[2287] | 1 | !!---------------------------------------------------------------------- |
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[9598] | 2 | !! NEMO/OCE 4.0 , NEMO Consortium (2018) |
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[2287] | 3 | !! $Id$ |
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[10068] | 4 | !! Software governed by the CeCILL license (see ./LICENSE) |
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[2287] | 5 | !!---------------------------------------------------------------------- |
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| 6 | |
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[2202] | 7 | SUBROUTINE obs_int_z1d( kpk, kkco, k1dint, kdep, & |
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| 8 | & pobsdep, pobsk, pobs2k, & |
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| 9 | & pobs, pdep, pobsmask ) |
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| 10 | !!--------------------------------------------------------------------- |
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| 11 | !! |
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| 12 | !! *** ROUTINE obs_int_z1d *** |
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| 13 | !! |
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| 14 | !! ** Purpose : Vertical interpolation to the observation point. |
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| 15 | !! |
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| 16 | !! ** Method : If k1dint = 0 then use linear interpolation. |
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| 17 | !! If k1dint = 1 then use cubic spline interpolation. |
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| 18 | !! |
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| 19 | !! ** Action : |
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| 20 | !! |
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| 21 | !! References : |
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| 22 | !! |
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| 23 | !! History |
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| 24 | !! ! 97-11 (A. Weaver, S. Ricci, N. Daget) |
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| 25 | !! ! 06-03 (G. Smith) Conversion to F90 for use with NEMOVAR |
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| 26 | !! ! 06-10 (A. Weaver) Cleanup |
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| 27 | !! ! 07-01 (K. Mogensen) Use profile rather than single level |
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| 28 | !!--------------------------------------------------------------------- |
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| 29 | |
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| 30 | !! * Arguments |
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| 31 | INTEGER, INTENT(IN) :: kpk ! Number of vertical levels |
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| 32 | INTEGER, INTENT(IN) :: k1dint ! 0 = linear; 1 = cubic spline interpolation |
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| 33 | INTEGER, INTENT(IN) :: kdep ! Number of levels in profile |
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| 34 | INTEGER, INTENT(IN), DIMENSION(kdep) :: & |
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| 35 | & kkco ! Array indicies for interpolation |
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| 36 | REAL(KIND=wp), INTENT(IN), DIMENSION(kdep) :: & |
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| 37 | & pobsdep ! Depth of the observation |
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| 38 | REAL(KIND=wp), INTENT(IN), DIMENSION(kpk) :: & |
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| 39 | & pobsk, & ! Model profile at a given (lon,lat) |
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| 40 | & pobs2k, & ! 2nd derivative of the interpolating function |
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| 41 | & pdep, & ! Model depth array |
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| 42 | & pobsmask ! Vertical mask |
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| 43 | REAL(KIND=wp), INTENT(OUT), DIMENSION(kdep) :: & |
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| 44 | & pobs ! Model equivalent at observation point |
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| 45 | |
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| 46 | !! * Local declarations |
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| 47 | REAL(KIND=wp) :: z1dm ! Distance above and below obs to model grid points |
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| 48 | REAL(KIND=wp) :: z1dp |
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| 49 | REAL(KIND=wp) :: zsum ! Dummy variables for computation |
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| 50 | REAL(KIND=wp) :: zsum2 |
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| 51 | INTEGER :: jdep ! Observation depths loop variable |
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| 52 | |
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| 53 | !------------------------------------------------------------------------ |
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| 54 | ! Loop over all observation depths |
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| 55 | !------------------------------------------------------------------------ |
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| 56 | |
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| 57 | DO jdep = 1, kdep |
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| 58 | |
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| 59 | !--------------------------------------------------------------------- |
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| 60 | ! Initialization |
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| 61 | !--------------------------------------------------------------------- |
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| 62 | z1dm = ( pdep(kkco(jdep)) - pobsdep(jdep) ) |
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| 63 | z1dp = ( pobsdep(jdep) - pdep(kkco(jdep)-1) ) |
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| 64 | IF ( pobsmask(kkco(jdep)) == 0.0_wp ) z1dp = 0.0_wp |
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| 65 | |
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| 66 | zsum = z1dm + z1dp |
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| 67 | |
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| 68 | IF ( k1dint == 0 ) THEN |
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| 69 | |
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| 70 | !----------------------------------------------------------------- |
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| 71 | ! Linear interpolation |
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| 72 | !----------------------------------------------------------------- |
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| 73 | pobs(jdep) = ( z1dm * pobsk(kkco(jdep)-1) & |
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| 74 | & + z1dp * pobsk(kkco(jdep) ) ) / zsum |
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| 75 | |
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| 76 | ELSEIF ( k1dint == 1 ) THEN |
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| 77 | |
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| 78 | !----------------------------------------------------------------- |
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| 79 | ! Cubic spline interpolation |
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| 80 | !----------------------------------------------------------------- |
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| 81 | zsum2 = zsum * zsum |
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| 82 | pobs(jdep) = ( z1dm * pobsk (kkco(jdep)-1) & |
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| 83 | & + z1dp * pobsk (kkco(jdep) ) & |
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| 84 | & + ( z1dm * ( z1dm * z1dm - zsum2 ) * pobs2k(kkco(jdep)-1) & |
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| 85 | & + z1dp * ( z1dp * z1dp - zsum2 ) * pobs2k(kkco(jdep) ) & |
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| 86 | & ) / 6.0_wp & |
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| 87 | & ) / zsum |
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| 88 | |
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| 89 | ENDIF |
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| 90 | END DO |
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| 91 | |
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| 92 | END SUBROUTINE obs_int_z1d |
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| 93 | |
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| 94 | SUBROUTINE obs_int_z1d_spl( kpk, pobsk, pobs2k, & |
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| 95 | & pdep, pobsmask ) |
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| 96 | !!-------------------------------------------------------------------- |
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| 97 | !! |
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| 98 | !! *** ROUTINE obs_int_z1d_spl *** |
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| 99 | !! |
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| 100 | !! ** Purpose : Compute the local vector of vertical second-derivatives |
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| 101 | !! of the interpolating function used with a cubic spline. |
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| 102 | !! |
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| 103 | !! ** Method : |
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| 104 | !! |
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| 105 | !! Top and bottom boundary conditions on the 2nd derivative are |
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| 106 | !! set to zero. |
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| 107 | !! |
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| 108 | !! ** Action : |
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| 109 | !! |
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| 110 | !! References : |
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| 111 | !! |
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| 112 | !! History |
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| 113 | !! ! 01-11 (A. Weaver, S. Ricci, N. Daget) |
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| 114 | !! ! 06-03 (G. Smith) Conversion to F90 for use with NEMOVAR |
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| 115 | !! ! 06-10 (A. Weaver) Cleanup |
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| 116 | !!---------------------------------------------------------------------- |
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| 117 | |
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| 118 | !! * Arguments |
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| 119 | INTEGER, INTENT(IN) :: kpk ! Number of vertical levels |
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| 120 | REAL(KIND=wp), INTENT(IN), DIMENSION(kpk) :: & |
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| 121 | & pobsk, & ! Model profile at a given (lon,lat) |
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| 122 | & pdep, & ! Model depth array |
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| 123 | & pobsmask ! Vertical mask |
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| 124 | REAL(KIND=wp), INTENT(OUT), DIMENSION(kpk) :: & |
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| 125 | & pobs2k ! 2nd derivative of the interpolating function |
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| 126 | |
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| 127 | !! * Local declarations |
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| 128 | INTEGER :: jk |
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| 129 | REAL(KIND=wp) :: za |
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| 130 | REAL(KIND=wp) :: zb |
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| 131 | REAL(KIND=wp) :: zc |
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| 132 | REAL(KIND=wp) :: zpa |
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| 133 | REAL(KIND=wp) :: zkm |
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| 134 | REAL(KIND=wp) :: zkp |
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| 135 | REAL(KIND=wp) :: zk |
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| 136 | REAL(KIND=wp), DIMENSION(kpk-1) :: & |
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| 137 | & zs, & |
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| 138 | & zp, & |
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| 139 | & zu, & |
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| 140 | & zv |
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| 141 | |
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| 142 | !----------------------------------------------------------------------- |
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| 143 | ! Matrix initialisation |
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| 144 | !----------------------------------------------------------------------- |
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| 145 | zs(1) = 0.0_wp |
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| 146 | zp(1) = 0.0_wp |
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| 147 | zv(1) = -0.5_wp |
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| 148 | DO jk = 2, kpk-1 |
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| 149 | zs(jk) = ( pdep(jk ) - pdep(jk-1) ) & |
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| 150 | & / ( pdep(jk+1) - pdep(jk-1) ) |
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| 151 | zp(jk) = zs(jk) * zv(jk-1) + 2.0_wp |
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| 152 | zv(jk) = ( zs(jk) - 1.0_wp ) / zp(jk) |
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| 153 | END DO |
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| 154 | |
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| 155 | !----------------------------------------------------------------------- |
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| 156 | ! Solution of the tridiagonal system |
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| 157 | !----------------------------------------------------------------------- |
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| 158 | |
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| 159 | ! Top boundary condition |
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| 160 | zu(1) = 0.0_wp |
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| 161 | |
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| 162 | DO jk = 2, kpk-1 |
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| 163 | za = pdep(jk+1) - pdep(jk-1) |
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| 164 | zb = pdep(jk+1) - pdep(jk ) |
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| 165 | zc = pdep(jk ) - pdep(jk-1) |
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| 166 | |
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| 167 | zpa = 6.0_wp / ( zp(jk) * za ) |
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| 168 | zkm = zpa / zc |
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| 169 | zkp = zpa / zb |
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| 170 | zk = - ( zkm + zkp ) |
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| 171 | |
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| 172 | zu(jk) = pobsk(jk+1) * zkp & |
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| 173 | & + pobsk(jk ) * zk & |
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| 174 | & + pobsk(jk-1) * zkm & |
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| 175 | & + zu(jk-1) * ( -zs(jk) / zp(jk) ) |
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| 176 | END DO |
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| 177 | |
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| 178 | !----------------------------------------------------------------------- |
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| 179 | ! Second derivative |
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| 180 | !----------------------------------------------------------------------- |
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| 181 | pobs2k(kpk) = 0.0_wp |
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| 182 | |
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| 183 | ! Bottom boundary condition |
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| 184 | DO jk = kpk-1, 1, -1 |
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| 185 | pobs2k(jk) = zv(jk) * pobs2k(jk+1) + zu(jk) |
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| 186 | IF ( pobsmask(jk+1) == 0.0_wp ) pobs2k(jk) = 0.0_wp |
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| 187 | END DO |
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| 188 | |
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| 189 | END SUBROUTINE obs_int_z1d_spl |
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| 190 | |
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| 191 | |
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