/
BAtoHilmRhoH.f95
739 lines (642 loc) · 27.7 KB
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BAtoHilmRhoH.f95
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subroutine BAtoHilmRhoH(cilm, ba, grid, lmax, nmax, mass, r0, rho, gridtype, &
w, plx, zero, filter_type, filter_deg, lmax_calc, &
exitstatus)
!-------------------------------------------------------------------------------
!
! This routine will compute the next estimate of Moho coefficients
! given an initial estimate of the moho in a gridded data file. This
! is simply Equation 18 in Wieczorek and Phillips (1998), modified to
! take into account lateral variations in density as from eq. 30 of
! Wieczorek (2007). Note that the degree-0 topography must be included
! in the gridded relief. Note that the array plx is optional, and should
! not be precomputed when memory is an issue (i.e., lmax>360).
!
! Calling Parameters
!
! IN
! ba Bouguer Anomaly spherical harmonic coefficients.
! grid Initial estimate of Moho refief, gridded according
! to a call to Makegrid.
! lmax Maxmimum spherical harmonic degree to compute.
! nmax Order of potential coefficient expansion.
! mass Mass of planet.
! R0 The radius that the coefficients are referenced to.
! rho Laterally varying density contrast between the mantle
! and crust.
! gridtype 1 = Gauss-Legendre quadrature grid corresponding
! to LMAX. 2 = N by N Driscoll and Healy grid
! corresponding to LMAX. 3 = N by 2N Driscoll and Healy
! grid corresponding to LMAX.
!
! OUT
! cilm Estimate of Moho relief spherical harmonic coefficients,
! with dimensions (2, lmax+1, lmax+1).
!
! OPTIONAL
! w Gauss-Legendre points used in integrations (for
! GRIDTYPE=1, determined from a call to SHGLQ).
! zero Array of dimension lmax+1 that contains the latitudinal
! gridpoints used in the Gauss-Legendre quadrature
! integration scheme (For GRIDTYPE=1). Only needed if plx
! is not included.
! plx Input array of Associated Legendre Polnomials computed
! at the Gauss points (for GRIDTYPE=1, determined from a
! call to SHGLQ). If this is not included, then the
! optional array zero MUST be inlcuded.
! filter_deg If specified, each interation will be filtered
! according to equation 18 in Wieczorek and Phillips
! (1998), where the value of filter_deg corresponds to
! the spherical harmonic degree where the filter is 1/2.
! filter_type If filter_deg is specified, this must be as well.
! A value of (0) corresponds to none, (1) corresponds to
! the minimum amplitude filter in Wieczorek and Phillips
! (1998), whereas as value of (2) corresponds to a minimum
! curvature filter.
! lmax_calc Maximum degree to compute spherical harmonic
! expansions.
!
! OPTIONAL (OUT)
! exitstatus If present, instead of executing a STOP when an error
! is encountered, the variable exitstatus will be
! returned describing the error.
! 0 = No errors;
! 1 = Improper dimensions of input array;
! 2 = Improper bounds for input variable;
! 3 = Error allocating memory;
! 4 = File IO error.
!
! All units assumed to be SI.
!
! Copyright (c) 2005-2019, SHTOOLS
! All rights reserved.
!
!------------------------------------------------------------------------------
use SHTOOLS, only: SHExpandGLQ, SHExpandDH, DownContFilterMA, &
DownContFilterMC, MakeGridGLQ, MakeGridDH
use ftypes
implicit none
real(dp), intent(out) :: cilm(:,:,:)
real(dp), intent(in) :: ba(:,:,:), grid(:,:), mass, r0, rho(:,:)
real(dp), intent(in), optional :: plx(:,:), zero(:), w(:)
integer(int32), intent(in) :: lmax, nmax, gridtype
integer(int32), intent(in), optional :: filter_type, filter_deg, lmax_calc
integer(int32), intent(out), optional :: exitstatus
real(dp) :: prod, pi, d, filter(lmax+1)
real(dp), allocatable :: cilmn(:, :, :), grid2(:,:)
integer(int32) :: j, l, n, nlong, nlat, astat(2), lmax_out, lmax_calc2, &
n_out
if (present(exitstatus)) exitstatus = 0
pi = acos(-1.0_dp)
if (present(lmax_calc)) then
if (lmax_calc > lmax .or. lmax_calc < 0) then
print*, "Error -- BAtoHilmRhoH"
print*, "LMAX_CALC must be less than or equal to LMAX."
print*, "LMAX = ", lmax
print*, "LMAX_CALC = ", lmax_calc
if (present(exitstatus)) then
exitstatus = 2
return
else
stop
end if
end if
lmax_calc2 = lmax_calc
else
lmax_calc2 = lmax
end if
if (size(cilm(:,1,1)) < 2 .or. size(cilm(1,:,1)) < lmax_calc2+1 .or. &
size(cilm(1,1,:)) < lmax_calc2+1) then
print*, "Error --- BAtoHilmRhoH"
print*, "CILM must be dimensioned as (2, LMAX+1, LMAX+1) " // &
"where LMAX is ", lmax_calc2
print*, "Input dimension is ", size(cilm(:,1,1)), size(cilm(1,:,1)), &
size(cilm(1,1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
else if (size(ba(:,1,1)) < 2 .or. size(ba(1,:,1)) < lmax_calc2+1 .or. &
size(ba(1,1,:)) < lmax_calc2+1) then
print*, "Error --- BAtoHilmRhoH"
print*, "BA must be dimensioned as (2, LMAX+1, LMAX+1) " // &
"where LMAX is ", lmax_calc2
print*, "Input dimension is ", size(ba(:,1,1)), size(ba(1,:,1)), &
size(ba(1,1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
end if
if (gridtype == 1) then
nlat = lmax+1
nlong = 2 * lmax + 1
else if (gridtype == 2) then
nlat = 2 * lmax+2
nlong = nlat
else if (gridtype == 3) then
nlat = 2 * lmax+2
nlong = 2 * nlat
else
print*, "Error --- BAtoHilmRhoH"
print*, "GRIDTYPE must be 1 (Gauss-Legendre Quadrature), " // &
"2 (Driscoll-Healy NxN) or 3 (Driscoll-Healy Nx2N)"
if (present(exitstatus)) then
exitstatus = 2
return
else
stop
end if
end if
if (size(grid(1,:)) < nlong .or. size(grid(:,1)) < nlat .or. &
size(rho(1,:)) < nlong .or. size(rho(:,1)) < nlat) then
print*, "Error --- BAtoHilmRhoH"
print*, "GRID and RHO must be dimensioned as (NLAT, NLONG) where"
print*, "NLAT = ", nlat
print*, "NLONG = ", nlong
print*, "Input dimension of GRID is ", size(grid(1,:)), size(grid(:,1))
print*, "Input dimension of RHO is ", size(rho(1,:)), size(rho(:,1))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
end if
if (present(w)) then
if (gridtype /= 1) then
print*, "Error --- BAtoHilmRhoH"
print*, "W can only be present when GRIDTYPE is 1 " // &
"(Gauss-Legendre Quadrature)"
print*, "GRIDTYPE = ", gridtype
if (present(exitstatus)) then
exitstatus = 5
return
else
stop
end if
else if(size(w) < lmax+1) then
print*, "Error --- BAtoHilmRhoH"
print*, "W must be dimensioned as (LMAX+1) where LMAX is ", lmax
print*, "Input dimension is ", size(w)
if (present(exitstatus)) then
exitstatus = 5
return
else
stop
end if
end if
end if
if (present(zero)) then
if (gridtype /= 1) then
print*, "Error --- BAtoHilmRhoH"
print*, "ZERO can only be present when GRIDTYPE is 1 " //&
"(Gauss-Legendre Quadrature)"
print*, "GRIDTYPE = ", gridtype
if (present(exitstatus)) then
exitstatus = 5
return
else
stop
end if
else if (size(zero) < lmax + 1) then
print*, "Error --- BAtoHilmRhoH"
print*, "ZERO must be dimensioned as (LMAX+1) where LMAX is ", lmax
print*, "Input dimension is ", size(zero)
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
end if
end if
if (present(plx)) then
if (gridtype /= 1) then
print*, "Error --- BAtoHilmRhoH"
print*, "PLX can only be present when GRIDTYPE is 1 " // &
"(Gauss-Legendre Quadrature)"
print*, "GRIDTYPE = ", gridtype
if (present(exitstatus)) then
exitstatus = 5
return
else
stop
end if
else if (size(plx(:,1)) < lmax+1 .or. &
size(plx(1,:)) < (lmax+1)*(lmax+2)/2) then
print*, "Error --- BAtoHilmRhoH"
print*, "PLX must be dimensioned as (LMAX+1, " // &
"(LMAX+1)*(LMAX+2)/2) where LMAX is ", lmax
print*, "Input dimension is ", size(plx(:,1)), size(plx(1,:))
if (present(exitstatus)) then
exitstatus = 1
return
else
stop
end if
end if
end if
if (present(w)) then
if (present(plx) .and. present(zero)) then
print*, "Error --- BAtoHilmRhoH"
print*, "If the optional parameter W is present, then only " // &
"one of PLX and ZERO must also be present."
if (present(exitstatus)) then
exitstatus = 5
return
else
stop
end if
end if
if (.not. present(plx) .and. .not. present(zero)) then
print*, "Error --- BAtoHilmRhoH"
print*, "If the optional parameter W is present, then one " // &
"of PLX or ZERO must also be present."
if (present(exitstatus)) then
exitstatus = 5
return
else
stop
end if
end if
end if
if (present(filter_type)) then
if (filter_type /=0 .and. filter_type /=1 .and. filter_type /=2) then
print*, "Error --- BAtoHilmRhoH"
print*, "FILTER_TYPE must be either 0 (none), " // &
"1 (minimum amplitude), or 2 (minimum curvature)"
print*, "Input value is ", filter_type
if (present(exitstatus)) then
exitstatus = 2
return
else
stop
end if
end if
if (filter_type == 1 .or. filter_type == 2) then
if (.not. present(filter_deg)) then
print*, "Error --- BAtoHilmRhoH"
print*, "If FILTER_TYPE is present and equal to 1 or 2, " // &
"so mush FILTER_DEG."
if (present(exitstatus)) then
exitstatus = 5
return
else
stop
end if
end if
end if
end if
allocate (cilmn(2, lmax_calc2+1, lmax_calc2+1), stat = astat(1))
allocate (grid2(nlat, nlong), stat = astat(2))
if (astat(1) /= 0 .or. astat(2) /= 0) then
print*, "Error --- BAtoHilmRhoH"
print*, "Problem allocating arrays CILMN and GRID2", astat(1), astat(2)
if (present(exitstatus)) then
exitstatus = 3
return
else
stop
end if
end if
!--------------------------------------------------------------------------
!
! Do the expansions
!
!--------------------------------------------------------------------------
cilm = 0.0_dp
cilmn = 0.0_dp
grid2(1:nlat,1:nlong) = grid(1:nlat,1:nlong)
if (gridtype == 1) then
if (present(plx)) then
if (present(exitstatus)) then
call SHExpandGLQ(cilmn, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), &
plx = plx(1:lmax+1, 1:(lmax+1)*(lmax+2)/2), &
norm = 1, csphase = 1, lmax_calc = 0, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandGLQ(cilmn, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), &
plx = plx(1:lmax+1, 1:(lmax+1)*(lmax+2)/2), &
norm = 1, csphase = 1, lmax_calc = 0)
end if
else
if (present(exitstatus)) then
call SHExpandGLQ(cilmn, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), zero = zero(1:lmax+1), &
norm = 1, csphase = 1, lmax_calc = 0, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandGLQ(cilmn, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), zero = zero(1:lmax+1), &
norm = 1, csphase = 1, lmax_calc = 0)
end if
end if
else if (gridtype == 2) then
if (present(exitstatus)) then
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilmn, lmax_out, &
norm = 1, sampling = 1, csphase = 1, &
lmax_calc = 0, exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilmn, lmax_out, &
norm = 1, sampling = 1, csphase = 1, lmax_calc = 0)
end if
else if (gridtype == 3) then
if (present(exitstatus)) then
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilmn, lmax_out, &
norm = 1, sampling = 2, csphase = 1, &
lmax_calc = 0, exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilmn, lmax_out, &
norm = 1, sampling = 2, csphase = 1, lmax_calc = 0)
end if
end if
d = cilmn(1,1,1)
! calculate (rho*h)_00
grid2(1:nlat,1:nlong) = (grid(1:nlat,1:nlong) - d) * rho(1:nlat,1:nlong)
if (gridtype == 1) then
if (present(plx)) then
if (present(exitstatus)) then
call SHExpandGLQ(cilmn, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), &
plx = plx(1:lmax+1, 1:(lmax+1)*(lmax+2)/2), &
norm = 1, csphase = 1, lmax_calc = 0, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandGLQ(cilmn, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), &
plx = plx(1:lmax+1, 1:(lmax+1)*(lmax+2)/2), &
norm = 1, csphase = 1, lmax_calc = 0)
end if
else
if (present(exitstatus)) then
call SHExpandGLQ(cilmn, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), zero = zero(1:lmax+1), &
norm = 1, csphase = 1, lmax_calc = 0, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandGLQ(cilmn, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), zero = zero(1:lmax+1), &
norm = 1, csphase = 1, lmax_calc = 0)
end if
end if
else if (gridtype == 2) then
if (present(exitstatus)) then
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilmn, lmax_out, &
norm = 1, sampling = 1, csphase = 1, &
lmax_calc = 0, exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilmn, lmax_out, &
norm = 1, sampling = 1, csphase = 1, lmax_calc = 0)
end if
else if (gridtype == 3) then
if (present(exitstatus)) then
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilmn, lmax_out, &
norm = 1, sampling = 2, csphase = 1, &
lmax_calc = 0, exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilmn, lmax_out, &
norm = 1, sampling = 2, csphase = 1, lmax_calc = 0)
end if
end if
cilm(1,1,1) = cilmn(1,1,1)
! Calculate first term resulting from Bouguer anomaly
filter = 1.0_dp
if (present(filter_type) .and. present(filter_deg)) then
do l = 1, lmax_calc2
if (filter_type == 1) then
filter(l+1) = DownContFilterMA(l, filter_deg, r0, d)
else if(filter_type == 2) then
filter(l+1) = DownContFilterMC(l, filter_deg, r0, d)
end if
end do
end if
do l = 1, lmax_calc2
cilm(1:2,l+1,1:l+1) = filter(l+1) * ba(1:2,l+1,1:l+1) * mass &
* dble(2*l+1) * ((r0 / d)**l) &
/ (4.0_dp * pi * d**2)
end do
! calculate higher order terms
do n = 2, nmax
grid2(1:nlat,1:nlong) = rho(1:nlat,1:nlong) &
* ((grid(1:nlat,1:nlong) - d) / d)**n
if (gridtype == 1) then
if (present(plx)) then
if (present(exitstatus)) then
call SHExpandGLQ(cilmn, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), &
plx=plx(1:lmax+1, 1:(lmax+1)*(lmax+2)/2), &
norm = 1, csphase = 1, &
lmax_calc = lmax_calc2, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandGLQ(cilmn, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), &
plx=plx(1:lmax+1, 1:(lmax+1)*(lmax+2)/2), &
norm = 1, csphase = 1, &
lmax_calc = lmax_calc2)
end if
else
if (present(exitstatus)) then
call SHExpandGLQ(cilmn, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), zero = zero(1:lmax+1), &
norm = 1, csphase = 1, &
lmax_calc = lmax_calc2, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandGLQ(cilmn, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), zero = zero(1:lmax+1), &
norm = 1, csphase = 1, &
lmax_calc = lmax_calc2)
end if
end if
else if (gridtype == 2) then
if (present(exitstatus)) then
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilmn, lmax_out, &
norm = 1, sampling = 1, csphase = 1, &
lmax_calc = lmax_calc2, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilmn, lmax_out, &
norm = 1, sampling = 1, csphase = 1, &
lmax_calc = lmax_calc2)
end if
else if (gridtype == 3) then
if (present(exitstatus)) then
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilmn, lmax_out, &
norm = 1, sampling = 2, csphase = 1, &
lmax_calc = lmax_calc2, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilmn, lmax_out, &
norm = 1, sampling = 2, csphase = 1, &
lmax_calc = lmax_calc2)
end if
end if
do l = 1, lmax_calc2
prod = 1.0_dp
do j = 1, n
prod = prod * dble(l+4-j)
end do
prod = d * prod / (dble(l+3) * fact(n))
cilm(1:2,l+1,1:l+1) = cilm(1:2,l+1,1:l+1) &
- filter(l+1)*cilmn(1:2,l+1,1:l+1) * prod
end do
end do
! make grid of (h*rho)_lm
if (gridtype == 1) then
if (present(plx)) then
if (present(exitstatus)) then
call MakeGridGLQ(grid2(1:nlat,1:nlong), cilm, lmax, &
plx = plx(1:lmax+1, 1:(lmax+1)*(lmax+2)/2), &
norm = 1, csphase = 1, &
lmax_calc = lmax_calc2, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call MakeGridGLQ(grid2(1:nlat,1:nlong), cilm, lmax, &
plx = plx(1:lmax+1, 1:(lmax+1)*(lmax+2)/2), &
norm = 1, csphase = 1, lmax_calc = lmax_calc2)
end if
else
if (present(exitstatus)) then
call MakeGridGLQ(grid2(1:nlat,1:nlong), cilm, lmax, &
zero = zero(1:lmax+1), norm = 1, csphase = 1,&
lmax_calc = lmax_calc2, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call MakeGridGLQ(grid2(1:nlat,1:nlong), cilm, lmax, &
zero = zero(1:lmax+1), norm = 1, csphase = 1,&
lmax_calc = lmax_calc2)
end if
end if
else if (gridtype == 2) then
if (present(exitstatus)) then
call MakeGridDH(grid2(1:nlat,1:nlong), n_out, cilm, lmax, &
norm = 1, sampling = 1, csphase = 1, &
lmax_calc = lmax_calc2, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call MakeGridDH(grid2(1:nlat,1:nlong), n_out, cilm, lmax, &
norm = 1, sampling = 1, csphase = 1, &
lmax_calc = lmax_calc2)
end if
else if (gridtype == 3) then
if (present(exitstatus)) then
call MakeGridDH(grid2(1:nlat,1:nlong), n_out, cilm, lmax, &
norm = 1, sampling = 2, csphase = 1, &
lmax_calc = lmax_calc2, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call MakeGridDH(grid2(1:nlat,1:nlong), n_out, cilm, lmax, &
norm = 1, sampling = 2, csphase = 1, &
lmax_calc = lmax_calc2)
end if
end if
! convert grid
grid2(1:nlat,1:nlong) = grid2(1:nlat,1:nlong) / rho(1:nlat,1:nlong)
if (gridtype == 1) then
if (present(plx)) then
if (present(exitstatus)) then
call SHExpandGLQ(cilm, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), &
plx = plx(1:lmax+1, 1:(lmax+1)*(lmax+2)/2), &
norm = 1, csphase = 1, &
lmax_calc = lmax_calc2, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandGLQ(cilm, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), &
plx = plx(1:lmax+1, 1:(lmax+1)*(lmax+2)/2), &
norm = 1, csphase = 1, lmax_calc = lmax_calc2)
end if
else
if (present(exitstatus)) then
call SHExpandGLQ(cilm, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), zero = zero(1:lmax+1), &
norm = 1, csphase = 1, &
lmax_calc = lmax_calc2, &
exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandGLQ(cilm, lmax, grid2(1:nlat,1:nlong), &
w(1:lmax+1), zero = zero(1:lmax+1), &
norm = 1, csphase = 1, &
lmax_calc = lmax_calc2)
end if
end if
else if (gridtype == 2) then
if (present(exitstatus)) then
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilm, lmax_out, &
norm = 1, sampling = 1, csphase = 1, &
lmax_calc = lmax_calc2, exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilm, lmax_out, &
norm = 1, sampling = 1, csphase = 1, &
lmax_calc = lmax_calc2)
end if
else if (gridtype == 3) then
if (present(exitstatus)) then
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilm, lmax_out, &
norm = 1, sampling = 2, csphase = 1, &
lmax_calc = lmax_calc2, exitstatus = exitstatus)
if (exitstatus /= 0) return
else
call SHExpandDH(grid2(1:nlat,1:nlong), nlat, cilm, lmax_out, &
norm = 1, sampling = 2, csphase = 1, &
lmax_calc = lmax_calc2)
end if
end if
cilm(1,1,1) = d
deallocate (cilmn)
deallocate (grid2)
CONTAINS
function fact(i)
!----------------------------------------------------------------------
!
! This function computes the factorial of an integer
!
!----------------------------------------------------------------------
implicit none
integer(int32) :: i, j
real(dp) :: fact
if (i == 0) then
fact = 1.0_dp
else if (i < 0) then
print*, "Argument to FACT must be positive"
if (present(exitstatus)) then
exitstatus = 2
return
else
stop
end if
else
fact = 1.0_dp
do j = 1, i
fact = fact * j
end do
end if
end function fact
end subroutine BAtoHilmRhoH