1 |
module fyhyp_m |
2 |
|
3 |
IMPLICIT NONE |
4 |
|
5 |
contains |
6 |
|
7 |
SUBROUTINE fyhyp(yzoomdeg, grossism, dzooma, tau, rrlatu, yyprimu, rrlatv, & |
8 |
yyprimv, rlatu2, yprimu2, rlatu1, yprimu1, champmin, champmax) |
9 |
|
10 |
! From LMDZ4/libf/dyn3d/fyhyp.F, version 1.2, 2005/06/03 09:11:32 |
11 |
|
12 |
! Author: P. Le Van, from analysis by R. Sadourny |
13 |
|
14 |
! Calcule les latitudes et dérivées dans la grille du GCM pour une |
15 |
! fonction f(y) à tangente hyperbolique. |
16 |
|
17 |
! Nota bene : il vaut mieux avoir grossism * dzoom < pi / 2 (rad), |
18 |
! en latitude. |
19 |
|
20 |
USE dimens_m, only: jjm |
21 |
USE paramet_m, only: JJP1 |
22 |
|
23 |
REAL, intent(in):: yzoomdeg |
24 |
|
25 |
REAL, intent(in):: grossism |
26 |
! grossissement (= 2 si 2 fois, = 3 si 3 fois, etc.) |
27 |
|
28 |
REAL, intent(in):: dzooma |
29 |
|
30 |
REAL, intent(in):: tau |
31 |
! raideur de la transition de l'intérieur à l'extérieur du zoom |
32 |
|
33 |
! arguments de sortie |
34 |
|
35 |
REAL rrlatu(jjp1), yyprimu(jjp1), rrlatv(jjm), yyprimv(jjm) |
36 |
real rlatu2(jjm), yprimu2(jjm), rlatu1(jjm), yprimu1(jjm) |
37 |
DOUBLE PRECISION champmin, champmax |
38 |
|
39 |
! Local: |
40 |
|
41 |
INTEGER, PARAMETER:: nmax=30000, nmax2=2*nmax |
42 |
REAL dzoom ! distance totale de la zone du zoom (en radians) |
43 |
DOUBLE PRECISION ylat(jjp1), yprim(jjp1) |
44 |
DOUBLE PRECISION yuv |
45 |
DOUBLE PRECISION, save:: yt(0:nmax2) |
46 |
DOUBLE PRECISION fhyp(0:nmax2), beta |
47 |
DOUBLE PRECISION, save:: ytprim(0:nmax2) |
48 |
DOUBLE PRECISION fxm(0:nmax2) |
49 |
DOUBLE PRECISION, save:: yf(0:nmax2) |
50 |
DOUBLE PRECISION yypr(0:nmax2) |
51 |
DOUBLE PRECISION yvrai(jjp1), yprimm(jjp1), ylatt(jjp1) |
52 |
DOUBLE PRECISION pi, pis2, epsilon, y0, pisjm |
53 |
DOUBLE PRECISION yo1, yi, ylon2, ymoy, yprimin |
54 |
DOUBLE PRECISION yfi, yf1, ffdy |
55 |
DOUBLE PRECISION ypn, deply, y00 |
56 |
SAVE y00, deply |
57 |
|
58 |
INTEGER i, j, it, ik, iter, jlat |
59 |
INTEGER jpn, jjpn |
60 |
SAVE jpn |
61 |
DOUBLE PRECISION a0, a1, a2, a3, yi2, heavyy0, heavyy0m |
62 |
DOUBLE PRECISION fa(0:nmax2), fb(0:nmax2) |
63 |
REAL y0min, y0max |
64 |
|
65 |
DOUBLE PRECISION heavyside |
66 |
|
67 |
!------------------------------------------------------------------- |
68 |
|
69 |
pi = 2.*asin(1.) |
70 |
pis2 = pi/2. |
71 |
pisjm = pi/real(jjm) |
72 |
epsilon = 1e-3 |
73 |
y0 = yzoomdeg*pi/180. |
74 |
|
75 |
IF (dzooma<1.) THEN |
76 |
dzoom = dzooma*pi |
77 |
ELSE IF (dzooma<12.) THEN |
78 |
print *, "Le paramètre dzoomy pour fyhyp est trop petit. L'augmenter " & |
79 |
// "et relancer." |
80 |
STOP 1 |
81 |
ELSE |
82 |
dzoom = dzooma*pi/180. |
83 |
END IF |
84 |
|
85 |
print *, 'yzoom(rad), grossism, tau, dzoom (rad):' |
86 |
print *, y0, grossism, tau, dzoom |
87 |
|
88 |
DO i = 0, nmax2 |
89 |
yt(i) = -pis2 + real(i)*pi/nmax2 |
90 |
END DO |
91 |
|
92 |
heavyy0m = heavyside(-y0) |
93 |
heavyy0 = heavyside(y0) |
94 |
y0min = 2.*y0*heavyy0m - pis2 |
95 |
y0max = 2.*y0*heavyy0 + pis2 |
96 |
|
97 |
fa = 999.999 |
98 |
fb = 999.999 |
99 |
|
100 |
DO i = 0, nmax2 |
101 |
IF (yt(i)<y0) THEN |
102 |
fa(i) = tau*(yt(i)-y0 + dzoom/2.) |
103 |
fb(i) = (yt(i)-2.*y0*heavyy0m + pis2)*(y0-yt(i)) |
104 |
ELSE IF (yt(i)>y0) THEN |
105 |
fa(i) = tau*(y0-yt(i) + dzoom/2.) |
106 |
fb(i) = (2.*y0*heavyy0-yt(i) + pis2)*(yt(i)-y0) |
107 |
END IF |
108 |
|
109 |
IF (200.*fb(i)<-fa(i)) THEN |
110 |
fhyp(i) = -1. |
111 |
ELSE IF (200.*fb(i)<fa(i)) THEN |
112 |
fhyp(i) = 1. |
113 |
ELSE |
114 |
fhyp(i) = tanh(fa(i)/fb(i)) |
115 |
END IF |
116 |
|
117 |
IF (yt(i)==y0) fhyp(i) = 1. |
118 |
IF (yt(i)==y0min .OR. yt(i)==y0max) fhyp(i) = -1. |
119 |
END DO |
120 |
|
121 |
! Calcul de beta |
122 |
|
123 |
ffdy = 0. |
124 |
|
125 |
DO i = 1, nmax2 |
126 |
ymoy = 0.5*(yt(i-1) + yt(i)) |
127 |
IF (ymoy<y0) THEN |
128 |
fa(i) = tau*(ymoy-y0 + dzoom/2.) |
129 |
fb(i) = (ymoy-2.*y0*heavyy0m + pis2)*(y0-ymoy) |
130 |
ELSE IF (ymoy>y0) THEN |
131 |
fa(i) = tau*(y0-ymoy + dzoom/2.) |
132 |
fb(i) = (2.*y0*heavyy0-ymoy + pis2)*(ymoy-y0) |
133 |
END IF |
134 |
|
135 |
IF (200.*fb(i)<-fa(i)) THEN |
136 |
fxm(i) = -1. |
137 |
ELSE IF (200.*fb(i)<fa(i)) THEN |
138 |
fxm(i) = 1. |
139 |
ELSE |
140 |
fxm(i) = tanh(fa(i)/fb(i)) |
141 |
END IF |
142 |
IF (ymoy==y0) fxm(i) = 1. |
143 |
IF (ymoy==y0min .OR. yt(i)==y0max) fxm(i) = -1. |
144 |
ffdy = ffdy + fxm(i)*(yt(i)-yt(i-1)) |
145 |
END DO |
146 |
|
147 |
beta = (grossism*ffdy-pi)/(ffdy-pi) |
148 |
|
149 |
IF (2. * beta - grossism <= 0.) THEN |
150 |
print *, 'Attention ! La valeur beta calculee dans la routine fyhyp ' & |
151 |
// 'est mauvaise. Modifier les valeurs de grossismy, tauy ou ' & |
152 |
// 'dzoomy et relancer.' |
153 |
STOP 1 |
154 |
END IF |
155 |
|
156 |
! calcul de Ytprim |
157 |
|
158 |
DO i = 0, nmax2 |
159 |
ytprim(i) = beta + (grossism-beta)*fhyp(i) |
160 |
END DO |
161 |
|
162 |
! Calcul de Yf |
163 |
|
164 |
yf(0) = -pis2 |
165 |
DO i = 1, nmax2 |
166 |
yypr(i) = beta + (grossism-beta)*fxm(i) |
167 |
END DO |
168 |
|
169 |
DO i = 1, nmax2 |
170 |
yf(i) = yf(i-1) + yypr(i)*(yt(i)-yt(i-1)) |
171 |
END DO |
172 |
|
173 |
! yuv = 0. si calcul des latitudes aux pts. U |
174 |
! yuv = 0.5 si calcul des latitudes aux pts. V |
175 |
|
176 |
loop_ik: DO ik = 1, 4 |
177 |
IF (ik==1) THEN |
178 |
yuv = 0. |
179 |
jlat = jjm + 1 |
180 |
ELSE IF (ik==2) THEN |
181 |
yuv = 0.5 |
182 |
jlat = jjm |
183 |
ELSE IF (ik==3) THEN |
184 |
yuv = 0.25 |
185 |
jlat = jjm |
186 |
ELSE IF (ik==4) THEN |
187 |
yuv = 0.75 |
188 |
jlat = jjm |
189 |
END IF |
190 |
|
191 |
yo1 = 0. |
192 |
DO j = 1, jlat |
193 |
yo1 = 0. |
194 |
ylon2 = -pis2 + pisjm*(real(j) + yuv-1.) |
195 |
yfi = ylon2 |
196 |
|
197 |
it = nmax2 |
198 |
DO while (it >= 1 .and. yfi < yf(it)) |
199 |
it = it - 1 |
200 |
END DO |
201 |
|
202 |
yi = yt(it) |
203 |
IF (it==nmax2) THEN |
204 |
it = nmax2 - 1 |
205 |
yf(it + 1) = pis2 |
206 |
END IF |
207 |
|
208 |
! Interpolation entre yi(it) et yi(it + 1) pour avoir Y(yi) |
209 |
! et Y'(yi) |
210 |
|
211 |
CALL coefpoly(yf(it), yf(it + 1), ytprim(it), ytprim(it + 1), & |
212 |
yt(it), yt(it + 1), a0, a1, a2, a3) |
213 |
|
214 |
yf1 = yf(it) |
215 |
yprimin = a1 + 2.*a2*yi + 3.*a3*yi*yi |
216 |
|
217 |
iter = 1 |
218 |
DO |
219 |
yi = yi - (yf1-yfi)/yprimin |
220 |
IF (abs(yi-yo1)<=epsilon .or. iter == 300) exit |
221 |
yo1 = yi |
222 |
yi2 = yi*yi |
223 |
yf1 = a0 + a1*yi + a2*yi2 + a3*yi2*yi |
224 |
yprimin = a1 + 2.*a2*yi + 3.*a3*yi2 |
225 |
END DO |
226 |
if (abs(yi-yo1) > epsilon) then |
227 |
print *, 'Pas de solution.', j, ylon2 |
228 |
STOP 1 |
229 |
end if |
230 |
|
231 |
yprimin = a1 + 2.*a2*yi + 3.*a3*yi*yi |
232 |
yprim(j) = pi/(jjm*yprimin) |
233 |
yvrai(j) = yi |
234 |
END DO |
235 |
|
236 |
DO j = 1, jlat - 1 |
237 |
IF (yvrai(j + 1)<yvrai(j)) THEN |
238 |
print *, 'Problème avec rlat(', j + 1, ') plus petit que rlat(', & |
239 |
j, ')' |
240 |
STOP 1 |
241 |
END IF |
242 |
END DO |
243 |
|
244 |
print *, 'Reorganisation des latitudes pour avoir entre - pi/2 et pi/2' |
245 |
|
246 |
IF (ik==1) THEN |
247 |
ypn = pis2 |
248 |
DO j = jlat, 1, -1 |
249 |
IF (yvrai(j)<=ypn) exit |
250 |
END DO |
251 |
|
252 |
jpn = j |
253 |
y00 = yvrai(jpn) |
254 |
deply = pis2 - y00 |
255 |
END IF |
256 |
|
257 |
DO j = 1, jjm + 1 - jpn |
258 |
ylatt(j) = -pis2 - y00 + yvrai(jpn + j-1) |
259 |
yprimm(j) = yprim(jpn + j-1) |
260 |
END DO |
261 |
|
262 |
jjpn = jpn |
263 |
IF (jlat==jjm) jjpn = jpn - 1 |
264 |
|
265 |
DO j = 1, jjpn |
266 |
ylatt(j + jjm + 1-jpn) = yvrai(j) + deply |
267 |
yprimm(j + jjm + 1-jpn) = yprim(j) |
268 |
END DO |
269 |
|
270 |
! Fin de la reorganisation |
271 |
|
272 |
DO j = 1, jlat |
273 |
ylat(j) = ylatt(jlat + 1-j) |
274 |
yprim(j) = yprimm(jlat + 1-j) |
275 |
END DO |
276 |
|
277 |
DO j = 1, jlat |
278 |
yvrai(j) = ylat(j)*180./pi |
279 |
END DO |
280 |
|
281 |
IF (ik==1) THEN |
282 |
DO j = 1, jlat |
283 |
rrlatu(j) = ylat(j) |
284 |
yyprimu(j) = yprim(j) |
285 |
END DO |
286 |
ELSE IF (ik==2) THEN |
287 |
DO j = 1, jlat |
288 |
rrlatv(j) = ylat(j) |
289 |
yyprimv(j) = yprim(j) |
290 |
END DO |
291 |
ELSE IF (ik==3) THEN |
292 |
DO j = 1, jlat |
293 |
rlatu2(j) = ylat(j) |
294 |
yprimu2(j) = yprim(j) |
295 |
END DO |
296 |
ELSE IF (ik==4) THEN |
297 |
DO j = 1, jlat |
298 |
rlatu1(j) = ylat(j) |
299 |
yprimu1(j) = yprim(j) |
300 |
END DO |
301 |
END IF |
302 |
END DO loop_ik |
303 |
|
304 |
DO j = 1, jjm |
305 |
ylat(j) = rrlatu(j) - rrlatu(j + 1) |
306 |
END DO |
307 |
champmin = 1e12 |
308 |
champmax = -1e12 |
309 |
DO j = 1, jjm |
310 |
champmin = min(champmin, ylat(j)) |
311 |
champmax = max(champmax, ylat(j)) |
312 |
END DO |
313 |
champmin = champmin*180./pi |
314 |
champmax = champmax*180./pi |
315 |
|
316 |
END SUBROUTINE fyhyp |
317 |
|
318 |
end module fyhyp_m |