[2202] | 1 | !!---------------------------------------------------------------------- |
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[2287] | 2 | !! NEMO/OPA 3.3 , NEMO Consortium (2010) |
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| 3 | !! $Id$ |
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| 4 | !! Software governed by the CeCILL licence (NEMOGCM/NEMO_CeCILL.txt) |
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[2202] | 5 | !!---------------------------------------------------------------------- |
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[2287] | 6 | |
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[2202] | 7 | SUBROUTINE obs_int_h2d_init( kpk, kpk2, k2dint, plam, pphi, & |
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| 8 | & pglam, pgphi, pmask, pweig, pobsmask, & |
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| 9 | & iminpoints ) |
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| 10 | !!----------------------------------------------------------------------- |
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| 11 | !! |
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| 12 | !! *** ROUTINE obs_int_h2d *** |
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| 13 | !! |
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| 14 | !! ** Purpose : Computes weights for horizontal interpolation to the |
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| 15 | !! observation point. |
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| 16 | !! |
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| 17 | !! ** Method : Horizontal interpolation to the observation point using |
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| 18 | !! model values at the corners of the surrounding grid |
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| 19 | !! points. |
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| 20 | !! |
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| 21 | !! Interpolation Schemes : |
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| 22 | !! |
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| 23 | !! 1) k2dint = 0: Distance-weighted interpolation scheme 1 |
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| 24 | !! |
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| 25 | !! The interpolation weights are computed as a weighted |
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| 26 | !! sum of the distance between the model grid points (A) |
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| 27 | !! and the observation point (B). Distance (s) is computed |
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| 28 | !! using the great-circle distance formula: |
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| 29 | !! |
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| 30 | !! s(AB) = arcos( sin( phiA ) x sin( phiB ) |
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| 31 | !! + cos( phiA ) x cos( phiB ) |
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| 32 | !! x cos( lamB - lamA ) ) |
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| 33 | !! |
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| 34 | !! 2) k2dint = 1: Distance-weighted interpolation scheme 2 |
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| 35 | !! |
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| 36 | !! As k2dint = 0 but with distance (ds) computed using |
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| 37 | !! a small-angle approximation to the great-circle formula: |
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| 38 | !! |
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| 39 | !! ds(AB) = sqrt( ( phiB - phiA )^{2} |
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| 40 | !! + ( ( lamB - lamA ) * cos( phiB ) )^{2} ) |
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| 41 | !! |
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| 42 | !! 3) k2dint = 2: Bilinear interpolation on a geographical grid |
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| 43 | !! |
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| 44 | !! The interpolation is split into two 1D interpolations in |
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| 45 | !! the longitude and latitude directions, respectively. |
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| 46 | !! |
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| 47 | !! 4) k2dint = 3: General bilinear remapping interpolation |
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| 48 | !! |
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| 49 | !! An iterative scheme that involves first mapping a |
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| 50 | !! quadrilateral cell into a cell with coordinates |
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| 51 | !! (0,0), (1,0), (0,1) and (1,1). |
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| 52 | !! |
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| 53 | !! 5) k2dint = 4: Polynomial interpolation |
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| 54 | !! |
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| 55 | !! The interpolation weights are computed by fitting a |
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| 56 | !! polynomial function of the form |
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| 57 | !! |
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| 58 | !! P(i) = a1(i) + a2(i) * phi + a3(i) * plam |
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| 59 | !! + a4(i) * phi * plam |
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| 60 | !! |
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| 61 | !! through the model values at the four surrounding grid points. |
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| 62 | !! |
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| 63 | !! ** Action : |
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| 64 | !! |
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| 65 | !! References : Jones, P.: A users guide for SCRIP: A Spherical |
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| 66 | !! Coordinate Remapping and Interpolation Package. |
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| 67 | !! Version 1.4. Los Alomos. |
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| 68 | !! |
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| 69 | !! http://www.acl.lanl.gov/climate/software/SCRIP/SCRIPmain.html |
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| 70 | !! |
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| 71 | !! History : |
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| 72 | !! ! 97-11 (A. Weaver, N. Daget) |
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| 73 | !! ! 06-03 (A. Vidard) NEMOVAR migration |
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| 74 | !! ! 06-10 (A. Weaver) Cleanup |
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| 75 | !! ! 07-08 (K. Mogensen) Split in two routines for easier adj. |
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| 76 | !!----------------------------------------------------------------------- |
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| 77 | !! * Modules used |
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| 78 | !! * Arguments |
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| 79 | INTEGER, INTENT(IN) :: & |
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| 80 | & kpk, & ! Parameter values for automatic arrays |
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| 81 | & kpk2, & |
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| 82 | & k2dint ! Interpolation scheme options |
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| 83 | ! = 0 distance-weighted (great circle) |
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| 84 | ! = 1 distance-weighted (small angle) |
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| 85 | ! = 2 bilinear (geographical grid) |
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| 86 | ! = 3 bilinear (quadrilateral grid) |
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| 87 | ! = 4 polynomial (quadrilateral grid) |
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| 88 | REAL(KIND=wp), INTENT(INOUT) :: & |
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| 89 | & plam, & |
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| 90 | & pphi ! Geographical (lat,lon) coordinates of |
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| 91 | ! observation |
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| 92 | REAL(KIND=wp), DIMENSION(2,2), INTENT(IN) :: & |
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| 93 | & pglam, & ! Model variable lat |
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| 94 | & pgphi ! Model variable lon |
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| 95 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
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| 96 | & pmask ! Model variable mask |
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| 97 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(OUT) :: & |
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| 98 | & pweig ! Weights for interpolation |
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| 99 | REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: & |
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| 100 | & pobsmask ! Vertical mask for observations |
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| 101 | INTEGER, INTENT(IN), OPTIONAL :: & |
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| 102 | & iminpoints ! Reject point which is not surrounded |
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| 103 | ! by at least iminpoints sea points |
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| 104 | |
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| 105 | !! * Local declarations |
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| 106 | INTEGER :: & |
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| 107 | & jk |
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| 108 | INTEGER :: & |
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| 109 | & ikmax, & |
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| 110 | & iamb1, & |
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| 111 | & iamb2 |
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| 112 | REAL(KIND=wp) :: & |
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| 113 | & zphimm, & |
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| 114 | & zphimp, & |
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| 115 | & zphipm, & |
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| 116 | & zphipp, & |
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| 117 | & zlammm, & |
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| 118 | & zlammp, & |
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| 119 | & zlampm, & |
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| 120 | & zlampp, & |
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| 121 | & zphimin, & |
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| 122 | & zphimax, & |
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| 123 | & zlammin, & |
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| 124 | & zlammax |
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| 125 | REAL(KIND=wp), DIMENSION(kpk2) :: & |
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| 126 | & z2dmm, & |
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| 127 | & z2dmp, & |
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| 128 | & z2dpm, & |
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| 129 | & z2dpp, & |
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| 130 | & z2dmmt, & |
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| 131 | & z2dmpt, & |
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| 132 | & z2dpmt, & |
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| 133 | & z2dppt, & |
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| 134 | & zsum |
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| 135 | LOGICAL :: & |
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| 136 | & ll_ds1, & |
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| 137 | & ll_skip, & |
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| 138 | & ll_fail |
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| 139 | |
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| 140 | !------------------------------------------------------------------------ |
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| 141 | ! Constants for the 360 degrees ambiguity |
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| 142 | !------------------------------------------------------------------------ |
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| 143 | iamb1 = 10 ! dlam < iamb1 * dphi |
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| 144 | iamb2 = 3 ! Special treatment if iamb2 * lam < max(lam) |
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| 145 | |
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| 146 | !------------------------------------------------------------------------ |
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| 147 | ! Initialize number of levels |
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| 148 | !------------------------------------------------------------------------ |
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| 149 | IF ( kpk2 == 1 ) THEN |
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| 150 | ikmax = 1 |
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| 151 | ELSEIF ( kpk2 == kpk) THEN |
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| 152 | ikmax = kpk-1 |
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| 153 | ENDIF |
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| 154 | !------------------------------------------------------------------------ |
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| 155 | ! Initialize the cell corners |
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| 156 | !------------------------------------------------------------------------ |
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| 157 | zphimm = pgphi(1,1) |
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| 158 | zphimp = pgphi(1,2) |
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| 159 | zphipm = pgphi(2,1) |
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| 160 | zphipp = pgphi(2,2) |
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| 161 | zlammm = pglam(1,1) |
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| 162 | zlammp = pglam(1,2) |
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| 163 | zlampm = pglam(2,1) |
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| 164 | zlampp = pglam(2,2) |
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| 165 | |
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| 166 | !------------------------------------------------------------------------ |
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| 167 | ! Treat the 360 degrees ambiguity |
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| 168 | !------------------------------------------------------------------------ |
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| 169 | DO WHILE ( ( zlammm < 0.0_wp ).OR.( zlammm > 360.0_wp ) & |
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| 170 | & .OR.( zlampm < 0.0_wp ).OR.( zlampm > 360.0_wp ) & |
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| 171 | & .OR.( zlampp < 0.0_wp ).OR.( zlampp > 360.0_wp ) & |
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| 172 | & .OR.( zlammp < 0.0_wp ).OR.( zlammp > 360.0_wp ) ) |
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| 173 | |
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| 174 | IF ( zlammm < 0.0_wp ) zlammm = zlammm + 360.0_wp |
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| 175 | IF ( zlammm > 360.0_wp ) zlammm = zlammm - 360.0_wp |
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| 176 | IF ( zlammp < 0.0_wp ) zlammp = zlammp + 360.0_wp |
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| 177 | IF ( zlammp > 360.0_wp ) zlammp = zlammp - 360.0_wp |
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| 178 | IF ( zlampm < 0.0_wp ) zlampm = zlampm + 360.0_wp |
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| 179 | IF ( zlampm > 360.0_wp ) zlampm = zlampm - 360.0_wp |
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| 180 | IF ( zlampp < 0.0_wp ) zlampp = zlampp + 360.0_wp |
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| 181 | IF ( zlampp > 360.0_wp ) zlampp = zlampp - 360.0_wp |
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| 182 | |
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| 183 | END DO |
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| 184 | |
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| 185 | DO WHILE ( ( plam < 0.0_wp ) .OR. ( plam > 360.0_wp ) ) |
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| 186 | IF ( plam < 0.0_wp ) plam = plam + 360.0_wp |
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| 187 | IF ( plam > 360.0_wp ) plam = plam - 360.0_wp |
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| 188 | END DO |
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| 189 | |
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| 190 | !------------------------------------------------------------------------ |
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| 191 | ! Special case for observation on grid points |
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| 192 | !------------------------------------------------------------------------ |
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| 193 | ll_skip = .FALSE. |
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| 194 | IF ( ( ABS( zphimm - pphi ) < 1.0e-6_wp ) .AND. & |
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| 195 | & ( ABS( zlammm - plam ) < 1.0e-6_wp ) ) THEN |
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| 196 | z2dmm(:) = 1.0_wp |
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| 197 | z2dpm(:) = 0.0_wp |
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| 198 | z2dmp(:) = 0.0_wp |
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| 199 | z2dpp(:) = 0.0_wp |
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| 200 | ll_skip = .TRUE. |
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| 201 | ENDIF |
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| 202 | IF ( ( ABS( zphipm - pphi ) < 1.0e-6_wp ) .AND. & |
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| 203 | & ( ABS( zlampm - plam ) < 1.0e-6_wp ) ) THEN |
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| 204 | z2dmm(:) = 0.0_wp |
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| 205 | z2dpm(:) = 1.0_wp |
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| 206 | z2dmp(:) = 0.0_wp |
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| 207 | z2dpp(:) = 0.0_wp |
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| 208 | ll_skip = .TRUE. |
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| 209 | ENDIF |
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| 210 | IF ( ( ABS( zphimp - pphi ) < 1.0e-6_wp ) .AND. & |
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| 211 | & ( ABS( zlammp - plam ) < 1.0e-6_wp ) ) THEN |
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| 212 | z2dmm(:) = 0.0_wp |
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| 213 | z2dpm(:) = 0.0_wp |
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| 214 | z2dmp(:) = 1.0_wp |
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| 215 | z2dpp(:) = 0.0_wp |
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| 216 | ll_skip = .TRUE. |
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| 217 | ENDIF |
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| 218 | IF ( ( ABS( zphipp - pphi ) < 1.0e-6_wp ) .AND. & |
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| 219 | & ( ABS( zlampp - plam ) < 1.0e-6_wp ) ) THEN |
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| 220 | z2dmm(:) = 0.0_wp |
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| 221 | z2dpm(:) = 0.0_wp |
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| 222 | z2dmp(:) = 0.0_wp |
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| 223 | z2dpp(:) = 1.0_wp |
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| 224 | ll_skip = .TRUE. |
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| 225 | ENDIF |
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| 226 | |
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| 227 | IF ( .NOT.ll_skip ) THEN |
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| 228 | |
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| 229 | zphimin = MIN( zphimm, zphipm, zphipp, zphimp ) |
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| 230 | zphimax = MAX( zphimm, zphipm, zphipp, zphimp ) |
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| 231 | zlammin = MIN( zlammm, zlampm, zlampp, zlammp ) |
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| 232 | zlammax = MAX( zlammm, zlampm, zlampp, zlammp ) |
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| 233 | |
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| 234 | IF ( ( ( zlammax - zlammin ) / ( zphimax - zphimin ) ) > iamb1 ) THEN |
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| 235 | IF ( iamb2 * zlammm < zlammax ) zlammm = zlammm + 360.0_wp |
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| 236 | IF ( iamb2 * zlammp < zlammax ) zlammp = zlammp + 360.0_wp |
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| 237 | IF ( iamb2 * zlampm < zlammax ) zlampm = zlampm + 360.0_wp |
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| 238 | IF ( iamb2 * zlampp < zlammax ) zlampp = zlampp + 360.0_wp |
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| 239 | ENDIF |
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| 240 | |
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| 241 | zlammin = MIN( zlammm, zlampm, zlampp, zlammp ) |
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| 242 | IF ( zlammm > ( zlammin + 180.0_wp ) ) zlammm = zlammm - 360.0_wp |
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| 243 | IF ( zlammp > ( zlammin + 180.0_wp ) ) zlammp = zlammp - 360.0_wp |
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| 244 | IF ( zlampm > ( zlammin + 180.0_wp ) ) zlampm = zlampm - 360.0_wp |
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| 245 | IF ( zlampp > ( zlammin + 180.0_wp ) ) zlampp = zlampp - 360.0_wp |
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| 246 | |
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| 247 | IF ( plam < zlammin ) plam = plam + 360.0_wp |
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| 248 | z2dmm = 0.0_wp |
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| 249 | z2dmp = 0.0_wp |
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| 250 | z2dpm = 0.0_wp |
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| 251 | z2dpp = 0.0_wp |
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| 252 | SELECT CASE (k2dint) |
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| 253 | |
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| 254 | CASE(0) |
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| 255 | CALL obs_int_h2d_ds1( kpk2, ikmax, & |
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| 256 | & pphi, plam, pmask, & |
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| 257 | & zphimm, zlammm, zphimp, zlammp, & |
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| 258 | & zphipm, zlampm, zphipp, zlampp, & |
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| 259 | & z2dmm, z2dmp, z2dpm, z2dpp ) |
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| 260 | CASE(1) |
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| 261 | CALL obs_int_h2d_ds2( kpk2, ikmax, & |
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| 262 | & pphi, plam, pmask, & |
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| 263 | & zphimm, zlammm, zphimp, zlammp, & |
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| 264 | & zphipm, zlampm, zphipp, zlampp, & |
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| 265 | & z2dmm, z2dmp, z2dpm, z2dpp ) |
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| 266 | CASE(2) |
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| 267 | CALL obs_int_h2d_bil( kpk2, ikmax, & |
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| 268 | & pphi, plam, pmask, & |
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| 269 | & zlammp, & |
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| 270 | & zphipm, zphipp, zlampp, & |
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| 271 | & z2dmm, z2dmp, z2dpm, z2dpp ) |
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| 272 | CASE(3) |
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| 273 | CALL obs_int_h2d_bir( kpk2, ikmax, & |
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| 274 | & pphi, plam, pmask, & |
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| 275 | & zphimm, zlammm, zphimp, zlammp, & |
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| 276 | & zphipm, zlampm, zphipp, zlampp, & |
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| 277 | & z2dmm, z2dmp, z2dpm, z2dpp, ll_fail ) |
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| 278 | IF (ll_fail) THEN |
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| 279 | IF(lwp) THEN |
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| 280 | WRITE(numout,*)'Bilinear weight computation failed' |
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| 281 | WRITE(numout,*)'Switching to great circle distance' |
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| 282 | WRITE(numout,*) |
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| 283 | ENDIF |
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| 284 | CALL obs_int_h2d_ds1( kpk2, ikmax, & |
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| 285 | & pphi, plam, pmask, & |
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| 286 | & zphimm, zlammm, zphimp, zlammp, & |
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| 287 | & zphipm, zlampm, zphipp, zlampp, & |
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| 288 | & z2dmm, z2dmp, z2dpm, z2dpp ) |
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| 289 | ENDIF |
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| 290 | CASE(4) |
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| 291 | CALL obs_int_h2d_pol( kpk2, ikmax, & |
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| 292 | & pphi, plam, pmask, & |
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| 293 | & zphimm, zlammm, zphimp, zlammp, & |
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| 294 | & zphipm, zlampm, zphipp, zlampp, & |
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| 295 | & z2dmm, z2dmp, z2dpm, z2dpp ) |
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| 296 | END SELECT |
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| 297 | |
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| 298 | ENDIF |
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| 299 | !------------------------------------------------------------------------ |
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| 300 | ! Compute weights for interpolation to the observation point |
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| 301 | !------------------------------------------------------------------------ |
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| 302 | pobsmask(:) = 0.0_wp |
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| 303 | pweig(:,:,:) = 0.0_wp |
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| 304 | ! ll_ds1 is used for failed interpolations |
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| 305 | ll_ds1 = .FALSE. |
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| 306 | DO jk = 1, ikmax |
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| 307 | IF (PRESENT(iminpoints)) THEN |
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| 308 | IF (NINT(SUM(pmask(:,:,jk)))<iminpoints) CYCLE |
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| 309 | ENDIF |
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| 310 | zsum(jk) = z2dmm(jk) + z2dmp(jk) + z2dpm(jk) + z2dpp(jk) |
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| 311 | IF ( zsum(jk) /= 0.0_wp ) THEN |
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| 312 | pweig(1,1,jk) = z2dmm(jk) |
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| 313 | pweig(1,2,jk) = z2dmp(jk) |
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| 314 | pweig(2,1,jk) = z2dpm(jk) |
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| 315 | pweig(2,2,jk) = z2dpp(jk) |
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| 316 | ! Set the vertical mask |
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| 317 | IF ( ( ( z2dmm(jk) > 0.0_wp ) .AND. & |
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| 318 | & ( pmask(1,1,jk) == 1.0_wp ) ) .OR. & |
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| 319 | & ( ( z2dmp(jk) > 0.0_wp ) .AND. & |
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| 320 | & ( pmask(1,2,jk) == 1.0_wp ) ) .OR. & |
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| 321 | & ( ( z2dpm(jk) > 0.0_wp ) .AND. & |
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| 322 | & ( pmask(2,1,jk) == 1.0_wp ) ) .OR. & |
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| 323 | & ( ( z2dpp(jk) > 0.0_wp ) .AND. & |
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| 324 | & ( pmask(2,2,jk) == 1.0_wp ) ) ) pobsmask(jk)=1.0_wp |
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| 325 | ELSE |
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| 326 | ! If the interpolation has failed due to the point |
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| 327 | ! being on the intersect of two land points retry with |
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| 328 | ! k2dint = 0 |
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| 329 | IF ( ( pmask(1,1,jk) /= 0.0_wp ).OR. & |
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| 330 | & ( pmask(1,2,jk) /= 0.0_wp ).OR. & |
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| 331 | & ( pmask(2,1,jk) /= 0.0_wp ).OR. & |
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| 332 | & ( pmask(2,2,jk) /= 0.0_wp ) ) THEN |
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| 333 | ! If ll_ds1 is false compute k2dint = 0 weights |
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| 334 | IF ( .NOT.ll_ds1 ) THEN |
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| 335 | CALL obs_int_h2d_ds1( kpk2, ikmax, & |
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| 336 | & pphi, plam, pmask, & |
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| 337 | & zphimm, zlammm, zphimp, zlammp, & |
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| 338 | & zphipm, zlampm, zphipp, zlampp, & |
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| 339 | & z2dmmt, z2dmpt, z2dpmt, z2dppt ) |
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| 340 | ll_ds1 = .TRUE. |
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| 341 | ENDIF |
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| 342 | zsum(jk) = z2dmmt(jk) + z2dmpt(jk) + z2dpmt(jk) + z2dppt(jk) |
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| 343 | IF ( zsum(jk) /= 0.0_wp ) THEN |
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| 344 | pweig(1,1,jk) = z2dmmt(jk) |
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| 345 | pweig(1,2,jk) = z2dmpt(jk) |
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| 346 | pweig(2,1,jk) = z2dpmt(jk) |
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| 347 | pweig(2,2,jk) = z2dppt(jk) |
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| 348 | ! Set the vertical mask |
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| 349 | IF ( ( ( z2dmmt(jk) > 0.0_wp ) .AND. & |
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| 350 | & ( pmask(1,1,jk) == 1.0_wp ) ) .OR. & |
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| 351 | & ( ( z2dmpt(jk) > 0.0_wp ) .AND. & |
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| 352 | & ( pmask(1,2,jk) == 1.0_wp ) ) .OR. & |
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| 353 | & ( ( z2dpmt(jk) > 0.0_wp) .AND. & |
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| 354 | & ( pmask(2,1,jk) == 1.0_wp ) ) .OR. & |
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| 355 | & ( ( z2dppt(jk) > 0.0_wp ) .AND. & |
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| 356 | & ( pmask(2,2,jk) == 1.0_wp ) ) ) & |
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| 357 | & pobsmask(jk)=1.0_wp |
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| 358 | ENDIF |
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| 359 | ENDIF |
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| 360 | ENDIF |
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| 361 | END DO |
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| 362 | |
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| 363 | END SUBROUTINE obs_int_h2d_init |
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| 364 | |
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| 365 | SUBROUTINE obs_int_h2d( kpk, kpk2, & |
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| 366 | & pweig, pmod, pobsk ) |
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| 367 | !!----------------------------------------------------------------------- |
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| 368 | !! |
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| 369 | !! *** ROUTINE obs_int_h2d *** |
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| 370 | !! |
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| 371 | !! ** Purpose : Horizontal interpolation to the observation point. |
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| 372 | !! |
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| 373 | !! ** Method : Horizontal interpolation to the observation point using |
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| 374 | !! model values at the corners of the surrounding grid |
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| 375 | !! points. |
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| 376 | !! |
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| 377 | !! ** Action : |
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| 378 | !! |
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| 379 | !! References : |
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| 380 | !! |
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| 381 | !! History : |
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| 382 | !! ! 97-11 (A. Weaver, N. Daget) |
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| 383 | !! ! 06-03 (A. Vidard) NEMOVAR migration |
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| 384 | !! ! 06-10 (A. Weaver) Cleanup |
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| 385 | !! ! 07-08 (K. Mogensen) Split in two routines for easier adj. |
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| 386 | !!----------------------------------------------------------------------- |
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| 387 | !! * Modules used |
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| 388 | !! * Arguments |
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| 389 | INTEGER, INTENT(IN) :: & |
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| 390 | & kpk, & ! Parameter values for automatic arrays |
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| 391 | & kpk2 |
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| 392 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
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| 393 | & pweig ! Interpolation weights |
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| 394 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
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| 395 | & pmod ! Model variable to interpolate |
---|
| 396 | REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: & |
---|
| 397 | & pobsk ! Model profile interpolated to obs (i,j) pt |
---|
| 398 | |
---|
| 399 | !! * Local declarations |
---|
| 400 | INTEGER :: & |
---|
| 401 | & jk |
---|
| 402 | INTEGER :: & |
---|
| 403 | & ikmax |
---|
| 404 | REAL(KIND=wp) :: & |
---|
| 405 | & zsum |
---|
| 406 | !------------------------------------------------------------------------ |
---|
| 407 | ! Initialize number of levels |
---|
| 408 | !------------------------------------------------------------------------ |
---|
| 409 | IF ( kpk2 == 1 ) THEN |
---|
| 410 | ikmax = 1 |
---|
| 411 | ELSEIF ( kpk2 == kpk) THEN |
---|
| 412 | ikmax = kpk-1 |
---|
| 413 | ENDIF |
---|
| 414 | !------------------------------------------------------------------------ |
---|
| 415 | ! Interpolate to the observation point |
---|
| 416 | !------------------------------------------------------------------------ |
---|
| 417 | pobsk(:) = obfillflt |
---|
| 418 | DO jk = 1, ikmax |
---|
| 419 | zsum = pweig(1,1,jk) + pweig(1,2,jk) + pweig(2,1,jk) + pweig(2,2,jk) |
---|
| 420 | IF ( zsum /= 0.0_wp ) THEN |
---|
| 421 | pobsk(jk) = ( pweig(1,1,jk) * pmod(1,1,jk) & |
---|
| 422 | & + pweig(1,2,jk) * pmod(1,2,jk) & |
---|
| 423 | & + pweig(2,1,jk) * pmod(2,1,jk) & |
---|
| 424 | & + pweig(2,2,jk) * pmod(2,2,jk) & |
---|
| 425 | & ) / zsum |
---|
| 426 | ENDIF |
---|
| 427 | END DO |
---|
| 428 | |
---|
| 429 | END SUBROUTINE obs_int_h2d |
---|
| 430 | |
---|
| 431 | SUBROUTINE obs_int_h2d_ds1( kpk2, kmax, & |
---|
| 432 | & pphi, plam, pmask, & |
---|
| 433 | & pphimm, plammm, pphimp, plammp, & |
---|
| 434 | & pphipm, plampm, pphipp, plampp, & |
---|
| 435 | & p2dmm, p2dmp, p2dpm, p2dpp ) |
---|
| 436 | !!----------------------------------------------------------------------- |
---|
| 437 | !! |
---|
| 438 | !! *** ROUTINE obs_int_h2d_ds1 *** |
---|
| 439 | !! |
---|
| 440 | !! ** Purpose : Distance-weighted interpolation scheme (k2dint = 0) |
---|
| 441 | !! |
---|
| 442 | !! ** Method : The interpolation weights are computed as a weighted |
---|
| 443 | !! sum of the distance between the model grid points (A) |
---|
| 444 | !! and the observation point (B). |
---|
| 445 | !! |
---|
| 446 | !! Distance (s) is computed using the great-circle distance formula: |
---|
| 447 | !! |
---|
| 448 | !! s(AB) = arcos( sin( phiA ) x sin( phiB ) |
---|
| 449 | !! + cos( phiA ) x cos( phiB ) x cos( lamB - lamA ) |
---|
| 450 | !! |
---|
| 451 | !! ** Action : |
---|
| 452 | !! |
---|
| 453 | !! History : |
---|
| 454 | !! ! 97-11 (A. Weaver, N. Daget) |
---|
| 455 | !! ! 06-10 (A. Weaver) Cleanup |
---|
| 456 | !!----------------------------------------------------------------------- |
---|
| 457 | |
---|
| 458 | !! * Modules used |
---|
| 459 | |
---|
| 460 | !! * Arguments |
---|
| 461 | INTEGER, INTENT(IN) :: & |
---|
| 462 | & kpk2, & ! Parameter values for automatic arrays |
---|
| 463 | & kmax |
---|
| 464 | REAL(KIND=wp), INTENT(IN) :: & |
---|
| 465 | & pphi, & ! Geographical location of observation |
---|
| 466 | & plam, & |
---|
| 467 | & pphimm, & ! Geographical location of surrounding |
---|
| 468 | & pphimp, & ! model grid points |
---|
| 469 | & pphipm, & |
---|
| 470 | & pphipp, & |
---|
| 471 | & plammm, & |
---|
| 472 | & plammp, & |
---|
| 473 | & plampm, & |
---|
| 474 | & plampp |
---|
| 475 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
---|
| 476 | & pmask ! Model variable mask |
---|
| 477 | REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: & |
---|
| 478 | & p2dmm, & ! Interpolation weights |
---|
| 479 | & p2dmp, & |
---|
| 480 | & p2dpm, & |
---|
| 481 | & p2dpp |
---|
| 482 | |
---|
| 483 | !! * Local declarations |
---|
| 484 | INTEGER :: & |
---|
| 485 | & jk |
---|
| 486 | REAL(KIND=wp) :: & |
---|
| 487 | & zphi2, & |
---|
| 488 | & zlam2, & |
---|
| 489 | & zcola, & |
---|
| 490 | & za2, & |
---|
| 491 | & zb2, & |
---|
| 492 | & zc2, & |
---|
| 493 | & zphimm2, & |
---|
| 494 | & zphimp2, & |
---|
| 495 | & zphipm2, & |
---|
| 496 | & zphipp2, & |
---|
| 497 | & zlammm2, & |
---|
| 498 | & zlammp2, & |
---|
| 499 | & zlampm2, & |
---|
| 500 | & zlampp2, & |
---|
| 501 | & za1mm, & |
---|
| 502 | & za1mp, & |
---|
| 503 | & za1pm, & |
---|
| 504 | & za1pp, & |
---|
| 505 | & zcomm, & |
---|
| 506 | & zcomp, & |
---|
| 507 | & zcopm, & |
---|
| 508 | & zcopp, & |
---|
| 509 | & zb1mm, & |
---|
| 510 | & zb1mp, & |
---|
| 511 | & zb1pm, & |
---|
| 512 | & zb1pp, & |
---|
| 513 | & zc1mm, & |
---|
| 514 | & zc1mp, & |
---|
| 515 | & zc1pm, & |
---|
| 516 | & zc1pp, & |
---|
| 517 | & zsopmpp, & |
---|
| 518 | & zsommmp, & |
---|
| 519 | & zsomm, & |
---|
| 520 | & zsomp, & |
---|
| 521 | & zsopm, & |
---|
| 522 | & zsopp |
---|
| 523 | |
---|
| 524 | !------------------------------------------------------------------------ |
---|
| 525 | ! Distance-weighted interpolation using the great circle formula |
---|
| 526 | !------------------------------------------------------------------------ |
---|
| 527 | zphi2 = pphi * rad |
---|
| 528 | zlam2 = plam * rad |
---|
| 529 | zcola = COS( zphi2 ) |
---|
| 530 | za2 = SIN( zphi2 ) |
---|
| 531 | zb2 = zcola * COS( zlam2 ) |
---|
| 532 | zc2 = zcola * SIN( zlam2 ) |
---|
| 533 | |
---|
| 534 | zphimm2 = pphimm * rad |
---|
| 535 | zphimp2 = pphimp * rad |
---|
| 536 | zphipm2 = pphipm * rad |
---|
| 537 | zphipp2 = pphipp * rad |
---|
| 538 | |
---|
| 539 | zlammm2 = plammm * rad |
---|
| 540 | zlammp2 = plammp * rad |
---|
| 541 | zlampm2 = plampm * rad |
---|
| 542 | zlampp2 = plampp * rad |
---|
| 543 | |
---|
| 544 | za1mm = SIN( zphimm2 ) |
---|
| 545 | za1mp = SIN( zphimp2 ) |
---|
| 546 | za1pm = SIN( zphipm2 ) |
---|
| 547 | za1pp = SIN( zphipp2 ) |
---|
| 548 | |
---|
| 549 | zcomm = COS( zphimm2 ) |
---|
| 550 | zcomp = COS( zphimp2 ) |
---|
| 551 | zcopm = COS( zphipm2 ) |
---|
| 552 | zcopp = COS( zphipp2 ) |
---|
| 553 | |
---|
| 554 | zb1mm = zcomm * COS( zlammm2 ) |
---|
| 555 | zb1mp = zcomp * COS( zlammp2 ) |
---|
| 556 | zb1pm = zcopm * COS( zlampm2 ) |
---|
| 557 | zb1pp = zcopp * COS( zlampp2 ) |
---|
| 558 | |
---|
| 559 | zc1mm = zcomm * SIN( zlammm2 ) |
---|
| 560 | zc1mp = zcomp * SIN( zlammp2 ) |
---|
| 561 | zc1pm = zcopm * SIN( zlampm2 ) |
---|
| 562 | zc1pp = zcopp * SIN( zlampp2 ) |
---|
| 563 | |
---|
| 564 | ! Function for arcsin(sqrt(1-x^2) version of great-circle formula |
---|
| 565 | zsomm = grt_cir_dis( za1mm, za2, zb1mm, zb2, zc1mm, zc2 ) |
---|
| 566 | zsomp = grt_cir_dis( za1mp, za2, zb1mp, zb2, zc1mp, zc2 ) |
---|
| 567 | zsopm = grt_cir_dis( za1pm, za2, zb1pm, zb2, zc1pm, zc2 ) |
---|
| 568 | zsopp = grt_cir_dis( za1pp, za2, zb1pp, zb2, zc1pp, zc2 ) |
---|
| 569 | |
---|
| 570 | zsopmpp = zsopm * zsopp |
---|
| 571 | zsommmp = zsomm * zsomp |
---|
| 572 | DO jk = 1, kmax |
---|
| 573 | p2dmm(jk) = zsomp * zsopmpp * pmask(1,1,jk) |
---|
| 574 | p2dmp(jk) = zsomm * zsopmpp * pmask(1,2,jk) |
---|
| 575 | p2dpm(jk) = zsopp * zsommmp * pmask(2,1,jk) |
---|
| 576 | p2dpp(jk) = zsopm * zsommmp * pmask(2,2,jk) |
---|
| 577 | END DO |
---|
| 578 | |
---|
| 579 | END SUBROUTINE obs_int_h2d_ds1 |
---|
| 580 | |
---|
| 581 | SUBROUTINE obs_int_h2d_ds2( kpk2, kmax, & |
---|
| 582 | & pphi, plam, pmask, & |
---|
| 583 | & pphimm, plammm, pphimp, plammp, & |
---|
| 584 | & pphipm, plampm, pphipp, plampp, & |
---|
| 585 | & p2dmm, p2dmp, p2dpm, p2dpp ) |
---|
| 586 | !!----------------------------------------------------------------------- |
---|
| 587 | !! |
---|
| 588 | !! *** ROUTINE obs_int_h2d_ds2 *** |
---|
| 589 | !! |
---|
| 590 | !! ** Purpose : Distance-weighted interpolation scheme (k2dint = 1) |
---|
| 591 | !! |
---|
| 592 | !! ** Method : As k2dint = 0 but with distance (ds) computed using a |
---|
| 593 | !! small-angle approximation to the great-circle distance |
---|
| 594 | !! formula: |
---|
| 595 | !! |
---|
| 596 | !! ds(AB) = sqrt( ( phiB - phiA )^{2} |
---|
| 597 | !! + ( ( lamB - lamA ) * cos( phiB ) )^{2} ) |
---|
| 598 | !! |
---|
| 599 | !! ** Action : |
---|
| 600 | !! |
---|
| 601 | !! History : |
---|
| 602 | !! ! 97-11 (A. Weaver, N. Daget) |
---|
| 603 | !! ! 06-10 (A. Weaver) Cleanup |
---|
| 604 | !!----------------------------------------------------------------------- |
---|
| 605 | |
---|
| 606 | !!----------------------------------------------------------------------- |
---|
| 607 | !! * Modules used |
---|
| 608 | !!----------------------------------------------------------------------- |
---|
| 609 | !! * Arguments |
---|
| 610 | INTEGER, INTENT(IN) :: & |
---|
| 611 | & kpk2, & ! Parameter values for automatic arrays |
---|
| 612 | & kmax |
---|
| 613 | REAL(KIND=wp), INTENT(IN) :: & |
---|
| 614 | & pphi, & ! Geographical location of observation |
---|
| 615 | & plam, & |
---|
| 616 | & pphimm, & ! Geographical location of surrounding |
---|
| 617 | & pphimp, & ! model grid points |
---|
| 618 | & pphipm, & |
---|
| 619 | & pphipp, & |
---|
| 620 | & plammm, & |
---|
| 621 | & plammp, & |
---|
| 622 | & plampm, & |
---|
| 623 | & plampp |
---|
| 624 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
---|
| 625 | & pmask ! Model variable mask |
---|
| 626 | REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: & |
---|
| 627 | & p2dmm, & ! Interpolation weights |
---|
| 628 | & p2dmp, & |
---|
| 629 | & p2dpm, & |
---|
| 630 | & p2dpp |
---|
| 631 | |
---|
| 632 | !! * Local declarations |
---|
| 633 | INTEGER :: & |
---|
| 634 | & jk |
---|
| 635 | REAL(KIND=wp) :: & |
---|
| 636 | & zcosp, & |
---|
| 637 | & zdlmm, & |
---|
| 638 | & zdlmp, & |
---|
| 639 | & zdlpm, & |
---|
| 640 | & zdlpp, & |
---|
| 641 | & zdpmm, & |
---|
| 642 | & zdpmp, & |
---|
| 643 | & zdppm, & |
---|
| 644 | & zdppp, & |
---|
| 645 | & zsomm, & |
---|
| 646 | & zsomp, & |
---|
| 647 | & zsopm, & |
---|
| 648 | & zsopp, & |
---|
| 649 | & zsopmpp, & |
---|
| 650 | & zsommmp |
---|
| 651 | |
---|
| 652 | !------------------------------------------------------------------------ |
---|
| 653 | ! Distance-weighted interpolation with a small angle approximation |
---|
| 654 | !------------------------------------------------------------------------ |
---|
| 655 | zcosp = COS( pphi * rad ) |
---|
| 656 | |
---|
| 657 | zdlmm = plammm - plam |
---|
| 658 | zdlmp = plammp - plam |
---|
| 659 | zdlpm = plampm - plam |
---|
| 660 | zdlpp = plampp - plam |
---|
| 661 | |
---|
| 662 | zdpmm = pphimm - pphi |
---|
| 663 | zdpmp = pphimp - pphi |
---|
| 664 | zdppm = pphipm - pphi |
---|
| 665 | zdppp = pphipp - pphi |
---|
| 666 | |
---|
| 667 | zsomm = grt_cir_dis_saa( zdlmm, zdpmm, zcosp ) |
---|
| 668 | zsomp = grt_cir_dis_saa( zdlmp, zdpmp, zcosp ) |
---|
| 669 | zsopm = grt_cir_dis_saa( zdlpm, zdppm, zcosp ) |
---|
| 670 | zsopp = grt_cir_dis_saa( zdlpp, zdppp, zcosp ) |
---|
| 671 | |
---|
| 672 | zsopmpp = zsopm * zsopp |
---|
| 673 | zsommmp = zsomm * zsomp |
---|
| 674 | |
---|
| 675 | DO jk = 1, kmax |
---|
| 676 | p2dmm(jk) = zsomp * zsopmpp * pmask(1,1,jk) |
---|
| 677 | p2dmp(jk) = zsomm * zsopmpp * pmask(1,2,jk) |
---|
| 678 | p2dpm(jk) = zsopp * zsommmp * pmask(2,1,jk) |
---|
| 679 | p2dpp(jk) = zsopm * zsommmp * pmask(2,2,jk) |
---|
| 680 | END DO |
---|
| 681 | |
---|
| 682 | END SUBROUTINE obs_int_h2d_ds2 |
---|
| 683 | |
---|
| 684 | SUBROUTINE obs_int_h2d_bil( kpk2, kmax, & |
---|
| 685 | & pphi, plam, pmask, & |
---|
| 686 | & plammp, pphipm, pphipp, plampp, & |
---|
| 687 | & p2dmm, p2dmp, p2dpm, p2dpp) |
---|
| 688 | !!----------------------------------------------------------------------- |
---|
| 689 | !! |
---|
| 690 | !! *** ROUTINE obs_int_h2d_bil *** |
---|
| 691 | !! |
---|
| 692 | !! ** Purpose : Bilinear interpolation on a geographical grid (k2dint = 2) |
---|
| 693 | !! |
---|
| 694 | !! ** Method : The interpolation is split into two 1D interpolations in |
---|
| 695 | !! the longitude and latitude directions, respectively. |
---|
| 696 | !! |
---|
| 697 | !! An iterative scheme that involves first mapping a quadrilateral |
---|
| 698 | !! cell into a cell with coordinates (0,0), (1,0), (0,1) and (1,1). |
---|
| 699 | !! |
---|
| 700 | !! ** Action : |
---|
| 701 | !! |
---|
| 702 | !! History : |
---|
| 703 | !! ! 97-11 (A. Weaver, N. Daget) |
---|
| 704 | !! ! 06-10 (A. Weaver) Cleanup |
---|
| 705 | !!----------------------------------------------------------------------- |
---|
| 706 | |
---|
| 707 | !! * Arguments |
---|
| 708 | INTEGER, INTENT(IN) :: & |
---|
| 709 | & kpk2, & ! Parameter values for automatic arrays |
---|
| 710 | & kmax |
---|
| 711 | REAL(KIND=wp), INTENT(IN) :: & |
---|
| 712 | & pphi, & ! Geographical location of observation |
---|
| 713 | & plam, & |
---|
| 714 | & pphipm, & ! Geographical location of surrounding |
---|
| 715 | & pphipp, & ! model grid points |
---|
| 716 | & plammp, & |
---|
| 717 | & plampp |
---|
| 718 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
---|
| 719 | & pmask ! Model variable mask |
---|
| 720 | REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: & |
---|
| 721 | & p2dmm, & ! Interpolation weights |
---|
| 722 | & p2dmp, & |
---|
| 723 | & p2dpm, & |
---|
| 724 | & p2dpp |
---|
| 725 | |
---|
| 726 | !! * Local declarations |
---|
| 727 | INTEGER :: & |
---|
| 728 | & jk |
---|
| 729 | REAL(KIND=wp) :: & |
---|
| 730 | & zdlmp, & |
---|
| 731 | & zdppm, & |
---|
| 732 | & zdlpp, & |
---|
| 733 | & zdppp |
---|
| 734 | |
---|
| 735 | !---------------------------------------------------------------------- |
---|
| 736 | ! Bilinear interpolation for geographical grid |
---|
| 737 | !---------------------------------------------------------------------- |
---|
| 738 | zdlmp = ABS(plam - plammp) |
---|
| 739 | zdppm = ABS(pphi - pphipm) |
---|
| 740 | zdlpp = ABS(plampp - plam) |
---|
| 741 | zdppp = ABS(pphipp - pphi) |
---|
| 742 | |
---|
| 743 | DO jk = 1, kmax |
---|
| 744 | p2dmm(jk) = zdlpp * zdppp * pmask(1,1,jk) |
---|
| 745 | p2dmp(jk) = zdlpp * zdppm * pmask(1,2,jk) |
---|
| 746 | p2dpm(jk) = zdlmp * zdppp * pmask(2,1,jk) |
---|
| 747 | p2dpp(jk) = zdlmp * zdppm * pmask(2,2,jk) |
---|
| 748 | END DO |
---|
| 749 | |
---|
| 750 | END SUBROUTINE obs_int_h2d_bil |
---|
| 751 | |
---|
| 752 | SUBROUTINE obs_int_h2d_bir( kpk2, kmax, & |
---|
| 753 | & pphi, plam, pmask, & |
---|
| 754 | & pphimm, plammm, pphimp, plammp, & |
---|
| 755 | & pphipm, plampm, pphipp, plampp, & |
---|
| 756 | & p2dmm, p2dmp, p2dpm, p2dpp, ldfail ) |
---|
| 757 | !!----------------------------------------------------------------------- |
---|
| 758 | !! |
---|
| 759 | !! *** ROUTINE obs_int_h2d_bir *** |
---|
| 760 | !! |
---|
| 761 | !! ** Purpose : General bilinear remapping interpolation (k2dint = 3) |
---|
| 762 | !! |
---|
| 763 | !! ** Method : An iterative scheme that involves first mapping a |
---|
| 764 | !! quadrilateral cell into a cell with coordinates |
---|
| 765 | !! (0,0), (1,0), (0,1) and (1,1). |
---|
| 766 | !! |
---|
| 767 | !! ** Action : |
---|
| 768 | !! |
---|
| 769 | !! History : |
---|
| 770 | !! ! 97-11 (A. Weaver, N. Daget) |
---|
| 771 | !! ! 06-10 (A. Weaver) Cleanup |
---|
| 772 | !!----------------------------------------------------------------------- |
---|
| 773 | |
---|
| 774 | !! * Arguments |
---|
| 775 | INTEGER, INTENT(IN) :: & |
---|
| 776 | & kpk2, & ! Parameter values for automatic arrays |
---|
| 777 | & kmax |
---|
| 778 | REAL(KIND=wp), INTENT(IN) :: & |
---|
| 779 | & pphi, & ! Geographical location of observation |
---|
| 780 | & plam, & |
---|
| 781 | & pphimm, & ! Geographical location of surrounding |
---|
| 782 | & pphimp, & ! model grid points |
---|
| 783 | & pphipm, & |
---|
| 784 | & pphipp, & |
---|
| 785 | & plammm, & |
---|
| 786 | & plammp, & |
---|
| 787 | & plampm, & |
---|
| 788 | & plampp |
---|
| 789 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
---|
| 790 | & pmask ! Model variable mask |
---|
| 791 | REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: & |
---|
| 792 | & p2dmm, & ! Interpolation weights |
---|
| 793 | & p2dmp, & |
---|
| 794 | & p2dpm, & |
---|
| 795 | & p2dpp |
---|
| 796 | LOGICAL, INTENT(OUT) :: & |
---|
| 797 | & ldfail |
---|
| 798 | !! * Local declarations |
---|
| 799 | INTEGER :: & |
---|
| 800 | & jk |
---|
| 801 | REAL(KIND=wp) :: & |
---|
| 802 | & zbiwmm, & |
---|
| 803 | & zbiwmp, & |
---|
| 804 | & zbiwpm, & |
---|
| 805 | & zbiwpp |
---|
| 806 | |
---|
| 807 | !---------------------------------------------------------------------- |
---|
| 808 | ! Bilinear remapping interpolation for general quadrilateral grid |
---|
| 809 | !---------------------------------------------------------------------- |
---|
| 810 | CALL bil_wgt( pphimm, pphimp, pphipm, pphipp, & |
---|
| 811 | & plammm, plammp, plampm, plampp, & |
---|
| 812 | & zbiwmm, zbiwmp, zbiwpm, zbiwpp, & |
---|
| 813 | & pphi , plam, ldfail ) |
---|
| 814 | |
---|
| 815 | IF ( .NOT.ldfail ) THEN |
---|
| 816 | DO jk = 1, kmax |
---|
| 817 | p2dmm(jk) = zbiwmm * pmask(1,1,jk) |
---|
| 818 | p2dmp(jk) = zbiwmp * pmask(1,2,jk) |
---|
| 819 | p2dpm(jk) = zbiwpm * pmask(2,1,jk) |
---|
| 820 | p2dpp(jk) = zbiwpp * pmask(2,2,jk) |
---|
| 821 | END DO |
---|
| 822 | ENDIF |
---|
| 823 | |
---|
| 824 | END SUBROUTINE obs_int_h2d_bir |
---|
| 825 | |
---|
| 826 | SUBROUTINE obs_int_h2d_pol( kpk2, kmax, & |
---|
| 827 | & pphi, plam, pmask, & |
---|
| 828 | & pphimm, plammm, pphimp, plammp, & |
---|
| 829 | & pphipm, plampm, pphipp, plampp, & |
---|
| 830 | & p2dmm, p2dmp, p2dpm, p2dpp ) |
---|
| 831 | !!----------------------------------------------------------------------- |
---|
| 832 | !! |
---|
| 833 | !! *** ROUTINE obs_int_h2d_pol *** |
---|
| 834 | !! |
---|
| 835 | !! ** Purpose : Polynomial interpolation (k2dint = 4) |
---|
| 836 | !! |
---|
| 837 | !! ** Method : The interpolation weights are computed by fitting a |
---|
| 838 | !! polynomial function of the form |
---|
| 839 | !! |
---|
| 840 | !! P(i) = a1(i) + a2(i) * phi + a3(i) * plam + a4(i) * phi * plam |
---|
| 841 | !! |
---|
| 842 | !! through the model values at four surrounding grid pts (i=1,4). |
---|
| 843 | !! As k2dint = 0 but with distance (ds) computed using a small- |
---|
| 844 | !! angle approximation to the great-circle distance formula: |
---|
| 845 | !! |
---|
| 846 | !! ds(AB) = sqrt( ( phiB - phiA )^{2} |
---|
| 847 | !! + ( ( lamB - lamA ) * cos( phiB ) )^{2} ) |
---|
| 848 | !! |
---|
| 849 | !! ** Action : |
---|
| 850 | !! |
---|
| 851 | !! History : |
---|
| 852 | !! ! 97-11 (A. Weaver, N. Daget) |
---|
| 853 | !! ! 06-10 (A. Weaver) Cleanup |
---|
| 854 | !!----------------------------------------------------------------------- |
---|
| 855 | |
---|
| 856 | !! * Arguments |
---|
| 857 | INTEGER, INTENT(IN) :: & |
---|
| 858 | & kpk2, & ! Parameter values for automatic arrays |
---|
| 859 | & kmax |
---|
| 860 | REAL(KIND=wp), INTENT(IN) :: & |
---|
| 861 | & pphi, & ! Geographical location of observation |
---|
| 862 | & plam, & |
---|
| 863 | & pphimm, & ! Geographical location of surrounding |
---|
| 864 | & pphimp, & ! model grid points |
---|
| 865 | & pphipm, & |
---|
| 866 | & pphipp, & |
---|
| 867 | & plammm, & |
---|
| 868 | & plammp, & |
---|
| 869 | & plampm, & |
---|
| 870 | & plampp |
---|
| 871 | REAL(KIND=wp), DIMENSION(2,2,kpk2), INTENT(IN) :: & |
---|
| 872 | & pmask ! Model variable mask |
---|
| 873 | REAL(KIND=wp), DIMENSION(kpk2), INTENT(OUT) :: & |
---|
| 874 | & p2dmm, & ! Interpolation weights |
---|
| 875 | & p2dmp, & |
---|
| 876 | & p2dpm, & |
---|
| 877 | & p2dpp |
---|
| 878 | |
---|
| 879 | !! * Local declarations |
---|
| 880 | INTEGER :: & |
---|
| 881 | & jk |
---|
| 882 | REAL(KIND=wp) :: & |
---|
| 883 | & zplp |
---|
| 884 | REAL(KIND=wp), DIMENSION(4,4) :: & |
---|
| 885 | & zmat, & |
---|
| 886 | & zmati |
---|
| 887 | |
---|
| 888 | !------------------------------------------------------------------------ |
---|
| 889 | ! Polynomial interpolation |
---|
| 890 | !------------------------------------------------------------------------ |
---|
| 891 | zmat(1,1) = 1.0_wp |
---|
| 892 | zmat(1,2) = 1.0_wp |
---|
| 893 | zmat(1,3) = 1.0_wp |
---|
| 894 | zmat(1,4) = 1.0_wp |
---|
| 895 | zmat(2,1) = plammm |
---|
| 896 | zmat(2,2) = plammp |
---|
| 897 | zmat(2,3) = plampm |
---|
| 898 | zmat(2,4) = plampp |
---|
| 899 | zmat(3,1) = pphimm |
---|
| 900 | zmat(3,2) = pphimp |
---|
| 901 | zmat(3,3) = pphipm |
---|
| 902 | zmat(3,4) = pphipp |
---|
| 903 | zmat(4,1) = plammm * pphimm |
---|
| 904 | zmat(4,2) = plammp * pphimp |
---|
| 905 | zmat(4,3) = plampm * pphipm |
---|
| 906 | zmat(4,4) = plampp * pphipp |
---|
| 907 | |
---|
| 908 | CALL lu_invmat( zmat, 4, zmati ) |
---|
| 909 | |
---|
| 910 | zplp = plam * pphi |
---|
| 911 | DO jk = 1, kmax |
---|
| 912 | p2dmm(jk) = ABS( zmati(1,1) + zmati(1,2) * plam & |
---|
| 913 | & + zmati(1,3) * pphi + zmati(1,4) * zplp ) & |
---|
| 914 | & * pmask(1,1,jk) |
---|
| 915 | p2dmp(jk) = ABS( zmati(2,1) + zmati(2,2) * plam & |
---|
| 916 | & + zmati(2,3) * pphi + zmati(2,4) * zplp ) & |
---|
| 917 | & * pmask(1,2,jk) |
---|
| 918 | p2dpm(jk) = ABS( zmati(3,1) + zmati(3,2) * plam & |
---|
| 919 | & + zmati(3,3) * pphi + zmati(3,4) * zplp ) & |
---|
| 920 | & * pmask(2,1,jk) |
---|
| 921 | p2dpp(jk) = ABS( zmati(4,1) + zmati(4,2) * plam & |
---|
| 922 | & + zmati(4,3) * pphi + zmati(4,4) * zplp ) & |
---|
| 923 | & * pmask(2,2,jk) |
---|
| 924 | END DO |
---|
| 925 | |
---|
| 926 | END SUBROUTINE obs_int_h2d_pol |
---|
| 927 | |
---|
| 928 | SUBROUTINE bil_wgt( pphimm, pphimp, pphipm, pphipp, & |
---|
| 929 | & plammm, plammp, plampm, plampp, & |
---|
| 930 | & pbiwmm, pbiwmp, pbiwpm, pbiwpp, & |
---|
| 931 | & pphi , plam, ldfail ) |
---|
| 932 | !!------------------------------------------------------------------- |
---|
| 933 | !! |
---|
| 934 | !! *** ROUTINE bil_wgt *** |
---|
| 935 | !! |
---|
| 936 | !! ** Purpose : Compute the weights for a bilinear remapping |
---|
| 937 | !! interpolation scheme. |
---|
| 938 | !! |
---|
| 939 | !! ** Method : This scheme is appropriate for bilinear interpolation |
---|
| 940 | !! on a general quadrilateral grid. |
---|
| 941 | !! This scheme is also used in OASIS. |
---|
| 942 | !! |
---|
| 943 | !! This routine is a derivative of the SCRIP software. |
---|
| 944 | !! Copyright 1997, 1998 the Regents of the University |
---|
| 945 | !! of California. See SCRIP_Copyright.txt. |
---|
| 946 | !! |
---|
| 947 | !! ** Action : |
---|
| 948 | !! |
---|
| 949 | !! References : Jones, P.: A user's guide for SCRIP: A Spherical |
---|
| 950 | !! Coordinate Remapping and Interpolation Package. |
---|
| 951 | !! Version 1.4. Los Alamos. |
---|
| 952 | !! |
---|
| 953 | !! http://www.acl.lanl.gov/climate/software/SCRIP/SCRIPmain.html |
---|
| 954 | !! |
---|
| 955 | !! History |
---|
| 956 | !! ! 97-11 (A. Weaver, N. Daget) |
---|
| 957 | !! ! 06-03 (A. Vidard) |
---|
| 958 | !! ! 06-10 (A. Weaver) Cleanup |
---|
| 959 | !!----------------------------------------------------------------------- |
---|
| 960 | |
---|
| 961 | !! * Arguments |
---|
| 962 | REAL(KIND=wp), INTENT(IN) :: & |
---|
| 963 | & pphi, & ! Geographical location of observation |
---|
| 964 | & plam, & |
---|
| 965 | & pphimm, & ! Geographical location of surrounding |
---|
| 966 | & pphimp, & ! model grid points |
---|
| 967 | & pphipm, & |
---|
| 968 | & pphipp, & |
---|
| 969 | & plammm, & |
---|
| 970 | & plammp, & |
---|
| 971 | & plampm, & |
---|
| 972 | & plampp |
---|
| 973 | REAL(KIND=wp), INTENT(OUT) :: & |
---|
| 974 | & pbiwmm, & ! Interpolation weights |
---|
| 975 | & pbiwmp, & |
---|
| 976 | & pbiwpm, & |
---|
| 977 | & pbiwpp |
---|
| 978 | LOGICAL, INTENT(out) :: & |
---|
| 979 | & ldfail |
---|
| 980 | |
---|
| 981 | !! * Local declarations |
---|
| 982 | INTEGER :: & |
---|
| 983 | & jiter |
---|
| 984 | INTEGER :: & |
---|
| 985 | & itermax |
---|
| 986 | REAL(KIND=wp) :: & |
---|
| 987 | & zphi, & ! Geographical location of observation |
---|
| 988 | & zlam, & |
---|
| 989 | & zphimm, & ! Geographical location of surrounding |
---|
| 990 | & zphimp, & ! model grid points |
---|
| 991 | & zphipm, & |
---|
| 992 | & zphipp, & |
---|
| 993 | & zlammm, & |
---|
| 994 | & zlammp, & |
---|
| 995 | & zlampm, & |
---|
| 996 | & zlampp, & |
---|
| 997 | & zdth1, & |
---|
| 998 | & zdth2, & |
---|
| 999 | & zdth3, & |
---|
| 1000 | & zdthp, & |
---|
| 1001 | & zdph1, & |
---|
| 1002 | & zdph2, & |
---|
| 1003 | & zdph3, & |
---|
| 1004 | & zdphp, & |
---|
| 1005 | & zmat1, & |
---|
| 1006 | & zmat2, & |
---|
| 1007 | & zmat3, & |
---|
| 1008 | & zmat4, & |
---|
| 1009 | & zdeli, & |
---|
| 1010 | & zdelj, & |
---|
| 1011 | & ziguess, & |
---|
| 1012 | & zjguess, & |
---|
| 1013 | & zeps, & |
---|
| 1014 | & zdeterm, & |
---|
| 1015 | & z2pi, & |
---|
| 1016 | & zhpi |
---|
| 1017 | |
---|
| 1018 | ! Initialization |
---|
| 1019 | |
---|
| 1020 | ! Conversion to radians |
---|
| 1021 | |
---|
| 1022 | zphi = pphi * rad |
---|
| 1023 | zlam = plam * rad |
---|
| 1024 | zphimm = pphimm * rad |
---|
| 1025 | zphimp = pphimp * rad |
---|
| 1026 | zphipm = pphipm * rad |
---|
| 1027 | zphipp = pphipp * rad |
---|
| 1028 | zlammm = plammm * rad |
---|
| 1029 | zlammp = plammp * rad |
---|
| 1030 | zlampm = plampm * rad |
---|
| 1031 | zlampp = plampp * rad |
---|
| 1032 | |
---|
| 1033 | ldfail = .FALSE. |
---|
| 1034 | |
---|
| 1035 | zdth1 = zphipm - zphimm |
---|
| 1036 | zdth2 = zphimp - zphimm |
---|
| 1037 | zdth3 = zphipp - zphipm - zdth2 |
---|
| 1038 | |
---|
| 1039 | zdph1 = zlampm - zlammm |
---|
| 1040 | zdph2 = zlammp - zlammm |
---|
| 1041 | zdph3 = zlampp - zlampm |
---|
| 1042 | |
---|
| 1043 | z2pi = 2.0_wp * rpi |
---|
| 1044 | |
---|
| 1045 | IF ( zdph1 > 3.0_wp * rpi ) zdph1 = zdph1 - z2pi |
---|
| 1046 | IF ( zdph2 > 3.0_wp * rpi ) zdph2 = zdph2 - z2pi |
---|
| 1047 | IF ( zdph3 > 3.0_wp * rpi ) zdph3 = zdph3 - z2pi |
---|
| 1048 | IF ( zdph1 < -3.0_wp * rpi ) zdph1 = zdph1 + z2pi |
---|
| 1049 | IF ( zdph2 < -3.0_wp * rpi ) zdph2 = zdph2 + z2pi |
---|
| 1050 | IF ( zdph3 < -3.0_wp * rpi ) zdph3 = zdph3 + z2pi |
---|
| 1051 | |
---|
| 1052 | zdph3 = zdph3 - zdph2 |
---|
| 1053 | |
---|
| 1054 | ziguess = 0.5_wp |
---|
| 1055 | zjguess = 0.5_wp |
---|
| 1056 | |
---|
| 1057 | itermax = 100 |
---|
| 1058 | |
---|
[2474] | 1059 | IF ( wp == sp ) THEN |
---|
| 1060 | zeps = 1.0e-6_wp ! Single precision |
---|
| 1061 | ELSE |
---|
| 1062 | zeps = 1.0e-10_wp ! Double precision |
---|
| 1063 | ENDIF |
---|
[2202] | 1064 | |
---|
| 1065 | !------------------------------------------------------------------------ |
---|
| 1066 | ! Iterate to determine (i,j) in new coordinate system |
---|
| 1067 | !------------------------------------------------------------------------ |
---|
| 1068 | jiter_loop: DO jiter = 1, itermax |
---|
| 1069 | |
---|
| 1070 | zdthp = zphi - zphimm - zdth1 * ziguess - zdth2 * zjguess & |
---|
| 1071 | & - zdth3 * ziguess * zjguess |
---|
| 1072 | zdphp = zlam - zlammm |
---|
| 1073 | |
---|
| 1074 | zhpi = 0.5_wp * rpi |
---|
| 1075 | IF ( zdphp > 3.0_wp * zhpi ) zdphp = zdphp - z2pi |
---|
| 1076 | IF ( zdphp < -3.0_wp * zhpi ) zdphp = zdphp + z2pi |
---|
| 1077 | |
---|
| 1078 | zdphp = zdphp - zdph1 * ziguess - zdph2 * zjguess & |
---|
| 1079 | & - zdph3 * ziguess * zjguess |
---|
| 1080 | |
---|
| 1081 | zmat1 = zdth1 + zdth3 * zjguess |
---|
| 1082 | zmat2 = zdth2 + zdth3 * ziguess |
---|
| 1083 | zmat3 = zdph1 + zdph3 * zjguess |
---|
| 1084 | zmat4 = zdph2 + zdph3 * ziguess |
---|
| 1085 | |
---|
| 1086 | ! Matrix determinant |
---|
| 1087 | zdeterm = zmat1 * zmat4 - zmat2 * zmat3 |
---|
| 1088 | |
---|
| 1089 | zdeli = ( zdthp * zmat4 - zmat2 * zdphp) / zdeterm |
---|
| 1090 | zdelj = ( zmat1 * zdphp - zdthp * zmat3) / zdeterm |
---|
| 1091 | |
---|
| 1092 | IF ( ABS( zdeli ) < zeps .AND. ABS( zdelj ) < zeps ) EXIT jiter_loop |
---|
| 1093 | |
---|
| 1094 | ziguess = ziguess + zdeli |
---|
| 1095 | zjguess = zjguess + zdelj |
---|
| 1096 | |
---|
| 1097 | ! DJL prevent ziguess and zjguess from going outside the range |
---|
| 1098 | ! 0 to 1 |
---|
| 1099 | ! prevents interpolated value going wrong |
---|
| 1100 | ! for example sea ice concentration gt 1 |
---|
| 1101 | |
---|
| 1102 | IF ( ziguess < 0 ) ziguess = 0.0_wp |
---|
| 1103 | IF ( zjguess < 0 ) zjguess = 0.0_wp |
---|
| 1104 | IF ( ziguess > 1 ) ziguess = 1.0_wp |
---|
| 1105 | IF ( zjguess > 1 ) zjguess = 1.0_wp |
---|
| 1106 | |
---|
| 1107 | END DO jiter_loop |
---|
| 1108 | |
---|
| 1109 | IF ( jiter <= itermax ) THEN |
---|
| 1110 | |
---|
| 1111 | ! Successfully found i,j, now compute the weights |
---|
| 1112 | |
---|
| 1113 | pbiwmm = ( 1.0_wp - ziguess ) * ( 1.0_wp - zjguess ) |
---|
| 1114 | pbiwmp = ( 1.0_wp - ziguess ) * zjguess |
---|
| 1115 | pbiwpm = ziguess * ( 1.0_wp - zjguess ) |
---|
| 1116 | pbiwpp = ziguess * zjguess |
---|
| 1117 | |
---|
| 1118 | ELSEIF ( jiter > itermax ) THEN |
---|
| 1119 | |
---|
| 1120 | IF(lwp) THEN |
---|
| 1121 | |
---|
| 1122 | WRITE(numout,*)'Obs lat/lon : ',pphi, plam |
---|
| 1123 | WRITE(numout,*)'Grid lats : ',pphimm, pphimp, pphipm, pphipp |
---|
| 1124 | WRITE(numout,*)'Grid lons : ',plammm, plammp, plampm, plampp |
---|
| 1125 | WRITE(numout,*)'Current i,j : ',ziguess, zjguess |
---|
| 1126 | WRITE(numout,*)'Weights : ',pbiwmm, pbiwmp, pbiwpm, pbiwpp |
---|
| 1127 | WRITE(numout,*)'jiter = ',jiter |
---|
| 1128 | WRITE(numout,*)'zeps = ',zeps |
---|
| 1129 | WRITE(numout,*)'zdeli, zdelj = ',zdeli, zdelj |
---|
| 1130 | WRITE(numout,*)' Iterations for i,j exceed max iteration count!' |
---|
| 1131 | WRITE(numout,*) |
---|
| 1132 | |
---|
| 1133 | ldfail = .TRUE. |
---|
| 1134 | |
---|
| 1135 | ENDIF |
---|
| 1136 | |
---|
| 1137 | ENDIF |
---|
| 1138 | |
---|
| 1139 | END SUBROUTINE bil_wgt |
---|
| 1140 | |
---|
| 1141 | SUBROUTINE lu_invmat( pmatin, kdim, pmatou ) |
---|
| 1142 | !!----------------------------------------------------------------------- |
---|
| 1143 | !! |
---|
| 1144 | !! *** ROUTINE lu_invmat *** |
---|
| 1145 | !! |
---|
| 1146 | !! ** Purpose : Invert a matrix using LU decomposition. |
---|
| 1147 | !! |
---|
| 1148 | !! ** Method : |
---|
| 1149 | !! |
---|
| 1150 | !! ** Action : |
---|
| 1151 | !! |
---|
| 1152 | !! References : |
---|
| 1153 | !! |
---|
| 1154 | !! History |
---|
| 1155 | !! ! 02-11 (A. Weaver, N. Daget) |
---|
| 1156 | !! ! 06-03 (A. Vidard) |
---|
| 1157 | !! ! 06-10 (A. Weaver) Cleanup |
---|
| 1158 | !! ! 06-11 (NEMOVAR task force) Fix declaration of zd. |
---|
| 1159 | !!----------------------------------------------------------------------- |
---|
| 1160 | |
---|
| 1161 | !! * Arguments |
---|
| 1162 | INTEGER, INTENT(IN) :: & |
---|
| 1163 | & kdim ! Array dimension |
---|
| 1164 | REAL(KIND=wp), DIMENSION(kdim,kdim), INTENT(IN) :: & |
---|
| 1165 | & pmatin |
---|
| 1166 | REAL(KIND=wp), DIMENSION(kdim,kdim), INTENT(OUT) :: & |
---|
| 1167 | & pmatou |
---|
| 1168 | |
---|
| 1169 | !! * Local declarations |
---|
| 1170 | INTEGER :: & |
---|
| 1171 | & ji, & |
---|
| 1172 | & jj |
---|
| 1173 | INTEGER, DIMENSION(kdim) :: & |
---|
| 1174 | & indx |
---|
| 1175 | REAL(KIND=wp), DIMENSION(kdim,kdim) :: & |
---|
| 1176 | & zmat |
---|
| 1177 | REAL(KIND=wp) :: & |
---|
| 1178 | & zd |
---|
| 1179 | |
---|
| 1180 | ! Invert the matrix |
---|
| 1181 | DO jj = 1, kdim |
---|
| 1182 | DO ji = 1, kdim |
---|
| 1183 | pmatou(ji,jj) = 0.0_wp |
---|
| 1184 | zmat(ji,jj) = pmatin(ji,jj) |
---|
| 1185 | END DO |
---|
| 1186 | pmatou(jj,jj) = 1.0_wp |
---|
| 1187 | END DO |
---|
| 1188 | CALL lu_decomp( zmat, kdim, kdim, indx, zd ) |
---|
| 1189 | DO jj = 1, kdim |
---|
| 1190 | CALL lu_backsb( zmat, kdim, kdim, indx, pmatou(1,jj) ) |
---|
| 1191 | END DO |
---|
| 1192 | |
---|
| 1193 | END SUBROUTINE lu_invmat |
---|
| 1194 | |
---|
| 1195 | SUBROUTINE lu_decomp( pmatin, kdim1, kdim2, kindex, pflt ) |
---|
| 1196 | !!----------------------------------------------------------------------- |
---|
| 1197 | !! |
---|
| 1198 | !! *** ROUTINE lu_decomp *** |
---|
| 1199 | !! |
---|
| 1200 | !! ** Purpose : Compute the LU decomposition of a matrix |
---|
| 1201 | !! |
---|
| 1202 | !! ** Method : |
---|
| 1203 | !! |
---|
| 1204 | !! ** Action : |
---|
| 1205 | !! |
---|
| 1206 | !! References : |
---|
| 1207 | !! |
---|
| 1208 | !! History |
---|
| 1209 | !! ! 02-11 (A. Weaver, N. Daget) |
---|
| 1210 | !! ! 06-03 (A. Vidard) |
---|
| 1211 | !! ! 06-10 (A. Weaver) Cleanup |
---|
| 1212 | !!----------------------------------------------------------------------- |
---|
| 1213 | |
---|
| 1214 | !! * Arguments |
---|
| 1215 | INTEGER, INTENT(IN) :: & |
---|
| 1216 | & kdim1, & ! Array dimensions |
---|
| 1217 | & kdim2 |
---|
| 1218 | INTEGER, DIMENSION(kdim1), INTENT(OUT) :: & |
---|
| 1219 | & kindex |
---|
| 1220 | REAL(KIND=wp), INTENT(OUT) :: & |
---|
| 1221 | & pflt |
---|
| 1222 | REAL(KIND=wp), DIMENSION(kdim2,kdim2), INTENT(INOUT) :: & |
---|
| 1223 | & pmatin |
---|
| 1224 | |
---|
| 1225 | !! * Local declarations |
---|
| 1226 | INTEGER, PARAMETER :: & |
---|
| 1227 | & jpmax = 100 |
---|
| 1228 | REAL(KIND=wp), PARAMETER :: & |
---|
| 1229 | & pptiny = 1.0e-20_wp |
---|
| 1230 | REAL(KIND=wp), DIMENSION(jpmax) :: & |
---|
| 1231 | & zvv |
---|
| 1232 | INTEGER :: & |
---|
| 1233 | & ji, & |
---|
| 1234 | & jj, & |
---|
| 1235 | & jk |
---|
| 1236 | INTEGER :: & |
---|
| 1237 | & imax |
---|
| 1238 | REAL(KIND=wp) :: & |
---|
| 1239 | & zsum, & |
---|
| 1240 | & zdum, & |
---|
| 1241 | & zaamax |
---|
| 1242 | |
---|
| 1243 | ! Main computation |
---|
| 1244 | pflt = 1.0_wp |
---|
| 1245 | DO ji = 1, kdim1 |
---|
| 1246 | zaamax = 0.0_wp |
---|
| 1247 | DO jj = 1, kdim1 |
---|
| 1248 | IF ( ABS( pmatin(ji,jj) ) > zaamax ) zaamax = ABS( pmatin(ji,jj) ) |
---|
| 1249 | END DO |
---|
| 1250 | IF ( zaamax == 0.0_wp ) THEN |
---|
| 1251 | CALL ctl_stop( 'singular matrix' ) |
---|
| 1252 | ENDIF |
---|
| 1253 | zvv(ji) = 1.0_wp / zaamax |
---|
| 1254 | END DO |
---|
| 1255 | DO jj = 1, kdim1 |
---|
| 1256 | DO ji = 1, jj-1 |
---|
| 1257 | zsum = pmatin(ji,jj) |
---|
| 1258 | DO jk = 1, ji-1 |
---|
| 1259 | zsum = zsum - pmatin(ji,jk) * pmatin(jk,jj) |
---|
| 1260 | END DO |
---|
| 1261 | pmatin(ji,jj) = zsum |
---|
| 1262 | END DO |
---|
| 1263 | zaamax = 0.0_wp |
---|
| 1264 | DO ji = jj, kdim1 |
---|
| 1265 | zsum = pmatin(ji,jj) |
---|
| 1266 | DO jk = 1, jj-1 |
---|
| 1267 | zsum = zsum - pmatin(ji,jk) * pmatin(jk,jj) |
---|
| 1268 | END DO |
---|
| 1269 | pmatin(ji,jj) = zsum |
---|
| 1270 | zdum = zvv(ji) * ABS( zsum ) |
---|
| 1271 | IF ( zdum >= zaamax ) THEN |
---|
| 1272 | imax = ji |
---|
| 1273 | zaamax = zdum |
---|
| 1274 | ENDIF |
---|
| 1275 | END DO |
---|
| 1276 | IF ( jj /= imax ) THEN |
---|
| 1277 | DO jk = 1, kdim1 |
---|
| 1278 | zdum = pmatin(imax,jk) |
---|
| 1279 | pmatin(imax,jk) = pmatin(jj,jk) |
---|
| 1280 | pmatin(jj,jk) = zdum |
---|
| 1281 | END DO |
---|
| 1282 | pflt = -pflt |
---|
| 1283 | zvv(imax) = zvv(jj) |
---|
| 1284 | ENDIF |
---|
| 1285 | kindex(jj) = imax |
---|
| 1286 | IF ( pmatin(jj,jj) == 0.0_wp ) pmatin(jj,jj) = pptiny |
---|
| 1287 | IF ( jj /= kdim1 ) THEN |
---|
| 1288 | zdum = 1.0_wp / pmatin(jj,jj) |
---|
| 1289 | DO ji = jj+1, kdim1 |
---|
| 1290 | pmatin(ji,jj) = pmatin(ji,jj) * zdum |
---|
| 1291 | END DO |
---|
| 1292 | ENDIF |
---|
| 1293 | END DO |
---|
| 1294 | |
---|
| 1295 | END SUBROUTINE lu_decomp |
---|
| 1296 | |
---|
| 1297 | SUBROUTINE lu_backsb( pmat, kdim1, kdim2, kindex, pvect ) |
---|
| 1298 | !!----------------------------------------------------------------------- |
---|
| 1299 | !! |
---|
| 1300 | !! *** ROUTINE lu_backsb *** |
---|
| 1301 | !! |
---|
| 1302 | !! ** Purpose : Back substitution |
---|
| 1303 | !! |
---|
| 1304 | !! ** Method : |
---|
| 1305 | !! |
---|
| 1306 | !! ** Action : |
---|
| 1307 | !! |
---|
| 1308 | !! References : |
---|
| 1309 | !! |
---|
| 1310 | !! History |
---|
| 1311 | !! ! 02-11 (A. Weaver, N. Daget) |
---|
| 1312 | !! ! 06-03 (A. Vidard) |
---|
| 1313 | !! ! 06-10 (A. Weaver) Cleanup |
---|
| 1314 | !!----------------------------------------------------------------------- |
---|
| 1315 | |
---|
| 1316 | !! * Arguments |
---|
| 1317 | INTEGER, INTENT(IN) :: & |
---|
| 1318 | & kdim1, & ! Array dimensions |
---|
| 1319 | & kdim2 |
---|
| 1320 | INTEGER, DIMENSION(kdim1), INTENT(IN) :: & |
---|
| 1321 | & kindex |
---|
| 1322 | REAL(KIND=wp), DIMENSION(kdim1), INTENT(INOUT) :: & |
---|
| 1323 | & pvect |
---|
| 1324 | REAL(KIND=wp), DIMENSION(kdim2,kdim2), INTENT(IN) :: & |
---|
| 1325 | & pmat |
---|
| 1326 | |
---|
| 1327 | !! * Local declarations |
---|
| 1328 | INTEGER :: & |
---|
| 1329 | & ji, & |
---|
| 1330 | & jii, & |
---|
| 1331 | & jj, & |
---|
| 1332 | & jll |
---|
| 1333 | REAL(KIND=wp) :: & |
---|
| 1334 | & zsum |
---|
| 1335 | |
---|
| 1336 | ! Main computation |
---|
| 1337 | jii = 0 |
---|
| 1338 | DO ji = 1, kdim1 |
---|
| 1339 | jll = kindex(ji) |
---|
| 1340 | zsum = pvect(jll) |
---|
| 1341 | pvect(jll) = pvect(ji) |
---|
| 1342 | IF ( jii /= 0 ) THEN |
---|
| 1343 | DO jj = jii, ji-1 |
---|
| 1344 | zsum = zsum - pmat(ji,jj) * pvect(jj) |
---|
| 1345 | END DO |
---|
| 1346 | ELSEIF ( zsum /= 0.0_wp ) THEN |
---|
| 1347 | jii = ji |
---|
| 1348 | ENDIF |
---|
| 1349 | pvect(ji) = zsum |
---|
| 1350 | END DO |
---|
| 1351 | DO ji = kdim1, 1, -1 |
---|
| 1352 | zsum = pvect(ji) |
---|
| 1353 | DO jj = ji+1, kdim1 |
---|
| 1354 | zsum = zsum - pmat(ji,jj) * pvect(jj) |
---|
| 1355 | END DO |
---|
| 1356 | pvect(ji) = zsum / pmat(ji,ji) |
---|
| 1357 | END DO |
---|
| 1358 | |
---|
| 1359 | END SUBROUTINE lu_backsb |
---|