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tcr_fgd.f
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program tcr
*
* 2019/02/07 for FOD
* 2019/12/10 for SOD
* 2020/11/19 for FGD
* 2021/02/05 for FGD
*
integer nvar, nt, nite
real dt, xmiss, cs, cd
parameter ( nvar = 5, nt = 201, nite = 1000 )
parameter ( dt = 1. )
parameter ( xmiss = -999. )
* Geoffroy et al. 2013
c parameter ( cs = 8.2 ) !! CMIP5 MME mean upper layer heat capacity
c parameter ( cd = 109. ) !! CMIP5 MME mean deeper layer heat capacity
* Smith et al. 2020
parameter ( cs = 8.2075 ) !! CMIP6 MME mean upper layer heat capacity
parameter ( cd = 97.6382 ) !! CMIP6 MME mean deeper layer heat capacity
real erf( nvar )
real fdb( nvar )
real ecs( nvar )
real gamma( nvar )
real eps( nvar )
real epsgamma( nvar )
real df( nvar )
real frc1( nvar )
real frc2( nvar )
real tstep( nvar ) !! T for step 2xCO2
real t1ppt( nvar ) !! T for 1%
real tstep_bak( nt,nvar ) !! T for step 2xCO2
real t1ppt_bak( nt,nvar ) !! T for 1%
real tcrout( nvar ) !! TCR
real dum( nvar )
real t
real b, b_ast, delta, phi_f, phi_s
real tau_f, tau_s, af, as, fact1, fact2, fact3
real x1, y1, z1, x2, y2, z2
integer m, n, i, j, ite
* see the bottom for .ctl files
character cfo(3)*90
data cfo(1)
&/'./erf_evolution.grd'/
data cfo(2)
&/'./ecs_evolution.grd'/
data cfo(3)
&/'./tcr_evolution.grd'/
* vars: 5%, 17%, mean, 83%, 95%
data erf !! 2xCO2
& / 3.5, 3.698, 4.0, 4.302, 4.5 / !! FGD
data fdb !! lambda from process (sign reversed)
& / 1.8131, 1.5395, 1.1608, 0.7821, 0.5085 /!! FGD
data ecs !! ECS from process
& / 2.15, 2.54, 3.44, 5.23, 7.81 /!! FGD
data gamma !! CMIP6 gamma
& / 0.4161, 0.4958, 0.6177, 0.7397, 0.8193 /
data eps !! CMIP6 epsiron
& / 0.8336, 1.0227, 1.3123, 1.6018, 1.7910 /
data epsgamma !! CMIP6 epsiron x gamma
& / 0.3688, 0.5450, 0.8148, 1.0845, 1.2607 /
open ( 91, file=cfo(1), form='unformatted' )
open ( 92, file=cfo(2), form='unformatted' )
open ( 93, file=cfo(3), form='unformatted' )
*
do m = 1, nvar
df( m ) = erf( m ) / 70.
enddo
*
dum = xmiss
*
* ERF
*
write( 6,* )
& ' @@@ ERF '
t = 0.
frc1 = 0.
frc2 = 0.
do n = 1, nt
t = dt * real( n-1 )
do m = 1, nvar
frc1( m ) = erf( m ) !! F2xCO2
frc2( m ) = df( m ) * t !! F(t)
if( t .ge. 70. ) frc2( m ) = frc1( m )
enddo
do m = 1, nvar
write( 91 ) frc1( m )
enddo
do m = 1, nvar
write( 91 ) frc2( m )
enddo
enddo
*
* ECS & TCR (varying F and lambda only)
*
write( 6,* )
& ' @@@ ECS & TCR (varying F and lambda only) '
t = 0.
tstep = 0.
t1ppt = 0.
do n = 1, nt
t = dt * real( n-1 )
do m = 1, nvar
b = ( fdb( m ) + epsgamma( 3 ) ) / cs
& + epsgamma( 3 ) / cd / eps( 3 )
b_ast = ( fdb( m ) + epsgamma( 3 ) ) / cs
& - epsgamma( 3 ) / cd / eps( 3 )
delta = b**2 - 4. * ( fdb( m )*epsgamma( 3 ) )
& / ( cs * cd * eps( 3 ) )
phi_f = cs * ( b_ast - sqrt( delta ) ) / 2. / epsgamma( 3 )
phi_s = cs * ( b_ast + sqrt( delta ) ) / 2. / epsgamma( 3 )
tau_f = cs * cd * eps( 3 ) * ( b - sqrt( delta ) )
& / ( 2.*fdb( m )*epsgamma( 3 ) )
tau_s = cs * cd * eps( 3 ) * ( b + sqrt( delta ) )
& / ( 2.*fdb( m )*epsgamma( 3 ) )
af = fdb( m ) / cs - 1. / tau_s
af = af * ( tau_f * tau_s ) / ( tau_s - tau_f )
as = 1. - af
fact1 = af * exp( -t/tau_f )
& + as * exp( -t/tau_s )
fact2 = tau_f * af * ( 1. - exp( -t/tau_f ) )
& + tau_s * as * ( 1. - exp( -t/tau_s ) )
fact3 = tau_f * af * ( 1. - exp( -70./tau_f ) )
& * exp( -( t-70. )/tau_f )
& + tau_s * as * ( 1. - exp( -70./tau_s ) )
& * exp( -( t-70. )/tau_s )
tstep( m ) = ecs( m ) * ( 1. - fact1 ) !! F2xCO2 / lambda
t1ppt( m ) = ecs( m ) * df( m ) / erf( m )
& * ( t - fact2 )
if( t .gt. 70. ) then
t1ppt( m ) = ecs( m ) * ( 1. - df( m )/erf( m )*fact3 )
endif
if( n .gt. 140 ) then
tstep( m ) = ecs( m )
t1ppt( m ) = xmiss
else if( n .gt. 130 ) then
tstep( m ) = xmiss
t1ppt( m ) = xmiss
endif
enddo
do m = 1, nvar
write( 92 ) tstep( m )
enddo
do m = 1, nvar
write( 92 ) t1ppt( m )
enddo
do m = 1, nvar
tstep_bak( n,m ) = tstep( m )
t1ppt_bak( n,m ) = t1ppt( m )
enddo
if( n .eq. 70 ) then
write( 6,* )
& ' TCR (5%, 17%, mean, 83%, 95%) = '
write( 6,* ) t1ppt
endif
enddo !! n
*
* ECS & TCR (varying F and lambda, and epsiron & gamma)
*
write( 6,* )
& ' @@@ ECS & TCR (varying F and lambda, and epsiron & gamma) '
t = 0.
tstep = 0.
t1ppt = 0.
do n = 1, nt
t = dt * real( n-1 )
do m = 1, nvar
b = ( fdb( 3 ) + epsgamma( m ) ) / cs
& + epsgamma( m ) / cd / eps( m )
b_ast = ( fdb( 3 ) + epsgamma( m ) ) / cs
& - epsgamma( m ) / cd / eps( m )
delta = b**2 - 4. * ( fdb( 3 )*epsgamma( m ) )
& / ( cs * cd * eps( m ) )
phi_f = cs * ( b_ast - sqrt( delta ) ) / 2. / epsgamma( m )
phi_s = cs * ( b_ast + sqrt( delta ) ) / 2. / epsgamma( m )
tau_f = cs * cd * eps( m ) * ( b - sqrt( delta ) )
& / ( 2.*fdb( 3 )*epsgamma( m ) )
tau_s = cs * cd * eps( m ) * ( b + sqrt( delta ) )
& / ( 2.*fdb( 3 )*epsgamma( m ) )
af = fdb( 3 ) / cs - 1. / tau_s
af = af * ( tau_f * tau_s ) / ( tau_s - tau_f )
as = 1. - af
fact1 = af * exp( -t/tau_f )
& + as * exp( -t/tau_s )
fact2 = tau_f * af * ( 1. - exp( -t/tau_f ) )
& + tau_s * as * ( 1. - exp( -t/tau_s ) )
fact3 = tau_f * af * ( 1. - exp( -70./tau_f ) )
& * exp( -( t-70. )/tau_f )
& + tau_s * as * ( 1. - exp( -70./tau_s ) )
& * exp( -( t-70. )/tau_s )
tstep( m ) = ecs( 3 ) * ( 1. - fact1 ) !! F2xCO2 / lambda
t1ppt( m ) = ecs( 3 ) * df( 3 ) / erf( 3 )
& * ( t - fact2 )
if( t .gt. 70. ) then
t1ppt( m ) = ecs( 3 ) * ( 1. - df( 3 )/erf( 3 )*fact3 )
endif
if( n .gt. 140 ) then
tstep( m ) = ecs( m )
t1ppt( m ) = xmiss
else if( n .gt. 130 ) then
tstep( m ) = xmiss
t1ppt( m ) = xmiss
endif
enddo !! m
*
* multiply uncertainty
*
if( n .le. 130 ) then
do m = 1, nvar
x1 = tstep_bak( n,m ) - tstep( 3 )
y1 = tstep( m ) - tstep( 3 )
z1 = sqrt( x1**2 + y1**2 )
x2 = t1ppt_bak( n,m ) - t1ppt( 3 )
y2 = t1ppt( m ) - t1ppt( 3 )
z2 = sqrt( x2**2 + y2**2 )
if( m .lt. 3 ) then
tstep( m ) = tstep( 3 ) - z1
t1ppt( m ) = t1ppt( 3 ) - z2
else if( m .gt. 3 ) then
tstep( m ) = tstep( 3 ) + z1
t1ppt( m ) = t1ppt( 3 ) + z2
endif
enddo
endif
do m = 1, nvar
write( 93 ) tstep( m )
enddo
do m = 1, nvar
write( 93 ) t1ppt( m )
enddo
do m = 1, nvar
if( n .lt. 130 ) then
write( 93 ) dum( m )
elseif( n .lt. 140 ) then
write( 93 ) tcrout( m )
elseif( n .eq. 140 ) then
write( 93 ) dum( m )
else
write( 93 ) ecs( m )
endif
enddo
if( n .eq. 70 ) then
do m = 1, nvar
tcrout( m ) = t1ppt( m )
enddo
write( 6,* )
& ' TCR (5%, 17%, mean, 83%, 95%) = '
write( 6,* ) t1ppt
endif
enddo !! n
*
close( 91 )
close( 92 )
close( 93 )
stop
end
********************************
* .ctl file (copy and delete * below)
*
* ZDEF:
* z=1 5%ile
* z=2 17%ile
* z=3 mean
* z=4 83%ile
* z=5 95%ile
* TDEF: year
* t=>141 is ECS
********************************
*dset ^erf_evolution.grd
*options sequential
*undef -999.
*title ERF
*ydef 1 linear -90.000000 1.25
*xdef 1 linear 0.000000 1.250000
*zdef 5 linear 1 1
*tdef 201 linear 00Z01Jan0000 1yr
*vars 2
*f1 5 99 ERF 2xCO2
*f2 5 99 ERF time dependent
*ENDVARS
********************************
*dset ^ecs_evolution.grd
*options sequential
*undef -999.
*title ECS/TCR
*ydef 1 linear -90.000000 1.25
*xdef 1 linear 0.000000 1.250000
*zdef 5 linear 1 1
*tdef 201 linear 00Z01Jan000 1yr
*vars 2
*t1 5 99 temperature response to 2xCO2
*t2 5 99 temperature response to 1% increase
*ENDVARS
********************************
*dset ^tcr_evolution.grd
*options sequential
*undef -999.
*title TCR
*ydef 1 linear -90.000000 1.25
*xdef 1 linear 0.000000 1.250000
*zdef 5 linear 1 1
*tdef 201 linear 00Z01Jan000 1yr
*vars 3
*t1 5 99 temperature response to 2xCO2
*t2 5 99 temperature response to 1% increase
*tf 5 99 temperature response (TCR & ECS)
*ENDVARS