PUBLIC INTERFACE / DATA / ROUTINES / NAMELIST / DIAGNOSTICS / CHANGES / ERRORS / REFERENCES / NOTES

## Vert_diff_mod

         Contact:   Isaac Held
         Reviewers:

#### OVERVIEW

         Adds the tendencies due to vertical diffusion to the tendencies
         of model prognostic variables

         All three dimensional fields are assumed to be (lon, lat, level)
          with the third index starting at the top of the model and
          ending at the bottom

         For tracers, it is the tendency of the mixing ratio (parts
            per unit mass) that is computed, not of the density (parts
            per unit volume) and analogously for all other fields

         If the dependence of the surface heat flux and evaporation
           on surface temperature is treated explicitly, then a single
           subroutine updates the tendencies of all fields

         If the dependence of the surface heat flux and evaporation
           on surface temperature is treated implicitly, then interfaces
           are provided for dividing the up and down sweeps of the
           standard tridiagonal elimination into two parts.  One can
           visualize this procedure as starting with a downward
           sweep through the atmosphere, which continue through the
           surface, then re-emerges and continues up the atmosphere.
           A sample program is included below to help the user undertand
           the approriate calling sequence

         Diffusion of heat takes the form of mixing of the "dry static
           energy temperature", T + g*z/cp.

         Details are provided in vert_diff.tech.ps

#### OTHER MODULES USED

         constants_mod
         fms_mod
         field_manager_mod
         tracer_manager_mod

#### PUBLIC INTERFACE

      use vert_diff_mod [,only: gcm_vert_diff_init       , &
                                gcm_vert_diff_end        , &
                                vert_diff                , &
                                gcm_vert_diff            , &
                                gcm_vert_diff_down       , &
                                gcm_vert_diff_up         , &
                                surf_diff_type

      gcm_vert_diff_init : initializes module

      gcm_vert_diff_end : clears memory

      vert_diff : adds tendency (derivative with respect to time)
                  due to vertical diffusion to tendencies of a single field --
                  to be used only if surface flux is not implicitly
                  dependent on surface parameters (it can be implicit
                  function of the value within the lowest atmospheric
                  layer of the field being diffused)

      gcm_vert_diff  :
                  adds tendency due to vertical diffusion to tendencies
                  of temperature, specific humidity, two components of
                  momentum, and mixing ratios of any # of other tracers,
                  to be used only if surface fluxes are not implicitly
                  dependent on surface parameters (the surface heat flux and
                  evaporation can be implicit functions of atmospheric
                  temperature and specific humidity, respectively, in the
                  lowest atmospheric layer).  Diffusivities for
                  specific humidity, heat, and all tracers are assumed to be
                  equal.

      gcm_vert_diff_down :  Downward sweep of tridiagonal solver

      gcm_vert_diff_up   :  Upward sweep of tridiagonal solver

      surf_diff_type : type defined to hold fields required outside of this
                       module when the dependence of surface fluxes on surface
                       temperature is treated implicitly

    notes:
     1) there is no namelist
     2) no data files or restart files are required
     3) a line is appended to the file logfile.out if it already exists
        containing the version number of the module -- if it does not
        exist the file is created in the working directory

#### PUBLIC ROUTINES

    ==========================================================================

     subroutine gcm_vert_diff_init(Tri_surf, idim, jdim, kdim, &
                                   conserve_energy,
    			       use_virtual_temp_vert_diff,
    			       do_mcm_plev)

        integer, intent(in)  :: idim, jdim, kdim
            the three "global" dimensions of the fields to be diffused,
            with kdim being the number of vertical levels;
            "global" refers to the entire field residing on a processor

        type(surf_diff_type), intent(inout) :: Tri_surf
            where data needed outside of module is stored

        logical, intent(in) :: conserve_energy
             .true. => kinetic energy that is lost due to vertical diffusion
    	 is returned as heat in the temperature tendency so as to
    	 conserve energy

        logical, intent(in) :: use_virtual_temp_vert_diff

        logical, intent(in) :: do_mcm_plev

    ==========================================================================

     subroutine gcm_vert_diff_end()

            no arguments

    ==========================================================================

     subroutine vert_diff(delt, xi, t, q, diff, p_half, z_full, &
                    flux, dflux_datmos, factor, dt_xi, kbot)

        input:

             delt -- real
               time step , seconds
               if using leapfrog step, set equal to 2*dt = time(i+1) - time(i-1)

             xi -- real, dimension(:,:,:)
                field to be diffused,
                      at time step i   for   two-time level schemes
                      at time step i-1 for three-time level (leapfrog) schemes
                   units up to user

             t -- real, dimension(:,:,:)
                temperature ( degrees K)
                  used only for computation of density
                  shape must conform to that of xi

             q -- real, dimension(:,:,:)
                specific humidity (dimensionless)
                  used only for computation of density
                  shape must conform to that of xi
                  (set = 0 to ignore effects of vapor on density)

             diff -- real, dimension(:,:,:)
                 kinematic diffusivity (m*2/s)
                 shape must conform to that of xi
                 diff(:,:,k) is the diffusivity evaluated at the interface
                     between the k-1 and k levels
                 the value diff(:,:,1) is not used

             p_half -- real, dimension(:,:,:)
                 pressure at interface between model levels
                 size(p_half,3) must = 1 + size(xi,3)
                 units = Pascals

             z_full -- real, dimension(:,:,:)
                 height of the level where xi is defined
                 shape must conform to that of xi
                 units = meters

             factor -- real
                 used if one wants to modify the units of the flux input
                 The units for flux are [factor]*[xi]*kg/(m**2 s)
                    where [xi} is the unit for the field xi
                 Thus, if xi = temperature in K, and if you want to input the
                   flux in W/(m**2) set factor = heat capacity per unit mass
                   in (J/(kg K))

             dflux_datmos -- real, dimension(:,:)
                 shape must conform to first two dimensions of xi.
                 Set = 0.0 if the surface flux is treated explicitly.
                 If dependence of flux on lowest level of atmosphere is
                 treated implicitly, set equal to derivative of flux
                 with respect to value of xi in lowest model layer.
                 Units = [factor]*kg/(m**2 s)

        input/output:

             flux -- real, dimension(:,:)
                 Surface flux (positive upwards)
                 shape must conform to first two dimensions of xi
                 Units = [factor]*[xi]*kg/(m**2 s)
                 Flux should be evaluated with atmospheric fields
                         from time i   for two-time level schemes
                         from time i-1 for leapgrog
                 If dflux_datmos is non-zero, input flux is modified by
                 the implicit correction
                     flux(i+1) = flux(i or i-1) + delt*dflux_datmos*dt_xi(:,:,N)
                     where dt_xi is the final (output) tendency and
                     N = size(dt_xi,3) is the lowest model level

             dt_xi -- real, dimension(:,:,:)
                 Tendency of xi
                 shape must conform to that of xi
                 input is the tendency due to all other processes
                     that have been added prior to this call
                 output will be the tendency modified by the effects of diffusion
                 Because the algorithm is implicit, the final tendency
                    depends on which other processes contribute to
                    the tendency before, and which after, this call

         optional input:

              kbot -- integer,dimension(:,:)
                 shape must conform to first two dimensions of xi

                 For use with models in which different columns
                 have different number of levels above the surface.
                 The levels k <= kbot are assumed to be above the surface.

                 If kbot is present, the module will function properly
                 if  diff = 0 for levels below the surface. Also, to avoid
                 division by zero, be sure that the underground
                 input temperatures are non-zero and that the pressure
                 thicknesses of the underground layers are non-zero as well.

    ==========================================================================

     subroutine  gcm_vert_diff(delt, u, v, t, q, tr, diff_m, diff_t,     &
                        p_half, z_full,                                  &
                        dtau_du, dtau_dv, dsens_datmos, devap_datmos,    &
                        sens, evap, tau_u, tau_v, flux_tr,               &
                        dt_u, dt_v, dt_t, dt_q, dt_tr, dissipative_heat, &
    		    kbot)

        input:

             delt -- real
               time step , seconds
               if using leapfrog step, set equal to 2*dt = time(i+1) - time(i-1)

             u -- real, dimension(:,:,:)   zonal wind (m/sec)
             v -- real, dimension(:,:,:)   meridional wind (m/sec)
             T -- real, dimension(:,:,:)   temperature  (K)
             q -- real, dimension(:,:,:)   specific humidity
                                             (non-dimensional -- Kg water/Kg air)
             tr -- real, dimension(:,:,:,:) tracers
                                              (units arbitrary)
                                            size(tr,4) = number of tracers

                  fields to be diffused,
                      at time step i   for   two-time level schemes
                      at time step i-1 for three-time level (leapfrog) schemes
                  (t and q also used to compute density)

             diff_m -- real, dimension(:,:,:)
                 kinematic diffusivity for momentum (m*2/s)
             diff_t -- real, dimension(:,:,:)
                 kinematic diffusivity for heat, water vapor, tracers (m*2/s)

                 shape must conform to those of u, v, t, q
                 diff_m(:,:,k) and dsiff_t(:,:,k) are the diffusivities
                     evaluated at the interface between the k-1 and k levels
                 the values diff_m(:,:,1) and diff_m(:,:,1) are not used

             p_half -- real, dimension(:,:,:)
                 pressure at interface between model levels
                 size(p_half,3) must = 1 + size(t,3)
                 units = Pascals

             z_full -- real, dimension(:,:,:)
                 height of the levels where t, q, u, v, tr are defined
                 shape must conform to that of xi
                 units = meters

             dtau_du  -- real, dimension(:,:)
             dtau_dv  -- real, dimension(:,:)
             dsens_datmos -- real, dimension(:,:)
             devap_datmos -- real, dimension(:,:)
                 shape must conform to first two dimensions of input fields
                 Set = 0.0 if the surface flux is treated explicitly
                 If dependence of flux on lowest level of atmosphere is
                 treated implicitly, set

                    dtau_du = derivative of surface stress with respect to
                         zonal wind component in lowest model layer.
                         Units = kg/(m**2 s)

                    dtau_dv = derivative of surface stress with respect to
                         meridional wind component in lowest model layer.
                         Units = kg/(m**2 s)

                    dsens_datmos = derivative of surface sensible heat flux
                         with respect to temperature in lowest model layer.
                         Units = W/(m**2 K)

                    devap_datmos = derivative of surface flux of water vapor
                         with respect to specific humidity in lowest model layer.
                         Units = kg/(m**2 s)

        input/output:

             sens, evap, tau_u, tau_v -- real, dimension(:,:)
                 Surface fluxes (positive upwards)
                 shape must conform to first two dimensions of input fields

                 Units:  sens   : W/(m**2) = J /(m**2 s)
                         evap   : Kg/(m**2 s)
                         tau_u  : Kg/(m s**2) = (Kg m/s)/(m**2 s)
                                   = (Kg/(m**3))((m/s)**2) = Pascals
                         tau_v  : as above

                 Flux should be evaluated with atmospheric fields
                         from time i   for two-time level schemes
                         from time i-1 for leapgrog

                 If dflux_datmos is non-zero, input flux is modified by
                 the implicit correction to be
                     flux(i+1) = flux(i or i-1) + delt*dflux_datmos*dt_xi(:,:,N)
                     where dt_xi is the final (output) tendency and
                     N is the lowest model level

             flux_tr -- real, dimension(:,:,:)
                       with size(flux,tr_3) = number of tracers
                       (although listed as inout, the implicit treatment of
                        tracer fluxes is not implemented here, so the
                        ouput tracer flux will be identical to the input flux

             dt_u, dt_v, dt_t, dt_q -- real, dimension(:,:,:)
                 Tendency of u, v, t, q
                 shape must conform to that of u, v etc
                 input is the tendency due to all other processes
                     that have been added prior to this call
                 output will be the tendency modified by the effects of diffusion
                 Because the algorithm is implicit, the final tendency
                    depends on which other processes have contributed to
                    the tendency before, and which after, this call

                 Units of dt_xi are [xi]/s where [xi] are units of xi

             dt_tr -- real, dimension(:,:,:,:)
                 Tracer tendency (see above)  size(dt_tr,4) = number of tracers

         output:
             dissipative_heat -- real, dimension(:,:,:)
                 shape must conform to that of u, v, t, etc
    	     units: deg_K/s

    	     (computed when do_conserve_energy = .true.
    	      and added to dt_t before temperature is diffused)

         optional input:

              kbot -- integer,dimension(:,:)
                 shape must conform to first two dimensions of xi

                 For use with models in which different columns
                 have different number of levels above the surface.
                 The levels k <= kbot are assumed to be above the surface.

                 If kbot is present, the interface will function properly
                 if  diff = 0 for levels below the surface. Also, to avoid
                 division by zero, be sure that the underground
                 input temperatures are non-zero and that the pressure
                 thicknesses of the underground layers are non-zero as well.

    ==========================================================================

     type surf_diff_type

       a public type used to store data needed by the
           multi-step version of the diffusion algorithm

      real, pointer, dimension(:,:) :: dtmass,    &
                                       dflux_t,   &
                                       dflux_q,   &
                                       delta_t,   &
                                       delta_q

            for full description of these fields, and the rationale for
                  saving these particular fields,
                     see  vert_diff.tech.ps

         dtmass = dt/mass, where dt = atmospheric time step (sec)
                  ((i+1)-(i-1), not (i+1)-i, if atmos model is leapfrog)
                  mass = mass of lowest atmospheric layer (Kg/m2)
                  (defined in gcm_vert_diff_down -- not used elsewhere)

         dflux_t = derivative of the temperature flux at the top of the lowest
                   atmospheric layer with respect to the temperature
                   of that layer  (J/(m2 K))
                   (defined in gcm_vert_diff_down -- not used elsewhere)

         dflux_q = derivative of the flux of specific humidity
                   at the top of the lowest atmospheric layer with respect to
                   the specific humidity of that layer  (--/(m2 K))
                   (defined in gcm_vert_diff_down -- not used elsewhere)

         delta_t = the increment in temperature in the lowest atmospheric
                   layer (((i+1)-(i-1) if atmos model is leapfrog) (K)
                   (defined in  gcm_vert_diff_down as the increment computed up
                   to this point in model, including effect of vertical
                   diffusive flux at top of lowest model level, presumed
                   to be modified to include effects of surface fluxes
                   outside of this module, then used to start upward
                   tridiagonal sweep,
                   see  vert_diff.tech.ps

         delta_q = similarly for the increment in specific humidity
                    (non-dimensional  = Kg/Kg)

    ==========================================================================

     subroutine gcm_vert_diff_down (is, js, delt,                              &
                              u, v, t, q, tr,                                  &
                              diff_m, diff_t, p_half, p_full, z_full,          &
                              tau_u, tau_v, dtau_du, dtau_dv,                  &
                              flux_tr,                                         &
                              dt_u, dt_v, dt_t, dt_q, dt_tr,                   &
                              dissipative_heat, Tri_surf,                      &
                              kbot)

        input:

             is, js -- integers
                 the location in the global lon-lat grid of the rectangular
                 domain on which diffusion is to be performed
                 the size of the domain is determined by the size ofthe input
                 i.e, longitude index ranges from is to is + size(t,1) -1
                       latitude index ranges from js to js + size(t,2) -1

             delt -- real
               time step , seconds
               if using leapfrog step, set equal to 2*dt = time(i+1) - time(i-1)

             u -- real, dimension(:,:,:)   zonal wind (m/sec)
             v -- real, dimension(:,:,:)   meridional wind (m/sec)
             T -- real, dimension(:,:,:)   temperature  (K)
             q -- real, dimension(:,:,:)   specific humidity
                                             (non-dimensional -- Kg water/Kg air)
             tr -- real, dimension(:,:,:,:) tracers
                                              (units arbitrary)
                                            size(tr,4) = number of tracers

                  input fields to be diffused,
                      values at time step i   for   two-time level schemes
                      at time step i-1 for three-time level (leapfrog) schemes
                  (t and q also used to compute density)

             diff_m -- real, dimension(:,:,:)
                 kinematic diffusivity for momentum (m*2/s)
             diff_t -- real, dimension(:,:,:)
                 kinematic diffusivity for heat, water vapor, tracers (m*2/s)

                 shape must conform to those of u, v, t, q
                 diff_m(:,:,k) and dsiff_t(:,:,k) are the diffusivities
                     evaluated at the interface between the k-1 and k levels
                 the values diff_m(:,:,1) and diff_m(:,:,1) are not used

             p_half -- real, dimension(:,:,:)
                 pressure at interface between model levels
                 size(p_half,3) must = 1 + size(t,3)
                 units = Pascals

             p_full -- real, dimension(:,:,:)
                 pressure at full model levels
                 size(p_half,3) must = size(t,3)
                 units = Pascals

             z_full -- real, dimension(:,:,:)
                 height of the levels where t, q, u, v, tr are defined
                 shape must conform to that of xi
                 units = meters

    	 dtau_du, dtau_dv  -- real, dimension(:,:)
    	     shape must conform to first two dimensions of input fields
    	     Set = 0.0 if the surface flux is treated explicitly. If
    	     dependence of flux on lowest level of atmosphere is
    	     treated implicitly, set = derivatives of surface stress
    	     with respect to wind components in lowest model layer.
                 Units = kg/(m**2 s)

            dt_t, dt_q -- real, dimension(:,:,:)
                 Tendency of t, q  up to this point
                 (The final value of dt_t and dt_q are output by
                  gcm_vert_diff_up)
                 Units are [xi]/s where [xi] = [T], [q]

        input/output:

             tau_u, tau_v -- real, dimension(:,:)
                 Surface stresses (positive upwards)
                 shape must conform to first two dimensions of input fields

                 Units:  Kg/(m s**2) = (Kg m/s)/(m**2 s)
                                   = (Kg/(m**3))((m/s)**2) = Pascals

                 Flux should be evaluated at time i   for two-time level schemes
                                       and at time i-1 for leapgrog
                 If dtau_du or dtau_dv is non-zero, input stress is modified by
                 the implicit correction
                     tau_u(i+1) = tau_u(i or i-1) + delt*dtau_du*dt_u(:,:,N)
                     where dt_u is the final (output) tendency and
                     N is the lowest model level; similarly for tau_v

             flux_tr -- real, dimension(:,:,:)
                       with size(flux,tr_3) = number of tracers
                       (although listed as inout, the implicit treatment of
                        tracer fluxes is not implemented here, so the
                        ouput tracer flux will be identical to the input flux

             dt_u, dt_v,  -- real, dimension(:,:,:)
                 Tendency of u and v
                 shape must conform to that of u, v etc
                 input is the tendency due to all other processes
                     that have been added prior to this call
                 output will be the tendency modified by the
                     effects of diffusion
                 Units are [xi]/s where [xi] = [u], [v] etc

            dt_tr -- real, dimension(:,:,:,:)
                 Tracer tendency (see above)  size(dt_tr,4) = number of tracer

            Tri_surf -- type(surf_diff_type)
                 information needed to pass
                   => surface modules => gcm_vert_diff_up

         output:

            dissipative_heat -- real, dimension(:,:,:)
                 shape must conform to that of u, v, t, etc
    	     units: deg_K/s

    	     (computed when do_conserve_energy = .true.
    	      and added to dt_t before temperature is diffused)

         optional input:

              kbot -- integer,dimension(:,:)
                 shape must conform to first two dimensions of xi

                 For use with models in which different columns
                 have different number of levels above the surface.
                 The levels k <= kbot are assumed to be above the surface.

                 If kbot is present, the interface will function properly
                 if  diff = 0 for levels below the surface. Also, to avoid
                 division by zero, be sure that the underground
                 input temperatures are non-zero and that the pressure
                 thicknesses of the underground layers are non-zero as well.

    ==========================================================================

    subroutine gcm_vert_diff_up (is, js, delt, Tri_surf, dt_t, dt_q, kbot)

       input:

             is, js -- integers
                 the location in the global lon-lat grid of the rectangular
                 domain on which diffusion is to be performed
                 the size of the domain is determined by the size ofthe input
                 i.e, longitude index ranges from is to is + size(dt_t,1) -1
                       latitude index ranges from js to js + size(dt_t,2) -1

             delt -- real
               time step , seconds
               if using leapfrog step, set equal to 2*dt = time(i+1) - time(i-1)

             Tri_surf -- type(surf_diff_type)
                 information passed from  information
                   surface modules and gcm_vert_diff_down

             dt_t, dt_q -- real, dimension(:,:,:)

                 The tendencies modified by the effects of diffusion
                 Because the algorithm is implicit, the final tendency
                    depends on which other processes have contributed to
                    the tendency before, and which after, this call

                 Units of dt_xi are [xi]/s where [xi] are units of xi

         optional input:

              kbot -- integer,dimension(:,:)
                 shape must conform to first two dimensions of xi

                 For use with models in which different columns
                 have different number of levels above the surface.
                 The levels k <= kbot are assumed to be above the surface.

                 If kbot is present, the interface will function properly
                 if  diff = 0 for levels below the surface. Also, to avoid
                 division by zero, be sure that the underground
                 input temperatures are non-zero and that the pressure
                 thicknesses of the underground layers are non-zero as well.

    ==========================================================================

    subroutine gcm_vert_diff_end

#### CHANGE HISTORY

    Changes prior to the CVS revision history

         v1.1 incorporates parts of v1.0 of tq_surf_flux_mod so as
                to centralize all parts of the code that are related to
                the implicit vertical diffusion

         The code has been reorganized substantially from v1.0 but
                the algorithm has not changed

#### NOTES

         A pseudo-program using the multistep algorithm:

             do atmospheric loop
                 call gcm_vert_diff_down
             end do

             call surface modules

             do atmospheric loop
                 call gcm_vert_diff_up
             end do

#### FUTURE PLANS

         (??)