2 |
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|
3 |
IMPLICIT NONE |
IMPLICIT NONE |
4 |
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|
5 |
INTEGER jfiltnu, jfiltsu, jfiltnv, jfiltsv |
INTEGER jfiltnu, jfiltnv |
6 |
! jfiltn index of the last scalar line filtered in NH |
! index of the last line filtered in northern hemisphere at rlat[uv] |
7 |
! jfilts index of the first line filtered in SH |
! latitudes |
8 |
|
|
9 |
! North: |
integer jfiltsu, jfiltsv |
10 |
real, allocatable:: matriceun(:, :, :), matrinvn(:, :, :) |
! index of the first line filtered in southern hemisphere at |
11 |
! (iim, iim, 2:jfiltnu) |
! rlat[uv] latitudes |
12 |
|
|
13 |
real, allocatable:: matricevn(:, :, :) ! (iim, iim, jfiltnv) |
! Filtre pour les champs situes sur la grille scalaire (longitudes |
14 |
|
! rlonv, latitudes rlatu) : |
15 |
! South: |
real, pointer:: matriceun(:, :, :) ! (iim, iim, jfiltnu - 1) |
16 |
real, allocatable:: matriceus(:, :, :), matrinvs(:, :, :) |
real, pointer:: matriceus(:, :, :) ! (iim, iim, jjm - jfiltsu + 1) |
17 |
! (iim, iim, jfiltsu:jjm) |
|
18 |
|
! Filtre pour les champs situes sur la grille scalaire (longitudes |
19 |
real, allocatable:: matricevs(:, :, :) ! (iim, iim, jfiltsv:jjm) |
! rlonv, latitudes rlatu), pour le filtre inverse : |
20 |
|
real, pointer:: matrinvn(:, :, :) ! (iim, iim, jfiltnu - 1) |
21 |
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real, pointer:: matrinvs(:, :, :) ! (iim, iim, jjm - jfiltsu + 1) |
22 |
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23 |
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! Filtre pour les champs situes sur la grille de la vorticit\'e |
24 |
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! (longitudes rlonu, latitudes rlatv) |
25 |
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real, pointer:: matricevn(:, :, :) ! (iim, iim, jfiltnv) matrice |
26 |
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real, pointer:: matricevs(:, :, :) ! (iim, iim, jjm - jfiltsv + 1) |
27 |
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|
28 |
contains |
contains |
29 |
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|
30 |
SUBROUTINE inifilr |
SUBROUTINE inifilr |
31 |
|
|
32 |
! From filtrez/inifilr.F, version 1.1.1.1 2004/05/19 12:53:09 |
! From filtrez/inifilr.F, version 1.1.1.1, 2004/05/19 12:53:09 |
33 |
! H. Upadhyaya, O. Sharma |
! H. Upadhyaya, O. Sharma |
34 |
|
|
35 |
! This routine computes the eigenfunctions of the laplacian on the |
! This procedure computes the filtering coefficients for scalar |
36 |
! stretched grid, and the filtering coefficients. The modes are |
! lines and meridional wind v lines. The modes are filtered from |
37 |
! filtered from modfrst to iim. |
! modfrst to iim. We filter all those latitude lines where coefil |
38 |
|
! < 1. No filtering at poles. colat0 is to be used when alpha |
39 |
|
! (stretching coefficient) is set equal to zero for the regular |
40 |
|
! grid case. |
41 |
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|
42 |
USE dimens_m, ONLY : iim, jjm |
USE dimens_m, ONLY : iim, jjm |
43 |
USE dynetat0_m, ONLY : rlatu, rlatv, xprimu, grossismx |
USE dynetat0_m, ONLY : rlatu, rlatv, xprimu, grossismx |
44 |
use inifgn_m, only: inifgn |
use inifgn_m, only: inifgn |
45 |
|
use inifilr_hemisph_m, only: inifilr_hemisph |
46 |
use jumble, only: new_unit |
use jumble, only: new_unit |
47 |
use nr_util, only: pi |
use nr_util, only: pi, ifirstloc, assert |
48 |
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|
49 |
! Local: |
! Local: |
50 |
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51 |
REAL dlatu(jjm) |
REAL dlatu(jjm) |
52 |
REAL rlamda(2: iim) |
REAL rlamda(2:iim) ! > 0, in descending order |
53 |
real eignvl(iim) ! eigenvalues sorted in descending order |
real eignvl(iim) ! eigenvalues (<= 0) sorted in descending order |
54 |
REAL cof |
INTEGER j, unit |
|
INTEGER i, j, k, unit |
|
55 |
REAL colat0 ! > 0 |
REAL colat0 ! > 0 |
56 |
REAL eignft(iim, iim), coff |
integer j1 ! index of negative latitude closest to the equator |
57 |
|
|
58 |
real eignfnu(iim, iim), eignfnv(iim, iim) |
real eignfnu(iim, iim), eignfnv(iim, iim) |
59 |
! eigenfunctions of the discrete laplacian |
! eigenvectors of the discrete second derivative with respect to |
60 |
|
! longitude, at rlon[uv] longitudes |
|
! Filtering coefficients (lamda_max * cos(rlat) / lamda): |
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real coefilu(iim, jjm), coefilv(iim, jjm) |
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real coefilu2(iim, jjm), coefilv2(iim, jjm) |
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! Index of the mode from where modes are filtered: |
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integer, allocatable:: modfrstnu(:), modfrstsu(:) |
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integer, allocatable:: modfrstnv(:), modfrstsv(:) |
|
61 |
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62 |
!----------------------------------------------------------- |
!----------------------------------------------------------- |
63 |
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65 |
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66 |
CALL inifgn(eignvl, eignfnu, eignfnv) |
CALL inifgn(eignvl, eignfnu, eignfnv) |
67 |
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! compute eigenvalues and eigenfunctions |
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! compute the filtering coefficients for scalar lines and |
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! meridional wind v-lines |
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! we filter all those latitude lines where coefil < 1 |
|
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! NO FILTERING AT POLES |
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! colat0 is to be used when alpha (stretching coefficient) |
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! is set equal to zero for the regular grid case |
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68 |
! Calcul de colat0 |
! Calcul de colat0 |
69 |
forall (j = 1:jjm) dlatu(j) = rlatu(j) - rlatu(j + 1) |
forall (j = 1:jjm) dlatu(j) = rlatu(j) - rlatu(j + 1) |
70 |
colat0 = min(0.5, minval(dlatu) / minval(xprimu(:iim))) |
colat0 = min(0.5, minval(dlatu) / minval(xprimu(:iim))) |
71 |
PRINT *, 'colat0 = ', colat0 |
PRINT *, 'colat0 = ', colat0 |
72 |
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|
73 |
rlamda = iim / (pi * colat0 / grossismx) / sqrt(abs(eignvl(2: iim))) |
rlamda = iim / pi / colat0 * grossismx / sqrt(- eignvl(2: iim)) |
74 |
|
print *, "1 / rlamda(iim) = ", 1. / rlamda(iim) |
75 |
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|
76 |
! Determination de jfiltnu, jfiltsu, jfiltnv, jfiltsv |
! This is demonstrated in the notes but just to be sure: |
77 |
|
call assert(rlamda(iim) * colat0 >= 1. - epsilon(0.), & |
78 |
|
"inifilr rlamda(iim) * colat0") |
79 |
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80 |
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call new_unit(unit) |
81 |
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open(unit, file = "modfrst.csv", status = "replace", action = "write") |
82 |
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write(unit, fmt = *) '"rlat (degrees)" modfrst' ! title line |
83 |
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84 |
jfiltnu = (jjm + 1) / 2 |
j1 = ifirstloc(rlatu <= 0.) |
|
do while (cos(rlatu(jfiltnu)) >= colat0 & |
|
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.or. rlamda(iim) * cos(rlatu(jfiltnu)) >= 1.) |
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jfiltnu = jfiltnu - 1 |
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end do |
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jfiltsu = jjm / 2 + 2 |
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do while (cos(rlatu(jfiltsu)) >= colat0 & |
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.or. rlamda(iim) * cos(rlatu(jfiltsu)) >= 1.) |
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jfiltsu = jfiltsu + 1 |
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end do |
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jfiltnv = jjm / 2 |
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do while ((cos(rlatv(jfiltnv)) >= colat0 & |
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.or. rlamda(iim) * cos(rlatv(jfiltnv)) >= 1.) .and. jfiltnv >= 2) |
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jfiltnv = jfiltnv - 1 |
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end do |
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if (cos(rlatv(jfiltnv)) >= colat0 & |
|
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.or. rlamda(iim) * cos(rlatv(jfiltnv)) >= 1.) then |
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! {jfiltnv == 1} |
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PRINT *, 'Could not find jfiltnv.' |
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STOP 1 |
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END IF |
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jfiltsv = (jjm + 1)/ 2 + 1 |
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do while ((cos(rlatv(jfiltsv)) >= colat0 & |
|
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.or. rlamda(iim) * cos(rlatv(jfiltsv)) >= 1.) .and. jfiltsv <= jjm - 1) |
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jfiltsv = jfiltsv + 1 |
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end do |
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IF (cos(rlatv(jfiltsv)) >= colat0 & |
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.or. rlamda(iim) * cos(rlatv(jfiltsv)) >= 1.) THEN |
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! {jfiltsv == jjm} |
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PRINT *, 'Could not find jfiltsv.' |
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STOP 1 |
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END IF |
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85 |
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86 |
|
call inifilr_hemisph(rlatu(j1 - 1:2:- 1), rlamda, unit, eignfnv, jfiltnu, & |
87 |
|
matriceun, matrinvn) |
88 |
|
jfiltnu = j1 - jfiltnu |
89 |
|
matriceun = matriceun(:, :, jfiltnu - 1:1:- 1) |
90 |
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matrinvn = matrinvn(:, :, jfiltnu - 1:1:- 1) |
91 |
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92 |
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call inifilr_hemisph(- rlatu(j1:jjm), rlamda, unit, eignfnv, jfiltsu, & |
93 |
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matriceus, matrinvs) |
94 |
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jfiltsu = j1 - 1 + jfiltsu |
95 |
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96 |
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j1 = ifirstloc(rlatv <= 0.) |
97 |
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98 |
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call inifilr_hemisph(rlatv(j1 - 1:1:- 1), rlamda, unit, eignfnu, jfiltnv, & |
99 |
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matricevn) |
100 |
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jfiltnv = j1 - jfiltnv |
101 |
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matricevn = matricevn(:, :, jfiltnv:1:- 1) |
102 |
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103 |
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call inifilr_hemisph(- rlatv(j1:jjm), rlamda, unit, eignfnu, jfiltsv, & |
104 |
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matricevs) |
105 |
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jfiltsv = j1 - 1 + jfiltsv |
106 |
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107 |
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close(unit) |
108 |
PRINT *, 'jfiltnu =', jfiltnu |
PRINT *, 'jfiltnu =', jfiltnu |
109 |
PRINT *, 'jfiltsu =', jfiltsu |
PRINT *, 'jfiltsu =', jfiltsu |
110 |
PRINT *, 'jfiltnv =', jfiltnv |
PRINT *, 'jfiltnv =', jfiltnv |
111 |
PRINT *, 'jfiltsv =', jfiltsv |
PRINT *, 'jfiltsv =', jfiltsv |
112 |
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! Determination de coefilu, coefilv, modfrst[ns][uv]: |
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allocate(modfrstnu(2:jfiltnu), modfrstsu(jfiltsu:jjm)) |
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allocate(modfrstnv(jfiltnv), modfrstsv(jfiltsv:jjm)) |
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coefilu = 0. |
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coefilv = 0. |
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coefilu2 = 0. |
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coefilv2 = 0. |
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DO j = 2, jfiltnu |
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modfrstnu(j) = 2 |
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do while (rlamda(modfrstnu(j)) * cos(rlatu(j)) >= 1. & |
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.and. modfrstnu(j) <= iim - 1) |
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modfrstnu(j) = modfrstnu(j) + 1 |
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end do |
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if (rlamda(modfrstnu(j)) * cos(rlatu(j)) < 1.) then |
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DO k = modfrstnu(j), iim |
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cof = rlamda(k) * cos(rlatu(j)) |
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coefilu(k, j) = cof - 1. |
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coefilu2(k, j) = cof**2 - 1. |
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end DO |
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end if |
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END DO |
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DO j = 1, jfiltnv |
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modfrstnv(j) = 2 |
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do while (rlamda(modfrstnv(j)) * cos(rlatv(j)) >= 1. & |
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.and. modfrstnv(j) <= iim - 1) |
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modfrstnv(j) = modfrstnv(j) + 1 |
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end do |
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if (rlamda(modfrstnv(j)) * cos(rlatv(j)) < 1.) then |
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DO k = modfrstnv(j), iim |
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cof = rlamda(k) * cos(rlatv(j)) |
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coefilv(k, j) = cof - 1. |
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coefilv2(k, j) = cof**2 - 1. |
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end DO |
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end if |
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end DO |
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DO j = jfiltsu, jjm |
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modfrstsu(j) = 2 |
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do while (rlamda(modfrstsu(j)) * cos(rlatu(j)) >= 1. & |
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.and. modfrstsu(j) <= iim - 1) |
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modfrstsu(j) = modfrstsu(j) + 1 |
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end do |
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if (rlamda(modfrstsu(j)) * cos(rlatu(j)) < 1.) then |
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DO k = modfrstsu(j), iim |
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cof = rlamda(k) * cos(rlatu(j)) |
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coefilu(k, j) = cof - 1. |
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coefilu2(k, j) = cof**2 - 1. |
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end DO |
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end if |
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end DO |
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DO j = jfiltsv, jjm |
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modfrstsv(j) = 2 |
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do while (rlamda(modfrstsv(j)) * cos(rlatv(j)) >= 1. & |
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.and. modfrstsv(j) <= iim - 1) |
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modfrstsv(j) = modfrstsv(j) + 1 |
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end do |
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if (rlamda(modfrstsv(j)) * cos(rlatv(j)) < 1.) then |
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DO k = modfrstsv(j), iim |
|
|
cof = rlamda(k) * cos(rlatv(j)) |
|
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coefilv(k, j) = cof - 1. |
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coefilv2(k, j) = cof**2 - 1. |
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end DO |
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end if |
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END DO |
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call new_unit(unit) |
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open(unit, file = "inifilr_out.txt", status = "replace", action = "write") |
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write(unit, fmt = *) '"EIGNVL"', eignvl |
|
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write(unit, fmt = *) '"modfrstnu"', modfrstnu |
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write(unit, fmt = *) '"modfrstsu"', modfrstsu |
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write(unit, fmt = *) '"modfrstnv"', modfrstnv |
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write(unit, fmt = *) '"modfrstsv"', modfrstsv |
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close(unit) |
|
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allocate(matriceun(iim, iim, 2:jfiltnu), matrinvn(iim, iim, 2:jfiltnu)) |
|
|
allocate(matricevn(iim, iim, jfiltnv)) |
|
|
allocate(matricevs(iim, iim, jfiltsv:jjm)) |
|
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allocate(matriceus(iim, iim, jfiltsu:jjm), matrinvs(iim, iim, jfiltsu:jjm)) |
|
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! Calcul de la matrice filtre 'matriceu' pour les champs situes |
|
|
! sur la grille scalaire |
|
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|
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DO j = 2, jfiltnu |
|
|
DO i = 1, iim |
|
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IF (i < modfrstnu(j)) then |
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|
coff = 0. |
|
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else |
|
|
coff = coefilu(i, j) |
|
|
end IF |
|
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eignft(i, :) = eignfnv(:, i) * coff |
|
|
END DO |
|
|
matriceun(:, :, j) = matmul(eignfnv, eignft) |
|
|
END DO |
|
|
|
|
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DO j = jfiltsu, jjm |
|
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DO i = 1, iim |
|
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IF (i < modfrstsu(j)) then |
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coff = 0. |
|
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else |
|
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coff = coefilu(i, j) |
|
|
end IF |
|
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eignft(i, :) = eignfnv(:, i) * coff |
|
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END DO |
|
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matriceus(:, :, j) = matmul(eignfnv, eignft) |
|
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END DO |
|
|
|
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! Calcul de la matrice filtre 'matricev' pour les champs situes |
|
|
! sur la grille de V ou de Z |
|
|
|
|
|
DO j = 1, jfiltnv |
|
|
DO i = 1, iim |
|
|
IF (i < modfrstnv(j)) then |
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|
coff = 0. |
|
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else |
|
|
coff = coefilv(i, j) |
|
|
end IF |
|
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eignft(i, :) = eignfnu(:, i) * coff |
|
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END DO |
|
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matricevn(:, :, j) = matmul(eignfnu, eignft) |
|
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END DO |
|
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DO j = jfiltsv, jjm |
|
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DO i = 1, iim |
|
|
IF (i < modfrstsv(j)) then |
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coff = 0. |
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else |
|
|
coff = coefilv(i, j) |
|
|
end IF |
|
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eignft(i, :) = eignfnu(:, i) * coff |
|
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END DO |
|
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matricevs(:, :, j) = matmul(eignfnu, eignft) |
|
|
END DO |
|
|
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|
! Calcul de la matrice filtre 'matrinv' pour les champs situes |
|
|
! sur la grille scalaire , pour le filtre inverse |
|
|
|
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DO j = 2, jfiltnu |
|
|
DO i = 1, iim |
|
|
IF (i < modfrstnu(j)) then |
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coff = 0. |
|
|
else |
|
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coff = coefilu(i, j) / (1. + coefilu(i, j)) |
|
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end IF |
|
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eignft(i, :) = eignfnv(:, i) * coff |
|
|
END DO |
|
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matrinvn(:, :, j) = matmul(eignfnv, eignft) |
|
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END DO |
|
|
|
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DO j = jfiltsu, jjm |
|
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DO i = 1, iim |
|
|
IF (i < modfrstsu(j)) then |
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coff = 0. |
|
|
else |
|
|
coff = coefilu(i, j) / (1. + coefilu(i, j)) |
|
|
end IF |
|
|
eignft(i, :) = eignfnv(:, i) * coff |
|
|
END DO |
|
|
matrinvs(:, :, j) = matmul(eignfnv, eignft) |
|
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END DO |
|
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113 |
END SUBROUTINE inifilr |
END SUBROUTINE inifilr |
114 |
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|
115 |
end module inifilr_m |
end module inifilr_m |