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0002 <TITLE>module vert_diff_mod</TITLE>
0003 <BODY BGCOLOR="#AABBCC" TEXT="#332211" >
0004
0005 <DIV ALIGN="CENTER"> <FONT SIZE=1>
0006 <A HREF="#INTERFACE">PUBLIC INTERFACE</A> /
0007 <A HREF="#DATA_TYPES">DATA</A> /
0008 <A HREF="#ROUTINES">ROUTINES</A> /
0009 <A HREF="#NAMELIST">NAMELIST</A> /
0010 <A HREF="#DIAGNOSTICS">DIAGNOSTICS</A> /
0011 <A HREF="#CHANGES">CHANGES</A> /
0012 <A HREF="#ERRORS">ERRORS</A> /
0013 <A HREF="#REFERENCES">REFERENCES</A> /
0014 <A HREF="#NOTES">NOTES</A>
0015 </FONT>
0016 <BR><BR></DIV><HR>
0017
0018
0019 <H2>Vert_diff_mod</H2>
0020 <A NAME="HEADER">
0021 <PRE>
0022 <B>Contact:</B> Isaac Held
0023 <B>Reviewers:</B>
0024
0025 </PRE>
0026 </A>
0027
0028 <A NAME="OVERVIEW">
0029 <HR>
0030 <H4>OVERVIEW</H4>
0031
0032 <PRE>
0033
0034 Adds the tendencies due to vertical diffusion to the tendencies
0035 of model prognostic variables
0036
0037
0038 </PRE>
0039 </A>
0040
0041 <A NAME="DESCRIPTION">
0042
0043 <PRE>
0044
0045 All three dimensional fields are assumed to be (lon, lat, level)
0046 with the third index starting at the top of the model and
0047 ending at the bottom
0048
0049 For tracers, it is the tendency of the mixing ratio (parts
0050 per unit mass) that is computed, not of the density (parts
0051 per unit volume) and analogously for all other fields
0052
0053 If the dependence of the surface heat flux and evaporation
0054 on surface temperature is treated explicitly, then a single
0055 subroutine updates the tendencies of all fields
0056
0057 If the dependence of the surface heat flux and evaporation
0058 on surface temperature is treated implicitly, then interfaces
0059 are provided for dividing the up and down sweeps of the
0060 standard tridiagonal elimination into two parts. One can
0061 visualize this procedure as starting with a downward
0062 sweep through the atmosphere, which continue through the
0063 surface, then re-emerges and continues up the atmosphere.
0064 A sample program is included below to help the user undertand
0065 the approriate calling sequence
0066
0067 Diffusion of heat takes the form of mixing of the "dry static
0068 energy temperature", T + g*z/cp.
0069
0070 Details are provided in <A HREF="vert_diff.tech.ps">vert_diff.tech.ps</A>
0071
0072
0073 </PRE>
0074 </A>
0075
0076 <A NAME="MODULES_USED">
0077 <HR>
0078 <H4>OTHER MODULES USED</H4>
0079
0080 <PRE>
0081
0082 constants_mod
0083 fms_mod
0084 field_manager_mod
0085 tracer_manager_mod
0086
0087 </PRE>
0088 </A>
0089
0090 <A NAME="INTERFACE">
0091 <HR>
0092 <H4>PUBLIC INTERFACE</H4>
0093
0094 <PRE>
0095
0096 use vert_diff_mod [,only: gcm_vert_diff_init , &
0097 gcm_vert_diff_end , &
0098 vert_diff , &
0099 gcm_vert_diff , &
0100 gcm_vert_diff_down , &
0101 gcm_vert_diff_up , &
0102 surf_diff_type
0103
0104
0105 gcm_vert_diff_init : initializes module
0106
0107 gcm_vert_diff_end : clears memory
0108
0109 vert_diff : adds tendency (derivative with respect to time)
0110 due to vertical diffusion to tendencies of a single field --
0111 to be used only if surface flux is not implicitly
0112 dependent on surface parameters (it can be implicit
0113 function of the value within the lowest atmospheric
0114 layer of the field being diffused)
0115
0116 gcm_vert_diff :
0117 adds tendency due to vertical diffusion to tendencies
0118 of temperature, specific humidity, two components of
0119 momentum, and mixing ratios of any # of other tracers,
0120 to be used only if surface fluxes are not implicitly
0121 dependent on surface parameters (the surface heat flux and
0122 evaporation can be implicit functions of atmospheric
0123 temperature and specific humidity, respectively, in the
0124 lowest atmospheric layer). Diffusivities for
0125 specific humidity, heat, and all tracers are assumed to be
0126 equal.
0127
0128 gcm_vert_diff_down : Downward sweep of tridiagonal solver
0129
0130 gcm_vert_diff_up : Upward sweep of tridiagonal solver
0131
0132 surf_diff_type : type defined to hold fields required outside of this
0133 module when the dependence of surface fluxes on surface
0134 temperature is treated implicitly
0135
0136
0137 notes:
0138 1) there is no namelist
0139 2) no data files or restart files are required
0140 3) a line is appended to the file logfile.out if it already exists
0141 containing the version number of the module -- if it does not
0142 exist the file is created in the working directory
0143
0144
0145 </PRE>
0146 </A><!-- END INTERFACE -->
0147 <!--------------------------------------------------------------------->
0148 <A NAME="ROUTINES">
0149 <HR>
0150 <H4>PUBLIC ROUTINES</H4>
0151 <!-- BEGIN ROUTINES -->
0152 <PRE>
0153
0154 ==========================================================================
0155
0156 subroutine gcm_vert_diff_init(Tri_surf, idim, jdim, kdim, &
0157 conserve_energy,
0158 use_virtual_temp_vert_diff,
0159 do_mcm_plev)
0160
0161 integer, intent(in) :: idim, jdim, kdim
0162 the three "global" dimensions of the fields to be diffused,
0163 with kdim being the number of vertical levels;
0164 "global" refers to the entire field residing on a processor
0165
0166 type(surf_diff_type), intent(inout) :: Tri_surf
0167 where data needed outside of module is stored
0168
0169 logical, intent(in) :: conserve_energy
0170 .true. => kinetic energy that is lost due to vertical diffusion
0171 is returned as heat in the temperature tendency so as to
0172 conserve energy
0173
0174 logical, intent(in) :: use_virtual_temp_vert_diff
0175
0176 logical, intent(in) :: do_mcm_plev
0177
0178 ==========================================================================
0179
0180 subroutine gcm_vert_diff_end()
0181
0182 no arguments
0183
0184 ==========================================================================
0185
0186 subroutine vert_diff(delt, xi, t, q, diff, p_half, z_full, &
0187 flux, dflux_datmos, factor, dt_xi, kbot)
0188
0189 input:
0190
0191 delt -- real
0192 time step , seconds
0193 if using leapfrog step, set equal to 2*dt = time(i+1) - time(i-1)
0194
0195 xi -- real, dimension(:,:,:)
0196 field to be diffused,
0197 at time step i for two-time level schemes
0198 at time step i-1 for three-time level (leapfrog) schemes
0199 units up to user
0200
0201 t -- real, dimension(:,:,:)
0202 temperature ( degrees K)
0203 used only for computation of density
0204 shape must conform to that of xi
0205
0206 q -- real, dimension(:,:,:)
0207 specific humidity (dimensionless)
0208 used only for computation of density
0209 shape must conform to that of xi
0210 (set = 0 to ignore effects of vapor on density)
0211
0212 diff -- real, dimension(:,:,:)
0213 kinematic diffusivity (m*2/s)
0214 shape must conform to that of xi
0215 diff(:,:,k) is the diffusivity evaluated at the interface
0216 between the k-1 and k levels
0217 the value diff(:,:,1) is not used
0218
0219 p_half -- real, dimension(:,:,:)
0220 pressure at interface between model levels
0221 size(p_half,3) must = 1 + size(xi,3)
0222 units = Pascals
0223
0224 z_full -- real, dimension(:,:,:)
0225 height of the level where xi is defined
0226 shape must conform to that of xi
0227 units = meters
0228
0229 factor -- real
0230 used if one wants to modify the units of the flux input
0231 The units for flux are [factor]*[xi]*kg/(m**2 s)
0232 where [xi} is the unit for the field xi
0233 Thus, if xi = temperature in K, and if you want to input the
0234 flux in W/(m**2) set factor = heat capacity per unit mass
0235 in (J/(kg K))
0236
0237 dflux_datmos -- real, dimension(:,:)
0238 shape must conform to first two dimensions of xi.
0239 Set = 0.0 if the surface flux is treated explicitly.
0240 If dependence of flux on lowest level of atmosphere is
0241 treated implicitly, set equal to derivative of flux
0242 with respect to value of xi in lowest model layer.
0243 Units = [factor]*kg/(m**2 s)
0244
0245
0246 input/output:
0247
0248 flux -- real, dimension(:,:)
0249 Surface flux (positive upwards)
0250 shape must conform to first two dimensions of xi
0251 Units = [factor]*[xi]*kg/(m**2 s)
0252 Flux should be evaluated with atmospheric fields
0253 from time i for two-time level schemes
0254 from time i-1 for leapgrog
0255 If dflux_datmos is non-zero, input flux is modified by
0256 the implicit correction
0257 flux(i+1) = flux(i or i-1) + delt*dflux_datmos*dt_xi(:,:,N)
0258 where dt_xi is the final (output) tendency and
0259 N = size(dt_xi,3) is the lowest model level
0260
0261 dt_xi -- real, dimension(:,:,:)
0262 Tendency of xi
0263 shape must conform to that of xi
0264 input is the tendency due to all other processes
0265 that have been added prior to this call
0266 output will be the tendency modified by the effects of diffusion
0267 Because the algorithm is implicit, the final tendency
0268 depends on which other processes contribute to
0269 the tendency before, and which after, this call
0270
0271 optional input:
0272
0273 kbot -- integer,dimension(:,:)
0274 shape must conform to first two dimensions of xi
0275
0276 For use with models in which different columns
0277 have different number of levels above the surface.
0278 The levels k <= kbot are assumed to be above the surface.
0279
0280 If kbot is present, the module will function properly
0281 if diff = 0 for levels below the surface. Also, to avoid
0282 division by zero, be sure that the underground
0283 input temperatures are non-zero and that the pressure
0284 thicknesses of the underground layers are non-zero as well.
0285
0286 ==========================================================================
0287
0288 subroutine gcm_vert_diff(delt, u, v, t, q, tr, diff_m, diff_t, &
0289 p_half, z_full, &
0290 dtau_datmos, dsens_datmos, devap_datmos, &
0291 sens, evap, tau_u, tau_v, flux_tr, &
0292 dt_u, dt_v, dt_t, dt_q, dt_tr, dissipative_heat, &
0293 kbot)
0294
0295 input:
0296
0297 delt -- real
0298 time step , seconds
0299 if using leapfrog step, set equal to 2*dt = time(i+1) - time(i-1)
0300
0301 u -- real, dimension(:,:,:) zonal wind (m/sec)
0302 v -- real, dimension(:,:,:) meridional wind (m/sec)
0303 T -- real, dimension(:,:,:) temperature (K)
0304 q -- real, dimension(:,:,:) specific humidity
0305 (non-dimensional -- Kg water/Kg air)
0306 tr -- real, dimension(:,:,:,:) tracers
0307 (units arbitrary)
0308 size(tr,4) = number of tracers
0309
0310 fields to be diffused,
0311 at time step i for two-time level schemes
0312 at time step i-1 for three-time level (leapfrog) schemes
0313 (t and q also used to compute density)
0314
0315 diff_m -- real, dimension(:,:,:)
0316 kinematic diffusivity for momentum (m*2/s)
0317 diff_t -- real, dimension(:,:,:)
0318 kinematic diffusivity for heat, water vapor, tracers (m*2/s)
0319
0320 shape must conform to those of u, v, t, q
0321 diff_m(:,:,k) and dsiff_t(:,:,k) are the diffusivities
0322 evaluated at the interface between the k-1 and k levels
0323 the values diff_m(:,:,1) and diff_m(:,:,1) are not used
0324
0325 p_half -- real, dimension(:,:,:)
0326 pressure at interface between model levels
0327 size(p_half,3) must = 1 + size(t,3)
0328 units = Pascals
0329
0330 z_full -- real, dimension(:,:,:)
0331 height of the levels where t, q, u, v, tr are defined
0332 shape must conform to that of xi
0333 units = meters
0334
0335
0336 dtau_datmos -- real, dimension(:,:)
0337 dsens_datmos -- real, dimension(:,:)
0338 devap_datmos -- real, dimension(:,:)
0339 shape must conform to first two dimensions of input fields
0340 Set = 0.0 if the surface flux is treated explicitly
0341 If dependence of flux on lowest level of atmosphere is
0342 treated implicitly, set
0343
0344 dtau_datmos = derivative of surface stress with respect to
0345 wind component in lowest model layer.
0346 Units = kg/(m**2 s)
0347
0348 dsens_datmos = derivative of surface sensible heat flux
0349 with respect to temperature in lowest model layer.
0350 Units = W/(m**2 K)
0351
0352 devap_datmos = derivative of surface flux of water vapor
0353 with respect to specific humidity in lowest model layer.
0354 Units = kg/(m**2 s)
0355
0356
0357 input/output:
0358
0359 sens, evap, tau_u, tau_v -- real, dimension(:,:)
0360 Surface fluxes (positive upwards)
0361 shape must conform to first two dimensions of input fields
0362
0363 Units: sens : W/(m**2) = J /(m**2 s)
0364 evap : Kg/(m**2 s)
0365 tau_u : Kg/(m s**2) = (Kg m/s)/(m**2 s)
0366 = (Kg/(m**3))((m/s)**2) = Pascals
0367 tau_v : as above
0368
0369 Flux should be evaluated with atmospheric fields
0370 from time i for two-time level schemes
0371 from time i-1 for leapgrog
0372
0373 If dflux_datmos is non-zero, input flux is modified by
0374 the implicit correction to be
0375 flux(i+1) = flux(i or i-1) + delt*dflux_datmos*dt_xi(:,:,N)
0376 where dt_xi is the final (output) tendency and
0377 N is the lowest model level
0378
0379 flux_tr -- real, dimension(:,:,:)
0380 with size(flux,tr_3) = number of tracers
0381 (although listed as inout, the implicit treatment of
0382 tracer fluxes is not implemented here, so the
0383 ouput tracer flux will be identical to the input flux
0384
0385
0386 dt_u, dt_v, dt_t, dt_q -- real, dimension(:,:,:)
0387 Tendency of u, v, t, q
0388 shape must conform to that of u, v etc
0389 input is the tendency due to all other processes
0390 that have been added prior to this call
0391 output will be the tendency modified by the effects of diffusion
0392 Because the algorithm is implicit, the final tendency
0393 depends on which other processes have contributed to
0394 the tendency before, and which after, this call
0395
0396 Units of dt_xi are [xi]/s where [xi] are units of xi
0397
0398 dt_tr -- real, dimension(:,:,:,:)
0399 Tracer tendency (see above) size(dt_tr,4) = number of tracers
0400
0401 output:
0402 dissipative_heat -- real, dimension(:,:,:)
0403 shape must conform to that of u, v, t, etc
0404 units: deg_K/s
0405
0406 (computed when do_conserve_energy = .true.
0407 and added to dt_t before temperature is diffused)
0408
0409 optional input:
0410
0411 kbot -- integer,dimension(:,:)
0412 shape must conform to first two dimensions of xi
0413
0414 For use with models in which different columns
0415 have different number of levels above the surface.
0416 The levels k <= kbot are assumed to be above the surface.
0417
0418 If kbot is present, the interface will function properly
0419 if diff = 0 for levels below the surface. Also, to avoid
0420 division by zero, be sure that the underground
0421 input temperatures are non-zero and that the pressure
0422 thicknesses of the underground layers are non-zero as well.
0423
0424 ==========================================================================
0425
0426 type surf_diff_type
0427
0428 a public type used to store data needed by the
0429 multi-step version of the diffusion algorithm
0430
0431
0432 real, pointer, dimension(:,:) :: dtmass, &
0433 dflux_t, &
0434 dflux_q, &
0435 delta_t, &
0436 delta_q
0437
0438
0439
0440 for full description of these fields, and the rationale for
0441 saving these particular fields,
0442 see <A HREF="vert_diff.tech.ps">vert_diff.tech.ps</A>
0443
0444 dtmass = dt/mass, where dt = atmospheric time step (sec)
0445 ((i+1)-(i-1), not (i+1)-i, if atmos model is leapfrog)
0446 mass = mass of lowest atmospheric layer (Kg/m2)
0447 (defined in gcm_vert_diff_down -- not used elsewhere)
0448
0449 dflux_t = derivative of the temperature flux at the top of the lowest
0450 atmospheric layer with respect to the temperature
0451 of that layer (J/(m2 K))
0452 (defined in gcm_vert_diff_down -- not used elsewhere)
0453
0454 dflux_q = derivative of the flux of specific humidity
0455 at the top of the lowest atmospheric layer with respect to
0456 the specific humidity of that layer (--/(m2 K))
0457 (defined in gcm_vert_diff_down -- not used elsewhere)
0458
0459 delta_t = the increment in temperature in the lowest atmospheric
0460 layer (((i+1)-(i-1) if atmos model is leapfrog) (K)
0461 (defined in gcm_vert_diff_down as the increment computed up
0462 to this point in model, including effect of vertical
0463 diffusive flux at top of lowest model level, presumed
0464 to be modified to include effects of surface fluxes
0465 outside of this module, then used to start upward
0466 tridiagonal sweep,
0467 see <A HREF="vert_diff.tech.ps">vert_diff.tech.ps</A>
0468
0469 delta_q = similarly for the increment in specific humidity
0470 (non-dimensional = Kg/Kg)
0471
0472
0473 ==========================================================================
0474
0475 subroutine gcm_vert_diff_down (is, js, delt, &
0476 u, v, t, q, tr, &
0477 diff_m, diff_t, p_half, p_full, z_full, &
0478 tau_u, tau_v, dtau_datmos, &
0479 flux_tr, &
0480 dt_u, dt_v, dt_t, dt_q, dt_tr, &
0481 dissipative_heat, Tri_surf, &
0482 kbot)
0483
0484 input:
0485
0486 is, js -- integers
0487 the location in the global lon-lat grid of the rectangular
0488 domain on which diffusion is to be performed
0489 the size of the domain is determined by the size ofthe input
0490 i.e, longitude index ranges from is to is + size(t,1) -1
0491 latitude index ranges from js to js + size(t,2) -1
0492
0493 delt -- real
0494 time step , seconds
0495 if using leapfrog step, set equal to 2*dt = time(i+1) - time(i-1)
0496
0497 u -- real, dimension(:,:,:) zonal wind (m/sec)
0498 v -- real, dimension(:,:,:) meridional wind (m/sec)
0499 T -- real, dimension(:,:,:) temperature (K)
0500 q -- real, dimension(:,:,:) specific humidity
0501 (non-dimensional -- Kg water/Kg air)
0502 tr -- real, dimension(:,:,:,:) tracers
0503 (units arbitrary)
0504 size(tr,4) = number of tracers
0505
0506 input fields to be diffused,
0507 values at time step i for two-time level schemes
0508 at time step i-1 for three-time level (leapfrog) schemes
0509 (t and q also used to compute density)
0510
0511 diff_m -- real, dimension(:,:,:)
0512 kinematic diffusivity for momentum (m*2/s)
0513 diff_t -- real, dimension(:,:,:)
0514 kinematic diffusivity for heat, water vapor, tracers (m*2/s)
0515
0516 shape must conform to those of u, v, t, q
0517 diff_m(:,:,k) and dsiff_t(:,:,k) are the diffusivities
0518 evaluated at the interface between the k-1 and k levels
0519 the values diff_m(:,:,1) and diff_m(:,:,1) are not used
0520
0521 p_half -- real, dimension(:,:,:)
0522 pressure at interface between model levels
0523 size(p_half,3) must = 1 + size(t,3)
0524 units = Pascals
0525
0526 p_full -- real, dimension(:,:,:)
0527 pressure at full model levels
0528 size(p_half,3) must = size(t,3)
0529 units = Pascals
0530
0531 z_full -- real, dimension(:,:,:)
0532 height of the levels where t, q, u, v, tr are defined
0533 shape must conform to that of xi
0534 units = meters
0535
0536 dtau_datmos -- real, dimension(:,:)
0537 shape must conform to first two dimensions of input fields
0538 Set = 0.0 if the surface flux is treated explicitly. If
0539 dependence of flux on lowest level of atmosphere is
0540 treated implicitly, set = derivative of surface stress
0541 with respect to wind component in lowest model layer.
0542 Units = kg/(m**2 s)
0543
0544 dt_t, dt_q -- real, dimension(:,:,:)
0545 Tendency of t, q up to this point
0546 (The final value of dt_t and dt_q are output by
0547 gcm_vert_diff_up)
0548 Units are [xi]/s where [xi] = [T], [q]
0549
0550
0551 input/output:
0552
0553 tau_u, tau_v -- real, dimension(:,:)
0554 Surface stresses (positive upwards)
0555 shape must conform to first two dimensions of input fields
0556
0557 Units: Kg/(m s**2) = (Kg m/s)/(m**2 s)
0558 = (Kg/(m**3))((m/s)**2) = Pascals
0559
0560
0561 Flux should be evaluated at time i for two-time level schemes
0562 and at time i-1 for leapgrog
0563 If dtau_datmos is non-zero, input stress is modified by
0564 the implicit correction
0565 tau_u(i+1) = tau_u(i or i-1) + delt*dtau_datmos*dt_u(:,:,N)
0566 where dt_u is the final (output) tendency and
0567 N is the lowest model level; similarly for tau_v
0568
0569 flux_tr -- real, dimension(:,:,:)
0570 with size(flux,tr_3) = number of tracers
0571 (although listed as inout, the implicit treatment of
0572 tracer fluxes is not implemented here, so the
0573 ouput tracer flux will be identical to the input flux
0574
0575
0576 dt_u, dt_v, -- real, dimension(:,:,:)
0577 Tendency of u and v
0578 shape must conform to that of u, v etc
0579 input is the tendency due to all other processes
0580 that have been added prior to this call
0581 output will be the tendency modified by the
0582 effects of diffusion
0583 Units are [xi]/s where [xi] = [u], [v] etc
0584
0585 dt_tr -- real, dimension(:,:,:,:)
0586 Tracer tendency (see above) size(dt_tr,4) = number of tracer
0587
0588 Tri_surf -- type(surf_diff_type)
0589 information needed to pass
0590 => surface modules => gcm_vert_diff_up
0591
0592 output:
0593
0594 dissipative_heat -- real, dimension(:,:,:)
0595 shape must conform to that of u, v, t, etc
0596 units: deg_K/s
0597
0598 (computed when do_conserve_energy = .true.
0599 and added to dt_t before temperature is diffused)
0600
0601 optional input:
0602
0603 kbot -- integer,dimension(:,:)
0604 shape must conform to first two dimensions of xi
0605
0606 For use with models in which different columns
0607 have different number of levels above the surface.
0608 The levels k <= kbot are assumed to be above the surface.
0609
0610 If kbot is present, the interface will function properly
0611 if diff = 0 for levels below the surface. Also, to avoid
0612 division by zero, be sure that the underground
0613 input temperatures are non-zero and that the pressure
0614 thicknesses of the underground layers are non-zero as well.
0615
0616 ==========================================================================
0617
0618 subroutine gcm_vert_diff_up (is, js, delt, Tri_surf, dt_t, dt_q, kbot)
0619
0620 input:
0621
0622 is, js -- integers
0623 the location in the global lon-lat grid of the rectangular
0624 domain on which diffusion is to be performed
0625 the size of the domain is determined by the size ofthe input
0626 i.e, longitude index ranges from is to is + size(dt_t,1) -1
0627 latitude index ranges from js to js + size(dt_t,2) -1
0628
0629 delt -- real
0630 time step , seconds
0631 if using leapfrog step, set equal to 2*dt = time(i+1) - time(i-1)
0632
0633 Tri_surf -- type(surf_diff_type)
0634 information passed from information
0635 surface modules and gcm_vert_diff_down
0636
0637
0638 dt_t, dt_q -- real, dimension(:,:,:)
0639
0640 The tendencies modified by the effects of diffusion
0641 Because the algorithm is implicit, the final tendency
0642 depends on which other processes have contributed to
0643 the tendency before, and which after, this call
0644
0645 Units of dt_xi are [xi]/s where [xi] are units of xi
0646
0647 optional input:
0648
0649 kbot -- integer,dimension(:,:)
0650 shape must conform to first two dimensions of xi
0651
0652 For use with models in which different columns
0653 have different number of levels above the surface.
0654 The levels k <= kbot are assumed to be above the surface.
0655
0656 If kbot is present, the interface will function properly
0657 if diff = 0 for levels below the surface. Also, to avoid
0658 division by zero, be sure that the underground
0659 input temperatures are non-zero and that the pressure
0660 thicknesses of the underground layers are non-zero as well.
0661
0662 ==========================================================================
0663
0664 subroutine gcm_vert_diff_end
0665
0666 </PRE>
0667 </A>
0668
0669 <A NAME="CHANGES">
0670 <HR>
0671 <H4>CHANGE HISTORY</H4>
0672
0673 <PRE>
0674
0675
0676 <b>Changes prior to the CVS revision history</b>
0677
0678 v1.1 incorporates parts of v1.0 of tq_surf_flux_mod so as
0679 to centralize all parts of the code that are related to
0680 the implicit vertical diffusion
0681
0682 The code has been reorganized substantially from v1.0 but
0683 the algorithm has not changed
0684
0685
0686 </PRE>
0687 </A>
0688
0689 <A NAME="NOTES">
0690 <HR>
0691 <H4>NOTES</H4>
0692
0693 <PRE>
0694
0695 A pseudo-program using the multistep algorithm:
0696
0697 do atmospheric loop
0698 call gcm_vert_diff_down
0699 end do
0700
0701 call surface modules
0702
0703 do atmospheric loop
0704 call gcm_vert_diff_up
0705 end do
0706
0707 </PRE>
0708 </A>
0709
0710 <A NAME="PLANS">
0711 <HR>
0712 <H4>FUTURE PLANS</H4>
0713
0714 <PRE>
0715
0716 (??)
0717
0718 </PRE>
0719 </A>
0720
0721
0722 <HR>
0723 </BODY>
0724 </HTML>
