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greb.model.f90
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!
!----------------------------------------------------------
! The Globally Resolved Energy Balance (GREB) Model
!----------------------------------------------------------
!
! Authors; Dietmar Dommenget and Janine Flöter
! with numerical opitmizations by Micheal Rezny
!
! Reference: Conceptual Understanding of Climate Change with a Globally Resolved Energy Balance Model
! by Dietmar Dommenget and Janine Flöter, submitted to Climate Dynamics 2010.
!
!
! input fields: The GREB model needs the following fields to be specified before
! the main subroutine greb_model is called:
!
! z_topo(xdim,ydim): topography (<0 are ocean points) [m]
! glacier(xdim,ydim): glacier mask ( >0.5 are glacier points )
! Tclim(xdim,ydim,nstep_yr): mean Tsurf [K]
! uclim(xdim,ydim,nstep_yr): mean zonal wind speed [m/s]
! vclim(xdim,ydim,nstep_yr): mean meridional wind speed [m/s]
! qclim(xdim,ydim,nstep_yr): mean atmospheric humidity [kg/kg]
! mldclim(xdim,ydim,nstep_yr): mean ocean mixed layer depth [m]
! Toclim(xdim,ydim,nstep_yr): mean deep ocean temperature [K]
! swetclim(xdim,ydim,nstep_yr): soil wetnees, fraction of total [0-1]
! sw_solar(ydim,nstep_yr): 24hrs mean solar radiation [W/m^2]
!
!
!+++++++++++++++++++++++++++++++++++++++
module mo_numerics
!+++++++++++++++++++++++++++++++++++++++
! declare output folder name (ajr, 2014-03-11)
character(len=256) :: outfldr
! numerical parameter
integer, parameter :: xdim = 96, ydim = 48 ! field dimensions
integer, parameter :: ndays_yr = 365 ! number of days per year
integer, parameter :: dt = 12*3600 ! time step [s]
integer, parameter :: dt_crcl = 0.5*3600 ! time step circulation [s]
integer, parameter :: ndt_days = 24*3600/dt ! number of timesteps per day
integer, parameter :: nstep_yr = ndays_yr*ndt_days ! number of timesteps per year
integer :: time_flux = 0 ! length of integration for flux correction [yrs]
integer :: time_ctrl = 0 ! length of integration for control run [yrs]
integer :: time_scnr = 0 ! length of integration for scenario run [yrs]
integer :: ipx = 1 ! points for diagonstic print outs
integer :: ipy = 1 ! points for diagonstic print outs
integer, parameter, dimension(12) :: jday_mon = (/31,28,31,30,31,30,31,31,30,31,30,31/) ! days per
real, parameter :: dlon = 360./xdim ! linear increment in lon
real, parameter :: dlat = 180./ydim ! linear increment in lat
integer :: ireal = 4 ! record length for IO (machine dependent)
! ireal = 4 for Mac Book Pro
namelist / numerics / time_flux, time_ctrl, time_scnr
end module mo_numerics
!+++++++++++++++++++++++++++++++++++++++
module mo_physics
!+++++++++++++++++++++++++++++++++++++++
use mo_numerics
integer :: log_exp = 0 ! process control logics for sens. exp.
! physical parameter (natural constants)
parameter( pi = 3.1416 )
parameter( sig = 5.6704e-8 ) ! stefan-boltzmann constant [W/m^2/K^4]
parameter( rho_ocean = 999.1 ) ! density of water at T=15C [kg/m^2]
parameter( rho_land = 2600. ) ! density of solid rock [kg/m^2]
parameter( rho_air = 1.2 ) ! density of air at 20C at NN
parameter( cp_ocean = 4186. ) ! specific heat capacity of water at T=15C [J/kg/K]
parameter( cp_land = cp_ocean/4.5 ) ! specific heat capacity of dry land [J/kg/K]
parameter( cp_air = 1005. ) ! specific heat capacity of air [J/kg/K]
parameter( eps = 1. ) ! emissivity for IR
! physical parameter (model values)
parameter( d_ocean = 50. ) ! depth of ocean column [m]
parameter( d_land = 2. ) ! depth of land column [m]
parameter( d_air = 5000. ) ! depth of air column [m]
parameter( cap_ocean = cp_ocean*rho_ocean ) ! heat capacity 1m ocean [J/K/m^2]
parameter( cap_land = cp_land*rho_land*d_land ) ! heat capacity land [J/K/m^2]
parameter( cap_air = cp_air*rho_air*d_air ) ! heat capacity air [J/K/m^2]
parameter( ct_sens = 22.5 ) ! coupling for sensible heat
parameter( da_ice = 0.25 ) ! albedo diff for ice covered points
parameter( a_no_ice = 0.1 ) ! albedo for non-ice covered points
parameter( a_cloud = 0.35 ) ! albedo for clouds
parameter( Tl_ice1 = 273.15-10. ) ! temperature range of land snow-albedo feedback
parameter( Tl_ice2 = 273.15 ) ! temperature range of land snow-albedo feedback
parameter( To_ice1 = 273.15-7. ) ! temperature range of ocean ice-albedo feedback
parameter( To_ice2 = 273.15-1.7 ) ! temperature range of ocean ice-albedo feedback
parameter( co_turb = 5.0 ) ! turbolent mixing to deep ocean [W/K/m^2]
parameter( kappa = 8e5 ) ! atmos. diffusion coefficient [m^2/s]
parameter( ce = 2e-3 ) ! laten heat transfer coefficient for ocean
parameter( cq_latent = 2.257e6 ) ! latent heat of condensation/evapoartion f water [J/kg]
parameter( cq_rain = -0.1/24./3600. ) ! decrease in air water vapor due to rain [1/s]
parameter( z_air = 8400. ) ! scaling height atmos. heat, CO2
parameter( z_vapor = 5000. ) ! scaling height atmos. water vapor diffusion
parameter( r_qviwv = 2.6736e3) ! regres. factor between viwv and q_air [kg/m^3]
! parameter emissivity
real, parameter, dimension(10) :: p_emi = (/9.0721, 106.7252, 61.5562, 0.0179, 0.0028, &
& 0.0570, 0.3462, 2.3406, 0.7032, 1.0662/)
! declare climate fields
real, dimension(xdim,ydim) :: z_topo, glacier,z_ocean
real, dimension(xdim,ydim,nstep_yr) :: Tclim, uclim, vclim, qclim, mldclim, Toclim, cldclim
real, dimension(xdim,ydim,nstep_yr) :: TF_correct, qF_correct, ToF_correct, swetclim, dTrad
real, dimension(ydim,nstep_yr) :: sw_solar
! declare constant fields
real, dimension(xdim,ydim) :: cap_surf
integer jday, ityr
! declare some program constants
real, dimension(xdim, ydim) :: wz_air, wz_vapor
real, dimension(xdim,ydim,nstep_yr) :: uclim_m, uclim_p
real, dimension(xdim,ydim,nstep_yr) :: vclim_m, vclim_p
real :: t0, t1, t2
namelist / physics / log_exp
end module mo_physics
!+++++++++++++++++++++++++++++++++++++++
module mo_diagnostics
!+++++++++++++++++++++++++++++++++++++++
USE mo_numerics, ONLY: xdim, ydim
! declare diagnostic fields
real, dimension(xdim,ydim) :: Tsmn, Tamn, qmn, swmn, lwmn, qlatmn, qsensmn, &
& ftmn, fqmn, amn, Tomn
! declare output fields
real, dimension(xdim,ydim) :: Tmm, Tamm, Tomm, qmm, apmm
end module mo_diagnostics
!+++++++++++++++++++++++++++++++++++++++
subroutine greb_model
!+++++++++++++++++++++++++++++++++++++++
! climate model main loop
use mo_numerics
use mo_physics
use mo_diagnostics
! declare temporary fields
real, dimension(xdim,ydim) :: Ts0, Ts1, Ta0, Ta1, To0, To1, q0, q1, &
& ts_ini, ta_ini, q_ini, to_ini
open(21,file=trim(outfldr)//'control',ACCESS='DIRECT',FORM='UNFORMATTED', RECL=ireal*xdim*ydim)
open(22,file=trim(outfldr)//'scenario',ACCESS='DIRECT',FORM='UNFORMATTED', RECL=ireal*xdim*ydim)
dTrad = -0.16*Tclim -5. ! offset Tatmos-rad
! set ocean depth
z_ocean=0
do i=1,nstep_yr
where(mldclim(:,:,i).gt.z_ocean) z_ocean = mldclim(:,:,i)
end do
z_ocean = 3.0*z_ocean
if (log_exp == 1) where(z_topo > 1.) z_topo = 1.0 ! sens. exp. constant topo
if (log_exp <= 2) cldclim = 0.7 ! sens. exp. constant cloud cover
if (log_exp <= 3) qclim = 0.0052 ! sens. exp. constant water vapor
if (log_exp <= 9) mldclim = d_ocean ! sens. exp. no deep ocean
if (log_exp == 11) mldclim = d_ocean ! sens. exp. no deep ocean
! heat capacity global [J/K/m^2]
where (z_topo > 0.) cap_surf = cap_land
where (z_topo <= 0.) cap_surf = cap_ocean*mldclim(:,:,1)
! initialize fields
Ts_ini = Tclim(:,:,nstep_yr) ! initial value temp. surf
Ta_ini = Ts_ini ! initial value atm. temp.
To_ini = Toclim(:,:,nstep_yr) ! initial value temp. surf
q_ini = qclim(:,:,nstep_yr) ! initial value atmos water vapor
CO2_ctrl = 340.
if (log_exp == 12 .or. log_exp == 13 ) CO2_ctrl = 298. ! A1B scenario
! define some program constants
wz_air = exp(-z_topo/z_air)
wz_vapor = exp(-z_topo/z_vapor)
where (uclim(:,:,:) >= 0.0)
uclim_m = uclim
uclim_p = 0.0
elsewhere
uclim_m = 0.0
uclim_p = uclim
end where
where (vclim(:,:,:) >= 0.0)
vclim_m = vclim
vclim_p = 0.0
elsewhere
vclim_m = 0.0
vclim_p = vclim
end where
! compute Q-flux corrections
print*,'% flux correction ', CO2_ctrl
call qflux_correction(CO2_ctrl, Ts_ini, Ta_ini, q_ini, To_ini)
! test write qflux
do irec=1, nstep_yr
write(21,rec=irec) TF_correct(:,:,irec)
end do
! control run
print*,'% CONTROL RUN CO2=',CO2_ctrl,' time=', time_ctrl,'yr'
Ts1 = Ts_ini; Ta1 = Ta_ini; To1 = To_ini; q1 = q_ini; ! initialize fields
mon=1; year=1970; irec=0; Tmm=0.; Tamm=0.; qmm=0.; apmm=0.;
do it=1, time_ctrl*nstep_yr ! main time loop
call time_loop(it, isrec, year, CO2_ctrl, irec, mon, 21, Ts1, Ta1, q1, To1, Ts0,Ta0, q0, To0 )
Ts1=Ts0; Ta1=Ta0; q1=q0; To1=To0
end do
! scenario run
print*,'% SCENARIO EXP: ',log_exp,' time=', time_scnr,'yr'
Ts1 = Ts_ini; Ta1 = Ta_ini; q1 = q_ini; To1 = To_ini ! initialize fields
year=1940; CO2=280.0; mon=1; irec=0; Tmm=0.; Tamm=0.; qmm=0.; apmm=0.;
do it=1, time_scnr*nstep_yr ! main time loop
call co2_level(it, year, CO2)
! sens. exp. SST+1
if(log_exp >= 14 .and. log_exp <= 16) CO2 = CO2_ctrl
if(log_exp >= 14 .and. log_exp <= 16) where (z_topo < 0.0) Ts1 = Tclim(:,:,ityr)+1.0
call time_loop(it,isrec, year, CO2, irec, mon, 22, Ts1, Ta1, q1, To1, Ts0,Ta0, q0, To0 )
Ts1=Ts0; Ta1=Ta0; q1=q0; To1=To0
if (mod(it,nstep_yr) == 0) year=year+1
end do
end subroutine
!+++++++++++++++++++++++++++++++++++++++
subroutine time_loop(it, isrec, year, CO2, irec, mon, ionum, Ts1, Ta1, q1, To1, Ts0,Ta0, q0, To0)
!+++++++++++++++++++++++++++++++++++++++
! main time loop
use mo_numerics
use mo_physics
real, dimension(xdim,ydim):: Ts1, Ta1, q1, To1, Ts0,Ta0, q0, To0, sw, &
& albedo, Q_sens, Q_lat, Q_lat_air, dq_eva, &
& dq_rain, dTa_crcl, dq_crcl, dq, dT_ocean, dTo, &
& LW_surf, LWair_down, LWair_up, em
jday = mod((it-1)/ndt_days,ndays_yr)+1 ! current calendar day in year
ityr = mod((it-1),nstep_yr)+1 ! time step in year
call tendencies(CO2, Ts1, Ta1, To1, q1, albedo, SW, LW_surf, Q_lat, &
& Q_sens, Q_lat_air, dq_eva, dq_rain, dq_crcl, &
& dTa_crcl, dT_ocean, dTo, LWair_down, LWair_up, em)
! surface temperature
Ts0 = Ts1 +dT_ocean +dt*( SW +LW_surf -LWair_down +Q_lat +Q_sens +TF_correct(:,:,ityr)) / cap_surf
! air temperature
Ta0 = Ta1 +dTa_crcl +dt*( LWair_up +LWair_down -em*LW_surf +Q_lat_air -Q_sens )/cap_air
! deep ocean temperature
To0 = To1 +dTo +ToF_correct(:,:,ityr)
! air water vapor
dq = dt*(dq_eva+dq_rain) +dq_crcl + qF_correct(:,:,ityr)
where(dq .le. -q1 ) dq = -0.9*q1 ! no negative q; numerical stability
q0 = q1 + dq
! sea ice heat capacity
call seaice(Ts0)
! write output
call output(it, ionum, irec, mon, ts0, ta0, to0, q0, albedo)
! diagnostics: annual means plots
call diagonstics(it, year, CO2, ts0, ta0, to0, q0, albedo, sw, lw_surf, q_lat, q_sens)
end subroutine time_loop
!+++++++++++++++++++++++++++++++++++++++
subroutine tendencies(CO2, Ts1, Ta1, To1, q1, albedo, SW, LW_surf, Q_lat, Q_sens, Q_lat_air, dq_eva, &
& dq_rain, dq_crcl, dTa_crcl, dT_ocean, dTo, LWair_down, LWair_up, em)
!+++++++++++++++++++++++++++++++++++++++
use mo_numerics
use mo_physics
! declare temporary fields
real, dimension(xdim,ydim) :: Ts1, Ta1, To1, q1, albedo, sw, LWair_up, &
& LWair_down, em, Q_sens, Q_lat, Q_lat_air, &
& dq_eva, dq_rain, dTa_crcl, dq_crcl, LW_surf, &
& dT_ocean, dTo
! SW radiation model
call SWradiation(Ts1, sw, albedo)
! LW radiation model
call LWradiation(Ts1, Ta1, q1, CO2, LW_surf, LWair_up, LWair_down, em)
! sensible heat flux
Q_sens = ct_sens*(Ta1-Ts1)
! hydro. model
call hydro(Ts1, q1, Q_lat, Q_lat_air, dq_eva, dq_rain)
! atmos. circulation
!$omp parallel sections
!$omp section
call circulation(Ta1, dTa_crcl, z_air, wz_air) ! air temp
!$omp section
call circulation( q1, dq_crcl, z_vapor, wz_vapor) ! atmos water vapor
!$omp end parallel sections
! deep ocean interaction
call deep_ocean(Ts1, To1, dT_ocean, dTo)
end subroutine tendencies
!+++++++++++++++++++++++++++++++++++++++
subroutine qflux_correction(CO2_ctrl, Ts1, Ta1, q1, To1)
!+++++++++++++++++++++++++++++++++++++++
! compute heat flux correction values
USE mo_numerics
USE mo_physics
! declare temporary fields
real, dimension(xdim,ydim) :: Ts0, Ts1, Ta0, Ta1, To0, To1, q0, q1, sw, albedo, &
& Q_sens, Q_lat, Q_lat_air, dq_eva, dq_rain, LW_surf, &
& LWair_down, LWair_up, em, dTa_crcl, dq_crcl, dTs, &
& dTa, dq, T_error, dT_ocean, dTo
! time loop
do it=1, time_flux*ndt_days*ndays_yr
jday = mod((it-1)/ndt_days,ndays_yr)+1 ! current calendar day in year
ityr = mod((it-1),nstep_yr)+1 ! time step in year
call tendencies(CO2_ctrl, Ts1, Ta1, To1, q1, albedo, SW, LW_surf, Q_lat, &
& Q_sens, Q_lat_air, dq_eva, dq_rain, dq_crcl, dTa_crcl, &
& dT_ocean, dTo, LWair_down, LWair_up, em)
! surface temperature without heat flux correction
dTs = dt*( sw +LW_surf -LWair_down +Q_lat +Q_sens) / cap_surf
Ts0 = Ts1 +dTs +dT_ocean
! air temperature
dTa = dt*( LWair_up +LWair_down -em*LW_surf +Q_lat_air -Q_sens)/cap_air
Ta0 = Ta1 + dTa +dTa_crcl
! deep ocean temperature without heat flux correction
To0 = To1 +dTo
! air water vapor without flux correction
dq = dt*(dq_eva+dq_rain)
q0 = q1 +dq +dq_crcl
! heat flux correction Tsurf
T_error = Tclim(:,:,ityr) -Ts0 ! error relative to Tclim
TF_correct(:,:,ityr) = T_error*cap_surf/dt ! heat flux in [W/m^2]
! surface temperature with heat flux correction
Ts0 = Ts1 +dTs +dT_ocean +TF_correct(:,:,ityr)*dt/ cap_surf
! heat flux correction deep ocean
ToF_correct(:,:,ityr) = Toclim(:,:,ityr) -To0 ! heat flux in [K/dt]
! deep ocean temperature with heat flux correction
To0 = To1 +dTo +ToF_correct(:,:,ityr)
! water vapor flux correction
qF_correct(:,:,ityr) = qclim(:,:,ityr) -q0
! air water vapor with flux correction
q0 = q1 + dq +dq_crcl + qF_correct(:,:,ityr)
! sea ice heat capacity
call seaice(Ts0)
! diagnostics: annual means plots
call diagonstics(it, 0.0, CO2_ctrl, ts0, ta0, to0, q0, albedo, sw, lw_surf, q_lat, q_sens)
! memory
Ts1=Ts0; Ta1=Ta0; q1=q0; To1=To0;
end do
end subroutine qflux_correction
!+++++++++++++++++++++++++++++++++++++++
subroutine SWradiation(Tsurf, sw, albedo)
!+++++++++++++++++++++++++++++++++++++++
! SW radiation model
USE mo_numerics, ONLY: xdim, ydim
USE mo_physics, ONLY: ityr, sw_solar,da_ice, a_no_ice, a_cloud, z_topo &
& , Tl_ice1, Tl_ice2, To_ice1, To_ice2, glacier &
& , cldclim, log_exp
! declare temporary fields
real, dimension(xdim,ydim) :: Tsurf, sw, albedo, a_surf, a_atmos
! atmos albedo
a_atmos=cldclim(:,:,ityr)*a_cloud
! surface albedo
! Land: ice -> albedo linear function of T_surf
where(z_topo >= 0. .and. Tsurf <= Tl_ice1) a_surf = a_no_ice+da_ice ! ice
where(z_topo >= 0. .and. Tsurf >= Tl_ice2) a_surf = a_no_ice ! no ice
where(z_topo >= 0. .and. Tsurf > Tl_ice1 .and. Tsurf < Tl_ice2 ) &
& a_surf = a_no_ice +da_ice*(1-(Tsurf-Tl_ice1)/(Tl_ice2-Tl_ice1))
! Ocean: ice -> albedo/heat capacity linear function of T_surf
where(z_topo < 0. .and. Tsurf <= To_ice1) a_surf = a_no_ice+da_ice ! ice
where(z_topo < 0. .and. Tsurf >= To_ice2) a_surf = a_no_ice ! no ice
where(z_topo < 0. .and. Tsurf > To_ice1 .and. Tsurf < To_ice2 ) &
& a_surf = a_no_ice+da_ice*(1-(Tsurf-To_ice1)/(To_ice2-To_ice1))
! glacier -> no albedo changes
where(glacier > 0.5) a_surf = a_no_ice+da_ice
if (log_exp <= 5) a_surf = a_no_ice
! SW flux
albedo=a_surf+a_atmos-a_surf*a_atmos
forall (i=1:xdim)
sw(i,:)=SW_solar(:,ityr)*(1-albedo(i,:))
end forall
end subroutine SWradiation
!+++++++++++++++++++++++++++++++++++++++
subroutine LWradiation(Tsurf, Tair, q, CO2, LWsurf, LWair_up, LWair_down, em)
!+++++++++++++++++++++++++++++++++++++++
! new approach with LW atmos
USE mo_numerics, ONLY: xdim, ydim
USE mo_physics, ONLY: sig, eps, qclim, cldclim, z_topo, jday, ityr, &
& r_qviwv, z_air, z_vapor, dTrad, p_emi, log_exp
! declare temporary fields
real, dimension(xdim,ydim) :: Tsurf, Tair, q, LWsurf, LWair, e_co2, e_cloud, &
& LWair_up, LWair_down, e_vapor, em
e_co2 = exp(-z_topo/z_air)*CO2 ! CO2
e_vapor = exp(-z_topo/z_air)*r_qviwv*q ! water vapor
e_cloud = cldclim(:,:,ityr) ! clouds
if(log_exp == 11) e_vapor = exp(-z_topo/z_air)*r_qviwv*qclim(:,:,ityr) ! sens. exp. linear-function
! total
em = p_emi(4)*log( p_emi(1)*e_co2 +p_emi(2)*e_vapor +p_emi(3) ) +p_emi(7) &
& +p_emi(5)*log( p_emi(1)*e_co2 +p_emi(3) ) &
& +p_emi(6)*log( p_emi(2)*e_vapor +p_emi(3) )
em = (p_emi(8)-e_cloud)/p_emi(9)*(em-p_emi(10))+p_emi(10)
if(log_exp == 11) em = em +0.022/(0.15*24.)*r_qviwv*(q-qclim(:,:,ityr)) ! sens. exp. linear-function
LWsurf = -sig*Tsurf**4
LWair_down = -em*sig*(Tair+dTrad(:,:,ityr))**4
LWair_up = LWair_down
end subroutine LWradiation
!+++++++++++++++++++++++++++++++++++++++
subroutine hydro(Tsurf, q, Qlat, Qlat_air, dq_eva, dq_rain)
!+++++++++++++++++++++++++++++++++++++++
! hydrological model for latent heat and water vapor
USE mo_numerics, ONLY: xdim, ydim
USE mo_physics, ONLY: rho_air, uclim, vclim, z_topo, swetclim, ityr, &
& ce, cq_latent, cq_rain, z_air, r_qviwv, log_exp
! declare temporary fields
real, dimension(xdim,ydim) :: Tsurf, q, Qlat, Qlat_air, qs, dq_eva, &
& dq_rain, abswind
Qlat=0.; Qlat_air=0.; dq_eva=0.; dq_rain=0.
if(log_exp <= 6 .or. log_exp == 13 .or. log_exp == 15) return
abswind = sqrt(uclim(:,:,ityr)**2 +vclim(:,:,ityr)**2)
where(z_topo > 0. ) abswind = sqrt(abswind**2 +2.0**2) ! land
where(z_topo < 0. ) abswind = sqrt(abswind**2 +3.0**2) ! ocean
! saturated humiditiy (max. air water vapor)
qs = 3.75e-3*exp(17.08085*(Tsurf-273.15)/(Tsurf-273.15+234.175));
qs = qs*exp(-z_topo/z_air) ! scale qs by topography
! latent heat flux surface
Qlat = (q-qs)*abswind*cq_latent*rho_air*ce*swetclim(:,:,ityr)
! change in water vapor
dq_eva = -Qlat/cq_latent/r_qviwv ! evaporation
dq_rain = cq_rain*q ! rain
! latent heat flux atmos
Qlat_air = -dq_rain*cq_latent*r_qviwv
end subroutine hydro
!+++++++++++++++++++++++++++++++++++++++
subroutine seaice(Tsurf)
!+++++++++++++++++++++++++++++++++++++++
! SW radiation model
USE mo_numerics, ONLY: xdim, ydim
USE mo_physics, ONLY: ityr, z_topo, cap_surf, cap_land, cap_ocean, &
& log_exp, To_ice1, To_ice2, glacier, mldclim
! declare temporary fields
real, dimension(xdim,ydim) :: Tsurf
where(z_topo < 0. .and. Tsurf <= To_ice1) cap_surf = cap_land ! sea ice
where(z_topo < 0. .and. Tsurf >= To_ice2) cap_surf = cap_ocean*mldclim(:,:,ityr) ! open ocean
where(z_topo < 0. .and. Tsurf > To_ice1 .and. Tsurf < To_ice2 ) &
& cap_surf = cap_land + (cap_ocean*mldclim(:,:,ityr)-cap_land) &
& /(To_ice2-To_ice1)*(Tsurf-To_ice1)
if( log_exp <= 5 ) then
where(z_topo > 0. ) cap_surf = cap_land ! sea ice
where(z_topo < 0. ) cap_surf = cap_ocean*mldclim(:,:,ityr) ! open ocean
end if
! glacier -> no sea ice change
where(glacier > 0.5) cap_surf = cap_land ! ice sheet
end subroutine seaice
!+++++++++++++++++++++++++++++++++++++++
subroutine deep_ocean(Ts, To, dT_ocean, dTo)
!+++++++++++++++++++++++++++++++++++++++
! deep ocean model
USE mo_numerics, ONLY: xdim, ydim, nstep_yr, dt
USE mo_physics, ONLY: ityr, z_topo, mldclim, log_exp, To_ice2, &
& cap_ocean, co_turb, z_ocean
! declare temporary fields
real, dimension(xdim,ydim) :: Ts, To, dT_ocean, dTo, dmld, Tx
dT_ocean = 0.0; dTo = 0.0
if ( log_exp <= 9 .or. log_exp == 11 ) return
if ( log_exp >= 14 .and. log_exp <= 16 ) return
if (ityr > 1) dmld = mldclim(:,:,ityr)-mldclim(:,:,ityr-1)
if (ityr == 1) dmld = mldclim(:,:,ityr)-mldclim(:,:,nstep_yr)
! entrainment & detrainment
where ( z_topo < 0 .and. Ts >= To_ice2 .and. dmld < 0) &
& dTo = -dmld/(z_ocean-mldclim(:,:,ityr))*(Ts-To)
where ( z_topo < 0 .and. Ts >= To_ice2 .and. dmld > 0) &
& dT_ocean = dmld/mldclim(:,:,ityr)*(To-Ts)
c_effmix = 0.5
dTo = c_effmix*dTo
dT_ocean = c_effmix*dT_ocean
! turbulent mixing
Tx = max(To_ice2,Ts)
dTo = dTo + dt*co_turb*(Tx-To)/(cap_ocean*(z_ocean-mldclim(:,:,ityr)))
dT_ocean = dT_ocean + dt*co_turb*(To-Tx)/(cap_ocean*mldclim(:,:,ityr))
end subroutine deep_ocean
!+++++++++++++++++++++++++++++++++++++++
subroutine circulation(X_in, dX_crcl, h_scl, wz)
!+++++++++++++++++++++++++++++++++++++++
! circulation with shorter time step
USE mo_numerics, ONLY: xdim, ydim, dt, dt_crcl
USE mo_physics, ONLY: log_exp, z_vapor
implicit none
real, dimension(xdim,ydim), intent(in) :: X_in, wz
real, intent(in) :: h_scl
real, dimension(xdim,ydim), intent(out) :: dX_crcl
real, dimension(xdim,ydim) :: X, dx_diffuse, dx_advec
integer time, tt
if(log_exp <= 4 ) return
if(log_exp .eq. 7 .and. h_scl .eq. z_vapor) return
if(log_exp .eq. 16 .and. h_scl .eq. z_vapor) return
time=max(1,nint(float(dt)/dt_crcl))
X = X_in;
if(log_exp .eq. 8 .and. h_scl .eq. z_vapor) then
do tt=1, time ! time loop circulation
call diffusion(X, dx_diffuse, h_scl, wz)
X = X + dx_diffuse
end do ! time loop
else
do tt=1, time ! time loop circulation
call diffusion(X, dx_diffuse, h_scl, wz)
call advection(X, dx_advec, h_scl, wz)
X = X + dx_diffuse + dx_advec
end do ! time loop
end if
dX_crcl = X - X_in
end subroutine circulation
!+++++++++++++++++++++++++++++++++++++++
subroutine diffusion(T1, dX_diffuse,h_scl, wz)
!+++++++++++++++++++++++++++++++++++++++
! diffusion
USE mo_numerics, ONLY: xdim, ydim, dt, dlon, dlat, dt_crcl
USE mo_physics, ONLY: pi, z_topo, log_exp, kappa, z_vapor
implicit none
real, dimension(xdim,ydim), intent(in) :: T1, wz
real , intent(in) :: h_scl
real, dimension(xdim,ydim), intent(out) :: dX_diffuse
integer :: i
integer, dimension(ydim) :: ilat = (/(i,i=1,ydim)/)
real, dimension(ydim) :: lat, dxlat, ccx
real, dimension(xdim) :: T1h, dTxh
real, dimension(xdim,ydim) :: dTx, dTy
real :: deg, dd, dx, dy, dyy, ccy, ccx2
integer :: j, k, km1, kp1, jm1, jm2, jm3, jp1, jp2, jp3
integer :: time2, dtdff2, tt2
deg = 2.*pi*6.371e6/360.; ! length of 1deg latitude [m]
dx = dlon; dy=dlat; dyy=dy*deg
lat = dlat*ilat-dlat/2.-90.; dxlat=dx*deg*cos(2.*pi/360.*lat)
ccy=kappa*dt_crcl/dyy**2
ccx=kappa*dt_crcl/dxlat**2
! latitudinal
do k=1, ydim
km1=k-1; kp1=k+1
if ( k>=2 .and. k<=ydim-1) dTy(:,k)=ccy*( &
& wz(:,km1)*(T1(:,km1)-T1(:,k)) +wz(:,kp1)*(T1(:,kp1)-T1(:,k)) )
if ( k==1 ) dTy(:,k)=ccy*wz(:,kp1)*(-T1(:,k)+T1(:,kp1))
if ( k==ydim ) dTy(:,k)=ccy*wz(:,km1)*(T1(:,km1)-T1(:,k))
! longitudinal
if ( dxlat(k) > 2.5e5) then ! unitl 25degree
j = 1
jp1 = j+1; jp2 = j+2; jp3 = j+3; jm1 = xdim; jm2 = xdim-1; jm3 = xdim-2
dTx(j,k)=ccx(k)*( &
& 10*( wz(jm1,k)*(T1(jm1,k)-T1(j,k)) +wz(jp1,k)*(T1(jp1,k) -T1(j,k)) ) &
& +4*( wz(jm2,k)*(T1(jm2,k)-T1(jm1,k)) +wz(jm1,k)*(T1(j,k) -T1(jm1,k)) ) &
& +4*( wz(jp1,k)*(T1(j,k) -T1(jp1,k)) +wz(jp2,k)*(T1(jp2,k) -T1(jp1,k)) ) &
& +1*( wz(jm3,k)*(T1(jm3,k)-T1(jm2,k)) +wz(jm2,k)*(T1(jm1,k) -T1(jm2,k)) ) &
& +1*( wz(jp2,k)*(T1(jp1,k)-T1(jp2,k)) +wz(jp3,k)*(T1(jp3,k) -T1(jp2,k)) ) )/20.
j = 2
jp1 = j+1; jp2 = j+2; jp3 = j+3; jm1 = j-1; jm2 = xdim; jm3 = xdim-1
dTx(j,k)=ccx(k)*( &
& 10*( wz(jm1,k)*(T1(jm1,k)-T1(j,k)) +wz(jp1,k)*(T1(jp1,k) -T1(j,k)) ) &
& +4*( wz(jm2,k)*(T1(jm2,k)-T1(jm1,k)) +wz(jm1,k)*(T1(j,k) -T1(jm1,k)) ) &
& +4*( wz(jp1,k)*(T1(j,k) -T1(jp1,k)) +wz(jp2,k)*(T1(jp2,k) -T1(jp1,k)) ) &
& +1*( wz(jm3,k)*(T1(jm3,k)-T1(jm2,k)) +wz(jm2,k)*(T1(jm1,k) -T1(jm2,k)) ) &
& +1*( wz(jp2,k)*(T1(jp1,k)-T1(jp2,k)) +wz(jp3,k)*(T1(jp3,k) -T1(jp2,k)) ) )/20.
j = 3
jp1 = j+1; jp2 = j+2; jp3 = j+3; jm1 = j-1; jm2 = j-2; jm3 = xdim
dTx(j,k)=ccx(k)*( &
& 10*( wz(jm1,k)*(T1(jm1,k)-T1(j,k)) +wz(jp1,k)*(T1(jp1,k) -T1(j,k)) ) &
& +4*( wz(jm2,k)*(T1(jm2,k)-T1(jm1,k)) +wz(jm1,k)*(T1(j,k) -T1(jm1,k)) ) &
& +4*( wz(jp1,k)*(T1(j,k) -T1(jp1,k)) +wz(jp2,k)*(T1(jp2,k) -T1(jp1,k)) ) &
& +1*( wz(jm3,k)*(T1(jm3,k)-T1(jm2,k)) +wz(jm2,k)*(T1(jm1,k) -T1(jm2,k)) ) &
& +1*( wz(jp2,k)*(T1(jp1,k)-T1(jp2,k)) +wz(jp3,k)*(T1(jp3,k) -T1(jp2,k)) ) )/20.
do j=4, xdim-3 ! longitudinal
jm1=j-1; jp1=j+1; jm2=j-2; jp2=j+2; jm3=j-3; jp3=j+3
! 3.order solution: stable unitl 84degree (dx=2.5degree, a=5e5)
dTx(j,k)=ccx(k)*( &
& 10*( wz(jm1,k)*(T1(jm1,k)-T1(j,k)) +wz(jp1,k)*(T1(jp1,k) -T1(j,k)) ) &
& +4*( wz(jm2,k)*(T1(jm2,k)-T1(jm1,k)) +wz(jm1,k)*(T1(j,k) -T1(jm1,k)) ) &
& +4*( wz(jp1,k)*(T1(j,k) -T1(jp1,k)) +wz(jp2,k)*(T1(jp2,k) -T1(jp1,k)) ) &
& +1*( wz(jm3,k)*(T1(jm3,k)-T1(jm2,k)) +wz(jm2,k)*(T1(jm1,k) -T1(jm2,k)) ) &
& +1*( wz(jp2,k)*(T1(jp1,k)-T1(jp2,k)) +wz(jp3,k)*(T1(jp3,k) -T1(jp2,k)) ) )/20.
end do
j = xdim-2
jm1 = j-1; jm2 = j-2; jm3 = j-3; jp1 = j+1; jp2 = j+2; jp3 = 1;
dTx(j,k)=ccx(k)*( &
& 10*( wz(jm1,k)*(T1(jm1,k)-T1(j,k)) +wz(jp1,k)*(T1(jp1,k) -T1(j,k)) ) &
& +4*( wz(jm2,k)*(T1(jm2,k)-T1(jm1,k)) +wz(jm1,k)*(T1(j,k) -T1(jm1,k)) ) &
& +4*( wz(jp1,k)*(T1(j,k) -T1(jp1,k)) +wz(jp2,k)*(T1(jp2,k) -T1(jp1,k)) ) &
& +1*( wz(jm3,k)*(T1(jm3,k)-T1(jm2,k)) +wz(jm2,k)*(T1(jm1,k) -T1(jm2,k)) ) &
& +1*( wz(jp2,k)*(T1(jp1,k)-T1(jp2,k)) +wz(jp3,k)*(T1(jp3,k) -T1(jp2,k)) ) )/20.
j = xdim-1
jm1 = j-1; jm2 = j-2; jm3 = j-3; jp1 = j+1; jp2 = 1; jp3 = 2
dTx(j,k)=ccx(k)*( &
& 10*( wz(jm1,k)*(T1(jm1,k)-T1(j,k)) +wz(jp1,k)*(T1(jp1,k) -T1(j,k)) ) &
& +4*( wz(jm2,k)*(T1(jm2,k)-T1(jm1,k)) +wz(jm1,k)*(T1(j,k) -T1(jm1,k)) ) &
& +4*( wz(jp1,k)*(T1(j,k) -T1(jp1,k)) +wz(jp2,k)*(T1(jp2,k) -T1(jp1,k)) ) &
& +1*( wz(jm3,k)*(T1(jm3,k)-T1(jm2,k)) +wz(jm2,k)*(T1(jm1,k) -T1(jm2,k)) ) &
& +1*( wz(jp2,k)*(T1(jp1,k)-T1(jp2,k)) +wz(jp3,k)*(T1(jp3,k) -T1(jp2,k)) ) )/20.
j = xdim
jm1 = j-1; jm2 = j-2; jm3 = j-3; jp1 = 1; jp2 = 2; jp3 = 3
dTx(j,k)=ccx(k)*( &
& 10*( wz(jm1,k)*(T1(jm1,k)-T1(j,k)) +wz(jp1,k)*(T1(jp1,k) -T1(j,k)) ) &
& +4*( wz(jm2,k)*(T1(jm2,k)-T1(jm1,k)) +wz(jm1,k)*(T1(j,k) -T1(jm1,k)) ) &
& +4*( wz(jp1,k)*(T1(j,k) -T1(jp1,k)) +wz(jp2,k)*(T1(jp2,k) -T1(jp1,k)) ) &
& +1*( wz(jm3,k)*(T1(jm3,k)-T1(jm2,k)) +wz(jm2,k)*(T1(jm1,k) -T1(jm2,k)) ) &
& +1*( wz(jp2,k)*(T1(jp1,k)-T1(jp2,k)) +wz(jp3,k)*(T1(jp3,k) -T1(jp2,k)) ) )/20.
else ! high resolution -> smaller time steps
dd=max(1,nint(dt_crcl/(1.*dxlat(k)**2/kappa))); dtdff2=dt_crcl/dd
time2=max(1,nint(float(dt_crcl)/float(dtdff2)))
ccx2=kappa*dtdff2/dxlat(k)**2
T1h=T1(:,k)
do tt2=1, time2 ! additional time loop
j = 1
jp1 = j+1; jp2 = j+2; jp3 = j+3; jm1 = xdim; jm2 = xdim-1; jm3 = xdim-2
dTxh(j) = ccx2*( &
& 10*( wz(jm1,k)*(T1h(jm1)-T1h(j)) +wz(jp1,k)*(T1h(jp1) -T1h(j)) ) &
& +4*( wz(jm2,k)*(T1h(jm2)-T1h(jm1)) +wz(jm1,k)*(T1h(j) -T1h(jm1)) ) &
& +4*( wz(jp1,k)*(T1h(j) -T1h(jp1)) +wz(jp2,k)*(T1h(jp2) -T1h(jp1)) ) &
& +1*( wz(jm3,k)*(T1h(jm3)-T1h(jm2)) +wz(jm2,k)*(T1h(jm1) -T1h(jm2)) ) &
& +1*( wz(jp2,k)*(T1h(jp1)-T1h(jp2)) +wz(jp3,k)*(T1h(jp3) -T1h(jp2)) ) )/20.
j = 2
jp1 = j+1; jp2 = j+2; jp3 = j+3; jm1 = j-1; jm2 = xdim; jm3 = xdim-1
dTxh(j) = ccx2*( &
& 10*( wz(jm1,k)*(T1h(jm1)-T1h(j)) +wz(jp1,k)*(T1h(jp1) -T1h(j)) ) &
& +4*( wz(jm2,k)*(T1h(jm2)-T1h(jm1)) +wz(jm1,k)*(T1h(j) -T1h(jm1)) ) &
& +4*( wz(jp1,k)*(T1h(j) -T1h(jp1)) +wz(jp2,k)*(T1h(jp2) -T1h(jp1)) ) &
& +1*( wz(jm3,k)*(T1h(jm3)-T1h(jm2)) +wz(jm2,k)*(T1h(jm1) -T1h(jm2)) ) &
& +1*( wz(jp2,k)*(T1h(jp1)-T1h(jp2)) +wz(jp3,k)*(T1h(jp3) -T1h(jp2)) ) )/20.
j = 3
jp1 = j+1; jp2 = j+2; jp3 = j+3; jm1 = j-1; jm2 = j-2; jm3 = xdim;
dTxh(j) = ccx2*( &
& 10*( wz(jm1,k)*(T1h(jm1)-T1h(j)) +wz(jp1,k)*(T1h(jp1) -T1h(j)) ) &
& +4*( wz(jm2,k)*(T1h(jm2)-T1h(jm1)) +wz(jm1,k)*(T1h(j) -T1h(jm1)) ) &
& +4*( wz(jp1,k)*(T1h(j) -T1h(jp1)) +wz(jp2,k)*(T1h(jp2) -T1h(jp1)) ) &
& +1*( wz(jm3,k)*(T1h(jm3)-T1h(jm2)) +wz(jm2,k)*(T1h(jm1) -T1h(jm2)) ) &
& +1*( wz(jp2,k)*(T1h(jp1)-T1h(jp2)) +wz(jp3,k)*(T1h(jp3) -T1h(jp2)) ) )/20.
do j=4, xdim-3 ! longitudinal
jm1=j-1; jp1=j+1; jm2=j-2; jp2=j+2; jm3=j-3; jp3=j+3
dTxh(j)=ccx2*( &
& 10*( wz(jm1,k)*(T1h(jm1)-T1h(j)) +wz(jp1,k)*(T1h(jp1) -T1h(j)) ) &
& +4*( wz(jm2,k)*(T1h(jm2)-T1h(jm1)) +wz(jm1,k)*(T1h(j) -T1h(jm1)) ) &
& +4*( wz(jp1,k)*(T1h(j) -T1h(jp1)) +wz(jp2,k)*(T1h(jp2) -T1h(jp1)) ) &
& +1*( wz(jm3,k)*(T1h(jm3)-T1h(jm2)) +wz(jm2,k)*(T1h(jm1) -T1h(jm2)) ) &
& +1*( wz(jp2,k)*(T1h(jp1)-T1h(jp2)) +wz(jp3,k)*(T1h(jp3) -T1h(jp2)) ) )/20.
end do ! longitudinal
j = xdim-2
jm1 = j-1; jm2 = j-2; jm3 = j-3; jp1 = j+1; jp2 = j+2; jp3 = 1
dTxh(j) = ccx2*( &
& 10*( wz(jm1,k)*(T1h(jm1)-T1h(j)) +wz(jp1,k)*(T1h(jp1) -T1h(j)) ) &
& +4*( wz(jm2,k)*(T1h(jm2)-T1h(jm1)) +wz(jm1,k)*(T1h(j) -T1h(jm1)) ) &
& +4*( wz(jp1,k)*(T1h(j) -T1h(jp1)) +wz(jp2,k)*(T1h(jp2) -T1h(jp1)) ) &
& +1*( wz(jm3,k)*(T1h(jm3)-T1h(jm2)) +wz(jm2,k)*(T1h(jm1) -T1h(jm2)) ) &
& +1*( wz(jp2,k)*(T1h(jp1)-T1h(jp2)) +wz(jp3,k)*(T1h(jp3) -T1h(jp2)) ) )/20.
j = xdim-1
jm1 = j-1; jm2 = j-2; jm3 = j-3; jp1 = j+1; jp2 = 1; jp3 = 2
dTxh(j) = ccx2*( &
& 10*( wz(jm1,k)*(T1h(jm1)-T1h(j)) +wz(jp1,k)*(T1h(jp1) -T1h(j)) ) &
& +4*( wz(jm2,k)*(T1h(jm2)-T1h(jm1)) +wz(jm1,k)*(T1h(j) -T1h(jm1)) ) &
& +4*( wz(jp1,k)*(T1h(j) -T1h(jp1)) +wz(jp2,k)*(T1h(jp2) -T1h(jp1)) ) &
& +1*( wz(jm3,k)*(T1h(jm3)-T1h(jm2)) +wz(jm2,k)*(T1h(jm1) -T1h(jm2)) ) &
& +1*( wz(jp2,k)*(T1h(jp1)-T1h(jp2)) +wz(jp3,k)*(T1h(jp3) -T1h(jp2)) ) )/20.
j = xdim
jm1 = j-1; jm2 = j-2; jm3 = j-3; jp1 = 1; jp2 = 2; jp3 = 3
dTxh(j) = ccx2*( &
& 10*( wz(jm1,k)*(T1h(jm1)-T1h(j)) +wz(jp1,k)*(T1h(jp1) -T1h(j)) ) &
& +4*( wz(jm2,k)*(T1h(jm2)-T1h(jm1)) +wz(jm1,k)*(T1h(j) -T1h(jm1)) ) &
& +4*( wz(jp1,k)*(T1h(j) -T1h(jp1)) +wz(jp2,k)*(T1h(jp2) -T1h(jp1)) ) &
& +1*( wz(jm3,k)*(T1h(jm3)-T1h(jm2)) +wz(jm2,k)*(T1h(jm1) -T1h(jm2)) ) &
& +1*( wz(jp2,k)*(T1h(jp1)-T1h(jp2)) +wz(jp3,k)*(T1h(jp3) -T1h(jp2)) ) )/20.
where(dTxh .le. -T1h ) dTxh = -0.9*T1h ! no negative q; numerical stability
T1h=T1h+dTxh
end do ! additional time loop
dTx(:,k)=T1h-T1(:,k)
end if
end do ! y-loop
dX_diffuse = wz * (dTx + dTy);
end subroutine diffusion
!+++++++++++++++++++++++++++++++++++++++
subroutine advection(T1, dX_advec,h_scl, wz)
!+++++++++++++++++++++++++++++++++++++++
! advection after DD
USE mo_numerics, ONLY: xdim, ydim, dt, dlon, dlat, dt_crcl
USE mo_physics, ONLY: pi, z_topo, uclim, vclim, ityr, z_vapor, log_exp
USE mo_physics, ONLY: uclim_m, uclim_p, vclim_m, vclim_p
implicit none
real, dimension(xdim,ydim), intent(in) :: T1, wz
real , intent(in) :: h_scl
real, dimension(xdim,ydim), intent(out) :: dX_advec
integer :: i
integer, dimension(ydim):: ilat = (/(i,i=1,ydim)/)
real, dimension(ydim) :: lat, dxlat, ccx
real, dimension(xdim) :: T1h, dTxh
real, dimension(xdim,ydim) :: ddx, T, dTx, dTy
integer time2, dtdff2, tt2
real :: deg, dx, dy, dd, dyy, ccy, ccx2
integer :: j, k, km1, km2, kp1, kp2, jm1, jm2, jm3, jp1, jp2, jp3
deg = 2.*pi*6.371e6/360.; ! length of 1deg latitude [m]
dx = dlon; dy=dlat; dyy=dy*deg
lat = dlat*ilat-dlat/2.-90.; dxlat=dx*deg*cos(2.*pi/360.*lat)
ccy=dt_crcl/dyy/2.
ccx=dt_crcl/dxlat/2.
! latitudinal
k=1
kp1=k+1; kp2=k+2
do j = 1, xdim
dTy(j,k) = ccy * ( &
& vclim_p(j,k,ityr)*( wz(j,kp1)*(T1(j,k)-T1(j,kp1)) &
& +wz(j,kp2)*(T1(j,k)-T1(j,kp2)) ) )/3.
end do
k=2
km1=k-1; kp1=k+1; kp2=k+2
do j = 1, xdim
dTy(j,k) = ccy * ( &
& -vclim_m(j,k,ityr)*( wz(j,km1)*(T1(j,k)-T1(j,km1))) &
& + vclim_p(j,k,ityr)*( wz(j,kp1)*(T1(j,k)-T1(j,kp1)) &
& +wz(j,kp2)*(T1(j,k)-T1(j,kp2)) )/3. )
end do
do k=3, ydim-2
km1=k-1; kp1=k+1; km2=k-2; kp2=k+2
do j = 1, xdim
dTy(j,k) = ccy * ( &
& -vclim_m(j,k,ityr)*( wz(j,km1)*(T1(j,k)-T1(j,km1)) &
& +wz(j,km2)*(T1(j,k)-T1(j,km2)) ) &
& + vclim_p(j,k,ityr)*( wz(j,kp1)*(T1(j,k)-T1(j,kp1)) &
& +wz(j,kp2)*(T1(j,k)-T1(j,kp2)) ) )/3.
end do
end do
k=ydim-1
km1=k-1; kp1=k+1; km2=k-2
do j = 1, xdim
dTy(j,k) = ccy * ( &
& -vclim_m(j,k,ityr)*( wz(j,km1)*(T1(j,k)-T1(j,km1)) &
& +wz(j,km2)*(T1(j,k)-T1(j,km2)) )/3. &
& + vclim_p(j,k,ityr)*( wz(j,kp1)*(T1(j,k)-T1(j,kp1)) ) )
end do
k=ydim
km1=k-1; km2=k-2
do j = 1, xdim
dTy(j,k) = ccy * ( &
& -vclim_m(j,k,ityr)*( wz(j,km1)*(T1(j,k)-T1(j,km1)) &
& +wz(j,km2)*(T1(j,k)-T1(j,km2)) ) )/3.
end do
! longitudinal
do k=1, ydim
if ( dxlat(k) > 2.5e5) then ! unitl 25degree
j = 1
jm1 = xdim; jm2 = xdim-1; jp1 = j+1; jp2 = j+2
dTx(j,k)= ccx(k) * ( &
& -uclim_m(j,k,ityr)*( wz(jm1,k)*(T1(j,k)-T1(jm1,k)) &
& +wz(jm2,k)*(T1(j,k)-T1(jm2,k)) ) &
& + uclim_p(j,k,ityr)*( wz(jp1,k)*(T1(j,k)-T1(jp1,k)) &
& +wz(jp2,k)*(T1(j,k)-T1(jp2,k)) ) )/3.
j = 2
jm1 = j-1; jm2 = xdim; jp1 = j+1; jp2 = j+2
dTx(j,k)= ccx(k) * ( &
& -uclim_m(j,k,ityr)*( wz(jm1,k)*(T1(j,k)-T1(jm1,k)) &
& +wz(jm2,k)*(T1(j,k)-T1(jm2,k)) ) &
& + uclim_p(j,k,ityr)*( wz(jp1,k)*(T1(j,k)-T1(jp1,k)) &
& +wz(jp2,k)*(T1(j,k)-T1(jp2,k)) ) )/3.
do j=3, xdim-2 ! longitudinal
jm1=j-1; jp1=j+1; jm2=j-2; jp2=j+2
dTx(j,k)= ccx(k) * ( &
& -uclim_m(j,k,ityr)*( wz(jm1,k)*(T1(j,k)-T1(jm1,k)) &
& +wz(jm2,k)*(T1(j,k)-T1(jm2,k)) ) &
& + uclim_p(j,k,ityr)*( wz(jp1,k)*(T1(j,k)-T1(jp1,k)) &
& +wz(jp2,k)*(T1(j,k)-T1(jp2,k)) ) )/3.
end do
j = xdim-1
jm1 = j-1; jm2 = j-2; jp1 = j+1; jp2 = 1
dTx(j,k)= ccx(k) * ( &
& -uclim_m(j,k,ityr)*( wz(jm1,k)*(T1(j,k)-T1(jm1,k)) &
& +wz(jm2,k)*(T1(j,k)-T1(jm2,k)) ) &
& + uclim_p(j,k,ityr)*( wz(jp1,k)*(T1(j,k)-T1(jp1,k)) &
& +wz(jp2,k)*(T1(j,k)-T1(jp2,k)) ) )/3.
j = xdim
jm1 = j-1; jm2 = j-2; jp1 = 1; jp2 = 2
dTx(j,k)= ccx(k) * ( &
& -uclim_m(j,k,ityr)*( wz(jm1,k)*(T1(j,k)-T1(jm1,k)) &
& +wz(jm2,k)*(T1(j,k)-T1(jm2,k)) ) &
& + uclim_p(j,k,ityr)*( wz(jp1,k)*(T1(j,k)-T1(jp1,k)) &
& +wz(jp2,k)*(T1(j,k)-T1(jp2,k)) ) )/3.
else ! high resolution -> smaller time steps
dd=max(1,nint(dt_crcl/(dxlat(k)/10.0/1.))); dtdff2=dt_crcl/dd
time2=max(1,nint(float(dt_crcl)/float(dtdff2)))
ccx2=dtdff2/dxlat(k)/2
T1h=T1(:,k)
do tt2=1, time2 ! additional time loop
j = 1
jm1=xdim; jm2=xdim-1; jm3=xdim-2; jp1=j+1; jp2=j+2; jp3=j+3
dTxh(j)= ccx2 * ( &
& -uclim_m(j,k,ityr)*( 10*wz(jm1,k)*(T1h(j) - T1h(jm1) ) &
& +4*wz(jm2,k)*(T1h(jm1) - T1h(jm2) ) &
& +1*wz(jm3,k)*(T1h(jm2) - T1h(jm3) ) ) &
& + uclim_p(j,k,ityr)*( 10*wz(jp1,k)*(T1h(j) - T1h(jp1) ) &
& +4*wz(jp2,k)*(T1h(jp1) - T1h(jp2) ) &
& +1*wz(jp3,k)*(T1h(jp2) - T1h(jp3) ) ) ) /20.
j = 2
jm1=j-1; jm2=xdim; jm3=xdim-1; jp1=j+1; jp2=j+2; jp3=j+3
dTxh(j)= ccx2 * ( &
& -uclim_m(j,k,ityr)*( 10*wz(jm1,k)*(T1h(j) - T1h(jm1) ) &
& +4*wz(jm2,k)*(T1h(jm1) - T1h(jm2) ) &
& +1*wz(jm3,k)*(T1h(jm2) - T1h(jm3) ) ) &
& + uclim_p(j,k,ityr)*( 10*wz(jp1,k)*(T1h(j) - T1h(jp1) ) &
& +4*wz(jp2,k)*(T1h(jp1) - T1h(jp2) ) &
& +1*wz(jp3,k)*(T1h(jp2) - T1h(jp3) ) ) ) /20.
j = 3
jm1=j-1; jm2=j-2; jm3=xdim; jp1=j+1; jp2=j+2; jp3=j+3
dTxh(j)= ccx2 * ( &
& -uclim_m(j,k,ityr)*( 10*wz(jm1,k)*(T1h(j) - T1h(jm1) ) &
& +4*wz(jm2,k)*(T1h(jm1) - T1h(jm2) ) &
& +1*wz(jm3,k)*(T1h(jm2) - T1h(jm3) ) ) &
& + uclim_p(j,k,ityr)*( 10*wz(jp1,k)*(T1h(j) - T1h(jp1) ) &
& +4*wz(jp2,k)*(T1h(jp1) - T1h(jp2) ) &
& +1*wz(jp3,k)*(T1h(jp2) - T1h(jp3) ) ) ) /20.
do j=4, xdim-3 ! longitudinal
jm1=j-1; jp1=j+1; jm2=j-2; jp2=j+2; jm3=j-3; jp3=j+3
dTxh(j)= ccx2 * ( &
& -uclim_m(j,k,ityr)*( 10*wz(jm1,k)*(T1h(j) - T1h(jm1) ) &
& +4*wz(jm2,k)*(T1h(jm1) - T1h(jm2) ) &
& +1*wz(jm3,k)*(T1h(jm2) - T1h(jm3) ) ) &
& + uclim_p(j,k,ityr)*( 10*wz(jp1,k)*(T1h(j) - T1h(jp1) ) &
& +4*wz(jp2,k)*(T1h(jp1) - T1h(jp2) ) &
& +1*wz(jp3,k)*(T1h(jp2) - T1h(jp3) ) ) ) /20.
end do ! longitudinal
j = xdim-2
jm1=j-1; jm2=j-2; jm3=j-3; jp1=xdim-1; jp2=xdim-1; jp3=1
dTxh(j)= ccx2 * ( &
& -uclim_m(j,k,ityr)*( 10*wz(jm1,k)*(T1h(j) - T1h(jm1) ) &
& +4*wz(jm2,k)*(T1h(jm1) - T1h(jm2) ) &
& +1*wz(jm3,k)*(T1h(jm2) - T1h(jm3) ) ) &
& + uclim_p(j,k,ityr)*( 10*wz(jp1,k)*(T1h(j) - T1h(jp1) ) &
& +4*wz(jp2,k)*(T1h(jp1) - T1h(jp2) ) &
& +1*wz(jp3,k)*(T1h(jp2) - T1h(jp3) ) ) ) /20.
j = xdim-1
jm1=j-1; jm2=j-2; jm3=j-3; jp1=xdim; jp2=1; jp3=2
dTxh(j)= ccx2 * ( &
& -uclim_m(j,k,ityr)*( 10*wz(jm1,k)*(T1h(j) - T1h(jm1) ) &
& +4*wz(jm2,k)*(T1h(jm1) - T1h(jm2) ) &
& +1*wz(jm3,k)*(T1h(jm2) - T1h(jm3) ) ) &
& + uclim_p(j,k,ityr)*( 10*wz(jp1,k)*(T1h(j) - T1h(jp1) ) &
& +4*wz(jp2,k)*(T1h(jp1) - T1h(jp2) ) &
& +1*wz(jp3,k)*(T1h(jp2) - T1h(jp3) ) ) ) /20.
j = xdim
jm1=j-1; jm2=j-2; jm3=j-3; jp1=1; jp2=2; jp3=3
dTxh(j)= ccx2 * ( &
& -uclim_m(j,k,ityr)*( 10*wz(jm1,k)*(T1h(j) - T1h(jm1) ) &
& +4*wz(jm2,k)*(T1h(jm1) - T1h(jm2) ) &
& +1*wz(jm3,k)*(T1h(jm2) - T1h(jm3) ) ) &
& + uclim_p(j,k,ityr)*( 10*wz(jp1,k)*(T1h(j) - T1h(jp1) ) &
& +4*wz(jp2,k)*(T1h(jp1) - T1h(jp2) ) &
& +1*wz(jp3,k)*(T1h(jp2) - T1h(jp3) ) ) ) /20.
where(dTxh .le. -T1h ) dTxh = -0.9*T1h ! no negative q; numerical stability
T1h = T1h + dTxh
end do ! additional time loop
dTx(:,k) = T1h - T1(:,k)
end if
end do ! y-loop
dX_advec = dTx + dTy;
end subroutine advection
!+++++++++++++++++++++++++++++++++++++++
subroutine co2_level(it, year, CO2)
!+++++++++++++++++++++++++++++++++++++++
USE mo_numerics, ONLY: ndays_yr, ndt_days
USE mo_physics, ONLY: log_exp
CO2 = 680.
if( log_exp .eq. 12 .or. log_exp .eq. 13 ) then
CO2_1950=310.; CO2_2000=370.; CO2_2050=520.
if (year <= 2000.) CO2=CO2_1950 + 60./50.*(year-1950.)
if (year > 2000. .and. year <= 2050.) CO2=CO2_2000 + 150./50.*(year-2000.)
if (year > 2050. .and. year <= 2100.) CO2=CO2_2050 + 180./50.*(year-2050.)
end if
end subroutine co2_level
!+++++++++++++++++++++++++++++++++++++++
subroutine diagonstics(it, year, CO2, ts0, ta0, to0, q0, albedo, sw, lw_surf, q_lat, q_sens)
!+++++++++++++++++++++++++++++++++++++++
! diagonstics plots
USE mo_numerics, ONLY: ndays_yr, xdim, ydim, ipx ,ipy, ndt_days, nstep_yr
USE mo_physics, ONLY: ityr, TF_correct, qF_correct, cap_surf, Tclim
use mo_diagnostics
! declare temporary fields
real, dimension(xdim,ydim) :: Ts0, Ta0, To0, q0, sw, albedo, Q_sens, Q_lat, LW_surf
! diagnostics: annual means
tsmn=tsmn+Ts0; tamn=tamn+ta0; tomn=tomn+to0; qmn=qmn+q0; amn=amn+albedo
swmn=swmn+sw; lwmn=lwmn+LW_surf; qlatmn=qlatmn+q_lat; qsensmn=qsensmn+Q_sens;
ftmn=ftmn+TF_correct(:,:,ityr); fqmn=fqmn+qF_correct(:,:,ityr);
if ( ityr == nstep_yr ) then
tsmn = tsmn/nstep_yr; tamn = tamn/nstep_yr; tomn = tomn/nstep_yr;
qmn = qmn/nstep_yr;
amn = amn/nstep_yr; swmn = swmn/nstep_yr; lwmn = lwmn/nstep_yr;
qlatmn = qlatmn/nstep_yr; qsensmn = qsensmn/nstep_yr; ftmn = ftmn/nstep_yr;
fqmn = fqmn/nstep_yr;
print *, year, sum(tsmn)/(96*48)-273.15, tsmn(48,24+3)-273.15, tsmn(16,24+14)-273.15
tsmn=0.; tamn=0.; qmn=0.; amn=0.; swmn=0.; ! reset annual mean values
lwmn=0.; qlatmn=0.; qsensmn=0.; ftmn=0.; fqmn=0.; ! reset annual mean values
end if
end subroutine diagonstics
!+++++++++++++++++++++++++++++++++++++++
subroutine output(it, iunit, irec, mon, ts0, ta0, to0, q0, albedo)
!+++++++++++++++++++++++++++++++++++++++
! write output
USE mo_numerics, ONLY: xdim, ydim, jday_mon, ndt_days
USE mo_physics, ONLY: jday
use mo_diagnostics, ONLY: Tmm, Tamm, Tomm, qmm, apmm
! declare temporary fields
real, dimension(xdim,ydim) :: Ts0, Ta0, To0, q0, albedo
! diagnostics: monthly means
Tmm=Tmm+Ts0; Tamm=Tamm+ta0; Tomm=Tomm+to0; qmm=qmm+q0; apmm=apmm+albedo