 - u_*t over u_*)(1 + u_*t^2/u_*^2)
! qwhite: Streamwise Sand Flux; [kg m-1 s-1]
! c : 2.6
! ust : threhold friction velocity [m/s]
! ustar : friction velocity [m/s]
!
real(8) :: c
real, intent(in) :: ustar, rho, g
real(8), intent(in) :: ust
real(8), intent(out) :: qwhite_out
real(8) :: a, b
! default setting:
c = 2.3d0
a = rho/g
IF (ustar.lt.ust) THEN
qwhite_out = 0.d0
ELSE
b = ust/ustar
qwhite_out = c*a*ustar**3.*(1.-b)*(1.+b)**2.
ENDIF
END subroutine qwhite
!*****************************************************************************
subroutine vhlys(p, k, xm, alpha, u, d, vhlys_out)
!
! Volume removal according to Lu and Shao (1999), Equation (8)
! alpha: impact angle [^o]
! u : impact velocity [m/s]
! p : plastic pressure [N/m^2]
! xm : particle mass [kg]
! d : particle diameter [m]
!
!
REAL(8),intent(in) :: alpha, xm, u, d, p
REAL(8) :: beta
REAL(8), PARAMETER :: pi=3.1415927d0
REAL(8) :: t1, t2, t3
INTEGER,intent(in) :: k
real(8),intent(out) :: vhlys_out
beta = dsqrt( p*k*d/xm )
t1 = u*u/(beta*beta)*( dsin(2.d0*alpha) - 4.d0*dsin(alpha)*dsin(alpha) )
t2 = u*dsin(alpha)/beta
t3 = 7.5d0*pi*t2**3.d0/d
vhlys_out = d*( t1 + t3 )
END subroutine vhlys
!*****************************************************************************
! A routine for correction of ust for soil moisture content
!
! w : volumetric soil moisture
! isl: soil texture type, ranging from 1 to 12
!
! Author: Yaping Shao, 5/05/2001
! Reference: Fecan et al. (1999), Ann. Geophysicae,17,149-157
!
! Data based on Shao and Jung, 2000, unpublished manuscript
! Data invented for sand, loamy sand, sandy loam, loam, clay loam, and clay
! Soil classes:
! 1 sand, 2 loamy sand, 3 sandy loam, 4 loam, 5 silty loam, 6 silt, 7 sandy clay loam, 8 clay loam,
! 9 silty clay loam, 10 sandy clay, 11 silty clay, 12 clay
!----------------------------------------------------------------------
subroutine h_c (w, wr, isl, h)
real(8) :: a(12), b(12)!, thr(12)
real(8), intent(in) :: w
real(8), intent(out) :: h
real, intent(in) :: wr
integer, intent(in) :: isl
character*100 :: msg ! error message string
! data thr/0.001, 0.003, 0.037, 0.049, 0.061, 0.072, 0.084, 0.095, 0.110, 0.126, 0.141, 0.156/
data a /21.19, 33.03, 44.87, 17.79, 20.81, 23.83, 26.84, 29.86, 27.51, 25.17, 22.82, 20.47/
data b / 0.68, 0.71, 0.85, 0.61, 0.66, 0.71, 0.75, 0.80, 0.75, 0.70, 0.64, 0.59/
if ( w.lt.0. ) then
write(msg, *) 'soil moisture correction (h_c): w = ', w, ' < 0'
call wrf_error_fatal(msg)
! stop
endif
if ( w.le.wr ) then
h = 1.0
else
h = sqrt( 1 + a(isl)*( w-wr )**b(isl) )
endif
END subroutine h_c
!*****************************************************************************
subroutine pmass(rhop, d, pmass_out)
!
! Particle Mass
! rhop: particle density [kg m^-3]
! d : particle size [m]
!
REAL(8), PARAMETER :: pi=3.1415927d0
REAL(8),intent(in) :: rhop, d
real(8),intent(out) :: pmass_out
pmass_out = (pi*rhop*d**3.d0)/6.d0
END subroutine pmass
!*****************************************************************************
subroutine r_c (x,r)
!
! Y. Shao 17-07-92
! CORRECTION FUNCTION FOR UST(D) BASED ON Raupach et al. (1992)
! x = frontal area index
!
! R_C = (1 - sig m x)^{1/2} (1 + m beta x)^{1/2}
! Note I deife R_C = u_{*tR}/u_{*tS}
! While Raupach et al. defined
! R_C = u_{*tS}/u_{*tR} and their R function is
! R_C = (1 - sig m x)^{-1/2} (1 + m beta x)^{-1/2}
!
! sig : basal to frontal area; about 1
! m : parameter less than 1; about 0.5
! beta : a ratio of drag coef.; about 90. ; changed to 200 (recommendation by Y. Shao based on data by Gillies et al.)
!
real(8) :: xc
real(8), intent(in) :: x
real(8), intent(out) :: r
real(8), parameter :: sig=1., m=0.5, beta=200.
!
xc = 1./(sig*m)
IF (x.ge.xc) THEN
r = 999. ! Full covered surface
ELSE
r = dsqrt(1.-sig*m*x)*dsqrt(1.+m*beta*x)
ENDIF
!
END subroutine r_c
END MODULE qf03