[2352] | 1 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
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| 2 | ! |
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| 3 | ! this module contains necessary routines for computing addresses |
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| 4 | ! and weights for a conservative interpolation between any two |
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| 5 | ! grids on a sphere. the weights are computed by performing line |
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| 6 | ! integrals around all overlap regions of the two grids. see |
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| 7 | ! Dukowicz and Kodis, SIAM J. Sci. Stat. Comput. 8, 305 (1987) and |
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| 8 | ! Jones, P.W. Monthly Weather Review (submitted). |
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| 9 | ! |
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| 10 | !----------------------------------------------------------------------- |
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| 11 | ! |
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[9295] | 12 | ! CVS:$Id$ |
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[2352] | 13 | ! |
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| 14 | ! Copyright (c) 1997, 1998 the Regents of the University of |
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| 15 | ! California. |
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| 16 | ! |
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| 17 | ! This software and ancillary information (herein called software) |
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| 18 | ! called SCRIP is made available under the terms described here. |
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| 19 | ! The software has been approved for release with associated |
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| 20 | ! LA-CC Number 98-45. |
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| 21 | ! |
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| 22 | ! Unless otherwise indicated, this software has been authored |
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| 23 | ! by an employee or employees of the University of California, |
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| 24 | ! operator of the Los Alamos National Laboratory under Contract |
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| 25 | ! No. W-7405-ENG-36 with the U.S. Department of Energy. The U.S. |
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| 26 | ! Government has rights to use, reproduce, and distribute this |
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| 27 | ! software. The public may copy and use this software without |
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| 28 | ! charge, provided that this Notice and any statement of authorship |
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| 29 | ! are reproduced on all copies. Neither the Government nor the |
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| 30 | ! University makes any warranty, express or implied, or assumes |
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| 31 | ! any liability or responsibility for the use of this software. |
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| 32 | ! |
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| 33 | ! If software is modified to produce derivative works, such modified |
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| 34 | ! software should be clearly marked, so as not to confuse it with |
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| 35 | ! the version available from Los Alamos National Laboratory. |
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| 36 | ! |
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| 37 | !*********************************************************************** |
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| 38 | |
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| 39 | module remap_conservative |
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| 40 | |
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| 41 | !----------------------------------------------------------------------- |
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| 42 | |
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| 43 | use kinds_mod ! defines common data types |
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| 44 | use constants ! defines common constants |
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| 45 | use timers ! module for timing |
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| 46 | use grids ! module containing grid information |
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| 47 | use remap_vars ! module containing remap information |
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| 48 | |
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| 49 | implicit none |
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| 50 | |
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| 51 | !----------------------------------------------------------------------- |
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| 52 | ! |
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| 53 | ! module variables |
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| 54 | ! |
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| 55 | !----------------------------------------------------------------------- |
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| 56 | |
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| 57 | integer (kind=int_kind), save :: & |
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| 58 | num_srch_cells ! num cells in restricted search arrays |
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| 59 | |
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| 60 | integer (kind=int_kind), dimension(:), allocatable, save :: & |
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| 61 | srch_add ! global address of cells in srch arrays |
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| 62 | |
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| 63 | real (kind=dbl_kind), parameter :: & |
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| 64 | north_thresh = 1.45_dbl_kind, & ! threshold for coord transf. |
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| 65 | south_thresh =-2.00_dbl_kind ! threshold for coord transf. |
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| 66 | |
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| 67 | real (kind=dbl_kind), dimension(:,:), allocatable, save :: & |
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| 68 | srch_corner_lat, & ! lat of each corner of srch cells |
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| 69 | srch_corner_lon ! lon of each corner of srch cells |
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| 70 | |
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| 71 | !*********************************************************************** |
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| 72 | |
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| 73 | contains |
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| 74 | |
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| 75 | !*********************************************************************** |
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| 76 | |
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| 77 | subroutine remap_conserv |
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| 78 | |
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| 79 | !----------------------------------------------------------------------- |
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| 80 | ! |
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| 81 | ! this routine traces the perimeters of every grid cell on each |
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| 82 | ! grid checking for intersections with the other grid and computing |
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| 83 | ! line integrals for each subsegment. |
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| 84 | ! |
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| 85 | !----------------------------------------------------------------------- |
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| 86 | |
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| 87 | !----------------------------------------------------------------------- |
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| 88 | ! |
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| 89 | ! local variables |
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| 90 | ! |
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| 91 | !----------------------------------------------------------------------- |
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| 92 | |
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| 93 | integer (kind=int_kind), parameter :: & |
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| 94 | max_subseg = 10000 ! max number of subsegments per segment |
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| 95 | ! to prevent infinite loop |
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| 96 | |
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| 97 | integer (kind=int_kind) :: & |
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| 98 | grid1_add, & ! current linear address for grid1 cell |
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| 99 | grid2_add, & ! current linear address for grid2 cell |
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| 100 | min_add, & ! addresses for restricting search of |
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| 101 | max_add, & ! destination grid |
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| 102 | n, nwgt, & ! generic counters |
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| 103 | corner, & ! corner of cell that segment starts from |
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| 104 | next_corn, & ! corner of cell that segment ends on |
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| 105 | num_subseg ! number of subsegments |
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| 106 | |
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| 107 | logical (kind=log_kind) :: & |
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| 108 | lcoinc, & ! flag for coincident segments |
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| 109 | lrevers, & ! flag for reversing direction of segment |
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| 110 | lbegin ! flag for first integration of a segment |
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| 111 | |
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| 112 | logical (kind=log_kind), dimension(:), allocatable :: & |
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| 113 | srch_mask ! mask for restricting searches |
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| 114 | |
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| 115 | real (kind=dbl_kind) :: & |
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| 116 | intrsct_lat, intrsct_lon, & ! lat/lon of next intersect |
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| 117 | beglat, endlat, beglon, endlon, & ! endpoints of current seg. |
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| 118 | norm_factor ! factor for normalizing wts |
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| 119 | |
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| 120 | real (kind=dbl_kind), dimension(:), allocatable :: & |
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| 121 | grid2_centroid_lat, grid2_centroid_lon, & ! centroid coords |
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| 122 | grid1_centroid_lat, grid1_centroid_lon ! on each grid |
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| 123 | |
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| 124 | real (kind=dbl_kind), dimension(2) :: begseg ! begin lat/lon for |
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| 125 | ! full segment |
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| 126 | |
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| 127 | real (kind=dbl_kind), dimension(6) :: weights ! local wgt array |
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| 128 | |
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| 129 | !----------------------------------------------------------------------- |
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| 130 | ! |
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| 131 | ! initialize centroid arrays |
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| 132 | ! |
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| 133 | !----------------------------------------------------------------------- |
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| 134 | |
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| 135 | allocate( grid1_centroid_lat(grid1_size), & |
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| 136 | grid1_centroid_lon(grid1_size), & |
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| 137 | grid2_centroid_lat(grid2_size), & |
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| 138 | grid2_centroid_lon(grid2_size)) |
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| 139 | |
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| 140 | grid1_centroid_lat = zero |
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| 141 | grid1_centroid_lon = zero |
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| 142 | grid2_centroid_lat = zero |
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| 143 | grid2_centroid_lon = zero |
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| 144 | |
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| 145 | !----------------------------------------------------------------------- |
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| 146 | ! |
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| 147 | ! integrate around each cell on grid1 |
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| 148 | ! |
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| 149 | !----------------------------------------------------------------------- |
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| 150 | |
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| 151 | allocate(srch_mask(grid2_size)) |
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| 152 | |
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| 153 | print *,'grid1 sweep ' |
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| 154 | do grid1_add = 1,grid1_size |
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| 155 | |
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| 156 | !*** |
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| 157 | !*** restrict searches first using search bins |
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| 158 | !*** |
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| 159 | |
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| 160 | call timer_start(1) |
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| 161 | min_add = grid2_size |
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| 162 | max_add = 1 |
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| 163 | do n=1,num_srch_bins |
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| 164 | if (grid1_add >= bin_addr1(1,n) .and. & |
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| 165 | grid1_add <= bin_addr1(2,n)) then |
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| 166 | min_add = min(min_add, bin_addr2(1,n)) |
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| 167 | max_add = max(max_add, bin_addr2(2,n)) |
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| 168 | endif |
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| 169 | end do |
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| 170 | |
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| 171 | !*** |
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| 172 | !*** further restrict searches using bounding boxes |
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| 173 | !*** |
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| 174 | |
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| 175 | num_srch_cells = 0 |
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| 176 | do grid2_add = min_add,max_add |
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| 177 | srch_mask(grid2_add) = (grid2_bound_box(1,grid2_add) <= & |
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| 178 | grid1_bound_box(2,grid1_add)) .and. & |
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| 179 | (grid2_bound_box(2,grid2_add) >= & |
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| 180 | grid1_bound_box(1,grid1_add)) .and. & |
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| 181 | (grid2_bound_box(3,grid2_add) <= & |
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| 182 | grid1_bound_box(4,grid1_add)) .and. & |
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| 183 | (grid2_bound_box(4,grid2_add) >= & |
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| 184 | grid1_bound_box(3,grid1_add)) |
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| 185 | |
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| 186 | if (srch_mask(grid2_add)) num_srch_cells = num_srch_cells+1 |
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| 187 | end do |
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| 188 | |
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| 189 | !*** |
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| 190 | !*** create search arrays |
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| 191 | !*** |
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| 192 | |
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| 193 | allocate(srch_add(num_srch_cells), & |
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| 194 | srch_corner_lat(grid2_corners,num_srch_cells), & |
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| 195 | srch_corner_lon(grid2_corners,num_srch_cells)) |
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| 196 | |
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| 197 | n = 0 |
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| 198 | gather1: do grid2_add = min_add,max_add |
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| 199 | if (srch_mask(grid2_add)) then |
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| 200 | n = n+1 |
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| 201 | srch_add(n) = grid2_add |
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| 202 | srch_corner_lat(:,n) = grid2_corner_lat(:,grid2_add) |
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| 203 | srch_corner_lon(:,n) = grid2_corner_lon(:,grid2_add) |
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| 204 | endif |
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| 205 | end do gather1 |
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| 206 | call timer_stop(1) |
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| 207 | |
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| 208 | !*** |
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| 209 | !*** integrate around this cell |
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| 210 | !*** |
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| 211 | |
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| 212 | do corner = 1,grid1_corners |
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| 213 | next_corn = mod(corner,grid1_corners) + 1 |
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| 214 | |
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| 215 | !*** |
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| 216 | !*** define endpoints of the current segment |
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| 217 | !*** |
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| 218 | |
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| 219 | beglat = grid1_corner_lat(corner,grid1_add) |
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| 220 | beglon = grid1_corner_lon(corner,grid1_add) |
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| 221 | endlat = grid1_corner_lat(next_corn,grid1_add) |
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| 222 | endlon = grid1_corner_lon(next_corn,grid1_add) |
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| 223 | lrevers = .false. |
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| 224 | |
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| 225 | !*** |
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| 226 | !*** to ensure exact path taken during both |
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| 227 | !*** sweeps, always integrate segments in the same |
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| 228 | !*** direction (SW to NE). |
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| 229 | !*** |
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| 230 | |
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| 231 | if ((endlat < beglat) .or. & |
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| 232 | (endlat == beglat .and. endlon < beglon)) then |
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| 233 | beglat = grid1_corner_lat(next_corn,grid1_add) |
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| 234 | beglon = grid1_corner_lon(next_corn,grid1_add) |
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| 235 | endlat = grid1_corner_lat(corner,grid1_add) |
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| 236 | endlon = grid1_corner_lon(corner,grid1_add) |
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| 237 | lrevers = .true. |
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| 238 | endif |
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| 239 | |
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| 240 | begseg(1) = beglat |
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| 241 | begseg(2) = beglon |
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| 242 | lbegin = .true. |
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| 243 | num_subseg = 0 |
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| 244 | |
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| 245 | !*** |
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| 246 | !*** if this is a constant-longitude segment, skip the rest |
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| 247 | !*** since the line integral contribution will be zero. |
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| 248 | !*** |
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| 249 | |
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| 250 | if (endlon /= beglon) then |
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| 251 | |
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| 252 | !*** |
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| 253 | !*** integrate along this segment, detecting intersections |
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| 254 | !*** and computing the line integral for each sub-segment |
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| 255 | !*** |
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| 256 | |
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| 257 | do while (beglat /= endlat .or. beglon /= endlon) |
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| 258 | |
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| 259 | !*** |
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| 260 | !*** prevent infinite loops if integration gets stuck |
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| 261 | !*** near cell or threshold boundary |
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| 262 | !*** |
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| 263 | |
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| 264 | num_subseg = num_subseg + 1 |
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| 265 | if (num_subseg > max_subseg) then |
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| 266 | stop 'integration stalled: num_subseg exceeded limit' |
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| 267 | endif |
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| 268 | |
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| 269 | !*** |
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| 270 | !*** find next intersection of this segment with a grid |
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| 271 | !*** line on grid 2. |
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| 272 | !*** |
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| 273 | |
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| 274 | call timer_start(2) |
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| 275 | call intersection(grid2_add,intrsct_lat,intrsct_lon,lcoinc, & |
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| 276 | beglat, beglon, endlat, endlon, begseg, & |
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| 277 | lbegin, lrevers) |
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| 278 | call timer_stop(2) |
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| 279 | lbegin = .false. |
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| 280 | |
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| 281 | !*** |
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| 282 | !*** compute line integral for this subsegment. |
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| 283 | !*** |
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| 284 | |
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| 285 | call timer_start(3) |
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| 286 | if (grid2_add /= 0) then |
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| 287 | call line_integral(weights, num_wts, & |
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| 288 | beglon, intrsct_lon, beglat, intrsct_lat, & |
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| 289 | grid1_center_lat(grid1_add), & |
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| 290 | grid1_center_lon(grid1_add), & |
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| 291 | grid2_center_lat(grid2_add), & |
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| 292 | grid2_center_lon(grid2_add)) |
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| 293 | else |
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| 294 | call line_integral(weights, num_wts, & |
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| 295 | beglon, intrsct_lon, beglat, intrsct_lat, & |
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| 296 | grid1_center_lat(grid1_add), & |
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| 297 | grid1_center_lon(grid1_add), & |
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| 298 | grid1_center_lat(grid1_add), & |
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| 299 | grid1_center_lon(grid1_add)) |
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| 300 | endif |
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| 301 | call timer_stop(3) |
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| 302 | |
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| 303 | !*** |
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| 304 | !*** if integrating in reverse order, change |
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| 305 | !*** sign of weights |
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| 306 | !*** |
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| 307 | |
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| 308 | if (lrevers) then |
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| 309 | weights = -weights |
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| 310 | endif |
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| 311 | |
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| 312 | !*** |
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| 313 | !*** store the appropriate addresses and weights. |
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| 314 | !*** also add contributions to cell areas and centroids. |
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| 315 | !*** |
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| 316 | |
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| 317 | !if (grid1_add == 119247) then |
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| 318 | ! print *,grid1_add,grid2_add,corner,weights(1) |
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| 319 | ! print *,grid1_corner_lat(:,grid1_add) |
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| 320 | ! print *,grid1_corner_lon(:,grid1_add) |
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| 321 | ! print *,grid2_corner_lat(:,grid2_add) |
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| 322 | ! print *,grid2_corner_lon(:,grid2_add) |
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| 323 | ! print *,beglat,beglon,intrsct_lat,intrsct_lon |
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| 324 | !endif |
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| 325 | |
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| 326 | if (grid2_add /= 0) then |
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| 327 | if (grid1_mask(grid1_add)) then |
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| 328 | call timer_start(4) |
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| 329 | call store_link_cnsrv(grid1_add, grid2_add, weights) |
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| 330 | call timer_stop(4) |
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| 331 | grid1_frac(grid1_add) = grid1_frac(grid1_add) + & |
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| 332 | weights(1) |
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| 333 | grid2_frac(grid2_add) = grid2_frac(grid2_add) + & |
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| 334 | weights(num_wts+1) |
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| 335 | endif |
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| 336 | |
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| 337 | endif |
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| 338 | |
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| 339 | grid1_area(grid1_add) = grid1_area(grid1_add) + weights(1) |
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| 340 | grid1_centroid_lat(grid1_add) = & |
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| 341 | grid1_centroid_lat(grid1_add) + weights(2) |
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| 342 | grid1_centroid_lon(grid1_add) = & |
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| 343 | grid1_centroid_lon(grid1_add) + weights(3) |
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| 344 | |
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| 345 | !*** |
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| 346 | !*** reset beglat and beglon for next subsegment. |
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| 347 | !*** |
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| 348 | |
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| 349 | beglat = intrsct_lat |
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| 350 | beglon = intrsct_lon |
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| 351 | end do |
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| 352 | |
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| 353 | endif |
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| 354 | |
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| 355 | !*** |
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| 356 | !*** end of segment |
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| 357 | !*** |
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| 358 | |
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| 359 | end do |
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| 360 | |
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| 361 | !*** |
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| 362 | !*** finished with this cell: deallocate search array and |
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| 363 | !*** start on next cell |
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| 364 | |
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| 365 | deallocate(srch_add, srch_corner_lat, srch_corner_lon) |
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| 366 | |
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| 367 | end do |
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| 368 | |
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| 369 | deallocate(srch_mask) |
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| 370 | |
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| 371 | !----------------------------------------------------------------------- |
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| 372 | ! |
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| 373 | ! integrate around each cell on grid2 |
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| 374 | ! |
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| 375 | !----------------------------------------------------------------------- |
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| 376 | |
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| 377 | allocate(srch_mask(grid1_size)) |
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| 378 | |
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| 379 | print *,'grid2 sweep ' |
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| 380 | do grid2_add = 1,grid2_size |
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| 381 | |
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| 382 | !*** |
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| 383 | !*** restrict searches first using search bins |
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| 384 | !*** |
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| 385 | |
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| 386 | call timer_start(5) |
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| 387 | min_add = grid1_size |
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| 388 | max_add = 1 |
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| 389 | do n=1,num_srch_bins |
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| 390 | if (grid2_add >= bin_addr2(1,n) .and. & |
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| 391 | grid2_add <= bin_addr2(2,n)) then |
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| 392 | min_add = min(min_add, bin_addr1(1,n)) |
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| 393 | max_add = max(max_add, bin_addr1(2,n)) |
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| 394 | endif |
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| 395 | end do |
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| 396 | |
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| 397 | !*** |
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| 398 | !*** further restrict searches using bounding boxes |
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| 399 | !*** |
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| 400 | |
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| 401 | num_srch_cells = 0 |
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| 402 | do grid1_add = min_add, max_add |
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| 403 | srch_mask(grid1_add) = (grid1_bound_box(1,grid1_add) <= & |
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| 404 | grid2_bound_box(2,grid2_add)) .and. & |
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| 405 | (grid1_bound_box(2,grid1_add) >= & |
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| 406 | grid2_bound_box(1,grid2_add)) .and. & |
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| 407 | (grid1_bound_box(3,grid1_add) <= & |
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| 408 | grid2_bound_box(4,grid2_add)) .and. & |
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| 409 | (grid1_bound_box(4,grid1_add) >= & |
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| 410 | grid2_bound_box(3,grid2_add)) |
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| 411 | |
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| 412 | if (srch_mask(grid1_add)) num_srch_cells = num_srch_cells+1 |
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| 413 | end do |
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| 414 | |
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| 415 | allocate(srch_add(num_srch_cells), & |
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| 416 | srch_corner_lat(grid1_corners,num_srch_cells), & |
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| 417 | srch_corner_lon(grid1_corners,num_srch_cells)) |
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| 418 | |
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| 419 | n = 0 |
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| 420 | gather2: do grid1_add = min_add,max_add |
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| 421 | if (srch_mask(grid1_add)) then |
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| 422 | n = n+1 |
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| 423 | srch_add(n) = grid1_add |
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| 424 | srch_corner_lat(:,n) = grid1_corner_lat(:,grid1_add) |
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| 425 | srch_corner_lon(:,n) = grid1_corner_lon(:,grid1_add) |
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| 426 | endif |
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| 427 | end do gather2 |
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| 428 | call timer_stop(5) |
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| 429 | |
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| 430 | !*** |
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| 431 | !*** integrate around this cell |
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| 432 | !*** |
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| 433 | |
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| 434 | do corner = 1,grid2_corners |
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| 435 | next_corn = mod(corner,grid2_corners) + 1 |
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| 436 | |
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| 437 | beglat = grid2_corner_lat(corner,grid2_add) |
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| 438 | beglon = grid2_corner_lon(corner,grid2_add) |
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| 439 | endlat = grid2_corner_lat(next_corn,grid2_add) |
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| 440 | endlon = grid2_corner_lon(next_corn,grid2_add) |
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| 441 | lrevers = .false. |
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| 442 | |
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| 443 | !*** |
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| 444 | !*** to ensure exact path taken during both |
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| 445 | !*** sweeps, always integrate in the same direction |
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| 446 | !*** |
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| 447 | |
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| 448 | if ((endlat < beglat) .or. & |
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| 449 | (endlat == beglat .and. endlon < beglon)) then |
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| 450 | beglat = grid2_corner_lat(next_corn,grid2_add) |
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| 451 | beglon = grid2_corner_lon(next_corn,grid2_add) |
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| 452 | endlat = grid2_corner_lat(corner,grid2_add) |
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| 453 | endlon = grid2_corner_lon(corner,grid2_add) |
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| 454 | lrevers = .true. |
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| 455 | endif |
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| 456 | |
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| 457 | begseg(1) = beglat |
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| 458 | begseg(2) = beglon |
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| 459 | lbegin = .true. |
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| 460 | |
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| 461 | !*** |
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| 462 | !*** if this is a constant-longitude segment, skip the rest |
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| 463 | !*** since the line integral contribution will be zero. |
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| 464 | !*** |
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| 465 | |
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| 466 | if (endlon /= beglon) then |
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| 467 | num_subseg = 0 |
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| 468 | |
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| 469 | !*** |
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| 470 | !*** integrate along this segment, detecting intersections |
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| 471 | !*** and computing the line integral for each sub-segment |
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| 472 | !*** |
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| 473 | |
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| 474 | do while (beglat /= endlat .or. beglon /= endlon) |
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| 475 | |
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| 476 | !*** |
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| 477 | !*** prevent infinite loops if integration gets stuck |
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| 478 | !*** near cell or threshold boundary |
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| 479 | !*** |
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| 480 | |
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| 481 | num_subseg = num_subseg + 1 |
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| 482 | if (num_subseg > max_subseg) then |
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| 483 | stop 'integration stalled: num_subseg exceeded limit' |
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| 484 | endif |
---|
| 485 | |
---|
| 486 | !*** |
---|
| 487 | !*** find next intersection of this segment with a line |
---|
| 488 | !*** on grid 2. |
---|
| 489 | !*** |
---|
| 490 | |
---|
| 491 | call timer_start(6) |
---|
| 492 | call intersection(grid1_add,intrsct_lat,intrsct_lon,lcoinc, & |
---|
| 493 | beglat, beglon, endlat, endlon, begseg, & |
---|
| 494 | lbegin, lrevers) |
---|
| 495 | call timer_stop(6) |
---|
| 496 | lbegin = .false. |
---|
| 497 | |
---|
| 498 | !*** |
---|
| 499 | !*** compute line integral for this subsegment. |
---|
| 500 | !*** |
---|
| 501 | |
---|
| 502 | call timer_start(7) |
---|
| 503 | if (grid1_add /= 0) then |
---|
| 504 | call line_integral(weights, num_wts, & |
---|
| 505 | beglon, intrsct_lon, beglat, intrsct_lat, & |
---|
| 506 | grid1_center_lat(grid1_add), & |
---|
| 507 | grid1_center_lon(grid1_add), & |
---|
| 508 | grid2_center_lat(grid2_add), & |
---|
| 509 | grid2_center_lon(grid2_add)) |
---|
| 510 | else |
---|
| 511 | call line_integral(weights, num_wts, & |
---|
| 512 | beglon, intrsct_lon, beglat, intrsct_lat, & |
---|
| 513 | grid2_center_lat(grid2_add), & |
---|
| 514 | grid2_center_lon(grid2_add), & |
---|
| 515 | grid2_center_lat(grid2_add), & |
---|
| 516 | grid2_center_lon(grid2_add)) |
---|
| 517 | endif |
---|
| 518 | call timer_stop(7) |
---|
| 519 | |
---|
| 520 | if (lrevers) then |
---|
| 521 | weights = -weights |
---|
| 522 | endif |
---|
| 523 | |
---|
| 524 | !*** |
---|
| 525 | !*** store the appropriate addresses and weights. |
---|
| 526 | !*** also add contributions to cell areas and centroids. |
---|
| 527 | !*** if there is a coincidence, do not store weights |
---|
| 528 | !*** because they have been captured in the previous loop. |
---|
| 529 | !*** the grid1 mask is the master mask |
---|
| 530 | !*** |
---|
| 531 | |
---|
| 532 | !if (grid1_add == 119247) then |
---|
| 533 | ! print *,grid1_add,grid2_add,corner,weights(1) |
---|
| 534 | ! print *,grid1_corner_lat(:,grid1_add) |
---|
| 535 | ! print *,grid1_corner_lon(:,grid1_add) |
---|
| 536 | ! print *,grid2_corner_lat(:,grid2_add) |
---|
| 537 | ! print *,grid2_corner_lon(:,grid2_add) |
---|
| 538 | ! print *,beglat,beglon,intrsct_lat,intrsct_lon |
---|
| 539 | !endif |
---|
| 540 | |
---|
| 541 | if (.not. lcoinc .and. grid1_add /= 0) then |
---|
| 542 | if (grid1_mask(grid1_add)) then |
---|
| 543 | call timer_start(8) |
---|
| 544 | call store_link_cnsrv(grid1_add, grid2_add, weights) |
---|
| 545 | call timer_stop(8) |
---|
| 546 | grid1_frac(grid1_add) = grid1_frac(grid1_add) + & |
---|
| 547 | weights(1) |
---|
| 548 | grid2_frac(grid2_add) = grid2_frac(grid2_add) + & |
---|
| 549 | weights(num_wts+1) |
---|
| 550 | endif |
---|
| 551 | |
---|
| 552 | endif |
---|
| 553 | |
---|
| 554 | grid2_area(grid2_add) = grid2_area(grid2_add) + & |
---|
| 555 | weights(num_wts+1) |
---|
| 556 | grid2_centroid_lat(grid2_add) = & |
---|
| 557 | grid2_centroid_lat(grid2_add) + weights(num_wts+2) |
---|
| 558 | grid2_centroid_lon(grid2_add) = & |
---|
| 559 | grid2_centroid_lon(grid2_add) + weights(num_wts+3) |
---|
| 560 | |
---|
| 561 | !*** |
---|
| 562 | !*** reset beglat and beglon for next subsegment. |
---|
| 563 | !*** |
---|
| 564 | |
---|
| 565 | beglat = intrsct_lat |
---|
| 566 | beglon = intrsct_lon |
---|
| 567 | end do |
---|
| 568 | |
---|
| 569 | endif |
---|
| 570 | |
---|
| 571 | !*** |
---|
| 572 | !*** end of segment |
---|
| 573 | !*** |
---|
| 574 | |
---|
| 575 | end do |
---|
| 576 | |
---|
| 577 | !*** |
---|
| 578 | !*** finished with this cell: deallocate search array and |
---|
| 579 | !*** start on next cell |
---|
| 580 | |
---|
| 581 | deallocate(srch_add, srch_corner_lat, srch_corner_lon) |
---|
| 582 | |
---|
| 583 | end do |
---|
| 584 | |
---|
| 585 | deallocate(srch_mask) |
---|
| 586 | |
---|
| 587 | !----------------------------------------------------------------------- |
---|
| 588 | ! |
---|
| 589 | ! correct for situations where N/S pole not explicitly included in |
---|
| 590 | ! grid (i.e. as a grid corner point). if pole is missing from only |
---|
| 591 | ! one grid, need to correct only the area and centroid of that |
---|
| 592 | ! grid. if missing from both, do complete weight calculation. |
---|
| 593 | ! |
---|
| 594 | !----------------------------------------------------------------------- |
---|
| 595 | |
---|
| 596 | !*** North Pole |
---|
| 597 | weights(1) = pi2 |
---|
| 598 | weights(2) = pi*pi |
---|
| 599 | weights(3) = zero |
---|
| 600 | weights(4) = pi2 |
---|
| 601 | weights(5) = pi*pi |
---|
| 602 | weights(6) = zero |
---|
| 603 | |
---|
| 604 | grid1_add = 0 |
---|
| 605 | pole_loop1: do n=1,grid1_size |
---|
| 606 | if (grid1_area(n) < -three*pih .and. & |
---|
| 607 | grid1_center_lat(n) > zero) then |
---|
| 608 | grid1_add = n |
---|
| 609 | exit pole_loop1 |
---|
| 610 | endif |
---|
| 611 | end do pole_loop1 |
---|
| 612 | |
---|
| 613 | grid2_add = 0 |
---|
| 614 | pole_loop2: do n=1,grid2_size |
---|
| 615 | if (grid2_area(n) < -three*pih .and. & |
---|
| 616 | grid2_center_lat(n) > zero) then |
---|
| 617 | grid2_add = n |
---|
| 618 | exit pole_loop2 |
---|
| 619 | endif |
---|
| 620 | end do pole_loop2 |
---|
| 621 | |
---|
| 622 | if (grid1_add /=0) then |
---|
| 623 | grid1_area(grid1_add) = grid1_area(grid1_add) + weights(1) |
---|
| 624 | grid1_centroid_lat(grid1_add) = & |
---|
| 625 | grid1_centroid_lat(grid1_add) + weights(2) |
---|
| 626 | grid1_centroid_lon(grid1_add) = & |
---|
| 627 | grid1_centroid_lon(grid1_add) + weights(3) |
---|
| 628 | endif |
---|
| 629 | |
---|
| 630 | if (grid2_add /=0) then |
---|
| 631 | grid2_area(grid2_add) = grid2_area(grid2_add) + & |
---|
| 632 | weights(num_wts+1) |
---|
| 633 | grid2_centroid_lat(grid2_add) = & |
---|
| 634 | grid2_centroid_lat(grid2_add) + weights(num_wts+2) |
---|
| 635 | grid2_centroid_lon(grid2_add) = & |
---|
| 636 | grid2_centroid_lon(grid2_add) + weights(num_wts+3) |
---|
| 637 | endif |
---|
| 638 | |
---|
| 639 | if (grid1_add /= 0 .and. grid2_add /=0) then |
---|
| 640 | call store_link_cnsrv(grid1_add, grid2_add, weights) |
---|
| 641 | |
---|
| 642 | grid1_frac(grid1_add) = grid1_frac(grid1_add) + & |
---|
| 643 | weights(1) |
---|
| 644 | grid2_frac(grid2_add) = grid2_frac(grid2_add) + & |
---|
| 645 | weights(num_wts+1) |
---|
| 646 | endif |
---|
| 647 | |
---|
| 648 | !*** South Pole |
---|
| 649 | weights(1) = pi2 |
---|
| 650 | weights(2) = -pi*pi |
---|
| 651 | weights(3) = zero |
---|
| 652 | weights(4) = pi2 |
---|
| 653 | weights(5) = -pi*pi |
---|
| 654 | weights(6) = zero |
---|
| 655 | |
---|
| 656 | grid1_add = 0 |
---|
| 657 | pole_loop3: do n=1,grid1_size |
---|
| 658 | if (grid1_area(n) < -three*pih .and. & |
---|
| 659 | grid1_center_lat(n) < zero) then |
---|
| 660 | grid1_add = n |
---|
| 661 | exit pole_loop3 |
---|
| 662 | endif |
---|
| 663 | end do pole_loop3 |
---|
| 664 | |
---|
| 665 | grid2_add = 0 |
---|
| 666 | pole_loop4: do n=1,grid2_size |
---|
| 667 | if (grid2_area(n) < -three*pih .and. & |
---|
| 668 | grid2_center_lat(n) < zero) then |
---|
| 669 | grid2_add = n |
---|
| 670 | exit pole_loop4 |
---|
| 671 | endif |
---|
| 672 | end do pole_loop4 |
---|
| 673 | |
---|
| 674 | if (grid1_add /=0) then |
---|
| 675 | grid1_area(grid1_add) = grid1_area(grid1_add) + weights(1) |
---|
| 676 | grid1_centroid_lat(grid1_add) = & |
---|
| 677 | grid1_centroid_lat(grid1_add) + weights(2) |
---|
| 678 | grid1_centroid_lon(grid1_add) = & |
---|
| 679 | grid1_centroid_lon(grid1_add) + weights(3) |
---|
| 680 | endif |
---|
| 681 | |
---|
| 682 | if (grid2_add /=0) then |
---|
| 683 | grid2_area(grid2_add) = grid2_area(grid2_add) + & |
---|
| 684 | weights(num_wts+1) |
---|
| 685 | grid2_centroid_lat(grid2_add) = & |
---|
| 686 | grid2_centroid_lat(grid2_add) + weights(num_wts+2) |
---|
| 687 | grid2_centroid_lon(grid2_add) = & |
---|
| 688 | grid2_centroid_lon(grid2_add) + weights(num_wts+3) |
---|
| 689 | endif |
---|
| 690 | |
---|
| 691 | if (grid1_add /= 0 .and. grid2_add /=0) then |
---|
| 692 | call store_link_cnsrv(grid1_add, grid2_add, weights) |
---|
| 693 | |
---|
| 694 | grid1_frac(grid1_add) = grid1_frac(grid1_add) + & |
---|
| 695 | weights(1) |
---|
| 696 | grid2_frac(grid2_add) = grid2_frac(grid2_add) + & |
---|
| 697 | weights(num_wts+1) |
---|
| 698 | endif |
---|
| 699 | |
---|
| 700 | !----------------------------------------------------------------------- |
---|
| 701 | ! |
---|
| 702 | ! finish centroid computation |
---|
| 703 | ! |
---|
| 704 | !----------------------------------------------------------------------- |
---|
| 705 | |
---|
| 706 | where (grid1_area /= zero) |
---|
| 707 | grid1_centroid_lat = grid1_centroid_lat/grid1_area |
---|
| 708 | grid1_centroid_lon = grid1_centroid_lon/grid1_area |
---|
| 709 | end where |
---|
| 710 | |
---|
| 711 | where (grid2_area /= zero) |
---|
| 712 | grid2_centroid_lat = grid2_centroid_lat/grid2_area |
---|
| 713 | grid2_centroid_lon = grid2_centroid_lon/grid2_area |
---|
| 714 | end where |
---|
| 715 | |
---|
| 716 | !----------------------------------------------------------------------- |
---|
| 717 | ! |
---|
| 718 | ! include centroids in weights and normalize using destination |
---|
| 719 | ! area if requested |
---|
| 720 | ! |
---|
| 721 | !----------------------------------------------------------------------- |
---|
| 722 | |
---|
| 723 | do n=1,num_links_map1 |
---|
| 724 | grid1_add = grid1_add_map1(n) |
---|
| 725 | grid2_add = grid2_add_map1(n) |
---|
| 726 | do nwgt=1,num_wts |
---|
| 727 | weights( nwgt) = wts_map1(nwgt,n) |
---|
| 728 | if (num_maps > 1) then |
---|
| 729 | weights(num_wts+nwgt) = wts_map2(nwgt,n) |
---|
| 730 | endif |
---|
| 731 | end do |
---|
| 732 | |
---|
| 733 | select case(norm_opt) |
---|
| 734 | case (norm_opt_dstarea) |
---|
| 735 | if (grid2_area(grid2_add) /= zero) then |
---|
| 736 | if (luse_grid2_area) then |
---|
| 737 | norm_factor = one/grid2_area_in(grid2_add) |
---|
| 738 | else |
---|
| 739 | norm_factor = one/grid2_area(grid2_add) |
---|
| 740 | endif |
---|
| 741 | else |
---|
| 742 | norm_factor = zero |
---|
| 743 | endif |
---|
| 744 | case (norm_opt_frcarea) |
---|
| 745 | if (grid2_frac(grid2_add) /= zero) then |
---|
| 746 | if (luse_grid2_area) then |
---|
| 747 | norm_factor = grid2_area(grid2_add)/ & |
---|
| 748 | (grid2_frac(grid2_add)* & |
---|
| 749 | grid2_area_in(grid2_add)) |
---|
| 750 | else |
---|
| 751 | norm_factor = one/grid2_frac(grid2_add) |
---|
| 752 | endif |
---|
| 753 | else |
---|
| 754 | norm_factor = zero |
---|
| 755 | endif |
---|
| 756 | case (norm_opt_none) |
---|
| 757 | norm_factor = one |
---|
| 758 | end select |
---|
| 759 | |
---|
| 760 | wts_map1(1,n) = weights(1)*norm_factor |
---|
| 761 | wts_map1(2,n) = (weights(2) - weights(1)* & |
---|
| 762 | grid1_centroid_lat(grid1_add))* & |
---|
| 763 | norm_factor |
---|
| 764 | wts_map1(3,n) = (weights(3) - weights(1)* & |
---|
| 765 | grid1_centroid_lon(grid1_add))* & |
---|
| 766 | norm_factor |
---|
| 767 | |
---|
| 768 | if (num_maps > 1) then |
---|
| 769 | select case(norm_opt) |
---|
| 770 | case (norm_opt_dstarea) |
---|
| 771 | if (grid1_area(grid1_add) /= zero) then |
---|
| 772 | if (luse_grid1_area) then |
---|
| 773 | norm_factor = one/grid1_area_in(grid1_add) |
---|
| 774 | else |
---|
| 775 | norm_factor = one/grid1_area(grid1_add) |
---|
| 776 | endif |
---|
| 777 | else |
---|
| 778 | norm_factor = zero |
---|
| 779 | endif |
---|
| 780 | case (norm_opt_frcarea) |
---|
| 781 | if (grid1_frac(grid1_add) /= zero) then |
---|
| 782 | if (luse_grid1_area) then |
---|
| 783 | norm_factor = grid1_area(grid1_add)/ & |
---|
| 784 | (grid1_frac(grid1_add)* & |
---|
| 785 | grid1_area_in(grid1_add)) |
---|
| 786 | else |
---|
| 787 | norm_factor = one/grid1_frac(grid1_add) |
---|
| 788 | endif |
---|
| 789 | else |
---|
| 790 | norm_factor = zero |
---|
| 791 | endif |
---|
| 792 | case (norm_opt_none) |
---|
| 793 | norm_factor = one |
---|
| 794 | end select |
---|
| 795 | |
---|
| 796 | wts_map2(1,n) = weights(num_wts+1)*norm_factor |
---|
| 797 | wts_map2(2,n) = (weights(num_wts+2) - weights(num_wts+1)* & |
---|
| 798 | grid2_centroid_lat(grid2_add))* & |
---|
| 799 | norm_factor |
---|
| 800 | wts_map2(3,n) = (weights(num_wts+3) - weights(num_wts+1)* & |
---|
| 801 | grid2_centroid_lon(grid2_add))* & |
---|
| 802 | norm_factor |
---|
| 803 | endif |
---|
| 804 | |
---|
| 805 | end do |
---|
| 806 | |
---|
| 807 | print *, 'Total number of links = ',num_links_map1 |
---|
| 808 | |
---|
| 809 | where (grid1_area /= zero) grid1_frac = grid1_frac/grid1_area |
---|
| 810 | where (grid2_area /= zero) grid2_frac = grid2_frac/grid2_area |
---|
| 811 | |
---|
| 812 | !----------------------------------------------------------------------- |
---|
| 813 | ! |
---|
| 814 | ! perform some error checking on final weights |
---|
| 815 | ! |
---|
| 816 | !----------------------------------------------------------------------- |
---|
| 817 | |
---|
| 818 | grid2_centroid_lat = zero |
---|
| 819 | grid2_centroid_lon = zero |
---|
| 820 | |
---|
| 821 | do n=1,grid1_size |
---|
| 822 | if (grid1_area(n) < -.01) then |
---|
| 823 | print *,'Grid 1 area error: ',n,grid1_area(n) |
---|
| 824 | endif |
---|
| 825 | if (grid1_centroid_lat(n) < -pih-.01 .or. & |
---|
| 826 | grid1_centroid_lat(n) > pih+.01) then |
---|
| 827 | print *,'Grid 1 centroid lat error: ',n,grid1_centroid_lat(n) |
---|
| 828 | endif |
---|
| 829 | grid1_centroid_lat(n) = zero |
---|
| 830 | grid1_centroid_lon(n) = zero |
---|
| 831 | end do |
---|
| 832 | |
---|
| 833 | do n=1,grid2_size |
---|
| 834 | if (grid2_area(n) < -.01) then |
---|
| 835 | print *,'Grid 2 area error: ',n,grid2_area(n) |
---|
| 836 | endif |
---|
| 837 | if (grid2_centroid_lat(n) < -pih-.01 .or. & |
---|
| 838 | grid2_centroid_lat(n) > pih+.01) then |
---|
| 839 | print *,'Grid 2 centroid lat error: ',n,grid2_centroid_lat(n) |
---|
| 840 | endif |
---|
| 841 | grid2_centroid_lat(n) = zero |
---|
| 842 | grid2_centroid_lon(n) = zero |
---|
| 843 | end do |
---|
| 844 | |
---|
| 845 | do n=1,num_links_map1 |
---|
| 846 | grid1_add = grid1_add_map1(n) |
---|
| 847 | grid2_add = grid2_add_map1(n) |
---|
| 848 | |
---|
| 849 | if (wts_map1(1,n) < -.01) then |
---|
| 850 | print *,'Map 1 weight < 0 ',grid1_add,grid2_add,wts_map1(1,n) |
---|
| 851 | endif |
---|
| 852 | if (norm_opt /= norm_opt_none .and. wts_map1(1,n) > 1.01) then |
---|
| 853 | print *,'Map 1 weight > 1 ',grid1_add,grid2_add,wts_map1(1,n) |
---|
| 854 | endif |
---|
| 855 | grid2_centroid_lat(grid2_add) = & |
---|
| 856 | grid2_centroid_lat(grid2_add) + wts_map1(1,n) |
---|
| 857 | |
---|
| 858 | if (num_maps > 1) then |
---|
| 859 | if (wts_map2(1,n) < -.01) then |
---|
| 860 | print *,'Map 2 weight < 0 ',grid1_add,grid2_add, & |
---|
| 861 | wts_map2(1,n) |
---|
| 862 | endif |
---|
| 863 | if (norm_opt /= norm_opt_none .and. wts_map2(1,n) > 1.01) then |
---|
| 864 | print *,'Map 2 weight < 0 ',grid1_add,grid2_add, & |
---|
| 865 | wts_map2(1,n) |
---|
| 866 | endif |
---|
| 867 | grid1_centroid_lat(grid1_add) = & |
---|
| 868 | grid1_centroid_lat(grid1_add) + wts_map2(1,n) |
---|
| 869 | endif |
---|
| 870 | end do |
---|
| 871 | |
---|
| 872 | do n=1,grid2_size |
---|
| 873 | select case(norm_opt) |
---|
| 874 | case (norm_opt_dstarea) |
---|
| 875 | norm_factor = grid2_frac(grid2_add) |
---|
| 876 | case (norm_opt_frcarea) |
---|
| 877 | norm_factor = one |
---|
| 878 | case (norm_opt_none) |
---|
| 879 | if (luse_grid2_area) then |
---|
| 880 | norm_factor = grid2_area_in(grid2_add) |
---|
| 881 | else |
---|
| 882 | norm_factor = grid2_area(grid2_add) |
---|
| 883 | endif |
---|
| 884 | end select |
---|
| 885 | if (abs(grid2_centroid_lat(grid2_add)-norm_factor) > .01) then |
---|
| 886 | print *,'Error: sum of wts for map1 ',grid2_add, & |
---|
| 887 | grid2_centroid_lat(grid2_add),norm_factor |
---|
| 888 | endif |
---|
| 889 | end do |
---|
| 890 | |
---|
| 891 | if (num_maps > 1) then |
---|
| 892 | do n=1,grid1_size |
---|
| 893 | select case(norm_opt) |
---|
| 894 | case (norm_opt_dstarea) |
---|
| 895 | norm_factor = grid1_frac(grid1_add) |
---|
| 896 | case (norm_opt_frcarea) |
---|
| 897 | norm_factor = one |
---|
| 898 | case (norm_opt_none) |
---|
| 899 | if (luse_grid1_area) then |
---|
| 900 | norm_factor = grid1_area_in(grid1_add) |
---|
| 901 | else |
---|
| 902 | norm_factor = grid1_area(grid1_add) |
---|
| 903 | endif |
---|
| 904 | end select |
---|
| 905 | if (abs(grid1_centroid_lat(grid1_add)-norm_factor) > .01) then |
---|
| 906 | print *,'Error: sum of wts for map2 ',grid1_add, & |
---|
| 907 | grid1_centroid_lat(grid1_add),norm_factor |
---|
| 908 | endif |
---|
| 909 | end do |
---|
| 910 | endif |
---|
| 911 | !----------------------------------------------------------------------- |
---|
| 912 | |
---|
| 913 | end subroutine remap_conserv |
---|
| 914 | |
---|
| 915 | !*********************************************************************** |
---|
| 916 | |
---|
| 917 | subroutine intersection(location,intrsct_lat,intrsct_lon,lcoinc, & |
---|
| 918 | beglat, beglon, endlat, endlon, begseg, & |
---|
| 919 | lbegin, lrevers) |
---|
| 920 | |
---|
| 921 | !----------------------------------------------------------------------- |
---|
| 922 | ! |
---|
| 923 | ! this routine finds the next intersection of a destination grid |
---|
| 924 | ! line with the line segment given by beglon, endlon, etc. |
---|
| 925 | ! a coincidence flag is returned if the segment is entirely |
---|
| 926 | ! coincident with an ocean grid line. the cells in which to search |
---|
| 927 | ! for an intersection must have already been restricted in the |
---|
| 928 | ! calling routine. |
---|
| 929 | ! |
---|
| 930 | !----------------------------------------------------------------------- |
---|
| 931 | |
---|
| 932 | !----------------------------------------------------------------------- |
---|
| 933 | ! |
---|
| 934 | ! intent(in): |
---|
| 935 | ! |
---|
| 936 | !----------------------------------------------------------------------- |
---|
| 937 | |
---|
| 938 | logical (kind=log_kind), intent(in) :: & |
---|
| 939 | lbegin, & ! flag for first integration along this segment |
---|
| 940 | lrevers ! flag whether segment integrated in reverse |
---|
| 941 | |
---|
| 942 | real (kind=dbl_kind), intent(in) :: & |
---|
| 943 | beglat, beglon, & ! beginning lat/lon endpoints for segment |
---|
| 944 | endlat, endlon ! ending lat/lon endpoints for segment |
---|
| 945 | |
---|
| 946 | real (kind=dbl_kind), dimension(2), intent(inout) :: & |
---|
| 947 | begseg ! begin lat/lon of full segment |
---|
| 948 | |
---|
| 949 | !----------------------------------------------------------------------- |
---|
| 950 | ! |
---|
| 951 | ! intent(out): |
---|
| 952 | ! |
---|
| 953 | !----------------------------------------------------------------------- |
---|
| 954 | |
---|
| 955 | integer (kind=int_kind), intent(out) :: & |
---|
| 956 | location ! address in destination array containing this |
---|
| 957 | ! segment |
---|
| 958 | |
---|
| 959 | logical (kind=log_kind), intent(out) :: & |
---|
| 960 | lcoinc ! flag segments which are entirely coincident |
---|
| 961 | ! with a grid line |
---|
| 962 | |
---|
| 963 | real (kind=dbl_kind), intent(out) :: & |
---|
| 964 | intrsct_lat, intrsct_lon ! lat/lon coords of next intersect. |
---|
| 965 | |
---|
| 966 | !----------------------------------------------------------------------- |
---|
| 967 | ! |
---|
| 968 | ! local variables |
---|
| 969 | ! |
---|
| 970 | !----------------------------------------------------------------------- |
---|
| 971 | |
---|
| 972 | integer (kind=int_kind) :: n, next_n, cell, srch_corners, pole_loc |
---|
| 973 | |
---|
| 974 | integer (kind=int_kind), save :: & |
---|
| 975 | last_loc ! save location when crossing threshold |
---|
| 976 | |
---|
| 977 | logical (kind=log_kind) :: & |
---|
| 978 | loutside ! flags points outside grid |
---|
| 979 | |
---|
| 980 | logical (kind=log_kind), save :: & |
---|
| 981 | lthresh = .false. ! flags segments crossing threshold bndy |
---|
| 982 | |
---|
| 983 | real (kind=dbl_kind) :: & |
---|
| 984 | lon1, lon2, & ! local longitude variables for segment |
---|
| 985 | lat1, lat2, & ! local latitude variables for segment |
---|
| 986 | grdlon1, grdlon2, & ! local longitude variables for grid cell |
---|
| 987 | grdlat1, grdlat2, & ! local latitude variables for grid cell |
---|
| 988 | vec1_lat, vec1_lon, & ! vectors and cross products used |
---|
| 989 | vec2_lat, vec2_lon, & ! during grid search |
---|
| 990 | cross_product, & |
---|
| 991 | eps, offset, & ! small offset away from intersect |
---|
| 992 | s1, s2, determ, & ! variables used for linear solve to |
---|
| 993 | mat1, mat2, mat3, mat4, rhs1, rhs2 ! find intersection |
---|
| 994 | |
---|
| 995 | real (kind=dbl_kind), save :: & |
---|
| 996 | intrsct_lat_off, intrsct_lon_off ! lat/lon coords offset |
---|
| 997 | ! for next search |
---|
| 998 | |
---|
| 999 | !----------------------------------------------------------------------- |
---|
| 1000 | ! |
---|
| 1001 | ! initialize defaults, flags, etc. |
---|
| 1002 | ! |
---|
| 1003 | !----------------------------------------------------------------------- |
---|
| 1004 | |
---|
| 1005 | location = 0 |
---|
| 1006 | lcoinc = .false. |
---|
| 1007 | intrsct_lat = endlat |
---|
| 1008 | intrsct_lon = endlon |
---|
| 1009 | |
---|
| 1010 | if (num_srch_cells == 0) return |
---|
| 1011 | |
---|
| 1012 | if (beglat > north_thresh .or. beglat < south_thresh) then |
---|
| 1013 | |
---|
| 1014 | if (lthresh) location = last_loc |
---|
| 1015 | call pole_intersection(location, & |
---|
| 1016 | intrsct_lat,intrsct_lon,lcoinc,lthresh, & |
---|
| 1017 | beglat, beglon, endlat, endlon, begseg, lrevers) |
---|
| 1018 | if (lthresh) then |
---|
| 1019 | last_loc = location |
---|
| 1020 | intrsct_lat_off = intrsct_lat |
---|
| 1021 | intrsct_lon_off = intrsct_lon |
---|
| 1022 | endif |
---|
| 1023 | return |
---|
| 1024 | |
---|
| 1025 | endif |
---|
| 1026 | |
---|
| 1027 | loutside = .false. |
---|
| 1028 | if (lbegin) then |
---|
| 1029 | lat1 = beglat |
---|
| 1030 | lon1 = beglon |
---|
| 1031 | else |
---|
| 1032 | lat1 = intrsct_lat_off |
---|
| 1033 | lon1 = intrsct_lon_off |
---|
| 1034 | endif |
---|
| 1035 | lat2 = endlat |
---|
| 1036 | lon2 = endlon |
---|
| 1037 | if ((lon2-lon1) > three*pih) then |
---|
| 1038 | lon2 = lon2 - pi2 |
---|
| 1039 | else if ((lon2-lon1) < -three*pih) then |
---|
| 1040 | lon2 = lon2 + pi2 |
---|
| 1041 | endif |
---|
| 1042 | s1 = zero |
---|
| 1043 | |
---|
| 1044 | !----------------------------------------------------------------------- |
---|
| 1045 | ! |
---|
| 1046 | ! search for location of this segment in ocean grid using cross |
---|
| 1047 | ! product method to determine whether a point is enclosed by a cell |
---|
| 1048 | ! |
---|
| 1049 | !----------------------------------------------------------------------- |
---|
| 1050 | |
---|
| 1051 | call timer_start(12) |
---|
| 1052 | srch_corners = size(srch_corner_lat,DIM=1) |
---|
| 1053 | srch_loop: do |
---|
| 1054 | |
---|
| 1055 | !*** |
---|
| 1056 | !*** if last segment crossed threshold, use that location |
---|
| 1057 | !*** |
---|
| 1058 | |
---|
| 1059 | if (lthresh) then |
---|
| 1060 | do cell=1,num_srch_cells |
---|
| 1061 | if (srch_add(cell) == last_loc) then |
---|
| 1062 | location = last_loc |
---|
| 1063 | eps = tiny |
---|
| 1064 | exit srch_loop |
---|
| 1065 | endif |
---|
| 1066 | end do |
---|
| 1067 | endif |
---|
| 1068 | |
---|
| 1069 | !*** |
---|
| 1070 | !*** otherwise normal search algorithm |
---|
| 1071 | !*** |
---|
| 1072 | |
---|
| 1073 | cell_loop: do cell=1,num_srch_cells |
---|
| 1074 | corner_loop: do n=1,srch_corners |
---|
| 1075 | next_n = MOD(n,srch_corners) + 1 |
---|
| 1076 | |
---|
| 1077 | !*** |
---|
| 1078 | !*** here we take the cross product of the vector making |
---|
| 1079 | !*** up each cell side with the vector formed by the vertex |
---|
| 1080 | !*** and search point. if all the cross products are |
---|
| 1081 | !*** positive, the point is contained in the cell. |
---|
| 1082 | !*** |
---|
| 1083 | |
---|
| 1084 | vec1_lat = srch_corner_lat(next_n,cell) - & |
---|
| 1085 | srch_corner_lat(n ,cell) |
---|
| 1086 | vec1_lon = srch_corner_lon(next_n,cell) - & |
---|
| 1087 | srch_corner_lon(n ,cell) |
---|
| 1088 | vec2_lat = lat1 - srch_corner_lat(n,cell) |
---|
| 1089 | vec2_lon = lon1 - srch_corner_lon(n,cell) |
---|
| 1090 | |
---|
| 1091 | !*** |
---|
| 1092 | !*** if endpoint coincident with vertex, offset |
---|
| 1093 | !*** the endpoint |
---|
| 1094 | !*** |
---|
| 1095 | |
---|
| 1096 | if (vec2_lat == 0 .and. vec2_lon == 0) then |
---|
| 1097 | lat1 = lat1 + 1.d-10*(lat2-lat1) |
---|
| 1098 | lon1 = lon1 + 1.d-10*(lon2-lon1) |
---|
| 1099 | vec2_lat = lat1 - srch_corner_lat(n,cell) |
---|
| 1100 | vec2_lon = lon1 - srch_corner_lon(n,cell) |
---|
| 1101 | endif |
---|
| 1102 | |
---|
| 1103 | !*** |
---|
| 1104 | !*** check for 0,2pi crossings |
---|
| 1105 | !*** |
---|
| 1106 | |
---|
| 1107 | if (vec1_lon > pi) then |
---|
| 1108 | vec1_lon = vec1_lon - pi2 |
---|
| 1109 | else if (vec1_lon < -pi) then |
---|
| 1110 | vec1_lon = vec1_lon + pi2 |
---|
| 1111 | endif |
---|
| 1112 | if (vec2_lon > pi) then |
---|
| 1113 | vec2_lon = vec2_lon - pi2 |
---|
| 1114 | else if (vec2_lon < -pi) then |
---|
| 1115 | vec2_lon = vec2_lon + pi2 |
---|
| 1116 | endif |
---|
| 1117 | |
---|
| 1118 | cross_product = vec1_lon*vec2_lat - vec2_lon*vec1_lat |
---|
| 1119 | |
---|
| 1120 | !*** |
---|
| 1121 | !*** if the cross product for a side is zero, the point |
---|
| 1122 | !*** lies exactly on the side or the side is degenerate |
---|
| 1123 | !*** (zero length). if degenerate, set the cross |
---|
| 1124 | !*** product to a positive number. otherwise perform |
---|
| 1125 | !*** another cross product between the side and the |
---|
| 1126 | !*** segment itself. |
---|
| 1127 | !*** if this cross product is also zero, the line is |
---|
| 1128 | !*** coincident with the cell boundary - perform the |
---|
| 1129 | !*** dot product and only choose the cell if the dot |
---|
| 1130 | !*** product is positive (parallel vs anti-parallel). |
---|
| 1131 | !*** |
---|
| 1132 | |
---|
| 1133 | if (cross_product == zero) then |
---|
| 1134 | if (vec1_lat /= zero .or. vec1_lon /= zero) then |
---|
| 1135 | vec2_lat = lat2 - lat1 |
---|
| 1136 | vec2_lon = lon2 - lon1 |
---|
| 1137 | |
---|
| 1138 | if (vec2_lon > pi) then |
---|
| 1139 | vec2_lon = vec2_lon - pi2 |
---|
| 1140 | else if (vec2_lon < -pi) then |
---|
| 1141 | vec2_lon = vec2_lon + pi2 |
---|
| 1142 | endif |
---|
| 1143 | |
---|
| 1144 | cross_product = vec1_lon*vec2_lat - vec2_lon*vec1_lat |
---|
| 1145 | else |
---|
| 1146 | cross_product = one |
---|
| 1147 | endif |
---|
| 1148 | |
---|
| 1149 | if (cross_product == zero) then |
---|
| 1150 | lcoinc = .true. |
---|
| 1151 | cross_product = vec1_lon*vec2_lon + vec1_lat*vec2_lat |
---|
| 1152 | if (lrevers) cross_product = -cross_product |
---|
| 1153 | endif |
---|
| 1154 | endif |
---|
| 1155 | |
---|
| 1156 | !*** |
---|
| 1157 | !*** if cross product is less than zero, this cell |
---|
| 1158 | !*** doesn't work |
---|
| 1159 | !*** |
---|
| 1160 | |
---|
| 1161 | if (cross_product < zero) exit corner_loop |
---|
| 1162 | |
---|
| 1163 | end do corner_loop |
---|
| 1164 | |
---|
| 1165 | !*** |
---|
| 1166 | !*** if cross products all positive, we found the location |
---|
| 1167 | !*** |
---|
| 1168 | |
---|
| 1169 | if (n > srch_corners) then |
---|
| 1170 | location = srch_add(cell) |
---|
| 1171 | |
---|
| 1172 | !*** |
---|
| 1173 | !*** if the beginning of this segment was outside the |
---|
| 1174 | !*** grid, invert the segment so the intersection found |
---|
| 1175 | !*** will be the first intersection with the grid |
---|
| 1176 | !*** |
---|
| 1177 | |
---|
| 1178 | if (loutside) then |
---|
| 1179 | lat2 = beglat |
---|
| 1180 | lon2 = beglon |
---|
| 1181 | location = 0 |
---|
| 1182 | eps = -tiny |
---|
| 1183 | else |
---|
| 1184 | eps = tiny |
---|
| 1185 | endif |
---|
| 1186 | |
---|
| 1187 | exit srch_loop |
---|
| 1188 | endif |
---|
| 1189 | |
---|
| 1190 | !*** |
---|
| 1191 | !*** otherwise move on to next cell |
---|
| 1192 | !*** |
---|
| 1193 | |
---|
| 1194 | end do cell_loop |
---|
| 1195 | |
---|
| 1196 | !*** |
---|
| 1197 | !*** if still no cell found, the point lies outside the grid. |
---|
| 1198 | !*** take some baby steps along the segment to see if any |
---|
| 1199 | !*** part of the segment lies inside the grid. |
---|
| 1200 | !*** |
---|
| 1201 | |
---|
| 1202 | loutside = .true. |
---|
| 1203 | s1 = s1 + 0.001_dbl_kind |
---|
| 1204 | lat1 = beglat + s1*(endlat - beglat) |
---|
| 1205 | lon1 = beglon + s1*(lon2 - beglon) |
---|
| 1206 | |
---|
| 1207 | !*** |
---|
| 1208 | !*** reached the end of the segment and still outside the grid |
---|
| 1209 | !*** return no intersection |
---|
| 1210 | !*** |
---|
| 1211 | |
---|
| 1212 | if (s1 >= one) return |
---|
| 1213 | |
---|
| 1214 | end do srch_loop |
---|
| 1215 | call timer_stop(12) |
---|
| 1216 | |
---|
| 1217 | !----------------------------------------------------------------------- |
---|
| 1218 | ! |
---|
| 1219 | ! now that a cell is found, search for the next intersection. |
---|
| 1220 | ! loop over sides of the cell to find intersection with side |
---|
| 1221 | ! must check all sides for coincidences or intersections |
---|
| 1222 | ! |
---|
| 1223 | !----------------------------------------------------------------------- |
---|
| 1224 | |
---|
| 1225 | call timer_start(13) |
---|
| 1226 | intrsct_loop: do n=1,srch_corners |
---|
| 1227 | next_n = mod(n,srch_corners) + 1 |
---|
| 1228 | |
---|
| 1229 | grdlon1 = srch_corner_lon(n ,cell) |
---|
| 1230 | grdlon2 = srch_corner_lon(next_n,cell) |
---|
| 1231 | grdlat1 = srch_corner_lat(n ,cell) |
---|
| 1232 | grdlat2 = srch_corner_lat(next_n,cell) |
---|
| 1233 | |
---|
| 1234 | !*** |
---|
| 1235 | !*** set up linear system to solve for intersection |
---|
| 1236 | !*** |
---|
| 1237 | |
---|
| 1238 | mat1 = lat2 - lat1 |
---|
| 1239 | mat2 = grdlat1 - grdlat2 |
---|
| 1240 | mat3 = lon2 - lon1 |
---|
| 1241 | mat4 = grdlon1 - grdlon2 |
---|
| 1242 | rhs1 = grdlat1 - lat1 |
---|
| 1243 | rhs2 = grdlon1 - lon1 |
---|
| 1244 | |
---|
| 1245 | if (mat3 > pi) then |
---|
| 1246 | mat3 = mat3 - pi2 |
---|
| 1247 | else if (mat3 < -pi) then |
---|
| 1248 | mat3 = mat3 + pi2 |
---|
| 1249 | endif |
---|
| 1250 | if (mat4 > pi) then |
---|
| 1251 | mat4 = mat4 - pi2 |
---|
| 1252 | else if (mat4 < -pi) then |
---|
| 1253 | mat4 = mat4 + pi2 |
---|
| 1254 | endif |
---|
| 1255 | if (rhs2 > pi) then |
---|
| 1256 | rhs2 = rhs2 - pi2 |
---|
| 1257 | else if (rhs2 < -pi) then |
---|
| 1258 | rhs2 = rhs2 + pi2 |
---|
| 1259 | endif |
---|
| 1260 | |
---|
| 1261 | determ = mat1*mat4 - mat2*mat3 |
---|
| 1262 | |
---|
| 1263 | !*** |
---|
| 1264 | !*** if the determinant is zero, the segments are either |
---|
| 1265 | !*** parallel or coincident. coincidences were detected |
---|
| 1266 | !*** above so do nothing. |
---|
| 1267 | !*** if the determinant is non-zero, solve for the linear |
---|
| 1268 | !*** parameters s for the intersection point on each line |
---|
| 1269 | !*** segment. |
---|
| 1270 | !*** if 0<s1,s2<1 then the segment intersects with this side. |
---|
| 1271 | !*** return the point of intersection (adding a small |
---|
| 1272 | !*** number so the intersection is off the grid line). |
---|
| 1273 | !*** |
---|
| 1274 | |
---|
| 1275 | if (abs(determ) > 1.e-30) then |
---|
| 1276 | |
---|
| 1277 | s1 = (rhs1*mat4 - mat2*rhs2)/determ |
---|
| 1278 | s2 = (mat1*rhs2 - rhs1*mat3)/determ |
---|
| 1279 | |
---|
| 1280 | if (s2 >= zero .and. s2 <= one .and. & |
---|
| 1281 | s1 > zero .and. s1 <= one) then |
---|
| 1282 | |
---|
| 1283 | !*** |
---|
| 1284 | !*** recompute intersection based on full segment |
---|
| 1285 | !*** so intersections are consistent for both sweeps |
---|
| 1286 | !*** |
---|
| 1287 | |
---|
| 1288 | if (.not. loutside) then |
---|
| 1289 | mat1 = lat2 - begseg(1) |
---|
| 1290 | mat3 = lon2 - begseg(2) |
---|
| 1291 | rhs1 = grdlat1 - begseg(1) |
---|
| 1292 | rhs2 = grdlon1 - begseg(2) |
---|
| 1293 | else |
---|
| 1294 | mat1 = begseg(1) - endlat |
---|
| 1295 | mat3 = begseg(2) - endlon |
---|
| 1296 | rhs1 = grdlat1 - endlat |
---|
| 1297 | rhs2 = grdlon1 - endlon |
---|
| 1298 | endif |
---|
| 1299 | |
---|
| 1300 | if (mat3 > pi) then |
---|
| 1301 | mat3 = mat3 - pi2 |
---|
| 1302 | else if (mat3 < -pi) then |
---|
| 1303 | mat3 = mat3 + pi2 |
---|
| 1304 | endif |
---|
| 1305 | if (rhs2 > pi) then |
---|
| 1306 | rhs2 = rhs2 - pi2 |
---|
| 1307 | else if (rhs2 < -pi) then |
---|
| 1308 | rhs2 = rhs2 + pi2 |
---|
| 1309 | endif |
---|
| 1310 | |
---|
| 1311 | determ = mat1*mat4 - mat2*mat3 |
---|
| 1312 | |
---|
| 1313 | !*** |
---|
| 1314 | !*** sometimes due to roundoff, the previous |
---|
| 1315 | !*** determinant is non-zero, but the lines |
---|
| 1316 | !*** are actually coincident. if this is the |
---|
| 1317 | !*** case, skip the rest. |
---|
| 1318 | !*** |
---|
| 1319 | |
---|
| 1320 | if (determ /= zero) then |
---|
| 1321 | s1 = (rhs1*mat4 - mat2*rhs2)/determ |
---|
| 1322 | s2 = (mat1*rhs2 - rhs1*mat3)/determ |
---|
| 1323 | |
---|
| 1324 | offset = s1 + eps/determ |
---|
| 1325 | if (offset > one) offset = one |
---|
| 1326 | |
---|
| 1327 | if (.not. loutside) then |
---|
| 1328 | intrsct_lat = begseg(1) + mat1*s1 |
---|
| 1329 | intrsct_lon = begseg(2) + mat3*s1 |
---|
| 1330 | intrsct_lat_off = begseg(1) + mat1*offset |
---|
| 1331 | intrsct_lon_off = begseg(2) + mat3*offset |
---|
| 1332 | else |
---|
| 1333 | intrsct_lat = endlat + mat1*s1 |
---|
| 1334 | intrsct_lon = endlon + mat3*s1 |
---|
| 1335 | intrsct_lat_off = endlat + mat1*offset |
---|
| 1336 | intrsct_lon_off = endlon + mat3*offset |
---|
| 1337 | endif |
---|
| 1338 | exit intrsct_loop |
---|
| 1339 | endif |
---|
| 1340 | |
---|
| 1341 | endif |
---|
| 1342 | endif |
---|
| 1343 | |
---|
| 1344 | !*** |
---|
| 1345 | !*** no intersection this side, move on to next side |
---|
| 1346 | !*** |
---|
| 1347 | |
---|
| 1348 | end do intrsct_loop |
---|
| 1349 | call timer_stop(13) |
---|
| 1350 | |
---|
| 1351 | !----------------------------------------------------------------------- |
---|
| 1352 | ! |
---|
| 1353 | ! if the segment crosses a pole threshold, reset the intersection |
---|
| 1354 | ! to be the threshold latitude. only check if this was not a |
---|
| 1355 | ! threshold segment since sometimes coordinate transform can end |
---|
| 1356 | ! up on other side of threshold again. |
---|
| 1357 | ! |
---|
| 1358 | !----------------------------------------------------------------------- |
---|
| 1359 | |
---|
| 1360 | if (lthresh) then |
---|
| 1361 | if (intrsct_lat < north_thresh .or. intrsct_lat > south_thresh) & |
---|
| 1362 | lthresh = .false. |
---|
| 1363 | else if (lat1 > zero .and. intrsct_lat > north_thresh) then |
---|
| 1364 | intrsct_lat = north_thresh + tiny |
---|
| 1365 | intrsct_lat_off = north_thresh + eps*mat1 |
---|
| 1366 | s1 = (intrsct_lat - begseg(1))/mat1 |
---|
| 1367 | intrsct_lon = begseg(2) + s1*mat3 |
---|
| 1368 | intrsct_lon_off = begseg(2) + (s1+eps)*mat3 |
---|
| 1369 | last_loc = location |
---|
| 1370 | lthresh = .true. |
---|
| 1371 | else if (lat1 < zero .and. intrsct_lat < south_thresh) then |
---|
| 1372 | intrsct_lat = south_thresh - tiny |
---|
| 1373 | intrsct_lat_off = south_thresh + eps*mat1 |
---|
| 1374 | s1 = (intrsct_lat - begseg(1))/mat1 |
---|
| 1375 | intrsct_lon = begseg(2) + s1*mat3 |
---|
| 1376 | intrsct_lon_off = begseg(2) + (s1+eps)*mat3 |
---|
| 1377 | last_loc = location |
---|
| 1378 | lthresh = .true. |
---|
| 1379 | endif |
---|
| 1380 | |
---|
| 1381 | !----------------------------------------------------------------------- |
---|
| 1382 | |
---|
| 1383 | end subroutine intersection |
---|
| 1384 | |
---|
| 1385 | !*********************************************************************** |
---|
| 1386 | |
---|
| 1387 | subroutine pole_intersection(location, & |
---|
| 1388 | intrsct_lat,intrsct_lon,lcoinc,lthresh, & |
---|
| 1389 | beglat, beglon, endlat, endlon, begseg, lrevers) |
---|
| 1390 | |
---|
| 1391 | !----------------------------------------------------------------------- |
---|
| 1392 | ! |
---|
| 1393 | ! this routine is identical to the intersection routine except |
---|
| 1394 | ! that a coordinate transformation (using a Lambert azimuthal |
---|
| 1395 | ! equivalent projection) is performed to treat polar cells more |
---|
| 1396 | ! accurately. |
---|
| 1397 | ! |
---|
| 1398 | !----------------------------------------------------------------------- |
---|
| 1399 | |
---|
| 1400 | !----------------------------------------------------------------------- |
---|
| 1401 | ! |
---|
| 1402 | ! intent(in): |
---|
| 1403 | ! |
---|
| 1404 | !----------------------------------------------------------------------- |
---|
| 1405 | |
---|
| 1406 | real (kind=dbl_kind), intent(in) :: & |
---|
| 1407 | beglat, beglon, & ! beginning lat/lon endpoints for segment |
---|
| 1408 | endlat, endlon ! ending lat/lon endpoints for segment |
---|
| 1409 | |
---|
| 1410 | real (kind=dbl_kind), dimension(2), intent(inout) :: & |
---|
| 1411 | begseg ! begin lat/lon of full segment |
---|
| 1412 | |
---|
| 1413 | logical (kind=log_kind), intent(in) :: & |
---|
| 1414 | lrevers ! flag true if segment integrated in reverse |
---|
| 1415 | |
---|
| 1416 | !----------------------------------------------------------------------- |
---|
| 1417 | ! |
---|
| 1418 | ! intent(out): |
---|
| 1419 | ! |
---|
| 1420 | !----------------------------------------------------------------------- |
---|
| 1421 | |
---|
| 1422 | integer (kind=int_kind), intent(inout) :: & |
---|
| 1423 | location ! address in destination array containing this |
---|
| 1424 | ! segment -- also may contain last location on |
---|
| 1425 | ! entry |
---|
| 1426 | |
---|
| 1427 | logical (kind=log_kind), intent(out) :: & |
---|
| 1428 | lcoinc ! flag segment coincident with grid line |
---|
| 1429 | |
---|
| 1430 | logical (kind=log_kind), intent(inout) :: & |
---|
| 1431 | lthresh ! flag segment crossing threshold boundary |
---|
| 1432 | |
---|
| 1433 | real (kind=dbl_kind), intent(out) :: & |
---|
| 1434 | intrsct_lat, intrsct_lon ! lat/lon coords of next intersect. |
---|
| 1435 | |
---|
| 1436 | !----------------------------------------------------------------------- |
---|
| 1437 | ! |
---|
| 1438 | ! local variables |
---|
| 1439 | ! |
---|
| 1440 | !----------------------------------------------------------------------- |
---|
| 1441 | |
---|
| 1442 | integer (kind=int_kind) :: n, next_n, cell, srch_corners, pole_loc |
---|
| 1443 | |
---|
| 1444 | logical (kind=log_kind) :: loutside ! flags points outside grid |
---|
| 1445 | |
---|
| 1446 | real (kind=dbl_kind) :: pi4, rns, & ! north/south conversion |
---|
| 1447 | x1, x2, & ! local x variables for segment |
---|
| 1448 | y1, y2, & ! local y variables for segment |
---|
| 1449 | begx, begy, & ! beginning x,y variables for segment |
---|
| 1450 | endx, endy, & ! beginning x,y variables for segment |
---|
| 1451 | begsegx, begsegy, & ! beginning x,y variables for segment |
---|
| 1452 | grdx1, grdx2, & ! local x variables for grid cell |
---|
| 1453 | grdy1, grdy2, & ! local y variables for grid cell |
---|
| 1454 | vec1_y, vec1_x, & ! vectors and cross products used |
---|
| 1455 | vec2_y, vec2_x, & ! during grid search |
---|
| 1456 | cross_product, eps, & ! eps=small offset away from intersect |
---|
| 1457 | s1, s2, determ, & ! variables used for linear solve to |
---|
| 1458 | mat1, mat2, mat3, mat4, rhs1, rhs2 ! find intersection |
---|
| 1459 | |
---|
| 1460 | real (kind=dbl_kind), dimension(:,:), allocatable :: & |
---|
| 1461 | srch_corner_x, & ! x of each corner of srch cells |
---|
| 1462 | srch_corner_y ! y of each corner of srch cells |
---|
| 1463 | |
---|
| 1464 | !*** |
---|
| 1465 | !*** save last intersection to avoid roundoff during coord |
---|
| 1466 | !*** transformation |
---|
| 1467 | !*** |
---|
| 1468 | |
---|
| 1469 | logical (kind=log_kind), save :: luse_last = .false. |
---|
| 1470 | |
---|
| 1471 | real (kind=dbl_kind), save :: & |
---|
| 1472 | intrsct_x, intrsct_y ! x,y for intersection |
---|
| 1473 | |
---|
| 1474 | !*** |
---|
| 1475 | !*** variables necessary if segment manages to hit pole |
---|
| 1476 | !*** |
---|
| 1477 | |
---|
| 1478 | integer (kind=int_kind), save :: & |
---|
| 1479 | avoid_pole_count = 0 ! count attempts to avoid pole |
---|
| 1480 | |
---|
| 1481 | real (kind=dbl_kind), save :: & |
---|
| 1482 | avoid_pole_offset = tiny ! endpoint offset to avoid pole |
---|
| 1483 | |
---|
| 1484 | !----------------------------------------------------------------------- |
---|
| 1485 | ! |
---|
| 1486 | ! initialize defaults, flags, etc. |
---|
| 1487 | ! |
---|
| 1488 | !----------------------------------------------------------------------- |
---|
| 1489 | |
---|
| 1490 | if (.not. lthresh) location = 0 |
---|
| 1491 | lcoinc = .false. |
---|
| 1492 | intrsct_lat = endlat |
---|
| 1493 | intrsct_lon = endlon |
---|
| 1494 | |
---|
| 1495 | loutside = .false. |
---|
| 1496 | s1 = zero |
---|
| 1497 | |
---|
| 1498 | !----------------------------------------------------------------------- |
---|
| 1499 | ! |
---|
| 1500 | ! convert coordinates |
---|
| 1501 | ! |
---|
| 1502 | !----------------------------------------------------------------------- |
---|
| 1503 | |
---|
| 1504 | allocate(srch_corner_x(size(srch_corner_lat,DIM=1), & |
---|
| 1505 | size(srch_corner_lat,DIM=2)), & |
---|
| 1506 | srch_corner_y(size(srch_corner_lat,DIM=1), & |
---|
| 1507 | size(srch_corner_lat,DIM=2))) |
---|
| 1508 | |
---|
| 1509 | if (beglat > zero) then |
---|
| 1510 | pi4 = quart*pi |
---|
| 1511 | rns = one |
---|
| 1512 | else |
---|
| 1513 | pi4 = -quart*pi |
---|
| 1514 | rns = -one |
---|
| 1515 | endif |
---|
| 1516 | |
---|
| 1517 | if (luse_last) then |
---|
| 1518 | x1 = intrsct_x |
---|
| 1519 | y1 = intrsct_y |
---|
| 1520 | else |
---|
| 1521 | x1 = rns*two*sin(pi4 - half*beglat)*cos(beglon) |
---|
| 1522 | y1 = two*sin(pi4 - half*beglat)*sin(beglon) |
---|
| 1523 | luse_last = .true. |
---|
| 1524 | endif |
---|
| 1525 | x2 = rns*two*sin(pi4 - half*endlat)*cos(endlon) |
---|
| 1526 | y2 = two*sin(pi4 - half*endlat)*sin(endlon) |
---|
| 1527 | srch_corner_x = rns*two*sin(pi4 - half*srch_corner_lat)* & |
---|
| 1528 | cos(srch_corner_lon) |
---|
| 1529 | srch_corner_y = two*sin(pi4 - half*srch_corner_lat)* & |
---|
| 1530 | sin(srch_corner_lon) |
---|
| 1531 | |
---|
| 1532 | begx = x1 |
---|
| 1533 | begy = y1 |
---|
| 1534 | endx = x2 |
---|
| 1535 | endy = y2 |
---|
| 1536 | begsegx = rns*two*sin(pi4 - half*begseg(1))*cos(begseg(2)) |
---|
| 1537 | begsegy = two*sin(pi4 - half*begseg(1))*sin(begseg(2)) |
---|
| 1538 | intrsct_x = endx |
---|
| 1539 | intrsct_y = endy |
---|
| 1540 | |
---|
| 1541 | !----------------------------------------------------------------------- |
---|
| 1542 | ! |
---|
| 1543 | ! search for location of this segment in ocean grid using cross |
---|
| 1544 | ! product method to determine whether a point is enclosed by a cell |
---|
| 1545 | ! |
---|
| 1546 | !----------------------------------------------------------------------- |
---|
| 1547 | |
---|
| 1548 | call timer_start(12) |
---|
| 1549 | srch_corners = size(srch_corner_lat,DIM=1) |
---|
| 1550 | srch_loop: do |
---|
| 1551 | |
---|
| 1552 | !*** |
---|
| 1553 | !*** if last segment crossed threshold, use that location |
---|
| 1554 | !*** |
---|
| 1555 | |
---|
| 1556 | if (lthresh) then |
---|
| 1557 | do cell=1,num_srch_cells |
---|
| 1558 | if (srch_add(cell) == location) then |
---|
| 1559 | eps = tiny |
---|
| 1560 | exit srch_loop |
---|
| 1561 | endif |
---|
| 1562 | end do |
---|
| 1563 | endif |
---|
| 1564 | |
---|
| 1565 | !*** |
---|
| 1566 | !*** otherwise normal search algorithm |
---|
| 1567 | !*** |
---|
| 1568 | |
---|
| 1569 | cell_loop: do cell=1,num_srch_cells |
---|
| 1570 | corner_loop: do n=1,srch_corners |
---|
| 1571 | next_n = MOD(n,srch_corners) + 1 |
---|
| 1572 | |
---|
| 1573 | !*** |
---|
| 1574 | !*** here we take the cross product of the vector making |
---|
| 1575 | !*** up each cell side with the vector formed by the vertex |
---|
| 1576 | !*** and search point. if all the cross products are |
---|
| 1577 | !*** positive, the point is contained in the cell. |
---|
| 1578 | !*** |
---|
| 1579 | |
---|
| 1580 | vec1_x = srch_corner_x(next_n,cell) - & |
---|
| 1581 | srch_corner_x(n ,cell) |
---|
| 1582 | vec1_y = srch_corner_y(next_n,cell) - & |
---|
| 1583 | srch_corner_y(n ,cell) |
---|
| 1584 | vec2_x = x1 - srch_corner_x(n,cell) |
---|
| 1585 | vec2_y = y1 - srch_corner_y(n,cell) |
---|
| 1586 | |
---|
| 1587 | !*** |
---|
| 1588 | !*** if endpoint coincident with vertex, offset |
---|
| 1589 | !*** the endpoint |
---|
| 1590 | !*** |
---|
| 1591 | |
---|
| 1592 | if (vec2_x == 0 .and. vec2_y == 0) then |
---|
| 1593 | x1 = x1 + 1.d-10*(x2-x1) |
---|
| 1594 | y1 = y1 + 1.d-10*(y2-y1) |
---|
| 1595 | vec2_x = x1 - srch_corner_x(n,cell) |
---|
| 1596 | vec2_y = y1 - srch_corner_y(n,cell) |
---|
| 1597 | endif |
---|
| 1598 | |
---|
| 1599 | cross_product = vec1_x*vec2_y - vec2_x*vec1_y |
---|
| 1600 | |
---|
| 1601 | !*** |
---|
| 1602 | !*** if the cross product for a side is zero, the point |
---|
| 1603 | !*** lies exactly on the side or the length of a side |
---|
| 1604 | !*** is zero. if the length is zero set det > 0. |
---|
| 1605 | !*** otherwise, perform another cross |
---|
| 1606 | !*** product between the side and the segment itself. |
---|
| 1607 | !*** if this cross product is also zero, the line is |
---|
| 1608 | !*** coincident with the cell boundary - perform the |
---|
| 1609 | !*** dot product and only choose the cell if the dot |
---|
| 1610 | !*** product is positive (parallel vs anti-parallel). |
---|
| 1611 | !*** |
---|
| 1612 | |
---|
| 1613 | if (cross_product == zero) then |
---|
| 1614 | if (vec1_x /= zero .or. vec1_y /= 0) then |
---|
| 1615 | vec2_x = x2 - x1 |
---|
| 1616 | vec2_y = y2 - y1 |
---|
| 1617 | cross_product = vec1_x*vec2_y - vec2_x*vec1_y |
---|
| 1618 | else |
---|
| 1619 | cross_product = one |
---|
| 1620 | endif |
---|
| 1621 | |
---|
| 1622 | if (cross_product == zero) then |
---|
| 1623 | lcoinc = .true. |
---|
| 1624 | cross_product = vec1_x*vec2_x + vec1_y*vec2_y |
---|
| 1625 | if (lrevers) cross_product = -cross_product |
---|
| 1626 | endif |
---|
| 1627 | endif |
---|
| 1628 | |
---|
| 1629 | !*** |
---|
| 1630 | !*** if cross product is less than zero, this cell |
---|
| 1631 | !*** doesn't work |
---|
| 1632 | !*** |
---|
| 1633 | |
---|
| 1634 | if (cross_product < zero) exit corner_loop |
---|
| 1635 | |
---|
| 1636 | end do corner_loop |
---|
| 1637 | |
---|
| 1638 | !*** |
---|
| 1639 | !*** if cross products all positive, we found the location |
---|
| 1640 | !*** |
---|
| 1641 | |
---|
| 1642 | if (n > srch_corners) then |
---|
| 1643 | location = srch_add(cell) |
---|
| 1644 | |
---|
| 1645 | !*** |
---|
| 1646 | !*** if the beginning of this segment was outside the |
---|
| 1647 | !*** grid, invert the segment so the intersection found |
---|
| 1648 | !*** will be the first intersection with the grid |
---|
| 1649 | !*** |
---|
| 1650 | |
---|
| 1651 | if (loutside) then |
---|
| 1652 | x2 = begx |
---|
| 1653 | y2 = begy |
---|
| 1654 | location = 0 |
---|
| 1655 | eps = -tiny |
---|
| 1656 | else |
---|
| 1657 | eps = tiny |
---|
| 1658 | endif |
---|
| 1659 | |
---|
| 1660 | exit srch_loop |
---|
| 1661 | endif |
---|
| 1662 | |
---|
| 1663 | !*** |
---|
| 1664 | !*** otherwise move on to next cell |
---|
| 1665 | !*** |
---|
| 1666 | |
---|
| 1667 | end do cell_loop |
---|
| 1668 | |
---|
| 1669 | !*** |
---|
| 1670 | !*** if no cell found, the point lies outside the grid. |
---|
| 1671 | !*** take some baby steps along the segment to see if any |
---|
| 1672 | !*** part of the segment lies inside the grid. |
---|
| 1673 | !*** |
---|
| 1674 | |
---|
| 1675 | loutside = .true. |
---|
| 1676 | s1 = s1 + 0.001_dbl_kind |
---|
| 1677 | x1 = begx + s1*(x2 - begx) |
---|
| 1678 | y1 = begy + s1*(y2 - begy) |
---|
| 1679 | |
---|
| 1680 | !*** |
---|
| 1681 | !*** reached the end of the segment and still outside the grid |
---|
| 1682 | !*** return no intersection |
---|
| 1683 | !*** |
---|
| 1684 | |
---|
| 1685 | if (s1 >= one) then |
---|
| 1686 | deallocate(srch_corner_x, srch_corner_y) |
---|
| 1687 | luse_last = .false. |
---|
| 1688 | return |
---|
| 1689 | endif |
---|
| 1690 | |
---|
| 1691 | end do srch_loop |
---|
| 1692 | call timer_stop(12) |
---|
| 1693 | |
---|
| 1694 | !----------------------------------------------------------------------- |
---|
| 1695 | ! |
---|
| 1696 | ! now that a cell is found, search for the next intersection. |
---|
| 1697 | ! loop over sides of the cell to find intersection with side |
---|
| 1698 | ! must check all sides for coincidences or intersections |
---|
| 1699 | ! |
---|
| 1700 | !----------------------------------------------------------------------- |
---|
| 1701 | |
---|
| 1702 | call timer_start(13) |
---|
| 1703 | intrsct_loop: do n=1,srch_corners |
---|
| 1704 | next_n = mod(n,srch_corners) + 1 |
---|
| 1705 | |
---|
| 1706 | grdy1 = srch_corner_y(n ,cell) |
---|
| 1707 | grdy2 = srch_corner_y(next_n,cell) |
---|
| 1708 | grdx1 = srch_corner_x(n ,cell) |
---|
| 1709 | grdx2 = srch_corner_x(next_n,cell) |
---|
| 1710 | |
---|
| 1711 | !*** |
---|
| 1712 | !*** set up linear system to solve for intersection |
---|
| 1713 | !*** |
---|
| 1714 | |
---|
| 1715 | mat1 = x2 - x1 |
---|
| 1716 | mat2 = grdx1 - grdx2 |
---|
| 1717 | mat3 = y2 - y1 |
---|
| 1718 | mat4 = grdy1 - grdy2 |
---|
| 1719 | rhs1 = grdx1 - x1 |
---|
| 1720 | rhs2 = grdy1 - y1 |
---|
| 1721 | |
---|
| 1722 | determ = mat1*mat4 - mat2*mat3 |
---|
| 1723 | |
---|
| 1724 | !*** |
---|
| 1725 | !*** if the determinant is zero, the segments are either |
---|
| 1726 | !*** parallel or coincident or one segment has zero length. |
---|
| 1727 | !*** coincidences were detected above so do nothing. |
---|
| 1728 | !*** if the determinant is non-zero, solve for the linear |
---|
| 1729 | !*** parameters s for the intersection point on each line |
---|
| 1730 | !*** segment. |
---|
| 1731 | !*** if 0<s1,s2<1 then the segment intersects with this side. |
---|
| 1732 | !*** return the point of intersection (adding a small |
---|
| 1733 | !*** number so the intersection is off the grid line). |
---|
| 1734 | !*** |
---|
| 1735 | |
---|
| 1736 | if (abs(determ) > 1.e-30) then |
---|
| 1737 | |
---|
| 1738 | s1 = (rhs1*mat4 - mat2*rhs2)/determ |
---|
| 1739 | s2 = (mat1*rhs2 - rhs1*mat3)/determ |
---|
| 1740 | |
---|
| 1741 | if (s2 >= zero .and. s2 <= one .and. & |
---|
| 1742 | s1 > zero .and. s1 <= one) then |
---|
| 1743 | |
---|
| 1744 | !*** |
---|
| 1745 | !*** recompute intersection using entire segment |
---|
| 1746 | !*** for consistency between sweeps |
---|
| 1747 | !*** |
---|
| 1748 | |
---|
| 1749 | if (.not. loutside) then |
---|
| 1750 | mat1 = x2 - begsegx |
---|
| 1751 | mat3 = y2 - begsegy |
---|
| 1752 | rhs1 = grdx1 - begsegx |
---|
| 1753 | rhs2 = grdy1 - begsegy |
---|
| 1754 | else |
---|
| 1755 | mat1 = x2 - endx |
---|
| 1756 | mat3 = y2 - endy |
---|
| 1757 | rhs1 = grdx1 - endx |
---|
| 1758 | rhs2 = grdy1 - endy |
---|
| 1759 | endif |
---|
| 1760 | |
---|
| 1761 | determ = mat1*mat4 - mat2*mat3 |
---|
| 1762 | |
---|
| 1763 | !*** |
---|
| 1764 | !*** sometimes due to roundoff, the previous |
---|
| 1765 | !*** determinant is non-zero, but the lines |
---|
| 1766 | !*** are actually coincident. if this is the |
---|
| 1767 | !*** case, skip the rest. |
---|
| 1768 | !*** |
---|
| 1769 | |
---|
| 1770 | if (determ /= zero) then |
---|
| 1771 | s1 = (rhs1*mat4 - mat2*rhs2)/determ |
---|
| 1772 | s2 = (mat1*rhs2 - rhs1*mat3)/determ |
---|
| 1773 | |
---|
| 1774 | if (.not. loutside) then |
---|
| 1775 | intrsct_x = begsegx + s1*mat1 |
---|
| 1776 | intrsct_y = begsegy + s1*mat3 |
---|
| 1777 | else |
---|
| 1778 | intrsct_x = endx + s1*mat1 |
---|
| 1779 | intrsct_y = endy + s1*mat3 |
---|
| 1780 | endif |
---|
| 1781 | |
---|
| 1782 | !*** |
---|
| 1783 | !*** convert back to lat/lon coordinates |
---|
| 1784 | !*** |
---|
| 1785 | |
---|
| 1786 | intrsct_lon = rns*atan2(intrsct_y,intrsct_x) |
---|
| 1787 | if (intrsct_lon < zero) & |
---|
| 1788 | intrsct_lon = intrsct_lon + pi2 |
---|
| 1789 | |
---|
| 1790 | if (abs(intrsct_x) > 1.d-10) then |
---|
| 1791 | intrsct_lat = (pi4 - & |
---|
| 1792 | asin(rns*half*intrsct_x/cos(intrsct_lon)))*two |
---|
| 1793 | else if (abs(intrsct_y) > 1.d-10) then |
---|
| 1794 | intrsct_lat = (pi4 - & |
---|
| 1795 | asin(half*intrsct_y/sin(intrsct_lon)))*two |
---|
| 1796 | else |
---|
| 1797 | intrsct_lat = two*pi4 |
---|
| 1798 | endif |
---|
| 1799 | |
---|
| 1800 | !*** |
---|
| 1801 | !*** add offset in transformed space for next pass. |
---|
| 1802 | !*** |
---|
| 1803 | |
---|
| 1804 | if (s1 - eps/determ < one) then |
---|
| 1805 | intrsct_x = intrsct_x - mat1*(eps/determ) |
---|
| 1806 | intrsct_y = intrsct_y - mat3*(eps/determ) |
---|
| 1807 | else |
---|
| 1808 | if (.not. loutside) then |
---|
| 1809 | intrsct_x = endx |
---|
| 1810 | intrsct_y = endy |
---|
| 1811 | intrsct_lat = endlat |
---|
| 1812 | intrsct_lon = endlon |
---|
| 1813 | else |
---|
| 1814 | intrsct_x = begsegx |
---|
| 1815 | intrsct_y = begsegy |
---|
| 1816 | intrsct_lat = begseg(1) |
---|
| 1817 | intrsct_lon = begseg(2) |
---|
| 1818 | endif |
---|
| 1819 | endif |
---|
| 1820 | |
---|
| 1821 | exit intrsct_loop |
---|
| 1822 | endif |
---|
| 1823 | endif |
---|
| 1824 | endif |
---|
| 1825 | |
---|
| 1826 | !*** |
---|
| 1827 | !*** no intersection this side, move on to next side |
---|
| 1828 | !*** |
---|
| 1829 | |
---|
| 1830 | end do intrsct_loop |
---|
| 1831 | call timer_stop(13) |
---|
| 1832 | |
---|
| 1833 | deallocate(srch_corner_x, srch_corner_y) |
---|
| 1834 | |
---|
| 1835 | !----------------------------------------------------------------------- |
---|
| 1836 | ! |
---|
| 1837 | ! if segment manages to cross over pole, shift the beginning |
---|
| 1838 | ! endpoint in order to avoid hitting pole directly |
---|
| 1839 | ! (it is ok for endpoint to be pole point) |
---|
| 1840 | ! |
---|
| 1841 | !----------------------------------------------------------------------- |
---|
| 1842 | |
---|
| 1843 | if (abs(intrsct_x) < 1.e-10 .and. abs(intrsct_y) < 1.e-10 .and. & |
---|
| 1844 | (endx /= zero .and. endy /=0)) then |
---|
| 1845 | if (avoid_pole_count > 2) then |
---|
| 1846 | avoid_pole_count = 0 |
---|
| 1847 | avoid_pole_offset = 10.*avoid_pole_offset |
---|
| 1848 | endif |
---|
| 1849 | |
---|
| 1850 | cross_product = begsegx*(endy-begsegy) - begsegy*(endx-begsegx) |
---|
| 1851 | intrsct_lat = begseg(1) |
---|
| 1852 | if (cross_product*intrsct_lat > zero) then |
---|
| 1853 | intrsct_lon = beglon + avoid_pole_offset |
---|
| 1854 | begseg(2) = begseg(2) + avoid_pole_offset |
---|
| 1855 | else |
---|
| 1856 | intrsct_lon = beglon - avoid_pole_offset |
---|
| 1857 | begseg(2) = begseg(2) - avoid_pole_offset |
---|
| 1858 | endif |
---|
| 1859 | |
---|
| 1860 | avoid_pole_count = avoid_pole_count + 1 |
---|
| 1861 | luse_last = .false. |
---|
| 1862 | else |
---|
| 1863 | avoid_pole_count = 0 |
---|
| 1864 | avoid_pole_offset = tiny |
---|
| 1865 | endif |
---|
| 1866 | |
---|
| 1867 | !----------------------------------------------------------------------- |
---|
| 1868 | ! |
---|
| 1869 | ! if the segment crosses a pole threshold, reset the intersection |
---|
| 1870 | ! to be the threshold latitude and do not reuse x,y intersect |
---|
| 1871 | ! on next entry. only check if did not cross threshold last |
---|
| 1872 | ! time - sometimes the coordinate transformation can place a |
---|
| 1873 | ! segment on the other side of the threshold again |
---|
| 1874 | ! |
---|
| 1875 | !----------------------------------------------------------------------- |
---|
| 1876 | |
---|
| 1877 | if (lthresh) then |
---|
| 1878 | if (intrsct_lat > north_thresh .or. intrsct_lat < south_thresh) & |
---|
| 1879 | lthresh = .false. |
---|
| 1880 | else if (beglat > zero .and. intrsct_lat < north_thresh) then |
---|
| 1881 | mat4 = endlat - begseg(1) |
---|
| 1882 | mat3 = endlon - begseg(2) |
---|
| 1883 | if (mat3 > pi) mat3 = mat3 - pi2 |
---|
| 1884 | if (mat3 < -pi) mat3 = mat3 + pi2 |
---|
| 1885 | intrsct_lat = north_thresh - tiny |
---|
| 1886 | s1 = (north_thresh - begseg(1))/mat4 |
---|
| 1887 | intrsct_lon = begseg(2) + s1*mat3 |
---|
| 1888 | luse_last = .false. |
---|
| 1889 | lthresh = .true. |
---|
| 1890 | else if (beglat < zero .and. intrsct_lat > south_thresh) then |
---|
| 1891 | mat4 = endlat - begseg(1) |
---|
| 1892 | mat3 = endlon - begseg(2) |
---|
| 1893 | if (mat3 > pi) mat3 = mat3 - pi2 |
---|
| 1894 | if (mat3 < -pi) mat3 = mat3 + pi2 |
---|
| 1895 | intrsct_lat = south_thresh + tiny |
---|
| 1896 | s1 = (south_thresh - begseg(1))/mat4 |
---|
| 1897 | intrsct_lon = begseg(2) + s1*mat3 |
---|
| 1898 | luse_last = .false. |
---|
| 1899 | lthresh = .true. |
---|
| 1900 | endif |
---|
| 1901 | |
---|
| 1902 | !*** |
---|
| 1903 | !*** if reached end of segment, do not use x,y intersect |
---|
| 1904 | !*** on next entry |
---|
| 1905 | !*** |
---|
| 1906 | |
---|
| 1907 | if (intrsct_lat == endlat .and. intrsct_lon == endlon) then |
---|
| 1908 | luse_last = .false. |
---|
| 1909 | endif |
---|
| 1910 | |
---|
| 1911 | !----------------------------------------------------------------------- |
---|
| 1912 | |
---|
| 1913 | end subroutine pole_intersection |
---|
| 1914 | |
---|
| 1915 | !*********************************************************************** |
---|
| 1916 | |
---|
| 1917 | subroutine line_integral(weights, num_wts, & |
---|
| 1918 | in_phi1, in_phi2, theta1, theta2, & |
---|
| 1919 | grid1_lat, grid1_lon, grid2_lat, grid2_lon) |
---|
| 1920 | |
---|
| 1921 | !----------------------------------------------------------------------- |
---|
| 1922 | ! |
---|
| 1923 | ! this routine computes the line integral of the flux function |
---|
| 1924 | ! that results in the interpolation weights. the line is defined |
---|
| 1925 | ! by the input lat/lon of the endpoints. |
---|
| 1926 | ! |
---|
| 1927 | !----------------------------------------------------------------------- |
---|
| 1928 | |
---|
| 1929 | !----------------------------------------------------------------------- |
---|
| 1930 | ! |
---|
| 1931 | ! intent(in): |
---|
| 1932 | ! |
---|
| 1933 | !----------------------------------------------------------------------- |
---|
| 1934 | |
---|
| 1935 | integer (kind=int_kind), intent(in) :: & |
---|
| 1936 | num_wts ! number of weights to compute |
---|
| 1937 | |
---|
| 1938 | real (kind=dbl_kind), intent(in) :: & |
---|
| 1939 | in_phi1, in_phi2, & ! longitude endpoints for the segment |
---|
| 1940 | theta1, theta2, & ! latitude endpoints for the segment |
---|
| 1941 | grid1_lat, grid1_lon, & ! reference coordinates for each |
---|
| 1942 | grid2_lat, grid2_lon ! grid (to ensure correct 0,2pi interv. |
---|
| 1943 | |
---|
| 1944 | !----------------------------------------------------------------------- |
---|
| 1945 | ! |
---|
| 1946 | ! intent(out): |
---|
| 1947 | ! |
---|
| 1948 | !----------------------------------------------------------------------- |
---|
| 1949 | |
---|
| 1950 | real (kind=dbl_kind), dimension(2*num_wts), intent(out) :: & |
---|
| 1951 | weights ! line integral contribution to weights |
---|
| 1952 | |
---|
| 1953 | !----------------------------------------------------------------------- |
---|
| 1954 | ! |
---|
| 1955 | ! local variables |
---|
| 1956 | ! |
---|
| 1957 | !----------------------------------------------------------------------- |
---|
| 1958 | |
---|
| 1959 | real (kind=dbl_kind) :: dphi, sinth1, sinth2, costh1, costh2, fac, & |
---|
| 1960 | phi1, phi2, phidiff1, phidiff2, sinint |
---|
| 1961 | real (kind=dbl_kind) :: f1, f2, fint |
---|
| 1962 | |
---|
| 1963 | !----------------------------------------------------------------------- |
---|
| 1964 | ! |
---|
| 1965 | ! weights for the general case based on a trapezoidal approx to |
---|
| 1966 | ! the integrals. |
---|
| 1967 | ! |
---|
| 1968 | !----------------------------------------------------------------------- |
---|
| 1969 | |
---|
| 1970 | sinth1 = SIN(theta1) |
---|
| 1971 | sinth2 = SIN(theta2) |
---|
| 1972 | costh1 = COS(theta1) |
---|
| 1973 | costh2 = COS(theta2) |
---|
| 1974 | |
---|
| 1975 | dphi = in_phi1 - in_phi2 |
---|
| 1976 | if (dphi > pi) then |
---|
| 1977 | dphi = dphi - pi2 |
---|
| 1978 | else if (dphi < -pi) then |
---|
| 1979 | dphi = dphi + pi2 |
---|
| 1980 | endif |
---|
| 1981 | dphi = half*dphi |
---|
| 1982 | |
---|
| 1983 | !----------------------------------------------------------------------- |
---|
| 1984 | ! |
---|
| 1985 | ! the first weight is the area overlap integral. the second and |
---|
| 1986 | ! fourth are second-order latitude gradient weights. |
---|
| 1987 | ! |
---|
| 1988 | !----------------------------------------------------------------------- |
---|
| 1989 | |
---|
| 1990 | weights( 1) = dphi*(sinth1 + sinth2) |
---|
| 1991 | weights(num_wts+1) = dphi*(sinth1 + sinth2) |
---|
| 1992 | weights( 2) = dphi*(costh1 + costh2 + (theta1*sinth1 + & |
---|
| 1993 | theta2*sinth2)) |
---|
| 1994 | weights(num_wts+2) = dphi*(costh1 + costh2 + (theta1*sinth1 + & |
---|
| 1995 | theta2*sinth2)) |
---|
| 1996 | |
---|
| 1997 | !----------------------------------------------------------------------- |
---|
| 1998 | ! |
---|
| 1999 | ! the third and fifth weights are for the second-order phi gradient |
---|
| 2000 | ! component. must be careful of longitude range. |
---|
| 2001 | ! |
---|
| 2002 | !----------------------------------------------------------------------- |
---|
| 2003 | |
---|
| 2004 | f1 = half*(costh1*sinth1 + theta1) |
---|
| 2005 | f2 = half*(costh2*sinth2 + theta2) |
---|
| 2006 | |
---|
| 2007 | phi1 = in_phi1 - grid1_lon |
---|
| 2008 | if (phi1 > pi) then |
---|
| 2009 | phi1 = phi1 - pi2 |
---|
| 2010 | else if (phi1 < -pi) then |
---|
| 2011 | phi1 = phi1 + pi2 |
---|
| 2012 | endif |
---|
| 2013 | |
---|
| 2014 | phi2 = in_phi2 - grid1_lon |
---|
| 2015 | if (phi2 > pi) then |
---|
| 2016 | phi2 = phi2 - pi2 |
---|
| 2017 | else if (phi2 < -pi) then |
---|
| 2018 | phi2 = phi2 + pi2 |
---|
| 2019 | endif |
---|
| 2020 | |
---|
| 2021 | if ((phi2-phi1) < pi .and. (phi2-phi1) > -pi) then |
---|
| 2022 | weights(3) = dphi*(phi1*f1 + phi2*f2) |
---|
| 2023 | else |
---|
| 2024 | if (phi1 > zero) then |
---|
| 2025 | fac = pi |
---|
| 2026 | else |
---|
| 2027 | fac = -pi |
---|
| 2028 | endif |
---|
| 2029 | fint = f1 + (f2-f1)*(fac-phi1)/abs(dphi) |
---|
| 2030 | weights(3) = half*phi1*(phi1-fac)*f1 - & |
---|
| 2031 | half*phi2*(phi2+fac)*f2 + & |
---|
| 2032 | half*fac*(phi1+phi2)*fint |
---|
| 2033 | endif |
---|
| 2034 | |
---|
| 2035 | phi1 = in_phi1 - grid2_lon |
---|
| 2036 | if (phi1 > pi) then |
---|
| 2037 | phi1 = phi1 - pi2 |
---|
| 2038 | else if (phi1 < -pi) then |
---|
| 2039 | phi1 = phi1 + pi2 |
---|
| 2040 | endif |
---|
| 2041 | |
---|
| 2042 | phi2 = in_phi2 - grid2_lon |
---|
| 2043 | if (phi2 > pi) then |
---|
| 2044 | phi2 = phi2 - pi2 |
---|
| 2045 | else if (phi2 < -pi) then |
---|
| 2046 | phi2 = phi2 + pi2 |
---|
| 2047 | endif |
---|
| 2048 | |
---|
| 2049 | if ((phi2-phi1) < pi .and. (phi2-phi1) > -pi) then |
---|
| 2050 | weights(num_wts+3) = dphi*(phi1*f1 + phi2*f2) |
---|
| 2051 | else |
---|
| 2052 | if (phi1 > zero) then |
---|
| 2053 | fac = pi |
---|
| 2054 | else |
---|
| 2055 | fac = -pi |
---|
| 2056 | endif |
---|
| 2057 | fint = f1 + (f2-f1)*(fac-phi1)/abs(dphi) |
---|
| 2058 | weights(num_wts+3) = half*phi1*(phi1-fac)*f1 - & |
---|
| 2059 | half*phi2*(phi2+fac)*f2 + & |
---|
| 2060 | half*fac*(phi1+phi2)*fint |
---|
| 2061 | endif |
---|
| 2062 | |
---|
| 2063 | !----------------------------------------------------------------------- |
---|
| 2064 | |
---|
| 2065 | end subroutine line_integral |
---|
| 2066 | |
---|
| 2067 | !*********************************************************************** |
---|
| 2068 | |
---|
| 2069 | subroutine store_link_cnsrv(add1, add2, weights) |
---|
| 2070 | |
---|
| 2071 | !----------------------------------------------------------------------- |
---|
| 2072 | ! |
---|
| 2073 | ! this routine stores the address and weight for this link in |
---|
| 2074 | ! the appropriate address and weight arrays and resizes those |
---|
| 2075 | ! arrays if necessary. |
---|
| 2076 | ! |
---|
| 2077 | !----------------------------------------------------------------------- |
---|
| 2078 | |
---|
| 2079 | !----------------------------------------------------------------------- |
---|
| 2080 | ! |
---|
| 2081 | ! input variables |
---|
| 2082 | ! |
---|
| 2083 | !----------------------------------------------------------------------- |
---|
| 2084 | |
---|
| 2085 | integer (kind=int_kind), intent(in) :: & |
---|
| 2086 | add1, & ! address on grid1 |
---|
| 2087 | add2 ! address on grid2 |
---|
| 2088 | |
---|
| 2089 | real (kind=dbl_kind), dimension(:), intent(in) :: & |
---|
| 2090 | weights ! array of remapping weights for this link |
---|
| 2091 | |
---|
| 2092 | !----------------------------------------------------------------------- |
---|
| 2093 | ! |
---|
| 2094 | ! local variables |
---|
| 2095 | ! |
---|
| 2096 | !----------------------------------------------------------------------- |
---|
| 2097 | |
---|
| 2098 | integer (kind=int_kind) :: nlink, min_link, max_link ! link index |
---|
| 2099 | |
---|
| 2100 | integer (kind=int_kind), dimension(:,:), allocatable, save :: & |
---|
| 2101 | link_add1, & ! min,max link add to restrict search |
---|
| 2102 | link_add2 ! min,max link add to restrict search |
---|
| 2103 | |
---|
| 2104 | logical (kind=log_kind), save :: first_call = .true. |
---|
| 2105 | |
---|
| 2106 | !----------------------------------------------------------------------- |
---|
| 2107 | ! |
---|
| 2108 | ! if all weights are zero, do not bother storing the link |
---|
| 2109 | ! |
---|
| 2110 | !----------------------------------------------------------------------- |
---|
| 2111 | |
---|
| 2112 | if (all(weights == zero)) return |
---|
| 2113 | |
---|
| 2114 | !----------------------------------------------------------------------- |
---|
| 2115 | ! |
---|
| 2116 | ! restrict the range of links to search for existing links |
---|
| 2117 | ! |
---|
| 2118 | !----------------------------------------------------------------------- |
---|
| 2119 | |
---|
| 2120 | if (first_call) then |
---|
| 2121 | allocate(link_add1(2,grid1_size), link_add2(2,grid2_size)) |
---|
| 2122 | link_add1 = 0 |
---|
| 2123 | link_add2 = 0 |
---|
| 2124 | first_call = .false. |
---|
| 2125 | min_link = 1 |
---|
| 2126 | max_link = 0 |
---|
| 2127 | else |
---|
| 2128 | min_link = min(link_add1(1,add1),link_add2(1,add2)) |
---|
| 2129 | max_link = max(link_add1(2,add1),link_add2(2,add2)) |
---|
| 2130 | if (min_link == 0) then |
---|
| 2131 | min_link = 1 |
---|
| 2132 | max_link = 0 |
---|
| 2133 | endif |
---|
| 2134 | endif |
---|
| 2135 | |
---|
| 2136 | !----------------------------------------------------------------------- |
---|
| 2137 | ! |
---|
| 2138 | ! if the link already exists, add the weight to the current weight |
---|
| 2139 | ! arrays |
---|
| 2140 | ! |
---|
| 2141 | !----------------------------------------------------------------------- |
---|
| 2142 | |
---|
| 2143 | do nlink=min_link,max_link |
---|
| 2144 | if (add1 == grid1_add_map1(nlink)) then |
---|
| 2145 | if (add2 == grid2_add_map1(nlink)) then |
---|
| 2146 | |
---|
| 2147 | wts_map1(:,nlink) = wts_map1(:,nlink) + weights(1:num_wts) |
---|
| 2148 | if (num_maps == 2) then |
---|
| 2149 | wts_map2(:,nlink) = wts_map2(:,nlink) + & |
---|
| 2150 | weights(num_wts+1:2*num_wts) |
---|
| 2151 | endif |
---|
| 2152 | return |
---|
| 2153 | |
---|
| 2154 | endif |
---|
| 2155 | endif |
---|
| 2156 | end do |
---|
| 2157 | |
---|
| 2158 | !----------------------------------------------------------------------- |
---|
| 2159 | ! |
---|
| 2160 | ! if the link does not yet exist, increment number of links and |
---|
| 2161 | ! check to see if remap arrays need to be increased to accomodate |
---|
| 2162 | ! the new link. then store the link. |
---|
| 2163 | ! |
---|
| 2164 | !----------------------------------------------------------------------- |
---|
| 2165 | |
---|
| 2166 | num_links_map1 = num_links_map1 + 1 |
---|
| 2167 | if (num_links_map1 > max_links_map1) & |
---|
| 2168 | call resize_remap_vars(1,resize_increment) |
---|
| 2169 | |
---|
| 2170 | grid1_add_map1(num_links_map1) = add1 |
---|
| 2171 | grid2_add_map1(num_links_map1) = add2 |
---|
| 2172 | wts_map1 (:,num_links_map1) = weights(1:num_wts) |
---|
| 2173 | |
---|
| 2174 | if (num_maps > 1) then |
---|
| 2175 | num_links_map2 = num_links_map2 + 1 |
---|
| 2176 | if (num_links_map2 > max_links_map2) & |
---|
| 2177 | call resize_remap_vars(2,resize_increment) |
---|
| 2178 | |
---|
| 2179 | grid1_add_map2(num_links_map2) = add1 |
---|
| 2180 | grid2_add_map2(num_links_map2) = add2 |
---|
| 2181 | wts_map2 (:,num_links_map2) = weights(num_wts+1:2*num_wts) |
---|
| 2182 | endif |
---|
| 2183 | |
---|
| 2184 | if (link_add1(1,add1) == 0) link_add1(1,add1) = num_links_map1 |
---|
| 2185 | if (link_add2(1,add2) == 0) link_add2(1,add2) = num_links_map1 |
---|
| 2186 | link_add1(2,add1) = num_links_map1 |
---|
| 2187 | link_add2(2,add2) = num_links_map1 |
---|
| 2188 | |
---|
| 2189 | !----------------------------------------------------------------------- |
---|
| 2190 | |
---|
| 2191 | end subroutine store_link_cnsrv |
---|
| 2192 | |
---|
| 2193 | !*********************************************************************** |
---|
| 2194 | |
---|
| 2195 | end module remap_conservative |
---|
| 2196 | |
---|
| 2197 | !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! |
---|