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Bbred.f90
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!---------------------------------------------
!!!!generate np bred vector
!--input:
!x0_start: the initial reference state
!p_start: initial random perturbations
!stan: rescaling factor
!ncl: the number of breeding cycles
!tcl: rescaling interval
!--output:
!pstart: output bred vectors
subroutine breeding(x0_start,nper,pstart,stan,ncl,tcl,xout,ptemp)
!subroutine breeding(x0_start,nper,pstart,stan,ncl,tcl,ptemp)
include 'sphectra.h'
include 'paramod.h'
!implicit none
integer::i,j,k
!integer::nx,ny
integer::ncl,tcl,nper
real::x0_start(nlong,nlat,nlevels)
real::pstart(nlong,nlat,nlevels,nper)
real::ptemp(nlong,nlat,nlevels,nper)
real::stan(nlevels)
real::x0(nlong,nlat,nlevels),x0_p(nlong,nlat,nlevels)
real::x1(nlong,nlat,nlevels),x1_p(nlong,nlat,nlevels)
real::xtemp(nlong,nlat,nlevels,0:1)
real::p0(nlong,nlat,nlevels),pp(nlong,nlat,nlevels),pout(nlong,nlat,nlevels)
real::xout(nlong,nlat,nlevels)
real::dl
x0=x0_start
ptemp=pstart
do i=1,ncl
xtemp=0.
xtemp(:,:,:,0)=x0(:,:,:)
!reference state
call integrate(tcl,tcl,1,xtemp)
x1(:,:,:)=xtemp(:,:,:,1) !x1 is the final state at the end of a breeding cycle
!================================
do j=1,nper
p0(:,:,:)=ptemp(:,:,:,j)
x0_p=x0+p0 !superpose a error vector on the initial state
xtemp=0.
!----perturbed states
xtemp(:,:,:,0)=x0_p(:,:,:)
call integrate(tcl,tcl,1,xtemp)
x1_p(:,:,:)=xtemp(:,:,:,1)
!================================
pp=x1_p-x1 !calculate the perturabtions
do k=1,nlevels
call field_rescale_2d(nlong,nlat,1,&
pp(:,:,k),stan(k),pout(:,:,k)) !rescale the perturbations
end do
ptemp(:,:,:,j)=pout(:,:,:)
end do
x0=x1
!write(132,rec=i)ptemp(:,:,2,:)
!write(41,rec=i)x1
end do
xout=x1 !output the final reference state xout
return
end subroutine
!-----------------------right-----------
!---------------------------------------------
!!!!generate np bred vector and calculate the growth rate
!in each cycle
!--input:
!x0_start: the initial reference state
!p_start: initial random perturbations
!stan: rescaling factor
!ncl: the number of breeding cycles
!tcl: rescaling interval
!--output:
!pstart: output bred vectors
subroutine breeding_errorgrowth(x0_start,nper,pstart,ncl,tcl,egrow)
include 'sphectra.h'
include 'paramod.h'
!implicit none
integer::i,j,k
!integer::nx,ny
integer::ncl,tcl,nper
real::x0_start(nlong,nlat,nlevels)
real::pstart(nlong,nlat,nlevels,nper)
real::ptemp(nlong,nlat,nlevels,nper)
real::stan(nlevels)
real::x0(nlong,nlat,nlevels),x0_p(nlong,nlat,nlevels)
real::x1(nlong,nlat,nlevels),x1_p(nlong,nlat,nlevels)
real::xtemp(nlong,nlat,nlevels,0:1)
real::p0(nlong,nlat,nlevels),pp(nlong,nlat,nlevels),pout(nlong,nlat,nlevels)
real::xout(nlong,nlat,nlevels)
real::dl,inisize(nper),endsize(nper)
real::egrow(nlong,nlat,nlevels,nper)
x0=x0_start
ptemp=pstart
!----calculate the size of initial error
!do i=1,nper
! call weight_rmse(.false.,nlong,nlat,nlevels,&
! pstart(:,:,:,i),pstart(:,:,:,i),inisize(i))
!end do
!------------
do i=1,ncl
xtemp=0.
endsize=0.
xtemp(:,:,:,0)=x0(:,:,:)
call integrate(tcl,tcl,1,xtemp)
x1(:,:,:)=xtemp(:,:,:,1) !x1 is the final state at the end of a breeding cycle
!================================
do j=1,nper
p0(:,:,:)=ptemp(:,:,:,j)
x0_p=x0+p0 !superpose a error vector on the initial state
xtemp=0.
!----
xtemp(:,:,:,0)=x0_p(:,:,:)
call integrate(tcl,tcl,1,xtemp)
x1_p(:,:,:)=xtemp(:,:,:,1)
!================================
pp=x1_p-x1 !calculate the perturabtions
!call weight_rmse(.false.,nlong,nlat,nlevels,pp,pp,endsize(j))
egrow(:,:,:,j)=abs(pp)-abs(p0)
!--------------------------------
!do k=1,nlevels
!call field_rescale_2d(nlong,nlat,1,&
!pp(:,:,k),stan(k),pout(:,:,k)) !rescale the perturbations
!end do
!ptemp(:,:,:,j)=pout(:,:,:)
end do
x0=x1
!write(31,rec=i)ptemp
!write(41,rec=i)x1
end do
write(*,*) "X1: ",x1(1,:,2)
pause
xout=x1 !output the final reference state xout
return
end subroutine
!----------------------------------------------
!This subroutine calculates nper NLLVs.
!--input:
!----y0_start:the initial reference state
!----nn:number of field grids.
!----ns:number of error samples
!----id0:position of initial condition in the data file
!----p0:initial perturbations
!----array:initial sequence from 1 to nn
!----stan:rescaled perturbation size
!----tcl:rescaling interval
!----ncl:number of breeding cycle
!--output:
!----pout:orthogonal vectors after breeding cycles
subroutine reorth(y0_start,nper,pstart,stan,ncl,tcl,pout)
include 'sphectra.h'
include 'paramod.h'
!implicit none
integer::i,j,k,id
integer::ncl,tcl
real::stan(nlevels)
real::per0(nlong,nlat,nlevels),per1(nlong,nlat,nlevels)
real::per1_all(nlong,nlat,nlevels,nper)
real::y0_start(nlong,nlat,nlevels)
real::y0(nlong,nlat,nlevels),y1(nlong,nlat,nlevels)
real::y0_p(nlong,nlat,nlevels),y1_p(nlong,nlat,nlevels)
real::ytemp0(nlong,nlat,nlevels,0:1)
real::pstart(nlong,nlat,nlevels,nper)
real::ptemp(nlong,nlat,nlevels,nper),pout(nlong,nlat,nlevels,nper)
!------------------
ptemp=pstart !do not change pstart
y0=y0_start !do not change y0_start(for breeding)
!---------------------
!y0--->y1
!+per0
!y0_p--->y1_p
outer: do k=1,ncl
ytemp0=0.
ytemp0(:,:,:,0)=y0(:,:,:)
!reference state
call integrate(tcl,tcl,1,ytemp0)
y1(:,:,:)=ytemp0(:,:,:,1) !the integration of reference
!-------------------------
inner: do i=1,nper
ytemp0=0.
per0=0.
dist=0.
per0(:,:,:)=ptemp(:,:,:,i)
y0_p=y0+per0
ytemp0(:,:,:,0)=y0_p(:,:,:)
call integrate(tcl,tcl,1,ytemp0)
y1_p(:,:,:)=ytemp0(:,:,:,1) !the integration of forecast
!!!-------------------------------------
per1=y1_p-y1
!if(k<=ncl)then !mod(k,ncl)/=0)then
! do j=1,nlevels
! call field_rescale_2d(nlong,nlat,per1(:,:,j),&
! stan(j),ptemp(:,:,j,i))
! end do
!else
per1_all(:,:,:,i)=per1(:,:,:) !if orthogonalizationis necessary
!deposite all the perturbations
!!!---------------------------------------
!endif
end do inner
!if(k>ncl)then!mod(k,ncl)==0)then
call gsr_gb(.false.,nlong,nlat,nlevels,nper,nper,&
per1_all,stan,ptemp)
!do j=1,ns
! call onetotwo(nn,errorstart(:,j),nx,ny,pstart(:,:,j))
!end do
!endif
y0=y1
!write(131,rec=(id-1)*ncl+k)ptemp(:,:,2,:)
end do outer
pout=ptemp
return
end subroutine
!!!---------------------------------------------------------------
!---------------------------------------------
!!!!generate np bred vector regionally rescaling
!--input:
!x0_start: the initial reference state
!p_start: initial random perturbations
!stan: rescaling factor
!ncl: the number of breeding cycles
!tcl: rescaling interval
!--output:
!pstart: output bred vectors
subroutine breeding_mask(x0_start,nper,pstart,stan,ncl,tcl,ptemp)
include 'sphectra.h'
include 'paramod.h'
!implicit none
integer::i,j,k
!integer::nx,ny
integer::ncl,tcl,nper
real::x0_start(nlong,nlat,nlevels)
real::pstart(nlong,nlat,nlevels,nper)
real::ptemp(nlong,nlat,nlevels,nper)
real::stan(nlong,nlat,nlevels)
real::x0(nlong,nlat,nlevels),x0_p(nlong,nlat,nlevels)
real::x1(nlong,nlat,nlevels),x1_p(nlong,nlat,nlevels)
real::xtemp(nlong,nlat,nlevels,0:1)
real::p0(nlong,nlat,nlevels),pp(nlong,nlat,nlevels),pout(nlong,nlat,nlevels)
real::xout(nlong,nlat,nlevels)
real::dl
x0=x0_start
ptemp=pstart
do i=1,ncl
xtemp=0.
xtemp(:,:,:,0)=x0(:,:,:)
call integrate(tcl,tcl,1,xtemp)
x1(:,:,:)=xtemp(:,:,:,1) !x1 is the final state at the end of a breeding cycle
!================================
do j=1,nper
p0(:,:,:)=ptemp(:,:,:,j)
x0_p=x0+p0 !superpose a error vector on the initial state
xtemp=0.
!----
xtemp(:,:,:,0)=x0_p(:,:,:)
call integrate(tcl,tcl,1,xtemp)
x1_p(:,:,:)=xtemp(:,:,:,1)
!================================
pp=x1_p-x1 !calculate the perturabtions
call region_rescale(smth_r,nlong,nlat,nlevels,pp,stan,pout)
!regional rescaling using the mask
ptemp(:,:,:,j)=pout(:,:,:)
end do
x0=x1
!write(31,rec=i)ptemp
!write(41,rec=i)x1
end do
xout=x1 !output the final reference state xout
return
end subroutine
!----------------------------------------------
!This subroutine calculates nper NLLVs regionally rescaled.
!--input:
!----y0_start:the initial reference state
!----nn:number of field grids.
!----ns:number of error samples
!----id0:position of initial condition in the data file
!----p0:initial perturbations
!----array:initial sequence from 1 to nn
!----stan:rescaled perturbation size
!----tcl:rescaling interval
!----ncl:number of breeding cycle
!--output:
!----pout:orthogonal vectors after breeding cycles
subroutine reorth_mask(y0_start,nper,pstart,stan,ncl,tcl,pout)
include 'sphectra.h'
include 'paramod.h'
!implicit none
integer::i,j,k
integer::ncl,tcl
real::stan(nlong,nlat,nlevels)
real::per0(nlong,nlat,nlevels),per1(nlong,nlat,nlevels)
real::per1_all(nlong,nlat,nlevels,nper)
real::y0_start(nlong,nlat,nlevels)
real::y0(nlong,nlat,nlevels),y1(nlong,nlat,nlevels)
real::y0_p(nlong,nlat,nlevels),y1_p(nlong,nlat,nlevels)
real::ytemp0(nlong,nlat,nlevels,0:1)
real::pstart(nlong,nlat,nlevels,nper)
real::ptemp(nlong,nlat,nlevels,nper),pout(nlong,nlat,nlevels,nper)
!------------------
ptemp=pstart !do not change pstart
y0=y0_start !do not change y0_start(for breeding)
!---------------------
!y0--->y1
!+per0
!y0_p--->y1_p
outer: do k=1,ncl
ytemp0=0.
ytemp0(:,:,:,0)=y0(:,:,:)
call integrate(tcl,tcl,1,ytemp0)
y1(:,:,:)=ytemp0(:,:,:,1) !the integration of reference
!-------------------------
inner: do i=1,nper
ytemp0=0.
per0=0.
dist=0.
per0(:,:,:)=ptemp(:,:,:,i)
y0_p=y0+per0
ytemp0(:,:,:,0)=y0_p(:,:,:)
call integrate(tcl,tcl,1,ytemp0)
y1_p(:,:,:)=ytemp0(:,:,:,1) !the integration of forecast
!!!-------------------------------------
per1=y1_p-y1
!if(mod(k,ncl)/=0)then
! do j=1,nlevels
! call field_rescale_2d(nlong,nlat,per1(:,:,j),&
! stan(j),ptemp(:,:,j,i))
! end do
!else
per1_all(:,:,:,i)=per1(:,:,:) !if orthogonalizationis necessary
!deposite all the perturbations
!!!---------------------------------------
!endif
end do inner
!if(mod(k,ncl)==0)then
call gsr_region(.false.,nlong,nlat,nlevels,nper,nper,&
per1_all,ptemp)
do i=1,nper
call region_rescale(smth_r,nlong,nlat,nlevels,ptemp(:,:,:,i),&
stan,pout(:,:,:,i))
end do
ptemp = pout
!do j=1,ns
! call onetotwo(nn,errorstart(:,j),nx,ny,pstart(:,:,j))
!end do
!endif
y0=y1
end do outer
!call gsr_region(.false.,nlong,nlat,nlevels,nper,nper,&
! ptemp,pout)
!pout=ptemp
return
end subroutine
!!!---------------------------------------------------------------
!---------------------------------------------
!!!!generate np bred vector
!--input:
!x0_start: the initial reference state
!p_start: initial random perturbations
!stan: rescaling factor
!ncl: the number of breeding cycles
!tcl: rescaling interval
!--output:
!pstart: output bred vectors
subroutine breeding_ana(x0_ref,nper,pstart,stan,ncl,tcl,ptemp)
!subroutine breeding(x0_start,nper,pstart,stan,ncl,tcl,ptemp)
include 'sphectra.h'
include 'paramod.h'
!implicit none
integer::i,j,k
!integer::nx,ny
integer::ncl,tcl,nper
real::x0_ref(nlong,nlat,nlevels,0:ncl)
real::pstart(nlong,nlat,nlevels,nper)
real::ptemp(nlong,nlat,nlevels,nper)
real::stan(nlevels)
real::x0(nlong,nlat,nlevels),x0_p(nlong,nlat,nlevels)
real::x1(nlong,nlat,nlevels),x1_p(nlong,nlat,nlevels)
real::xtemp(nlong,nlat,nlevels,0:1)
real::p0(nlong,nlat,nlevels),pp(nlong,nlat,nlevels),pout(nlong,nlat,nlevels)
real::xout(nlong,nlat,nlevels)
real::dl
ptemp=pstart
do i=1,ncl
!reference state
x0(:,:,:)=x0_ref(:,:,:,i-1)
x1(:,:,:)=x0_ref(:,:,:,i) !x1 is the final state at the end of a breeding cycle
!================================
do j=1,nper
p0(:,:,:)=ptemp(:,:,:,j)
x0_p=x0+p0 !superpose a error vector on the initial state
xtemp=0.
!----perturbed states
xtemp(:,:,:,0)=x0_p(:,:,:)
call integrate(tcl,tcl,1,xtemp)
x1_p(:,:,:)=xtemp(:,:,:,1)
!================================
pp=x1_p-x1 !calculate the perturabtions
do k=1,nlevels
call field_rescale_2d(nlong,nlat,1,&
pp(:,:,k),stan(k),pout(:,:,k)) !rescale the perturbations
end do
ptemp(:,:,:,j)=pout(:,:,:)
end do
end do
!xout=x1 !output the final reference state xout
return
end subroutine
!-----------------------right-----------
!This subroutine calculates nper NLLVs.
!--input:
!----y0_start:the initial reference state
!----nn:number of field grids.
!----ns:number of error samples
!----id0:position of initial condition in the data file
!----p0:initial perturbations
!----array:initial sequence from 1 to nn
!----stan:rescaled perturbation size
!----tcl:rescaling interval
!----ncl:number of breeding cycle
!--output:
!----pout:orthogonal vectors after breeding cycles
subroutine reorth_ana(y0_ref,nper,pstart,stan,ncl,tcl,pout)
include 'sphectra.h'
include 'paramod.h'
!implicit none
integer::i,j,k,id
integer::ncl,tcl
real::stan(nlevels)
real::per0(nlong,nlat,nlevels),per1(nlong,nlat,nlevels)
real::per1_all(nlong,nlat,nlevels,nper)
real::y0_ref(nlong,nlat,nlevels,0:ncl)
real::y0(nlong,nlat,nlevels),y1(nlong,nlat,nlevels)
real::y0_p(nlong,nlat,nlevels),y1_p(nlong,nlat,nlevels)
real::ytemp0(nlong,nlat,nlevels,0:1)
real::pstart(nlong,nlat,nlevels,nper)
real::ptemp(nlong,nlat,nlevels,nper),pout(nlong,nlat,nlevels,nper)
!------------------
ptemp=pstart !do not change pstart
!---------------------
!y0--->y1
!+per0
!y0_p--->y1_p
outer: do k=1,ncl
!reference state
y0(:,:,:)=y0_ref(:,:,:,k-1)
y1(:,:,:)=y0_ref(:,:,:,k)
!-------------------------
inner: do i=1,nper
ytemp0=0.
per0=0.
dist=0.
per0(:,:,:)=ptemp(:,:,:,i)
y0_p=y0+per0
ytemp0(:,:,:,0)=y0_p(:,:,:)
call integrate(tcl,tcl,1,ytemp0)
y1_p(:,:,:)=ytemp0(:,:,:,1) !the integration of forecast
!!!-------------------------------------
per1=y1_p-y1
!if(k<=ncl)then !mod(k,ncl)/=0)then
! do j=1,nlevels
! call field_rescale_2d(nlong,nlat,per1(:,:,j),&
! stan(j),ptemp(:,:,j,i))
! end do
!else
per1_all(:,:,:,i)=per1(:,:,:) !if orthogonalizationis necessary
!deposite all the perturbations
!!!---------------------------------------
!endif
end do inner
!if(k>ncl)then!mod(k,ncl)==0)then
call gsr_gb(.false.,nlong,nlat,nlevels,nper,nper,&
per1_all,stan,ptemp)
!do j=1,ns
! call onetotwo(nn,errorstart(:,j),nx,ny,pstart(:,:,j))
!end do
!endif
!write(131,rec=(id-1)*ncl+k)ptemp(:,:,2,:)
end do outer
pout=ptemp
return
end subroutine
!!!---------------------------------------------------------------