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, pi_d, twopi_d, arth
    use principal_cshift_m, only: principal_cshift
    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
    real d_rlonv(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, is2
    DOUBLE PRECISION xmoy, fxm
    DOUBLE PRECISION decalx

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

    print *, "Call sequence information: fxhyp"

    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

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

    xzoom = clon * pi_d / 180d0
    call fxhyp_loop_ik(1, decalx, xf, xtild, Xprimt, xzoom, rlonm025(:iim), &
         xprimm025(:iim), xuv = - 0.25d0)
    call fxhyp_loop_ik(2, decalx, xf, xtild, Xprimt, xzoom, rlonv(:iim), &
         xprimv(:iim), xuv = 0d0)
    call fxhyp_loop_ik(3, decalx, xf, xtild, Xprimt, xzoom, rlonu(:iim), &
         xprimu(:iim), xuv = 0.5d0)
    call fxhyp_loop_ik(4, decalx, xf, xtild, Xprimt, xzoom, rlonp025(:iim), &
         xprimp025(:iim), xuv = 0.25d0)

    is2 = 0

    IF (MINval(rlonm025(:iim)) < - pi - 0.1 &
         .or. MAXval(rlonm025(:iim)) > pi + 0.1) THEN
       IF (clon <= 0.) THEN
          is2 = 1

          do while (rlonm025(is2) < - pi .and. is2 < iim)
             is2 = is2 + 1
          end do

          if (rlonm025(is2) < - pi) then
             print *, 'Rlonm025 plus petit que - pi !'
             STOP 1
          end if
       ELSE
          is2 = iim

          do while (rlonm025(is2) > pi .and. is2 > 1)
             is2 = is2 - 1
          end do

          if (rlonm025(is2) > pi) then
             print *, 'Rlonm025 plus grand que pi !'
             STOP 1
          end if
       END IF
    END IF

    call principal_cshift(is2, rlonm025, xprimm025)
    call principal_cshift(is2, rlonv, xprimv)
    call principal_cshift(is2, rlonu, xprimu)
    call principal_cshift(is2, rlonp025, xprimp025)

    forall (i = 1: iim) d_rlonv(i) = rlonv(i + 1) - rlonv(i)
    print *, "Minimum longitude step:", MINval(d_rlonv) * 180. / pi, "degrees"
    print *, "Maximum longitude step:", MAXval(d_rlonv) * 180. / pi, "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	module fxhyp_m
2
3	IMPLICIT NONE
4
5	contains
6
7	SUBROUTINE fxhyp(xprimm025, rlonv, xprimv, rlonu, xprimu, xprimp025)
8
9	! From LMDZ4/libf/dyn3d/fxhyp.F, version 1.2, 2005/06/03 09:11:32
10	! Author: P. Le Van, from formulas by R. Sadourny
11
12	! Calcule les longitudes et dérivées dans la grille du GCM pour
13	! une fonction f(x) à dérivée tangente hyperbolique.
14
15	! Il vaut mieux avoir : grossismx \times dzoom < pi
16
17	! Le premier point scalaire pour une grille regulière (grossismx =
18	! 1., taux=0., clon=0.) est à - 180 degrés.
19
20	USE dimens_m, ONLY: iim
21	use fxhyp_loop_ik_m, only: fxhyp_loop_ik, nmax
22	use nr_util, only: pi, pi_d, twopi_d, arth
23	use principal_cshift_m, only: principal_cshift
24	use serre, only: clon, grossismx, dzoomx, taux
25
26	REAL, intent(out):: xprimm025(:), rlonv(:), xprimv(:) ! (iim + 1)
27	real, intent(out):: rlonu(:), xprimu(:), xprimp025(:) ! (iim + 1)
28
29	! Local:
30	real rlonm025(iim + 1), rlonp025(iim + 1)
31	REAL dzoom
32	real d_rlonv(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, is2
38	DOUBLE PRECISION xmoy, fxm
39	DOUBLE PRECISION decalx
40
41	!----------------------------------------------------------------------
42
43	print *, "Call sequence information: fxhyp"
44
45	dzoom = dzoomx * twopi_d
46	xtild = arth(- pi_d, pi_d / nmax, 2 * nmax + 1)
47
48	! Compute fhyp:
49	DO i = nmax, 2 * nmax
50	fa = taux * (dzoom / 2. - xtild(i))
51	fb = xtild(i) * (pi_d - xtild(i))
52
53	IF (200. * fb < - fa) THEN
54	fhyp(i) = - 1.
55	ELSE IF (200. * fb < fa) THEN
56	fhyp(i) = 1.
57	ELSE
58	IF (ABS(fa) < 1e-13 .AND. ABS(fb) < 1e-13) THEN
59	IF (200. * fb + fa < 1e-10) THEN
60	fhyp(i) = - 1.
61	ELSE IF (200. * fb - fa < 1e-10) THEN
62	fhyp(i) = 1.
63	END IF
64	ELSE
65	fhyp(i) = TANH(fa / fb)
66	END IF
67	END IF
68
69	IF (xtild(i) == 0.) fhyp(i) = 1.
70	IF (xtild(i) == pi_d) fhyp(i) = -1.
71	END DO
72
73	! Calcul de beta
74
75	ffdx = 0.
76
77	DO i = nmax + 1, 2 * nmax
78	xmoy = 0.5 * (xtild(i-1) + xtild(i))
79	fa = taux * (dzoom / 2. - xmoy)
80	fb = xmoy * (pi_d - xmoy)
81
82	IF (200. * fb < - fa) THEN
83	fxm = - 1.
84	ELSE IF (200. * fb < fa) THEN
85	fxm = 1.
86	ELSE
87	IF (ABS(fa) < 1e-13 .AND. ABS(fb) < 1e-13) THEN
88	IF (200. * fb + fa < 1e-10) THEN
89	fxm = - 1.
90	ELSE IF (200. * fb - fa < 1e-10) THEN
91	fxm = 1.
92	END IF
93	ELSE
94	fxm = TANH(fa / fb)
95	END IF
96	END IF
97
98	IF (xmoy == 0.) fxm = 1.
99	IF (xmoy == pi_d) fxm = -1.
100
101	ffdx = ffdx + fxm * (xtild(i) - xtild(i-1))
102	END DO
103
104	print *, "ffdx = ", ffdx
105	beta = (grossismx * ffdx - pi_d) / (ffdx - pi_d)
106	print *, "beta = ", beta
107
108	IF (2. * beta - grossismx <= 0.) THEN
109	print *, 'Bad choice of grossismx, taux, dzoomx.'
110	print *, 'Decrease dzoomx or grossismx.'
111	STOP 1
112	END IF
113
114	! calcul de Xprimt
115	Xprimt(nmax:2 * nmax) = beta + (grossismx - beta) * fhyp
116	xprimt(:nmax - 1) = xprimt(2 * nmax:nmax + 1:- 1)
117
118	! Calcul de Xf
119
120	DO i = nmax + 1, 2 * nmax
121	xmoy = 0.5 * (xtild(i-1) + xtild(i))
122	fa = taux * (dzoom / 2. - xmoy)
123	fb = xmoy * (pi_d - xmoy)
124
125	IF (200. * fb < - fa) THEN
126	fxm = - 1.
127	ELSE IF (200. * fb < fa) THEN
128	fxm = 1.
129	ELSE
130	fxm = TANH(fa / fb)
131	END IF
132
133	IF (xmoy == 0.) fxm = 1.
134	IF (xmoy == pi_d) fxm = -1.
135	xxpr(i) = beta + (grossismx - beta) * fxm
136	END DO
137
138	xxpr(:nmax) = xxpr(2 * nmax:nmax + 1:- 1)
139
140	Xf(0) = - pi_d
141
142	DO i=1, 2 * nmax - 1
143	Xf(i) = Xf(i-1) + xxpr(i) * (xtild(i) - xtild(i-1))
144	END DO
145
146	Xf(2 * nmax) = pi_d
147
148	IF (grossismx == 1.) THEN
149	decalx = 1d0
150	else
151	decalx = 0.75d0
152	END IF
153
154	xzoom = clon * pi_d / 180d0
155	call fxhyp_loop_ik(1, decalx, xf, xtild, Xprimt, xzoom, rlonm025(:iim), &
156	xprimm025(:iim), xuv = - 0.25d0)
157	call fxhyp_loop_ik(2, decalx, xf, xtild, Xprimt, xzoom, rlonv(:iim), &
158	xprimv(:iim), xuv = 0d0)
159	call fxhyp_loop_ik(3, decalx, xf, xtild, Xprimt, xzoom, rlonu(:iim), &
160	xprimu(:iim), xuv = 0.5d0)
161	call fxhyp_loop_ik(4, decalx, xf, xtild, Xprimt, xzoom, rlonp025(:iim), &
162	xprimp025(:iim), xuv = 0.25d0)
163
164	is2 = 0
165
166	IF (MINval(rlonm025(:iim)) < - pi - 0.1 &
167	.or. MAXval(rlonm025(:iim)) > pi + 0.1) THEN
168	IF (clon <= 0.) THEN
169	is2 = 1
170
171	do while (rlonm025(is2) < - pi .and. is2 < iim)
172	is2 = is2 + 1
173	end do
174
175	if (rlonm025(is2) < - pi) then
176	print *, 'Rlonm025 plus petit que - pi !'
177	STOP 1
178	end if
179	ELSE
180	is2 = iim
181
182	do while (rlonm025(is2) > pi .and. is2 > 1)
183	is2 = is2 - 1
184	end do
185
186	if (rlonm025(is2) > pi) then
187	print *, 'Rlonm025 plus grand que pi !'
188	STOP 1
189	end if
190	END IF
191	END IF
192
193	call principal_cshift(is2, rlonm025, xprimm025)
194	call principal_cshift(is2, rlonv, xprimv)
195	call principal_cshift(is2, rlonu, xprimu)
196	call principal_cshift(is2, rlonp025, xprimp025)
197
198	forall (i = 1: iim) d_rlonv(i) = rlonv(i + 1) - rlonv(i)
199	print , "Minimum longitude step:", MINval(d_rlonv) 180. / pi, "degrees"
200	print , "Maximum longitude step:", MAXval(d_rlonv) 180. / pi, "degrees"
201
202	DO i = 1, iim + 1
203	IF (rlonp025(i) < rlonv(i)) THEN
204	print *, 'rlonp025(', i, ') = ', rlonp025(i)
205	print *, "< rlonv(", i, ") = ", rlonv(i)
206	STOP 1
207	END IF
208
209	IF (rlonv(i) < rlonm025(i)) THEN
210	print *, 'rlonv(', i, ') = ', rlonv(i)
211	print *, "< rlonm025(", i, ") = ", rlonm025(i)
212	STOP 1
213	END IF
214
215	IF (rlonp025(i) > rlonu(i)) THEN
216	print *, 'rlonp025(', i, ') = ', rlonp025(i)
217	print *, "> rlonu(", i, ") = ", rlonu(i)
218	STOP 1
219	END IF
220	END DO
221
222	END SUBROUTINE fxhyp
223
224	end module fxhyp_m