trunk/dyn3d/fxhyp.f

module fxhyp_m

  IMPLICIT NONE

contains

  SUBROUTINE fxhyp(xprimm025, rlonv, xprimv, rlonu, xprimu, xprimp025)

    ! From LMDZ4/libf/dyn3d/fxhyp.F, version 1.2, 2005/06/03 09:11:32
    ! Author: P. Le Van, from formulas by R. Sadourny

    ! Calcule les longitudes et dérivées dans la grille du GCM pour
    ! une fonction f(x) à dérivée tangente hyperbolique.

    ! Il vaut mieux avoir : grossismx \times dzoom < pi

    ! Le premier point scalaire pour une grille regulière (grossismx =
    ! 1., taux=0., clon=0.) est à - 180 degrés.

    USE dimens_m, ONLY: iim
    use fxhyp_loop_ik_m, only: fxhyp_loop_ik, nmax
    use nr_util, only: pi_d, twopi_d, arth
    use serre, only: clon, grossismx, dzoomx, taux

    REAL, intent(out):: xprimm025(:), rlonv(:), xprimv(:) ! (iim + 1)
    real, intent(out):: rlonu(:), xprimu(:), xprimp025(:) ! (iim + 1)

    ! Local:

    real rlonm025(iim + 1), rlonp025(iim + 1)
    REAL dzoom
    DOUBLE PRECISION xlon(iim)
    DOUBLE PRECISION xtild(0:2 * nmax)
    DOUBLE PRECISION fhyp(nmax:2 * nmax), ffdx, beta, Xprimt(0:2 * nmax)
    DOUBLE PRECISION Xf(0:2 * nmax), xxpr(2 * nmax)
    DOUBLE PRECISION xzoom, fa, fb
    INTEGER i
    DOUBLE PRECISION xmoy, fxm
    DOUBLE PRECISION decalx

    !----------------------------------------------------------------------

    print *, "Call sequence information: fxhyp"

    xzoom = clon * pi_d / 180d0

    IF (grossismx == 1.) THEN
       decalx = 1d0
    else
       decalx = 0.75d0
    END IF

    dzoom = dzoomx * twopi_d
    xtild = arth(- pi_d, pi_d / nmax, 2 * nmax + 1)

    ! Compute fhyp:
    DO i = nmax, 2 * nmax
       fa = taux * (dzoom / 2. - xtild(i))
       fb = xtild(i) * (pi_d - xtild(i))

       IF (200. * fb < - fa) THEN
          fhyp(i) = - 1.
       ELSE IF (200. * fb < fa) THEN
          fhyp(i) = 1.
       ELSE
          IF (ABS(fa) < 1e-13 .AND. ABS(fb) < 1e-13) THEN
             IF (200. * fb + fa < 1e-10) THEN
                fhyp(i) = - 1.
             ELSE IF (200. * fb - fa < 1e-10) THEN
                fhyp(i) = 1.
             END IF
          ELSE
             fhyp(i) = TANH(fa / fb)
          END IF
       END IF

       IF (xtild(i) == 0.) fhyp(i) = 1.
       IF (xtild(i) == pi_d) fhyp(i) = -1.
    END DO

    ! Calcul de beta 

    ffdx = 0.

    DO i = nmax + 1, 2 * nmax
       xmoy = 0.5 * (xtild(i-1) + xtild(i))
       fa = taux * (dzoom / 2. - xmoy)
       fb = xmoy * (pi_d - xmoy)

       IF (200. * fb < - fa) THEN
          fxm = - 1.
       ELSE IF (200. * fb < fa) THEN
          fxm = 1.
       ELSE
          IF (ABS(fa) < 1e-13 .AND. ABS(fb) < 1e-13) THEN
             IF (200. * fb + fa < 1e-10) THEN
                fxm = - 1.
             ELSE IF (200. * fb - fa < 1e-10) THEN
                fxm = 1.
             END IF
          ELSE
             fxm = TANH(fa / fb)
          END IF
       END IF

       IF (xmoy == 0.) fxm = 1.
       IF (xmoy == pi_d) fxm = -1.

       ffdx = ffdx + fxm * (xtild(i) - xtild(i-1))
    END DO

    print *, "ffdx = ", ffdx
    beta = (grossismx * ffdx - pi_d) / (ffdx - pi_d)
    print *, "beta = ", beta

    IF (2. * beta - grossismx <= 0.) THEN
       print *, 'Bad choice of grossismx, taux, dzoomx.'
       print *, 'Decrease dzoomx or grossismx.'
       STOP 1
    END IF

    ! calcul de Xprimt 
    Xprimt(nmax:2 * nmax) = beta + (grossismx - beta) * fhyp
    xprimt(:nmax - 1) = xprimt(2 * nmax:nmax + 1:- 1)

    ! Calcul de Xf

    DO i = nmax + 1, 2 * nmax
       xmoy = 0.5 * (xtild(i-1) + xtild(i))
       fa = taux * (dzoom / 2. - xmoy)
       fb = xmoy * (pi_d - xmoy)

       IF (200. * fb < - fa) THEN
          fxm = - 1.
       ELSE IF (200. * fb < fa) THEN
          fxm = 1.
       ELSE
          fxm = TANH(fa / fb)
       END IF

       IF (xmoy == 0.) fxm = 1.
       IF (xmoy == pi_d) fxm = -1.
       xxpr(i) = beta + (grossismx - beta) * fxm
    END DO

    xxpr(:nmax) = xxpr(2 * nmax:nmax + 1:- 1)

    Xf(0) = - pi_d

    DO i=1, 2 * nmax - 1
       Xf(i) = Xf(i-1) + xxpr(i) * (xtild(i) - xtild(i-1))
    END DO

    Xf(2 * nmax) = pi_d

    call fxhyp_loop_ik(1, decalx, xf, xtild, Xprimt, xzoom, rlonm025, &
         xprimm025, xuv = - 0.25d0)
    call fxhyp_loop_ik(2, decalx, xf, xtild, Xprimt, xzoom, rlonv, xprimv, &
         xuv = 0d0)
    call fxhyp_loop_ik(3, decalx, xf, xtild, Xprimt, xzoom, rlonu, xprimu, &
         xuv = 0.5d0)
    call fxhyp_loop_ik(4, decalx, xf, xtild, Xprimt, xzoom, rlonp025, &
         xprimp025, xuv = 0.25d0)

    print *

    forall (i = 1: iim) xlon(i) = rlonv(i + 1) - rlonv(i)
    print *, "Minimum longitude step:", MINval(xlon) * 180. / pi_d, "degrees"
    print *, "Maximum longitude step:", MAXval(xlon) * 180. / pi_d, "degrees"

    DO i = 1, iim + 1
       IF (rlonp025(i) < rlonv(i)) THEN
          print *, 'rlonp025(', i, ') = ', rlonp025(i)
          print *, "< rlonv(", i, ") = ", rlonv(i)
          STOP 1
       END IF

       IF (rlonv(i) < rlonm025(i)) THEN 
          print *, 'rlonv(', i, ') = ', rlonv(i)
          print *, "< rlonm025(", i, ") = ", rlonm025(i)
          STOP 1
       END IF

       IF (rlonp025(i) > rlonu(i)) THEN
          print *, 'rlonp025(', i, ') = ', rlonp025(i)
          print *, "> rlonu(", i, ") = ", rlonu(i)
          STOP 1
       END IF
    END DO

  END SUBROUTINE fxhyp

end module fxhyp_m
1	guez	78	module fxhyp_m
2	guez	3
3	guez	78	IMPLICIT NONE
4	guez	3
5	guez	78	contains
6	guez	3
7	guez	119	SUBROUTINE fxhyp(xprimm025, rlonv, xprimv, rlonu, xprimu, xprimp025)
8	guez	3
9	guez	91	! From LMDZ4/libf/dyn3d/fxhyp.F, version 1.2, 2005/06/03 09:11:32
10	guez	119	! Author: P. Le Van, from formulas by R. Sadourny
11	guez	3
12	guez	78	! Calcule les longitudes et dérivées dans la grille du GCM pour
13	guez	119	! une fonction f(x) à dérivée tangente hyperbolique.
14	guez	3
15	guez	121	! Il vaut mieux avoir : grossismx \times dzoom < pi
16	guez	3
17	guez	120	! Le premier point scalaire pour une grille regulière (grossismx =
18			! 1., taux=0., clon=0.) est à - 180 degrés.
19
20	guez	78	USE dimens_m, ONLY: iim
21	guez	121	use fxhyp_loop_ik_m, only: fxhyp_loop_ik, nmax
22	guez	120	use nr_util, only: pi_d, twopi_d, arth
23	guez	119	use serre, only: clon, grossismx, dzoomx, taux
24	guez	3
25	guez	119	REAL, intent(out):: xprimm025(:), rlonv(:), xprimv(:) ! (iim + 1)
26			real, intent(out):: rlonu(:), xprimu(:), xprimp025(:) ! (iim + 1)
27	guez	3
28	guez	91	! Local:
29	guez	3
30	guez	119	real rlonm025(iim + 1), rlonp025(iim + 1)
31	guez	78	REAL dzoom
32	guez	121	DOUBLE PRECISION xlon(iim)
33			DOUBLE PRECISION xtild(0:2 * nmax)
34			DOUBLE PRECISION fhyp(nmax:2 * nmax), ffdx, beta, Xprimt(0:2 * nmax)
35			DOUBLE PRECISION Xf(0:2 * nmax), xxpr(2 * nmax)
36			DOUBLE PRECISION xzoom, fa, fb
37			INTEGER i
38			DOUBLE PRECISION xmoy, fxm
39	guez	91	DOUBLE PRECISION decalx
40	guez	3
41	guez	91	!----------------------------------------------------------------------
42
43	guez	120	print *, "Call sequence information: fxhyp"
44
45	guez	121	xzoom = clon * pi_d / 180d0
46	guez	3
47	guez	120	IF (grossismx == 1.) THEN
48	guez	121	decalx = 1d0
49	guez	119	else
50	guez	121	decalx = 0.75d0
51	guez	119	END IF
52	guez	3
53	guez	121	dzoom = dzoomx * twopi_d
54			xtild = arth(- pi_d, pi_d / nmax, 2 * nmax + 1)
55	guez	3
56	guez	121	! Compute fhyp:
57			DO i = nmax, 2 * nmax
58	guez	120	fa = taux * (dzoom / 2. - xtild(i))
59	guez	119	fb = xtild(i) * (pi_d - xtild(i))
60	guez	78
61	guez	120	IF (200. * fb < - fa) THEN
62	guez	119	fhyp(i) = - 1.
63			ELSE IF (200. * fb < fa) THEN
64			fhyp(i) = 1.
65	guez	3	ELSE
66	guez	121	IF (ABS(fa) < 1e-13 .AND. ABS(fb) < 1e-13) THEN
67	guez	120	IF (200. * fb + fa < 1e-10) THEN
68	guez	119	fhyp(i) = - 1.
69	guez	120	ELSE IF (200. * fb - fa < 1e-10) THEN
70	guez	119	fhyp(i) = 1.
71			END IF
72	guez	78	ELSE
73	guez	119	fhyp(i) = TANH(fa / fb)
74			END IF
75	guez	112	END IF
76	guez	3
77	guez	91	IF (xtild(i) == 0.) fhyp(i) = 1.
78	guez	119	IF (xtild(i) == pi_d) fhyp(i) = -1.
79	guez	112	END DO
80	guez	3
81	guez	91	! Calcul de beta
82	guez	3
83	guez	78	ffdx = 0.
84	guez	3
85	guez	121	DO i = nmax + 1, 2 * nmax
86	guez	78	xmoy = 0.5 * (xtild(i-1) + xtild(i))
87	guez	120	fa = taux * (dzoom / 2. - xmoy)
88	guez	119	fb = xmoy * (pi_d - xmoy)
89	guez	78
90	guez	120	IF (200. * fb < - fa) THEN
91	guez	78	fxm = - 1.
92	guez	119	ELSE IF (200. * fb < fa) THEN
93	guez	78	fxm = 1.
94			ELSE
95	guez	121	IF (ABS(fa) < 1e-13 .AND. ABS(fb) < 1e-13) THEN
96	guez	120	IF (200. * fb + fa < 1e-10) THEN
97	guez	78	fxm = - 1.
98	guez	120	ELSE IF (200. * fb - fa < 1e-10) THEN
99	guez	78	fxm = 1.
100	guez	119	END IF
101	guez	78	ELSE
102	guez	119	fxm = TANH(fa / fb)
103			END IF
104			END IF
105	guez	3
106	guez	91	IF (xmoy == 0.) fxm = 1.
107	guez	119	IF (xmoy == pi_d) fxm = -1.
108	guez	3
109	guez	78	ffdx = ffdx + fxm * (xtild(i) - xtild(i-1))
110	guez	119	END DO
111	guez	3
112	guez	121	print *, "ffdx = ", ffdx
113	guez	119	beta = (grossismx * ffdx - pi_d) / (ffdx - pi_d)
114	guez	121	print *, "beta = ", beta
115	guez	3
116	guez	119	IF (2. * beta - grossismx <= 0.) THEN
117	guez	122	print *, 'Bad choice of grossismx, taux, dzoomx.'
118			print *, 'Decrease dzoomx or grossismx.'
119	guez	78	STOP 1
120	guez	112	END IF
121	guez	78
122	guez	91	! calcul de Xprimt
123	guez	121	Xprimt(nmax:2 * nmax) = beta + (grossismx - beta) * fhyp
124			xprimt(:nmax - 1) = xprimt(2 * nmax:nmax + 1:- 1)
125	guez	78
126	guez	121	! Calcul de Xf
127	guez	78
128	guez	121	DO i = nmax + 1, 2 * nmax
129	guez	78	xmoy = 0.5 * (xtild(i-1) + xtild(i))
130	guez	120	fa = taux * (dzoom / 2. - xmoy)
131	guez	119	fb = xmoy * (pi_d - xmoy)
132	guez	78
133	guez	120	IF (200. * fb < - fa) THEN
134	guez	78	fxm = - 1.
135	guez	119	ELSE IF (200. * fb < fa) THEN
136	guez	78	fxm = 1.
137	guez	3	ELSE
138	guez	119	fxm = TANH(fa / fb)
139			END IF
140	guez	3
141	guez	91	IF (xmoy == 0.) fxm = 1.
142	guez	119	IF (xmoy == pi_d) fxm = -1.
143			xxpr(i) = beta + (grossismx - beta) * fxm
144			END DO
145	guez	3
146	guez	121	xxpr(:nmax) = xxpr(2 * nmax:nmax + 1:- 1)
147	guez	3
148	guez	121	Xf(0) = - pi_d
149
150			DO i=1, 2 * nmax - 1
151	guez	78	Xf(i) = Xf(i-1) + xxpr(i) * (xtild(i) - xtild(i-1))
152	guez	119	END DO
153	guez	3
154	guez	121	Xf(2 * nmax) = pi_d
155	guez	3
156	guez	121	call fxhyp_loop_ik(1, decalx, xf, xtild, Xprimt, xzoom, rlonm025, &
157			xprimm025, xuv = - 0.25d0)
158			call fxhyp_loop_ik(2, decalx, xf, xtild, Xprimt, xzoom, rlonv, xprimv, &
159			xuv = 0d0)
160			call fxhyp_loop_ik(3, decalx, xf, xtild, Xprimt, xzoom, rlonu, xprimu, &
161			xuv = 0.5d0)
162			call fxhyp_loop_ik(4, decalx, xf, xtild, Xprimt, xzoom, rlonp025, &
163			xprimp025, xuv = 0.25d0)
164	guez	120
165	guez	91	print *
166	guez	3
167	guez	121	forall (i = 1: iim) xlon(i) = rlonv(i + 1) - rlonv(i)
168	guez	122	print , "Minimum longitude step:", MINval(xlon) 180. / pi_d, "degrees"
169			print , "Maximum longitude step:", MAXval(xlon) 180. / pi_d, "degrees"
170	guez	3
171	guez	119	DO i = 1, iim + 1
172			IF (rlonp025(i) < rlonv(i)) THEN
173	guez	121	print *, 'rlonp025(', i, ') = ', rlonp025(i)
174			print *, "< rlonv(", i, ") = ", rlonv(i)
175	guez	119	STOP 1
176			END IF
177
178			IF (rlonv(i) < rlonm025(i)) THEN
179	guez	121	print *, 'rlonv(', i, ') = ', rlonv(i)
180			print *, "< rlonm025(", i, ") = ", rlonm025(i)
181	guez	119	STOP 1
182			END IF
183
184			IF (rlonp025(i) > rlonu(i)) THEN
185	guez	120	print *, 'rlonp025(', i, ') = ', rlonp025(i)
186			print *, "> rlonu(", i, ") = ", rlonu(i)
187	guez	119	STOP 1
188			END IF
189			END DO
190
191	guez	78	END SUBROUTINE fxhyp
192
193			end module fxhyp_m