| 1 | ! |
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| 2 | ! |
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| 3 | ! |
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| 4 | SUBROUTINE thermcell_flux(ngrid,nlay,ptimestep,masse, & |
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| 5 | lmin,lmax,entr_star,detr_star, & |
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| 6 | f,rhobarz,zlev,zw2,fm,entr,detr,zqla) |
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| 7 | |
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| 8 | |
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| 9 | !=============================================================================== |
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| 10 | ! Purpose: fluxes deduction |
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| 11 | ! |
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| 12 | ! Modif 2019/04 (AB alexandre.boissinot@lmd.jussieu.fr) |
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| 13 | ! |
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| 14 | !=============================================================================== |
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| 15 | |
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| 16 | USE print_control_mod, ONLY: prt_level |
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| 17 | USE thermcell_mod, ONLY: fomass_max, alpha_max |
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| 18 | |
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| 19 | IMPLICIT NONE |
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| 20 | |
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| 21 | |
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| 22 | !=============================================================================== |
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| 23 | ! Declaration |
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| 24 | !=============================================================================== |
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| 25 | |
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| 26 | ! Inputs: |
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| 27 | ! ------- |
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| 28 | |
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| 29 | INTEGER ngrid, nlay |
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| 30 | INTEGER lmin(ngrid) |
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| 31 | INTEGER lmax(ngrid) |
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| 32 | |
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| 33 | REAL entr_star(ngrid,nlay) |
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| 34 | REAL detr_star(ngrid,nlay) |
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| 35 | REAL zw2(ngrid,nlay+1) |
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| 36 | REAL zlev(ngrid,nlay+1) |
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| 37 | REAL masse(ngrid,nlay) |
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| 38 | REAL ptimestep |
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| 39 | REAL rhobarz(ngrid,nlay) |
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| 40 | REAL f(ngrid) |
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| 41 | REAL zqla(ngrid,nlay) |
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| 42 | REAL zmax(ngrid) |
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| 43 | |
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| 44 | ! Outputs: |
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| 45 | ! -------- |
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| 46 | |
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| 47 | REAL entr(ngrid,nlay) |
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| 48 | REAL detr(ngrid,nlay) |
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| 49 | REAL fm(ngrid,nlay+1) |
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| 50 | |
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| 51 | ! Local: |
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| 52 | ! ------ |
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| 53 | |
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| 54 | INTEGER ig, l, k |
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| 55 | INTEGER igout, lout ! Error grid point number and level |
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| 56 | |
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| 57 | REAL zfm ! Mass flux such as updraft fraction is equal to its maximal authorized value alpha_max |
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| 58 | REAL f_old ! Save initial value of mass flux |
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| 59 | REAL eee0 ! Save initial value of entrainment |
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| 60 | REAL ddd0 ! Save initial value of detrainment |
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| 61 | REAL eee ! eee0 - layer mass * maximal authorized mass fraction / dt |
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| 62 | REAL ddd ! ddd0 - eee |
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| 63 | REAL zzz ! Temporary variable set to mass flux |
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| 64 | REAL fact ! Factor between old norm and new norm |
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| 65 | |
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| 66 | INTEGER ncorecdetr ! detr > fm- counter |
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| 67 | INTEGER ncorecentr ! entr > e_max counter |
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| 68 | INTEGER ncorecalpha ! fm > zfm counter |
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| 69 | |
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| 70 | LOGICAL labort_physic |
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| 71 | |
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| 72 | CHARACTER (len=20) :: modname='thermcell_flux' |
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| 73 | CHARACTER (len=80) :: abort_message |
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| 74 | |
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| 75 | !=============================================================================== |
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| 76 | ! Initialization |
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| 77 | !=============================================================================== |
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| 78 | |
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| 79 | ncorecdetr = 0 |
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| 80 | ncorecentr = 0 |
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| 81 | ncorecalpha = 0 |
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| 82 | |
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| 83 | entr(:,:) = 0. |
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| 84 | detr(:,:) = 0. |
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| 85 | fm(:,:) = 0. |
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| 86 | |
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| 87 | !=============================================================================== |
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| 88 | ! Mass flux, entrainment and detrainment |
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| 89 | !=============================================================================== |
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| 90 | |
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| 91 | !------------------------------------------------------------------------------- |
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| 92 | ! Multiplication par la norme issue de la relation de fermeture |
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| 93 | !------------------------------------------------------------------------------- |
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| 94 | |
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| 95 | DO l=1,nlay |
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| 96 | entr(:,l) = f(:) * entr_star(:,l) |
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| 97 | detr(:,l) = f(:) * detr_star(:,l) |
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| 98 | ENDDO |
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| 99 | |
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| 100 | !------------------------------------------------------------------------------- |
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| 101 | ! Mass flux and boundary conditions |
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| 102 | !------------------------------------------------------------------------------- |
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| 103 | |
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| 104 | DO l=1,nlay |
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| 105 | DO ig=1,ngrid |
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| 106 | IF (l.lt.lmax(ig) .and. l.ge.lmin(ig)) THEN |
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| 107 | fm(ig,l+1) = fm(ig,l) + entr(ig,l) - detr(ig,l) |
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| 108 | ELSEIF (l.eq.lmax(ig)) THEN |
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| 109 | fm(ig,l+1) = 0. |
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| 110 | detr(ig,l) = fm(ig,l) + entr(ig,l) |
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| 111 | ELSE |
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| 112 | fm(ig,l+1) = 0. |
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| 113 | entr(ig,l) = 0. |
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| 114 | detr(ig,l) = 0. |
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| 115 | ENDIF |
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| 116 | ENDDO |
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| 117 | ENDDO |
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| 118 | |
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| 119 | !=============================================================================== |
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| 120 | ! Validity tests and corrections |
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| 121 | !=============================================================================== |
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| 122 | |
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| 123 | DO l=1,nlay |
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| 124 | |
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| 125 | !------------------------------------------------------------------------------- |
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| 126 | ! Is incoming mass flux positive ? |
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| 127 | !------------------------------------------------------------------------------- |
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| 128 | |
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| 129 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 130 | ! AB : I remove the correction and replace it by an uncompromising test. |
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| 131 | ! According to the previous derivations, we MUST have positive mass flux |
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| 132 | ! everywhere! Indeed, as soon as fm becomes negative, the plume stops. |
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| 133 | ! Then the only value which can be negative is the mass flux at the top of |
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| 134 | ! the plume. However, this value was set to zero a few lines above. |
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| 135 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 136 | |
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| 137 | labort_physic=.false. |
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| 138 | |
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| 139 | DO ig=1,ngrid |
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| 140 | IF (fm(ig,l).lt.0.) THEN |
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| 141 | labort_physic = .true. |
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| 142 | igout = ig |
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| 143 | lout = l |
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| 144 | ENDIF |
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| 145 | ENDDO |
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| 146 | |
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| 147 | IF (labort_physic) THEN |
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| 148 | print *, 'ERROR: mass flux has negative value(s)!' |
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| 149 | print *, 'ig,l,fm',igout, lout, fm(igout,lout) |
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| 150 | print *, 'lmin,lmax', lmin(igout), lmax(igout) |
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| 151 | print *, '-------------------------------' |
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| 152 | DO k=nlay,1,-1 |
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| 153 | print *, 'fm ', fm(igout,k+1) |
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| 154 | print *, 'entr,detr', entr(igout,k), detr(igout,k) |
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| 155 | ENDDO |
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| 156 | print *, 'fm-', fm(igout,1) |
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| 157 | print *, '-------------------------------' |
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| 158 | abort_message = 'Negative incoming fm in thermcell_flux' |
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| 159 | CALL abort_physic(modname,abort_message,1) |
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| 160 | ENDIF |
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| 161 | |
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| 162 | !------------------------------------------------------------------------------- |
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| 163 | ! Is entrainment positive ? |
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| 164 | !------------------------------------------------------------------------------- |
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| 165 | |
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| 166 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 167 | ! AB : According to the previous derivations, we MUST have positive entrainment |
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| 168 | ! and detrainment everywhere! |
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| 169 | ! Indeed, they are set to max between zero and a computed value. |
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| 170 | ! Then tests are uncompromising. |
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| 171 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 172 | |
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| 173 | DO ig=1,ngrid |
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| 174 | IF (entr(ig,l).lt.0.) THEN |
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| 175 | labort_physic = .true. |
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| 176 | igout = ig |
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| 177 | lout = l |
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| 178 | ENDIF |
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| 179 | ENDDO |
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| 180 | |
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| 181 | IF (labort_physic) THEN |
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| 182 | print *, 'ERROR: entrainment has negative value(s)!' |
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| 183 | print *, 'ig,l,entr', igout, lout, entr(igout,lout) |
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| 184 | print *, 'lmin,lmax', lmin(igout), lmax(igout) |
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| 185 | print *, '-------------------------------' |
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| 186 | DO k=nlay,1,-1 |
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| 187 | print *, 'fm ', fm(igout,k+1) |
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| 188 | print *, 'entr,detr', entr(igout,k), detr(igout,k) |
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| 189 | ENDDO |
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| 190 | print *, 'fm ', fm(igout,1) |
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| 191 | print *, '-------------------------------' |
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| 192 | abort_message = 'Negative entrainment in thermcell_flux' |
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| 193 | CALL abort_physic(modname,abort_message,1) |
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| 194 | ENDIF |
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| 195 | |
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| 196 | !------------------------------------------------------------------------------- |
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| 197 | ! Is detrainment positive ? |
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| 198 | !------------------------------------------------------------------------------- |
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| 199 | |
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| 200 | DO ig=1,ngrid |
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| 201 | IF (detr(ig,l).lt.0.) THEN |
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| 202 | labort_physic = .true. |
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| 203 | igout = ig |
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| 204 | lout = l |
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| 205 | ENDIF |
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| 206 | ENDDO |
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| 207 | |
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| 208 | IF (labort_physic) THEN |
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| 209 | print *, 'ERROR: detrainment has negative value(s)!' |
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| 210 | print *, 'ig,l,detr', igout, lout, detr(igout,lout) |
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| 211 | print *, 'lmin,lmax', lmin(igout), lmax(igout) |
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| 212 | print *, '-------------------------------' |
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| 213 | DO k=nlay,1,-1 |
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| 214 | print *, 'fm ', fm(igout,k+1) |
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| 215 | print *, 'entr,detr', entr(igout,k), detr(igout,k) |
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| 216 | ENDDO |
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| 217 | print *, 'fm ', fm(igout,1) |
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| 218 | print *, '-------------------------------' |
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| 219 | abort_message = 'Negative detrainment in thermcell_flux' |
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| 220 | CALL abort_physic(modname,abort_message,1) |
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| 221 | ENDIF |
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| 222 | |
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| 223 | !------------------------------------------------------------------------------- |
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| 224 | ! Is detrainment lesser than incoming mass flux ? |
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| 225 | !------------------------------------------------------------------------------- |
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| 226 | |
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| 227 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 228 | ! AB : Even if fm has no negative value, it can be lesser than detr. |
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| 229 | ! That's not suitable because when we will mix the plume with the |
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| 230 | ! environment, it will detrain more mass than it is physically able to do. |
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| 231 | ! When it occures, that imply that entr + fm is greater than detr, |
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| 232 | ! otherwise we get a negative outgoing mass flux (cf. above). |
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| 233 | ! That is why we correct the detrainment as follows. |
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| 234 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 235 | |
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| 236 | DO ig=1,ngrid |
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| 237 | IF (detr(ig,l).gt.fm(ig,l)) THEN |
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| 238 | detr(ig,l) = fm(ig,l) |
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| 239 | entr(ig,l) = fm(ig,l+1) |
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| 240 | |
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| 241 | IF (prt_level.ge.10) THEN |
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| 242 | print *, 'WARNING: Detrainment is modified in thermcell_flux!' |
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| 243 | print *, 'ig,l,lmax', ig, l, lmax(ig) |
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| 244 | ENDIF |
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| 245 | |
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| 246 | IF (prt_level.ge.100) THEN |
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| 247 | print *, 'fm+', fm(ig,l+1) |
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| 248 | print *, 'entr,detr', entr(ig,l), detr(ig,l) |
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| 249 | print *, 'fm-', fm(ig,l) |
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| 250 | ENDIF |
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| 251 | |
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| 252 | ncorecdetr = ncorecdetr + 1 |
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| 253 | |
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| 254 | ENDIF |
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| 255 | ENDDO |
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| 256 | |
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| 257 | !------------------------------------------------------------------------------- |
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| 258 | ! Is entrainment mass fraction lesser than fomass_max ? |
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| 259 | !------------------------------------------------------------------------------- |
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| 260 | |
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| 261 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 262 | ! AB : Entrainment is bigger than the maximal authorized value. |
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| 263 | ! If we consider that the excess entrainement is in fact plume air which |
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| 264 | ! is not detrained then we compensate it by decreasing detr. |
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| 265 | ! If it's not enough, we can increase entr in the layer above and decrease |
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| 266 | ! the outgoing mass flux in the current layer. |
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| 267 | ! If it's still unsufficient, code will abort (now commented). |
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| 268 | ! Else we reset entr to its intial value and we renormalize entrainment, |
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| 269 | ! detrainment and mass flux profiles such as we do not exceed the maximal |
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| 270 | ! authorized entrained mass. |
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| 271 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 272 | |
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| 273 | labort_physic=.false. |
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| 274 | |
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| 275 | DO ig=1,ngrid |
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| 276 | eee0 = entr(ig,l) |
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| 277 | ddd0 = detr(ig,l) |
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| 278 | eee = entr(ig,l) - masse(ig,l) * fomass_max / ptimestep |
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| 279 | ddd = detr(ig,l) - eee |
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| 280 | |
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| 281 | IF (eee.gt.0.) THEN |
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| 282 | entr(ig,l) = entr(ig,l) - eee |
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| 283 | ncorecentr = ncorecentr + 1 |
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| 284 | |
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| 285 | IF (prt_level.ge.10) THEN |
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| 286 | print *, 'WARNING: Entrainment is modified in thermcell_flux!' |
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| 287 | print *, 'ig,l,lmax', ig, l, lmax(ig) |
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| 288 | ENDIF |
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| 289 | |
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| 290 | IF (ddd.gt.0.) THEN ! detr in the current layer is reduced |
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| 291 | detr(ig,l) = ddd |
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| 292 | ELSEIF (l.eq.lmax(ig)) THEN ! detr in the last layer is adjusted |
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| 293 | detr(ig,l) = fm(ig,l) + entr(ig,l) |
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| 294 | ELSEIF (entr(ig,l+1).gt.ABS(ddd)) THEN ! detr in the current layer is set to 0 and entr in the layer above is reduced |
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| 295 | detr(ig,l) = 0. |
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| 296 | fm(ig,l+1) = fm(ig,l) + entr(ig,l) |
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| 297 | entr(ig,l+1) = entr(ig,l+1) + ddd |
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| 298 | ! ELSE |
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| 299 | ! entr(ig,l) = entr(ig,l) + eee |
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| 300 | ! igout=ig |
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| 301 | ! lout=l |
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| 302 | ! labort_physic=.true. |
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| 303 | ELSE |
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| 304 | fact = (eee0 - eee) / eee0 |
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| 305 | entr(ig,l) = eee0 |
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| 306 | detr(ig,:) = detr(ig,:) * fact |
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| 307 | entr(ig,:) = entr(ig,:) * fact |
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| 308 | fm(ig,:) = fm(ig,:) * fact |
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| 309 | |
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| 310 | IF (prt_level.ge.1) THEN |
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| 311 | print *, 'WARNING: Normalisation is modified in thermcell_flux!' |
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| 312 | print *, 'old f, new f :', f(ig), fact * f(ig) |
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| 313 | ENDIF |
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| 314 | ENDIF |
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| 315 | ENDIF |
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| 316 | ENDDO |
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| 317 | |
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| 318 | ! IF (labort_physic) THEN |
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| 319 | ! print *, 'ERROR: Entrainment is greater than its maximal authorized value!' |
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| 320 | ! print *, ' Nor detrainment neither entrainment can compensate it!' |
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| 321 | ! print *, 'ig,l,entr', igout, lout, entr(igout,lout) |
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| 322 | ! print *, 'lmin,lmax', lmin(igout), lmax(igout) |
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| 323 | ! print *, '--------------------' |
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| 324 | ! print *, 'e_max :', masse(igout,lout)*fomass_max/ptimestep |
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| 325 | ! print *, ' fomass_max :', fomass_max |
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| 326 | ! print *, ' masse :', masse(igout,lout) |
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| 327 | ! print *, ' ptimestep :', ptimestep |
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| 328 | ! print *, 'norm :', f(igout) |
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| 329 | ! print *, 'entr* :', entr_star(igout,lout) |
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| 330 | ! print *, '--------------------' |
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| 331 | ! DO k=nlay,1,-1 |
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| 332 | ! print *, 'fm ', fm(igout,k+1) |
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| 333 | ! print *, 'entr,detr', entr(igout,k), detr(igout,k) |
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| 334 | ! ENDDO |
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| 335 | ! print *, 'fm ', fm(igout,1) |
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| 336 | ! print *, '-------------------------------' |
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| 337 | ! abort_message = 'Entrainment is too large in thermcell_flux' |
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| 338 | ! CALL abort_physic (modname,abort_message,1) |
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| 339 | ! ENDIF |
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| 340 | |
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| 341 | !------------------------------------------------------------------------------- |
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| 342 | ! Is updraft fraction lesser than alpha_max ? |
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| 343 | !------------------------------------------------------------------------------- |
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| 344 | |
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| 345 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 346 | ! FH : Partie a revisiter. |
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| 347 | ! Il semble qu'etaient codees ici deux optiques dans le cas F/(rho*w) > 1 |
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| 348 | ! - soit limiter la hauteur du thermique en considerant que c'est |
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| 349 | ! la derniere chouche |
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| 350 | ! - soit limiter F a rho w. |
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| 351 | ! Dans le second cas, il faut en fait limiter a un peu moins que ca parce |
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| 352 | ! qu'on a des 1/(1-alpha) un peu plus loin dans thermcell_main et qu'il |
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| 353 | ! semble de toutes facons deraisonable d'avoir des fractions de 1... |
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| 354 | ! Ci-dessous, et dans l'etat actuel, le premier des deux if est sans doute inutile. |
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| 355 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 356 | |
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| 357 | DO ig=1,ngrid |
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| 358 | zfm = rhobarz(ig,l+1) * zw2(ig,l+1) * alpha_max |
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| 359 | |
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| 360 | IF (fm(ig,l+1) .gt. zfm) THEN |
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| 361 | f_old = fm(ig,l+1) |
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| 362 | fm(ig,l+1) = zfm |
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| 363 | detr(ig,l) = detr(ig,l) + f_old - fm(ig,l+1) |
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| 364 | |
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| 365 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 366 | ! AB : The previous change doesn't observe the equation df/dz = e - d. |
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| 367 | ! To avoid this issue, what is better to do? I choose to increase the |
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| 368 | ! entrainment in the layer above when l<lmax. If l=lmax then fm(l+1)=0 and |
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| 369 | ! there are never any problems. |
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| 370 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 371 | IF (l.lt.lmax(ig)) THEN |
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| 372 | entr(ig,l+1) = entr(ig,l+1) + f_old - fm(ig,l+1) |
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| 373 | ENDIF |
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| 374 | |
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| 375 | IF (prt_level.ge.10) THEN |
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| 376 | print *, 'Mass flux is modified in thermcell_flux' |
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| 377 | print *, 'ig,l,lmax', ig, l, lmax(ig) |
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| 378 | ENDIF |
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| 379 | |
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| 380 | IF (prt_level.ge.100) THEN |
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| 381 | print *, 'fm-', fm(ig,l) |
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| 382 | print *, 'entr,detr', entr(ig,l), detr(ig,l) |
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| 383 | print *, 'fm+', fm(ig,l+1) |
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| 384 | ENDIF |
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| 385 | |
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| 386 | ncorecalpha = ncorecalpha + 1 |
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| 387 | ENDIF |
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| 388 | ENDDO |
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| 389 | |
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| 390 | ENDDO |
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| 391 | |
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| 392 | !------------------------------------------------------------------------------- |
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| 393 | ! Boundary conditions |
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| 394 | !------------------------------------------------------------------------------- |
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| 395 | |
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| 396 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 397 | ! AB : test added to avoid problem when lmax = 0, which is not a fortran index. |
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| 398 | ! Theoretically, we always get lmax >= lmin >= linf > 0 |
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| 399 | !~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ |
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| 400 | DO ig=1,ngrid |
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| 401 | IF (lmax(ig).gt.0) THEN |
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| 402 | detr(ig,lmax(ig)) = fm(ig,lmax(ig)) + entr(ig,lmax(ig)) |
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| 403 | fm(ig,lmax(ig)+1) = 0. |
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| 404 | entr(ig,lmax(ig)) = 0. |
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| 405 | ENDIF |
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| 406 | ENDDO |
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| 407 | |
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| 408 | !------------------------------------------------------------------------------- |
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| 409 | ! Corrections display |
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| 410 | !------------------------------------------------------------------------------- |
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| 411 | |
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| 412 | IF (prt_level.GE.1) THEN |
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| 413 | |
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| 414 | IF (ncorecdetr.GE.1) THEN |
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| 415 | print *, 'WARNING: Detrainment is greater than mass flux!' |
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| 416 | print *, ' In', ncorecdetr, 'point(s)' |
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| 417 | ENDIF |
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| 418 | |
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| 419 | IF (ncorecentr.GE.1) THEN |
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| 420 | print *, 'WARNING: Entrained mass is greater than maximal authorized value!' |
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| 421 | print *, ' In', ncorecentr, 'point(s)' |
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| 422 | ENDIF |
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| 423 | |
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| 424 | IF (ncorecalpha.GE.1) THEN |
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| 425 | print *, 'WARNING: Updraft fraction is greater than maximal authorized value!' |
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| 426 | print *, ' In', ncorecalpha, 'point(s)' |
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| 427 | ENDIF |
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| 428 | |
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| 429 | ENDIF |
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| 430 | |
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| 431 | ! AB : temporary test added to check the validity of eq. df/dz = e - d |
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| 432 | ! DO l=1,nlay |
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| 433 | ! DO ig=1,ngrid |
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| 434 | ! test = abs(fm(ig,l) + entr(ig,l) - detr(ig,l) - fm(ig,l+1)) |
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| 435 | ! IF (test.gt.1.e-10) THEN |
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| 436 | ! print *, 'WARNING: df/dz != entr - detr' |
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| 437 | ! print *, 'ig,l', ig, l |
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| 438 | ! print *, 'fm+ :', fm(ig,l+1) |
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| 439 | ! print *, 'entr,detr', entr(ig,l), detr(ig,l) |
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| 440 | ! print *, 'fm :', fm(ig,l) |
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| 441 | ! print *, 'entr,detr', entr(ig,l-1), detr(ig,l-1) |
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| 442 | ! print *, 'fm- :', fm(ig,l-1) |
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| 443 | ! print *, 'err. :', test |
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| 444 | ! ENDIF |
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| 445 | ! ENDDO |
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| 446 | ! ENDDO |
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| 447 | |
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| 448 | |
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| 449 | RETURN |
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| 450 | END |
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