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IF( kt == nit000 .AND. kiter == 1 ) THEN
!
IF( lwp ) THEN
WRITE(numout,*)
WRITE(numout,*) 'rhg_cvg_eap : ice rheology convergence control'
WRITE(numout,*) '~~~~~~~'
ENDIF
!
IF( lwm ) THEN
clname = 'ice_cvg.nc'
IF( .NOT. Agrif_Root() ) clname = TRIM(Agrif_CFixed())//"_"//TRIM(clname)
istatus = NF90_CREATE( TRIM(clname), NF90_CLOBBER, ncvgid )
istatus = NF90_DEF_DIM( ncvgid, 'time' , NF90_UNLIMITED, idtime )
istatus = NF90_DEF_VAR( ncvgid, 'uice_cvg', NF90_DOUBLE , (/ idtime /), nvarid )
istatus = NF90_ENDDEF(ncvgid)
ENDIF
!
ENDIF
! time
it = ( kt - nit000 ) * kitermax + kiter
! convergence
IF( kiter == 1 ) THEN ! remove the first iteration for calculations of convergence (always very large)
zresm = 0._wp
ELSE
zresm = 0._wp
DO_2D( 0, 0, 0, 0 )
zresm = MAX( zresm, MAX( ABS( pu(ji,jj) - pub(ji,jj) ) * umask(ji,jj,1), &
& ABS( pv(ji,jj) - pvb(ji,jj) ) * vmask(ji,jj,1) ) * pmsk15(ji,jj) )
END_2D
CALL mpp_max( 'icedyn_rhg_evp', zresm ) ! max over the global domain
ENDIF
IF( lwm ) THEN
! write variables
istatus = NF90_PUT_VAR( ncvgid, nvarid, (/zresm/), (/it/), (/1/) )
! close file
IF( kt == nitend - nn_fsbc + 1 .AND. kiter == kitermax ) istatus = NF90_CLOSE(ncvgid)
ENDIF
END SUBROUTINE rhg_cvg_eap
SUBROUTINE update_stress_rdg( ksub, kndte, pdivu, ptension, pshear, pa11, pa12, &
& pstressp, pstressm, pstress12, pstrength, palphar, palphas )
!!---------------------------------------------------------------------
!! *** SUBROUTINE update_stress_rdg ***
!!
!! ** Purpose : Updates the stress depending on values of strain rate and structure
!! tensor and for the last subcycle step it computes closing and sliding rate
!!---------------------------------------------------------------------
INTEGER, INTENT(in ) :: ksub, kndte
REAL(wp), INTENT(in ) :: pstrength
REAL(wp), INTENT(in ) :: pdivu, ptension, pshear
REAL(wp), INTENT(in ) :: pa11, pa12
REAL(wp), INTENT( out) :: pstressp, pstressm, pstress12
REAL(wp), INTENT( out) :: palphar, palphas
INTEGER :: kx ,ky, ka
REAL(wp) :: zstemp11r, zstemp12r, zstemp22r
REAL(wp) :: zstemp11s, zstemp12s, zstemp22s
REAL(wp) :: za22, zQd11Qd11, zQd11Qd12, zQd12Qd12
REAL(wp) :: zQ11Q11, zQ11Q12, zQ12Q12
REAL(wp) :: zdtemp11, zdtemp12, zdtemp22
REAL(wp) :: zrotstemp11r, zrotstemp12r, zrotstemp22r
REAL(wp) :: zrotstemp11s, zrotstemp12s, zrotstemp22s
REAL(wp) :: zsig11, zsig12, zsig22
REAL(wp) :: zsgprm11, zsgprm12, zsgprm22
REAL(wp) :: zAngle_denom_gamma, zAngle_denom_alpha
REAL(wp) :: zTany_1, zTany_2
REAL(wp) :: zx, zy, zkxw, kyw, kaw
REAL(wp) :: zinvdx, zinvdy, zinvda
REAL(wp) :: zdtemp1, zdtemp2, zatempprime
REAL(wp), PARAMETER :: ppkfriction = 0.45_wp
! Factor to maintain the same stress as in EVP (see Section 3)
! Can be set to 1 otherwise
! REAL(wp), PARAMETER :: ppinvstressconviso = 1._wp/(1._wp+ppkfriction*ppkfriction)
REAL(wp), PARAMETER :: ppinvstressconviso = 1._wp
! next statement uses pphi set in main module (icedyn_rhg_eap)
REAL(wp), PARAMETER :: ppinvsin = 1._wp/sin(2._wp*pphi) * ppinvstressconviso
! compute eigenvalues, eigenvectors and angles for structure tensor, strain
! rates
! 1) structure tensor
za22 = 1._wp-pa11
zQ11Q11 = 1._wp
zQ12Q12 = rsmall
zQ11Q12 = rsmall
! gamma: angle between general coordiantes and principal axis of A
! here Tan2gamma = 2 a12 / (a11 - a22)
IF((ABS(pa11 - za22) > rsmall).OR.(ABS(pa12) > rsmall)) THEN
zAngle_denom_gamma = 1._wp/sqrt( ( pa11 - za22 )*( pa11 - za22) + &
4._wp*pa12*pa12 )
zQ11Q11 = 0.5_wp + ( pa11 - za22 )*0.5_wp*zAngle_denom_gamma !Cos^2
zQ12Q12 = 0.5_wp - ( pa11 - za22 )*0.5_wp*zAngle_denom_gamma !Sin^2
zQ11Q12 = pa12*zAngle_denom_gamma !CosSin
ENDIF
! rotation Q*atemp*Q^T
zatempprime = zQ11Q11*pa11 + 2.0_wp*zQ11Q12*pa12 + zQ12Q12*za22
! make first principal value the largest
zatempprime = max(zatempprime, 1.0_wp - zatempprime)
! 2) strain rate
zdtemp11 = 0.5_wp*(pdivu + ptension)
zdtemp12 = pshear*0.5_wp
zdtemp22 = 0.5_wp*(pdivu - ptension)
! here Tan2alpha = 2 dtemp12 / (dtemp11 - dtemp22)
zQd11Qd11 = 1.0_wp
zQd12Qd12 = rsmall
zQd11Qd12 = rsmall
IF((ABS( zdtemp11 - zdtemp22) > rsmall).OR. (ABS(zdtemp12) > rsmall)) THEN
zAngle_denom_alpha = 1.0_wp/sqrt( ( zdtemp11 - zdtemp22 )* &
( zdtemp11 - zdtemp22 ) + 4.0_wp*zdtemp12*zdtemp12)
zQd11Qd11 = 0.5_wp + ( zdtemp11 - zdtemp22 )*0.5_wp*zAngle_denom_alpha !Cos^2
zQd12Qd12 = 0.5_wp - ( zdtemp11 - zdtemp22 )*0.5_wp*zAngle_denom_alpha !Sin^2
zQd11Qd12 = zdtemp12*zAngle_denom_alpha !CosSin
ENDIF
zdtemp1 = zQd11Qd11*zdtemp11 + 2.0_wp*zQd11Qd12*zdtemp12 + zQd12Qd12*zdtemp22
zdtemp2 = zQd12Qd12*zdtemp11 - 2.0_wp*zQd11Qd12*zdtemp12 + zQd11Qd11*zdtemp22
! In cos and sin values
zx = 0._wp
IF ((ABS(zdtemp1) > rsmall).OR.(ABS(zdtemp2) > rsmall)) THEN
zx = atan2(zdtemp2,zdtemp1)
ENDIF
! to ensure the angle lies between pi/4 and 9 pi/4
IF (zx < rpi*0.25_wp) zx = zx + rpi*2.0_wp
! y: angle between major principal axis of strain rate and structure
! tensor
! y = gamma - alpha
! Expressesed componently with
! Tany = (Singamma*Cosgamma - Sinalpha*Cosgamma)/(Cos^2gamma - Sin^alpha)
zTany_1 = zQ11Q12 - zQd11Qd12
zTany_2 = zQ11Q11 - zQd12Qd12
zy = 0._wp
IF ((ABS(zTany_1) > rsmall).OR.(ABS(zTany_2) > rsmall)) THEN
zy = atan2(zTany_1,zTany_2)
ENDIF
! to make sure y is between 0 and pi
IF (zy > rpi) zy = zy - rpi
IF (zy < 0) zy = zy + rpi
! 3) update anisotropic stress tensor
zinvdx = real(nx_yield-1,kind=wp)/rpi
zinvdy = real(ny_yield-1,kind=wp)/rpi
zinvda = 2._wp*real(na_yield-1,kind=wp)
! % need 8 coords and 8 weights
! % range in kx
kx = int((zx-rpi*0.25_wp-rpi)*zinvdx) + 1
!!clem kx = MAX( 1, MIN( nx_yield-1, INT((zx-rpi*0.25_wp-rpi)*zinvdx) + 1 ) )
zkxw = kx - (zx-rpi*0.25_wp-rpi)*zinvdx
ky = int(zy*zinvdy) + 1
!!clem ky = MAX( 1, MIN( ny_yield-1, INT(zy*zinvdy) + 1 ) )
kyw = ky - zy*zinvdy
ka = int((zatempprime-0.5_wp)*zinvda) + 1
!!clem ka = MAX( 1, MIN( na_yield-1, INT((zatempprime-0.5_wp)*zinvda) + 1 ) )
kaw = ka - (zatempprime-0.5_wp)*zinvda
! % Determine sigma_r(A1,Zeta,y) and sigma_s (see Section A1 of Tsamados 2013)
!!$ zstemp11r = zkxw * kyw * kaw * s11r(kx ,ky ,ka ) &
!!$ & + (1._wp-zkxw) * kyw * kaw * s11r(kx+1,ky ,ka ) &
!!$ & + zkxw * (1._wp-kyw) * kaw * s11r(kx ,ky+1,ka ) &
!!$ & + zkxw * kyw * (1._wp-kaw) * s11r(kx ,ky ,ka+1) &
!!$ & + (1._wp-zkxw) * (1._wp-kyw) * kaw * s11r(kx+1,ky+1,ka ) &
!!$ & + (1._wp-zkxw) * kyw * (1._wp-kaw) * s11r(kx+1,ky ,ka+1) &
!!$ & + zkxw * (1._wp-kyw) * (1._wp-kaw) * s11r(kx ,ky+1,ka+1) &
!!$ & + (1._wp-zkxw) * (1._wp-kyw) * (1._wp-kaw) * s11r(kx+1,ky+1,ka+1)
!!$ zstemp12r = zkxw * kyw * kaw * s12r(kx ,ky ,ka ) &
!!$ & + (1._wp-zkxw) * kyw * kaw * s12r(kx+1,ky ,ka ) &
!!$ & + zkxw * (1._wp-kyw) * kaw * s12r(kx ,ky+1,ka ) &
!!$ & + zkxw * kyw * (1._wp-kaw) * s12r(kx ,ky ,ka+1) &
!!$ & + (1._wp-zkxw) * (1._wp-kyw) * kaw * s12r(kx+1,ky+1,ka ) &
!!$ & + (1._wp-zkxw) * kyw * (1._wp-kaw) * s12r(kx+1,ky ,ka+1) &
!!$ & + zkxw * (1._wp-kyw) * (1._wp-kaw) * s12r(kx ,ky+1,ka+1) &
!!$ & + (1._wp-zkxw) * (1._wp-kyw) * (1._wp-kaw) * s12r(kx+1,ky+1,ka+1)
!!$ zstemp22r = zkxw * kyw * kaw * s22r(kx ,ky ,ka ) &
!!$ & + (1._wp-zkxw) * kyw * kaw * s22r(kx+1,ky ,ka ) &
!!$ & + zkxw * (1._wp-kyw) * kaw * s22r(kx ,ky+1,ka ) &
!!$ & + zkxw * kyw * (1._wp-kaw) * s22r(kx ,ky ,ka+1) &
!!$ & + (1._wp-zkxw) * (1._wp-kyw) * kaw * s22r(kx+1,ky+1,ka ) &
!!$ & + (1._wp-zkxw) * kyw * (1._wp-kaw) * s22r(kx+1,ky ,ka+1) &
!!$ & + zkxw * (1._wp-kyw) * (1._wp-kaw) * s22r(kx ,ky+1,ka+1) &
!!$ & + (1._wp-zkxw) * (1._wp-kyw) * (1._wp-kaw) * s22r(kx+1,ky+1,ka+1)
!!$
!!$ zstemp11s = zkxw * kyw * kaw * s11s(kx ,ky ,ka ) &
!!$ & + (1._wp-zkxw) * kyw * kaw * s11s(kx+1,ky ,ka ) &
!!$ & + zkxw * (1._wp-kyw) * kaw * s11s(kx ,ky+1,ka ) &
!!$ & + zkxw * kyw * (1._wp-kaw) * s11s(kx ,ky ,ka+1) &
!!$ & + (1._wp-zkxw) * (1._wp-kyw) * kaw * s11s(kx+1,ky+1,ka ) &
!!$ & + (1._wp-zkxw) * kyw * (1._wp-kaw) * s11s(kx+1,ky ,ka+1) &
!!$ & + zkxw * (1._wp-kyw) * (1._wp-kaw) * s11s(kx ,ky+1,ka+1) &
!!$ & + (1._wp-zkxw) * (1._wp-kyw) * (1._wp-kaw) * s11s(kx+1,ky+1,ka+1)
!!$ zstemp12s = zkxw * kyw * kaw * s12s(kx ,ky ,ka ) &
!!$ & + (1._wp-zkxw) * kyw * kaw * s12s(kx+1,ky ,ka ) &
!!$ & + zkxw * (1._wp-kyw) * kaw * s12s(kx ,ky+1,ka ) &
!!$ & + zkxw * kyw * (1._wp-kaw) * s12s(kx ,ky ,ka+1) &
!!$ & + (1._wp-zkxw) * (1._wp-kyw) * kaw * s12s(kx+1,ky+1,ka ) &
!!$ & + (1._wp-zkxw) * kyw * (1._wp-kaw) * s12s(kx+1,ky ,ka+1) &
!!$ & + zkxw * (1._wp-kyw) * (1._wp-kaw) * s12s(kx ,ky+1,ka+1) &
!!$ & + (1._wp-zkxw) * (1._wp-kyw) * (1._wp-kaw) * s12s(kx+1,ky+1,ka+1)
!!$ zstemp22s = zkxw * kyw * kaw * s22s(kx ,ky ,ka ) &
!!$ & + (1._wp-zkxw) * kyw * kaw * s22s(kx+1,ky ,ka ) &
!!$ & + zkxw * (1._wp-kyw) * kaw * s22s(kx ,ky+1,ka ) &
!!$ & + zkxw * kyw * (1._wp-kaw) * s22s(kx ,ky ,ka+1) &
!!$ & + (1._wp-zkxw) * (1._wp-kyw) * kaw * s22s(kx+1,ky+1,ka ) &
!!$ & + (1._wp-zkxw) * kyw * (1._wp-kaw) * s22s(kx+1,ky ,ka+1) &
!!$ & + zkxw * (1._wp-kyw) * (1._wp-kaw) * s22s(kx ,ky+1,ka+1) &
!!$ & + (1._wp-zkxw) * (1._wp-kyw) * (1._wp-kaw) * s22s(kx+1,ky+1,ka+1)
zstemp11r = s11r(kx,ky,ka)
zstemp12r = s12r(kx,ky,ka)
zstemp22r = s22r(kx,ky,ka)
zstemp11s = s11s(kx,ky,ka)
zstemp12s = s12s(kx,ky,ka)
zstemp22s = s22s(kx,ky,ka)
! Calculate mean ice stress over a collection of floes (Equation 3 in
! Tsamados 2013)
zsig11 = pstrength*(zstemp11r + ppkfriction*zstemp11s) * ppinvsin
zsig12 = pstrength*(zstemp12r + ppkfriction*zstemp12s) * ppinvsin
zsig22 = pstrength*(zstemp22r + ppkfriction*zstemp22s) * ppinvsin
! Back - rotation of the stress from principal axes into general coordinates
! Update stress
zsgprm11 = zQ11Q11*zsig11 + zQ12Q12*zsig22 - 2._wp*zQ11Q12 *zsig12
zsgprm12 = zQ11Q12*zsig11 - zQ11Q12*zsig22 + (zQ11Q11 - zQ12Q12)*zsig12
zsgprm22 = zQ12Q12*zsig11 + zQ11Q11*zsig22 + 2._wp*zQ11Q12 *zsig12
pstressp = zsgprm11 + zsgprm22
pstress12 = zsgprm12
pstressm = zsgprm11 - zsgprm22
! Compute ridging and sliding functions in general coordinates
! (Equation 11 in Tsamados 2013)
IF (ksub == kndte) THEN
zrotstemp11r = zQ11Q11*zstemp11r - 2._wp*zQ11Q12* zstemp12r &
+ zQ12Q12*zstemp22r
zrotstemp12r = zQ11Q11*zstemp12r + zQ11Q12*(zstemp11r-zstemp22r) &
- zQ12Q12*zstemp12r
zrotstemp22r = zQ12Q12*zstemp11r + 2._wp*zQ11Q12* zstemp12r &
+ zQ11Q11*zstemp22r
zrotstemp11s = zQ11Q11*zstemp11s - 2._wp*zQ11Q12* zstemp12s &
+ zQ12Q12*zstemp22s
zrotstemp12s = zQ11Q11*zstemp12s + zQ11Q12*(zstemp11s-zstemp22s) &
- zQ12Q12*zstemp12s
zrotstemp22s = zQ12Q12*zstemp11s + 2._wp*zQ11Q12* zstemp12s &
+ zQ11Q11*zstemp22s
palphar = zrotstemp11r*zdtemp11 + 2._wp*zrotstemp12r*zdtemp12 &
+ zrotstemp22r*zdtemp22
palphas = zrotstemp11s*zdtemp11 + 2._wp*zrotstemp12s*zdtemp12 &
+ zrotstemp22s*zdtemp22
ENDIF
END SUBROUTINE update_stress_rdg
!=======================================================================
SUBROUTINE calc_ffrac( pstressp, pstressm, pstress12, pa11, pa12, &
& pmresult11, pmresult12 )
!!---------------------------------------------------------------------
!! *** ROUTINE calc_ffrac ***
!!
!! ** Purpose : Computes term in evolution equation for structure tensor
!! which determines the ice floe re-orientation due to fracture
!! ** Method : Eq. 7: Ffrac = -kf(A-S) or = 0 depending on sigma_1 and sigma_2
!!---------------------------------------------------------------------
REAL (wp), INTENT(in) :: pstressp, pstressm, pstress12, pa11, pa12
REAL (wp), INTENT(out) :: pmresult11, pmresult12
! local variables
REAL (wp) :: zsigma11, zsigma12, zsigma22 ! stress tensor elements
REAL (wp) :: zAngle_denom ! angle with principal component axis
REAL (wp) :: zsigma_1, zsigma_2 ! principal components of stress
REAL (wp) :: zQ11, zQ12, zQ11Q11, zQ11Q12, zQ12Q12
!!$ REAL (wp), PARAMETER :: ppkfrac = 0.0001_wp ! rate of fracture formation
REAL (wp), PARAMETER :: ppkfrac = 1.e-3_wp ! rate of fracture formation
REAL (wp), PARAMETER :: ppthreshold = 0.3_wp ! critical confinement ratio
!!---------------------------------------------------------------
!
zsigma11 = 0.5_wp*(pstressp+pstressm)
zsigma12 = pstress12
zsigma22 = 0.5_wp*(pstressp-pstressm)
! Here's the change - no longer calculate gamma,
! use trig formulation, angle signs are kept correct, don't worry
! rotate tensor to get into sigma principal axis
! here Tan2gamma = 2 sig12 / (sig11 - sig12)
! add rsmall to the denominator to stop 1/0 errors, makes very little
! error to the calculated angles < rsmall
zQ11Q11 = 0.1_wp
zQ12Q12 = rsmall
zQ11Q12 = rsmall
IF((ABS( zsigma11 - zsigma22) > rsmall).OR.(ABS(zsigma12) > rsmall)) THEN
zAngle_denom = 1.0_wp/sqrt( ( zsigma11 - zsigma22 )*( zsigma11 - &
zsigma22 ) + 4.0_wp*zsigma12*zsigma12)
zQ11Q11 = 0.5_wp + ( zsigma11 - zsigma22 )*0.5_wp*zAngle_denom !Cos^2
zQ12Q12 = 0.5_wp - ( zsigma11 - zsigma22 )*0.5_wp*zAngle_denom !Sin^2
zQ11Q12 = zsigma12*zAngle_denom !CosSin
ENDIF
zsigma_1 = zQ11Q11*zsigma11 + 2.0_wp*zQ11Q12*zsigma12 + zQ12Q12*zsigma22 ! S(1,1)
zsigma_2 = zQ12Q12*zsigma11 - 2.0_wp*zQ11Q12*zsigma12 + zQ11Q11*zsigma22 ! S(2,2)
! Pure divergence
IF ((zsigma_1 >= 0.0_wp).AND.(zsigma_2 >= 0.0_wp)) THEN
pmresult11 = 0.0_wp
pmresult12 = 0.0_wp
! Unconfined compression: cracking of blocks not along the axial splitting
! direction
! which leads to the loss of their shape, so we again model it through diffusion
ELSEIF ((zsigma_1 >= 0.0_wp).AND.(zsigma_2 < 0.0_wp)) THEN
pmresult11 = - ppkfrac * (pa11 - zQ12Q12)
pmresult12 = - ppkfrac * (pa12 + zQ11Q12)
! Shear faulting
ELSEIF (zsigma_2 == 0.0_wp) THEN
pmresult11 = 0.0_wp
pmresult12 = 0.0_wp
ELSEIF ((zsigma_1 <= 0.0_wp).AND.(zsigma_1/zsigma_2 <= ppthreshold)) THEN
pmresult11 = - ppkfrac * (pa11 - zQ12Q12)
pmresult12 = - ppkfrac * (pa12 + zQ11Q12)
! Horizontal spalling
ELSE
pmresult11 = 0.0_wp
pmresult12 = 0.0_wp
ENDIF
END SUBROUTINE calc_ffrac
SUBROUTINE rhg_eap_rst( cdrw, kt )
!!---------------------------------------------------------------------
!! *** ROUTINE rhg_eap_rst ***
!!
!! ** Purpose : Read or write RHG file in restart file
!!
!! ** Method : use of IOM library
!!----------------------------------------------------------------------
CHARACTER(len=*) , INTENT(in) :: cdrw ! "READ"/"WRITE" flag
INTEGER, OPTIONAL, INTENT(in) :: kt ! ice time-step
!
INTEGER :: iter ! local integer
INTEGER :: id1, id2, id3, id4, id5 ! local integers
INTEGER :: ix, iy, ip, iz, n, ia ! local integers
INTEGER, PARAMETER :: nz = 100
REAL(wp) :: ainit, xinit, yinit, pinit, zinit
REAL(wp) :: da, dx, dy, dp, dz, a1
!!clem
REAL(wp) :: zw1, zw2, zfac, ztemp
REAL(wp) :: zidx, zidy, zidz
REAL(wp) :: zsaak(6) ! temporary array
REAL(wp), PARAMETER :: eps6 = 1.0e-6_wp
!!----------------------------------------------------------------------
!
IF( TRIM(cdrw) == 'READ' ) THEN ! Read/initialize
! ! ---------------
IF( ln_rstart ) THEN !* Read the restart file
!
id1 = iom_varid( numrir, 'stress1_i' , ldstop = .FALSE. )
id2 = iom_varid( numrir, 'stress2_i' , ldstop = .FALSE. )
id3 = iom_varid( numrir, 'stress12_i', ldstop = .FALSE. )
id4 = iom_varid( numrir, 'aniso_11' , ldstop = .FALSE. )
id5 = iom_varid( numrir, 'aniso_12' , ldstop = .FALSE. )
!
IF( MIN( id1, id2, id3, id4, id5 ) > 0 ) THEN ! fields exist
CALL iom_get( numrir, jpdom_auto, 'stress1_i' , stress1_i , cd_type = 'T' )
CALL iom_get( numrir, jpdom_auto, 'stress2_i' , stress2_i , cd_type = 'T' )
CALL iom_get( numrir, jpdom_auto, 'stress12_i', stress12_i, cd_type = 'F' )
CALL iom_get( numrir, jpdom_auto, 'aniso_11' , aniso_11 , cd_type = 'T' )
CALL iom_get( numrir, jpdom_auto, 'aniso_12' , aniso_12 , cd_type = 'T' )
ELSE ! start rheology from rest
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) ' ==>>> previous run without rheology, set stresses to 0'
stress1_i (:,:) = 0._wp
stress2_i (:,:) = 0._wp
stress12_i(:,:) = 0._wp
aniso_11 (:,:) = 0.5_wp
aniso_12 (:,:) = 0._wp
ENDIF
ELSE !* Start from rest
IF(lwp) WRITE(numout,*)
IF(lwp) WRITE(numout,*) ' ==>>> start from rest: set stresses to 0'
stress1_i (:,:) = 0._wp
stress2_i (:,:) = 0._wp
stress12_i(:,:) = 0._wp
aniso_11 (:,:) = 0.5_wp
aniso_12 (:,:) = 0._wp
ENDIF
!
da = 0.5_wp/real(na_yield-1,kind=wp)
ainit = 0.5_wp - da
dx = rpi/real(nx_yield-1,kind=wp)
xinit = rpi + 0.25_wp*rpi - dx
dz = rpi/real(nz,kind=wp)
zinit = -rpi*0.5_wp
dy = rpi/real(ny_yield-1,kind=wp)
yinit = -dy
s11r(:,:,:) = 0._wp
s12r(:,:,:) = 0._wp
s22r(:,:,:) = 0._wp
s11s(:,:,:) = 0._wp
s12s(:,:,:) = 0._wp
s22s(:,:,:) = 0._wp
!!$ DO ia=1,na_yield
!!$ DO ix=1,nx_yield
!!$ DO iy=1,ny_yield
!!$ s11r(ix,iy,ia) = 0._wp
!!$ s12r(ix,iy,ia) = 0._wp
!!$ s22r(ix,iy,ia) = 0._wp
!!$ s11s(ix,iy,ia) = 0._wp
!!$ s12s(ix,iy,ia) = 0._wp
!!$ s22s(ix,iy,ia) = 0._wp
!!$ IF (ia <= na_yield-1) THEN
!!$ DO iz=1,nz
!!$ s11r(ix,iy,ia) = s11r(ix,iy,ia) + 1*w1(ainit+ia*da)* &
!!$ exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* &
!!$ s11kr(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz)*dz/sin(2._wp*pphi)
!!$ s12r(ix,iy,ia) = s12r(ix,iy,ia) + 1*w1(ainit+ia*da)* &
!!$ exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* &
!!$ s12kr(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz)*dz/sin(2._wp*pphi)
!!$ s22r(ix,iy,ia) = s22r(ix,iy,ia) + 1*w1(ainit+ia*da)* &
!!$ exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* &
!!$ s22kr(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz)*dz/sin(2._wp*pphi)
!!$ s11s(ix,iy,ia) = s11s(ix,iy,ia) + 1*w1(ainit+ia*da)* &
!!$ exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* &
!!$ s11ks(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz)*dz/sin(2._wp*pphi)
!!$ s12s(ix,iy,ia) = s12s(ix,iy,ia) + 1*w1(ainit+ia*da)* &
!!$ exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* &
!!$ s12ks(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz)*dz/sin(2._wp*pphi)
!!$ s22s(ix,iy,ia) = s22s(ix,iy,ia) + 1*w1(ainit+ia*da)* &
!!$ exp(-w2(ainit+ia*da)*(zinit+iz*dz)*(zinit+iz*dz))* &
!!$ s22ks(xinit+ix*dx,yinit+iy*dy,zinit+iz*dz)*dz/sin(2._wp*pphi)
!!$ ENDDO
!!$ IF (abs(s11r(ix,iy,ia)) < eps6) s11r(ix,iy,ia) = 0._wp
!!$ IF (abs(s12r(ix,iy,ia)) < eps6) s12r(ix,iy,ia) = 0._wp
!!$ IF (abs(s22r(ix,iy,ia)) < eps6) s22r(ix,iy,ia) = 0._wp
!!$ IF (abs(s11s(ix,iy,ia)) < eps6) s11s(ix,iy,ia) = 0._wp
!!$ IF (abs(s12s(ix,iy,ia)) < eps6) s12s(ix,iy,ia) = 0._wp
!!$ IF (abs(s22s(ix,iy,ia)) < eps6) s22s(ix,iy,ia) = 0._wp
!!$ ELSE
!!$ s11r(ix,iy,ia) = 0.5_wp*s11kr(xinit+ix*dx,yinit+iy*dy,0._wp)/sin(2._wp*pphi)
!!$ s12r(ix,iy,ia) = 0.5_wp*s12kr(xinit+ix*dx,yinit+iy*dy,0._wp)/sin(2._wp*pphi)
!!$ s22r(ix,iy,ia) = 0.5_wp*s22kr(xinit+ix*dx,yinit+iy*dy,0._wp)/sin(2._wp*pphi)
!!$ s11s(ix,iy,ia) = 0.5_wp*s11ks(xinit+ix*dx,yinit+iy*dy,0._wp)/sin(2._wp*pphi)
!!$ s12s(ix,iy,ia) = 0.5_wp*s12ks(xinit+ix*dx,yinit+iy*dy,0._wp)/sin(2._wp*pphi)
!!$ s22s(ix,iy,ia) = 0.5_wp*s22ks(xinit+ix*dx,yinit+iy*dy,0._wp)/sin(2._wp*pphi)
!!$ IF (abs(s11r(ix,iy,ia)) < eps6) s11r(ix,iy,ia) = 0._wp
!!$ IF (abs(s12r(ix,iy,ia)) < eps6) s12r(ix,iy,ia) = 0._wp
!!$ IF (abs(s22r(ix,iy,ia)) < eps6) s22r(ix,iy,ia) = 0._wp
!!$ IF (abs(s11s(ix,iy,ia)) < eps6) s11s(ix,iy,ia) = 0._wp
!!$ IF (abs(s12s(ix,iy,ia)) < eps6) s12s(ix,iy,ia) = 0._wp
!!$ IF (abs(s22s(ix,iy,ia)) < eps6) s22s(ix,iy,ia) = 0._wp
!!$ ENDIF
!!$ ENDDO
!!$ ENDDO
!!$ ENDDO
!! faster but still very slow => to be improved
zfac = dz/sin(2._wp*pphi)
DO ia = 1, na_yield-1
zw1 = w1(ainit+ia*da)
zw2 = w2(ainit+ia*da)
DO iz = 1, nz
zidz = zinit+iz*dz
ztemp = zw1 * EXP(-zw2*(zinit+iz*dz)*(zinit+iz*dz))
DO iy = 1, ny_yield
zidy = yinit+iy*dy
DO ix = 1, nx_yield
zidx = xinit+ix*dx
call all_skr_sks(zidx,zidy,zidz,zsaak)
zsaak = ztemp*zsaak*zfac
s11r(ix,iy,ia) = s11r(ix,iy,ia) + zsaak(1)
s12r(ix,iy,ia) = s12r(ix,iy,ia) + zsaak(2)
s22r(ix,iy,ia) = s22r(ix,iy,ia) + zsaak(3)
s11s(ix,iy,ia) = s11s(ix,iy,ia) + zsaak(4)
s12s(ix,iy,ia) = s12s(ix,iy,ia) + zsaak(5)
s22s(ix,iy,ia) = s22s(ix,iy,ia) + zsaak(6)
END DO
END DO
END DO
END DO
zfac = 1._wp/sin(2._wp*pphi)
ia = na_yield
DO iy = 1, ny_yield
zidy = yinit+iy*dy
DO ix = 1, nx_yield
zidx = xinit+ix*dx
call all_skr_sks(zidx,zidy,0._wp,zsaak)
zsaak = 0.5_wp*zsaak*zfac
s11r(ix,iy,ia) = zsaak(1)
s12r(ix,iy,ia) = zsaak(2)
s22r(ix,iy,ia) = zsaak(3)
s11s(ix,iy,ia) = zsaak(4)
s12s(ix,iy,ia) = zsaak(5)
s22s(ix,iy,ia) = zsaak(6)
ENDDO
ENDDO
WHERE (ABS(s11r(:,:,:)) < eps6) s11r(:,:,:) = 0._wp
WHERE (ABS(s12r(:,:,:)) < eps6) s12r(:,:,:) = 0._wp
WHERE (ABS(s22r(:,:,:)) < eps6) s22r(:,:,:) = 0._wp
WHERE (ABS(s11s(:,:,:)) < eps6) s11s(:,:,:) = 0._wp
WHERE (ABS(s12s(:,:,:)) < eps6) s12s(:,:,:) = 0._wp
WHERE (ABS(s22s(:,:,:)) < eps6) s22s(:,:,:) = 0._wp
ELSEIF( TRIM(cdrw) == 'WRITE' ) THEN ! Create restart file
! ! -------------------
IF(lwp) WRITE(numout,*) '---- rhg-rst ----'
iter = kt + nn_fsbc - 1 ! ice restarts are written at kt == nitrst - nn_fsbc + 1
!
CALL iom_rstput( iter, nitrst, numriw, 'stress1_i' , stress1_i )
CALL iom_rstput( iter, nitrst, numriw, 'stress2_i' , stress2_i )
CALL iom_rstput( iter, nitrst, numriw, 'stress12_i', stress12_i )
CALL iom_rstput( iter, nitrst, numriw, 'aniso_11' , aniso_11 )
CALL iom_rstput( iter, nitrst, numriw, 'aniso_12' , aniso_12 )
!
ENDIF
!
END SUBROUTINE rhg_eap_rst
FUNCTION w1(pa)
!!-------------------------------------------------------------------
!! Function : w1 (see Gaussian function psi in Tsamados et al 2013)
!!-------------------------------------------------------------------
REAL(wp), INTENT(in ) :: pa
REAL(wp) :: w1
!!-------------------------------------------------------------------
w1 = - 223.87569446_wp &
& + 2361.21986630_wp*pa &
& - 10606.56079975_wp*pa*pa &
& + 26315.50025642_wp*pa*pa*pa &
& - 38948.30444297_wp*pa*pa*pa*pa &
& + 34397.72407466_wp*pa*pa*pa*pa*pa &
& - 16789.98003081_wp*pa*pa*pa*pa*pa*pa &
& + 3495.82839237_wp*pa*pa*pa*pa*pa*pa*pa
END FUNCTION w1
FUNCTION w2(pa)
!!-------------------------------------------------------------------
!! Function : w2 (see Gaussian function psi in Tsamados et al 2013)
!!-------------------------------------------------------------------
REAL(wp), INTENT(in ) :: pa
REAL(wp) :: w2
!!-------------------------------------------------------------------
w2 = - 6670.68911883_wp &
& + 70222.33061536_wp*pa &
& - 314871.71525448_wp*pa*pa &
& + 779570.02793492_wp*pa*pa*pa &
& - 1151098.82436864_wp*pa*pa*pa*pa &
& + 1013896.59464498_wp*pa*pa*pa*pa*pa &
& - 493379.44906738_wp*pa*pa*pa*pa*pa*pa &
& + 102356.55151800_wp*pa*pa*pa*pa*pa*pa*pa
END FUNCTION w2
SUBROUTINE all_skr_sks( px, py, pz, allsk )
REAL(wp), INTENT(in ) :: px,py,pz
REAL(wp), INTENT(out ) :: allsk(6)
REAL(wp) :: zs12r0, zs21r0
REAL(wp) :: zs12s0, zs21s0
REAL(wp) :: zpih
REAL(wp) :: zn1t2i11, zn1t2i12, zn1t2i21, zn1t2i22
REAL(wp) :: zn2t1i11, zn2t1i12, zn2t1i21, zn2t1i22
REAL(wp) :: zt1t2i11, zt1t2i12, zt1t2i21, zt1t2i22
REAL(wp) :: zt2t1i11, zt2t1i12, zt2t1i21, zt2t1i22
REAL(wp) :: zd11, zd12, zd22
REAL(wp) :: zIIn1t2, zIIn2t1, zIIt1t2
REAL(wp) :: zHen1t2, zHen2t1
!!-------------------------------------------------------------------
zpih = 0.5_wp*rpi
zn1t2i11 = cos(pz+zpih-pphi) * cos(pz+pphi)
zn1t2i12 = cos(pz+zpih-pphi) * sin(pz+pphi)
zn1t2i21 = sin(pz+zpih-pphi) * cos(pz+pphi)
zn1t2i22 = sin(pz+zpih-pphi) * sin(pz+pphi)
zn2t1i11 = cos(pz-zpih+pphi) * cos(pz-pphi)
zn2t1i12 = cos(pz-zpih+pphi) * sin(pz-pphi)
zn2t1i21 = sin(pz-zpih+pphi) * cos(pz-pphi)
zn2t1i22 = sin(pz-zpih+pphi) * sin(pz-pphi)
zt1t2i11 = cos(pz-pphi) * cos(pz+pphi)
zt1t2i12 = cos(pz-pphi) * sin(pz+pphi)
zt1t2i21 = sin(pz-pphi) * cos(pz+pphi)
zt1t2i22 = sin(pz-pphi) * sin(pz+pphi)
zt2t1i11 = cos(pz+pphi) * cos(pz-pphi)
zt2t1i12 = cos(pz+pphi) * sin(pz-pphi)
zt2t1i21 = sin(pz+pphi) * cos(pz-pphi)
zt2t1i22 = sin(pz+pphi) * sin(pz-pphi)
! In expression of tensor d, with this formulatin d(x)=-d(x+pi)
! Solution, when diagonalizing always check sgn(a11-a22) if > then keep x else
! x=x-pi/2
zd11 = cos(py)*cos(py)*(cos(px)+sin(px)*tan(py)*tan(py))
zd12 = cos(py)*cos(py)*tan(py)*(-cos(px)+sin(px))
zd22 = cos(py)*cos(py)*(sin(px)+cos(px)*tan(py)*tan(py))
zIIn1t2 = zn1t2i11 * zd11 + (zn1t2i12 + zn1t2i21) * zd12 + zn1t2i22 * zd22
zIIn2t1 = zn2t1i11 * zd11 + (zn2t1i12 + zn2t1i21) * zd12 + zn2t1i22 * zd22
zIIt1t2 = zt1t2i11 * zd11 + (zt1t2i12 + zt1t2i21) * zd12 + zt1t2i22 * zd22
IF (-zIIn1t2>=rsmall) THEN
zHen1t2 = 1._wp
ELSE
zHen1t2 = 0._wp
ENDIF
IF (-zIIn2t1>=rsmall) THEN
zHen2t1 = 1._wp
ELSE
zHen2t1 = 0._wp
ENDIF
!!-------------------------------------------------------------------
!! Function : s11kr
!!-------------------------------------------------------------------
allsk(1) = (- zHen1t2 * zn1t2i11 - zHen2t1 * zn2t1i11)
!!-------------------------------------------------------------------
!! Function : s12kr
!!-------------------------------------------------------------------
zs12r0 = (- zHen1t2 * zn1t2i12 - zHen2t1 * zn2t1i12)
zs21r0 = (- zHen1t2 * zn1t2i21 - zHen2t1 * zn2t1i21)
allsk(2)=0.5_wp*(zs12r0+zs21r0)
!!-------------------------------------------------------------------
!! Function : s22kr
!!-------------------------------------------------------------------
allsk(3) = (- zHen1t2 * zn1t2i22 - zHen2t1 * zn2t1i22)
!!-------------------------------------------------------------------
!! Function : s11ks
!!-------------------------------------------------------------------
allsk(4) = sign(1._wp,zIIt1t2+rsmall)*(zHen1t2 * zt1t2i11 + zHen2t1 * zt2t1i11)
!!-------------------------------------------------------------------
!! Function : s12ks
!!-------------------------------------------------------------------
zs12s0 = sign(1._wp,zIIt1t2+rsmall)*(zHen1t2 * zt1t2i12 + zHen2t1 * zt2t1i12)
zs21s0 = sign(1._wp,zIIt1t2+rsmall)*(zHen1t2 * zt1t2i21 + zHen2t1 * zt2t1i21)
allsk(5)=0.5_wp*(zs12s0+zs21s0)
!!-------------------------------------------------------------------
!! Function : s22ks
!!-------------------------------------------------------------------
allsk(6) = sign(1._wp,zIIt1t2+rsmall)*(zHen1t2 * zt1t2i22 + zHen2t1 * zt2t1i22)
END SUBROUTINE all_skr_sks
#else
!!----------------------------------------------------------------------
!! Default option Empty module NO SI3 sea-ice model
!!----------------------------------------------------------------------
USE par_kind
USE lib_mpp
CONTAINS
SUBROUTINE ice_dyn_rhg_eap( kt, Kmm, pstress1_i, pstress2_i, pstress12_i, pshear_i, pdivu_i, pdelta_i, paniso_11, paniso_12, prdg_conv )
INTEGER , INTENT(in ) :: kt ! time step
INTEGER , INTENT(in ) :: Kmm ! ocean time level index
REAL(wp), DIMENSION(:,:), INTENT(in ) :: pstress1_i, pstress2_i, pstress12_i !
REAL(wp), DIMENSION(:,:), INTENT(in ) :: pshear_i , pdivu_i , pdelta_i !
REAL(wp), DIMENSION(:,:), INTENT(in ) :: paniso_11 , paniso_12 ! structure tensor components
REAL(wp), DIMENSION(:,:), INTENT(in ) :: prdg_conv ! for ridging
CALL ctl_stop('EAP rheology is currently dsabled due to issues with AGRIF preprocessing')
END SUBROUTINE ice_dyn_rhg_eap
SUBROUTINE rhg_eap_rst( cdrw, kt )
CHARACTER(len=*) , INTENT(in) :: cdrw ! "READ"/"WRITE" flag
INTEGER, OPTIONAL, INTENT(in) :: kt ! ice time-step
END SUBROUTINE rhg_eap_rst
#endif
!!==============================================================================
END MODULE icedyn_rhg_eap