[2696] | 1 | !> @file src/transform.f90 |
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| 2 | !------------------------------------------------------------------------------! |
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[2718] | 3 | ! This file is part of the PALM model system. |
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[2696] | 4 | ! |
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[2718] | 5 | ! PALM is free software: you can redistribute it and/or modify it under the |
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| 6 | ! terms of the GNU General Public License as published by the Free Software |
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| 7 | ! Foundation, either version 3 of the License, or (at your option) any later |
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[2696] | 8 | ! version. |
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| 9 | ! |
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[2718] | 10 | ! PALM is distributed in the hope that it will be useful, but WITHOUT ANY |
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| 11 | ! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR |
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| 12 | ! A PARTICULAR PURPOSE. See the GNU General Public License for more details. |
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[2696] | 13 | ! |
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| 14 | ! You should have received a copy of the GNU General Public License along with |
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| 15 | ! PALM. If not, see <http://www.gnu.org/licenses/>. |
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| 16 | ! |
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[2718] | 17 | ! Copyright 2017-2018 Leibniz Universitaet Hannover |
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| 18 | ! Copyright 2017-2018 Deutscher Wetterdienst Offenbach |
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[2696] | 19 | !------------------------------------------------------------------------------! |
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| 20 | ! |
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| 21 | ! Current revisions: |
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| 22 | ! ----------------- |
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[3183] | 23 | ! |
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| 24 | ! |
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| 25 | ! Former revisions: |
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| 26 | ! ----------------- |
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| 27 | ! $Id: transform.f90 3183 2018-07-27 14:25:55Z kanani $ |
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[3182] | 28 | ! Introduced new PALM grid stretching |
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| 29 | ! Removed unnecessary subroutine parameters |
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| 30 | ! Renamed kcur to k_intermediate |
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[2696] | 31 | ! |
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| 32 | ! |
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[3183] | 33 | ! 3182 2018-07-27 13:36:03Z suehring |
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[2696] | 34 | ! Initial revision |
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| 35 | ! |
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| 36 | ! |
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| 37 | ! |
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| 38 | ! Authors: |
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| 39 | ! -------- |
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| 40 | ! @author Eckhard Kadasch |
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| 41 | ! |
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| 42 | ! Description: |
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| 43 | ! ------------ |
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| 44 | !> The transform module provides INIFOR's low-level transformation and |
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| 45 | !> interpolation routines. The rotated-pole transformation routines phirot2phi, |
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| 46 | !> phi2phirot, rlarot2rla, rla2rlarot, uv2uvrot, and uvrot2uv are adapted from |
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| 47 | !> int2lm's utility routines. |
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| 48 | !------------------------------------------------------------------------------! |
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| 49 | MODULE transform |
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| 50 | |
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| 51 | USE control |
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| 52 | USE defs, & |
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| 53 | ONLY: TO_DEGREES, TO_RADIANS, PI, dp |
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| 54 | USE types |
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| 55 | USE util, & |
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| 56 | ONLY: real_to_str, str |
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| 57 | |
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| 58 | IMPLICIT NONE |
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| 59 | |
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| 60 | CONTAINS |
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| 61 | |
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| 62 | !------------------------------------------------------------------------------! |
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| 63 | ! Description: |
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| 64 | ! ------------ |
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| 65 | !> Interpolates linearly in the vertical direction in very column (i,j) of the |
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| 66 | !> output array outvar(i,j,:) using values of the source array invar. In cells |
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| 67 | !> that are outside the COSMO-DE domain, indicated by negative interpolation |
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| 68 | !> weights, extrapolate constantly from the cell above. |
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| 69 | !> |
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| 70 | !> Input parameters: |
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| 71 | !> ----------------- |
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| 72 | !> invar : Array of source data |
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| 73 | !> |
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| 74 | !> outgrid % kk : Array of vertical neighbour indices. kk(i,j,k,:) contain the |
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| 75 | !> indices of the two vertical neighbors of PALM-4U point (i,j,k) on the |
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| 76 | !> input grid corresponding to the source data invar. |
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| 77 | !> |
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| 78 | !> outgrid % w_verti : Array of weights for vertical linear interpolation |
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| 79 | !> corresponding to neighbour points indexed by kk. |
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| 80 | !> |
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| 81 | !> Output papameters: |
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| 82 | !> ------------------ |
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| 83 | !> outvar : Array of interpolated data |
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| 84 | !------------------------------------------------------------------------------! |
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| 85 | SUBROUTINE interpolate_1d(in_arr, out_arr, outgrid) |
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| 86 | TYPE(grid_definition), INTENT(IN) :: outgrid |
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| 87 | REAL(dp), INTENT(IN) :: in_arr(0:,0:,0:) |
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[3182] | 88 | REAL(dp), INTENT(OUT) :: out_arr(0:,0:,:) |
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[2696] | 89 | |
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[3182] | 90 | INTEGER :: i, j, k, l, nz |
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[2696] | 91 | |
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| 92 | nz = UBOUND(out_arr, 3) |
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| 93 | |
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[3182] | 94 | DO j = LBOUND(out_arr, 2), UBOUND(out_arr, 2) |
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| 95 | DO i = LBOUND(out_arr, 1), UBOUND(out_arr, 1) |
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| 96 | DO k = nz, LBOUND(out_arr, 3), -1 |
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[2696] | 97 | |
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| 98 | ! TODO: Remove IF clause and extrapolate based on a critical vertical |
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| 99 | ! TODO: index marking the lower bound of COSMO-DE data coverage. |
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| 100 | ! Check for negative interpolation weights indicating grid points |
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| 101 | ! below COSMO-DE domain and extrapolate from the top in such cells. |
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| 102 | IF (outgrid % w_verti(i,j,k,1) < -1.0_dp .AND. k < nz) THEN |
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| 103 | out_arr(i,j,k) = out_arr(i,j,k+1) |
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| 104 | ELSE |
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| 105 | out_arr(i,j,k) = 0.0_dp |
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| 106 | DO l = 1, 2 |
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[3182] | 107 | out_arr(i,j,k) = out_arr(i,j,k) + & |
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| 108 | outgrid % w_verti(i,j,k,l) * & |
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[2696] | 109 | in_arr(i,j,outgrid % kk(i,j,k, l) ) |
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| 110 | END DO |
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| 111 | END IF |
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| 112 | END DO |
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| 113 | END DO |
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| 114 | END DO |
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| 115 | END SUBROUTINE interpolate_1d |
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| 116 | |
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| 117 | |
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| 118 | !------------------------------------------------------------------------------! |
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| 119 | ! Description: |
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| 120 | ! ------------ |
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| 121 | !> Interpolates bi-linearly in horizontal planes on every k level of the output |
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| 122 | !> array outvar(:,:,k) using values of the source array invar(:,:,:). The source |
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| 123 | !> (invar) and interpolation array (outvar) need to have matching dimensions. |
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| 124 | !> |
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| 125 | !> Input parameters: |
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| 126 | !> ----------------- |
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| 127 | !> invar : Array of source data |
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| 128 | !> |
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| 129 | !> outgrid % ii, % jj : Array of neighbour indices in x and y direction. |
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| 130 | !> ii(i,j,k,:), and jj(i,j,k,:) contain the four horizontal neighbour points |
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| 131 | !> of PALM-4U point (i,j,k) on the input grid corresponding to the source |
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| 132 | !> data invar. (The outgrid carries the relationship with the ingrid in the |
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| 133 | ! form of the interpoaltion weights.) |
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| 134 | !> |
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| 135 | !> outgrid % w_horiz: Array of weights for horizontal bi-linear interpolation |
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| 136 | !> corresponding to neighbour points indexed by ii and jj. |
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| 137 | !> |
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| 138 | !> Output papameters: |
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| 139 | !> ------------------ |
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| 140 | !> outvar : Array of interpolated data |
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| 141 | !------------------------------------------------------------------------------! |
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| 142 | SUBROUTINE interpolate_2d(invar, outvar, outgrid, ncvar) |
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| 143 | ! I index 0-based for the indices of the outvar to be consistent with the |
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| 144 | ! outgrid indices and interpolation weights. |
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[3182] | 145 | TYPE(grid_definition), INTENT(IN) :: outgrid |
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| 146 | REAL(dp), INTENT(IN) :: invar(0:,0:,0:) |
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| 147 | REAL(dp), INTENT(OUT) :: outvar(0:,0:,0:) |
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[2696] | 148 | TYPE(nc_var), INTENT(IN), OPTIONAL :: ncvar |
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| 149 | |
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| 150 | INTEGER :: i, j, k, l |
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| 151 | |
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| 152 | ! TODO: check if input dimensions are consistent, i.e. ranges are correct |
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| 153 | IF (UBOUND(outvar, 3) .GT. UBOUND(invar, 3)) THEN |
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| 154 | message = "Output array for '" // TRIM(ncvar % name) // "' has ' more levels (" // & |
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| 155 | TRIM(str(UBOUND(outvar, 3))) // ") than input variable ("//& |
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| 156 | TRIM(str(UBOUND(invar, 3))) // ")." |
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| 157 | CALL abort('interpolate_2d', message) |
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| 158 | END IF |
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| 159 | |
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| 160 | DO k = 0, UBOUND(outvar, 3) |
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| 161 | DO j = 0, UBOUND(outvar, 2) |
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| 162 | DO i = 0, UBOUND(outvar, 1) |
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| 163 | outvar(i,j,k) = 0.0_dp |
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| 164 | DO l = 1, 4 |
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| 165 | |
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| 166 | outvar(i,j,k) = outvar(i,j,k) + & |
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| 167 | outgrid % w_horiz(i,j,l) * invar( outgrid % ii(i,j,l), & |
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| 168 | outgrid % jj(i,j,l), & |
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| 169 | k ) |
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| 170 | END DO |
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| 171 | END DO |
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| 172 | END DO |
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| 173 | END DO |
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| 174 | |
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| 175 | END SUBROUTINE interpolate_2d |
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| 176 | |
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| 177 | |
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| 178 | SUBROUTINE average_2d(in_arr, out_arr, imin, imax, jmin, jmax) |
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| 179 | REAL(dp), INTENT(IN) :: in_arr(0:,0:,0:) |
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| 180 | REAL(dp), INTENT(OUT) :: out_arr(0:) |
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| 181 | INTEGER, INTENT(IN) :: imin, imax, jmin, jmax |
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| 182 | |
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| 183 | INTEGER :: i, j, k |
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| 184 | REAL(dp) :: ni |
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| 185 | |
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| 186 | IF (imin < 0) CALL abort('average_2d', "imin < 0.") |
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| 187 | IF (jmin < 0) CALL abort('average_2d', "jmin < 0.") |
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| 188 | IF (imax > UBOUND(in_arr, 1)) CALL abort('average_2d', "imax out of i bound.") |
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| 189 | IF (jmax > UBOUND(in_arr, 2)) CALL abort('average_2d', "jmax out of j bound.") |
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| 190 | |
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| 191 | DO k = 0, UBOUND(out_arr, 1) |
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| 192 | |
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| 193 | out_arr(k) = 0.0_dp |
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| 194 | DO j = jmin, jmax |
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| 195 | DO i = imin, imax |
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| 196 | out_arr(k) = out_arr(k) + in_arr(i, j, k) |
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| 197 | END DO |
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| 198 | END DO |
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| 199 | |
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| 200 | END DO |
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| 201 | |
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| 202 | ! devide by number of grid points |
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| 203 | ni = 1.0_dp / ( (imax - imin + 1) * (jmax - jmin + 1) ) |
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| 204 | out_arr(:) = out_arr(:) * ni |
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| 205 | |
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| 206 | END SUBROUTINE average_2d |
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| 207 | |
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| 208 | |
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| 209 | SUBROUTINE interpolate_3d(source_array, palm_array, palm_intermediate, palm_grid) |
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| 210 | TYPE(grid_definition), INTENT(IN) :: palm_intermediate, palm_grid |
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| 211 | REAL(dp), DIMENSION(:,:,:), INTENT(IN) :: source_array |
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| 212 | REAL(dp), DIMENSION(:,:,:), INTENT(OUT) :: palm_array |
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| 213 | REAL(dp), DIMENSION(:,:,:), ALLOCATABLE :: intermediate_array |
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| 214 | INTEGER :: nx, ny, nz |
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| 215 | |
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| 216 | nx = palm_intermediate % nx |
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| 217 | ny = palm_intermediate % ny |
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| 218 | nz = palm_intermediate % nz ! nlev |
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| 219 | |
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| 220 | ! Interpolate from COSMO-DE to intermediate grid. Allocating with one |
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| 221 | ! less point in the vertical, since scalars like T have 50 instead of 51 |
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| 222 | ! points in COSMO-DE. |
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| 223 | ALLOCATE(intermediate_array(0:nx, 0:ny, 0:nz-1)) ! |
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| 224 | |
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| 225 | CALL interpolate_2d(source_array, intermediate_array, palm_intermediate) |
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| 226 | |
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| 227 | ! Interpolate from intermediate grid to palm_grid grid, includes |
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| 228 | ! extrapolation for cells below COSMO-DE domain. |
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| 229 | CALL interpolate_1d(intermediate_array, palm_array, palm_grid) |
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| 230 | |
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| 231 | DEALLOCATE(intermediate_array) |
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| 232 | |
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| 233 | END SUBROUTINE interpolate_3d |
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| 234 | |
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| 235 | |
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| 236 | SUBROUTINE average_profile(source_array, profile_array, imin, imax, jmin, jmax,& |
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| 237 | palm_intermediate, palm_grid) |
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| 238 | TYPE(grid_definition), INTENT(IN) :: palm_intermediate, palm_grid |
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| 239 | REAL(dp), DIMENSION(:,:,:), INTENT(IN) :: source_array |
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| 240 | INTEGER, INTENT(IN) :: imin, imax, jmin, jmax |
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| 241 | REAL(dp), DIMENSION(0:,0:,0:), INTENT(OUT) :: profile_array |
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| 242 | REAL(dp), DIMENSION(:,:,:), ALLOCATABLE :: intermediate_array |
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| 243 | INTEGER :: nx, ny, nz |
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| 244 | |
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| 245 | nx = palm_intermediate % nx |
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| 246 | ny = palm_intermediate % ny |
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| 247 | nz = palm_intermediate % nz |
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| 248 | ALLOCATE(intermediate_array(0:nx, 0:ny, 0:nz-1)) |
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| 249 | intermediate_array(:,:,:) = 0.0_dp |
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| 250 | |
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| 251 | ! average input array to intermediate profile |
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| 252 | CALL average_2d(source_array, intermediate_array(0,0,:), imin, imax, jmin, jmax) |
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| 253 | |
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| 254 | ! vertically interpolate to ouput array |
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| 255 | CALL interpolate_1d(intermediate_array, profile_array, palm_grid) |
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| 256 | |
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| 257 | DEALLOCATE(intermediate_array) |
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| 258 | |
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| 259 | END SUBROUTINE average_profile |
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| 260 | |
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| 261 | |
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| 262 | |
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| 263 | !-----------------------------------------------------------------------------! |
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| 264 | ! Description: |
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| 265 | ! ----------- |
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| 266 | !> This routine computes the inverse Plate Carree projection, i.e. in projects |
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| 267 | !> Cartesian coordinates (x,y) onto a sphere. It returns the latitude and |
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| 268 | !> lngitude of a geographical system centered at x0 and y0. |
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| 269 | !-----------------------------------------------------------------------------! |
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| 270 | SUBROUTINE inv_plate_carree(x, y, x0, y0, r, lat, lon) |
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| 271 | REAL(dp), INTENT(IN) :: x(:), y(:), x0, y0, r |
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| 272 | REAL(dp), INTENT(OUT) :: lat(:), lon(:) |
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| 273 | |
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| 274 | REAL(dp) :: ri |
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| 275 | |
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| 276 | ! TODO check dimensions of lat/lon and y/x match |
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| 277 | |
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| 278 | ri = 1.0_dp / r |
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| 279 | |
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| 280 | lat(:) = (y(:) - y0) * ri |
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| 281 | lon(:) = (x(:) - x0) * ri |
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| 282 | END SUBROUTINE |
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| 283 | |
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| 284 | |
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| 285 | !-----------------------------------------------------------------------------! |
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| 286 | ! Description: |
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| 287 | ! ------------ |
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| 288 | !> Computes the reverse Plate-Carree projection of a x or y position on a |
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| 289 | !> Cartesian grid. |
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| 290 | !> |
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| 291 | !> Input parameters: |
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| 292 | !> ----------------- |
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| 293 | !> xy : x or y coordinate of the Cartasian grid point [m]. |
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| 294 | !> |
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| 295 | !> xy0 : x or y coordinate that coincides with the origin of the underlying |
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| 296 | !> sperical system (crossing point of the equator and prime meridian) [m]. |
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| 297 | !> |
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| 298 | !> r : Radius of the of the underlying sphere, e.g. EARTH_RADIUS [m]. |
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| 299 | !> |
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| 300 | !> Returns: |
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| 301 | !> -------- |
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| 302 | !> project : Longitude (in case xy = x) or latitude (xy = y) of the given input |
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| 303 | !> coordinate xy. |
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| 304 | !------------------------------------------------------------------------------! |
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| 305 | ELEMENTAL REAL(dp) FUNCTION project(xy, xy0, r) |
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| 306 | REAL(dp), INTENT(IN) :: xy, xy0, r |
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| 307 | REAL(dp) :: ri |
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| 308 | |
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| 309 | ! If this elemental function is called with a large array as xy, it is |
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| 310 | ! computationally more efficient to precompute the inverse radius and |
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| 311 | ! then muliply. |
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| 312 | ri = 1.0_dp / r |
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| 313 | |
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| 314 | project = (xy - xy0) * ri |
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| 315 | |
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| 316 | END FUNCTION project |
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| 317 | |
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| 318 | |
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| 319 | REAL(dp) FUNCTION phic_to_phin(phi_c) |
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| 320 | REAL(dp), INTENT(IN) :: phi_c |
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| 321 | |
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| 322 | phic_to_phin = 0.5_dp * PI - ABS(phi_c) |
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| 323 | |
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| 324 | END FUNCTION phic_to_phin |
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| 325 | |
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| 326 | |
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| 327 | REAL(dp) FUNCTION lamc_to_lamn(phi_c, lam_c) |
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| 328 | REAL(dp), INTENT(IN) :: phi_c, lam_c |
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| 329 | |
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| 330 | lamc_to_lamn = lam_c |
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| 331 | IF (phi_c > 0.0_dp) THEN |
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| 332 | lamc_to_lamn = lam_c - SIGN(PI, lam_c) |
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| 333 | END IF |
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| 334 | |
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| 335 | END FUNCTION lamc_to_lamn |
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| 336 | |
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| 337 | |
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| 338 | REAL(dp) FUNCTION gamma_from_hemisphere(phi_cg, phi_ref) |
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| 339 | REAL(dp), INTENT(IN) :: phi_cg, phi_ref |
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| 340 | LOGICAL :: palm_centre_is_south_of_cosmo_origin |
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| 341 | |
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| 342 | palm_centre_is_south_of_cosmo_origin = (phi_cg < phi_ref) |
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| 343 | |
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| 344 | IF (palm_centre_is_south_of_cosmo_origin) THEN |
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| 345 | gamma_from_hemisphere = PI |
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| 346 | ELSE |
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| 347 | gamma_from_hemisphere = 0.0_dp |
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| 348 | END IF |
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| 349 | END FUNCTION gamma_from_hemisphere |
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| 350 | |
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| 351 | |
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| 352 | !------------------------------------------------------------------------------! |
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| 353 | ! Description: |
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| 354 | ! ------------ |
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| 355 | !> Computes the geographical coordinates corresponding to the given rotated-pole |
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| 356 | !> coordinates. |
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| 357 | !> |
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| 358 | !> In INIFOR, this routine is used to convert coordinates between two |
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| 359 | !> rotated-pole systems: COSMO-DE's rotated-pole system, and one centred at the |
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| 360 | !> PALM-4U domain centre. In this case, the PALM-4U system is thought of as the |
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| 361 | !> rotated-pole system and the routine is used to rotate back to COSMO-DE's |
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| 362 | !> system which is thought of as the geographical one. |
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| 363 | !> |
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| 364 | !> Input parameters: |
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| 365 | !> ----------------- |
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| 366 | !> phir(:), lamr(: ): latitudes and longitudes of the rotated-pole grid |
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| 367 | !> |
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| 368 | !> phip, lamp: latitude and longitude of the rotated north pole |
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| 369 | !> |
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| 370 | !> gam: "angle between the north poles. If [gam] is not present, the other |
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| 371 | !> system is the real geographical system." (original phiro2rot |
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| 372 | !> description) |
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| 373 | !> |
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| 374 | !> Output parameters: |
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| 375 | !> ------------------ |
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| 376 | !> phi(:,:), lam(:,:): geographical latitudes and logitudes |
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| 377 | !------------------------------------------------------------------------------! |
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| 378 | SUBROUTINE rotate_to_cosmo(phir, lamr, phip, lamp, phi, lam, gam) |
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| 379 | REAL(dp), INTENT(IN) :: phir(0:), lamr(0:), phip, lamp, gam |
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| 380 | REAL(dp), INTENT(OUT) :: phi(0:,0:), lam(0:,0:) |
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| 381 | |
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| 382 | INTEGER :: i, j |
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| 383 | |
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| 384 | IF ( SIZE(phi, 1) .NE. SIZE(lam, 1) .OR. & |
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| 385 | SIZE(phi, 2) .NE. SIZE(lam, 2) ) THEN |
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| 386 | PRINT *, "inifor: rotate_to_cosmo: Dimensions of phi and lambda do not match. Dimensions are:" |
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| 387 | PRINT *, "inifor: rotate_to_cosmo: phi: ", SIZE(phi, 1), SIZE(phi, 2) |
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| 388 | PRINT *, "inifor: rotate_to_cosmo: lam: ", SIZE(lam, 1), SIZE(lam, 2) |
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| 389 | STOP |
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| 390 | END IF |
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| 391 | |
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| 392 | IF ( SIZE(phir) .NE. SIZE(phi, 2) .OR. & |
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| 393 | SIZE(lamr) .NE. SIZE(phi, 1) ) THEN |
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| 394 | PRINT *, "inifor: rotate_to_cosmo: Dimensions of phir and lamr do not match. Dimensions are:" |
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| 395 | PRINT *, "inifor: rotate_to_cosmo: phir: ", SIZE(phir), SIZE(phi, 2) |
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| 396 | PRINT *, "inifor: rotate_to_cosmo: lamr: ", SIZE(lamr), SIZE(phi, 1) |
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| 397 | STOP |
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| 398 | END IF |
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| 399 | |
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| 400 | DO j = 0, UBOUND(phir, 1) |
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| 401 | DO i = 0, UBOUND(lamr, 1) |
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| 402 | |
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| 403 | phi(i,j) = phirot2phi(phir(j) * TO_DEGREES, & |
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| 404 | lamr(i) * TO_DEGREES, & |
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| 405 | phip * TO_DEGREES, & |
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| 406 | lamp * TO_DEGREES, & |
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| 407 | gam * TO_DEGREES) * TO_RADIANS |
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| 408 | |
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| 409 | lam(i,j) = rlarot2rla(phir(j) * TO_DEGREES, & |
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| 410 | lamr(i) * TO_DEGREES, & |
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| 411 | phip * TO_DEGREES, & |
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| 412 | lamp * TO_DEGREES, & |
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| 413 | gam * TO_DEGREES) * TO_RADIANS |
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| 414 | |
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| 415 | END DO |
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| 416 | END DO |
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| 417 | |
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| 418 | END SUBROUTINE rotate_to_cosmo |
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[3182] | 419 | |
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[2696] | 420 | |
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| 421 | |
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| 422 | !------------------------------------------------------------------------------! |
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| 423 | ! Description: |
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| 424 | ! ------------ |
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| 425 | !> Compute indices of PALM-4U grid point neighbours in the target |
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| 426 | !> system (COSMO-DE) by rounding up and down. (i,j) are the indices of |
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| 427 | !> the PALM-4U grid and (ii(i,j,1-4), jj(i,j,1-4)) contain the indices |
---|
| 428 | !> of the its four neigbouring points in the COSMO-DE grid. |
---|
| 429 | !> |
---|
| 430 | !> |
---|
| 431 | !> COSMO-DE grid |
---|
| 432 | !> ------------- |
---|
| 433 | !> jj, lat |
---|
[3182] | 434 | !> ^ j |
---|
| 435 | !> | \ i |
---|
[2696] | 436 | !> jj(i,j,2/3) + ... 2 ---\--------/------ 3 |
---|
| 437 | !> | | ^ \ / | |
---|
| 438 | !> | | |wp \ / | |
---|
| 439 | !> | | v \ / | |
---|
| 440 | !> latpos + ............ o/ (i,j) | |
---|
| 441 | !> | | : | |
---|
| 442 | !> | | :<----wl---->| |
---|
| 443 | !> jj(i,j,1/4) + ... 1 -------:----------- 4 |
---|
| 444 | !> | : : : |
---|
| 445 | !> | : : : |
---|
| 446 | !> | : lonpos : |
---|
| 447 | !> L-----+--------+------------+------> ii, lon |
---|
| 448 | !> ii(i,j,1/2) ii(i,j,3/4) |
---|
| 449 | !> |
---|
| 450 | !> |
---|
| 451 | !> Input parameters: |
---|
| 452 | !> ----------------- |
---|
| 453 | !> source_lat, source_lon : (rotated-pole) coordinates of the source grid (e.g. |
---|
| 454 | !> COSMO-DE) |
---|
| 455 | !> |
---|
| 456 | !> source_dxi, source_dyi : inverse grid spacings of the source grid. |
---|
| 457 | !> |
---|
| 458 | !> target_lat, target_lon : (rotated-pole) coordinates of the target grid (e.g. |
---|
| 459 | !> COSMO-DE) |
---|
| 460 | !> |
---|
| 461 | !> Output parameters: |
---|
| 462 | !> ------------------ |
---|
| 463 | !> palm_ii, palm_jj : x and y index arrays of horizontal neighbour columns |
---|
| 464 | !> |
---|
| 465 | !------------------------------------------------------------------------------! |
---|
[3182] | 466 | SUBROUTINE find_horizontal_neighbours(cosmo_lat, cosmo_lon, & |
---|
| 467 | palm_clat, palm_clon, & |
---|
| 468 | palm_ii, palm_jj) |
---|
[2696] | 469 | |
---|
| 470 | REAL(dp), DIMENSION(0:), INTENT(IN) :: cosmo_lat, cosmo_lon |
---|
| 471 | REAL(dp), DIMENSION(0:,0:), INTENT(IN) :: palm_clat, palm_clon |
---|
[3182] | 472 | REAL(dp) :: cosmo_dxi, cosmo_dyi |
---|
[2696] | 473 | INTEGER, DIMENSION(0:,0:,1:), INTENT(OUT) :: palm_ii, palm_jj |
---|
| 474 | |
---|
| 475 | REAL(dp) :: lonpos, latpos, lon0, lat0 |
---|
| 476 | INTEGER :: i, j |
---|
| 477 | |
---|
| 478 | lon0 = cosmo_lon(0) |
---|
| 479 | lat0 = cosmo_lat(0) |
---|
[3182] | 480 | cosmo_dxi = 1.0_dp / (cosmo_lon(1) - cosmo_lon(0)) |
---|
| 481 | cosmo_dyi = 1.0_dp / (cosmo_lat(1) - cosmo_lat(0)) |
---|
[2696] | 482 | |
---|
| 483 | DO j = 0, UBOUND(palm_clon, 2)!palm_grid % ny |
---|
| 484 | DO i = 0, UBOUND(palm_clon, 1)!palm_grid % nx |
---|
| 485 | ! Compute the floating point index corrseponding to PALM-4U grid point |
---|
| 486 | ! location along target grid (COSMO-DE) axes. |
---|
| 487 | lonpos = (palm_clon(i,j) - lon0) * cosmo_dxi |
---|
| 488 | latpos = (palm_clat(i,j) - lat0) * cosmo_dyi |
---|
| 489 | |
---|
| 490 | IF (lonpos < 0.0 .OR. latpos < 0.0) THEN |
---|
| 491 | PRINT *, " Error while finding neighbours: lonpos or latpos out of bounds!" |
---|
| 492 | PRINT *, " (i,j) = (", i, ",",j,")" |
---|
| 493 | PRINT *, " lonpos ", lonpos*TO_DEGREES, ", latpos ", latpos*TO_DEGREES |
---|
| 494 | PRINT *, " lon0 ", lon0 *TO_DEGREES, ", lat0 ", lat0*TO_DEGREES |
---|
| 495 | PRINT *, " PALM lon ", palm_clon(i,j)*TO_DEGREES, ", PALM lat ",palm_clat(i,j)*TO_DEGREES |
---|
| 496 | STOP |
---|
| 497 | END IF |
---|
| 498 | |
---|
| 499 | palm_ii(i,j,1) = FLOOR(lonpos) |
---|
| 500 | palm_ii(i,j,2) = FLOOR(lonpos) |
---|
| 501 | palm_ii(i,j,3) = CEILING(lonpos) |
---|
| 502 | palm_ii(i,j,4) = CEILING(lonpos) |
---|
| 503 | |
---|
| 504 | palm_jj(i,j,1) = FLOOR(latpos) |
---|
| 505 | palm_jj(i,j,2) = CEILING(latpos) |
---|
| 506 | palm_jj(i,j,3) = CEILING(latpos) |
---|
| 507 | palm_jj(i,j,4) = FLOOR(latpos) |
---|
| 508 | END DO |
---|
| 509 | END DO |
---|
| 510 | |
---|
| 511 | END SUBROUTINE find_horizontal_neighbours |
---|
| 512 | |
---|
| 513 | |
---|
| 514 | SUBROUTINE find_vertical_neighbours_and_weights(palm_grid, palm_intermediate) |
---|
| 515 | TYPE(grid_definition), INTENT(INOUT) :: palm_grid |
---|
| 516 | TYPE(grid_definition), INTENT(IN) :: palm_intermediate |
---|
| 517 | |
---|
[3182] | 518 | INTEGER :: i, j, k, nx, ny, nz, nlev, k_intermediate |
---|
[2696] | 519 | LOGICAL :: point_is_below_grid, point_is_above_grid, & |
---|
| 520 | point_is_in_current_cell |
---|
| 521 | REAL(dp) :: current_height, column_base, column_top, h_top, h_bottom, & |
---|
| 522 | weight |
---|
| 523 | |
---|
| 524 | nx = palm_grid % nx |
---|
| 525 | ny = palm_grid % ny |
---|
| 526 | nz = palm_grid % nz |
---|
| 527 | nlev = palm_intermediate % nz |
---|
| 528 | |
---|
| 529 | ! in each column of the fine grid, find vertical neighbours of every cell |
---|
| 530 | DO i = 0, nx |
---|
| 531 | DO j = 0, ny |
---|
| 532 | |
---|
[3182] | 533 | k_intermediate = 0 |
---|
[2696] | 534 | |
---|
| 535 | column_base = palm_intermediate % h(i,j,0) |
---|
| 536 | column_top = palm_intermediate % h(i,j,nlev) |
---|
| 537 | |
---|
| 538 | ! scan through palm_grid column until and set neighbour indices in |
---|
| 539 | ! case current_height is either below column_base, in the current |
---|
| 540 | ! cell, or above column_top. Keep increasing current cell index until |
---|
| 541 | ! the current cell overlaps with the current_height. |
---|
[3182] | 542 | DO k = 1, nz |
---|
[2696] | 543 | |
---|
| 544 | ! Memorize the top and bottom boundaries of the coarse cell and the |
---|
| 545 | ! current height within it |
---|
| 546 | current_height = palm_grid % z(k) + palm_grid % z0 |
---|
[3182] | 547 | h_top = palm_intermediate % h(i,j,k_intermediate+1) |
---|
| 548 | h_bottom = palm_intermediate % h(i,j,k_intermediate) |
---|
[2696] | 549 | |
---|
| 550 | point_is_above_grid = (current_height > column_top) !22000m, very unlikely |
---|
| 551 | point_is_below_grid = (current_height < column_base) |
---|
| 552 | |
---|
| 553 | point_is_in_current_cell = ( & |
---|
| 554 | current_height >= h_bottom .AND. & |
---|
| 555 | current_height < h_top & |
---|
| 556 | ) |
---|
| 557 | |
---|
| 558 | ! set default weights |
---|
| 559 | palm_grid % w_verti(i,j,k,1:2) = 0.0_dp |
---|
| 560 | |
---|
| 561 | IF (point_is_above_grid) THEN |
---|
| 562 | |
---|
| 563 | palm_grid % kk(i,j,k,1:2) = nlev |
---|
| 564 | palm_grid % w_verti(i,j,k,1:2) = - 2.0_dp |
---|
| 565 | |
---|
[3182] | 566 | message = "PALM-4U grid extends above COSMO-DE model top." |
---|
| 567 | CALL abort('find_vertical_neighbours_and_weights', message) |
---|
| 568 | |
---|
[2696] | 569 | ELSE IF (point_is_below_grid) THEN |
---|
| 570 | |
---|
| 571 | palm_grid % kk(i,j,k,1:2) = 0 |
---|
| 572 | palm_grid % w_verti(i,j,k,1:2) = - 2.0_dp |
---|
| 573 | |
---|
| 574 | ELSE |
---|
| 575 | ! cycle through intermediate levels until current |
---|
| 576 | ! intermediate-grid cell overlaps with current_height |
---|
[3182] | 577 | DO WHILE (.NOT. point_is_in_current_cell .AND. k_intermediate <= nlev-1) |
---|
| 578 | k_intermediate = k_intermediate + 1 |
---|
[2696] | 579 | |
---|
[3182] | 580 | h_top = palm_intermediate % h(i,j,k_intermediate+1) |
---|
| 581 | h_bottom = palm_intermediate % h(i,j,k_intermediate) |
---|
[2696] | 582 | point_is_in_current_cell = ( & |
---|
| 583 | current_height >= h_bottom .AND. & |
---|
| 584 | current_height < h_top & |
---|
| 585 | ) |
---|
| 586 | END DO |
---|
| 587 | |
---|
[3182] | 588 | ! k_intermediate = 48 indicates the last section (indices 48 and 49), i.e. |
---|
| 589 | ! k_intermediate = 49 is not the beginning of a valid cell. |
---|
| 590 | IF (k_intermediate > nlev-1) THEN |
---|
| 591 | message = "Index " // TRIM(str(k_intermediate)) // & |
---|
| 592 | " is above intermediate grid range." |
---|
[2696] | 593 | CALL abort('find_vertical_neighbours', message) |
---|
| 594 | END IF |
---|
| 595 | |
---|
[3182] | 596 | palm_grid % kk(i,j,k,1) = k_intermediate |
---|
| 597 | palm_grid % kk(i,j,k,2) = k_intermediate + 1 |
---|
[2696] | 598 | |
---|
| 599 | ! copmute vertical weights |
---|
| 600 | weight = (h_top - current_height) / (h_top - h_bottom) |
---|
| 601 | palm_grid % w_verti(i,j,k,1) = weight |
---|
| 602 | palm_grid % w_verti(i,j,k,2) = 1.0_dp - weight |
---|
| 603 | END IF |
---|
| 604 | |
---|
| 605 | END DO |
---|
| 606 | |
---|
| 607 | END DO |
---|
| 608 | END DO |
---|
| 609 | |
---|
| 610 | END SUBROUTINE find_vertical_neighbours_and_weights |
---|
| 611 | |
---|
| 612 | !------------------------------------------------------------------------------! |
---|
| 613 | ! Description: |
---|
| 614 | ! ------------ |
---|
| 615 | !> Compute the four weights for horizontal bilinear interpolation given the |
---|
| 616 | !> coordinates clon(i,j) clat(i,j) of the PALM-4U grid in the COSMO-DE |
---|
| 617 | !> rotated-pole grid and the neightbour indices ii(i,j,1-4) and jj(i,j,1-4). |
---|
| 618 | !> |
---|
| 619 | !> Input parameters: |
---|
| 620 | !> ----------------- |
---|
| 621 | !> palm_grid % clon : longitudes of PALM-4U scalars (cell centres) in COSMO-DE's rotated-pole grid [rad] |
---|
| 622 | !> |
---|
| 623 | !> palm_grid % clat : latitudes of PALM-4U cell centres in COSMO-DE's rotated-pole grid [rad] |
---|
| 624 | !> |
---|
| 625 | !> cosmo_grid % lon : rotated-pole longitudes of scalars (cell centres) of the COSMO-DE grid [rad] |
---|
| 626 | !> |
---|
| 627 | !> cosmo_grid % lat : rotated-pole latitudes of scalars (cell centers) of the COSMO-DE grid [rad] |
---|
| 628 | !> |
---|
| 629 | !> cosmo_grid % dxi : inverse grid spacing in the first dimension [m^-1] |
---|
| 630 | !> |
---|
| 631 | !> cosmo_grid % dyi : inverse grid spacing in the second dimension [m^-1] |
---|
| 632 | !> |
---|
| 633 | !> Output parameters: |
---|
| 634 | !> ------------------ |
---|
| 635 | !> palm_grid % w_horiz(:,:,1-4) : weights for bilinear horizontal interpolation |
---|
| 636 | ! |
---|
| 637 | ! COSMO-DE grid |
---|
| 638 | ! ------------- |
---|
| 639 | ! jj, lat |
---|
| 640 | ! ^ j |
---|
| 641 | ! | \ i |
---|
| 642 | ! jj(i,j,2/3) + ... 2 ---\--------/------ 3 |
---|
| 643 | ! | | ^ \ / | |
---|
| 644 | ! | | |wp \ / | |
---|
| 645 | ! | | v \ / | |
---|
| 646 | ! latpos + ............ o/ (i,j) | |
---|
| 647 | ! | | : | |
---|
| 648 | ! | | :<----wl---->| |
---|
| 649 | ! jj(i,j,1/4) + ... 1 -------:----------- 4 |
---|
| 650 | ! | : : : |
---|
| 651 | ! | : : : |
---|
| 652 | ! | : lonpos : |
---|
| 653 | ! L-----+--------+------------+------> ii, lon |
---|
| 654 | ! ii(i,j,1/2) ii(i,j,3/4) |
---|
| 655 | ! |
---|
| 656 | SUBROUTINE compute_horizontal_interp_weights(cosmo_lat, cosmo_lon, & |
---|
[3182] | 657 | palm_clat, palm_clon, palm_ii, palm_jj, palm_w_horiz) |
---|
[2696] | 658 | |
---|
| 659 | REAL(dp), DIMENSION(0:), INTENT(IN) :: cosmo_lat, cosmo_lon |
---|
[3182] | 660 | REAL(dp) :: cosmo_dxi, cosmo_dyi |
---|
[2696] | 661 | REAL(dp), DIMENSION(0:,0:), INTENT(IN) :: palm_clat, palm_clon |
---|
| 662 | INTEGER, DIMENSION(0:,0:,1:), INTENT(IN) :: palm_ii, palm_jj |
---|
| 663 | |
---|
| 664 | REAL(dp), DIMENSION(0:,0:,1:), INTENT(OUT) :: palm_w_horiz |
---|
| 665 | |
---|
| 666 | REAL(dp) :: wl, wp |
---|
| 667 | INTEGER :: i, j |
---|
| 668 | |
---|
[3182] | 669 | cosmo_dxi = 1.0_dp / (cosmo_lon(1) - cosmo_lon(0)) |
---|
| 670 | cosmo_dyi = 1.0_dp / (cosmo_lat(1) - cosmo_lat(0)) |
---|
| 671 | |
---|
[2696] | 672 | DO j = 0, UBOUND(palm_clon, 2) |
---|
| 673 | DO i = 0, UBOUND(palm_clon, 1) |
---|
| 674 | |
---|
| 675 | ! weight in lambda direction |
---|
| 676 | wl = ( cosmo_lon(palm_ii(i,j,4)) - palm_clon(i,j) ) * cosmo_dxi |
---|
| 677 | |
---|
| 678 | ! weight in phi direction |
---|
| 679 | wp = ( cosmo_lat(palm_jj(i,j,2)) - palm_clat(i,j) ) * cosmo_dyi |
---|
| 680 | |
---|
| 681 | IF (wl > 1.0_dp .OR. wl < 0.0_dp) THEN |
---|
| 682 | message = "Horizontal weight wl = " // TRIM(real_to_str(wl)) // & |
---|
| 683 | " is out bounds." |
---|
| 684 | CALL abort('compute_horizontal_interp_weights', message) |
---|
| 685 | END IF |
---|
| 686 | IF (wp > 1.0_dp .OR. wp < 0.0_dp) THEN |
---|
| 687 | message = "Horizontal weight wp = " // TRIM(real_to_str(wp)) // & |
---|
| 688 | " is out bounds." |
---|
| 689 | CALL abort('compute_horizontal_interp_weights', message) |
---|
| 690 | END IF |
---|
| 691 | |
---|
| 692 | palm_w_horiz(i,j,1) = wl * wp |
---|
| 693 | palm_w_horiz(i,j,2) = wl * (1.0_dp - wp) |
---|
| 694 | palm_w_horiz(i,j,3) = (1.0_dp - wl) * (1.0_dp - wp) |
---|
| 695 | palm_w_horiz(i,j,4) = 1.0_dp - SUM( palm_w_horiz(i,j,1:3) ) |
---|
| 696 | |
---|
| 697 | END DO |
---|
| 698 | END DO |
---|
| 699 | |
---|
| 700 | END SUBROUTINE compute_horizontal_interp_weights |
---|
| 701 | |
---|
| 702 | |
---|
| 703 | !------------------------------------------------------------------------------! |
---|
| 704 | ! Description: |
---|
| 705 | ! ------------ |
---|
| 706 | !> Interpolates u and v components of velocities located at cell faces to the |
---|
| 707 | !> cell centres by averaging neighbouring values. |
---|
| 708 | !> |
---|
| 709 | !> This routine is designed to be used with COSMO-DE arrays where there are the |
---|
| 710 | !> same number of grid points for scalars (centres) and velocities (faces). In |
---|
| 711 | !> COSMO-DE the velocity points are staggared one half grid spaceing up-grid |
---|
| 712 | !> which means the first centre point has to be omitted and is set to zero. |
---|
| 713 | SUBROUTINE centre_velocities(u_face, v_face, u_centre, v_centre) |
---|
| 714 | REAL(dp), DIMENSION(0:,0:,0:), INTENT(IN) :: u_face, v_face |
---|
| 715 | REAL(dp), DIMENSION(0:,0:,0:), INTENT(OUT) :: u_centre, v_centre |
---|
| 716 | INTEGER :: nx, ny |
---|
| 717 | |
---|
| 718 | nx = UBOUND(u_face, 1) |
---|
| 719 | ny = UBOUND(u_face, 2) |
---|
| 720 | |
---|
| 721 | u_centre(0,:,:) = 0.0_dp |
---|
| 722 | u_centre(1:,:,:) = 0.5_dp * ( u_face(0:nx-1,:,:) + u_face(1:,:,:) ) |
---|
| 723 | |
---|
| 724 | v_centre(:,0,:) = 0.0_dp |
---|
| 725 | v_centre(:,1:,:) = 0.5_dp * ( v_face(:,0:ny-1,:) + v_face(:,1:,:) ) |
---|
| 726 | END SUBROUTINE centre_velocities |
---|
| 727 | |
---|
| 728 | |
---|
| 729 | FUNCTION phirot2phi (phirot, rlarot, polphi, pollam, polgam) |
---|
| 730 | |
---|
| 731 | REAL(dp), INTENT (IN) :: polphi !< latitude of the rotated north pole |
---|
| 732 | REAL(dp), INTENT (IN) :: pollam !< longitude of the rotated north pole |
---|
| 733 | REAL(dp), INTENT (IN) :: phirot !< latitude in the rotated system |
---|
| 734 | REAL(dp), INTENT (IN) :: rlarot !< longitude in the rotated system |
---|
| 735 | REAL(dp), INTENT (IN) :: polgam !< angle between the north poles of the systems |
---|
| 736 | |
---|
| 737 | REAL(dp) :: phirot2phi !< latitude in the geographical system |
---|
| 738 | |
---|
| 739 | REAL(dp) :: zsinpol, zcospol, zphis, zrlas, zarg, zgam |
---|
| 740 | |
---|
| 741 | zsinpol = SIN(polphi * TO_RADIANS) |
---|
| 742 | zcospol = COS(polphi * TO_RADIANS) |
---|
| 743 | zphis = phirot * TO_RADIANS |
---|
| 744 | |
---|
| 745 | IF (rlarot > 180.0_dp) THEN |
---|
| 746 | zrlas = rlarot - 360.0_dp |
---|
| 747 | ELSE |
---|
| 748 | zrlas = rlarot |
---|
| 749 | END IF |
---|
| 750 | zrlas = zrlas * TO_RADIANS |
---|
| 751 | |
---|
| 752 | IF (polgam /= 0.0_dp) THEN |
---|
| 753 | zgam = polgam * TO_RADIANS |
---|
| 754 | zarg = zsinpol * SIN (zphis) + & |
---|
| 755 | zcospol * COS(zphis) * ( COS(zrlas) * COS(zgam) - & |
---|
| 756 | SIN(zgam) * SIN(zrlas) ) |
---|
| 757 | ELSE |
---|
| 758 | zarg = zcospol * COS (zphis) * COS (zrlas) + zsinpol * SIN (zphis) |
---|
| 759 | END IF |
---|
| 760 | |
---|
| 761 | phirot2phi = ASIN (zarg) * TO_DEGREES |
---|
| 762 | |
---|
| 763 | END FUNCTION phirot2phi |
---|
| 764 | |
---|
| 765 | |
---|
| 766 | FUNCTION phi2phirot (phi, rla, polphi, pollam) |
---|
| 767 | |
---|
| 768 | REAL(dp), INTENT (IN) :: polphi !< latitude of the rotated north pole |
---|
| 769 | REAL(dp), INTENT (IN) :: pollam !< longitude of the rotated north pole |
---|
| 770 | REAL(dp), INTENT (IN) :: phi !< latitude in the geographical system |
---|
| 771 | REAL(dp), INTENT (IN) :: rla !< longitude in the geographical system |
---|
| 772 | |
---|
| 773 | REAL(dp) :: phi2phirot !< longitude in the rotated system |
---|
| 774 | |
---|
| 775 | REAL(dp) :: zsinpol, zcospol, zlampol, zphi, zrla, zarg1, zarg2, zrla1 |
---|
| 776 | |
---|
| 777 | zsinpol = SIN(polphi * TO_RADIANS) |
---|
| 778 | zcospol = COS(polphi * TO_RADIANS) |
---|
| 779 | zlampol = pollam * TO_RADIANS |
---|
| 780 | zphi = phi * TO_RADIANS |
---|
| 781 | |
---|
| 782 | IF (rla > 180.0_dp) THEN |
---|
| 783 | zrla1 = rla - 360.0_dp |
---|
| 784 | ELSE |
---|
| 785 | zrla1 = rla |
---|
| 786 | END IF |
---|
| 787 | zrla = zrla1 * TO_RADIANS |
---|
| 788 | |
---|
| 789 | zarg1 = SIN(zphi) * zsinpol |
---|
| 790 | zarg2 = COS(zphi) * zcospol * COS(zrla - zlampol) |
---|
| 791 | |
---|
| 792 | phi2phirot = ASIN(zarg1 + zarg2) * TO_DEGREES |
---|
| 793 | |
---|
| 794 | END FUNCTION phi2phirot |
---|
| 795 | |
---|
| 796 | |
---|
| 797 | FUNCTION rlarot2rla(phirot, rlarot, polphi, pollam, polgam) |
---|
| 798 | |
---|
| 799 | REAL(dp), INTENT (IN) :: polphi !< latitude of the rotated north pole |
---|
| 800 | REAL(dp), INTENT (IN) :: pollam !< longitude of the rotated north pole |
---|
| 801 | REAL(dp), INTENT (IN) :: phirot !< latitude in the rotated system |
---|
| 802 | REAL(dp), INTENT (IN) :: rlarot !< longitude in the rotated system |
---|
| 803 | REAL(dp), INTENT (IN) :: polgam !< angle between the north poles of the systems |
---|
| 804 | |
---|
| 805 | REAL(dp) :: rlarot2rla !< latitude in the geographical system |
---|
| 806 | |
---|
| 807 | REAL(dp) :: zsinpol, zcospol, zlampol, zphis, zrlas, zarg1, zarg2, zgam |
---|
| 808 | |
---|
| 809 | zsinpol = SIN(TO_RADIANS * polphi) |
---|
| 810 | zcospol = COS(TO_RADIANS * polphi) |
---|
| 811 | zlampol = TO_RADIANS * pollam |
---|
| 812 | zphis = TO_RADIANS * phirot |
---|
| 813 | |
---|
| 814 | IF (rlarot > 180.0_dp) THEN |
---|
| 815 | zrlas = rlarot - 360.0_dp |
---|
| 816 | ELSE |
---|
| 817 | zrlas = rlarot |
---|
| 818 | END IF |
---|
| 819 | zrlas = TO_RADIANS * zrlas |
---|
| 820 | |
---|
| 821 | IF (polgam /= 0.0_dp) THEN |
---|
| 822 | zgam = TO_RADIANS * polgam |
---|
| 823 | zarg1 = SIN(zlampol) * (zcospol * SIN(zphis) - zsinpol*COS(zphis) * & |
---|
| 824 | (COS(zrlas) * COS(zgam) - SIN(zrlas) * SIN(zgam)) ) - & |
---|
| 825 | COS(zlampol) * COS(zphis) * ( SIN(zrlas) * COS(zgam) + & |
---|
| 826 | COS(zrlas) * SIN(zgam) ) |
---|
| 827 | |
---|
| 828 | zarg2 = COS (zlampol) * (zcospol * SIN(zphis) - zsinpol*COS(zphis) * & |
---|
| 829 | (COS(zrlas) * COS(zgam) - SIN(zrlas) * SIN(zgam)) ) + & |
---|
| 830 | SIN(zlampol) * COS(zphis) * ( SIN(zrlas) * COS(zgam) + & |
---|
| 831 | COS(zrlas) * SIN(zgam) ) |
---|
| 832 | ELSE |
---|
| 833 | zarg1 = SIN (zlampol) * (-zsinpol * COS(zrlas) * COS(zphis) + & |
---|
| 834 | zcospol * SIN(zphis)) - & |
---|
| 835 | COS (zlampol) * SIN(zrlas) * COS(zphis) |
---|
| 836 | zarg2 = COS (zlampol) * (-zsinpol * COS(zrlas) * COS(zphis) + & |
---|
| 837 | zcospol * SIN(zphis)) + & |
---|
| 838 | SIN (zlampol) * SIN(zrlas) * COS(zphis) |
---|
| 839 | END IF |
---|
| 840 | |
---|
| 841 | IF (zarg2 == 0.0_dp) zarg2 = 1.0E-20_dp |
---|
| 842 | |
---|
| 843 | rlarot2rla = ATAN2(zarg1,zarg2) * TO_DEGREES |
---|
| 844 | |
---|
| 845 | END FUNCTION rlarot2rla |
---|
| 846 | |
---|
| 847 | |
---|
| 848 | FUNCTION rla2rlarot ( phi, rla, polphi, pollam, polgam ) |
---|
| 849 | |
---|
| 850 | REAL(dp), INTENT (IN) :: polphi !< latitude of the rotated north pole |
---|
| 851 | REAL(dp), INTENT (IN) :: pollam !< longitude of the rotated north pole |
---|
| 852 | REAL(dp), INTENT (IN) :: phi !< latitude in geographical system |
---|
| 853 | REAL(dp), INTENT (IN) :: rla !< longitude in geographical system |
---|
| 854 | REAL(dp), INTENT (IN) :: polgam !< angle between the north poles of the systems |
---|
| 855 | |
---|
| 856 | REAL (KIND=dp) :: rla2rlarot !< latitude in the the rotated system |
---|
| 857 | |
---|
| 858 | REAL (KIND=dp) :: zsinpol, zcospol, zlampol, zphi, zrla, zarg1, zarg2, zrla1 |
---|
| 859 | |
---|
| 860 | zsinpol = SIN(polphi * TO_RADIANS) |
---|
| 861 | zcospol = COS(polphi * TO_RADIANS) |
---|
| 862 | zlampol = pollam * TO_RADIANS |
---|
| 863 | zphi = phi * TO_RADIANS |
---|
| 864 | |
---|
| 865 | IF (rla > 180.0_dp) THEN |
---|
| 866 | zrla1 = rla - 360.0_dp |
---|
| 867 | ELSE |
---|
| 868 | zrla1 = rla |
---|
| 869 | END IF |
---|
| 870 | zrla = zrla1 * TO_RADIANS |
---|
| 871 | |
---|
| 872 | zarg1 = - SIN (zrla-zlampol) * COS(zphi) |
---|
| 873 | zarg2 = - zsinpol * COS(zphi) * COS(zrla-zlampol) + zcospol * SIN(zphi) |
---|
| 874 | |
---|
| 875 | IF (zarg2 == 0.0_dp) zarg2 = 1.0E-20_dp |
---|
| 876 | |
---|
| 877 | rla2rlarot = ATAN2 (zarg1,zarg2) * TO_DEGREES |
---|
| 878 | |
---|
| 879 | IF (polgam /= 0.0_dp ) THEN |
---|
| 880 | rla2rlarot = polgam + rla2rlarot |
---|
| 881 | IF (rla2rlarot > 180._dp) rla2rlarot = rla2rlarot - 360.0_dp |
---|
| 882 | END IF |
---|
| 883 | |
---|
| 884 | END FUNCTION rla2rlarot |
---|
| 885 | |
---|
| 886 | |
---|
| 887 | SUBROUTINE uv2uvrot(u, v, rlat, rlon, pollat, pollon, urot, vrot) |
---|
| 888 | |
---|
| 889 | REAL(dp), INTENT (IN) :: u, v !< wind components in the true geographical system |
---|
| 890 | REAL(dp), INTENT (IN) :: rlat, rlon !< coordinates in the true geographical system |
---|
| 891 | REAL(dp), INTENT (IN) :: pollat, pollon !< latitude and longitude of the north pole of the rotated grid |
---|
| 892 | |
---|
| 893 | REAL(dp), INTENT (OUT) :: urot, vrot !< wind components in the rotated grid |
---|
| 894 | |
---|
| 895 | REAL (dp) :: zsinpol, zcospol, zlonp, zlat, zarg1, zarg2, znorm |
---|
| 896 | |
---|
| 897 | zsinpol = SIN(pollat * TO_RADIANS) |
---|
| 898 | zcospol = COS(pollat * TO_RADIANS) |
---|
| 899 | zlonp = (pollon-rlon) * TO_RADIANS |
---|
| 900 | zlat = rlat * TO_RADIANS |
---|
| 901 | |
---|
| 902 | zarg1 = zcospol * SIN(zlonp) |
---|
| 903 | zarg2 = zsinpol * COS(zlat) - zcospol * SIN(zlat) * COS(zlonp) |
---|
| 904 | znorm = 1.0_dp / SQRT(zarg1*zarg1 + zarg2*zarg2) |
---|
| 905 | |
---|
| 906 | urot = u * zarg2 * znorm - v * zarg1 * znorm |
---|
| 907 | vrot = u * zarg1 * znorm + v * zarg2 * znorm |
---|
| 908 | |
---|
| 909 | END SUBROUTINE uv2uvrot |
---|
| 910 | |
---|
| 911 | |
---|
| 912 | SUBROUTINE uvrot2uv (urot, vrot, rlat, rlon, pollat, pollon, u, v) |
---|
| 913 | |
---|
| 914 | REAL(dp), INTENT(IN) :: urot, vrot !< wind components in the rotated grid |
---|
| 915 | REAL(dp), INTENT(IN) :: rlat, rlon !< latitude and longitude in the true geographical system |
---|
| 916 | REAL(dp), INTENT(IN) :: pollat, pollon !< latitude and longitude of the north pole of the rotated grid |
---|
| 917 | |
---|
| 918 | REAL(dp), INTENT(OUT) :: u, v !< wind components in the true geographical system |
---|
| 919 | |
---|
| 920 | REAL(dp) :: zsinpol, zcospol, zlonp, zlat, zarg1, zarg2, znorm |
---|
| 921 | |
---|
| 922 | zsinpol = SIN(pollat * TO_RADIANS) |
---|
| 923 | zcospol = COS(pollat * TO_RADIANS) |
---|
| 924 | zlonp = (pollon-rlon) * TO_RADIANS |
---|
| 925 | zlat = rlat * TO_RADIANS |
---|
| 926 | |
---|
| 927 | zarg1 = zcospol * SIN(zlonp) |
---|
| 928 | zarg2 = zsinpol * COS(zlat) - zcospol * SIN(zlat) * COS(zlonp) |
---|
| 929 | znorm = 1.0_dp / SQRT(zarg1*zarg1 + zarg2*zarg2) |
---|
| 930 | |
---|
| 931 | u = urot * zarg2 * znorm + vrot * zarg1 * znorm |
---|
| 932 | v = - urot * zarg1 * znorm + vrot * zarg2 * znorm |
---|
| 933 | |
---|
| 934 | END SUBROUTINE uvrot2uv |
---|
| 935 | |
---|
| 936 | END MODULE |
---|
| 937 | |
---|