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correct_grids.f90
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program lowresmodel
implicit none
!variable declaration
integer, parameter :: Lx = 6000, Ly = 2000 !domain in km
integer, parameter :: Dx = 500, Dxm = Dx*1000 !grid resolution
real, parameter :: dT = 100 !time step, 100 seconds
integer, parameter :: ntime = 864 !time step as an integer because otherwise the do loop gets mad
integer, parameter :: Nx = (Lx/Dx) + 3, Ny = (Ly/Dx) + 3 !create grid points for array
integer :: i, j, t, n !define other potentially important variables
real :: time !TIME
real, dimension(Nx, Ny) :: h, u, v, q, hsurf, lq, zeta, ght, ken, pen !array creation with internal variables for each point
real, dimension(Nx, Ny, 3) :: hu0, hv0, hq0, us0, vs0, h0 ! Variables for time differencing
real, dimension(Nx, Ny) :: hu1, hu2, hu3, hv1, hv2, hv3, us1, us2, us3, vs1, vs2, vs3, hu, hv, us, vs, hq
real, dimension(Nx, Ny, 3) :: alp0, bet0, gam0, del0, eps0, ken0, ght0, q0, z0, phi0, totalen0
real, dimension(Nx, Ny, 3) :: u0, v0
real, dimension(Nx, Ny) :: alp, bet, gam, del, eps, phi
!Variables for further time-stepping
real, dimension(Nx, Ny) :: alp1, alp2, alp3, bet1, bet2, bet3
real, dimension(Nx, Ny) :: gam1, gam2, gam3, del1, del2, del3
real, dimension(Nx, Ny) :: eps1, eps2, eps3, ken1, ken2, ken3
real, dimension(Nx, Ny) :: ght1, ght2, ght3, phi1, phi2, phi3, totalen1, totalen2, totalen3
real, parameter :: g = 9.81, f = 1.0e-4, f1 = (23.0/12.0)*dT, f2 = (4.0/3.0*dT), f3 = (5.0/12.0)*dT !Constants
!showcase model info
print *, "Grid Type: C"
print *, "Domain (km):", Lx, Ly
print *, "Grid Resolution (km):", Dx
print *, "X-Direction Grid Point #:", Nx
print *, "Y-Direction Grid Point #:", Ny
call initgrid(hsurf, Dx, Nx, Ny)
! Set initial conditions
u(:,:) = 0.0
u(1:Nx,2:Ny-1) = 20.0 ! uniform zonal wind
v(:,:) = 0.0
v(1:Nx,2:Ny-1) = 0.1
u0(:,:,1) = u(:,:)
v0(:,:,1) = v(:,:)
h(:,:) = 0.0
do i = 1,Nx
h(i,2:Ny-1) = 5000-hsurf(i, 2:Ny-1) ! horizontal free surface
end do
h0(:,:,1) = h(:,:)
hu0(:,:,1) = 0.0
hv0(:,:,1) = 0.0
us0(:,:,1) = 0.0
vs0(:,:,1) = 0.0
z0(:,:,1) = 0.0
hq0(:,:,1) = 0.0
ght0(:,:,1) = 0.0
ken0(:,:,1) = 0.0
q0(:,:,1) = 0.0
totalen0(:,:,1) = 0.0
! zero everywhere because q is zero everywhere
alp0(:,:,1) = 0.0
bet0(:,:,1) = 0.0
gam0(:,:,1) = 0.0
del0(:,:,1) = 0.0
eps0(:,:,1) = 0.0
phi0(:,:,1) = 0.0
do i = 2, Nx-1
do j = 2, Ny-1
hu0(i,j,1) = (h(i-1,j) + h(i+1,j))/2.0
hv0(i,j,1) = (h(i,j-1) + h(i,j+1))/2.0
z0(i,j,1)=(u(i,j-1)-u(i,j+1)+v(i+1,j)-v(i-1,j))/Dxm
hq0(i,j,1)=(h(i,j) + h(i-1,j) + h(i-1,j-1) + h(i,j-1))/4.0
ght0(i,j,1) = g*(hsurf(i,j) + h(i,j))
ken0(i,j,1)=(u(i,j)**2 + u(i+1,j)**2 + v(i,j)**2 + v(i,j+1)**2)/4.
end do
do j = 1, Ny-1
ken0(i,j,1)=(u(i,j)**2 + u(i+1,j)**2 + v(i,j)**2 + v(i,j+1)**2)/4.
end do
do j = 1, Ny
ght0(i,j,1) = g*(hsurf(i,j) + h(i,j))
end do
end do
us0(:,:,1)= hu0(:,:,1)*u(:,:)
vs0(:,:,1)= hv0(:,:,1)*v(:,:)
us0(1,:,1) = us0(Nx-1,:,1)
us0(Nx,:,1) = us0(2,:,1)
vs0(1,:,1) = vs0(Nx-1,:,1)
vs0(Nx,:,1) = vs0(2,:,1)
u(1,:) = u(Nx-1,:)
u(Nx,:) = u(2,:)
v(1,:) = v(Nx-1,:)
v(Nx,:) = v(2,:)
hu0(1,:,1) = hu0(Nx-1,:,1)
hu0(Nx,:,1) = hu0(2,:,1)
hv0(1,:,1) = hv0(Nx-1,:,1)
hv0(Nx,:,1) = hv0(2,:,1)
z0(1,:,1) = z0(Nx-1,:,1)
z0(Nx,:,1) = z0(2,:,1)
hq0(1,:,1) = hq0(Nx-1,:,1)
hq0(Nx,:,1) = hq0(2,:,1)
ght0(1,:,1) = ght0(Nx-1,:,1)
ght0(Nx,:,1) = ght0(2,:,1)
ken0(1,:,1) = ken0(Nx-1,:,1)
ken0(Nx,:,1) = ken0(2,:,1)
totalen0(:,:,1) = ken0(:,:,1) + ght0(:,:,1)
! We can print out the initial conditions
! Time-stepping loop
do n = 2, 3
do i = 2, Nx-1
do j = 1, Ny-1
h0(i,j,n) = h0(i,j,n-1) - dT * (us0(i+1,j,n-1) - us0(i,j,n-1) + vs0(i,j+1,n-1) - vs0(i,j,n-1))/Dxm
end do
do j = 2, Ny-1
! Calculate u
u0(i,j,n) = u0(i,j,n-1) + dT * (alp0(i,j,n-1) * vs0(i,j+1,n-1) + bet0(i,j,n-1) * vs0(i-1,j+1,n-1) + &
gam0(i,j,n-1) * vs0(i-1,j,n-1) + del0(i,j,n-1) * vs0(i,j,n-1) - eps0(i,j,n-1) * &
us0(i+1,j,n-1) + eps0(i-1,j,n-1) * us0(i-1,j,n-1) - (ken0(i,j,n-1) - &
ght0(i,j,n-1) + ken0(i-1,j,n-1) + ght0(i,j,n-1)) / Dxm)
! Calculate v
v0(i,j,n) = v0(i,j,n-1) - dT * (gam0(i+1,j,n-1) * us0(i+1,j,n-1) + del0(i,j,n-1) * us0(i,j,n-1) + &
alp0(i,j-1, n-1) * us0(i,j-1,n-1) + bet0(i+1,j-1,n-1) * us0(i+1,j-1,n-1) + phi0(i,j,n-1) * &
vs0(i,j+1,n-1) - phi0(i,j-1,n-1) * vs0(i,j-1,n-1) + (ken0(i,j,n-1) + &
ght0(i,j,n-1) - ken0(i,j-1,n-1) - ght0(i,j-1,n-1)) / Dxm)
! Calculate zeta (z0)
z0(i,j,n) = (u0(i,j-1,n) - u0(i,j,n) + v0(i,j,n) - v0(i-1,j,n)) / Dxm
end do
end do
h0(1,:,n) = h0(Nx-1,:,n)
h0(Nx,:,n) = h0(2,:,n)
u0(1,:,n) = u0(Nx-1,:,n)
u0(Nx,:,n) = u0(2,:,n)
v0(1,:,n) = v0(Nx-1,:,n)
v0(Nx,:,n) = v0(2,:,n)
z0(1,:,n) = z0(Nx-1,:,n)
z0(Nx,:,n) = z0(2,:,n)
do i = 2, Nx-1
do j = 1, Ny-1
ken0(i,j,n)=(u0(i,j,n)**2 + u0(i+1,j,n)**2 + v0(i,j,n)**2 + v0(i,j+1,n)**2)/4.
end do
do j = 2, Ny-1
! hu0, hv0, and hq0
hu0(i,j,n) = (h0(i-1,j,n) + h0(i+1,j,n)) / 2.0
hv0(i,j,n) = (h0(i,j-1,n) + h0(i,j+1,n)) / 2.0
hq0(i,j,n)=(h0(i,j,n) + h0(i-1,j,n) + h0(i-1,j-1,n) + h0(i,j-1,n)) / 4.0
! Calculate Potential Vorticity
q0(i,j,n) = (f + z0(i,j,n)) / hq0(i,j,n)
end do
end do
ght0(:,:,n) = g*(hsurf(:,:) + h0(:,:,n))
hu0(1,:,n) = hu0(Nx-1,:,n)
hu0(Nx,:,n) = hu0(2,:,n)
hv0(1,:,n) = hv0(Nx-1,:,n)
hv0(Nx,:,n) = hv0(2,:,n)
hq0(1,:,n) = hq0(Nx-1,:,n)
hq0(Nx,:,n) = hq0(2,:,n)
ght0(1,:,n) = ght0(Nx-1,:,n)
ght0(Nx,:,n) = ght0(2,:,n)
q0(1,:,n) = q0(Nx-1,:,n)
q0(Nx,:,n) = q0(2,:,n)
do i = 2, Nx-1
do j = 2, Ny-1
! Compute Greek letters
alp0(i, j, n) = ((1.0/24.0)*(2*q0(i+1,j+1,n) + q0(i,j+1,n) + 2*q0(i,j,n) + q0(i+1,j,n)))
bet0(i, j, n) = ((1.0/24.0)*(q0(i,j+1,n) + 2*q0(i-1,j+1,n) + q0(i-1,j,n) + 2*q0(i,j,n)))
gam0(i, j, n) = ((1.0/24.0)*(2*q0(i,j+1,n) + q0(i-1,j+1,n) + 2*q0(i-1,j,n) + q0(i,j,n)))
del0(i, j, n) = ((1.0/24.0)*(q0(i+1,j+1,n) + 2*q0(i,j+1,n) + q0(i,j,n) + 2*q0(i+1,j,n)))
eps0(i, j, n) = ((1.0/24.0)*(q0(i+1,j+1,n) + q0(i,j+1,n) - q0(i,j,n) - q0(i+1,j,n)))
phi0(i, j, n) = ((1.0/24.0)*(-q0(i+1,j+1,n) + q0(i,j+1,n) + q0(i,j,n) - q0(i+1,j,n)))
end do
end do
totalen0(:,:,n) = ken0(:,:,n) + ght0(:,:,n)
us0(:,:,n)= hu0(:,:,n)*u0(:,:,n)
vs0(:,:,n)= hv0(:,:,n)*v0(:,:,n)
us0(1,:,n) = us0(Nx-1,:,n)
us0(Nx,:,n) = us0(2,:,n)
vs0(1,:,n) = vs0(Nx-1,:,n)
vs0(Nx,:,n) = vs0(2,:,n)
alp0(1,:,n) = alp0(Nx-1,:,n)
alp0(Nx,:,n) = alp0(2,:,n)
bet0(1,:,n) = bet0(Nx-1,:,n)
bet0(Nx,:,n) = bet0(2,:,n)
gam0(1,:,n) = gam0(Nx-1,:,n)
gam0(Nx,:,n) = gam0(2,:,n)
del0(1,:,n) = del0(Nx-1,:,n)
del0(Nx,:,n) = del0(2,:,n)
eps0(1,:,n) = eps0(Nx-1,:,n)
eps0(Nx,:,n) = eps0(2,:,n)
phi0(1,:,n) = phi0(Nx-1,:,n)
phi0(Nx,:,n) = phi0(2,:,n)
end do ! time loop
!Update previous values prior to next time step
us1(:,:) = us0(:,:,1)
us2(:,:) = us0(:,:,2)
us3(:,:) = us0(:,:,3)
hu1(:,:) = h0(:,:,1)
hu2(:,:) = h0(:,:,2)
hu3(:,:) = h0(:,:,3)
vs1(:,:) = vs0(:,:,1)
vs2(:,:) = vs0(:,:,2)
vs3(:,:) = vs0(:,:,3)
hv1(:,:) = hv0(:,:,1)
hv2(:,:)= hv0(:,:,2)
hv3(:,:) = hv0(:,:,3)
alp1(:,:) = alp0(:,:,1)
alp2(:,:) = alp0(:,:,2)
alp3(:,:)= alp0(:,:,3)
bet1(:,:) = bet0(:,:,1)
bet2(:,:) = bet0(:,:,2)
bet3(:,:)= bet0(:,:,3)
gam1(:,:) = gam0(:,:,1)
gam2(:,:) = gam0(:,:,2)
gam3(:,:)= gam0(:,:,3)
del1(:,:) = del0(:,:,1)
del2(:,:) = del0(:,:,2)
del3(:,:)= del0(:,:,3)
eps1(:,:) = eps0(:,:,1)
eps2(:,:) = eps0(:,:,2)
eps3(:,:)= eps0(:,:,3)
ken1(:,:) = ken0(:,:,1)
ken2(:,:) = ken0(:,:,2)
ken3(:,:)= ken0(:,:,3)
ght1(:,:) = ght0(:,:,1)
ght2(:,:) = ght0(:,:,2)
ght3(:,:)= ght0(:,:,3)
h(:,:) = h0(:,:,3)
u(:,:) = u0(:,:,3)
v(:,:) = v0(:,:,3)
! Adams-Bashforth scheme
do n = 4, ntime
do i = 2, Nx-1
do j = 2, Ny-1
h(i,j) = h(i,j) - f1*(us3(i+1,j) - us3(i,j) + vs3(i,j+1) - vs3(i,j)) + &
f2*(us2(i+1,j) - us2(i,j) + vs2(i,j+1) - vs2(i,j)) - &
f3*(us1(i+1,j) - us1(i,j) + vs1(i,j+1) - vs1(i,j))
u(i,j) = u(i,j) + f1 * (alp3(i,j) * vs3(i,j+1) + bet3(i,j) * vs3(i-1,j+1) + gam3(i,j) * vs3(i-1,j) + &
del3(i,j) * vs3(i,j) - eps3(i,j) * us3(i+1,j) + eps3(i-1,j) * us3(i-1,j) - (ken3(i,j) - &
ght3(i,j) + ken3(i-1,j) + ght3(i,j)) / Dxm) - &
f2 * (alp2(i,j) * vs2(i,j+1) + bet2(i,j) * vs2(i-1,j+1) + gam2(i,j) * vs2(i-1,j) + &
del2(i,j) * vs2(i,j) - eps2(i,j) * us2(i+1,j) + eps2(i-1,j) * us2(i-1,j) - (ken2(i,j) - &
ght2(i,j) + ken2(i-1,j) + ght2(i,j)) / Dxm) + &
f3 * (alp1(i,j) * vs1(i,j+1) + bet1(i,j) * vs1(i-1,j+1) + gam1(i,j) * vs1(i-1,j) + &
del1(i,j) * vs1(i,j) - eps1(i,j) * us1(i+1,j) + eps1(i-1,j) * us1(i-1,j) - (ken1(i,j) - &
ght1(i,j) + ken1(i-1,j) + ght1(i,j)) / Dxm)
v(i,j) = v(i,j) - f1 * (gam3(i+1,j) * us3(i+1,j) + del3(i,j) * us3(i,j) + alp3(i,j-1) * us3(i,j-1) + &
bet3(i+1,j-1) * us3(i+1,j-1) + phi3(i,j) * vs3(i,j+1) - phi3(i,j-1) * vs3(i,j-1) + &
(ken3(i,j) + ght3(i,j) - ken3(i,j-1) - ght3(i,j-1)) / Dxm) - &
f2 * (gam2(i+1,j) * us2(i+1,j) + del2(i,j) * us2(i,j) + alp2(i,j-1) * us2(i,j-1) + &
bet2(i+1,j-1) * us2(i+1,j-1) + phi2(i,j) * vs2(i,j+1) - phi2(i,j-1) * vs2(i,j-1) + &
(ken2(i,j) + ght2(i,j) - ken2(i,j-1) - ght2(i,j-1)) / Dxm) + &
f3 * (gam1(i+1,j) * us1(i+1,j) + del1(i,j) * us1(i,j) + alp1(i,j-1) * us1(i,j-1) + &
bet1(i+1,j-1) * us1(i+1,j-1) + phi1(i,j) * vs1(i,j+1) - phi1(i,j-1) * vs1(i,j-1) + &
(ken1(i,j) + ght1(i,j) - ken1(i,j-1) - ght3(i,j-1)) / Dxm)
zeta(i,j) = (u(i,j-1) - u(i,j) + v(i,j) - v(i-1,j)) / Dxm
end do
end do
us(2:Nx-1,2:Ny-1)= hu(2:Nx-1,2:Ny-1)*u(2:Nx-1,2:Ny-1)
vs(2:Nx-1,2:Ny-1)= hv(2:Nx-1,2:Ny-1)*v(2:Nx-1,2:Ny-1)
h(1,:) = h(Nx-1,:)
h(Nx,:) = h(2,:)
u(1,:) = u(Nx-1,:)
u(Nx,:) = u(2,:)
v(1,:) = v(Nx-1,:)
v(Nx,:) = v(2,:)
do i = 2, Nx-1
do j = 2, Ny-1
hu(i,j) = (h(i-1,j) + h(i+1,j))/2.0
hv(i,j) = (h(i,j-1) + h(i,j+1))/2.0
q(i,j) = (f + zeta(i,j)) / hq(i,j)
alp(i, j) = ((1.0/24.0)*(2*q(i+1,j+1) + q(i,j+1) + 2*q(i,j) + q(i+1,j)))
bet(i, j) = ((1.0/24.0)*(q(i,j+1) + 2*q(i-1,j+1) + q(i-1,j) + 2*q(i,j)))
gam(i, j) = ((1.0/24.0)*(2*q(i,j+1) + q(i-1,j+1) + 2*q(i-1,j) + q(i,j)))
del(i, j) = ((1.0/24.0)*(q(i+1,j+1) + 2*q(i,j+1) + q(i,j) + 2*q(i+1,j)))
eps(i, j) = ((1.0/24.0)*(q(i+1,j+1) + q(i,j+1) - q(i,j) - q(i+1,j)))
phi(i, j) = ((1.0/24.0)*(q(i,j+1) + q(i,j) - q(i+1,j) - q(i+1,j+1)))
hq(i,j)=(h(i,j) + h(i-1,j) + h(i-1,j-1) + h(i,j-1))/4.0
end do
do j = 1, Ny-1
ken(i,j)=(u(i,j)**2 + u(i+1,j)**2 + v(i,j)**2 + v(i,j+1)**2)/4.
ght(i,j) = g*(hsurf(i,j) + h(i,j))
end do
end do
hu(1,:) = hu(Nx-1,:)
hu(Nx,:) = hu(2,:)
hv(1,:) = hv(Nx-1,:)
hv(Nx,:) = hv(2,:)
us(1,:) = us(Nx-1,:)
us(Nx,:) = us(2,:)
vs(1,:) = vs(Nx-1,:)
vs(Nx,:) = vs(2,:)
alp(1,:) = alp(Nx-1,:)
alp(Nx,:) = alp(2,:)
bet(1,:) = bet(Nx-1,:)
bet(Nx,:) = bet(2,:)
gam(1,:) = gam(Nx-1,:)
gam(Nx,:) = gam(2,:)
del(1,:) = del(Nx-1,:)
del(Nx,:) = del(2,:)
eps(1,:) = eps(Nx-1,:)
eps(Nx,:) = eps(2,:)
phi(1,:) = phi(Nx-1,:)
phi(Nx,:) = phi(2,:)
q(1,:) = q(Nx-1,:)
q(Nx,:) = q(2,:)
zeta(1,:) = zeta(Nx-1,:)
zeta(Nx,:) = zeta(2,:)
ken(1,:) = ken(Nx-1,:)
ken(Nx,:) = ken(2,:)
ght(1,:) = ght(Nx-1,:)
ght(Nx,:) = ght(2,:)
us1 = us2
us2 = us3
us3 = us
hu1 = hu2
hu2 = hu3
hu3 = hu
hv1 = hv2
hv2 = hv3
hv3 = hv
alp1 = alp2
alp2 = alp3
alp3 = alp
bet1 = bet2
bet2 = bet3
bet3 = bet
gam1 = gam2
gam2 = gam3
gam3 = gam
del1 = del2
del2 = del3
del3 = del
eps1 = eps2
eps2 = eps3
eps3 = eps
phi1 = phi2
phi2 = phi3
phi3 = phi
ken1 = ken2
ken2 = ken3
ken3 = ken
ght1 = ght2
ght2 = ght3
ght3 = ght
end do
totalen1(:,:) = ken1(:,:) + ght1(:,:)
totalen2(:,:) = ken2(:,:) + ght2(:,:)
totalen3(:,:) = ken3(:,:) + ght3(:,:)
! We probably have to print something or write something here
! open(unit=10, file='topo.dat', access='direct', form='unformatted', status='unknown', action='write', recl=4*Nx*Ny) !scary thing
! write(10, rec=1) hsurf
end program lowresmodel
subroutine initgrid(hsurf, Dx, Nx, Ny) !creates grid, ridge, and topography.
implicit none
integer, parameter :: Lx = 6000, Ly = 2000
integer, intent(in) :: Dx, Nx, Ny
real, dimension(Nx,Ny), intent(out) :: hsurf
integer :: i, j
hsurf(:,:)=0.0
!grid resolution thing (topography)
hsurf((Nx)/2 + 1,:) = 2000
if (Dx==250) then
hsurf((Nx)/2,:) = 1000
hsurf((Nx)/2 + 2,:) = 1000
endif
if (Dx==125) then
hsurf((Nx)/2 - 1,:) = 500
hsurf((Nx)/2 + 3,:) = 500
endif
end subroutine initgrid