| 1 | ! |
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| 2 | MODULE bilinear_interp |
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| 3 | ! |
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| 4 | USE agrif_modutil |
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| 5 | ! |
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| 6 | !************************************************************************ |
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| 7 | ! * |
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| 8 | ! MODULE BILINEAR INTERP * |
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| 9 | ! * |
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| 10 | ! bilinear interpolation routines from SCRIP package * |
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| 11 | ! * |
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| 12 | !http://climate.lanl.gov/Software/SCRIP/ * |
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| 13 | ! * |
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| 14 | !Bilinear remapping * |
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| 15 | ! * |
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| 16 | !************************************************************************ |
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| 17 | ! |
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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 | ! variables that describe each grid |
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| 23 | !----------------------------------------------------------------------- |
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| 24 | ! |
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| 25 | INTEGER :: grid1_size,grid2_size,grid1_rank, grid2_rank |
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| 26 | ! |
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| 27 | INTEGER, DIMENSION(:), ALLOCATABLE :: grid1_dims, grid2_dims |
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| 28 | ! |
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| 29 | |
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| 30 | !----------------------------------------------------------------------- |
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| 31 | ! grid coordinates and masks |
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| 32 | !----------------------------------------------------------------------- |
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| 33 | ! |
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| 34 | LOGICAL, DIMENSION(:), ALLOCATABLE :: grid1_mask,grid2_mask |
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| 35 | ! each grid center in radians |
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| 36 | REAL*8,DIMENSION(:), ALLOCATABLE :: & |
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| 37 | grid1_center_lat, & |
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| 38 | grid1_center_lon, & |
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| 39 | grid2_center_lat, & |
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| 40 | grid2_center_lon, & |
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| 41 | grid1_frac, & ! fractional area of grid cells |
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| 42 | grid2_frac ! participating in remapping |
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| 43 | ! |
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| 44 | ! lat/lon bounding box for use in restricting grid searches |
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| 45 | ! |
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| 46 | REAL*8,DIMENSION(:,:), ALLOCATABLE :: grid1_bound_box,grid2_bound_box |
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| 47 | ! |
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| 48 | !----------------------------------------------------------------------- |
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| 49 | ! bins for restricting searches |
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| 50 | !----------------------------------------------------------------------- |
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| 51 | ! |
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| 52 | ! num of bins for restricted srch |
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| 53 | INTEGER, PARAMETER :: num_srch_bins = 90 |
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| 54 | ! |
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| 55 | ! min,max adds for grid cells in this lat bin |
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| 56 | ! |
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| 57 | INTEGER,DIMENSION(:,:), ALLOCATABLE :: bin_addr1,bin_addr2 |
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| 58 | ! |
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| 59 | ! min,max longitude for each search bin |
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| 60 | ! |
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| 61 | REAL*8, DIMENSION(:,:), ALLOCATABLE :: bin_lats,bin_lons |
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| 62 | |
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| 63 | REAL*8, PARAMETER :: zero = 0.0, & |
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| 64 | one = 1.0, & |
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| 65 | two = 2.0, & |
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| 66 | three = 3.0, & |
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| 67 | four = 4.0, & |
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| 68 | five = 5.0, & |
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| 69 | half = 0.5, & |
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| 70 | quart = 0.25, & |
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| 71 | bignum = 1.e+20, & |
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| 72 | tiny = 1.e-14, & |
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| 73 | pi = 3.14159265359, & |
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| 74 | pi2 = two*pi, & |
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| 75 | pih = half*pi |
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| 76 | |
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| 77 | REAL*8, PARAMETER :: deg2rad = pi/180. |
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| 78 | ! |
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| 79 | ! max iteration count for i,j iteration |
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| 80 | ! |
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| 81 | INTEGER , PARAMETER :: max_iter = 100 |
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| 82 | ! |
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| 83 | ! convergence criterion |
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| 84 | ! |
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| 85 | REAL*8, PARAMETER :: converge = 1.e-10 |
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| 86 | |
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| 87 | |
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| 88 | ! |
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| 89 | INTEGER, PARAMETER :: norm_opt_none = 1 & |
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| 90 | ,norm_opt_dstarea = 2 & |
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| 91 | ,norm_opt_frcarea = 3 |
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| 92 | ! |
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| 93 | INTEGER, PARAMETER :: map_type_conserv = 1 & |
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| 94 | ,map_type_bilinear = 2 & |
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| 95 | ,map_type_bicubic = 3 & |
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| 96 | ,map_type_distwgt = 4 |
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| 97 | ! |
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| 98 | INTEGER :: max_links_map1 & ! current size of link arrays |
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| 99 | ,num_links_map1 & ! actual number of links for remapping |
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| 100 | ,max_links_map2 & ! current size of link arrays |
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| 101 | ,num_links_map2 & ! actual number of links for remapping |
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| 102 | ,num_maps & ! num of remappings for this grid pair |
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| 103 | ,num_wts & ! num of weights used in remapping |
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| 104 | ,map_type & ! identifier for remapping method |
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| 105 | ,norm_opt & ! option for normalization (conserv only) |
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| 106 | ,resize_increment ! default amount to increase array size |
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| 107 | |
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| 108 | INTEGER , DIMENSION(:), ALLOCATABLE :: & |
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| 109 | grid1_add_map1, & ! grid1 address for each link in mapping 1 |
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| 110 | grid2_add_map1, & ! grid2 address for each link in mapping 1 |
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| 111 | grid1_add_map2, & ! grid1 address for each link in mapping 2 |
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| 112 | grid2_add_map2 ! grid2 address for each link in mapping 2 |
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| 113 | |
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| 114 | REAL*8, DIMENSION(:,:), ALLOCATABLE :: & |
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| 115 | wts_map1, & ! map weights for each link (num_wts,max_links) |
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| 116 | wts_map2 ! map weights for each link (num_wts,max_links) |
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| 117 | ! |
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| 118 | CONTAINS |
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| 119 | ! |
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| 120 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 121 | !************************************************************************ |
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| 122 | ! SUBROUTINE GRID_INIT |
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| 123 | !************************************************************************ |
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| 124 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 125 | ! |
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| 126 | SUBROUTINE get_remap_matrix(grid1_lat,grid2_lat,grid1_lon,grid2_lon,mask, & |
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| 127 | remap_matrix,source_add,destination_add) |
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| 128 | ! |
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| 129 | !----------------------------------------------------------------------- |
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| 130 | !this routine makes any necessary changes (e.g. for 0,2pi longitude range) |
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| 131 | !----------------------------------------------------------------------- |
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| 132 | ! |
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| 133 | REAL*8,DIMENSION(:,:) :: grid1_lat,grid2_lat,grid1_lon,grid2_lon |
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| 134 | LOGICAL,DIMENSION(:,:) :: mask |
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| 135 | ! |
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| 136 | INTEGER,DIMENSION(:),ALLOCATABLE :: source_add,destination_add |
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| 137 | REAL*8,DIMENSION(:,:), ALLOCATABLE :: remap_matrix |
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| 138 | ! |
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| 139 | !----------------------------------------------------------------------- |
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| 140 | ! local variables |
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| 141 | !----------------------------------------------------------------------- |
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| 142 | ! |
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| 143 | INTEGER :: n,nele,i,j,ip1,jp1,n_add,e_add,ne_add,nx,ny |
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| 144 | INTEGER :: xpos,ypos |
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| 145 | ! |
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| 146 | ! integer mask |
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| 147 | ! |
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| 148 | INTEGER, DIMENSION(:), ALLOCATABLE :: imask |
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| 149 | ! |
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| 150 | ! lat/lon intervals for search bins |
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| 151 | ! |
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| 152 | REAL*8 :: dlat,dlon |
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| 153 | ! |
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| 154 | ! temps for computing bounding boxes |
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| 155 | ! |
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| 156 | REAL*8, DIMENSION(4) :: tmp_lats, tmp_lons |
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| 157 | ! |
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| 158 | ! write(*,*)'proceed to Bilinear interpolation ...' |
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| 159 | ! |
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| 160 | ! IF(ALLOCATED(wts_map1)) DEALLOCATE(wts_map1) |
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| 161 | ! IF(ALLOCATED(grid1_add_map1)) DEALLOCATE(grid1_add_map1) |
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| 162 | ! IF(ALLOCATED(grid2_add_map1)) DEALLOCATE(grid2_add_map1) |
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| 163 | |
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| 164 | |
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| 165 | ! |
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| 166 | ALLOCATE(grid1_dims(2),grid2_dims(2)) |
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| 167 | ! |
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| 168 | grid1_dims(1) = SIZE(grid1_lat,2) |
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| 169 | grid1_dims(2) = SIZE(grid1_lat,1) |
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| 170 | grid2_dims(1) = SIZE(grid2_lat,2) |
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| 171 | grid2_dims(2) = SIZE(grid2_lat,1) |
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| 172 | grid1_size = SIZE(grid1_lat,2) * SIZE(grid1_lat,1) |
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| 173 | grid2_size = SIZE(grid2_lat,2) * SIZE(grid2_lat,1) |
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| 174 | ! |
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| 175 | !----------------------------------------------------------------------- |
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| 176 | ! allocate grid coordinates/masks and read data |
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| 177 | !----------------------------------------------------------------------- |
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| 178 | ! |
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| 179 | ALLOCATE( grid2_mask(grid2_size), & |
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| 180 | grid1_bound_box (4,grid1_size), & |
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| 181 | grid2_bound_box (4,grid2_size), & |
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| 182 | grid1_frac (grid1_size), & |
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| 183 | grid2_frac (grid2_size)) |
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| 184 | ALLOCATE(imask(grid1_size)) |
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| 185 | ! |
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| 186 | ! |
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| 187 | grid1_frac = zero |
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| 188 | grid2_frac = zero |
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| 189 | |
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| 190 | ! |
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| 191 | ! 2D array -> 1D array |
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| 192 | ! |
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| 193 | ALLOCATE(grid1_center_lat(SIZE(grid1_lat,1)*SIZE(grid1_lat,2))) |
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| 194 | CALL tab2Dto1D(grid1_lat,grid1_center_lat) |
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| 195 | |
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| 196 | ALLOCATE(grid1_center_lon(SIZE(grid1_lon,1)*SIZE(grid1_lon,2))) |
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| 197 | CALL tab2Dto1D(grid1_lon,grid1_center_lon) |
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| 198 | |
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| 199 | ALLOCATE(grid2_center_lat(SIZE(grid2_lat,1)*SIZE(grid2_lat,2))) |
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| 200 | CALL tab2Dto1D(grid2_lat,grid2_center_lat) |
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| 201 | |
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| 202 | ALLOCATE(grid2_center_lon(SIZE(grid2_lon,1)*SIZE(grid2_lon,2))) |
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| 203 | CALL tab2Dto1D(grid2_lon,grid2_center_lon) |
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| 204 | |
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| 205 | ALLOCATE(grid1_mask(SIZE(grid1_lat,1)*SIZE(grid1_lat,2))) |
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| 206 | CALL logtab2Dto1D(mask,grid1_mask) |
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| 207 | ! |
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| 208 | ! Write(*,*) ,'grid1_mask = ',grid1_mask |
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| 209 | ! |
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| 210 | ! degrees to radian |
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| 211 | ! |
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| 212 | grid1_center_lat = grid1_center_lat*deg2rad |
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| 213 | grid1_center_lon = grid1_center_lon*deg2rad |
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| 214 | grid2_center_lat = grid2_center_lat*deg2rad |
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| 215 | grid2_center_lon = grid2_center_lon*deg2rad |
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| 216 | |
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| 217 | !----------------------------------------------------------------------- |
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| 218 | ! convert longitudes to 0,2pi interval |
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| 219 | !----------------------------------------------------------------------- |
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| 220 | |
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| 221 | WHERE (grid1_center_lon .GT. pi2) grid1_center_lon = & |
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| 222 | grid1_center_lon - pi2 |
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| 223 | WHERE (grid1_center_lon .LT. zero) grid1_center_lon = & |
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| 224 | grid1_center_lon + pi2 |
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| 225 | WHERE (grid2_center_lon .GT. pi2) grid2_center_lon = & |
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| 226 | grid2_center_lon - pi2 |
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| 227 | WHERE (grid2_center_lon .LT. zero) grid2_center_lon = & |
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| 228 | grid2_center_lon + pi2 |
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| 229 | |
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| 230 | !----------------------------------------------------------------------- |
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| 231 | ! |
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| 232 | ! make sure input latitude range is within the machine values |
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| 233 | ! for +/- pi/2 |
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| 234 | ! |
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| 235 | !----------------------------------------------------------------------- |
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| 236 | |
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| 237 | WHERE (grid1_center_lat > pih) grid1_center_lat = pih |
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| 238 | WHERE (grid1_center_lat < -pih) grid1_center_lat = -pih |
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| 239 | WHERE (grid2_center_lat > pih) grid2_center_lat = pih |
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| 240 | WHERE (grid2_center_lat < -pih) grid2_center_lat = -pih |
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| 241 | |
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| 242 | !----------------------------------------------------------------------- |
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| 243 | ! |
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| 244 | ! compute bounding boxes for restricting future grid searches |
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| 245 | ! |
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| 246 | !----------------------------------------------------------------------- |
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| 247 | ! |
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| 248 | nx = grid1_dims(1) |
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| 249 | ny = grid1_dims(2) |
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| 250 | |
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| 251 | DO n=1,grid1_size |
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| 252 | |
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| 253 | !*** find N,S and NE points to this grid point |
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| 254 | |
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| 255 | j = (n - 1)/nx +1 |
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| 256 | i = n - (j-1)*nx |
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| 257 | |
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| 258 | IF (i < nx) THEN |
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| 259 | ip1 = i + 1 |
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| 260 | ELSE |
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| 261 | !*** assume cyclic |
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| 262 | ip1 = 1 |
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| 263 | !*** but if it is not, correct |
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| 264 | e_add = (j - 1)*nx + ip1 |
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| 265 | IF (ABS(grid1_center_lat(e_add) - & |
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| 266 | grid1_center_lat(n )) > pih) THEN |
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| 267 | ip1 = i |
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| 268 | ENDIF |
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| 269 | ip1=nx |
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| 270 | ENDIF |
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| 271 | |
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| 272 | IF (j < ny) THEN |
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| 273 | jp1 = j+1 |
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| 274 | ELSE |
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| 275 | !*** assume cyclic |
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| 276 | jp1 = 1 |
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| 277 | !*** but if it is not, correct |
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| 278 | n_add = (jp1 - 1)*nx + i |
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| 279 | IF (ABS(grid1_center_lat(n_add) - & |
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| 280 | grid1_center_lat(n )) > pih) THEN |
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| 281 | jp1 = j |
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| 282 | ENDIF |
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| 283 | jp1=ny |
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| 284 | ENDIF |
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| 285 | |
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| 286 | n_add = (jp1 - 1)*nx + i |
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| 287 | e_add = (j - 1)*nx + ip1 |
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| 288 | ne_add = (jp1 - 1)*nx + ip1 |
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| 289 | |
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| 290 | !*** find N,S and NE lat/lon coords and check bounding box |
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| 291 | |
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| 292 | tmp_lats(1) = grid1_center_lat(n) |
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| 293 | tmp_lats(2) = grid1_center_lat(e_add) |
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| 294 | tmp_lats(3) = grid1_center_lat(ne_add) |
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| 295 | tmp_lats(4) = grid1_center_lat(n_add) |
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| 296 | |
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| 297 | tmp_lons(1) = grid1_center_lon(n) |
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| 298 | tmp_lons(2) = grid1_center_lon(e_add) |
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| 299 | tmp_lons(3) = grid1_center_lon(ne_add) |
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| 300 | tmp_lons(4) = grid1_center_lon(n_add) |
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| 301 | |
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| 302 | grid1_bound_box(1,n) = MINVAL(tmp_lats) |
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| 303 | grid1_bound_box(2,n) = MAXVAL(tmp_lats) |
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| 304 | |
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| 305 | grid1_bound_box(3,n) = MINVAL(tmp_lons) |
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| 306 | grid1_bound_box(4,n) = MAXVAL(tmp_lons) |
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| 307 | END DO |
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| 308 | |
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| 309 | nx = grid2_dims(1) |
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| 310 | ny = grid2_dims(2) |
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| 311 | |
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| 312 | DO n=1,grid2_size |
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| 313 | |
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| 314 | !*** find N,S and NE points to this grid point |
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| 315 | |
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| 316 | j = (n - 1)/nx +1 |
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| 317 | i = n - (j-1)*nx |
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| 318 | |
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| 319 | IF (i < nx) THEN |
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| 320 | ip1 = i + 1 |
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| 321 | ELSE |
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| 322 | !*** assume cyclic |
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| 323 | ip1 = 1 |
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| 324 | !*** but if it is not, correct |
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| 325 | e_add = (j - 1)*nx + ip1 |
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| 326 | IF (ABS(grid2_center_lat(e_add) - & |
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| 327 | grid2_center_lat(n )) > pih) THEN |
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| 328 | ip1 = i |
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| 329 | ENDIF |
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| 330 | ENDIF |
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| 331 | |
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| 332 | IF (j < ny) THEN |
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| 333 | jp1 = j+1 |
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| 334 | ELSE |
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| 335 | !*** assume cyclic |
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| 336 | jp1 = 1 |
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| 337 | !*** but if it is not, correct |
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| 338 | n_add = (jp1 - 1)*nx + i |
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| 339 | IF (ABS(grid2_center_lat(n_add) - & |
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| 340 | grid2_center_lat(n )) > pih) THEN |
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| 341 | jp1 = j |
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| 342 | ENDIF |
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| 343 | ENDIF |
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| 344 | |
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| 345 | n_add = (jp1 - 1)*nx + i |
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| 346 | e_add = (j - 1)*nx + ip1 |
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| 347 | ne_add = (jp1 - 1)*nx + ip1 |
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| 348 | |
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| 349 | !*** find N,S and NE lat/lon coords and check bounding box |
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| 350 | |
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| 351 | tmp_lats(1) = grid2_center_lat(n) |
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| 352 | tmp_lats(2) = grid2_center_lat(e_add) |
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| 353 | tmp_lats(3) = grid2_center_lat(ne_add) |
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| 354 | tmp_lats(4) = grid2_center_lat(n_add) |
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| 355 | |
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| 356 | tmp_lons(1) = grid2_center_lon(n) |
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| 357 | tmp_lons(2) = grid2_center_lon(e_add) |
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| 358 | tmp_lons(3) = grid2_center_lon(ne_add) |
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| 359 | tmp_lons(4) = grid2_center_lon(n_add) |
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| 360 | |
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| 361 | grid2_bound_box(1,n) = MINVAL(tmp_lats) |
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| 362 | grid2_bound_box(2,n) = MAXVAL(tmp_lats) |
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| 363 | grid2_bound_box(3,n) = MINVAL(tmp_lons) |
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| 364 | grid2_bound_box(4,n) = MAXVAL(tmp_lons) |
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| 365 | END DO |
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| 366 | ! |
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| 367 | ! |
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| 368 | ! |
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| 369 | WHERE (ABS(grid1_bound_box(4,:) - grid1_bound_box(3,:)) > pi) |
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| 370 | grid1_bound_box(3,:) = zero |
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| 371 | grid1_bound_box(4,:) = pi2 |
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| 372 | END WHERE |
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| 373 | |
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| 374 | WHERE (ABS(grid2_bound_box(4,:) - grid2_bound_box(3,:)) > pi) |
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| 375 | grid2_bound_box(3,:) = zero |
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| 376 | grid2_bound_box(4,:) = pi2 |
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| 377 | END WHERE |
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| 378 | |
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| 379 | !*** |
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| 380 | !*** try to check for cells that overlap poles |
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| 381 | !*** |
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| 382 | |
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| 383 | WHERE (grid1_center_lat > grid1_bound_box(2,:)) & |
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| 384 | grid1_bound_box(2,:) = pih |
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| 385 | |
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| 386 | WHERE (grid1_center_lat < grid1_bound_box(1,:)) & |
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| 387 | grid1_bound_box(1,:) = -pih |
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| 388 | |
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| 389 | WHERE (grid2_center_lat > grid2_bound_box(2,:)) & |
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| 390 | grid2_bound_box(2,:) = pih |
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| 391 | |
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| 392 | WHERE (grid2_center_lat < grid2_bound_box(1,:)) & |
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| 393 | grid2_bound_box(1,:) = -pih |
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| 394 | |
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| 395 | !----------------------------------------------------------------------- |
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| 396 | ! set up and assign address ranges to search bins in order to |
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| 397 | ! further restrict later searches |
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| 398 | !----------------------------------------------------------------------- |
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| 399 | |
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| 400 | ALLOCATE(bin_addr1(2,num_srch_bins)) |
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| 401 | ALLOCATE(bin_addr2(2,num_srch_bins)) |
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| 402 | ALLOCATE(bin_lats (2,num_srch_bins)) |
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| 403 | ALLOCATE(bin_lons (2,num_srch_bins)) |
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| 404 | |
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| 405 | dlat = pi/num_srch_bins |
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| 406 | |
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| 407 | DO n=1,num_srch_bins |
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| 408 | bin_lats(1,n) = (n-1)*dlat - pih |
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| 409 | bin_lats(2,n) = n*dlat - pih |
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| 410 | bin_lons(1,n) = zero |
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| 411 | bin_lons(2,n) = pi2 |
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| 412 | bin_addr1(1,n) = grid1_size + 1 |
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| 413 | bin_addr1(2,n) = 0 |
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| 414 | bin_addr2(1,n) = grid2_size + 1 |
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| 415 | bin_addr2(2,n) = 0 |
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| 416 | END DO |
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| 417 | |
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| 418 | DO nele=1,grid1_size |
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| 419 | DO n=1,num_srch_bins |
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| 420 | IF (grid1_bound_box(1,nele) <= bin_lats(2,n) .AND. & |
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| 421 | grid1_bound_box(2,nele) >= bin_lats(1,n)) THEN |
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| 422 | bin_addr1(1,n) = MIN(nele,bin_addr1(1,n)) |
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| 423 | bin_addr1(2,n) = MAX(nele,bin_addr1(2,n)) |
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| 424 | ENDIF |
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| 425 | END DO |
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| 426 | END DO |
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| 427 | |
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| 428 | DO nele=1,grid2_size |
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| 429 | DO n=1,num_srch_bins |
|---|
| 430 | IF (grid2_bound_box(1,nele) <= bin_lats(2,n) .AND. & |
|---|
| 431 | grid2_bound_box(2,nele) >= bin_lats(1,n)) THEN |
|---|
| 432 | bin_addr2(1,n) = MIN(nele,bin_addr2(1,n)) |
|---|
| 433 | bin_addr2(2,n) = MAX(nele,bin_addr2(2,n)) |
|---|
| 434 | ENDIF |
|---|
| 435 | END DO |
|---|
| 436 | END DO |
|---|
| 437 | ! |
|---|
| 438 | CALL init_remap_vars |
|---|
| 439 | CALL remap_bilin |
|---|
| 440 | |
|---|
| 441 | ALLOCATE(remap_matrix(SIZE(wts_map1,1),SIZE(wts_map1,2)), & |
|---|
| 442 | source_add(SIZE(grid1_add_map1)), & |
|---|
| 443 | destination_add(SIZE(grid2_add_map1))) |
|---|
| 444 | |
|---|
| 445 | DO j = 1,SIZE(wts_map1,2) |
|---|
| 446 | DO i = 1,SIZE(wts_map1,1) |
|---|
| 447 | |
|---|
| 448 | remap_matrix(i,j) = wts_map1(i,j) |
|---|
| 449 | |
|---|
| 450 | END DO |
|---|
| 451 | END DO |
|---|
| 452 | |
|---|
| 453 | |
|---|
| 454 | source_add(:) = grid1_add_map1(:) |
|---|
| 455 | destination_add(:) = grid2_add_map1(:) |
|---|
| 456 | ! |
|---|
| 457 | WHERE(destination_add == 0) |
|---|
| 458 | destination_add = 1 |
|---|
| 459 | END WHERE |
|---|
| 460 | |
|---|
| 461 | WHERE(source_add == 0) |
|---|
| 462 | source_add = 1 |
|---|
| 463 | END WHERE |
|---|
| 464 | ! |
|---|
| 465 | !DEALLOCATE(grid1_bound_box,grid2_bound_box,grid1_center_lat,grid1_center_lon) |
|---|
| 466 | !DEALLOCATE(grid2_center_lat,grid2_center_lon,grid2_add_map1,grid1_add_map1,wts_map1) |
|---|
| 467 | !DEALLOCATE(grid1_frac,grid2_frac,grid1_dims,grid2_dims,grid2_mask,imask) |
|---|
| 468 | !DEALLOCATE(bin_addr1,bin_addr2,bin_lats,bin_lons) |
|---|
| 469 | !DEALLOCATE(grid1_mask) |
|---|
| 470 | ! |
|---|
| 471 | !----------------------------------------------------------------------- |
|---|
| 472 | |
|---|
| 473 | END SUBROUTINE get_remap_matrix |
|---|
| 474 | |
|---|
| 475 | |
|---|
| 476 | |
|---|
| 477 | |
|---|
| 478 | |
|---|
| 479 | |
|---|
| 480 | |
|---|
| 481 | |
|---|
| 482 | |
|---|
| 483 | |
|---|
| 484 | |
|---|
| 485 | |
|---|
| 486 | |
|---|
| 487 | |
|---|
| 488 | |
|---|
| 489 | |
|---|
| 490 | |
|---|
| 491 | |
|---|
| 492 | |
|---|
| 493 | |
|---|
| 494 | |
|---|
| 495 | |
|---|
| 496 | |
|---|
| 497 | |
|---|
| 498 | !*********************************************************************** |
|---|
| 499 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
|---|
| 500 | !************************************************************************ |
|---|
| 501 | ! SUBROUTINE REMAP_BILINEAR |
|---|
| 502 | !************************************************************************ |
|---|
| 503 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
|---|
| 504 | |
|---|
| 505 | SUBROUTINE remap_bilin |
|---|
| 506 | |
|---|
| 507 | !----------------------------------------------------------------------- |
|---|
| 508 | ! this routine computes the weights for a bilinear interpolation. |
|---|
| 509 | !----------------------------------------------------------------------- |
|---|
| 510 | |
|---|
| 511 | !----------------------------------------------------------------------- |
|---|
| 512 | ! local variables |
|---|
| 513 | !----------------------------------------------------------------------- |
|---|
| 514 | |
|---|
| 515 | INTEGER :: n,icount,dst_add,iter,nmap,nbmasked |
|---|
| 516 | ! |
|---|
| 517 | ! address for the four source points |
|---|
| 518 | ! |
|---|
| 519 | INTEGER, DIMENSION(4) :: src_add,involved_pts |
|---|
| 520 | INTEGER, DIMENSION(1) :: minlon |
|---|
| 521 | INTEGER, DIMENSION(1) :: minlat |
|---|
| 522 | REAL*8, DIMENSION(4) :: distx,disty |
|---|
| 523 | REAL*8 :: normalize |
|---|
| 524 | ! |
|---|
| 525 | ! latitudes longitudes of four bilinear corners |
|---|
| 526 | ! |
|---|
| 527 | REAL*8, DIMENSION(4) :: src_lats,src_lons |
|---|
| 528 | ! |
|---|
| 529 | ! bilinear weights for four corners |
|---|
| 530 | ! |
|---|
| 531 | REAL*8, DIMENSION(4) :: wgts |
|---|
| 532 | ! |
|---|
| 533 | REAL*8 :: & |
|---|
| 534 | plat, plon, & ! lat/lon coords of destination point |
|---|
| 535 | iguess, jguess, & ! current guess for bilinear coordinate |
|---|
| 536 | thguess, phguess, & ! current guess for lat/lon coordinate |
|---|
| 537 | deli, delj, & ! corrections to i,j |
|---|
| 538 | dth1, dth2, dth3, & ! some latitude differences |
|---|
| 539 | dph1, dph2, dph3, & ! some longitude differences |
|---|
| 540 | dthp, dphp, & ! difference between point and sw corner |
|---|
| 541 | mat1, mat2, mat3, mat4, & ! matrix elements |
|---|
| 542 | determinant, & ! matrix determinant |
|---|
| 543 | sum_wgts ! sum of weights for normalization |
|---|
| 544 | |
|---|
| 545 | INTEGER lastsrc_add |
|---|
| 546 | REAL*8,DIMENSION(:),ALLOCATABLE :: cos_grid1_center_lat |
|---|
| 547 | REAL*8,DIMENSION(:),ALLOCATABLE :: cos_grid1_center_lon |
|---|
| 548 | REAL*8,DIMENSION(:),ALLOCATABLE :: sin_grid1_center_lat |
|---|
| 549 | REAL*8,DIMENSION(:),ALLOCATABLE :: sin_grid1_center_lon |
|---|
| 550 | INTEGER :: i |
|---|
| 551 | ! |
|---|
| 552 | grid2_mask = .TRUE. |
|---|
| 553 | ! |
|---|
| 554 | ! |
|---|
| 555 | nmap = 1 |
|---|
| 556 | ! |
|---|
| 557 | !*** |
|---|
| 558 | !*** loop over destination grid |
|---|
| 559 | !*** |
|---|
| 560 | ! print*,'grid2_size =',grid2_size |
|---|
| 561 | ! |
|---|
| 562 | lastsrc_add=1 |
|---|
| 563 | ! |
|---|
| 564 | Allocate(cos_grid1_center_lat(size(grid1_center_lat))) |
|---|
| 565 | Allocate(sin_grid1_center_lat(size(grid1_center_lat))) |
|---|
| 566 | Allocate(cos_grid1_center_lon(size(grid1_center_lon))) |
|---|
| 567 | Allocate(sin_grid1_center_lon(size(grid1_center_lon))) |
|---|
| 568 | |
|---|
| 569 | do i=1,size(grid1_center_lat) |
|---|
| 570 | cos_grid1_center_lat(i)=cos(grid1_center_lat(i)) |
|---|
| 571 | sin_grid1_center_lat(i)=sin(grid1_center_lat(i)) |
|---|
| 572 | ENDDO |
|---|
| 573 | |
|---|
| 574 | do i=1,size(grid1_center_lon) |
|---|
| 575 | cos_grid1_center_lon(i)=cos(grid1_center_lon(i)) |
|---|
| 576 | sin_grid1_center_lon(i)=sin(grid1_center_lon(i)) |
|---|
| 577 | ENDDO |
|---|
| 578 | |
|---|
| 579 | grid_loop1: DO dst_add = 1, grid2_size |
|---|
| 580 | |
|---|
| 581 | IF (.NOT. grid2_mask(dst_add)) CYCLE grid_loop1 |
|---|
| 582 | ! |
|---|
| 583 | plat = grid2_center_lat(dst_add) |
|---|
| 584 | plon = grid2_center_lon(dst_add) |
|---|
| 585 | !*** |
|---|
| 586 | !*** find nearest square of grid points on source grid |
|---|
| 587 | !*** |
|---|
| 588 | CALL grid_search_bilin(src_add, src_lats, src_lons, & |
|---|
| 589 | plat, plon, grid1_dims, & |
|---|
| 590 | grid1_center_lat, cos_grid1_center_lat, sin_grid1_center_lat, & |
|---|
| 591 | grid1_center_lon, cos_grid1_center_lon, sin_grid1_center_lon, & |
|---|
| 592 | grid1_bound_box, bin_addr1, bin_addr2,lastsrc_add) |
|---|
| 593 | !*** |
|---|
| 594 | !*** check to see if points are land points |
|---|
| 595 | !*** |
|---|
| 596 | ! |
|---|
| 597 | IF (src_add(1) > 0) THEN |
|---|
| 598 | ! |
|---|
| 599 | DO n=1,4 |
|---|
| 600 | ! if(.not. grid1_mask(src_add(n))) nbmasked = nbmasked + 1 |
|---|
| 601 | IF(.NOT. grid1_mask(src_add(n))) src_add(1) = 0 |
|---|
| 602 | END DO |
|---|
| 603 | ! |
|---|
| 604 | ENDIF |
|---|
| 605 | ! |
|---|
| 606 | ! |
|---|
| 607 | |
|---|
| 608 | !*** |
|---|
| 609 | !*** if point found, find local i,j coordinates for weights |
|---|
| 610 | !*** |
|---|
| 611 | IF (src_add(1) > 0) THEN |
|---|
| 612 | grid2_frac(dst_add) = one |
|---|
| 613 | !*** |
|---|
| 614 | !*** iterate to find i,j for bilinear approximation |
|---|
| 615 | !*** |
|---|
| 616 | dth1 = src_lats(2) - src_lats(1) |
|---|
| 617 | dth2 = src_lats(4) - src_lats(1) |
|---|
| 618 | dth3 = src_lats(3) - src_lats(2) - dth2 |
|---|
| 619 | |
|---|
| 620 | dph1 = src_lons(2) - src_lons(1) |
|---|
| 621 | dph2 = src_lons(4) - src_lons(1) |
|---|
| 622 | dph3 = src_lons(3) - src_lons(2) |
|---|
| 623 | |
|---|
| 624 | IF (dph1 > three*pih) dph1 = dph1 - pi2 |
|---|
| 625 | IF (dph2 > three*pih) dph2 = dph2 - pi2 |
|---|
| 626 | IF (dph3 > three*pih) dph3 = dph3 - pi2 |
|---|
| 627 | IF (dph1 < -three*pih) dph1 = dph1 + pi2 |
|---|
| 628 | IF (dph2 < -three*pih) dph2 = dph2 + pi2 |
|---|
| 629 | IF (dph3 < -three*pih) dph3 = dph3 + pi2 |
|---|
| 630 | |
|---|
| 631 | dph3 = dph3 - dph2 |
|---|
| 632 | |
|---|
| 633 | iguess = half |
|---|
| 634 | jguess = half |
|---|
| 635 | |
|---|
| 636 | iter_loop1: DO iter=1,max_iter |
|---|
| 637 | |
|---|
| 638 | dthp = plat - src_lats(1) - dth1*iguess - & |
|---|
| 639 | dth2*jguess - dth3*iguess*jguess |
|---|
| 640 | dphp = plon - src_lons(1) |
|---|
| 641 | |
|---|
| 642 | IF (dphp > three*pih) dphp = dphp - pi2 |
|---|
| 643 | IF (dphp < -three*pih) dphp = dphp + pi2 |
|---|
| 644 | |
|---|
| 645 | dphp = dphp - dph1*iguess - dph2*jguess - & |
|---|
| 646 | dph3*iguess*jguess |
|---|
| 647 | |
|---|
| 648 | mat1 = dth1 + dth3*jguess |
|---|
| 649 | mat2 = dth2 + dth3*iguess |
|---|
| 650 | mat3 = dph1 + dph3*jguess |
|---|
| 651 | mat4 = dph2 + dph3*iguess |
|---|
| 652 | |
|---|
| 653 | determinant = mat1*mat4 - mat2*mat3 |
|---|
| 654 | |
|---|
| 655 | deli = (dthp*mat4 - mat2*dphp)/determinant |
|---|
| 656 | delj = (mat1*dphp - dthp*mat3)/determinant |
|---|
| 657 | |
|---|
| 658 | IF (ABS(deli) < converge .AND. & |
|---|
| 659 | ABS(delj) < converge) EXIT iter_loop1 |
|---|
| 660 | |
|---|
| 661 | iguess = iguess + deli |
|---|
| 662 | jguess = jguess + delj |
|---|
| 663 | |
|---|
| 664 | END DO iter_loop1 |
|---|
| 665 | |
|---|
| 666 | IF (iter <= max_iter) THEN |
|---|
| 667 | |
|---|
| 668 | !*** |
|---|
| 669 | !*** successfully found i,j - compute weights |
|---|
| 670 | !*** |
|---|
| 671 | |
|---|
| 672 | wgts(1) = (one-iguess)*(one-jguess) |
|---|
| 673 | wgts(2) = iguess*(one-jguess) |
|---|
| 674 | wgts(3) = iguess*jguess |
|---|
| 675 | wgts(4) = (one-iguess)*jguess |
|---|
| 676 | ! |
|---|
| 677 | ! |
|---|
| 678 | CALL store_link_bilin(dst_add, src_add, wgts, nmap) |
|---|
| 679 | |
|---|
| 680 | ELSE |
|---|
| 681 | PRINT *,'Point coords: ',plat,plon |
|---|
| 682 | PRINT *,'Dest grid lats: ',src_lats |
|---|
| 683 | PRINT *,'Dest grid lons: ',src_lons |
|---|
| 684 | PRINT *,'Dest grid addresses: ',src_add |
|---|
| 685 | PRINT *,'Current i,j : ',iguess, jguess |
|---|
| 686 | STOP 'Iteration for i,j exceed max iteration count' |
|---|
| 687 | ENDIF |
|---|
| 688 | ! |
|---|
| 689 | !*** |
|---|
| 690 | !*** search for bilinear failed - use a distance-weighted |
|---|
| 691 | !*** average instead (this is typically near the pole) |
|---|
| 692 | !*** |
|---|
| 693 | ELSE IF (src_add(1) < 0) THEN |
|---|
| 694 | |
|---|
| 695 | src_add = ABS(src_add) |
|---|
| 696 | icount = 0 |
|---|
| 697 | DO n=1,4 |
|---|
| 698 | ! |
|---|
| 699 | IF (grid1_mask(src_add(n))) THEN |
|---|
| 700 | icount = icount + 1 |
|---|
| 701 | ELSE |
|---|
| 702 | src_lats(n) = zero |
|---|
| 703 | ENDIF |
|---|
| 704 | ! |
|---|
| 705 | END DO |
|---|
| 706 | |
|---|
| 707 | IF (icount > 0) THEN |
|---|
| 708 | ! |
|---|
| 709 | !*** renormalize weights |
|---|
| 710 | ! |
|---|
| 711 | sum_wgts = SUM(src_lats) |
|---|
| 712 | wgts(1) = src_lats(1)/sum_wgts |
|---|
| 713 | wgts(2) = src_lats(2)/sum_wgts |
|---|
| 714 | wgts(3) = src_lats(3)/sum_wgts |
|---|
| 715 | wgts(4) = src_lats(4)/sum_wgts |
|---|
| 716 | ! |
|---|
| 717 | grid2_frac(dst_add) = one |
|---|
| 718 | CALL store_link_bilin(dst_add, src_add, wgts, nmap) |
|---|
| 719 | ENDIF |
|---|
| 720 | |
|---|
| 721 | ! |
|---|
| 722 | ENDIF |
|---|
| 723 | END DO grid_loop1 |
|---|
| 724 | ! |
|---|
| 725 | ! Call sort_add(grid2_add_map1, grid1_add_map1, wts_map1) |
|---|
| 726 | ! |
|---|
| 727 | ! |
|---|
| 728 | !----------------------------------------------------------------------- |
|---|
| 729 | |
|---|
| 730 | deallocate(cos_grid1_center_lat) |
|---|
| 731 | deallocate(cos_grid1_center_lon) |
|---|
| 732 | deallocate(sin_grid1_center_lat) |
|---|
| 733 | deallocate(sin_grid1_center_lon) |
|---|
| 734 | END SUBROUTINE remap_bilin |
|---|
| 735 | |
|---|
| 736 | |
|---|
| 737 | |
|---|
| 738 | |
|---|
| 739 | |
|---|
| 740 | |
|---|
| 741 | |
|---|
| 742 | |
|---|
| 743 | |
|---|
| 744 | |
|---|
| 745 | |
|---|
| 746 | |
|---|
| 747 | |
|---|
| 748 | |
|---|
| 749 | |
|---|
| 750 | |
|---|
| 751 | |
|---|
| 752 | |
|---|
| 753 | !*********************************************************************** |
|---|
| 754 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
|---|
| 755 | !************************************************************************ |
|---|
| 756 | ! SUBROUTINE GRID_SEARCH_BILIN |
|---|
| 757 | !************************************************************************ |
|---|
| 758 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
|---|
| 759 | ! |
|---|
| 760 | SUBROUTINE grid_search_bilin(src_add, src_lats, src_lons, & |
|---|
| 761 | plat, plon, src_grid_dims, & |
|---|
| 762 | src_center_lat, cos_src_center_lat, sin_src_center_lat, & |
|---|
| 763 | src_center_lon, cos_src_center_lon, sin_src_center_lon,& |
|---|
| 764 | src_grid_bound_box, & |
|---|
| 765 | src_bin_add, dst_bin_add,lastsrc_add) |
|---|
| 766 | |
|---|
| 767 | !----------------------------------------------------------------------- |
|---|
| 768 | ! |
|---|
| 769 | ! this routine finds the location of the search point plat, plon |
|---|
| 770 | ! in the source grid and returns the corners needed for a bilinear |
|---|
| 771 | ! interpolation. |
|---|
| 772 | ! |
|---|
| 773 | !----------------------------------------------------------------------- |
|---|
| 774 | |
|---|
| 775 | !----------------------------------------------------------------------- |
|---|
| 776 | ! output variables |
|---|
| 777 | !----------------------------------------------------------------------- |
|---|
| 778 | ! |
|---|
| 779 | ! address of each corner point enclosing P |
|---|
| 780 | ! |
|---|
| 781 | INTEGER,DIMENSION(4) :: src_add |
|---|
| 782 | REAL*8,DIMENSION(4) :: src_lats,src_lons |
|---|
| 783 | ! |
|---|
| 784 | !----------------------------------------------------------------------- |
|---|
| 785 | ! input variables |
|---|
| 786 | !----------------------------------------------------------------------- |
|---|
| 787 | ! |
|---|
| 788 | ! latitude, longitude of the search point |
|---|
| 789 | ! |
|---|
| 790 | REAL*8, INTENT(in) :: plat,plon |
|---|
| 791 | ! |
|---|
| 792 | ! size of each src grid dimension |
|---|
| 793 | ! |
|---|
| 794 | INTEGER, DIMENSION(2), INTENT(in) :: src_grid_dims |
|---|
| 795 | ! |
|---|
| 796 | ! latitude, longitude of each src grid center |
|---|
| 797 | ! |
|---|
| 798 | REAL*8, DIMENSION(:), INTENT(in) :: src_center_lat,src_center_lon |
|---|
| 799 | REAL*8, DIMENSION(:), INTENT(in) :: cos_src_center_lat |
|---|
| 800 | REAL*8, DIMENSION(:), INTENT(in) :: sin_src_center_lat |
|---|
| 801 | REAL*8, DIMENSION(:), INTENT(in) :: cos_src_center_lon |
|---|
| 802 | REAL*8, DIMENSION(:), INTENT(in) :: sin_src_center_lon |
|---|
| 803 | ! |
|---|
| 804 | ! bound box for source grid |
|---|
| 805 | ! |
|---|
| 806 | REAL*8, DIMENSION(:,:), INTENT(in) :: src_grid_bound_box |
|---|
| 807 | ! |
|---|
| 808 | ! latitude bins for restricting searches |
|---|
| 809 | ! |
|---|
| 810 | INTEGER, DIMENSION(:,:), INTENT(in) ::src_bin_add,dst_bin_add |
|---|
| 811 | |
|---|
| 812 | INTEGER,OPTIONAL :: lastsrc_add |
|---|
| 813 | INTEGER :: loopsrc,l1,l2 |
|---|
| 814 | ! |
|---|
| 815 | !----------------------------------------------------------------------- |
|---|
| 816 | ! local variables |
|---|
| 817 | !----------------------------------------------------------------------- |
|---|
| 818 | ! |
|---|
| 819 | INTEGER :: n,next_n,srch_add,nx, ny,min_add, max_add, & |
|---|
| 820 | i, j, jp1, ip1, n_add, e_add, ne_add |
|---|
| 821 | |
|---|
| 822 | |
|---|
| 823 | REAL*8 :: vec1_lat, vec1_lon,vec2_lat, vec2_lon, cross_product, & |
|---|
| 824 | cross_product_last,coslat_dst, sinlat_dst, coslon_dst, & |
|---|
| 825 | sinlon_dst,dist_min, distance |
|---|
| 826 | |
|---|
| 827 | !----------------------------------------------------------------------- |
|---|
| 828 | ! restrict search first using bins |
|---|
| 829 | !----------------------------------------------------------------------- |
|---|
| 830 | |
|---|
| 831 | src_add = 0 |
|---|
| 832 | |
|---|
| 833 | min_add = SIZE(src_center_lat) |
|---|
| 834 | max_add = 1 |
|---|
| 835 | DO n=1,num_srch_bins |
|---|
| 836 | IF (plat >= bin_lats(1,n) .AND. plat <= bin_lats(2,n) .AND. & |
|---|
| 837 | plon >= bin_lons(1,n) .AND. plon <= bin_lons(2,n)) THEN |
|---|
| 838 | min_add = MIN(min_add, src_bin_add(1,n)) |
|---|
| 839 | max_add = MAX(max_add, src_bin_add(2,n)) |
|---|
| 840 | ENDIF |
|---|
| 841 | END DO |
|---|
| 842 | |
|---|
| 843 | !----------------------------------------------------------------------- |
|---|
| 844 | ! now perform a more detailed search |
|---|
| 845 | !----------------------------------------------------------------------- |
|---|
| 846 | |
|---|
| 847 | nx = src_grid_dims(1) |
|---|
| 848 | ny = src_grid_dims(2) |
|---|
| 849 | |
|---|
| 850 | loopsrc=0 |
|---|
| 851 | DO WHILE (loopsrc <= max_add) |
|---|
| 852 | |
|---|
| 853 | |
|---|
| 854 | l1=MAX(min_add,lastsrc_add-loopsrc) |
|---|
| 855 | l2=MIN(max_add,lastsrc_add+loopsrc) |
|---|
| 856 | |
|---|
| 857 | loopsrc = loopsrc+1 |
|---|
| 858 | |
|---|
| 859 | srch_loop: DO srch_add = l1,l2,MAX(l2-l1,1) |
|---|
| 860 | |
|---|
| 861 | !*** first check bounding box |
|---|
| 862 | |
|---|
| 863 | IF (plat <= src_grid_bound_box(2,srch_add) .AND. & |
|---|
| 864 | plat >= src_grid_bound_box(1,srch_add) .AND. & |
|---|
| 865 | plon <= src_grid_bound_box(4,srch_add) .AND. & |
|---|
| 866 | plon >= src_grid_bound_box(3,srch_add)) THEN |
|---|
| 867 | !*** |
|---|
| 868 | !*** we are within bounding box so get really serious |
|---|
| 869 | !*** |
|---|
| 870 | !*** determine neighbor addresses |
|---|
| 871 | ! |
|---|
| 872 | j = (srch_add - 1)/nx +1 |
|---|
| 873 | i = srch_add - (j-1)*nx |
|---|
| 874 | ! |
|---|
| 875 | IF (i < nx) THEN |
|---|
| 876 | ip1 = i + 1 |
|---|
| 877 | ELSE |
|---|
| 878 | ip1 = 1 |
|---|
| 879 | ENDIF |
|---|
| 880 | ! |
|---|
| 881 | IF (j < ny) THEN |
|---|
| 882 | jp1 = j+1 |
|---|
| 883 | ELSE |
|---|
| 884 | jp1 = 1 |
|---|
| 885 | ENDIF |
|---|
| 886 | ! |
|---|
| 887 | n_add = (jp1 - 1)*nx + i |
|---|
| 888 | e_add = (j - 1)*nx + ip1 |
|---|
| 889 | ne_add = (jp1 - 1)*nx + ip1 |
|---|
| 890 | ! |
|---|
| 891 | src_lats(1) = src_center_lat(srch_add) |
|---|
| 892 | src_lats(2) = src_center_lat(e_add) |
|---|
| 893 | src_lats(3) = src_center_lat(ne_add) |
|---|
| 894 | src_lats(4) = src_center_lat(n_add) |
|---|
| 895 | ! |
|---|
| 896 | src_lons(1) = src_center_lon(srch_add) |
|---|
| 897 | src_lons(2) = src_center_lon(e_add) |
|---|
| 898 | src_lons(3) = src_center_lon(ne_add) |
|---|
| 899 | src_lons(4) = src_center_lon(n_add) |
|---|
| 900 | ! |
|---|
| 901 | !*** |
|---|
| 902 | !*** for consistency, we must make sure all lons are in |
|---|
| 903 | !*** same 2pi interval |
|---|
| 904 | !*** |
|---|
| 905 | ! |
|---|
| 906 | vec1_lon = src_lons(1) - plon |
|---|
| 907 | IF (vec1_lon > pi) THEN |
|---|
| 908 | src_lons(1) = src_lons(1) - pi2 |
|---|
| 909 | ELSE IF (vec1_lon < -pi) THEN |
|---|
| 910 | src_lons(1) = src_lons(1) + pi2 |
|---|
| 911 | ENDIF |
|---|
| 912 | DO n=2,4 |
|---|
| 913 | vec1_lon = src_lons(n) - src_lons(1) |
|---|
| 914 | IF (vec1_lon > pi) THEN |
|---|
| 915 | src_lons(n) = src_lons(n) - pi2 |
|---|
| 916 | ELSE IF (vec1_lon < -pi) THEN |
|---|
| 917 | src_lons(n) = src_lons(n) + pi2 |
|---|
| 918 | ENDIF |
|---|
| 919 | END DO |
|---|
| 920 | ! |
|---|
| 921 | corner_loop: DO n=1,4 |
|---|
| 922 | next_n = MOD(n,4) + 1 |
|---|
| 923 | !*** |
|---|
| 924 | !*** here we take the cross product of the vector making |
|---|
| 925 | !*** up each box side with the vector formed by the vertex |
|---|
| 926 | !*** and search point. if all the cross products are |
|---|
| 927 | !*** positive, the point is contained in the box. |
|---|
| 928 | !*** |
|---|
| 929 | vec1_lat = src_lats(next_n) - src_lats(n) |
|---|
| 930 | vec1_lon = src_lons(next_n) - src_lons(n) |
|---|
| 931 | vec2_lat = plat - src_lats(n) |
|---|
| 932 | vec2_lon = plon - src_lons(n) |
|---|
| 933 | !*** |
|---|
| 934 | !*** check for 0,2pi crossings |
|---|
| 935 | !*** |
|---|
| 936 | IF (vec1_lon > three*pih) THEN |
|---|
| 937 | vec1_lon = vec1_lon - pi2 |
|---|
| 938 | ELSE IF (vec1_lon < -three*pih) THEN |
|---|
| 939 | vec1_lon = vec1_lon + pi2 |
|---|
| 940 | ENDIF |
|---|
| 941 | IF (vec2_lon > three*pih) THEN |
|---|
| 942 | vec2_lon = vec2_lon - pi2 |
|---|
| 943 | ELSE IF (vec2_lon < -three*pih) THEN |
|---|
| 944 | vec2_lon = vec2_lon + pi2 |
|---|
| 945 | ENDIF |
|---|
| 946 | ! |
|---|
| 947 | cross_product = vec1_lon*vec2_lat - vec2_lon*vec1_lat |
|---|
| 948 | ! |
|---|
| 949 | !*** |
|---|
| 950 | !*** if cross product is less than zero, this cell |
|---|
| 951 | !*** doesn't work |
|---|
| 952 | !*** |
|---|
| 953 | IF (n == 1) cross_product_last = cross_product |
|---|
| 954 | IF (cross_product*cross_product_last < zero) & |
|---|
| 955 | EXIT corner_loop |
|---|
| 956 | cross_product_last = cross_product |
|---|
| 957 | ! |
|---|
| 958 | END DO corner_loop |
|---|
| 959 | !*** |
|---|
| 960 | !*** if cross products all same sign, we found the location |
|---|
| 961 | !*** |
|---|
| 962 | IF (n > 4) THEN |
|---|
| 963 | src_add(1) = srch_add |
|---|
| 964 | src_add(2) = e_add |
|---|
| 965 | src_add(3) = ne_add |
|---|
| 966 | src_add(4) = n_add |
|---|
| 967 | ! |
|---|
| 968 | lastsrc_add = srch_add |
|---|
| 969 | RETURN |
|---|
| 970 | ENDIF |
|---|
| 971 | !*** |
|---|
| 972 | !*** otherwise move on to next cell |
|---|
| 973 | !*** |
|---|
| 974 | ENDIF !bounding box check |
|---|
| 975 | END DO srch_loop |
|---|
| 976 | |
|---|
| 977 | |
|---|
| 978 | ENDDO |
|---|
| 979 | |
|---|
| 980 | |
|---|
| 981 | !*** |
|---|
| 982 | !*** if no cell found, point is likely either in a box that |
|---|
| 983 | !*** straddles either pole or is outside the grid. fall back |
|---|
| 984 | !*** to a distance-weighted average of the four closest |
|---|
| 985 | !*** points. go ahead and compute weights here, but store |
|---|
| 986 | !*** in src_lats and return -add to prevent the parent |
|---|
| 987 | !*** routine from computing bilinear weights |
|---|
| 988 | !*** |
|---|
| 989 | !print *,'Could not find location for ',plat,plon |
|---|
| 990 | !print *,'Using nearest-neighbor average for this point' |
|---|
| 991 | ! |
|---|
| 992 | coslat_dst = COS(plat) |
|---|
| 993 | sinlat_dst = SIN(plat) |
|---|
| 994 | coslon_dst = COS(plon) |
|---|
| 995 | sinlon_dst = SIN(plon) |
|---|
| 996 | ! |
|---|
| 997 | dist_min = bignum |
|---|
| 998 | src_lats = bignum |
|---|
| 999 | DO srch_add = min_add,max_add |
|---|
| 1000 | ! distance = ACOS(coslat_dst*COS(src_center_lat(srch_add))* & |
|---|
| 1001 | ! (coslon_dst*COS(src_center_lon(srch_add)) + & |
|---|
| 1002 | ! sinlon_dst*SIN(src_center_lon(srch_add)))+ & |
|---|
| 1003 | ! sinlat_dst*SIN(src_center_lat(srch_add))) |
|---|
| 1004 | |
|---|
| 1005 | distance = ACOS(coslat_dst*cos_src_center_lat(srch_add)* & |
|---|
| 1006 | (coslon_dst*cos_src_center_lon(srch_add) + & |
|---|
| 1007 | sinlon_dst*sin_src_center_lon(srch_add))+ & |
|---|
| 1008 | sinlat_dst*sin_src_center_lat(srch_add)) |
|---|
| 1009 | |
|---|
| 1010 | IF (distance < dist_min) THEN |
|---|
| 1011 | sort_loop: DO n=1,4 |
|---|
| 1012 | IF (distance < src_lats(n)) THEN |
|---|
| 1013 | DO i=4,n+1,-1 |
|---|
| 1014 | src_add (i) = src_add (i-1) |
|---|
| 1015 | src_lats(i) = src_lats(i-1) |
|---|
| 1016 | END DO |
|---|
| 1017 | src_add (n) = -srch_add |
|---|
| 1018 | src_lats(n) = distance |
|---|
| 1019 | dist_min = src_lats(4) |
|---|
| 1020 | EXIT sort_loop |
|---|
| 1021 | ENDIF |
|---|
| 1022 | END DO sort_loop |
|---|
| 1023 | ENDIF |
|---|
| 1024 | END DO |
|---|
| 1025 | ! |
|---|
| 1026 | src_lons = one/(src_lats + tiny) |
|---|
| 1027 | distance = SUM(src_lons) |
|---|
| 1028 | src_lats = src_lons/distance |
|---|
| 1029 | |
|---|
| 1030 | !----------------------------------------------------------------------- |
|---|
| 1031 | |
|---|
| 1032 | END SUBROUTINE grid_search_bilin |
|---|
| 1033 | |
|---|
| 1034 | |
|---|
| 1035 | !*********************************************************************** |
|---|
| 1036 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
|---|
| 1037 | !************************************************************************ |
|---|
| 1038 | ! SUBROUTINE STORE_LINK_BILIN |
|---|
| 1039 | !************************************************************************ |
|---|
| 1040 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
|---|
| 1041 | |
|---|
| 1042 | SUBROUTINE store_link_bilin(dst_add, src_add, weights, nmap) |
|---|
| 1043 | |
|---|
| 1044 | !----------------------------------------------------------------------- |
|---|
| 1045 | ! this routine stores the address and weight for four links |
|---|
| 1046 | ! associated with one destination point in the appropriate address |
|---|
| 1047 | ! and weight arrays and resizes those arrays if necessary. |
|---|
| 1048 | !----------------------------------------------------------------------- |
|---|
| 1049 | |
|---|
| 1050 | !----------------------------------------------------------------------- |
|---|
| 1051 | ! input variables |
|---|
| 1052 | !----------------------------------------------------------------------- |
|---|
| 1053 | ! |
|---|
| 1054 | INTEGER :: dst_add,nmap |
|---|
| 1055 | ! |
|---|
| 1056 | INTEGER, DIMENSION(4) :: src_add |
|---|
| 1057 | ! |
|---|
| 1058 | REAL*8, DIMENSION(4) :: weights |
|---|
| 1059 | |
|---|
| 1060 | !----------------------------------------------------------------------- |
|---|
| 1061 | ! |
|---|
| 1062 | ! local variables |
|---|
| 1063 | ! |
|---|
| 1064 | !----------------------------------------------------------------------- |
|---|
| 1065 | |
|---|
| 1066 | INTEGER :: n,num_links_old |
|---|
| 1067 | |
|---|
| 1068 | !----------------------------------------------------------------------- |
|---|
| 1069 | ! increment number of links and check to see if remap arrays need |
|---|
| 1070 | ! to be increased to accomodate the new link. then store the |
|---|
| 1071 | ! link. |
|---|
| 1072 | !----------------------------------------------------------------------- |
|---|
| 1073 | |
|---|
| 1074 | num_links_old = num_links_map1 |
|---|
| 1075 | num_links_map1 = num_links_old + 4 |
|---|
| 1076 | |
|---|
| 1077 | IF (num_links_map1 > max_links_map1) & |
|---|
| 1078 | CALL resize_remap_vars(1,resize_increment) |
|---|
| 1079 | |
|---|
| 1080 | DO n=1,4 |
|---|
| 1081 | grid1_add_map1(num_links_old+n) = src_add(n) |
|---|
| 1082 | grid2_add_map1(num_links_old+n) = dst_add |
|---|
| 1083 | wts_map1 (1,num_links_old+n) = weights(n) |
|---|
| 1084 | END DO |
|---|
| 1085 | |
|---|
| 1086 | !----------------------------------------------------------------------- |
|---|
| 1087 | |
|---|
| 1088 | END SUBROUTINE store_link_bilin |
|---|
| 1089 | |
|---|
| 1090 | |
|---|
| 1091 | |
|---|
| 1092 | |
|---|
| 1093 | |
|---|
| 1094 | |
|---|
| 1095 | |
|---|
| 1096 | |
|---|
| 1097 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
|---|
| 1098 | !************************************************************************ |
|---|
| 1099 | ! SUBROUTINE INIT_REMAP_VARS |
|---|
| 1100 | !************************************************************************ |
|---|
| 1101 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
|---|
| 1102 | ! |
|---|
| 1103 | SUBROUTINE init_remap_vars |
|---|
| 1104 | |
|---|
| 1105 | !----------------------------------------------------------------------- |
|---|
| 1106 | ! |
|---|
| 1107 | ! this routine initializes some variables and provides an initial |
|---|
| 1108 | ! allocation of arrays (fairly large so frequent resizing |
|---|
| 1109 | ! unnecessary). |
|---|
| 1110 | ! |
|---|
| 1111 | !----------------------------------------------------------------------- |
|---|
| 1112 | |
|---|
| 1113 | !----------------------------------------------------------------------- |
|---|
| 1114 | ! determine the number of weights |
|---|
| 1115 | !----------------------------------------------------------------------- |
|---|
| 1116 | num_wts = 1 ! bilinear interpolation |
|---|
| 1117 | !----------------------------------------------------------------------- |
|---|
| 1118 | ! initialize num_links and set max_links to four times the largest |
|---|
| 1119 | ! of the destination grid sizes initially (can be changed later). |
|---|
| 1120 | ! set a default resize increment to increase the size of link |
|---|
| 1121 | ! arrays if the number of links exceeds the initial size |
|---|
| 1122 | !----------------------------------------------------------------------- |
|---|
| 1123 | |
|---|
| 1124 | num_links_map1 = 0 |
|---|
| 1125 | max_links_map1 = 4*grid2_size |
|---|
| 1126 | IF (num_maps > 1) THEN |
|---|
| 1127 | num_links_map2 = 0 |
|---|
| 1128 | max_links_map1 = MAX(4*grid1_size,4*grid2_size) |
|---|
| 1129 | max_links_map2 = max_links_map1 |
|---|
| 1130 | ENDIF |
|---|
| 1131 | |
|---|
| 1132 | resize_increment = 0.1*MAX(grid1_size,grid2_size) |
|---|
| 1133 | |
|---|
| 1134 | !----------------------------------------------------------------------- |
|---|
| 1135 | ! allocate address and weight arrays for mapping 1 |
|---|
| 1136 | !----------------------------------------------------------------------- |
|---|
| 1137 | |
|---|
| 1138 | ALLOCATE (grid1_add_map1(max_links_map1), & |
|---|
| 1139 | grid2_add_map1(max_links_map1), & |
|---|
| 1140 | wts_map1(num_wts, max_links_map1)) |
|---|
| 1141 | |
|---|
| 1142 | grid1_add_map1 = 0. |
|---|
| 1143 | grid2_add_map1 = 0. |
|---|
| 1144 | wts_map1 = 0. |
|---|
| 1145 | |
|---|
| 1146 | !----------------------------------------------------------------------- |
|---|
| 1147 | |
|---|
| 1148 | END SUBROUTINE init_remap_vars |
|---|
| 1149 | |
|---|
| 1150 | |
|---|
| 1151 | |
|---|
| 1152 | |
|---|
| 1153 | |
|---|
| 1154 | |
|---|
| 1155 | |
|---|
| 1156 | |
|---|
| 1157 | |
|---|
| 1158 | |
|---|
| 1159 | |
|---|
| 1160 | |
|---|
| 1161 | |
|---|
| 1162 | |
|---|
| 1163 | !*********************************************************************** |
|---|
| 1164 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
|---|
| 1165 | !************************************************************************ |
|---|
| 1166 | ! SUBROUTINE RESIZE_REMAP_VAR |
|---|
| 1167 | !************************************************************************ |
|---|
| 1168 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
|---|
| 1169 | |
|---|
| 1170 | SUBROUTINE resize_remap_vars(nmap, increment) |
|---|
| 1171 | |
|---|
| 1172 | !----------------------------------------------------------------------- |
|---|
| 1173 | ! this routine resizes remapping arrays by increasing(decreasing) |
|---|
| 1174 | ! the max_links by increment |
|---|
| 1175 | !----------------------------------------------------------------------- |
|---|
| 1176 | |
|---|
| 1177 | !----------------------------------------------------------------------- |
|---|
| 1178 | ! input variables |
|---|
| 1179 | !----------------------------------------------------------------------- |
|---|
| 1180 | |
|---|
| 1181 | INTEGER :: & |
|---|
| 1182 | nmap, & ! identifies which mapping array to resize |
|---|
| 1183 | increment ! the number of links to add(subtract) to arrays |
|---|
| 1184 | |
|---|
| 1185 | !----------------------------------------------------------------------- |
|---|
| 1186 | ! local variables |
|---|
| 1187 | !----------------------------------------------------------------------- |
|---|
| 1188 | |
|---|
| 1189 | INTEGER :: & |
|---|
| 1190 | ierr, & ! error flag |
|---|
| 1191 | mxlinks ! size of link arrays |
|---|
| 1192 | |
|---|
| 1193 | INTEGER, DIMENSION(:), ALLOCATABLE :: & |
|---|
| 1194 | add1_tmp, & ! temp array for resizing address arrays |
|---|
| 1195 | add2_tmp ! temp array for resizing address arrays |
|---|
| 1196 | ! |
|---|
| 1197 | ! temp array for resizing weight arrays |
|---|
| 1198 | ! |
|---|
| 1199 | REAL*8, DIMENSION(:,:), ALLOCATABLE :: wts_tmp |
|---|
| 1200 | ! |
|---|
| 1201 | !----------------------------------------------------------------------- |
|---|
| 1202 | !*** |
|---|
| 1203 | !*** allocate temporaries to hold original values |
|---|
| 1204 | !*** |
|---|
| 1205 | mxlinks = SIZE(grid1_add_map1) |
|---|
| 1206 | ALLOCATE (add1_tmp(mxlinks), add2_tmp(mxlinks), & |
|---|
| 1207 | wts_tmp(num_wts,mxlinks)) |
|---|
| 1208 | |
|---|
| 1209 | add1_tmp = grid1_add_map1 |
|---|
| 1210 | add2_tmp = grid2_add_map1 |
|---|
| 1211 | wts_tmp = wts_map1 |
|---|
| 1212 | |
|---|
| 1213 | !*** |
|---|
| 1214 | !*** deallocate originals and increment max_links then |
|---|
| 1215 | !*** reallocate arrays at new size |
|---|
| 1216 | !*** |
|---|
| 1217 | |
|---|
| 1218 | DEALLOCATE (grid1_add_map1, grid2_add_map1, wts_map1) |
|---|
| 1219 | max_links_map1 = mxlinks + increment |
|---|
| 1220 | ALLOCATE (grid1_add_map1(max_links_map1), & |
|---|
| 1221 | grid2_add_map1(max_links_map1), & |
|---|
| 1222 | wts_map1(num_wts,max_links_map1)) |
|---|
| 1223 | !*** |
|---|
| 1224 | !*** restore original values from temp arrays and |
|---|
| 1225 | !*** deallocate temps |
|---|
| 1226 | !*** |
|---|
| 1227 | mxlinks = MIN(mxlinks, max_links_map1) |
|---|
| 1228 | grid1_add_map1(1:mxlinks) = add1_tmp (1:mxlinks) |
|---|
| 1229 | grid2_add_map1(1:mxlinks) = add2_tmp (1:mxlinks) |
|---|
| 1230 | wts_map1 (:,1:mxlinks) = wts_tmp(:,1:mxlinks) |
|---|
| 1231 | DEALLOCATE(add1_tmp, add2_tmp, wts_tmp) |
|---|
| 1232 | |
|---|
| 1233 | !----------------------------------------------------------------------- |
|---|
| 1234 | ! |
|---|
| 1235 | END SUBROUTINE resize_remap_vars |
|---|
| 1236 | ! |
|---|
| 1237 | !************************************************************************ |
|---|
| 1238 | ! |
|---|
| 1239 | END MODULE bilinear_interp |
|---|
| 1240 | |
|---|
| 1241 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
|---|
| 1242 | |
|---|
