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test_bv.f90
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test_bv.f90
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program test_bv
!$$$ program documentation block
! . . .
! program name: test_bv
! programmer: da,cheng org: umd date: 2015-Jan-11
!
! purpose:
!
! revision history:
! 2015-Jan-11 da - creator
!
! file dependencies:
!
! attributes:
! language: fortran 90
! machine :
!
!
!$$$ end documentation block
use mod_type, only : rdef
use mod_lorenz63_fwd, only : lorenz63_rk4, t_lorenz63, step, get_tlm
use mod_rnorm, only : rnorm, set_random_seed
implicit none
integer,parameter :: nx = 3
integer :: ncycle, nspin
type(t_lorenz63) :: xb, x, x2, xInfy, xInfyRun2
real(rdef) :: buft
integer :: i, j, itry
real(rdef) :: dx(nx), dx2(nx), dxInfy(nx), dxInfyRun2(nx)
real(rdef) :: dx0(nx), dx0Run2(nx)
real(rdef) :: le1, le2, leInfy
real(rdef) :: sum1, sum2, sumInfy
real(rdef) :: fracForLLECalc
integer :: nsum
integer :: ntry
real(rdef),allocatable :: lle_table(:,:) ! ntry*3 |lle1|lle2|lleInfy|
!----------------------------------------------------------------------------------
! 0. configuration for lorenz63 model
!----------------------------------------------------------------------------------
!xb%dt = 0.008d0 ! length for one time step
xb%dt = 0.001d0 ! length for one time step
xb%nt = 1 ! generate nt-step forecast
xb%para = (/ 10.0d0, 28.0d0, 8.0d0/3.0d0 /)
nspin = 200000 ! spin up the model with nspin steps, then the final state
! is used as the initial condition
ncycle = 80000000 ! total n-step forecast cycles
fracForLLECalc = 0.18 ! start to calculate LLE after cylce > ncyclc&fracForLLECalc
ntry = 10
allocate(lle_table(ntry,4))
do itry = 1, ntry
call set_random_seed( iseed=itry+62 )
do i = 1, nx
dx0(i) = rnorm()
dx0Run2(i) = rnorm()
enddo
print*, "-----------------------------------------------"
print*, "try #", itry, "random_seed=", itry+62
print*, "START: random initial perturbations before rescaling, dx0, dx0Run2 = ", dx0, dx0Run2
!----------------------------------------------------------------------------------
! 1. spin up the lorenz 63 model
!----------------------------------------------------------------------------------
!xb%x0 = [ 0.1d0, 0.1d0, 0.1d0 ]
do i = 1, nx
xb%x0(i) = rnorm()
enddo
Write(6,*) "spin up lorenz63 model: dt =", xb%dt, ", nspin =", nspin
Call lorenz63_rk4( xb%x0(:), xb%xn(:), xb%para, nspin, xb%dt )
xb%x0(:) = xb%xn(:)
Write(6,*) ""
Write(6,*) "INITIAL CONDITION: x=", xb%x0(:)
!----------------------------------------------------------------------------------
! 2. rescale initial perturbations
!----------------------------------------------------------------------------------
print*, ""
dx = dx0 ![ 0.6, 0.2, 0.5]
!dx = dx/sqrt(sum(dx*dx))
dx = dx/sum(abs(dx))
print*, "l1-norm:",dx,sum(abs(dx))
dx2 = dx0 ![ 0.05, 0.1, 0.8]
dx2 = dx2/sqrt(sum(dx2*dx2))
print*, "l2-norm:", dx2,sum(dx2*dx2)
dxInfy = dx0 ![ 0.01, 2.0, 0.01]
dxInfy = dxInfy/maxval(abs(dxInfy))
print*, "lInfy-norm for member 1:", dxInfy,maxval(abs(dxInfy))
dxInfyRun2 = dx0Run2 ![ 0.01, 2.0, 0.01]
dxInfyRun2 = dxInfyRun2/maxval(abs(dxInfyRun2))
print*, "lInfy-norm for member 2:", dxInfy,maxval(abs(dxInfyRun2))
x%x0(:) = xb%x0(:) + dx
x2%x0(:) = xb%x0(:) + dx2
xInfy%x0(:) = xb%x0(:) + dxInfy
xInfyRun2%x0(:) = xb%x0(:) + dxInfyRun2
sum1 = 0.d0; sum2 = 0.d0; sumInfy = 0.d0
nsum = 0
!----------------------------------------------------------------------------------
! 3. breeding
!----------------------------------------------------------------------------------
do i = 1, ncycle
call step(xb%x0(:), xb%para, xb%dt, buft, xb%xn(:))
call step(x%x0(:), xb%para, xb%dt, buft, x%xn(:))
call step(x2%x0(:), xb%para, xb%dt, buft, x2%xn(:))
call step(xInfy%x0(:), xb%para, xb%dt, buft, xInfy%xn(:))
call step(xInfyRun2%x0(:), xb%para, xb%dt, buft, xInfyRun2%xn(:))
! BV now
dx(:) = x%xn(:) - xb%xn(:)
dx2(:) = x2%xn(:) - xb%xn(:)
dxInfy(:) = xInfy%xn(:) - xb%xn(:)
dxInfyRun2(:) = xInfyRun2%xn(:) - xb%xn(:)
if (i > ncycle*fracForLLECalc) then
le1 = log( sum(abs(dx)) / sum(abs(x%x0-xb%x0)) ) / xb%dt
le2 = log( sqrt(sum(dx2*dx2)) / sqrt(sum((x2%x0-xb%x0)*(x2%x0-xb%x0))) )/xb%dt
leInfy = log( maxval(abs(dxInfy)) / maxval(abs(xInfy%x0-xb%x0)) )/xb%dt
sum1 = sum1 + le1; sum2 = sum2 + le2; sumInfy = sumInfy + leInfy
nsum = nsum + 1
end if
if (i<=5 .or. i== int(ncycle*fracForLLECalc) .or. mod(i,int(ncycle/10.))==0) then ! check local LLV
print*, ""
print*, "CHECK Local LLV at time step: ", i
print*, "llv1=", dx
print*, "llv2=", dx2
print*, "llvInfy for member 1=", dxInfy
print*, "llvInfy for member 2=", dxInfyRun2
endif
! rescale BV
dx = dx/sum(abs(dx))
dx2 = dx2/sqrt(sum(dx2*dx2))
dxInfy = dxInfy / maxval(abs(dxInfy))
dxInfyRun2 = dxInfyRun2 / maxval(abs(dxInfyRun2))
xb%x0(:) = xb%xn(:)
x%x0(:) = xb%x0(:) + dx(:)
x2%x0(:) = xb%x0(:) + dx2(:)
xInfy%x0(:) = xb%x0(:) + dxInfy(:)
xInfyRun2%x0(:) = xb%x0(:) + dxInfyRun2(:)
enddo
print*, ""
print*, "SECTION_RESULTS: lle1, lle2, lleInfy, n=", sum1/nsum, sum2/nsum, sumInfy/nsum, nsum
lle_table(itry,1) = sum1/nsum
lle_table(itry,2) = sum2/nsum
lle_table(itry,3) = sumInfy/nsum
enddo
print*, "RESULTS SUMMARY:"
print*, "| try# | lle1 | lle2 | lleInfy|"
print*, "-------------------------------"
do itry = 1, ntry
print*, itry, (lle_table(itry,j), j=1,3)
enddo
print*, "-------------------------------"
print*, "avg", (sum(lle_table(:,j))/ntry, j=1,3)
endprogram