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SwanDiffPar.ftn90
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SwanDiffPar.ftn90
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subroutine SwanDiffPar ( ac2, dep2, spcsig )
!
! --|-----------------------------------------------------------|--
! | Delft University of Technology |
! | Faculty of Civil Engineering and Geosciences |
! | Environmental Fluid Mechanics Section |
! | P.O. Box 5048, 2600 GA Delft, The Netherlands |
! | |
! | Programmer: Marcel Zijlema |
! --|-----------------------------------------------------------|--
!
!
! SWAN (Simulating WAves Nearshore); a third generation wave model
! Copyright (C) 1993-2024 Delft University of Technology
!
! This program is free software: you can redistribute it and/or modify
! it under the terms of the GNU General Public License as published by
! the Free Software Foundation, either version 3 of the License, or
! (at your option) any later version.
!
! This program is distributed in the hope that it will be useful,
! but WITHOUT ANY WARRANTY; without even the implied warranty of
! MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
! GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License
! along with this program. If not, see <http://www.gnu.org/licenses/>.
!
!
! Authors
!
! 41.02: Marcel Zijlema
!
! Updates
!
! 41.02, February 2009: New subroutine
!
! Purpose
!
! Computes diffraction parameter and its derivatives in vertices
!
! Method
!
! Diffraction is approximated using the eikonal equation which
! relates the wavenumber K to the separation factor k. Several
! expressions of the eikonal equation have been presented in
! the literature:
! DH
! Battjes (1968): K^2 = k^2 + --
! H
!
! where H is the wave height and D is the Laplacian operator.
!
! D.(pDH)
! Berkhoff (1972): K^2 = k^2 + -------
! pH
!
! where p = cc_g and D is the gradient operator in this case.
!
! In both cases, the eikonal equation may be written as follows:
!
! K = k (1+delta)^0.5
!
! with
!
! D.(pDH)
! delta = -------
! k^2 pH
!
! From implementation point of view, the Battjes' eikonal
! equation can be obtained if
! c_g = k
!
! Modules used
!
use ocpcomm4
use swcomm2
use swcomm3
use swcomm4
use m_diffr
use SwanGriddata
use SwanGridobjects
!
implicit none
!
! Argument variables
!
real, dimension(MDC,MSC,nverts), intent(in) :: ac2 ! action density at current time level
real, dimension(nverts), intent(in) :: dep2 ! water depth at current time level
real, dimension(MSC), intent(in) :: spcsig ! relative frequency bins
!
! Local variables
!
integer :: icell ! index of present cell
integer, save :: ient = 0 ! number of entries in this subroutine
integer :: ivert ! loop counter over vertices
integer :: jc ! loop counter
integer :: jcell ! index of next cell
integer, parameter :: jeiko=1 ! choice parameter:
! 0 = eikonal equation according to Battjes (1968)
! 1 = eikonal equation according to Berkhoff (1972)
!
integer, dimension(3) :: v ! vertices in present cell
!
real :: area0 ! area of present cell
real :: area1 ! area of next cell
double precision :: carea ! twices the area of centroid dual around present vertex
real :: cg0 ! mean group velocity in centroid of present cell
real :: cg1 ! mean group velocity in centroid of next cell
real :: cslat ! cosine of latitude
real :: ctot ! zeroth moment of energy times group velocity
real :: delta ! local diffraction parameter
real :: denom ! a denominator
real :: deploc ! local depth
real :: dgx0 ! x-component of diffusion gradient inside present cell
real :: dgx1 ! x-component of diffusion gradient inside next cell
real :: dgxdx ! x-gradient of x-diffusion gradient component
real :: dgy0 ! y-component of diffusion gradient inside present cell
real :: dgy1 ! y-component of diffusion gradient inside next cell
real :: dgydy ! y-gradient of y-diffusion gradient component
real :: dhsdx ! x-gradient of wave height
real :: dhsdy ! y-gradient of wave height
real :: difp0 ! diffraction parameter in centroid of present cell
real :: difp1 ! diffraction parameter in centroid of next cell
real :: etot ! zeroth moment of the variance spectrum
real :: fmax ! upper bound of frequency space for integration
real :: fmin ! lower bound of frequency space for integration
real :: k0 ! mean wave number in centroid of present cell
real :: k1 ! mean wave number in centroid of next cell
real :: ktot ! zeroth moment of energy times wave number
double precision :: x0 ! x-coordinate of the centroid of present cell
double precision :: x1 ! x-coordinate of the centroid of next cell
double precision :: y0 ! y-coordinate of the centroid of present cell
double precision :: y1 ! y-coordinate of the centroid of next cell
!
real, dimension(MSC) :: cgloc ! group velocity
real, dimension(MSC) :: kloc ! wave number
real, dimension(MSC) :: n ! ratio of group and phase velocity
real, dimension(MSC) :: nd ! derivative of n with respect to depth
real, dimension(MDC) :: ecs ! help array containing (co)sine of spectral directions
!
real, dimension(:), allocatable :: cg ! mean group velocity
real, dimension(:), allocatable :: hs ! wave height
real, dimension(:), allocatable :: k ! mean wave number
!
real :: SwanIntgratSpc ! integration of variance over a part of frequency space
!
type(celltype), dimension(:), pointer :: cell ! datastructure for cells with their attributes
type(verttype), dimension(:), pointer :: vert ! datastructure for vertices with their attributes
!
! Structure
!
! Description of the pseudo code
!
! Source text
!
if (ltrace) call strace (ient,'SwanDiffPar')
!
! point to vertex and cell objects
!
vert => gridobject%vert_grid
cell => gridobject%cell_grid
!
! allocation and initialization of wave height and mean wave parameters
!
allocate(hs(nverts))
allocate( k(nverts))
allocate(cg(nverts))
!
hs = 0.
k = 10.
cg = 0.
!
! compute total energy, mean wave number and mean group velocity in vertices
!
do ivert = 1, nverts
!
deploc = dep2(ivert)
!
if ( deploc <= DEPMIN ) cycle
!
! compute group velocity and wave number for all frequencies
!
call KSCIP1 (MSC,spcsig,deploc,kloc,cgloc,n,nd)
!
! integration over f in [0,infty]
!
fmin = 0.
fmax = 1000.
ecs = 1.
!
etot = SwanIntgratSpc(0. , fmin, fmax, spcsig, ecs, &
kloc , ecs , 0. , 0. , ac2(:,:,ivert), &
1 )
!
ktot = SwanIntgratSpc(1. , fmin, fmax, spcsig, ecs, &
kloc , ecs , 0. , 0. , ac2(:,:,ivert), &
3 )
!
ctot = SwanIntgratSpc(1. , fmin, fmax, spcsig, ecs, &
cgloc, ecs , 0. , 0. , ac2(:,:,ivert), &
4 )
!
if ( etot > 0. ) then
hs(ivert) = 4.*sqrt(etot)
k (ivert) = ktot/etot
cg(ivert) = ctot/etot
endif
!
enddo
!
if ( jeiko == 0 ) cg = k
!
! compute diffraction parameter in vertices
!
DIFPARAM = 1.
!
vertexloop : do ivert = 1, nverts
!
if ( vert(ivert)%atti(VMARKER) == 1 ) cycle vertexloop ! boundary vertex
!
cslat = cos(DEGRAD*(vert(ivert)%attr(VERTY) + YOFFS))
!
! compute contributions to the Laplacian in present vertex
!
carea = 0d0
dgxdx = 0.
dgydy = 0.
!
! loop over cells around considered vertex
!
do jc = 1, vert(ivert)%noc
!
! get present cell and its vertices
!
icell = vert(ivert)%cell(jc)%atti(CELLID)
!
v(1) = cell(icell)%atti(CELLV1)
v(2) = cell(icell)%atti(CELLV2)
v(3) = cell(icell)%atti(CELLV3)
!
if ( dep2(v(1)) <= DEPMIN .or. dep2(v(2)) <= DEPMIN .or. dep2(v(3)) <= DEPMIN ) cycle vertexloop
!
! determine centroid of present cell
!
x0 = cell(icell)%attr(CELLCX)
y0 = cell(icell)%attr(CELLCY)
area0 = cell(icell)%attr(CELLAREA)
!
! determine mean wave number and group velocity in centroid in present cell
!
cg0 = ( cg(v(1)) + cg(v(2)) + cg(v(3)) )/ 3.
k0 = ( k (v(1)) + k (v(2)) + k (v(3)) )/ 3.
!
! determine derivatives of wave height inside present cell
!
dhsdx = 0.5*( hs(v(1))*(ycugrd(v(2))-ycugrd(v(3))) + &
hs(v(2))*(ycugrd(v(3))-ycugrd(v(1))) + &
hs(v(3))*(ycugrd(v(1))-ycugrd(v(2))) )/area0
!
dhsdy = 0.5*( hs(v(1))*(xcugrd(v(3))-xcugrd(v(2))) + &
hs(v(2))*(xcugrd(v(1))-xcugrd(v(3))) + &
hs(v(3))*(xcugrd(v(2))-xcugrd(v(1))) )/area0
!
! in case of spherical coordinates, transform back to Cartesian coordinates
!
if ( KSPHER > 0 ) then
!
dhsdx = dhsdx/(cslat * LENDEG)
dhsdy = dhsdy/LENDEG
!
endif
!
! determine diffusion gradients in centroid of present cell
!
dgx0 = cg0*dhsdx/k0
dgy0 = cg0*dhsdy/k0
!
! get next cell in counterclockwise direction
!
jcell = vert(ivert)%cell(jc)%atti(NEXTCELL)
!
v(1) = cell(jcell)%atti(CELLV1)
v(2) = cell(jcell)%atti(CELLV2)
v(3) = cell(jcell)%atti(CELLV3)
!
! determine centroid of next cell
!
x1 = cell(jcell)%attr(CELLCX)
y1 = cell(jcell)%attr(CELLCY)
area1 = cell(jcell)%attr(CELLAREA)
!
! determine mean wave number and group velocity in centroid in next cell
!
cg1 = ( cg(v(1)) + cg(v(2)) + cg(v(3)) )/ 3.
k1 = ( k (v(1)) + k (v(2)) + k (v(3)) )/ 3.
!
! determine derivatives of wave height inside next cell
!
dhsdx = 0.5*( hs(v(1))*(ycugrd(v(2))-ycugrd(v(3))) + &
hs(v(2))*(ycugrd(v(3))-ycugrd(v(1))) + &
hs(v(3))*(ycugrd(v(1))-ycugrd(v(2))) )/area1
!
dhsdy = 0.5*( hs(v(1))*(xcugrd(v(3))-xcugrd(v(2))) + &
hs(v(2))*(xcugrd(v(1))-xcugrd(v(3))) + &
hs(v(3))*(xcugrd(v(2))-xcugrd(v(1))) )/area1
!
! in case of spherical coordinates, transform back to Cartesian coordinates
!
if ( KSPHER > 0 ) then
!
dhsdx = dhsdx/(cslat * LENDEG)
dhsdy = dhsdy/LENDEG
!
endif
!
! determine diffusion gradients in centroid of next cell
!
dgx1 = cg1*dhsdx/k1
dgy1 = cg1*dhsdy/k1
!
! compute contribution to area of centroid dual
!
carea = carea + x0*y1 - x1*y0
!
! compute contribution to x-gradient of x-diffusion gradient in centroid dual
!
dgxdx = dgxdx + ( dgx0 + dgx1 ) * real( y1 - y0 )
!
! compute contribution to y-gradient of y-diffusion gradient in centroid dual
!
dgydy = dgydy + ( dgy0 + dgy1 ) * real( x0 - x1 )
!
enddo
!
if ( carea > 0d0 ) then
!
dgxdx = dgxdx/real(carea)
dgydy = dgydy/real(carea)
!
! in case of spherical coordinates, transform back to Cartesian coordinates
!
if ( KSPHER > 0 ) then
!
dgxdx = dgxdx/(cslat * LENDEG)
dgydy = dgydy/LENDEG
!
endif
!
denom = k(ivert)*cg(ivert)*hs(ivert)
!
if ( denom > 0. ) then
delta = (dgxdx + dgydy)/denom
else
delta = 0.
endif
!
if ( delta > -1. ) DIFPARAM(ivert) = sqrt(1.+delta)
!
endif
!
enddo vertexloop
!
! deallocation of wave parameters
!
deallocate(cg)
deallocate(hs)
deallocate(k )
!
! compute derivatives of diffraction parameter in vertices
!
DIFPARDX = 0.
DIFPARDY = 0.
!
vertexloop2 : do ivert = 1, nverts
!
if ( vert(ivert)%atti(VMARKER) == 1 ) cycle vertexloop2 ! boundary vertex
!
cslat = cos(DEGRAD*(vert(ivert)%attr(VERTY) + YOFFS))
!
carea = 0d0
dgxdx = 0.
dgydy = 0.
!
! loop over cells around considered vertex
!
do jc = 1, vert(ivert)%noc
!
! get present cell and its vertices
!
icell = vert(ivert)%cell(jc)%atti(CELLID)
!
v(1) = cell(icell)%atti(CELLV1)
v(2) = cell(icell)%atti(CELLV2)
v(3) = cell(icell)%atti(CELLV3)
!
if ( dep2(v(1)) <= DEPMIN .or. dep2(v(2)) <= DEPMIN .or. dep2(v(3)) <= DEPMIN ) cycle vertexloop2
!
! determine centroid of present cell
!
x0 = cell(icell)%attr(CELLCX)
y0 = cell(icell)%attr(CELLCY)
!
! determine diffraction parameter in centroid in present cell
!
difp0 = ( DIFPARAM(v(1)) + DIFPARAM(v(2)) + DIFPARAM(v(3)) )/ 3.
!
! get next cell in counterclockwise direction
!
jcell = vert(ivert)%cell(jc)%atti(NEXTCELL)
!
v(1) = cell(jcell)%atti(CELLV1)
v(2) = cell(jcell)%atti(CELLV2)
v(3) = cell(jcell)%atti(CELLV3)
!
! determine centroid of next cell
!
x1 = cell(jcell)%attr(CELLCX)
y1 = cell(jcell)%attr(CELLCY)
!
! determine diffraction parameter in centroid of next cell
!
difp1 = ( DIFPARAM(v(1)) + DIFPARAM(v(2)) + DIFPARAM(v(3)) )/ 3.
!
! compute contribution to area of centroid dual
!
carea = carea + x0*y1 - x1*y0
!
! compute x-gradient of diffraction parameter
!
dgxdx = dgxdx + ( difp0 + difp1 ) * real( y1 - y0 )
!
! compute y-gradient of diffraction parameter
!
dgydy = dgydy + ( difp0 + difp1 ) * real( x0 - x1 )
!
enddo
!
if ( carea > 0d0 ) then
!
dgxdx = dgxdx/real(carea)
dgydy = dgydy/real(carea)
!
! in case of spherical coordinates, transform back to Cartesian coordinates
!
if ( KSPHER > 0 ) then
!
dgxdx = dgxdx/(cslat * LENDEG)
dgydy = dgydy/LENDEG
!
endif
!
DIFPARDX(ivert) = dgxdx
DIFPARDY(ivert) = dgydy
!
endif
!
enddo vertexloop2
!
end subroutine SwanDiffPar