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! |
SUBROUTINE ppm3d(igd, q, ps1, ps2, u, v, w, ndt, iord, jord, kord, nc, imr, & |
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! $Header: /home/cvsroot/LMDZ4/libf/dyn3d/ppm3d.F,v 1.1.1.1 2004/05/19 12:53:07 lmdzadmin Exp $ |
jnp, j1, nlay, ap, bp, pt, ae, fill, dum, umax) |
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! |
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! implicit none |
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cFrom lin@explorer.gsfc.nasa.gov Wed Apr 15 17:44:44 1998 |
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cDate: Wed, 15 Apr 1998 11:37:03 -0400 |
! rajout de déclarations |
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cFrom: lin@explorer.gsfc.nasa.gov |
! integer Jmax,kmax,ndt0,nstep,k,j,i,ic,l,js,jn,imh,iad,jad,krd |
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cTo: Frederic.Hourdin@lmd.jussieu.fr |
! integer iu,iiu,j2,jmr,js0,jt |
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cSubject: 3D transport module of the GSFC CTM and GEOS GCM |
! real dtdy,dtdy5,rcap,iml,jn0,imjm,pi,dl,dp |
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|
! real dt,cr1,maxdt,ztc,d5,sum1,sum2,ru |
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cThis code is sent to you by S-J Lin, DAO, NASA-GSFC |
! ******************************************************************** |
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|
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cNote: this version is intended for machines like CRAY |
! ============= |
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C-90. No multitasking directives implemented. |
! INPUT: |
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|
! ============= |
| 17 |
|
|
| 18 |
C ******************************************************************** |
! Q(IMR,JNP,NLAY,NC): mixing ratios at current time (t) |
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C |
! NC: total number of constituents |
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C TransPort Core for Goddard Chemistry Transport Model (G-CTM), Goddard |
! IMR: first dimension (E-W); number of Grid intervals in E-W is IMR |
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C Earth Observing System General Circulation Model (GEOS-GCM), and Data |
! JNP: 2nd dimension (N-S); number of Grid intervals in N-S is JNP-1 |
| 22 |
C Assimilation System (GEOS-DAS). |
! NLAY: 3rd dimension (number of layers); vertical index increases from 1 |
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C |
! at |
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C ******************************************************************** |
! the model top to NLAY near the surface (see fig. below). |
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C |
! It is assumed that 6 <= NLAY <= JNP (for dynamic memory allocation) |
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C Purpose: given horizontal winds on a hybrid sigma-p surfaces, |
|
| 27 |
C one call to tpcore updates the 3-D mixing ratio |
! PS1(IMR,JNP): surface pressure at current time (t) |
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C fields one time step (NDT). [vertical mass flux is computed |
! PS2(IMR,JNP): surface pressure at mid-time-level (t+NDT/2) |
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C internally consistent with the discretized hydrostatic mass |
! PS2 is replaced by the predicted PS (at t+NDT) on output. |
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C continuity equation of the C-Grid GEOS-GCM (for IGD=1)]. |
! Note: surface pressure can have any unit or can be multiplied by any |
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C |
! const. |
| 32 |
C Schemes: Multi-dimensional Flux Form Semi-Lagrangian (FFSL) scheme based |
|
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C on the van Leer or PPM. |
! The pressure at layer edges are defined as follows: |
| 34 |
C (see Lin and Rood 1996). |
|
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C Version 4.5 |
! p(i,j,k) = AP(k)*PT + BP(k)*PS(i,j) (1) |
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C Last modified: Dec. 5, 1996 |
|
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C Major changes from version 4.0: a more general vertical hybrid sigma- |
! Where PT is a constant having the same unit as PS. |
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C pressure coordinate. |
! AP and BP are unitless constants given at layer edges |
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C Subroutines modified: xtp, ytp, fzppm, qckxyz |
! defining the vertical coordinate. |
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C Subroutines deleted: vanz |
! BP(1) = 0., BP(NLAY+1) = 1. |
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C |
! The pressure at the model top is PTOP = AP(1)*PT |
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C Author: Shian-Jiann Lin |
|
| 43 |
C mail address: |
! For pure sigma system set AP(k) = 1 for all k, PT = PTOP, |
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C Shian-Jiann Lin* |
! BP(k) = sige(k) (sigma at edges), PS = Psfc - PTOP. |
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C Code 910.3, NASA/GSFC, Greenbelt, MD 20771 |
|
| 46 |
C Phone: 301-286-9540 |
! Note: the sigma-P coordinate is a subset of Eq. 1, which in turn |
| 47 |
C E-mail: lin@dao.gsfc.nasa.gov |
! is a subset of the following even more general sigma-P-thelta coord. |
| 48 |
C |
! currently under development. |
| 49 |
C *affiliation: |
! p(i,j,k) = (AP(k)*PT + BP(k)*PS(i,j))/(D(k)-C(k)*TE**(-1/kapa)) |
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C Joint Center for Earth Systems Technology |
|
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C The University of Maryland Baltimore County |
! ///////////////////////////////// |
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C NASA - Goddard Space Flight Center |
! / \ ------------- PTOP -------------- AP(1), BP(1) |
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C References: |
! | |
| 54 |
C |
! delp(1) | ........... Q(i,j,1) ............ |
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C 1. Lin, S.-J., and R. B. Rood, 1996: Multidimensional flux form semi- |
! | |
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C Lagrangian transport schemes. Mon. Wea. Rev., 124, 2046-2070. |
! W(1) \ / --------------------------------- AP(2), BP(2) |
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C |
|
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C 2. Lin, S.-J., W. C. Chao, Y. C. Sud, and G. K. Walker, 1994: A class of |
|
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C the van Leer-type transport schemes and its applications to the moist- |
|
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C ure transport in a General Circulation Model. Mon. Wea. Rev., 122, |
! W(k-1) / \ --------------------------------- AP(k), BP(k) |
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C 1575-1593. |
! | |
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C |
! delp(K) | ........... Q(i,j,k) ............ |
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C ****6***0*********0*********0*********0*********0*********0**********72 |
! | |
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C |
! W(k) \ / --------------------------------- AP(k+1), BP(k+1) |
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subroutine ppm3d(IGD,Q,PS1,PS2,U,V,W,NDT,IORD,JORD,KORD,NC,IMR, |
|
| 66 |
& JNP,j1,NLAY,AP,BP,PT,AE,fill,dum,Umax) |
|
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c implicit none |
! / \ --------------------------------- AP(NLAY), BP(NLAY) |
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|
! | |
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c rajout de déclarations |
! delp(NLAY) | ........... Q(i,j,NLAY) ......... |
| 71 |
c integer Jmax,kmax,ndt0,nstep,k,j,i,ic,l,js,jn,imh,iad,jad,krd |
! | |
| 72 |
c integer iu,iiu,j2,jmr,js0,jt |
! W(NLAY)=0 \ / ------------- surface ----------- AP(NLAY+1), BP(NLAY+1) |
| 73 |
c real dtdy,dtdy5,rcap,iml,jn0,imjm,pi,dl,dp |
! ////////////////////////////////// |
| 74 |
c real dt,cr1,maxdt,ztc,d5,sum1,sum2,ru |
|
| 75 |
C |
! U(IMR,JNP,NLAY) & V(IMR,JNP,NLAY):winds (m/s) at mid-time-level (t+NDT/2) |
| 76 |
C ******************************************************************** |
! U and V may need to be polar filtered in advance in some cases. |
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C |
|
| 78 |
C ============= |
! IGD: grid type on which winds are defined. |
| 79 |
C INPUT: |
! IGD = 0: A-Grid [all variables defined at the same point from south |
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C ============= |
! pole (j=1) to north pole (j=JNP) ] |
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C |
|
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C Q(IMR,JNP,NLAY,NC): mixing ratios at current time (t) |
! IGD = 1 GEOS-GCM C-Grid |
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C NC: total number of constituents |
! [North] |
| 84 |
C IMR: first dimension (E-W); number of Grid intervals in E-W is IMR |
|
| 85 |
C JNP: 2nd dimension (N-S); number of Grid intervals in N-S is JNP-1 |
! V(i,j) |
| 86 |
C NLAY: 3rd dimension (number of layers); vertical index increases from 1 at |
! | |
| 87 |
C the model top to NLAY near the surface (see fig. below). |
! | |
| 88 |
C It is assumed that 6 <= NLAY <= JNP (for dynamic memory allocation) |
! | |
| 89 |
C |
! U(i-1,j)---Q(i,j)---U(i,j) [EAST] |
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C PS1(IMR,JNP): surface pressure at current time (t) |
! | |
| 91 |
C PS2(IMR,JNP): surface pressure at mid-time-level (t+NDT/2) |
! | |
| 92 |
C PS2 is replaced by the predicted PS (at t+NDT) on output. |
! | |
| 93 |
C Note: surface pressure can have any unit or can be multiplied by any |
! V(i,j-1) |
| 94 |
C const. |
|
| 95 |
C |
! U(i, 1) is defined at South Pole. |
| 96 |
C The pressure at layer edges are defined as follows: |
! V(i, 1) is half grid north of the South Pole. |
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C |
! V(i,JMR) is half grid south of the North Pole. |
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C p(i,j,k) = AP(k)*PT + BP(k)*PS(i,j) (1) |
|
| 99 |
C |
! V must be defined at j=1 and j=JMR if IGD=1 |
| 100 |
C Where PT is a constant having the same unit as PS. |
! V at JNP need not be given. |
| 101 |
C AP and BP are unitless constants given at layer edges |
|
| 102 |
C defining the vertical coordinate. |
! NDT: time step in seconds (need not be constant during the course of |
| 103 |
C BP(1) = 0., BP(NLAY+1) = 1. |
! the integration). Suggested value: 30 min. for 4x5, 15 min. for 2x2.5 |
| 104 |
C The pressure at the model top is PTOP = AP(1)*PT |
! (Lat-Lon) resolution. Smaller values are recommanded if the model |
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C |
! has a well-resolved stratosphere. |
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C For pure sigma system set AP(k) = 1 for all k, PT = PTOP, |
|
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C BP(k) = sige(k) (sigma at edges), PS = Psfc - PTOP. |
! J1 defines the size of the polar cap: |
| 108 |
C |
! South polar cap edge is located at -90 + (j1-1.5)*180/(JNP-1) deg. |
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C Note: the sigma-P coordinate is a subset of Eq. 1, which in turn |
! North polar cap edge is located at 90 - (j1-1.5)*180/(JNP-1) deg. |
| 110 |
C is a subset of the following even more general sigma-P-thelta coord. |
! There are currently only two choices (j1=2 or 3). |
| 111 |
C currently under development. |
! IMR must be an even integer if j1 = 2. Recommended value: J1=3. |
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C p(i,j,k) = (AP(k)*PT + BP(k)*PS(i,j))/(D(k)-C(k)*TE**(-1/kapa)) |
|
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C |
! IORD, JORD, and KORD are integers controlling various options in E-W, |
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C ///////////////////////////////// |
! N-S, |
| 115 |
C / \ ------------- PTOP -------------- AP(1), BP(1) |
! and vertical transport, respectively. Recommended values for positive |
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C | |
! definite scalars: IORD=JORD=3, KORD=5. Use KORD=3 for non- |
| 117 |
C delp(1) | ........... Q(i,j,1) ............ |
! positive definite scalars or when linear correlation between constituents |
| 118 |
C | |
! is to be maintained. |
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C W(1) \ / --------------------------------- AP(2), BP(2) |
|
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C |
! _ORD= |
| 121 |
C |
! 1: 1st order upstream scheme (too diffusive, not a useful option; it |
| 122 |
C |
! can be used for debugging purposes; this is THE only known "linear" |
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C W(k-1) / \ --------------------------------- AP(k), BP(k) |
! monotonic advection scheme.). |
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C | |
! 2: 2nd order van Leer (full monotonicity constraint; |
| 125 |
C delp(K) | ........... Q(i,j,k) ............ |
! see Lin et al 1994, MWR) |
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C | |
! 3: monotonic PPM* (slightly improved PPM of Collela & Woodward 1984) |
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C W(k) \ / --------------------------------- AP(k+1), BP(k+1) |
! 4: semi-monotonic PPM (same as 3, but overshoots are allowed) |
| 128 |
C |
! 5: positive-definite PPM (constraint on the subgrid distribution is |
| 129 |
C |
! only strong enough to prevent generation of negative values; |
| 130 |
C |
! both overshoots & undershoots are possible). |
| 131 |
C / \ --------------------------------- AP(NLAY), BP(NLAY) |
! 6: un-constrained PPM (nearly diffusion free; slightly faster but |
| 132 |
C | |
! positivity not quaranteed. Use this option only when the fields |
| 133 |
C delp(NLAY) | ........... Q(i,j,NLAY) ......... |
! and winds are very smooth). |
| 134 |
C | |
|
| 135 |
C W(NLAY)=0 \ / ------------- surface ----------- AP(NLAY+1), BP(NLAY+1) |
! *PPM: Piece-wise Parabolic Method |
| 136 |
C ////////////////////////////////// |
|
| 137 |
C |
! Note that KORD <=2 options are no longer supported. DO not use option 4 |
| 138 |
C U(IMR,JNP,NLAY) & V(IMR,JNP,NLAY):winds (m/s) at mid-time-level (t+NDT/2) |
! or 5. |
| 139 |
C U and V may need to be polar filtered in advance in some cases. |
! for non-positive definite scalars (such as Ertel Potential Vorticity). |
| 140 |
C |
|
| 141 |
C IGD: grid type on which winds are defined. |
! The implicit numerical diffusion decreases as _ORD increases. |
| 142 |
C IGD = 0: A-Grid [all variables defined at the same point from south |
! The last two options (ORDER=5, 6) should only be used when there is |
| 143 |
C pole (j=1) to north pole (j=JNP) ] |
! significant explicit diffusion (such as a turbulence parameterization). |
| 144 |
C |
! You |
| 145 |
C IGD = 1 GEOS-GCM C-Grid |
! might get dispersive results otherwise. |
| 146 |
C [North] |
! No filter of any kind is applied to the constituent fields here. |
| 147 |
C |
|
| 148 |
C V(i,j) |
! AE: Radius of the sphere (meters). |
| 149 |
C | |
! Recommended value for the planet earth: 6.371E6 |
| 150 |
C | |
|
| 151 |
C | |
! fill(logical): flag to do filling for negatives (see note below). |
| 152 |
C U(i-1,j)---Q(i,j)---U(i,j) [EAST] |
|
| 153 |
C | |
! Umax: Estimate (upper limit) of the maximum U-wind speed (m/s). |
| 154 |
C | |
! (220 m/s is a good value for troposphere model; 280 m/s otherwise) |
| 155 |
C | |
|
| 156 |
C V(i,j-1) |
! ============= |
| 157 |
C |
! Output |
| 158 |
C U(i, 1) is defined at South Pole. |
! ============= |
| 159 |
C V(i, 1) is half grid north of the South Pole. |
|
| 160 |
C V(i,JMR) is half grid south of the North Pole. |
! Q: mixing ratios at future time (t+NDT) (original values are |
| 161 |
C |
! over-written) |
| 162 |
C V must be defined at j=1 and j=JMR if IGD=1 |
! W(NLAY): large-scale vertical mass flux as diagnosed from the hydrostatic |
| 163 |
C V at JNP need not be given. |
! relationship. W will have the same unit as PS1 and PS2 (eg, mb). |
| 164 |
C |
! W must be divided by NDT to get the correct mass-flux unit. |
| 165 |
C NDT: time step in seconds (need not be constant during the course of |
! The vertical Courant number C = W/delp_UPWIND, where delp_UPWIND |
| 166 |
C the integration). Suggested value: 30 min. for 4x5, 15 min. for 2x2.5 |
! is the pressure thickness in the "upwind" direction. For example, |
| 167 |
C (Lat-Lon) resolution. Smaller values are recommanded if the model |
! C(k) = W(k)/delp(k) if W(k) > 0; |
| 168 |
C has a well-resolved stratosphere. |
! C(k) = W(k)/delp(k+1) if W(k) < 0. |
| 169 |
C |
! ( W > 0 is downward, ie, toward surface) |
| 170 |
C J1 defines the size of the polar cap: |
! PS2: predicted PS at t+NDT (original values are over-written) |
| 171 |
C South polar cap edge is located at -90 + (j1-1.5)*180/(JNP-1) deg. |
|
| 172 |
C North polar cap edge is located at 90 - (j1-1.5)*180/(JNP-1) deg. |
! ******************************************************************** |
| 173 |
C There are currently only two choices (j1=2 or 3). |
! NOTES: |
| 174 |
C IMR must be an even integer if j1 = 2. Recommended value: J1=3. |
! This forward-in-time upstream-biased transport scheme reduces to |
| 175 |
C |
! the 2nd order center-in-time center-in-space mass continuity eqn. |
| 176 |
C IORD, JORD, and KORD are integers controlling various options in E-W, N-S, |
! if Q = 1 (constant fields will remain constant). This also ensures |
| 177 |
C and vertical transport, respectively. Recommended values for positive |
! that the computed vertical velocity to be identical to GEOS-1 GCM |
| 178 |
C definite scalars: IORD=JORD=3, KORD=5. Use KORD=3 for non- |
! for on-line transport. |
| 179 |
C positive definite scalars or when linear correlation between constituents |
|
| 180 |
C is to be maintained. |
! A larger polar cap is used if j1=3 (recommended for C-Grid winds or when |
| 181 |
C |
! winds are noisy near poles). |
| 182 |
C _ORD= |
|
| 183 |
C 1: 1st order upstream scheme (too diffusive, not a useful option; it |
! Flux-Form Semi-Lagrangian transport in the East-West direction is used |
| 184 |
C can be used for debugging purposes; this is THE only known "linear" |
! when and where Courant number is greater than one. |
| 185 |
C monotonic advection scheme.). |
|
| 186 |
C 2: 2nd order van Leer (full monotonicity constraint; |
! The user needs to change the parameter Jmax or Kmax if the resolution |
| 187 |
C see Lin et al 1994, MWR) |
! is greater than 0.5 deg in N-S or 150 layers in the vertical direction. |
| 188 |
C 3: monotonic PPM* (slightly improved PPM of Collela & Woodward 1984) |
! (this TransPort Core is otherwise resolution independent and can be used |
| 189 |
C 4: semi-monotonic PPM (same as 3, but overshoots are allowed) |
! as a library routine). |
| 190 |
C 5: positive-definite PPM (constraint on the subgrid distribution is |
|
| 191 |
C only strong enough to prevent generation of negative values; |
! PPM is 4th order accurate when grid spacing is uniform (x & y); 3rd |
| 192 |
C both overshoots & undershoots are possible). |
! order accurate for non-uniform grid (vertical sigma coord.). |
| 193 |
C 6: un-constrained PPM (nearly diffusion free; slightly faster but |
|
| 194 |
C positivity not quaranteed. Use this option only when the fields |
! Time step is limitted only by transport in the meridional direction. |
| 195 |
C and winds are very smooth). |
! (the FFSL scheme is not implemented in the meridional direction). |
| 196 |
C |
|
| 197 |
C *PPM: Piece-wise Parabolic Method |
! Since only 1-D limiters are applied, negative values could |
| 198 |
C |
! potentially be generated when large time step is used and when the |
| 199 |
C Note that KORD <=2 options are no longer supported. DO not use option 4 or 5. |
! initial fields contain discontinuities. |
| 200 |
C for non-positive definite scalars (such as Ertel Potential Vorticity). |
! This does not necessarily imply the integration is unstable. |
| 201 |
C |
! These negatives are typically very small. A filling algorithm is |
| 202 |
C The implicit numerical diffusion decreases as _ORD increases. |
! activated if the user set "fill" to be true. |
| 203 |
C The last two options (ORDER=5, 6) should only be used when there is |
|
| 204 |
C significant explicit diffusion (such as a turbulence parameterization). You |
! The van Leer scheme used here is nearly as accurate as the original PPM |
| 205 |
C might get dispersive results otherwise. |
! due to the use of a 4th order accurate reference slope. The PPM imple- |
| 206 |
C No filter of any kind is applied to the constituent fields here. |
! mented here is an improvement over the original and is also based on |
| 207 |
C |
! the 4th order reference slope. |
| 208 |
C AE: Radius of the sphere (meters). |
|
| 209 |
C Recommended value for the planet earth: 6.371E6 |
! ****6***0*********0*********0*********0*********0*********0**********72 |
| 210 |
C |
|
| 211 |
C fill(logical): flag to do filling for negatives (see note below). |
! User modifiable parameters |
| 212 |
C |
|
| 213 |
C Umax: Estimate (upper limit) of the maximum U-wind speed (m/s). |
PARAMETER (jmax=361, kmax=150) |
| 214 |
C (220 m/s is a good value for troposphere model; 280 m/s otherwise) |
|
| 215 |
C |
! ****6***0*********0*********0*********0*********0*********0**********72 |
| 216 |
C ============= |
|
| 217 |
C Output |
! Input-Output arrays |
| 218 |
C ============= |
|
| 219 |
C |
|
| 220 |
C Q: mixing ratios at future time (t+NDT) (original values are over-written) |
REAL q(imr, jnp, nlay, nc), ps1(imr, jnp), ps2(imr, jnp), & |
| 221 |
C W(NLAY): large-scale vertical mass flux as diagnosed from the hydrostatic |
u(imr, jnp, nlay), v(imr, jnp, nlay), ap(nlay+1), bp(nlay+1), & |
| 222 |
C relationship. W will have the same unit as PS1 and PS2 (eg, mb). |
w(imr, jnp, nlay), ndt, val(nlay), umax |
| 223 |
C W must be divided by NDT to get the correct mass-flux unit. |
INTEGER igd, iord, jord, kord, nc, imr, jnp, j1, nlay, ae |
| 224 |
C The vertical Courant number C = W/delp_UPWIND, where delp_UPWIND |
INTEGER imrd2 |
| 225 |
C is the pressure thickness in the "upwind" direction. For example, |
REAL pt |
| 226 |
C C(k) = W(k)/delp(k) if W(k) > 0; |
LOGICAL cross, fill, dum |
| 227 |
C C(k) = W(k)/delp(k+1) if W(k) < 0. |
|
| 228 |
C ( W > 0 is downward, ie, toward surface) |
! Local dynamic arrays |
| 229 |
C PS2: predicted PS at t+NDT (original values are over-written) |
|
| 230 |
C |
REAL crx(imr, jnp), cry(imr, jnp), xmass(imr, jnp), ymass(imr, jnp), & |
| 231 |
C ******************************************************************** |
fx1(imr+1), dpi(imr, jnp, nlay), delp1(imr, jnp, nlay), & |
| 232 |
C NOTES: |
wk1(imr, jnp, nlay), pu(imr, jnp), pv(imr, jnp), dc2(imr, jnp), & |
| 233 |
C This forward-in-time upstream-biased transport scheme reduces to |
delp2(imr, jnp, nlay), dq(imr, jnp, nlay, nc), va(imr, jnp), & |
| 234 |
C the 2nd order center-in-time center-in-space mass continuity eqn. |
ua(imr, jnp), qtmp(-imr:2*imr) |
| 235 |
C if Q = 1 (constant fields will remain constant). This also ensures |
|
| 236 |
C that the computed vertical velocity to be identical to GEOS-1 GCM |
! Local static arrays |
| 237 |
C for on-line transport. |
|
| 238 |
C |
REAL dtdx(jmax), dtdx5(jmax), acosp(jmax), cosp(jmax), cose(jmax), & |
| 239 |
C A larger polar cap is used if j1=3 (recommended for C-Grid winds or when |
dap(kmax), dbk(kmax) |
| 240 |
C winds are noisy near poles). |
DATA ndt0, nstep/0, 0/ |
| 241 |
C |
DATA cross/.TRUE./ |
| 242 |
C Flux-Form Semi-Lagrangian transport in the East-West direction is used |
SAVE dtdy, dtdy5, rcap, js0, jn0, iml, dtdx, dtdx5, acosp, cosp, cose, dap, & |
| 243 |
C when and where Courant number is greater than one. |
dbk |
| 244 |
C |
|
| 245 |
C The user needs to change the parameter Jmax or Kmax if the resolution |
|
| 246 |
C is greater than 0.5 deg in N-S or 150 layers in the vertical direction. |
jmr = jnp - 1 |
| 247 |
C (this TransPort Core is otherwise resolution independent and can be used |
imjm = imr*jnp |
| 248 |
C as a library routine). |
j2 = jnp - j1 + 1 |
| 249 |
C |
nstep = nstep + 1 |
| 250 |
C PPM is 4th order accurate when grid spacing is uniform (x & y); 3rd |
|
| 251 |
C order accurate for non-uniform grid (vertical sigma coord.). |
! *********** Initialization ********************** |
| 252 |
C |
IF (nstep==1) THEN |
| 253 |
C Time step is limitted only by transport in the meridional direction. |
|
| 254 |
C (the FFSL scheme is not implemented in the meridional direction). |
WRITE (6, *) '------------------------------------ ' |
| 255 |
C |
WRITE (6, *) 'NASA/GSFC Transport Core Version 4.5' |
| 256 |
C Since only 1-D limiters are applied, negative values could |
WRITE (6, *) '------------------------------------ ' |
| 257 |
C potentially be generated when large time step is used and when the |
|
| 258 |
C initial fields contain discontinuities. |
WRITE (6, *) 'IMR=', imr, ' JNP=', jnp, ' NLAY=', nlay, ' j1=', j1 |
| 259 |
C This does not necessarily imply the integration is unstable. |
WRITE (6, *) 'NC=', nc, iord, jord, kord, ndt |
| 260 |
C These negatives are typically very small. A filling algorithm is |
|
| 261 |
C activated if the user set "fill" to be true. |
! controles sur les parametres |
| 262 |
C |
IF (nlay<6) THEN |
| 263 |
C The van Leer scheme used here is nearly as accurate as the original PPM |
WRITE (6, *) 'NLAY must be >= 6' |
| 264 |
C due to the use of a 4th order accurate reference slope. The PPM imple- |
STOP |
| 265 |
C mented here is an improvement over the original and is also based on |
END IF |
| 266 |
C the 4th order reference slope. |
IF (jnp<nlay) THEN |
| 267 |
C |
WRITE (6, *) 'JNP must be >= NLAY' |
| 268 |
C ****6***0*********0*********0*********0*********0*********0**********72 |
STOP |
| 269 |
C |
END IF |
| 270 |
C User modifiable parameters |
imrd2 = mod(imr, 2) |
| 271 |
C |
IF (j1==2 .AND. imrd2/=0) THEN |
| 272 |
parameter (Jmax = 361, kmax = 150) |
WRITE (6, *) 'if j1=2 IMR must be an even integer' |
| 273 |
C |
STOP |
| 274 |
C ****6***0*********0*********0*********0*********0*********0**********72 |
END IF |
| 275 |
C |
|
| 276 |
C Input-Output arrays |
|
| 277 |
C |
IF (jmax<jnp .OR. kmax<nlay) THEN |
| 278 |
|
WRITE (6, *) 'Jmax or Kmax is too small' |
| 279 |
real Q(IMR,JNP,NLAY,NC),PS1(IMR,JNP),PS2(IMR,JNP), |
STOP |
| 280 |
& U(IMR,JNP,NLAY),V(IMR,JNP,NLAY),AP(NLAY+1), |
END IF |
| 281 |
& BP(NLAY+1),W(IMR,JNP,NLAY),NDT,val(NLAY),Umax |
|
| 282 |
integer IGD,IORD,JORD,KORD,NC,IMR,JNP,j1,NLAY,AE |
DO k = 1, nlay |
| 283 |
integer IMRD2 |
dap(k) = (ap(k+1)-ap(k))*pt |
| 284 |
real PT |
dbk(k) = bp(k+1) - bp(k) |
| 285 |
logical cross, fill, dum |
END DO |
| 286 |
C |
|
| 287 |
C Local dynamic arrays |
pi = 4.*atan(1.) |
| 288 |
C |
dl = 2.*pi/float(imr) |
| 289 |
real CRX(IMR,JNP),CRY(IMR,JNP),xmass(IMR,JNP),ymass(IMR,JNP), |
dp = pi/float(jmr) |
| 290 |
& fx1(IMR+1),DPI(IMR,JNP,NLAY),delp1(IMR,JNP,NLAY), |
|
| 291 |
& WK1(IMR,JNP,NLAY),PU(IMR,JNP),PV(IMR,JNP),DC2(IMR,JNP), |
IF (igd==0) THEN |
| 292 |
& delp2(IMR,JNP,NLAY),DQ(IMR,JNP,NLAY,NC),VA(IMR,JNP), |
! Compute analytic cosine at cell edges |
| 293 |
& UA(IMR,JNP),qtmp(-IMR:2*IMR) |
CALL cosa(cosp, cose, jnp, pi, dp) |
| 294 |
C |
ELSE |
| 295 |
C Local static arrays |
! Define cosine consistent with GEOS-GCM (using dycore2.0 or later) |
| 296 |
C |
CALL cosc(cosp, cose, jnp, pi, dp) |
| 297 |
real DTDX(Jmax), DTDX5(Jmax), acosp(Jmax), |
END IF |
| 298 |
& cosp(Jmax), cose(Jmax), DAP(kmax),DBK(Kmax) |
|
| 299 |
data NDT0, NSTEP /0, 0/ |
DO j = 2, jmr |
| 300 |
data cross /.true./ |
acosp(j) = 1./cosp(j) |
| 301 |
SAVE DTDY, DTDY5, RCAP, JS0, JN0, IML, |
END DO |
| 302 |
& DTDX, DTDX5, ACOSP, COSP, COSE, DAP,DBK |
|
| 303 |
C |
! Inverse of the Scaled polar cap area. |
| 304 |
|
|
| 305 |
JMR = JNP -1 |
rcap = dp/(imr*(1.-cos((j1-1.5)*dp))) |
| 306 |
IMJM = IMR*JNP |
acosp(1) = rcap |
| 307 |
j2 = JNP - j1 + 1 |
acosp(jnp) = rcap |
| 308 |
NSTEP = NSTEP + 1 |
END IF |
| 309 |
C |
|
| 310 |
C *********** Initialization ********************** |
IF (ndt0/=ndt) THEN |
| 311 |
if(NSTEP.eq.1) then |
dt = ndt |
| 312 |
c |
ndt0 = ndt |
| 313 |
write(6,*) '------------------------------------ ' |
|
| 314 |
write(6,*) 'NASA/GSFC Transport Core Version 4.5' |
IF (umax<180.) THEN |
| 315 |
write(6,*) '------------------------------------ ' |
WRITE (6, *) 'Umax may be too small!' |
| 316 |
c |
END IF |
| 317 |
WRITE(6,*) 'IMR=',IMR,' JNP=',JNP,' NLAY=',NLAY,' j1=',j1 |
cr1 = abs(umax*dt)/(dl*ae) |
| 318 |
WRITE(6,*) 'NC=',NC,IORD,JORD,KORD,NDT |
maxdt = dp*ae/abs(umax) + 0.5 |
| 319 |
C |
WRITE (6, *) 'Largest time step for max(V)=', umax, ' is ', maxdt |
| 320 |
C controles sur les parametres |
IF (maxdt<abs(ndt)) THEN |
| 321 |
if(NLAY.LT.6) then |
WRITE (6, *) 'Warning!!! NDT maybe too large!' |
| 322 |
write(6,*) 'NLAY must be >= 6' |
END IF |
| 323 |
stop |
|
| 324 |
endif |
IF (cr1>=0.95) THEN |
| 325 |
if (JNP.LT.NLAY) then |
js0 = 0 |
| 326 |
write(6,*) 'JNP must be >= NLAY' |
jn0 = 0 |
| 327 |
stop |
iml = imr - 2 |
| 328 |
endif |
ztc = 0. |
| 329 |
IMRD2=mod(IMR,2) |
ELSE |
| 330 |
if (j1.eq.2.and.IMRD2.NE.0) then |
ztc = acos(cr1)*(180./pi) |
| 331 |
write(6,*) 'if j1=2 IMR must be an even integer' |
|
| 332 |
stop |
js0 = float(jmr)*(90.-ztc)/180. + 2 |
| 333 |
endif |
js0 = max(js0, j1+1) |
| 334 |
|
iml = min(6*js0/(j1-1)+2, 4*imr/5) |
| 335 |
C |
jn0 = jnp - js0 + 1 |
| 336 |
if(Jmax.lt.JNP .or. Kmax.lt.NLAY) then |
END IF |
| 337 |
write(6,*) 'Jmax or Kmax is too small' |
|
| 338 |
stop |
|
| 339 |
endif |
DO j = 2, jmr |
| 340 |
C |
dtdx(j) = dt/(dl*ae*cosp(j)) |
| 341 |
DO k=1,NLAY |
|
| 342 |
DAP(k) = (AP(k+1) - AP(k))*PT |
dtdx5(j) = 0.5*dtdx(j) |
| 343 |
DBK(k) = BP(k+1) - BP(k) |
END DO |
| 344 |
ENDDO |
|
| 345 |
C |
|
| 346 |
PI = 4. * ATAN(1.) |
dtdy = dt/(ae*dp) |
| 347 |
DL = 2.*PI / float(IMR) |
dtdy5 = 0.5*dtdy |
| 348 |
DP = PI / float(JMR) |
|
| 349 |
C |
END IF |
| 350 |
if(IGD.eq.0) then |
|
| 351 |
C Compute analytic cosine at cell edges |
! *********** End Initialization ********************** |
| 352 |
call cosa(cosp,cose,JNP,PI,DP) |
|
| 353 |
else |
! delp = pressure thickness: the psudo-density in a hydrostatic system. |
| 354 |
C Define cosine consistent with GEOS-GCM (using dycore2.0 or later) |
DO k = 1, nlay |
| 355 |
call cosc(cosp,cose,JNP,PI,DP) |
DO j = 1, jnp |
| 356 |
endif |
DO i = 1, imr |
| 357 |
C |
delp1(i, j, k) = dap(k) + dbk(k)*ps1(i, j) |
| 358 |
do 15 J=2,JMR |
delp2(i, j, k) = dap(k) + dbk(k)*ps2(i, j) |
| 359 |
15 acosp(j) = 1. / cosp(j) |
END DO |
| 360 |
C |
END DO |
| 361 |
C Inverse of the Scaled polar cap area. |
END DO |
| 362 |
C |
|
| 363 |
RCAP = DP / (IMR*(1.-COS((j1-1.5)*DP))) |
|
| 364 |
acosp(1) = RCAP |
IF (j1/=2) THEN |
| 365 |
acosp(JNP) = RCAP |
DO ic = 1, nc |
| 366 |
endif |
DO l = 1, nlay |
| 367 |
C |
DO i = 1, imr |
| 368 |
if(NDT0 .ne. NDT) then |
q(i, 2, l, ic) = q(i, 1, l, ic) |
| 369 |
DT = NDT |
q(i, jmr, l, ic) = q(i, jnp, l, ic) |
| 370 |
NDT0 = NDT |
END DO |
| 371 |
|
END DO |
| 372 |
if(Umax .lt. 180.) then |
END DO |
| 373 |
write(6,*) 'Umax may be too small!' |
END IF |
| 374 |
endif |
|
| 375 |
CR1 = abs(Umax*DT)/(DL*AE) |
! Compute "tracer density" |
| 376 |
MaxDT = DP*AE / abs(Umax) + 0.5 |
DO ic = 1, nc |
| 377 |
write(6,*)'Largest time step for max(V)=',Umax,' is ',MaxDT |
DO k = 1, nlay |
| 378 |
if(MaxDT .lt. abs(NDT)) then |
DO j = 1, jnp |
| 379 |
write(6,*) 'Warning!!! NDT maybe too large!' |
DO i = 1, imr |
| 380 |
endif |
dq(i, j, k, ic) = q(i, j, k, ic)*delp1(i, j, k) |
| 381 |
C |
END DO |
| 382 |
if(CR1.ge.0.95) then |
END DO |
| 383 |
JS0 = 0 |
END DO |
| 384 |
JN0 = 0 |
END DO |
| 385 |
IML = IMR-2 |
|
| 386 |
ZTC = 0. |
DO k = 1, nlay |
| 387 |
else |
|
| 388 |
ZTC = acos(CR1) * (180./PI) |
IF (igd==0) THEN |
| 389 |
C |
! Convert winds on A-Grid to Courant number on C-Grid. |
| 390 |
JS0 = float(JMR)*(90.-ZTC)/180. + 2 |
CALL a2c(u(1,1,k), v(1,1,k), imr, jmr, j1, j2, crx, cry, dtdx5, dtdy5) |
| 391 |
JS0 = max(JS0, J1+1) |
ELSE |
| 392 |
IML = min(6*JS0/(J1-1)+2, 4*IMR/5) |
! Convert winds on C-grid to Courant number |
| 393 |
JN0 = JNP-JS0+1 |
DO j = j1, j2 |
| 394 |
endif |
DO i = 2, imr |
| 395 |
C |
crx(i, j) = dtdx(j)*u(i-1, j, k) |
| 396 |
C |
END DO |
| 397 |
do J=2,JMR |
END DO |
| 398 |
DTDX(j) = DT / ( DL*AE*COSP(J) ) |
|
| 399 |
|
|
| 400 |
DTDX5(j) = 0.5*DTDX(j) |
DO j = j1, j2 |
| 401 |
enddo |
crx(1, j) = dtdx(j)*u(imr, j, k) |
| 402 |
C |
END DO |
| 403 |
|
|
| 404 |
DTDY = DT /(AE*DP) |
DO i = 1, imr*jmr |
| 405 |
DTDY5 = 0.5*DTDY |
cry(i, 2) = dtdy*v(i, 1, k) |
| 406 |
C |
END DO |
| 407 |
endif |
END IF |
| 408 |
C |
|
| 409 |
C *********** End Initialization ********************** |
! Determine JS and JN |
| 410 |
C |
js = j1 |
| 411 |
C delp = pressure thickness: the psudo-density in a hydrostatic system. |
jn = j2 |
| 412 |
do k=1,NLAY |
|
| 413 |
do j=1,JNP |
DO j = js0, j1 + 1, -1 |
| 414 |
do i=1,IMR |
DO i = 1, imr |
| 415 |
delp1(i,j,k)=DAP(k)+DBK(k)*PS1(i,j) |
IF (abs(crx(i,j))>1.) THEN |
| 416 |
delp2(i,j,k)=DAP(k)+DBK(k)*PS2(i,j) |
js = j |
| 417 |
enddo |
GO TO 2222 |
| 418 |
enddo |
END IF |
| 419 |
enddo |
END DO |
| 420 |
|
END DO |
| 421 |
C |
|
| 422 |
if(j1.ne.2) then |
2222 CONTINUE |
| 423 |
DO 40 IC=1,NC |
DO j = jn0, j2 - 1 |
| 424 |
DO 40 L=1,NLAY |
DO i = 1, imr |
| 425 |
DO 40 I=1,IMR |
IF (abs(crx(i,j))>1.) THEN |
| 426 |
Q(I, 2,L,IC) = Q(I, 1,L,IC) |
jn = j |
| 427 |
40 Q(I,JMR,L,IC) = Q(I,JNP,L,IC) |
GO TO 2233 |
| 428 |
endif |
END IF |
| 429 |
C |
END DO |
| 430 |
C Compute "tracer density" |
END DO |
| 431 |
DO 550 IC=1,NC |
2233 CONTINUE |
| 432 |
DO 44 k=1,NLAY |
|
| 433 |
DO 44 j=1,JNP |
IF (j1/=2) THEN ! Enlarged polar cap. |
| 434 |
DO 44 i=1,IMR |
DO i = 1, imr |
| 435 |
44 DQ(i,j,k,IC) = Q(i,j,k,IC)*delp1(i,j,k) |
dpi(i, 2, k) = 0. |
| 436 |
550 continue |
dpi(i, jmr, k) = 0. |
| 437 |
C |
END DO |
| 438 |
do 1500 k=1,NLAY |
END IF |
| 439 |
C |
|
| 440 |
if(IGD.eq.0) then |
! ******* Compute horizontal mass fluxes ************ |
| 441 |
C Convert winds on A-Grid to Courant number on C-Grid. |
|
| 442 |
call A2C(U(1,1,k),V(1,1,k),IMR,JMR,j1,j2,CRX,CRY,dtdx5,DTDY5) |
! N-S component |
| 443 |
else |
DO j = j1, j2 + 1 |
| 444 |
C Convert winds on C-grid to Courant number |
d5 = 0.5*cose(j) |
| 445 |
do 45 j=j1,j2 |
DO i = 1, imr |
| 446 |
do 45 i=2,IMR |
ymass(i, j) = cry(i, j)*d5*(delp2(i,j,k)+delp2(i,j-1,k)) |
| 447 |
45 CRX(i,J) = dtdx(j)*U(i-1,j,k) |
END DO |
| 448 |
|
END DO |
| 449 |
C |
|
| 450 |
do 50 j=j1,j2 |
DO j = j1, j2 |
| 451 |
50 CRX(1,J) = dtdx(j)*U(IMR,j,k) |
DO i = 1, imr |
| 452 |
C |
dpi(i, j, k) = (ymass(i,j)-ymass(i,j+1))*acosp(j) |
| 453 |
do 55 i=1,IMR*JMR |
END DO |
| 454 |
55 CRY(i,2) = DTDY*V(i,1,k) |
END DO |
| 455 |
endif |
|
| 456 |
C |
! Poles |
| 457 |
C Determine JS and JN |
sum1 = ymass(imr, j1) |
| 458 |
JS = j1 |
sum2 = ymass(imr, j2+1) |
| 459 |
JN = j2 |
DO i = 1, imr - 1 |
| 460 |
C |
sum1 = sum1 + ymass(i, j1) |
| 461 |
do j=JS0,j1+1,-1 |
sum2 = sum2 + ymass(i, j2+1) |
| 462 |
do i=1,IMR |
END DO |
| 463 |
if(abs(CRX(i,j)).GT.1.) then |
|
| 464 |
JS = j |
sum1 = -sum1*rcap |
| 465 |
go to 2222 |
sum2 = sum2*rcap |
| 466 |
endif |
DO i = 1, imr |
| 467 |
enddo |
dpi(i, 1, k) = sum1 |
| 468 |
enddo |
dpi(i, jnp, k) = sum2 |
| 469 |
C |
END DO |
| 470 |
2222 continue |
|
| 471 |
do j=JN0,j2-1 |
! E-W component |
| 472 |
do i=1,IMR |
|
| 473 |
if(abs(CRX(i,j)).GT.1.) then |
DO j = j1, j2 |
| 474 |
JN = j |
DO i = 2, imr |
| 475 |
go to 2233 |
pu(i, j) = 0.5*(delp2(i,j,k)+delp2(i-1,j,k)) |
| 476 |
endif |
END DO |
| 477 |
enddo |
END DO |
| 478 |
enddo |
|
| 479 |
2233 continue |
DO j = j1, j2 |
| 480 |
C |
pu(1, j) = 0.5*(delp2(1,j,k)+delp2(imr,j,k)) |
| 481 |
if(j1.ne.2) then ! Enlarged polar cap. |
END DO |
| 482 |
do i=1,IMR |
|
| 483 |
DPI(i, 2,k) = 0. |
DO j = j1, j2 |
| 484 |
DPI(i,JMR,k) = 0. |
DO i = 1, imr |
| 485 |
enddo |
xmass(i, j) = pu(i, j)*crx(i, j) |
| 486 |
endif |
END DO |
| 487 |
C |
END DO |
| 488 |
C ******* Compute horizontal mass fluxes ************ |
|
| 489 |
C |
DO j = j1, j2 |
| 490 |
C N-S component |
DO i = 1, imr - 1 |
| 491 |
do j=j1,j2+1 |
dpi(i, j, k) = dpi(i, j, k) + xmass(i, j) - xmass(i+1, j) |
| 492 |
D5 = 0.5 * COSE(j) |
END DO |
| 493 |
do i=1,IMR |
END DO |
| 494 |
ymass(i,j) = CRY(i,j)*D5*(delp2(i,j,k) + delp2(i,j-1,k)) |
|
| 495 |
enddo |
DO j = j1, j2 |
| 496 |
enddo |
dpi(imr, j, k) = dpi(imr, j, k) + xmass(imr, j) - xmass(1, j) |
| 497 |
C |
END DO |
| 498 |
do 95 j=j1,j2 |
|
| 499 |
DO 95 i=1,IMR |
DO j = j1, j2 |
| 500 |
95 DPI(i,j,k) = (ymass(i,j) - ymass(i,j+1)) * acosp(j) |
DO i = 1, imr - 1 |
| 501 |
C |
ua(i, j) = 0.5*(crx(i,j)+crx(i+1,j)) |
| 502 |
C Poles |
END DO |
| 503 |
sum1 = ymass(IMR,j1 ) |
END DO |
| 504 |
sum2 = ymass(IMR,J2+1) |
|
| 505 |
do i=1,IMR-1 |
DO j = j1, j2 |
| 506 |
sum1 = sum1 + ymass(i,j1 ) |
ua(imr, j) = 0.5*(crx(imr,j)+crx(1,j)) |
| 507 |
sum2 = sum2 + ymass(i,J2+1) |
END DO |
| 508 |
enddo |
! cccccccccccccccccccccccccccccccccccccccccccccccccccccc |
| 509 |
C |
! Rajouts pour LMDZ.3.3 |
| 510 |
sum1 = - sum1 * RCAP |
! cccccccccccccccccccccccccccccccccccccccccccccccccccccc |
| 511 |
sum2 = sum2 * RCAP |
DO i = 1, imr |
| 512 |
do i=1,IMR |
DO j = 1, jnp |
| 513 |
DPI(i, 1,k) = sum1 |
va(i, j) = 0. |
| 514 |
DPI(i,JNP,k) = sum2 |
END DO |
| 515 |
enddo |
END DO |
| 516 |
C |
|
| 517 |
C E-W component |
DO i = 1, imr*(jmr-1) |
| 518 |
C |
va(i, 2) = 0.5*(cry(i,2)+cry(i,3)) |
| 519 |
do j=j1,j2 |
END DO |
| 520 |
do i=2,IMR |
|
| 521 |
PU(i,j) = 0.5 * (delp2(i,j,k) + delp2(i-1,j,k)) |
IF (j1==2) THEN |
| 522 |
enddo |
imh = imr/2 |
| 523 |
enddo |
DO i = 1, imh |
| 524 |
C |
va(i, 1) = 0.5*(cry(i,2)-cry(i+imh,2)) |
| 525 |
do j=j1,j2 |
va(i+imh, 1) = -va(i, 1) |
| 526 |
PU(1,j) = 0.5 * (delp2(1,j,k) + delp2(IMR,j,k)) |
va(i, jnp) = 0.5*(cry(i,jnp)-cry(i+imh,jmr)) |
| 527 |
enddo |
va(i+imh, jnp) = -va(i, jnp) |
| 528 |
C |
END DO |
| 529 |
do 110 j=j1,j2 |
va(imr, 1) = va(1, 1) |
| 530 |
DO 110 i=1,IMR |
va(imr, jnp) = va(1, jnp) |
| 531 |
110 xmass(i,j) = PU(i,j)*CRX(i,j) |
END IF |
| 532 |
C |
|
| 533 |
DO 120 j=j1,j2 |
! ****6***0*********0*********0*********0*********0*********0**********72 |
| 534 |
DO 120 i=1,IMR-1 |
DO ic = 1, nc |
| 535 |
120 DPI(i,j,k) = DPI(i,j,k) + xmass(i,j) - xmass(i+1,j) |
|
| 536 |
C |
DO i = 1, imjm |
| 537 |
DO 130 j=j1,j2 |
wk1(i, 1, 1) = 0. |
| 538 |
130 DPI(IMR,j,k) = DPI(IMR,j,k) + xmass(IMR,j) - xmass(1,j) |
wk1(i, 1, 2) = 0. |
| 539 |
C |
END DO |
| 540 |
DO j=j1,j2 |
|
| 541 |
do i=1,IMR-1 |
! E-W advective cross term |
| 542 |
UA(i,j) = 0.5 * (CRX(i,j)+CRX(i+1,j)) |
DO j = j1, j2 |
| 543 |
enddo |
IF (j>js .AND. j<jn) GO TO 250 |
| 544 |
enddo |
|
| 545 |
C |
DO i = 1, imr |
| 546 |
DO j=j1,j2 |
qtmp(i) = q(i, j, k, ic) |
| 547 |
UA(imr,j) = 0.5 * (CRX(imr,j)+CRX(1,j)) |
END DO |
| 548 |
enddo |
|
| 549 |
ccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
DO i = -iml, 0 |
| 550 |
c Rajouts pour LMDZ.3.3 |
qtmp(i) = q(imr+i, j, k, ic) |
| 551 |
ccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
qtmp(imr+1-i) = q(1-i, j, k, ic) |
| 552 |
do i=1,IMR |
END DO |
| 553 |
do j=1,JNP |
|
| 554 |
VA(i,j)=0. |
DO i = 1, imr |
| 555 |
enddo |
iu = ua(i, j) |
| 556 |
enddo |
ru = ua(i, j) - iu |
| 557 |
|
iiu = i - iu |
| 558 |
do i=1,imr*(JMR-1) |
IF (ua(i,j)>=0.) THEN |
| 559 |
VA(i,2) = 0.5*(CRY(i,2)+CRY(i,3)) |
wk1(i, j, 1) = qtmp(iiu) + ru*(qtmp(iiu-1)-qtmp(iiu)) |
| 560 |
enddo |
ELSE |
| 561 |
C |
wk1(i, j, 1) = qtmp(iiu) + ru*(qtmp(iiu)-qtmp(iiu+1)) |
| 562 |
if(j1.eq.2) then |
END IF |
| 563 |
IMH = IMR/2 |
wk1(i, j, 1) = wk1(i, j, 1) - qtmp(i) |
| 564 |
do i=1,IMH |
END DO |
| 565 |
VA(i, 1) = 0.5*(CRY(i,2)-CRY(i+IMH,2)) |
250 END DO |
| 566 |
VA(i+IMH, 1) = -VA(i,1) |
|
| 567 |
VA(i, JNP) = 0.5*(CRY(i,JNP)-CRY(i+IMH,JMR)) |
IF (jn/=0) THEN |
| 568 |
VA(i+IMH,JNP) = -VA(i,JNP) |
DO j = js + 1, jn - 1 |
| 569 |
enddo |
|
| 570 |
VA(IMR,1)=VA(1,1) |
DO i = 1, imr |
| 571 |
VA(IMR,JNP)=VA(1,JNP) |
qtmp(i) = q(i, j, k, ic) |
| 572 |
endif |
END DO |
| 573 |
C |
|
| 574 |
C ****6***0*********0*********0*********0*********0*********0**********72 |
qtmp(0) = q(imr, j, k, ic) |
| 575 |
do 1000 IC=1,NC |
qtmp(imr+1) = q(1, j, k, ic) |
| 576 |
C |
|
| 577 |
do i=1,IMJM |
DO i = 1, imr |
| 578 |
wk1(i,1,1) = 0. |
iu = i - ua(i, j) |
| 579 |
wk1(i,1,2) = 0. |
wk1(i, j, 1) = ua(i, j)*(qtmp(iu)-qtmp(iu+1)) |
| 580 |
enddo |
END DO |
| 581 |
C |
END DO |
| 582 |
C E-W advective cross term |
END IF |
| 583 |
do 250 j=J1,J2 |
! ****6***0*********0*********0*********0*********0*********0**********72 |
| 584 |
if(J.GT.JS .and. J.LT.JN) GO TO 250 |
! Contribution from the N-S advection |
| 585 |
C |
DO i = 1, imr*(j2-j1+1) |
| 586 |
do i=1,IMR |
jt = float(j1) - va(i, j1) |
| 587 |
qtmp(i) = q(i,j,k,IC) |
wk1(i, j1, 2) = va(i, j1)*(q(i,jt,k,ic)-q(i,jt+1,k,ic)) |
| 588 |
enddo |
END DO |
| 589 |
C |
|
| 590 |
do i=-IML,0 |
DO i = 1, imjm |
| 591 |
qtmp(i) = q(IMR+i,j,k,IC) |
wk1(i, 1, 1) = q(i, 1, k, ic) + 0.5*wk1(i, 1, 1) |
| 592 |
qtmp(IMR+1-i) = q(1-i,j,k,IC) |
wk1(i, 1, 2) = q(i, 1, k, ic) + 0.5*wk1(i, 1, 2) |
| 593 |
enddo |
END DO |
| 594 |
C |
|
| 595 |
DO 230 i=1,IMR |
IF (cross) THEN |
| 596 |
iu = UA(i,j) |
! Add cross terms in the vertical direction. |
| 597 |
ru = UA(i,j) - iu |
IF (iord>=2) THEN |
| 598 |
iiu = i-iu |
iad = 2 |
| 599 |
if(UA(i,j).GE.0.) then |
ELSE |
| 600 |
wk1(i,j,1) = qtmp(iiu)+ru*(qtmp(iiu-1)-qtmp(iiu)) |
iad = 1 |
| 601 |
else |
END IF |
| 602 |
wk1(i,j,1) = qtmp(iiu)+ru*(qtmp(iiu)-qtmp(iiu+1)) |
|
| 603 |
endif |
IF (jord>=2) THEN |
| 604 |
wk1(i,j,1) = wk1(i,j,1) - qtmp(i) |
jad = 2 |
| 605 |
230 continue |
ELSE |
| 606 |
250 continue |
jad = 1 |
| 607 |
C |
END IF |
| 608 |
if(JN.ne.0) then |
CALL xadv(imr, jnp, j1, j2, wk1(1,1,2), ua, js, jn, iml, dc2, iad) |
| 609 |
do j=JS+1,JN-1 |
CALL yadv(imr, jnp, j1, j2, wk1(1,1,1), va, pv, w, jad) |
| 610 |
C |
DO j = 1, jnp |
| 611 |
do i=1,IMR |
DO i = 1, imr |
| 612 |
qtmp(i) = q(i,j,k,IC) |
q(i, j, k, ic) = q(i, j, k, ic) + dc2(i, j) + pv(i, j) |
| 613 |
enddo |
END DO |
| 614 |
C |
END DO |
| 615 |
qtmp(0) = q(IMR,J,k,IC) |
END IF |
| 616 |
qtmp(IMR+1) = q( 1,J,k,IC) |
|
| 617 |
C |
CALL xtp(imr, jnp, iml, j1, j2, jn, js, pu, dq(1,1,k,ic), wk1(1,1,2), & |
| 618 |
do i=1,imr |
crx, fx1, xmass, iord) |
| 619 |
iu = i - UA(i,j) |
|
| 620 |
wk1(i,j,1) = UA(i,j)*(qtmp(iu) - qtmp(iu+1)) |
CALL ytp(imr, jnp, j1, j2, acosp, rcap, dq(1,1,k,ic), wk1(1,1,1), cry, & |
| 621 |
enddo |
dc2, ymass, wk1(1,1,3), wk1(1,1,4), wk1(1,1,5), wk1(1,1,6), jord) |
| 622 |
enddo |
|
| 623 |
endif |
END DO |
| 624 |
C ****6***0*********0*********0*********0*********0*********0**********72 |
END DO |
| 625 |
C Contribution from the N-S advection |
|
| 626 |
do i=1,imr*(j2-j1+1) |
! ******* Compute vertical mass flux (same unit as PS) *********** |
| 627 |
JT = float(J1) - VA(i,j1) |
|
| 628 |
wk1(i,j1,2) = VA(i,j1) * (q(i,jt,k,IC) - q(i,jt+1,k,IC)) |
! 1st step: compute total column mass CONVERGENCE. |
| 629 |
enddo |
|
| 630 |
C |
DO j = 1, jnp |
| 631 |
do i=1,IMJM |
DO i = 1, imr |
| 632 |
wk1(i,1,1) = q(i,1,k,IC) + 0.5*wk1(i,1,1) |
cry(i, j) = dpi(i, j, 1) |
| 633 |
wk1(i,1,2) = q(i,1,k,IC) + 0.5*wk1(i,1,2) |
END DO |
| 634 |
enddo |
END DO |
| 635 |
C |
|
| 636 |
if(cross) then |
DO k = 2, nlay |
| 637 |
C Add cross terms in the vertical direction. |
DO j = 1, jnp |
| 638 |
if(IORD .GE. 2) then |
DO i = 1, imr |
| 639 |
iad = 2 |
cry(i, j) = cry(i, j) + dpi(i, j, k) |
| 640 |
else |
END DO |
| 641 |
iad = 1 |
END DO |
| 642 |
endif |
END DO |
| 643 |
C |
|
| 644 |
if(JORD .GE. 2) then |
DO j = 1, jnp |
| 645 |
jad = 2 |
DO i = 1, imr |
| 646 |
else |
|
| 647 |
jad = 1 |
! 2nd step: compute PS2 (PS at n+1) using the hydrostatic assumption. |
| 648 |
endif |
! Changes (increases) to surface pressure = total column mass |
| 649 |
call xadv(IMR,JNP,j1,j2,wk1(1,1,2),UA,JS,JN,IML,DC2,iad) |
! convergence |
| 650 |
call yadv(IMR,JNP,j1,j2,wk1(1,1,1),VA,PV,W,jad) |
|
| 651 |
do j=1,JNP |
ps2(i, j) = ps1(i, j) + cry(i, j) |
| 652 |
do i=1,IMR |
|
| 653 |
q(i,j,k,IC) = q(i,j,k,IC) + DC2(i,j) + PV(i,j) |
! 3rd step: compute vertical mass flux from mass conservation |
| 654 |
enddo |
! principle. |
| 655 |
enddo |
|
| 656 |
endif |
w(i, j, 1) = dpi(i, j, 1) - dbk(1)*cry(i, j) |
| 657 |
C |
w(i, j, nlay) = 0. |
| 658 |
call xtp(IMR,JNP,IML,j1,j2,JN,JS,PU,DQ(1,1,k,IC),wk1(1,1,2) |
END DO |
| 659 |
& ,CRX,fx1,xmass,IORD) |
END DO |
| 660 |
|
|
| 661 |
call ytp(IMR,JNP,j1,j2,acosp,RCAP,DQ(1,1,k,IC),wk1(1,1,1),CRY, |
DO k = 2, nlay - 1 |
| 662 |
& DC2,ymass,WK1(1,1,3),wk1(1,1,4),WK1(1,1,5),WK1(1,1,6),JORD) |
DO j = 1, jnp |
| 663 |
C |
DO i = 1, imr |
| 664 |
1000 continue |
w(i, j, k) = w(i, j, k-1) + dpi(i, j, k) - dbk(k)*cry(i, j) |
| 665 |
1500 continue |
END DO |
| 666 |
C |
END DO |
| 667 |
C ******* Compute vertical mass flux (same unit as PS) *********** |
END DO |
| 668 |
C |
|
| 669 |
C 1st step: compute total column mass CONVERGENCE. |
DO k = 1, nlay |
| 670 |
C |
DO j = 1, jnp |
| 671 |
do 320 j=1,JNP |
DO i = 1, imr |
| 672 |
do 320 i=1,IMR |
delp2(i, j, k) = dap(k) + dbk(k)*ps2(i, j) |
| 673 |
320 CRY(i,j) = DPI(i,j,1) |
END DO |
| 674 |
C |
END DO |
| 675 |
do 330 k=2,NLAY |
END DO |
| 676 |
do 330 j=1,JNP |
|
| 677 |
do 330 i=1,IMR |
krd = max(3, kord) |
| 678 |
CRY(i,j) = CRY(i,j) + DPI(i,j,k) |
DO ic = 1, nc |
| 679 |
330 continue |
|
| 680 |
C |
! ****6***0*********0*********0*********0*********0*********0**********72 |
| 681 |
do 360 j=1,JNP |
|
| 682 |
do 360 i=1,IMR |
CALL fzppm(imr, jnp, nlay, j1, dq(1,1,1,ic), w, q(1,1,1,ic), wk1, dpi, & |
| 683 |
C |
dc2, crx, cry, pu, pv, xmass, ymass, delp1, krd) |
| 684 |
C 2nd step: compute PS2 (PS at n+1) using the hydrostatic assumption. |
|
| 685 |
C Changes (increases) to surface pressure = total column mass convergence |
|
| 686 |
C |
IF (fill) CALL qckxyz(dq(1,1,1,ic), dc2, imr, jnp, nlay, j1, j2, cosp, & |
| 687 |
PS2(i,j) = PS1(i,j) + CRY(i,j) |
acosp, .FALSE., ic, nstep) |
| 688 |
C |
|
| 689 |
C 3rd step: compute vertical mass flux from mass conservation principle. |
! Recover tracer mixing ratio from "density" using predicted |
| 690 |
C |
! "air density" (pressure thickness) at time-level n+1 |
| 691 |
W(i,j,1) = DPI(i,j,1) - DBK(1)*CRY(i,j) |
|
| 692 |
W(i,j,NLAY) = 0. |
DO k = 1, nlay |
| 693 |
360 continue |
DO j = 1, jnp |
| 694 |
C |
DO i = 1, imr |
| 695 |
do 370 k=2,NLAY-1 |
q(i, j, k, ic) = dq(i, j, k, ic)/delp2(i, j, k) |
| 696 |
do 370 j=1,JNP |
END DO |
| 697 |
do 370 i=1,IMR |
END DO |
| 698 |
W(i,j,k) = W(i,j,k-1) + DPI(i,j,k) - DBK(k)*CRY(i,j) |
END DO |
| 699 |
370 continue |
|
| 700 |
C |
IF (j1/=2) THEN |
| 701 |
DO 380 k=1,NLAY |
DO k = 1, nlay |
| 702 |
DO 380 j=1,JNP |
DO i = 1, imr |
| 703 |
DO 380 i=1,IMR |
! j=1 c'est le pôle Sud, j=JNP c'est le pôle Nord |
| 704 |
delp2(i,j,k) = DAP(k) + DBK(k)*PS2(i,j) |
q(i, 2, k, ic) = q(i, 1, k, ic) |
| 705 |
380 continue |
q(i, jmr, k, ic) = q(i, jmp, k, ic) |
| 706 |
C |
END DO |
| 707 |
KRD = max(3, KORD) |
END DO |
| 708 |
do 4000 IC=1,NC |
END IF |
| 709 |
C |
END DO |
| 710 |
C****6***0*********0*********0*********0*********0*********0**********72 |
|
| 711 |
|
IF (j1/=2) THEN |
| 712 |
call FZPPM(IMR,JNP,NLAY,j1,DQ(1,1,1,IC),W,Q(1,1,1,IC),WK1,DPI, |
DO k = 1, nlay |
| 713 |
& DC2,CRX,CRY,PU,PV,xmass,ymass,delp1,KRD) |
DO i = 1, imr |
| 714 |
C |
w(i, 2, k) = w(i, 1, k) |
| 715 |
|
w(i, jmr, k) = w(i, jnp, k) |
| 716 |
if(fill) call qckxyz(DQ(1,1,1,IC),DC2,IMR,JNP,NLAY,j1,j2, |
END DO |
| 717 |
& cosp,acosp,.false.,IC,NSTEP) |
END DO |
| 718 |
C |
END IF |
| 719 |
C Recover tracer mixing ratio from "density" using predicted |
|
| 720 |
C "air density" (pressure thickness) at time-level n+1 |
RETURN |
| 721 |
C |
END SUBROUTINE ppm3d |
| 722 |
DO k=1,NLAY |
|
| 723 |
DO j=1,JNP |
! ****6***0*********0*********0*********0*********0*********0**********72 |
|
DO i=1,IMR |
|
|
Q(i,j,k,IC) = DQ(i,j,k,IC) / delp2(i,j,k) |
|
|
enddo |
|
|
enddo |
|
|
enddo |
|
|
C |
|
|
if(j1.ne.2) then |
|
|
DO 400 k=1,NLAY |
|
|
DO 400 I=1,IMR |
|
|
c j=1 c'est le pôle Sud, j=JNP c'est le pôle Nord |
|
|
Q(I, 2,k,IC) = Q(I, 1,k,IC) |
|
|
Q(I,JMR,k,IC) = Q(I,JMP,k,IC) |
|
|
400 CONTINUE |
|
|
endif |
|
|
4000 continue |
|
|
C |
|
|
if(j1.ne.2) then |
|
|
DO 5000 k=1,NLAY |
|
|
DO 5000 i=1,IMR |
|
|
W(i, 2,k) = W(i, 1,k) |
|
|
W(i,JMR,k) = W(i,JNP,k) |
|
|
5000 continue |
|
|
endif |
|
|
C |
|
|
RETURN |
|
|
END |
|
|
C |
|
|
C****6***0*********0*********0*********0*********0*********0**********72 |
|
|
subroutine FZPPM(IMR,JNP,NLAY,j1,DQ,WZ,P,DC,DQDT,AR,AL,A6, |
|
|
& flux,wk1,wk2,wz2,delp,KORD) |
|
|
parameter ( kmax = 150 ) |
|
|
parameter ( R23 = 2./3., R3 = 1./3.) |
|
|
real WZ(IMR,JNP,NLAY),P(IMR,JNP,NLAY),DC(IMR,JNP,NLAY), |
|
|
& wk1(IMR,*),delp(IMR,JNP,NLAY),DQ(IMR,JNP,NLAY), |
|
|
& DQDT(IMR,JNP,NLAY) |
|
|
C Assuming JNP >= NLAY |
|
|
real AR(IMR,*),AL(IMR,*),A6(IMR,*),flux(IMR,*),wk2(IMR,*), |
|
|
& wz2(IMR,*) |
|
|
C |
|
|
JMR = JNP - 1 |
|
|
IMJM = IMR*JNP |
|
|
NLAYM1 = NLAY - 1 |
|
|
C |
|
|
LMT = KORD - 3 |
|
|
C |
|
|
C ****6***0*********0*********0*********0*********0*********0**********72 |
|
|
C Compute DC for PPM |
|
|
C ****6***0*********0*********0*********0*********0*********0**********72 |
|
|
C |
|
|
do 1000 k=1,NLAYM1 |
|
|
do 1000 i=1,IMJM |
|
|
DQDT(i,1,k) = P(i,1,k+1) - P(i,1,k) |
|
|
1000 continue |
|
|
C |
|
|
DO 1220 k=2,NLAYM1 |
|
|
DO 1220 I=1,IMJM |
|
|
c0 = delp(i,1,k) / (delp(i,1,k-1)+delp(i,1,k)+delp(i,1,k+1)) |
|
|
c1 = (delp(i,1,k-1)+0.5*delp(i,1,k))/(delp(i,1,k+1)+delp(i,1,k)) |
|
|
c2 = (delp(i,1,k+1)+0.5*delp(i,1,k))/(delp(i,1,k-1)+delp(i,1,k)) |
|
|
tmp = c0*(c1*DQDT(i,1,k) + c2*DQDT(i,1,k-1)) |
|
|
Qmax = max(P(i,1,k-1),P(i,1,k),P(i,1,k+1)) - P(i,1,k) |
|
|
Qmin = P(i,1,k) - min(P(i,1,k-1),P(i,1,k),P(i,1,k+1)) |
|
|
DC(i,1,k) = sign(min(abs(tmp),Qmax,Qmin), tmp) |
|
|
1220 CONTINUE |
|
|
|
|
|
C |
|
|
C ****6***0*********0*********0*********0*********0*********0**********72 |
|
|
C Loop over latitudes (to save memory) |
|
|
C ****6***0*********0*********0*********0*********0*********0**********72 |
|
|
C |
|
|
DO 2000 j=1,JNP |
|
|
if((j.eq.2 .or. j.eq.JMR) .and. j1.ne.2) goto 2000 |
|
|
C |
|
|
DO k=1,NLAY |
|
|
DO i=1,IMR |
|
|
wz2(i,k) = WZ(i,j,k) |
|
|
wk1(i,k) = P(i,j,k) |
|
|
wk2(i,k) = delp(i,j,k) |
|
|
flux(i,k) = DC(i,j,k) !this flux is actually the monotone slope |
|
|
enddo |
|
|
enddo |
|
|
C |
|
|
C****6***0*********0*********0*********0*********0*********0**********72 |
|
|
C Compute first guesses at cell interfaces |
|
|
C First guesses are required to be continuous. |
|
|
C ****6***0*********0*********0*********0*********0*********0**********72 |
|
|
C |
|
|
C three-cell parabolic subgrid distribution at model top |
|
|
C two-cell parabolic with zero gradient subgrid distribution |
|
|
C at the surface. |
|
|
C |
|
|
C First guess top edge value |
|
|
DO 10 i=1,IMR |
|
|
C three-cell PPM |
|
|
C Compute a,b, and c of q = aP**2 + bP + c using cell averages and delp |
|
|
a = 3.*( DQDT(i,j,2) - DQDT(i,j,1)*(wk2(i,2)+wk2(i,3))/ |
|
|
& (wk2(i,1)+wk2(i,2)) ) / |
|
|
& ( (wk2(i,2)+wk2(i,3))*(wk2(i,1)+wk2(i,2)+wk2(i,3)) ) |
|
|
b = 2.*DQDT(i,j,1)/(wk2(i,1)+wk2(i,2)) - |
|
|
& R23*a*(2.*wk2(i,1)+wk2(i,2)) |
|
|
AL(i,1) = wk1(i,1) - wk2(i,1)*(R3*a*wk2(i,1) + 0.5*b) |
|
|
AL(i,2) = wk2(i,1)*(a*wk2(i,1) + b) + AL(i,1) |
|
|
C |
|
|
C Check if change sign |
|
|
if(wk1(i,1)*AL(i,1).le.0.) then |
|
|
AL(i,1) = 0. |
|
|
flux(i,1) = 0. |
|
|
else |
|
|
flux(i,1) = wk1(i,1) - AL(i,1) |
|
|
endif |
|
|
10 continue |
|
|
C |
|
|
C Bottom |
|
|
DO 15 i=1,IMR |
|
|
C 2-cell PPM with zero gradient right at the surface |
|
|
C |
|
|
fct = DQDT(i,j,NLAYM1)*wk2(i,NLAY)**2 / |
|
|
& ( (wk2(i,NLAY)+wk2(i,NLAYM1))*(2.*wk2(i,NLAY)+wk2(i,NLAYM1))) |
|
|
AR(i,NLAY) = wk1(i,NLAY) + fct |
|
|
AL(i,NLAY) = wk1(i,NLAY) - (fct+fct) |
|
|
if(wk1(i,NLAY)*AR(i,NLAY).le.0.) AR(i,NLAY) = 0. |
|
|
flux(i,NLAY) = AR(i,NLAY) - wk1(i,NLAY) |
|
|
15 continue |
|
|
|
|
|
C |
|
|
C****6***0*********0*********0*********0*********0*********0**********72 |
|
|
C 4th order interpolation in the interior. |
|
|
C****6***0*********0*********0*********0*********0*********0**********72 |
|
|
C |
|
|
DO 14 k=3,NLAYM1 |
|
|
DO 12 i=1,IMR |
|
|
c1 = DQDT(i,j,k-1)*wk2(i,k-1) / (wk2(i,k-1)+wk2(i,k)) |
|
|
c2 = 2. / (wk2(i,k-2)+wk2(i,k-1)+wk2(i,k)+wk2(i,k+1)) |
|
|
A1 = (wk2(i,k-2)+wk2(i,k-1)) / (2.*wk2(i,k-1)+wk2(i,k)) |
|
|
A2 = (wk2(i,k )+wk2(i,k+1)) / (2.*wk2(i,k)+wk2(i,k-1)) |
|
|
AL(i,k) = wk1(i,k-1) + c1 + c2 * |
|
|
& ( wk2(i,k )*(c1*(A1 - A2)+A2*flux(i,k-1)) - |
|
|
& wk2(i,k-1)*A1*flux(i,k) ) |
|
|
12 CONTINUE |
|
|
14 continue |
|
|
C |
|
|
do 20 i=1,IMR*NLAYM1 |
|
|
AR(i,1) = AL(i,2) |
|
|
20 continue |
|
|
C |
|
|
do 30 i=1,IMR*NLAY |
|
|
A6(i,1) = 3.*(wk1(i,1)+wk1(i,1) - (AL(i,1)+AR(i,1))) |
|
|
30 continue |
|
|
C |
|
|
C****6***0*********0*********0*********0*********0*********0**********72 |
|
|
C Top & Bot always monotonic |
|
|
call lmtppm(flux(1,1),A6(1,1),AR(1,1),AL(1,1),wk1(1,1),IMR,0) |
|
|
call lmtppm(flux(1,NLAY),A6(1,NLAY),AR(1,NLAY),AL(1,NLAY), |
|
|
& wk1(1,NLAY),IMR,0) |
|
|
C |
|
|
C Interior depending on KORD |
|
|
if(LMT.LE.2) |
|
|
& call lmtppm(flux(1,2),A6(1,2),AR(1,2),AL(1,2),wk1(1,2), |
|
|
& IMR*(NLAY-2),LMT) |
|
|
C |
|
|
C****6***0*********0*********0*********0*********0*********0**********72 |
|
|
C |
|
|
DO 140 i=1,IMR*NLAYM1 |
|
|
IF(wz2(i,1).GT.0.) then |
|
|
CM = wz2(i,1) / wk2(i,1) |
|
|
flux(i,2) = AR(i,1)+0.5*CM*(AL(i,1)-AR(i,1)+A6(i,1)*(1.-R23*CM)) |
|
|
else |
|
|
CP= wz2(i,1) / wk2(i,2) |
|
|
flux(i,2) = AL(i,2)+0.5*CP*(AL(i,2)-AR(i,2)-A6(i,2)*(1.+R23*CP)) |
|
|
endif |
|
|
140 continue |
|
|
C |
|
|
DO 250 i=1,IMR*NLAYM1 |
|
|
flux(i,2) = wz2(i,1) * flux(i,2) |
|
|
250 continue |
|
|
C |
|
|
do 350 i=1,IMR |
|
|
DQ(i,j, 1) = DQ(i,j, 1) - flux(i, 2) |
|
|
DQ(i,j,NLAY) = DQ(i,j,NLAY) + flux(i,NLAY) |
|
|
350 continue |
|
|
C |
|
|
do 360 k=2,NLAYM1 |
|
|
do 360 i=1,IMR |
|
|
360 DQ(i,j,k) = DQ(i,j,k) + flux(i,k) - flux(i,k+1) |
|
|
2000 continue |
|
|
return |
|
|
end |
|
|
C |
|
|
subroutine xtp(IMR,JNP,IML,j1,j2,JN,JS,PU,DQ,Q,UC, |
|
|
& fx1,xmass,IORD) |
|
|
dimension UC(IMR,*),DC(-IML:IMR+IML+1),xmass(IMR,JNP) |
|
|
& ,fx1(IMR+1),DQ(IMR,JNP),qtmp(-IML:IMR+1+IML) |
|
|
dimension PU(IMR,JNP),Q(IMR,JNP),ISAVE(IMR) |
|
|
C |
|
|
IMP = IMR + 1 |
|
|
C |
|
|
C van Leer at high latitudes |
|
|
jvan = max(1,JNP/18) |
|
|
j1vl = j1+jvan |
|
|
j2vl = j2-jvan |
|
|
C |
|
|
do 1310 j=j1,j2 |
|
|
C |
|
|
do i=1,IMR |
|
|
qtmp(i) = q(i,j) |
|
|
enddo |
|
|
C |
|
|
if(j.ge.JN .or. j.le.JS) goto 2222 |
|
|
C ************* Eulerian ********** |
|
|
C |
|
|
qtmp(0) = q(IMR,J) |
|
|
qtmp(-1) = q(IMR-1,J) |
|
|
qtmp(IMP) = q(1,J) |
|
|
qtmp(IMP+1) = q(2,J) |
|
|
C |
|
|
IF(IORD.eq.1 .or. j.eq.j1. or. j.eq.j2) THEN |
|
|
DO 1406 i=1,IMR |
|
|
iu = float(i) - uc(i,j) |
|
|
1406 fx1(i) = qtmp(iu) |
|
|
ELSE |
|
|
call xmist(IMR,IML,Qtmp,DC) |
|
|
DC(0) = DC(IMR) |
|
|
C |
|
|
if(IORD.eq.2 .or. j.le.j1vl .or. j.ge.j2vl) then |
|
|
DO 1408 i=1,IMR |
|
|
iu = float(i) - uc(i,j) |
|
|
1408 fx1(i) = qtmp(iu) + DC(iu)*(sign(1.,uc(i,j))-uc(i,j)) |
|
|
else |
|
|
call fxppm(IMR,IML,UC(1,j),Qtmp,DC,fx1,IORD) |
|
|
endif |
|
|
C |
|
|
ENDIF |
|
|
C |
|
|
DO 1506 i=1,IMR |
|
|
1506 fx1(i) = fx1(i)*xmass(i,j) |
|
|
C |
|
|
goto 1309 |
|
|
C |
|
|
C ***** Conservative (flux-form) Semi-Lagrangian transport ***** |
|
|
C |
|
|
2222 continue |
|
|
C |
|
|
do i=-IML,0 |
|
|
qtmp(i) = q(IMR+i,j) |
|
|
qtmp(IMP-i) = q(1-i,j) |
|
|
enddo |
|
|
C |
|
|
IF(IORD.eq.1 .or. j.eq.j1. or. j.eq.j2) THEN |
|
|
DO 1306 i=1,IMR |
|
|
itmp = INT(uc(i,j)) |
|
|
ISAVE(i) = i - itmp |
|
|
iu = i - uc(i,j) |
|
|
1306 fx1(i) = (uc(i,j) - itmp)*qtmp(iu) |
|
|
ELSE |
|
|
call xmist(IMR,IML,Qtmp,DC) |
|
|
C |
|
|
do i=-IML,0 |
|
|
DC(i) = DC(IMR+i) |
|
|
DC(IMP-i) = DC(1-i) |
|
|
enddo |
|
|
C |
|
|
DO 1307 i=1,IMR |
|
|
itmp = INT(uc(i,j)) |
|
|
rut = uc(i,j) - itmp |
|
|
ISAVE(i) = i - itmp |
|
|
iu = i - uc(i,j) |
|
|
1307 fx1(i) = rut*(qtmp(iu) + DC(iu)*(sign(1.,rut) - rut)) |
|
|
ENDIF |
|
|
C |
|
|
do 1308 i=1,IMR |
|
|
IF(uc(i,j).GT.1.) then |
|
|
CDIR$ NOVECTOR |
|
|
do ist = ISAVE(i),i-1 |
|
|
fx1(i) = fx1(i) + qtmp(ist) |
|
|
enddo |
|
|
elseIF(uc(i,j).LT.-1.) then |
|
|
do ist = i,ISAVE(i)-1 |
|
|
fx1(i) = fx1(i) - qtmp(ist) |
|
|
enddo |
|
|
CDIR$ VECTOR |
|
|
endif |
|
|
1308 continue |
|
|
do i=1,IMR |
|
|
fx1(i) = PU(i,j)*fx1(i) |
|
|
enddo |
|
|
C |
|
|
C *************************************** |
|
|
C |
|
|
1309 fx1(IMP) = fx1(1) |
|
|
DO 1215 i=1,IMR |
|
|
1215 DQ(i,j) = DQ(i,j) + fx1(i)-fx1(i+1) |
|
|
C |
|
|
C *************************************** |
|
|
C |
|
|
1310 continue |
|
|
return |
|
|
end |
|
|
C |
|
|
subroutine fxppm(IMR,IML,UT,P,DC,flux,IORD) |
|
|
parameter ( R3 = 1./3., R23 = 2./3. ) |
|
|
DIMENSION UT(*),flux(*),P(-IML:IMR+IML+1),DC(-IML:IMR+IML+1) |
|
|
DIMENSION AR(0:IMR),AL(0:IMR),A6(0:IMR) |
|
|
integer LMT |
|
|
c logical first |
|
|
c data first /.true./ |
|
|
c SAVE LMT |
|
|
c if(first) then |
|
|
C |
|
|
C correction calcul de LMT a chaque passage pour pouvoir choisir |
|
|
c plusieurs schemas PPM pour differents traceurs |
|
|
c IF (IORD.LE.0) then |
|
|
c if(IMR.GE.144) then |
|
|
c LMT = 0 |
|
|
c elseif(IMR.GE.72) then |
|
|
c LMT = 1 |
|
|
c else |
|
|
c LMT = 2 |
|
|
c endif |
|
|
c else |
|
|
c LMT = IORD - 3 |
|
|
c endif |
|
|
C |
|
|
LMT = IORD - 3 |
|
|
|
|
|
DO 10 i=1,IMR |
|
|
10 AL(i) = 0.5*(p(i-1)+p(i)) + (DC(i-1) - DC(i))*R3 |
|
|
C |
|
|
do 20 i=1,IMR-1 |
|
|
20 AR(i) = AL(i+1) |
|
|
AR(IMR) = AL(1) |
|
|
C |
|
|
do 30 i=1,IMR |
|
|
30 A6(i) = 3.*(p(i)+p(i) - (AL(i)+AR(i))) |
|
|
C |
|
|
if(LMT.LE.2) call lmtppm(DC(1),A6(1),AR(1),AL(1),P(1),IMR,LMT) |
|
|
C |
|
|
AL(0) = AL(IMR) |
|
|
AR(0) = AR(IMR) |
|
|
A6(0) = A6(IMR) |
|
|
C |
|
|
DO i=1,IMR |
|
|
IF(UT(i).GT.0.) then |
|
|
flux(i) = AR(i-1) + 0.5*UT(i)*(AL(i-1) - AR(i-1) + |
|
|
& A6(i-1)*(1.-R23*UT(i)) ) |
|
|
else |
|
|
flux(i) = AL(i) - 0.5*UT(i)*(AR(i) - AL(i) + |
|
|
& A6(i)*(1.+R23*UT(i))) |
|
|
endif |
|
|
enddo |
|
|
return |
|
|
end |
|
|
C |
|
|
subroutine xmist(IMR,IML,P,DC) |
|
|
parameter( R24 = 1./24.) |
|
|
dimension P(-IML:IMR+1+IML),DC(-IML:IMR+1+IML) |
|
|
C |
|
|
do 10 i=1,IMR |
|
|
tmp = R24*(8.*(p(i+1) - p(i-1)) + p(i-2) - p(i+2)) |
|
|
Pmax = max(P(i-1), p(i), p(i+1)) - p(i) |
|
|
Pmin = p(i) - min(P(i-1), p(i), p(i+1)) |
|
|
10 DC(i) = sign(min(abs(tmp),Pmax,Pmin), tmp) |
|
|
return |
|
|
end |
|
|
C |
|
|
subroutine ytp(IMR,JNP,j1,j2,acosp,RCAP,DQ,P,VC,DC2 |
|
|
& ,ymass,fx,A6,AR,AL,JORD) |
|
|
dimension P(IMR,JNP),VC(IMR,JNP),ymass(IMR,JNP) |
|
|
& ,DC2(IMR,JNP),DQ(IMR,JNP),acosp(JNP) |
|
|
C Work array |
|
|
DIMENSION fx(IMR,JNP),AR(IMR,JNP),AL(IMR,JNP),A6(IMR,JNP) |
|
|
C |
|
|
JMR = JNP - 1 |
|
|
len = IMR*(J2-J1+2) |
|
|
C |
|
|
if(JORD.eq.1) then |
|
|
DO 1000 i=1,len |
|
|
JT = float(J1) - VC(i,J1) |
|
|
1000 fx(i,j1) = p(i,JT) |
|
|
else |
|
|
|
|
|
call ymist(IMR,JNP,j1,P,DC2,4) |
|
|
C |
|
|
if(JORD.LE.0 .or. JORD.GE.3) then |
|
|
|
|
|
call fyppm(VC,P,DC2,fx,IMR,JNP,j1,j2,A6,AR,AL,JORD) |
|
|
|
|
|
else |
|
|
DO 1200 i=1,len |
|
|
JT = float(J1) - VC(i,J1) |
|
|
1200 fx(i,j1) = p(i,JT) + (sign(1.,VC(i,j1))-VC(i,j1))*DC2(i,JT) |
|
|
endif |
|
|
endif |
|
|
C |
|
|
DO 1300 i=1,len |
|
|
1300 fx(i,j1) = fx(i,j1)*ymass(i,j1) |
|
|
C |
|
|
DO 1400 j=j1,j2 |
|
|
DO 1400 i=1,IMR |
|
|
1400 DQ(i,j) = DQ(i,j) + (fx(i,j) - fx(i,j+1)) * acosp(j) |
|
|
C |
|
|
C Poles |
|
|
sum1 = fx(IMR,j1 ) |
|
|
sum2 = fx(IMR,J2+1) |
|
|
do i=1,IMR-1 |
|
|
sum1 = sum1 + fx(i,j1 ) |
|
|
sum2 = sum2 + fx(i,J2+1) |
|
|
enddo |
|
|
C |
|
|
sum1 = DQ(1, 1) - sum1 * RCAP |
|
|
sum2 = DQ(1,JNP) + sum2 * RCAP |
|
|
do i=1,IMR |
|
|
DQ(i, 1) = sum1 |
|
|
DQ(i,JNP) = sum2 |
|
|
enddo |
|
|
C |
|
|
if(j1.ne.2) then |
|
|
do i=1,IMR |
|
|
DQ(i, 2) = sum1 |
|
|
DQ(i,JMR) = sum2 |
|
|
enddo |
|
|
endif |
|
|
C |
|
|
return |
|
|
end |
|
|
C |
|
|
subroutine ymist(IMR,JNP,j1,P,DC,ID) |
|
|
parameter ( R24 = 1./24. ) |
|
|
dimension P(IMR,JNP),DC(IMR,JNP) |
|
|
C |
|
|
IMH = IMR / 2 |
|
|
JMR = JNP - 1 |
|
|
IJM3 = IMR*(JMR-3) |
|
|
C |
|
|
IF(ID.EQ.2) THEN |
|
|
do 10 i=1,IMR*(JMR-1) |
|
|
tmp = 0.25*(p(i,3) - p(i,1)) |
|
|
Pmax = max(p(i,1),p(i,2),p(i,3)) - p(i,2) |
|
|
Pmin = p(i,2) - min(p(i,1),p(i,2),p(i,3)) |
|
|
DC(i,2) = sign(min(abs(tmp),Pmin,Pmax),tmp) |
|
|
10 CONTINUE |
|
|
ELSE |
|
|
do 12 i=1,IMH |
|
|
C J=2 |
|
|
tmp = (8.*(p(i,3) - p(i,1)) + p(i+IMH,2) - p(i,4))*R24 |
|
|
Pmax = max(p(i,1),p(i,2),p(i,3)) - p(i,2) |
|
|
Pmin = p(i,2) - min(p(i,1),p(i,2),p(i,3)) |
|
|
DC(i,2) = sign(min(abs(tmp),Pmin,Pmax),tmp) |
|
|
C J=JMR |
|
|
tmp=(8.*(p(i,JNP)-p(i,JMR-1))+p(i,JMR-2)-p(i+IMH,JMR))*R24 |
|
|
Pmax = max(p(i,JMR-1),p(i,JMR),p(i,JNP)) - p(i,JMR) |
|
|
Pmin = p(i,JMR) - min(p(i,JMR-1),p(i,JMR),p(i,JNP)) |
|
|
DC(i,JMR) = sign(min(abs(tmp),Pmin,Pmax),tmp) |
|
|
12 CONTINUE |
|
|
do 14 i=IMH+1,IMR |
|
|
C J=2 |
|
|
tmp = (8.*(p(i,3) - p(i,1)) + p(i-IMH,2) - p(i,4))*R24 |
|
|
Pmax = max(p(i,1),p(i,2),p(i,3)) - p(i,2) |
|
|
Pmin = p(i,2) - min(p(i,1),p(i,2),p(i,3)) |
|
|
DC(i,2) = sign(min(abs(tmp),Pmin,Pmax),tmp) |
|
|
C J=JMR |
|
|
tmp=(8.*(p(i,JNP)-p(i,JMR-1))+p(i,JMR-2)-p(i-IMH,JMR))*R24 |
|
|
Pmax = max(p(i,JMR-1),p(i,JMR),p(i,JNP)) - p(i,JMR) |
|
|
Pmin = p(i,JMR) - min(p(i,JMR-1),p(i,JMR),p(i,JNP)) |
|
|
DC(i,JMR) = sign(min(abs(tmp),Pmin,Pmax),tmp) |
|
|
14 CONTINUE |
|
|
C |
|
|
do 15 i=1,IJM3 |
|
|
tmp = (8.*(p(i,4) - p(i,2)) + p(i,1) - p(i,5))*R24 |
|
|
Pmax = max(p(i,2),p(i,3),p(i,4)) - p(i,3) |
|
|
Pmin = p(i,3) - min(p(i,2),p(i,3),p(i,4)) |
|
|
DC(i,3) = sign(min(abs(tmp),Pmin,Pmax),tmp) |
|
|
15 CONTINUE |
|
|
ENDIF |
|
|
C |
|
|
if(j1.ne.2) then |
|
|
do i=1,IMR |
|
|
DC(i,1) = 0. |
|
|
DC(i,JNP) = 0. |
|
|
enddo |
|
|
else |
|
|
C Determine slopes in polar caps for scalars! |
|
|
C |
|
|
do 13 i=1,IMH |
|
|
C South |
|
|
tmp = 0.25*(p(i,2) - p(i+imh,2)) |
|
|
Pmax = max(p(i,2),p(i,1), p(i+imh,2)) - p(i,1) |
|
|
Pmin = p(i,1) - min(p(i,2),p(i,1), p(i+imh,2)) |
|
|
DC(i,1)=sign(min(abs(tmp),Pmax,Pmin),tmp) |
|
|
C North. |
|
|
tmp = 0.25*(p(i+imh,JMR) - p(i,JMR)) |
|
|
Pmax = max(p(i+imh,JMR),p(i,jnp), p(i,JMR)) - p(i,JNP) |
|
|
Pmin = p(i,JNP) - min(p(i+imh,JMR),p(i,jnp), p(i,JMR)) |
|
|
DC(i,JNP) = sign(min(abs(tmp),Pmax,pmin),tmp) |
|
|
13 continue |
|
|
C |
|
|
do 25 i=imh+1,IMR |
|
|
DC(i, 1) = - DC(i-imh, 1) |
|
|
DC(i,JNP) = - DC(i-imh,JNP) |
|
|
25 continue |
|
|
endif |
|
|
return |
|
|
end |
|
|
C |
|
|
subroutine fyppm(VC,P,DC,flux,IMR,JNP,j1,j2,A6,AR,AL,JORD) |
|
|
parameter ( R3 = 1./3., R23 = 2./3. ) |
|
|
real VC(IMR,*),flux(IMR,*),P(IMR,*),DC(IMR,*) |
|
|
C Local work arrays. |
|
|
real AR(IMR,JNP),AL(IMR,JNP),A6(IMR,JNP) |
|
|
integer LMT |
|
|
c logical first |
|
|
C data first /.true./ |
|
|
C SAVE LMT |
|
|
C |
|
|
IMH = IMR / 2 |
|
|
JMR = JNP - 1 |
|
|
j11 = j1-1 |
|
|
IMJM1 = IMR*(J2-J1+2) |
|
|
len = IMR*(J2-J1+3) |
|
|
C if(first) then |
|
|
C IF(JORD.LE.0) then |
|
|
C if(JMR.GE.90) then |
|
|
C LMT = 0 |
|
|
C elseif(JMR.GE.45) then |
|
|
C LMT = 1 |
|
|
C else |
|
|
C LMT = 2 |
|
|
C endif |
|
|
C else |
|
|
C LMT = JORD - 3 |
|
|
C endif |
|
|
C |
|
|
C first = .false. |
|
|
C endif |
|
|
C |
|
|
c modifs pour pouvoir choisir plusieurs schemas PPM |
|
|
LMT = JORD - 3 |
|
|
C |
|
|
DO 10 i=1,IMR*JMR |
|
|
AL(i,2) = 0.5*(p(i,1)+p(i,2)) + (DC(i,1) - DC(i,2))*R3 |
|
|
AR(i,1) = AL(i,2) |
|
|
10 CONTINUE |
|
|
C |
|
|
CPoles: |
|
|
C |
|
|
DO i=1,IMH |
|
|
AL(i,1) = AL(i+IMH,2) |
|
|
AL(i+IMH,1) = AL(i,2) |
|
|
C |
|
|
AR(i,JNP) = AR(i+IMH,JMR) |
|
|
AR(i+IMH,JNP) = AR(i,JMR) |
|
|
ENDDO |
|
|
|
|
|
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
|
|
c Rajout pour LMDZ.3.3 |
|
|
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
|
|
AR(IMR,1)=AL(1,1) |
|
|
AR(IMR,JNP)=AL(1,JNP) |
|
|
ccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc |
|
|
|
|
|
|
|
|
do 30 i=1,len |
|
|
30 A6(i,j11) = 3.*(p(i,j11)+p(i,j11) - (AL(i,j11)+AR(i,j11))) |
|
|
C |
|
|
if(LMT.le.2) call lmtppm(DC(1,j11),A6(1,j11),AR(1,j11) |
|
|
& ,AL(1,j11),P(1,j11),len,LMT) |
|
|
C |
|
|
|
|
|
DO 140 i=1,IMJM1 |
|
|
IF(VC(i,j1).GT.0.) then |
|
|
flux(i,j1) = AR(i,j11) + 0.5*VC(i,j1)*(AL(i,j11) - AR(i,j11) + |
|
|
& A6(i,j11)*(1.-R23*VC(i,j1)) ) |
|
|
else |
|
|
flux(i,j1) = AL(i,j1) - 0.5*VC(i,j1)*(AR(i,j1) - AL(i,j1) + |
|
|
& A6(i,j1)*(1.+R23*VC(i,j1))) |
|
|
endif |
|
|
140 continue |
|
|
return |
|
|
end |
|
|
C |
|
|
subroutine yadv(IMR,JNP,j1,j2,p,VA,ady,wk,IAD) |
|
|
REAL p(IMR,JNP),ady(IMR,JNP),VA(IMR,JNP) |
|
|
REAL WK(IMR,-1:JNP+2) |
|
|
C |
|
|
JMR = JNP-1 |
|
|
IMH = IMR/2 |
|
|
do j=1,JNP |
|
|
do i=1,IMR |
|
|
wk(i,j) = p(i,j) |
|
|
enddo |
|
|
enddo |
|
|
C Poles: |
|
|
do i=1,IMH |
|
|
wk(i, -1) = p(i+IMH,3) |
|
|
wk(i+IMH,-1) = p(i,3) |
|
|
wk(i, 0) = p(i+IMH,2) |
|
|
wk(i+IMH,0) = p(i,2) |
|
|
wk(i,JNP+1) = p(i+IMH,JMR) |
|
|
wk(i+IMH,JNP+1) = p(i,JMR) |
|
|
wk(i,JNP+2) = p(i+IMH,JNP-2) |
|
|
wk(i+IMH,JNP+2) = p(i,JNP-2) |
|
|
enddo |
|
|
|
|
|
IF(IAD.eq.2) then |
|
|
do j=j1-1,j2+1 |
|
|
do i=1,IMR |
|
|
JP = NINT(VA(i,j)) |
|
|
rv = JP - VA(i,j) |
|
|
JP = j - JP |
|
|
a1 = 0.5*(wk(i,jp+1)+wk(i,jp-1)) - wk(i,jp) |
|
|
b1 = 0.5*(wk(i,jp+1)-wk(i,jp-1)) |
|
|
ady(i,j) = wk(i,jp) + rv*(a1*rv + b1) - wk(i,j) |
|
|
enddo |
|
|
enddo |
|
|
|
|
|
ELSEIF(IAD.eq.1) then |
|
|
do j=j1-1,j2+1 |
|
|
do i=1,imr |
|
|
JP = float(j)-VA(i,j) |
|
|
ady(i,j) = VA(i,j)*(wk(i,jp)-wk(i,jp+1)) |
|
|
enddo |
|
|
enddo |
|
|
ENDIF |
|
|
C |
|
|
if(j1.ne.2) then |
|
|
sum1 = 0. |
|
|
sum2 = 0. |
|
|
do i=1,imr |
|
|
sum1 = sum1 + ady(i,2) |
|
|
sum2 = sum2 + ady(i,JMR) |
|
|
enddo |
|
|
sum1 = sum1 / IMR |
|
|
sum2 = sum2 / IMR |
|
|
C |
|
|
do i=1,imr |
|
|
ady(i, 2) = sum1 |
|
|
ady(i,JMR) = sum2 |
|
|
ady(i, 1) = sum1 |
|
|
ady(i,JNP) = sum2 |
|
|
enddo |
|
|
else |
|
|
C Poles: |
|
|
sum1 = 0. |
|
|
sum2 = 0. |
|
|
do i=1,imr |
|
|
sum1 = sum1 + ady(i,1) |
|
|
sum2 = sum2 + ady(i,JNP) |
|
|
enddo |
|
|
sum1 = sum1 / IMR |
|
|
sum2 = sum2 / IMR |
|
|
C |
|
|
do i=1,imr |
|
|
ady(i, 1) = sum1 |
|
|
ady(i,JNP) = sum2 |
|
|
enddo |
|
|
endif |
|
|
C |
|
|
return |
|
|
end |
|
|
C |
|
|
subroutine xadv(IMR,JNP,j1,j2,p,UA,JS,JN,IML,adx,IAD) |
|
|
REAL p(IMR,JNP),adx(IMR,JNP),qtmp(-IMR:IMR+IMR),UA(IMR,JNP) |
|
|
C |
|
|
JMR = JNP-1 |
|
|
do 1309 j=j1,j2 |
|
|
if(J.GT.JS .and. J.LT.JN) GO TO 1309 |
|
|
C |
|
|
do i=1,IMR |
|
|
qtmp(i) = p(i,j) |
|
|
enddo |
|
|
C |
|
|
do i=-IML,0 |
|
|
qtmp(i) = p(IMR+i,j) |
|
|
qtmp(IMR+1-i) = p(1-i,j) |
|
|
enddo |
|
|
C |
|
|
IF(IAD.eq.2) THEN |
|
|
DO i=1,IMR |
|
|
IP = NINT(UA(i,j)) |
|
|
ru = IP - UA(i,j) |
|
|
IP = i - IP |
|
|
a1 = 0.5*(qtmp(ip+1)+qtmp(ip-1)) - qtmp(ip) |
|
|
b1 = 0.5*(qtmp(ip+1)-qtmp(ip-1)) |
|
|
adx(i,j) = qtmp(ip) + ru*(a1*ru + b1) |
|
|
enddo |
|
|
ELSEIF(IAD.eq.1) then |
|
|
DO i=1,IMR |
|
|
iu = UA(i,j) |
|
|
ru = UA(i,j) - iu |
|
|
iiu = i-iu |
|
|
if(UA(i,j).GE.0.) then |
|
|
adx(i,j) = qtmp(iiu)+ru*(qtmp(iiu-1)-qtmp(iiu)) |
|
|
else |
|
|
adx(i,j) = qtmp(iiu)+ru*(qtmp(iiu)-qtmp(iiu+1)) |
|
|
endif |
|
|
enddo |
|
|
ENDIF |
|
|
C |
|
|
do i=1,IMR |
|
|
adx(i,j) = adx(i,j) - p(i,j) |
|
|
enddo |
|
|
1309 continue |
|
|
C |
|
|
C Eulerian upwind |
|
|
C |
|
|
do j=JS+1,JN-1 |
|
|
C |
|
|
do i=1,IMR |
|
|
qtmp(i) = p(i,j) |
|
|
enddo |
|
|
C |
|
|
qtmp(0) = p(IMR,J) |
|
|
qtmp(IMR+1) = p(1,J) |
|
|
C |
|
|
IF(IAD.eq.2) THEN |
|
|
qtmp(-1) = p(IMR-1,J) |
|
|
qtmp(IMR+2) = p(2,J) |
|
|
do i=1,imr |
|
|
IP = NINT(UA(i,j)) |
|
|
ru = IP - UA(i,j) |
|
|
IP = i - IP |
|
|
a1 = 0.5*(qtmp(ip+1)+qtmp(ip-1)) - qtmp(ip) |
|
|
b1 = 0.5*(qtmp(ip+1)-qtmp(ip-1)) |
|
|
adx(i,j) = qtmp(ip)- p(i,j) + ru*(a1*ru + b1) |
|
|
enddo |
|
|
ELSEIF(IAD.eq.1) then |
|
|
C 1st order |
|
|
DO i=1,IMR |
|
|
IP = i - UA(i,j) |
|
|
adx(i,j) = UA(i,j)*(qtmp(ip)-qtmp(ip+1)) |
|
|
enddo |
|
|
ENDIF |
|
|
enddo |
|
|
C |
|
|
if(j1.ne.2) then |
|
|
do i=1,IMR |
|
|
adx(i, 2) = 0. |
|
|
adx(i,JMR) = 0. |
|
|
enddo |
|
|
endif |
|
|
C set cross term due to x-adv at the poles to zero. |
|
|
do i=1,IMR |
|
|
adx(i, 1) = 0. |
|
|
adx(i,JNP) = 0. |
|
|
enddo |
|
|
return |
|
|
end |
|
|
C |
|
|
subroutine lmtppm(DC,A6,AR,AL,P,IM,LMT) |
|
|
C |
|
|
C A6 = CURVATURE OF THE TEST PARABOLA |
|
|
C AR = RIGHT EDGE VALUE OF THE TEST PARABOLA |
|
|
C AL = LEFT EDGE VALUE OF THE TEST PARABOLA |
|
|
C DC = 0.5 * MISMATCH |
|
|
C P = CELL-AVERAGED VALUE |
|
|
C IM = VECTOR LENGTH |
|
|
C |
|
|
C OPTIONS: |
|
|
C |
|
|
C LMT = 0: FULL MONOTONICITY |
|
|
C LMT = 1: SEMI-MONOTONIC CONSTRAINT (NO UNDERSHOOTS) |
|
|
C LMT = 2: POSITIVE-DEFINITE CONSTRAINT |
|
|
C |
|
|
parameter ( R12 = 1./12. ) |
|
|
dimension A6(IM),AR(IM),AL(IM),P(IM),DC(IM) |
|
|
C |
|
|
if(LMT.eq.0) then |
|
|
C Full constraint |
|
|
do 100 i=1,IM |
|
|
if(DC(i).eq.0.) then |
|
|
AR(i) = p(i) |
|
|
AL(i) = p(i) |
|
|
A6(i) = 0. |
|
|
else |
|
|
da1 = AR(i) - AL(i) |
|
|
da2 = da1**2 |
|
|
A6DA = A6(i)*da1 |
|
|
if(A6DA .lt. -da2) then |
|
|
A6(i) = 3.*(AL(i)-p(i)) |
|
|
AR(i) = AL(i) - A6(i) |
|
|
elseif(A6DA .gt. da2) then |
|
|
A6(i) = 3.*(AR(i)-p(i)) |
|
|
AL(i) = AR(i) - A6(i) |
|
|
endif |
|
|
endif |
|
|
100 continue |
|
|
elseif(LMT.eq.1) then |
|
|
C Semi-monotonic constraint |
|
|
do 150 i=1,IM |
|
|
if(abs(AR(i)-AL(i)) .GE. -A6(i)) go to 150 |
|
|
if(p(i).lt.AR(i) .and. p(i).lt.AL(i)) then |
|
|
AR(i) = p(i) |
|
|
AL(i) = p(i) |
|
|
A6(i) = 0. |
|
|
elseif(AR(i) .gt. AL(i)) then |
|
|
A6(i) = 3.*(AL(i)-p(i)) |
|
|
AR(i) = AL(i) - A6(i) |
|
|
else |
|
|
A6(i) = 3.*(AR(i)-p(i)) |
|
|
AL(i) = AR(i) - A6(i) |
|
|
endif |
|
|
150 continue |
|
|
elseif(LMT.eq.2) then |
|
|
do 250 i=1,IM |
|
|
if(abs(AR(i)-AL(i)) .GE. -A6(i)) go to 250 |
|
|
fmin = p(i) + 0.25*(AR(i)-AL(i))**2/A6(i) + A6(i)*R12 |
|
|
if(fmin.ge.0.) go to 250 |
|
|
if(p(i).lt.AR(i) .and. p(i).lt.AL(i)) then |
|
|
AR(i) = p(i) |
|
|
AL(i) = p(i) |
|
|
A6(i) = 0. |
|
|
elseif(AR(i) .gt. AL(i)) then |
|
|
A6(i) = 3.*(AL(i)-p(i)) |
|
|
AR(i) = AL(i) - A6(i) |
|
|
else |
|
|
A6(i) = 3.*(AR(i)-p(i)) |
|
|
AL(i) = AR(i) - A6(i) |
|
|
endif |
|
|
250 continue |
|
|
endif |
|
|
return |
|
|
end |
|
|
C |
|
|
subroutine A2C(U,V,IMR,JMR,j1,j2,CRX,CRY,dtdx5,DTDY5) |
|
|
dimension U(IMR,*),V(IMR,*),CRX(IMR,*),CRY(IMR,*),DTDX5(*) |
|
|
C |
|
|
do 35 j=j1,j2 |
|
|
do 35 i=2,IMR |
|
|
35 CRX(i,J) = dtdx5(j)*(U(i,j)+U(i-1,j)) |
|
|
C |
|
|
do 45 j=j1,j2 |
|
|
45 CRX(1,J) = dtdx5(j)*(U(1,j)+U(IMR,j)) |
|
|
C |
|
|
do 55 i=1,IMR*JMR |
|
|
55 CRY(i,2) = DTDY5*(V(i,2)+V(i,1)) |
|
|
return |
|
|
end |
|
|
C |
|
|
subroutine cosa(cosp,cose,JNP,PI,DP) |
|
|
dimension cosp(*),cose(*) |
|
|
JMR = JNP-1 |
|
|
do 55 j=2,JNP |
|
|
ph5 = -0.5*PI + (FLOAT(J-1)-0.5)*DP |
|
|
55 cose(j) = cos(ph5) |
|
|
C |
|
|
JEQ = (JNP+1) / 2 |
|
|
if(JMR .eq. 2*(JMR/2) ) then |
|
|
do j=JNP, JEQ+1, -1 |
|
|
cose(j) = cose(JNP+2-j) |
|
|
enddo |
|
|
else |
|
|
C cell edge at equator. |
|
|
cose(JEQ+1) = 1. |
|
|
do j=JNP, JEQ+2, -1 |
|
|
cose(j) = cose(JNP+2-j) |
|
|
enddo |
|
|
endif |
|
|
C |
|
|
do 66 j=2,JMR |
|
|
66 cosp(j) = 0.5*(cose(j)+cose(j+1)) |
|
|
cosp(1) = 0. |
|
|
cosp(JNP) = 0. |
|
|
return |
|
|
end |
|
|
C |
|
|
subroutine cosc(cosp,cose,JNP,PI,DP) |
|
|
dimension cosp(*),cose(*) |
|
|
C |
|
|
phi = -0.5*PI |
|
|
do 55 j=2,JNP-1 |
|
|
phi = phi + DP |
|
|
55 cosp(j) = cos(phi) |
|
|
cosp( 1) = 0. |
|
|
cosp(JNP) = 0. |
|
|
C |
|
|
do 66 j=2,JNP |
|
|
cose(j) = 0.5*(cosp(j)+cosp(j-1)) |
|
|
66 CONTINUE |
|
|
C |
|
|
do 77 j=2,JNP-1 |
|
|
cosp(j) = 0.5*(cose(j)+cose(j+1)) |
|
|
77 CONTINUE |
|
|
return |
|
|
end |
|
|
C |
|
|
SUBROUTINE qckxyz (Q,qtmp,IMR,JNP,NLAY,j1,j2,cosp,acosp, |
|
|
& cross,IC,NSTEP) |
|
|
C |
|
|
parameter( tiny = 1.E-60 ) |
|
|
DIMENSION Q(IMR,JNP,NLAY),qtmp(IMR,JNP),cosp(*),acosp(*) |
|
|
logical cross |
|
|
C |
|
|
NLAYM1 = NLAY-1 |
|
|
len = IMR*(j2-j1+1) |
|
|
ip = 0 |
|
|
C |
|
|
C Top layer |
|
|
L = 1 |
|
|
icr = 1 |
|
|
call filns(q(1,1,L),IMR,JNP,j1,j2,cosp,acosp,ipy,tiny) |
|
|
if(ipy.eq.0) goto 50 |
|
|
call filew(q(1,1,L),qtmp,IMR,JNP,j1,j2,ipx,tiny) |
|
|
if(ipx.eq.0) goto 50 |
|
|
C |
|
|
if(cross) then |
|
|
call filcr(q(1,1,L),IMR,JNP,j1,j2,cosp,acosp,icr,tiny) |
|
|
endif |
|
|
if(icr.eq.0) goto 50 |
|
|
C |
|
|
C Vertical filling... |
|
|
do i=1,len |
|
|
IF( Q(i,j1,1).LT.0.) THEN |
|
|
ip = ip + 1 |
|
|
Q(i,j1,2) = Q(i,j1,2) + Q(i,j1,1) |
|
|
Q(i,j1,1) = 0. |
|
|
endif |
|
|
enddo |
|
|
C |
|
|
50 continue |
|
|
DO 225 L = 2,NLAYM1 |
|
|
icr = 1 |
|
|
C |
|
|
call filns(q(1,1,L),IMR,JNP,j1,j2,cosp,acosp,ipy,tiny) |
|
|
if(ipy.eq.0) goto 225 |
|
|
call filew(q(1,1,L),qtmp,IMR,JNP,j1,j2,ipx,tiny) |
|
|
if(ipx.eq.0) go to 225 |
|
|
if(cross) then |
|
|
call filcr(q(1,1,L),IMR,JNP,j1,j2,cosp,acosp,icr,tiny) |
|
|
endif |
|
|
if(icr.eq.0) goto 225 |
|
|
C |
|
|
do i=1,len |
|
|
IF( Q(I,j1,L).LT.0.) THEN |
|
|
C |
|
|
ip = ip + 1 |
|
|
C From above |
|
|
qup = Q(I,j1,L-1) |
|
|
qly = -Q(I,j1,L) |
|
|
dup = min(qly,qup) |
|
|
Q(I,j1,L-1) = qup - dup |
|
|
Q(I,j1,L ) = dup-qly |
|
|
C Below |
|
|
Q(I,j1,L+1) = Q(I,j1,L+1) + Q(I,j1,L) |
|
|
Q(I,j1,L) = 0. |
|
|
ENDIF |
|
|
ENDDO |
|
|
225 CONTINUE |
|
|
C |
|
|
C BOTTOM LAYER |
|
|
sum = 0. |
|
|
L = NLAY |
|
|
C |
|
|
call filns(q(1,1,L),IMR,JNP,j1,j2,cosp,acosp,ipy,tiny) |
|
|
if(ipy.eq.0) goto 911 |
|
|
call filew(q(1,1,L),qtmp,IMR,JNP,j1,j2,ipx,tiny) |
|
|
if(ipx.eq.0) goto 911 |
|
|
C |
|
|
call filcr(q(1,1,L),IMR,JNP,j1,j2,cosp,acosp,icr,tiny) |
|
|
if(icr.eq.0) goto 911 |
|
|
C |
|
|
DO I=1,len |
|
|
IF( Q(I,j1,L).LT.0.) THEN |
|
|
ip = ip + 1 |
|
|
c |
|
|
C From above |
|
|
C |
|
|
qup = Q(I,j1,NLAYM1) |
|
|
qly = -Q(I,j1,L) |
|
|
dup = min(qly,qup) |
|
|
Q(I,j1,NLAYM1) = qup - dup |
|
|
C From "below" the surface. |
|
|
sum = sum + qly-dup |
|
|
Q(I,j1,L) = 0. |
|
|
ENDIF |
|
|
ENDDO |
|
|
C |
|
|
911 continue |
|
|
C |
|
|
if(ip.gt.IMR) then |
|
|
write(6,*) 'IC=',IC,' STEP=',NSTEP, |
|
|
& ' Vertical filling pts=',ip |
|
|
endif |
|
|
C |
|
|
if(sum.gt.1.e-25) then |
|
|
write(6,*) IC,NSTEP,' Mass source from the ground=',sum |
|
|
endif |
|
|
RETURN |
|
|
END |
|
|
C |
|
|
subroutine filcr(q,IMR,JNP,j1,j2,cosp,acosp,icr,tiny) |
|
|
dimension q(IMR,*),cosp(*),acosp(*) |
|
|
icr = 0 |
|
|
do 65 j=j1+1,j2-1 |
|
|
DO 50 i=1,IMR-1 |
|
|
IF(q(i,j).LT.0.) THEN |
|
|
icr = 1 |
|
|
dq = - q(i,j)*cosp(j) |
|
|
C N-E |
|
|
dn = q(i+1,j+1)*cosp(j+1) |
|
|
d0 = max(0.,dn) |
|
|
d1 = min(dq,d0) |
|
|
q(i+1,j+1) = (dn - d1)*acosp(j+1) |
|
|
dq = dq - d1 |
|
|
C S-E |
|
|
ds = q(i+1,j-1)*cosp(j-1) |
|
|
d0 = max(0.,ds) |
|
|
d2 = min(dq,d0) |
|
|
q(i+1,j-1) = (ds - d2)*acosp(j-1) |
|
|
q(i,j) = (d2 - dq)*acosp(j) + tiny |
|
|
endif |
|
|
50 continue |
|
|
if(icr.eq.0 .and. q(IMR,j).ge.0.) goto 65 |
|
|
DO 55 i=2,IMR |
|
|
IF(q(i,j).LT.0.) THEN |
|
|
icr = 1 |
|
|
dq = - q(i,j)*cosp(j) |
|
|
C N-W |
|
|
dn = q(i-1,j+1)*cosp(j+1) |
|
|
d0 = max(0.,dn) |
|
|
d1 = min(dq,d0) |
|
|
q(i-1,j+1) = (dn - d1)*acosp(j+1) |
|
|
dq = dq - d1 |
|
|
C S-W |
|
|
ds = q(i-1,j-1)*cosp(j-1) |
|
|
d0 = max(0.,ds) |
|
|
d2 = min(dq,d0) |
|
|
q(i-1,j-1) = (ds - d2)*acosp(j-1) |
|
|
q(i,j) = (d2 - dq)*acosp(j) + tiny |
|
|
endif |
|
|
55 continue |
|
|
C ***************************************** |
|
|
C i=1 |
|
|
i=1 |
|
|
IF(q(i,j).LT.0.) THEN |
|
|
icr = 1 |
|
|
dq = - q(i,j)*cosp(j) |
|
|
C N-W |
|
|
dn = q(IMR,j+1)*cosp(j+1) |
|
|
d0 = max(0.,dn) |
|
|
d1 = min(dq,d0) |
|
|
q(IMR,j+1) = (dn - d1)*acosp(j+1) |
|
|
dq = dq - d1 |
|
|
C S-W |
|
|
ds = q(IMR,j-1)*cosp(j-1) |
|
|
d0 = max(0.,ds) |
|
|
d2 = min(dq,d0) |
|
|
q(IMR,j-1) = (ds - d2)*acosp(j-1) |
|
|
q(i,j) = (d2 - dq)*acosp(j) + tiny |
|
|
endif |
|
|
C ***************************************** |
|
|
C i=IMR |
|
|
i=IMR |
|
|
IF(q(i,j).LT.0.) THEN |
|
|
icr = 1 |
|
|
dq = - q(i,j)*cosp(j) |
|
|
C N-E |
|
|
dn = q(1,j+1)*cosp(j+1) |
|
|
d0 = max(0.,dn) |
|
|
d1 = min(dq,d0) |
|
|
q(1,j+1) = (dn - d1)*acosp(j+1) |
|
|
dq = dq - d1 |
|
|
C S-E |
|
|
ds = q(1,j-1)*cosp(j-1) |
|
|
d0 = max(0.,ds) |
|
|
d2 = min(dq,d0) |
|
|
q(1,j-1) = (ds - d2)*acosp(j-1) |
|
|
q(i,j) = (d2 - dq)*acosp(j) + tiny |
|
|
endif |
|
|
C ***************************************** |
|
|
65 continue |
|
|
C |
|
|
do i=1,IMR |
|
|
if(q(i,j1).lt.0. .or. q(i,j2).lt.0.) then |
|
|
icr = 1 |
|
|
goto 80 |
|
|
endif |
|
|
enddo |
|
|
C |
|
|
80 continue |
|
|
C |
|
|
if(q(1,1).lt.0. .or. q(1,jnp).lt.0.) then |
|
|
icr = 1 |
|
|
endif |
|
|
C |
|
|
return |
|
|
end |
|
|
C |
|
|
subroutine filns(q,IMR,JNP,j1,j2,cosp,acosp,ipy,tiny) |
|
|
dimension q(IMR,*),cosp(*),acosp(*) |
|
|
c logical first |
|
|
c data first /.true./ |
|
|
c save cap1 |
|
|
C |
|
|
c if(first) then |
|
|
DP = 4.*ATAN(1.)/float(JNP-1) |
|
|
CAP1 = IMR*(1.-COS((j1-1.5)*DP))/DP |
|
|
c first = .false. |
|
|
c endif |
|
|
C |
|
|
ipy = 0 |
|
|
do 55 j=j1+1,j2-1 |
|
|
DO 55 i=1,IMR |
|
|
IF(q(i,j).LT.0.) THEN |
|
|
ipy = 1 |
|
|
dq = - q(i,j)*cosp(j) |
|
|
C North |
|
|
dn = q(i,j+1)*cosp(j+1) |
|
|
d0 = max(0.,dn) |
|
|
d1 = min(dq,d0) |
|
|
q(i,j+1) = (dn - d1)*acosp(j+1) |
|
|
dq = dq - d1 |
|
|
C South |
|
|
ds = q(i,j-1)*cosp(j-1) |
|
|
d0 = max(0.,ds) |
|
|
d2 = min(dq,d0) |
|
|
q(i,j-1) = (ds - d2)*acosp(j-1) |
|
|
q(i,j) = (d2 - dq)*acosp(j) + tiny |
|
|
endif |
|
|
55 continue |
|
|
C |
|
|
do i=1,imr |
|
|
IF(q(i,j1).LT.0.) THEN |
|
|
ipy = 1 |
|
|
dq = - q(i,j1)*cosp(j1) |
|
|
C North |
|
|
dn = q(i,j1+1)*cosp(j1+1) |
|
|
d0 = max(0.,dn) |
|
|
d1 = min(dq,d0) |
|
|
q(i,j1+1) = (dn - d1)*acosp(j1+1) |
|
|
q(i,j1) = (d1 - dq)*acosp(j1) + tiny |
|
|
endif |
|
|
enddo |
|
|
C |
|
|
j = j2 |
|
|
do i=1,imr |
|
|
IF(q(i,j).LT.0.) THEN |
|
|
ipy = 1 |
|
|
dq = - q(i,j)*cosp(j) |
|
|
C South |
|
|
ds = q(i,j-1)*cosp(j-1) |
|
|
d0 = max(0.,ds) |
|
|
d2 = min(dq,d0) |
|
|
q(i,j-1) = (ds - d2)*acosp(j-1) |
|
|
q(i,j) = (d2 - dq)*acosp(j) + tiny |
|
|
endif |
|
|
enddo |
|
|
C |
|
|
C Check Poles. |
|
|
if(q(1,1).lt.0.) then |
|
|
dq = q(1,1)*cap1/float(IMR)*acosp(j1) |
|
|
do i=1,imr |
|
|
q(i,1) = 0. |
|
|
q(i,j1) = q(i,j1) + dq |
|
|
if(q(i,j1).lt.0.) ipy = 1 |
|
|
enddo |
|
|
endif |
|
|
C |
|
|
if(q(1,JNP).lt.0.) then |
|
|
dq = q(1,JNP)*cap1/float(IMR)*acosp(j2) |
|
|
do i=1,imr |
|
|
q(i,JNP) = 0. |
|
|
q(i,j2) = q(i,j2) + dq |
|
|
if(q(i,j2).lt.0.) ipy = 1 |
|
|
enddo |
|
|
endif |
|
|
C |
|
|
return |
|
|
end |
|
|
C |
|
|
subroutine filew(q,qtmp,IMR,JNP,j1,j2,ipx,tiny) |
|
|
dimension q(IMR,*),qtmp(JNP,IMR) |
|
|
C |
|
|
ipx = 0 |
|
|
C Copy & swap direction for vectorization. |
|
|
do 25 i=1,imr |
|
|
do 25 j=j1,j2 |
|
|
25 qtmp(j,i) = q(i,j) |
|
|
C |
|
|
do 55 i=2,imr-1 |
|
|
do 55 j=j1,j2 |
|
|
if(qtmp(j,i).lt.0.) then |
|
|
ipx = 1 |
|
|
c west |
|
|
d0 = max(0.,qtmp(j,i-1)) |
|
|
d1 = min(-qtmp(j,i),d0) |
|
|
qtmp(j,i-1) = qtmp(j,i-1) - d1 |
|
|
qtmp(j,i) = qtmp(j,i) + d1 |
|
|
c east |
|
|
d0 = max(0.,qtmp(j,i+1)) |
|
|
d2 = min(-qtmp(j,i),d0) |
|
|
qtmp(j,i+1) = qtmp(j,i+1) - d2 |
|
|
qtmp(j,i) = qtmp(j,i) + d2 + tiny |
|
|
endif |
|
|
55 continue |
|
|
c |
|
|
i=1 |
|
|
do 65 j=j1,j2 |
|
|
if(qtmp(j,i).lt.0.) then |
|
|
ipx = 1 |
|
|
c west |
|
|
d0 = max(0.,qtmp(j,imr)) |
|
|
d1 = min(-qtmp(j,i),d0) |
|
|
qtmp(j,imr) = qtmp(j,imr) - d1 |
|
|
qtmp(j,i) = qtmp(j,i) + d1 |
|
|
c east |
|
|
d0 = max(0.,qtmp(j,i+1)) |
|
|
d2 = min(-qtmp(j,i),d0) |
|
|
qtmp(j,i+1) = qtmp(j,i+1) - d2 |
|
|
c |
|
|
qtmp(j,i) = qtmp(j,i) + d2 + tiny |
|
|
endif |
|
|
65 continue |
|
|
i=IMR |
|
|
do 75 j=j1,j2 |
|
|
if(qtmp(j,i).lt.0.) then |
|
|
ipx = 1 |
|
|
c west |
|
|
d0 = max(0.,qtmp(j,i-1)) |
|
|
d1 = min(-qtmp(j,i),d0) |
|
|
qtmp(j,i-1) = qtmp(j,i-1) - d1 |
|
|
qtmp(j,i) = qtmp(j,i) + d1 |
|
|
c east |
|
|
d0 = max(0.,qtmp(j,1)) |
|
|
d2 = min(-qtmp(j,i),d0) |
|
|
qtmp(j,1) = qtmp(j,1) - d2 |
|
|
c |
|
|
qtmp(j,i) = qtmp(j,i) + d2 + tiny |
|
|
endif |
|
|
75 continue |
|
|
C |
|
|
if(ipx.ne.0) then |
|
|
do 85 j=j1,j2 |
|
|
do 85 i=1,imr |
|
|
85 q(i,j) = qtmp(j,i) |
|
|
else |
|
|
C |
|
|
C Poles. |
|
|
if(q(1,1).lt.0. or. q(1,JNP).lt.0.) ipx = 1 |
|
|
endif |
|
|
return |
|
|
end |
|
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