source: palm/trunk/SOURCE/plant_canopy_model_mod.f90 @ 4377

!> @file plant_canopy_model_mod.f90
!------------------------------------------------------------------------------!
! This file is part of the PALM model system.
!
! PALM is free software: you can redistribute it and/or modify it under the
! terms of the GNU General Public License as published by the Free Software
! Foundation, either version 3 of the License, or (at your option) any later
! version.
!
! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
! A PARTICULAR PURPOSE.  See the GNU General Public License for more details.
!
! You should have received a copy of the GNU General Public License along with
! PALM. If not, see <http://www.gnu.org/licenses/>.
!
! Copyright 1997-2020 Leibniz Universitaet Hannover
! Copyright 2017-2019 Institute of Computer Science of the
!                     Czech Academy of Sciences, Prague
!------------------------------------------------------------------------------!
!
! Current revisions:
! ------------------
! 
! 
! Former revisions:
! -----------------
! $Id: plant_canopy_model_mod.f90 4363 2020-01-07 18:11:28Z gronemeier $
! Fix for last commit
! 
! 4362 2020-01-07 17:15:02Z suehring
! Input of plant canopy variables from static driver moved to plant-canopy 
! model
! 
! 4361 2020-01-07 12:22:38Z suehring
! - Remove unused arrays in pmc_rrd_local
! - Remove one exchange of ghost points
! 
! 4360 2020-01-07 11:25:50Z suehring
! - Bugfix, read restart data for time-averaged pcm output quantities
! - Output of plant-canopy quantities will fill values
! 
! 4356 2019-12-20 17:09:33Z suehring
! Correct single message call, local check must be given by the respective
! mpi rank.
! 
! 4346 2019-12-18 11:55:56Z motisi
! Introduction of wall_flags_total_0, which currently sets bits based on static
! topography information used in wall_flags_static_0
! 
! 4342 2019-12-16 13:49:14Z Giersch
! Use statements moved to module level, ocean dependency removed, redundant
! variables removed
! 
! 4341 2019-12-16 10:43:49Z motisi
! - Unification of variable names: pc_-variables now pcm_-variables 
!   (pc_latent_rate, pc_heating_rate, pc_transpiration_rate)
! - Removal of pcm_bowenratio output
! - Renamed canopy-mode 'block' to 'homogeneous'
! - Renamed value 'read_from_file_3d' to 'read_from_file'
! - Removal of confusing comment lines
! - Replacement of k_wall by topo_top_ind
! - Removal of Else-Statement in tendency-calculation
! 
! 4335 2019-12-12 16:39:05Z suehring
! Fix for LAD at building edges also implemented in vector branch.
! 
! 4331 2019-12-10 18:25:02Z suehring
! Typo corrected
! 
! 4329 2019-12-10 15:46:36Z motisi
! Renamed wall_flags_0 to wall_flags_static_0
! 
! 4314 2019-11-29 10:29:20Z suehring
! - Bugfix, plant canopy was still considered at building edges on for the u- 
!   and v-component.
! - Relax restriction of LAD on building tops. LAD is only omitted at 
!   locations where building grid points emerged artificially by the 
!   topography filtering.
! 
! 4309 2019-11-26 18:49:59Z suehring
! Typo
! 
! 4302 2019-11-22 13:15:56Z suehring
! Omit tall canopy mapped on top of buildings
! 
! 4279 2019-10-29 08:48:17Z scharf
! unused variables removed
! 
! 4258 2019-10-07 13:29:08Z scharf
! changed check for static driver and fixed bugs in initialization and header
! 
! 4258 2019-10-07 13:29:08Z suehring
! Check if any LAD is prescribed when plant-canopy model is applied.
! 
! 4226 2019-09-10 17:03:24Z suehring
! Bugfix, missing initialization of heating rate
! 
! 4221 2019-09-09 08:50:35Z suehring
! Further bugfix in 3d data output for plant canopy
! 
! 4216 2019-09-04 09:09:03Z suehring
! Bugfixes in 3d data output
! 
! 4205 2019-08-30 13:25:00Z suehring
! Missing working precision + bugfix in calculation of wind speed
! 
! 4188 2019-08-26 14:15:47Z suehring
! Minor adjustment in error number
! 
! 4187 2019-08-26 12:43:15Z suehring
! Give specific error numbers instead of PA0999
! 
! 4182 2019-08-22 15:20:23Z scharf
! Corrected "Former revisions" section
! 
! 4168 2019-08-16 13:50:17Z suehring
! Replace function get_topography_top_index by topo_top_ind
! 
! 4127 2019-07-30 14:47:10Z suehring
! Output of 3D plant canopy variables changed. It is now relative to the local
! terrain rather than located at the acutal vertical level in the model. This 
! way, the vertical dimension of the output can be significantly reduced. 
! (merge from branch resler) 
! 
! 3885 2019-04-11 11:29:34Z kanani
! Changes related to global restructuring of location messages and introduction 
! of additional debug messages
! 
! 3864 2019-04-05 09:01:56Z monakurppa
! unsed variables removed
! 
! 3745 2019-02-15 18:57:56Z suehring
! Bugfix in transpiration, floating invalid when temperature 
! becomes > 40 degrees
! 
! 3744 2019-02-15 18:38:58Z suehring
! Some interface calls moved to module_interface + cleanup
! 
! 3655 2019-01-07 16:51:22Z knoop
! unused variables removed
!
! 138 2007-11-28 10:03:58Z letzel
! Initial revision
!
! Description:
! ------------
!> 1) Initialization of the canopy model, e.g. construction of leaf area density 
!> profile (subroutine pcm_init).
!> 2) Calculation of sinks and sources of momentum, heat and scalar concentration 
!> due to canopy elements (subroutine pcm_tendency).
!
! @todo - precalculate constant terms in pcm_calc_transpiration_rate
! @todo - unify variable names (pcm_, pc_, ...)
!------------------------------------------------------------------------------!
 MODULE plant_canopy_model_mod

    USE arrays_3d,                                                             &
        ONLY:  dzu, dzw, e, exner, hyp, pt, q, s, tend, u, v, w, zu, zw

    USE basic_constants_and_equations_mod,                                     &
        ONLY:  c_p, degc_to_k, l_v, lv_d_cp, r_d, rd_d_rv

    USE bulk_cloud_model_mod,                                                  &
        ONLY: bulk_cloud_model, microphysics_seifert

    USE control_parameters,                                                    &
        ONLY: average_count_3d,                                                &
              coupling_char,                                                   &
              debug_output,                                                    &
              dt_3d,                                                           &
              dz,                                                              &
              humidity,                                                        &
              length,                                                          &
              message_string,                                                  &
              ocean_mode,                                                      &
              passive_scalar,                                                  &
              plant_canopy,                                                    &
              restart_string,                                                  &
              urban_surface

    USE grid_variables,                                                        &
        ONLY:  dx, dy

    USE indices,                                                               &
        ONLY:  nbgp, nxl, nxlg, nxlu, nxr, nxrg, nyn, nyng, nys, nysg, nysv,   &
               nz, nzb, nzt, topo_top_ind, wall_flags_total_0

    USE kinds

    USE netcdf_data_input_mod,                                                 &
        ONLY:  input_pids_static,                                              &
               char_fill,                                                      &
               check_existence,                                                &
               close_input_file,                                               &
               get_attribute,                                                  &
               get_dimension_length,                                           &
               get_variable,                                                   &
               inquire_num_variables,                                          &
               inquire_variable_names,                                         &
               input_file_static,                                              &
               num_var_pids,                                                   &
               open_read_file,                                                 &
               pids_id,                                                        &
               real_3d,                                                        &
               vars_pids

    USE pegrid

    USE surface_mod,                                                           &
        ONLY: surf_def_h, surf_lsm_h, surf_usm_h


    IMPLICIT NONE

    CHARACTER (LEN=30)   ::  canopy_mode = 'homogeneous'           !< canopy coverage
    LOGICAL              ::  plant_canopy_transpiration = .FALSE.  !< flag to switch calculation of transpiration and corresponding latent heat
                                                                   !< for resolved plant canopy inside radiation model
                                                                   !< (calls subroutine pcm_calc_transpiration_rate from module plant_canopy_mod)

    INTEGER(iwp) ::  pch_index = 0                                 !< plant canopy height/top index
    INTEGER(iwp) ::  lad_vertical_gradient_level_ind(10) = -9999   !< lad-profile levels (index)

    INTEGER(iwp), DIMENSION(:,:), ALLOCATABLE ::  pch_index_ji     !< local plant canopy top

    LOGICAL ::  calc_beta_lad_profile = .FALSE.   !< switch for calc. of lad from beta func.

    REAL(wp) ::  alpha_lad = 9999999.9_wp         !< coefficient for lad calculation
    REAL(wp) ::  beta_lad = 9999999.9_wp          !< coefficient for lad calculation
    REAL(wp) ::  canopy_drag_coeff = 0.0_wp       !< canopy drag coefficient (parameter)
    REAL(wp) ::  cthf = 0.0_wp                    !< canopy top heat flux
    REAL(wp) ::  dt_plant_canopy = 0.0_wp         !< timestep account. for canopy drag
    REAL(wp) ::  ext_coef = 0.6_wp                !< extinction coefficient
    REAL(wp) ::  lad_surface = 0.0_wp             !< lad surface value
    REAL(wp) ::  lai_beta = 0.0_wp                !< leaf area index (lai) for lad calc.
    REAL(wp) ::  leaf_scalar_exch_coeff = 0.0_wp  !< canopy scalar exchange coeff.
    REAL(wp) ::  leaf_surface_conc = 0.0_wp       !< leaf surface concentration

    REAL(wp) ::  lad_vertical_gradient(10) = 0.0_wp              !< lad gradient
    REAL(wp) ::  lad_vertical_gradient_level(10) = -9999999.9_wp !< lad-prof. levels (in m)

    REAL(wp) ::  lad_type_coef(0:10) = 1.0_wp   !< multiplicative coeficients for particular types
                                                !< of plant canopy (e.g. deciduous tree during winter)

    REAL(wp), DIMENSION(:), ALLOCATABLE ::  lad            !< leaf area density
    REAL(wp), DIMENSION(:), ALLOCATABLE ::  pre_lad        !< preliminary lad
    
    REAL(wp), DIMENSION(:,:,:), ALLOCATABLE ::  cum_lai_hf               !< cumulative lai for heatflux calc.
    REAL(wp), DIMENSION(:,:,:), ALLOCATABLE ::  lad_s                    !< lad on scalar-grid
    REAL(wp), DIMENSION(:,:,:), ALLOCATABLE ::  pcm_heating_rate         !< plant canopy heating rate
    REAL(wp), DIMENSION(:,:,:), ALLOCATABLE ::  pcm_transpiration_rate   !< plant canopy transpiration rate
    REAL(wp), DIMENSION(:,:,:), ALLOCATABLE ::  pcm_latent_rate          !< plant canopy latent heating rate

    REAL(wp), DIMENSION(:,:,:), ALLOCATABLE ::  pcm_heatrate_av          !< array for averaging plant canopy sensible heating rate
    REAL(wp), DIMENSION(:,:,:), ALLOCATABLE ::  pcm_latentrate_av        !< array for averaging plant canopy latent heating rate
    REAL(wp), DIMENSION(:,:,:), ALLOCATABLE ::  pcm_transpirationrate_av !< array for averaging plant canopy transpiration rate

    TYPE(real_3d) ::  basal_area_density_f    !< input variable for basal area density - resolved vegetation
    TYPE(real_3d) ::  leaf_area_density_f     !< input variable for leaf area density - resolved vegetation
    TYPE(real_3d) ::  root_area_density_lad_f !< input variable for root area density - resolved vegetation

    SAVE

    PRIVATE
    
!
!-- Public functions
    PUBLIC pcm_calc_transpiration_rate,                                       &
           pcm_check_data_output,                                             &
           pcm_check_parameters,                                              &
           pcm_3d_data_averaging,                                             &
           pcm_data_output_3d,                                                &
           pcm_define_netcdf_grid,                                            &
           pcm_header,                                                        &
           pcm_init,                                                          &
           pcm_parin,                                                         &
           pcm_rrd_local,                                                     &
           pcm_tendency,                                                      &
           pcm_wrd_local

!
!-- Public variables and constants
    PUBLIC canopy_drag_coeff, pcm_heating_rate, pcm_transpiration_rate,       &
           pcm_latent_rate, canopy_mode, cthf, dt_plant_canopy, lad, lad_s,   &
           pch_index, plant_canopy_transpiration

    INTERFACE pcm_calc_transpiration_rate
       MODULE PROCEDURE pcm_calc_transpiration_rate
    END INTERFACE pcm_calc_transpiration_rate

    INTERFACE pcm_check_data_output
       MODULE PROCEDURE pcm_check_data_output
    END INTERFACE pcm_check_data_output
    
    INTERFACE pcm_check_parameters
       MODULE PROCEDURE pcm_check_parameters
    END INTERFACE pcm_check_parameters

    INTERFACE pcm_3d_data_averaging
       MODULE PROCEDURE pcm_3d_data_averaging
    END INTERFACE pcm_3d_data_averaging

    INTERFACE pcm_data_output_3d
       MODULE PROCEDURE pcm_data_output_3d
    END INTERFACE pcm_data_output_3d

    INTERFACE pcm_define_netcdf_grid
       MODULE PROCEDURE pcm_define_netcdf_grid
    END INTERFACE pcm_define_netcdf_grid
    
     INTERFACE pcm_header
       MODULE PROCEDURE pcm_header
    END INTERFACE pcm_header        
    
    INTERFACE pcm_init
       MODULE PROCEDURE pcm_init
    END INTERFACE pcm_init

    INTERFACE pcm_parin
       MODULE PROCEDURE pcm_parin
    END INTERFACE pcm_parin

    INTERFACE pcm_read_plant_canopy_3d
       MODULE PROCEDURE pcm_read_plant_canopy_3d
    END INTERFACE pcm_read_plant_canopy_3d

    INTERFACE pcm_rrd_local
       MODULE PROCEDURE pcm_rrd_local
    END INTERFACE pcm_rrd_local

    INTERFACE pcm_tendency
       MODULE PROCEDURE pcm_tendency
       MODULE PROCEDURE pcm_tendency_ij
    END INTERFACE pcm_tendency

    INTERFACE pcm_wrd_local
       MODULE PROCEDURE pcm_wrd_local
    END INTERFACE pcm_wrd_local


 CONTAINS
 
 
!------------------------------------------------------------------------------!
! Description:
! ------------
!> Calculation of the plant canopy transpiration rate based on the Jarvis-Stewart
!> with parametrizations described in Daudet et al. (1999; Agricult. and Forest
!> Meteorol. 97) and Ngao, Adam and Saudreau (2017;  Agricult. and Forest Meteorol
!> 237-238). Model functions f1-f4 were adapted from Stewart (1998; Agric.
!> and Forest. Meteorol. 43) instead, because they are valid for broader intervals
!> of values. Funcion f4 used in form present in van Wijk et al. (1998;
!> Tree Physiology 20).
!>
!> This subroutine is called from subroutine radiation_interaction
!> after the calculation of radiation in plant canopy boxes.
!> (arrays pcbinsw and pcbinlw).
!>
!------------------------------------------------------------------------------!
 SUBROUTINE pcm_calc_transpiration_rate(i, j, k, kk, pcbsw, pcblw, pcbtr, pcblh)

!
!--  input parameters
     INTEGER(iwp), INTENT(IN) ::  i, j, k, kk        !< indices of the pc gridbox
     REAL(wp), INTENT(IN)     ::  pcbsw              !< sw radiation in gridbox (W)
     REAL(wp), INTENT(IN)     ::  pcblw              !< lw radiation in gridbox (W)
     REAL(wp), INTENT(OUT)    ::  pcbtr              !< transpiration rate dq/dt (kg/kg/s)
     REAL(wp), INTENT(OUT)    ::  pcblh              !< latent heat from transpiration dT/dt (K/s)

!--  variables and parameters for calculation of transpiration rate
     REAL(wp)             ::  sat_press, sat_press_d, temp, v_lad
     REAL(wp)             ::  d_fact, g_b, g_s, wind_speed, evapor_rate
     REAL(wp)             ::  f1, f2, f3, f4, vpd, rswc, e_eq, e_imp, rad
     REAL(wp), PARAMETER  ::  gama_psychr = 66.0_wp !< psychrometric constant (Pa/K)
     REAL(wp), PARAMETER  ::  g_s_max = 0.01        !< maximum stomatal conductivity (m/s)
     REAL(wp), PARAMETER  ::  m_soil = 0.4_wp       !< soil water content (needs to adjust or take from LSM)
     REAL(wp), PARAMETER  ::  m_wilt = 0.01_wp      !< wilting point soil water content (needs to adjust or take from LSM)
     REAL(wp), PARAMETER  ::  m_sat = 0.51_wp       !< saturation soil water content (needs to adjust or take from LSM)
     REAL(wp), PARAMETER  ::  t2_min = 0.0_wp       !< minimal temperature for calculation of f2
     REAL(wp), PARAMETER  ::  t2_max = 40.0_wp      !< maximal temperature for calculation of f2


!--  Temperature (deg C)
     temp = pt(k,j,i) * exner(k) - degc_to_k
!--  Coefficient for conversion of radiation to grid to radiation to unit leaves surface
     v_lad = 1.0_wp / ( MAX( lad_s(kk,j,i), 1.0E-10_wp ) * dx * dy * dz(1) )
!--  Magnus formula for the saturation pressure (see Ngao, Adam and Saudreau (2017) eq. 1)
!--  There are updated formulas available, kept consistent with the rest of the parametrization
     sat_press = 610.8_wp * exp(17.27_wp * temp/(temp + 237.3_wp))
!--  Saturation pressure derivative (derivative of the above)
     sat_press_d = sat_press * 17.27_wp * 237.3_wp / (temp + 237.3_wp)**2
!--  Wind speed
     wind_speed = SQRT( ( 0.5_wp * ( u(k,j,i) + u(k,j,i+1) ) )**2 +            &
                        ( 0.5_wp * ( v(k,j,i) + v(k,j+1,i) ) )**2 +            &
                        ( 0.5_wp * ( w(k,j,i) + w(k-1,j,i) ) )**2 )
!--  Aerodynamic conductivity (Daudet et al. (1999) eq. 14
     g_b = 0.01_wp * wind_speed + 0.0071_wp
!--  Radiation flux per leaf surface unit
     rad = pcbsw * v_lad
!--  First function for calculation of stomatal conductivity (radiation dependency)
!--  Stewart (1988; Agric. and Forest. Meteorol. 43) eq. 17
     f1 = rad * (1000.0_wp+42.1_wp) / 1000.0_wp / (rad+42.1_wp)
!--  Second function for calculation of stomatal conductivity (temperature dependency)
!--  Stewart (1988; Agric. and Forest. Meteorol. 43) eq. 21
     f2 = MAX(t2_min, (temp-t2_min) * MAX(0.0_wp,t2_max-temp)**((t2_max-16.9_wp)/(16.9_wp-t2_min)) / &
              ((16.9_wp-t2_min) * (t2_max-16.9_wp)**((t2_max-16.9_wp)/(16.9_wp-t2_min))) )
!--  Water pressure deficit
!--  Ngao, Adam and Saudreau (2017) eq. 6 but with water vapour partial pressure
     vpd = max( sat_press - q(k,j,i) * hyp(k) / rd_d_rv, 0._wp )
!--  Third function for calculation of stomatal conductivity (water pressure deficit dependency)
!--  Ngao, Adam and Saudreau (2017) Table 1, limited from below according to Stewart (1988)
!--  The coefficients of the linear dependence should better correspond to broad-leaved trees
!--  than the coefficients from Stewart (1988) which correspond to conifer trees.
     vpd = MIN(MAX(vpd,770.0_wp),3820.0_wp)
     f3 = -2E-4_wp * vpd + 1.154_wp
!--  Fourth function for calculation of stomatal conductivity (soil moisture dependency)
!--  Residual soil water content
!--  van Wijk et al. (1998; Tree Physiology 20) eq. 7
!--  TODO - over LSM surface might be calculated from LSM parameters
     rswc = ( m_sat - m_soil ) / ( m_sat - m_wilt )
!--  van Wijk et al. (1998; Tree Physiology 20) eq. 5-6 (it is a reformulation of eq. 22-23 of Stewart(1988))
     f4 = MAX(0.0_wp, MIN(1.0_wp - 0.041_wp * EXP(3.2_wp * rswc), 1.0_wp - 0.041_wp))
!--  Stomatal conductivity
!--  Stewart (1988; Agric. and Forest. Meteorol. 43) eq. 12
!--  (notation according to Ngao, Adam and Saudreau (2017) and others)
     g_s = g_s_max * f1 * f2 * f3 * f4 + 1.0E-10_wp
!--  Decoupling factor
!--  Daudet et al. (1999) eq. 6
     d_fact = (sat_press_d / gama_psychr + 2.0_wp ) /                        &
              (sat_press_d / gama_psychr + 2.0_wp + 2.0_wp * g_b / g_s )
!--  Equilibrium evaporation rate
!--  Daudet et al. (1999) eq. 4
     e_eq = (pcbsw + pcblw) * v_lad * sat_press_d /                         &
                 gama_psychr /( sat_press_d / gama_psychr + 2.0_wp ) / l_v
!--  Imposed evaporation rate
!--  Daudet et al. (1999) eq. 5
     e_imp = r_d * pt(k,j,i) * exner(k) / hyp(k) * c_p * g_s * vpd / gama_psychr / l_v
!--  Evaporation rate
!--  Daudet et al. (1999) eq. 3
!--  (evaporation rate is limited to non-negative values)
     evapor_rate = MAX(d_fact * e_eq + ( 1.0_wp - d_fact ) * e_imp, 0.0_wp)
!--  Conversion of evaporation rate to q tendency in gridbox
!--  dq/dt = E * LAD * V_g / (rho_air * V_g)
     pcbtr = evapor_rate * r_d * pt(k,j,i) * exner(k) * lad_s(kk,j,i) / hyp(k)  !-- = dq/dt
!--  latent heat from evaporation
     pcblh = pcbtr * lv_d_cp  !-- = - dT/dt

 END SUBROUTINE pcm_calc_transpiration_rate


!------------------------------------------------------------------------------!
! Description:
! ------------
!> Check data output for plant canopy model
!------------------------------------------------------------------------------!
 SUBROUTINE pcm_check_data_output( var, unit )

    CHARACTER (LEN=*) ::  unit  !< 
    CHARACTER (LEN=*) ::  var   !<


    SELECT CASE ( TRIM( var ) )

       CASE ( 'pcm_heatrate' )
          IF ( cthf == 0.0_wp  .AND. .NOT.  urban_surface )  THEN
             message_string = 'output of "' // TRIM( var ) // '" requi' //  &
                              'res setting of parameter cthf /= 0.0'
             CALL message( 'pcm_check_data_output', 'PA1000', 1, 2, 0, 6, 0 )
          ENDIF
          unit = 'K s-1'
    
       CASE ( 'pcm_transpirationrate' )
          unit = 'kg kg-1 s-1'

       CASE ( 'pcm_latentrate' )
          unit = 'K s-1'

       CASE ( 'pcm_lad' )
          unit = 'm2 m-3'


       CASE DEFAULT
          unit = 'illegal'

    END SELECT


 END SUBROUTINE pcm_check_data_output
 
 
!------------------------------------------------------------------------------!
! Description:
! ------------
!> Check parameters routine for plant canopy model
!------------------------------------------------------------------------------!
    SUBROUTINE pcm_check_parameters
           
       IF ( ocean_mode )  THEN
          message_string = 'plant_canopy = .TRUE. is not allowed in the '//    &
                           'ocean'
          CALL message( 'pcm_check_parameters', 'PA0696', 1, 2, 0, 6, 0 )
       ENDIF
           
       IF ( canopy_drag_coeff == 0.0_wp )  THEN
          message_string = 'plant_canopy = .TRUE. requires a non-zero drag '// &
                           'coefficient & given value is canopy_drag_coeff = 0.0'
          CALL message( 'pcm_check_parameters', 'PA0041', 1, 2, 0, 6, 0 )
       ENDIF

       IF ( ( alpha_lad /= 9999999.9_wp  .AND.  beta_lad == 9999999.9_wp ) .OR.&
              beta_lad /= 9999999.9_wp   .AND.  alpha_lad == 9999999.9_wp )  THEN
          message_string = 'using the beta function for the construction ' //  &
                           'of the leaf area density profile requires '    //  &
                           'both alpha_lad and beta_lad to be /= 9999999.9'
          CALL message( 'pcm_check_parameters', 'PA0118', 1, 2, 0, 6, 0 )
       ENDIF

       IF ( calc_beta_lad_profile  .AND.  lai_beta == 0.0_wp )  THEN
          message_string = 'using the beta function for the construction ' //  &
                           'of the leaf area density profile requires '    //  &
                           'a non-zero lai_beta, but given value is '      //  &
                           'lai_beta = 0.0'
          CALL message( 'pcm_check_parameters', 'PA0119', 1, 2, 0, 6, 0 )
       ENDIF

       IF ( calc_beta_lad_profile  .AND.  lad_surface /= 0.0_wp )  THEN
          message_string = 'simultaneous setting of alpha_lad /= 9999999.9 '// &
                           'combined with beta_lad /= 9999999.9 '           // &
                           'and lad_surface /= 0.0 is not possible, '       // &
                           'use either vertical gradients or the beta '     // &
                           'function for the construction of the leaf area '// &
                           'density profile'
          CALL message( 'pcm_check_parameters', 'PA0120', 1, 2, 0, 6, 0 )
       ENDIF 

       IF ( bulk_cloud_model  .AND.  microphysics_seifert )  THEN
          message_string = 'plant_canopy = .TRUE. requires cloud_scheme /=' // &
                          ' seifert_beheng'
          CALL message( 'pcm_check_parameters', 'PA0360', 1, 2, 0, 6, 0 )
       ENDIF
!
!--    If canopy shall be read from file, static input file must be present
       IF ( TRIM( canopy_mode ) == 'read_from_file' .AND.                   &
            .NOT. input_pids_static )  THEN
          message_string = 'canopy_mode = read_from_file requires ' //      &
                           'static input file'
          CALL message( 'pcm_check_parameters', 'PA0672', 1, 2, 0, 6, 0 )
       ENDIF

    END SUBROUTINE pcm_check_parameters 
 

!------------------------------------------------------------------------------!
!
! Description:
! ------------
!> Subroutine for averaging 3D data
!------------------------------------------------------------------------------!
 SUBROUTINE pcm_3d_data_averaging( mode, variable )

    CHARACTER (LEN=*) ::  mode    !<
    CHARACTER (LEN=*) :: variable !<

    INTEGER(iwp) ::  i            !<
    INTEGER(iwp) ::  j            !<
    INTEGER(iwp) ::  k            !<


    IF ( mode == 'allocate' )  THEN

       SELECT CASE ( TRIM( variable ) )

          CASE ( 'pcm_heatrate' )
             IF ( .NOT. ALLOCATED( pcm_heatrate_av ) )  THEN
                ALLOCATE( pcm_heatrate_av(0:pch_index,nysg:nyng,nxlg:nxrg) )
             ENDIF
             pcm_heatrate_av = 0.0_wp


          CASE ( 'pcm_latentrate' )
             IF ( .NOT. ALLOCATED( pcm_latentrate_av ) )  THEN
                ALLOCATE( pcm_latentrate_av(0:pch_index,nysg:nyng,nxlg:nxrg) )
             ENDIF
             pcm_latentrate_av = 0.0_wp


          CASE ( 'pcm_transpirationrate' )
             IF ( .NOT. ALLOCATED( pcm_transpirationrate_av ) )  THEN
                ALLOCATE( pcm_transpirationrate_av(0:pch_index,nysg:nyng,nxlg:nxrg) )
             ENDIF
             pcm_transpirationrate_av = 0.0_wp

          CASE DEFAULT
             CONTINUE

       END SELECT

    ELSEIF ( mode == 'sum' )  THEN

       SELECT CASE ( TRIM( variable ) )

          CASE ( 'pcm_heatrate' )
             IF ( ALLOCATED( pcm_heatrate_av ) ) THEN
                DO  i = nxl, nxr
                   DO  j = nys, nyn
                      IF ( pch_index_ji(j,i) /= 0 )  THEN
                         DO  k = 0, pch_index_ji(j,i)
                            pcm_heatrate_av(k,j,i) = pcm_heatrate_av(k,j,i) + pcm_heating_rate(k,j,i)
                         ENDDO
                      ENDIF
                   ENDDO
                ENDDO
             ENDIF


          CASE ( 'pcm_latentrate' )
             IF ( ALLOCATED( pcm_latentrate_av ) ) THEN
                DO  i = nxl, nxr
                   DO  j = nys, nyn
                      IF ( pch_index_ji(j,i) /= 0 )  THEN
                         DO  k = 0, pch_index_ji(j,i)
                            pcm_latentrate_av(k,j,i) = pcm_latentrate_av(k,j,i) + pcm_latent_rate(k,j,i)
                         ENDDO
                      ENDIF
                   ENDDO
                ENDDO
             ENDIF


          CASE ( 'pcm_transpirationrate' )
             IF ( ALLOCATED( pcm_transpirationrate_av ) ) THEN
                DO  i = nxl, nxr
                   DO  j = nys, nyn
                      IF ( pch_index_ji(j,i) /= 0 )  THEN
                         DO  k = 0, pch_index_ji(j,i)
                            pcm_transpirationrate_av(k,j,i) = pcm_transpirationrate_av(k,j,i) + pcm_transpiration_rate(k,j,i)
                         ENDDO
                      ENDIF
                   ENDDO
                ENDDO
             ENDIF

          CASE DEFAULT
             CONTINUE

       END SELECT

    ELSEIF ( mode == 'average' )  THEN

       SELECT CASE ( TRIM( variable ) )

          CASE ( 'pcm_heatrate' )
             IF ( ALLOCATED( pcm_heatrate_av ) ) THEN
                DO  i = nxlg, nxrg
                   DO  j = nysg, nyng
                      IF ( pch_index_ji(j,i) /= 0 )  THEN
                         DO  k = 0, pch_index_ji(j,i)
                            pcm_heatrate_av(k,j,i) = pcm_heatrate_av(k,j,i)                 &
                                                     / REAL( average_count_3d, KIND=wp )
                         ENDDO
                      ENDIF
                   ENDDO
                ENDDO
             ENDIF


          CASE ( 'pcm_latentrate' )
             IF ( ALLOCATED( pcm_latentrate_av ) ) THEN
                DO  i = nxlg, nxrg
                   DO  j = nysg, nyng
                      IF ( pch_index_ji(j,i) /= 0 )  THEN
                         DO  k = 0, pch_index_ji(j,i)
                            pcm_latentrate_av(k,j,i) = pcm_latentrate_av(k,j,i)              &
                                                       / REAL( average_count_3d, KIND=wp )
                         ENDDO
                      ENDIF
                   ENDDO
                ENDDO
             ENDIF


          CASE ( 'pcm_transpirationrate' )
             IF ( ALLOCATED( pcm_transpirationrate_av ) ) THEN
                DO  i = nxlg, nxrg
                   DO  j = nysg, nyng
                      IF ( pch_index_ji(j,i) /= 0 )  THEN
                         DO  k = 0, pch_index_ji(j,i)
                            pcm_transpirationrate_av(k,j,i) = pcm_transpirationrate_av(k,j,i)  &
                                                              / REAL( average_count_3d, KIND=wp )
                         ENDDO
                      ENDIF
                   ENDDO
                ENDDO
             ENDIF

       END SELECT

    ENDIF

 END SUBROUTINE pcm_3d_data_averaging

!------------------------------------------------------------------------------!
!
! Description:
! ------------
!> Subroutine defining 3D output variables. 
!> Note, 3D plant-canopy output has it's own vertical output dimension, meaning
!> that 3D output is relative to the model surface now rather than at the actual
!> grid point where the plant canopy is located. 
!------------------------------------------------------------------------------!
 SUBROUTINE pcm_data_output_3d( av, variable, found, local_pf, fill_value,     &
                                nzb_do, nzt_do )

    CHARACTER (LEN=*) ::  variable !< treated variable

    INTEGER(iwp) ::  av     !< flag indicating instantaneous or averaged data output
    INTEGER(iwp) ::  i      !< grid index x-direction
    INTEGER(iwp) ::  j      !< grid index y-direction
    INTEGER(iwp) ::  k      !< grid index z-direction
    INTEGER(iwp) ::  nzb_do !< lower limit of the data output (usually 0)
    INTEGER(iwp) ::  nzt_do !< vertical upper limit of the data output (usually nz_do3d)

    LOGICAL      ::  found  !< flag indicating if variable is found

    REAL(wp)     ::  fill_value !< fill value
    REAL(sp), DIMENSION(nxl:nxr,nys:nyn,nzb_do:nzt_do) ::  local_pf !< data output array


    found = .TRUE.

    local_pf = REAL( fill_value, KIND = 4 )

    SELECT CASE ( TRIM( variable ) )
!
!--    Note, to save memory arrays for heating are allocated from 0:pch_index.
!--    Thus, output must be relative to these array indices. Further, check
!--    whether the output is within the vertical output range,
!--    i.e. nzb_do:nzt_do, which is necessary as local_pf is only allocated
!--    for this index space. Note, plant-canopy output has a separate 
!--    vertical output coordinate zlad, so that output is mapped down to the 
!--    surface. 
       CASE ( 'pcm_heatrate' )
          IF ( av == 0 )  THEN
             DO  i = nxl, nxr
                DO  j = nys, nyn
                   DO  k = MAX( 1, nzb_do ), MIN( pch_index_ji(j,i), nzt_do )
                      local_pf(i,j,k) = pcm_heating_rate(k,j,i)
                   ENDDO
                ENDDO
             ENDDO
          ELSE
             DO  i = nxl, nxr
                DO  j = nys, nyn
                   DO  k = MAX( 1, nzb_do ), MIN( pch_index_ji(j,i), nzt_do )
                      local_pf(i,j,k) = pcm_heatrate_av(k,j,i)
                   ENDDO
                ENDDO
             ENDDO
          ENDIF

       CASE ( 'pcm_latentrate' )
          IF ( av == 0 )  THEN
             DO  i = nxl, nxr
                DO  j = nys, nyn
                   DO  k = MAX( 1, nzb_do ), MIN( pch_index_ji(j,i), nzt_do )
                      local_pf(i,j,k) = pcm_latent_rate(k,j,i)
                   ENDDO
                ENDDO
             ENDDO
          ELSE
             DO  i = nxl, nxr
                DO  j = nys, nyn
                   DO  k = MAX( 1, nzb_do ), MIN( pch_index_ji(j,i), nzt_do )
                      local_pf(i,j,k) = pcm_latentrate_av(k,j,i)
                   ENDDO
                ENDDO
             ENDDO
          ENDIF

       CASE ( 'pcm_transpirationrate' )
          IF ( av == 0 )  THEN
             DO  i = nxl, nxr
                DO  j = nys, nyn
                   DO  k = MAX( 1, nzb_do ), MIN( pch_index_ji(j,i), nzt_do )
                      local_pf(i,j,k) = pcm_transpiration_rate(k,j,i)
                   ENDDO
                ENDDO
             ENDDO
          ELSE
             DO  i = nxl, nxr
                DO  j = nys, nyn
                   DO  k = MAX( 1, nzb_do ), MIN( pch_index_ji(j,i), nzt_do )
                      local_pf(i,j,k) = pcm_transpirationrate_av(k,j,i)
                   ENDDO
                ENDDO
             ENDDO
          ENDIF

       CASE ( 'pcm_lad' )
          IF ( av == 0 )  THEN
             DO  i = nxl, nxr
                DO  j = nys, nyn
                   DO  k = MAX( 1, nzb_do ), MIN( pch_index_ji(j,i), nzt_do )
                      local_pf(i,j,k) = lad_s(k,j,i)
                   ENDDO
                ENDDO
             ENDDO
          ENDIF

       CASE DEFAULT
          found = .FALSE.

    END SELECT

 END SUBROUTINE pcm_data_output_3d 
         
!------------------------------------------------------------------------------!
!
! Description:
! ------------
!> Subroutine defining appropriate grid for netcdf variables.
!> It is called from subroutine netcdf.
!------------------------------------------------------------------------------!
 SUBROUTINE pcm_define_netcdf_grid( var, found, grid_x, grid_y, grid_z )

     CHARACTER (LEN=*), INTENT(IN)  ::  var         !< 
     LOGICAL, INTENT(OUT)           ::  found       !< 
     CHARACTER (LEN=*), INTENT(OUT) ::  grid_x      !< 
     CHARACTER (LEN=*), INTENT(OUT) ::  grid_y      !< 
     CHARACTER (LEN=*), INTENT(OUT) ::  grid_z      !< 

     found  = .TRUE.

!
!--  Check for the grid. zpc is zu(nzb:nzb+pch_index)
     SELECT CASE ( TRIM( var ) )

        CASE ( 'pcm_heatrate', 'pcm_lad', 'pcm_transpirationrate', 'pcm_latentrate')
           grid_x = 'x'
           grid_y = 'y'
           grid_z = 'zpc'

        CASE DEFAULT
           found  = .FALSE.
           grid_x = 'none'
           grid_y = 'none'
           grid_z = 'none'
     END SELECT

 END SUBROUTINE pcm_define_netcdf_grid
 
 
!------------------------------------------------------------------------------!
! Description:
! ------------
!> Header output for plant canopy model
!------------------------------------------------------------------------------!
 SUBROUTINE pcm_header ( io )
 
    CHARACTER (LEN=10) ::  coor_chr            !<

    CHARACTER (LEN=86) ::  coordinates         !<
    CHARACTER (LEN=86) ::  gradients           !<
    CHARACTER (LEN=86) ::  leaf_area_density   !<
    CHARACTER (LEN=86) ::  slices              !<
 
    INTEGER(iwp) :: i                !< 
    INTEGER(iwp),  INTENT(IN) ::  io !< Unit of the output file
    INTEGER(iwp) :: k                !<       
 
    REAL(wp) ::  canopy_height       !< canopy height (in m)
    
    canopy_height = zw(pch_index)

    WRITE ( io, 1 )  canopy_mode, canopy_height, pch_index,                    &
                       canopy_drag_coeff                                       
    IF ( passive_scalar )  THEN                                                
       WRITE ( io, 2 )  leaf_scalar_exch_coeff,                                &
                          leaf_surface_conc
    ENDIF

!
!   Heat flux at the top of vegetation
    WRITE ( io, 3 )  cthf

!
!   Leaf area density profile, calculated either from given vertical 
!   gradients or from beta probability density function.
    IF (  .NOT.  calc_beta_lad_profile )  THEN

!      Building output strings, starting with surface value
       WRITE ( leaf_area_density, '(F7.4)' )  lad_surface
       gradients = '------'
       slices = '     0'
       coordinates = '   0.0'
       DO i = 1, UBOUND(lad_vertical_gradient_level_ind, DIM=1)
          IF  ( lad_vertical_gradient_level_ind(i) /= -9999 ) THEN

             WRITE (coor_chr,'(F7.2)') lad(lad_vertical_gradient_level_ind(i))
             leaf_area_density = TRIM( leaf_area_density ) // ' ' // TRIM( coor_chr )

             WRITE (coor_chr,'(F7.2)') lad_vertical_gradient(i)
             gradients = TRIM( gradients ) // ' ' // TRIM( coor_chr )

             WRITE (coor_chr,'(I7)') lad_vertical_gradient_level_ind(i)
             slices = TRIM( slices ) // ' ' // TRIM( coor_chr )

             WRITE (coor_chr,'(F7.1)') lad_vertical_gradient_level(i)
             coordinates = TRIM( coordinates ) // ' '  // TRIM( coor_chr )
          ELSE
             EXIT
          ENDIF
       ENDDO

       WRITE ( io, 4 )  TRIM( coordinates ), TRIM( leaf_area_density ),        &
                          TRIM( gradients ), TRIM( slices )

    ELSE
    
       WRITE ( leaf_area_density, '(F7.4)' )  lad_surface
       coordinates = '   0.0'
       
       DO  k = 1, pch_index

          WRITE (coor_chr,'(F7.2)')  lad(k)
          leaf_area_density = TRIM( leaf_area_density ) // ' ' //              &
                              TRIM( coor_chr )                                 
                                                                               
          WRITE (coor_chr,'(F7.1)')  zu(k)                                     
          coordinates = TRIM( coordinates ) // ' '  // TRIM( coor_chr )        
                                                                               
       ENDDO                                                                   
                                                                               
       WRITE ( io, 5 ) TRIM( coordinates ), TRIM( leaf_area_density ),         &
                       alpha_lad, beta_lad, lai_beta

    ENDIF  

1   FORMAT (//' Vegetation canopy (drag) model:'/                              &
              ' ------------------------------'//                              &
              ' Canopy mode: ', A /                                            &
              ' Canopy height: ',F6.2,'m (',I4,' grid points)' /               &
              ' Leaf drag coefficient: ',F6.2 /)
2   FORMAT (/ ' Scalar exchange coefficient: ',F6.2 /                          &
              ' Scalar concentration at leaf surfaces in kg/m**3: ',F6.2 /)
3   FORMAT (' Predefined constant heatflux at the top of the vegetation: ',    &
             F6.2, ' K m/s')
4   FORMAT (/ ' Characteristic levels of the leaf area density:'//             &
              ' Height:              ',A,'  m'/                                &
              ' Leaf area density:   ',A,'  m**2/m**3'/                        &
              ' Gradient:            ',A,'  m**2/m**4'/                        &
              ' Gridpoint:           ',A)
5   FORMAT (//' Characteristic levels of the leaf area density and coefficients:'&
          //  ' Height:              ',A,'  m'/                                &
              ' Leaf area density:   ',A,'  m**2/m**3'/                        &
              ' Coefficient alpha: ',F6.2 /                                    &
              ' Coefficient beta: ',F6.2 /                                     &
              ' Leaf area index: ',F6.2,'  m**2/m**2' /)   
       
    END SUBROUTINE pcm_header
 
 
!------------------------------------------------------------------------------!
! Description:
! ------------
!> Initialization of the plant canopy model
!------------------------------------------------------------------------------!
    SUBROUTINE pcm_init

       INTEGER(iwp) ::  i   !< running index
       INTEGER(iwp) ::  j   !< running index
       INTEGER(iwp) ::  k   !< running index
       INTEGER(iwp) ::  m   !< running index

       REAL(wp) ::  canopy_height   !< canopy height for lad-profile construction
       REAL(wp) ::  gradient        !< gradient for lad-profile construction
       REAL(wp) ::  int_bpdf        !< vertical integral for lad-profile construction      
       REAL(wp) ::  lad_max         !< maximum LAD value in the model domain, used to perform a check

       IF ( debug_output )  CALL debug_message( 'pcm_init', 'start' )
!
!--    Allocate one-dimensional arrays for the computation of the 
!--    leaf area density (lad) profile
       ALLOCATE( lad(0:nz+1), pre_lad(0:nz+1) )
       lad = 0.0_wp
       pre_lad = 0.0_wp

!
!--    Set flag that indicates that the lad-profile shall be calculated by using
!--    a beta probability density function
       IF ( alpha_lad /= 9999999.9_wp  .AND.  beta_lad /= 9999999.9_wp )  THEN
          calc_beta_lad_profile = .TRUE.
       ENDIF
       
       
!
!--    Compute the profile of leaf area density used in the plant
!--    canopy model. The profile can either be constructed from
!--    prescribed vertical gradients of the leaf area density or by
!--    using a beta probability density function (see e.g. Markkanen et al., 
!--    2003: Boundary-Layer Meteorology, 106, 437-459) 
       IF (  .NOT.  calc_beta_lad_profile )  THEN   

!
!--       Use vertical gradients for lad-profile construction    
          i = 1
          gradient = 0.0_wp

          lad(0) = lad_surface
          lad_vertical_gradient_level_ind(1) = 0

          DO k = 1, pch_index
             IF ( i < 11 )  THEN
                IF ( lad_vertical_gradient_level(i) < zu(k)  .AND.          &
                     lad_vertical_gradient_level(i) >= 0.0_wp )  THEN
                   gradient = lad_vertical_gradient(i)
                   lad_vertical_gradient_level_ind(i) = k - 1
                   i = i + 1
                ENDIF
             ENDIF
             IF ( gradient /= 0.0_wp )  THEN
                IF ( k /= 1 )  THEN
                   lad(k) = lad(k-1) + dzu(k) * gradient
                ELSE
                   lad(k) = lad_surface + dzu(k) * gradient
                ENDIF
             ELSE
                lad(k) = lad(k-1)
             ENDIF
          ENDDO

!
!--       In case of no given leaf area density gradients, choose a vanishing
!--       gradient. This information is used for the HEADER and the RUN_CONTROL
!--       file.
          IF ( lad_vertical_gradient_level(1) == -9999999.9_wp )  THEN
             lad_vertical_gradient_level(1) = 0.0_wp
          ENDIF

       ELSE

! 
!--       Use beta function for lad-profile construction
          int_bpdf = 0.0_wp
          canopy_height = zw(pch_index)

          DO k = 0, pch_index
             int_bpdf = int_bpdf +                                             &
                      ( ( ( zw(k) / canopy_height )**( alpha_lad-1.0_wp ) ) *  &
                      ( ( 1.0_wp - ( zw(k) / canopy_height ) )**(              &
                          beta_lad-1.0_wp ) )                                  &
                      * ( ( zw(k+1)-zw(k) ) / canopy_height ) )
          ENDDO

!
!--       Preliminary lad profile (defined on w-grid)
          DO k = 0, pch_index
             pre_lad(k) =  lai_beta *                                          &
                        ( ( ( zw(k) / canopy_height )**( alpha_lad-1.0_wp ) )  &
                        * ( ( 1.0_wp - ( zw(k) / canopy_height ) )**(          &
                              beta_lad-1.0_wp ) ) / int_bpdf                   &
                        ) / canopy_height
          ENDDO

!
!--       Final lad profile (defined on scalar-grid level, since most prognostic
!--       quantities are defined there, hence, less interpolation is required 
!--       when calculating the canopy tendencies)
          lad(0) = pre_lad(0)
          DO k = 1, pch_index
             lad(k) = 0.5 * ( pre_lad(k-1) + pre_lad(k) )
          ENDDO

       ENDIF

!
!--    Allocate 3D-array for the leaf area density (lad_s).
       ALLOCATE( lad_s(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )

!
!--    Initialization of the canopy coverage in the model domain:
!--    Setting the parameter canopy_mode = 'homogeneous' initializes a canopy, which
!--    fully covers the domain surface
       SELECT CASE ( TRIM( canopy_mode ) )

          CASE( 'homogeneous' )

             DO  i = nxlg, nxrg
                DO  j = nysg, nyng
                   lad_s(:,j,i) = lad(:)
                ENDDO
             ENDDO

          CASE ( 'read_from_file' )
!
!--          Read plant canopy
             IF ( input_pids_static )  THEN
!
!--             Open the static input file
#if defined( __netcdf )
                CALL open_read_file( TRIM( input_file_static ) //              &
                                     TRIM( coupling_char ),                    &
                                     pids_id )

                CALL inquire_num_variables( pids_id, num_var_pids )
!
!--             Allocate memory to store variable names and read them
                ALLOCATE( vars_pids(1:num_var_pids) )
                CALL inquire_variable_names( pids_id, vars_pids )
!
!--             Read leaf area density - resolved vegetation
                IF ( check_existence( vars_pids, 'lad' ) )  THEN
                   leaf_area_density_f%from_file = .TRUE.
                   CALL get_attribute( pids_id, char_fill,                     &
                                       leaf_area_density_f%fill,               &
                                       .FALSE., 'lad' )
!
!--                Inquire number of vertical vegetation layer
                   CALL get_dimension_length( pids_id,                         &
                                              leaf_area_density_f%nz,          &
                                              'zlad' )
!
!--                Allocate variable for leaf-area density
                   ALLOCATE( leaf_area_density_f%var                           &
                                                (0:leaf_area_density_f%nz-1,   &
                                                 nys:nyn,nxl:nxr) )

                   CALL get_variable( pids_id, 'lad', leaf_area_density_f%var, &
                                      nxl, nxr, nys, nyn,                      &
                                      0, leaf_area_density_f%nz-1 )

                ELSE
                   leaf_area_density_f%from_file = .FALSE.
                ENDIF
!
!--             Read basal area density - resolved vegetation
                IF ( check_existence( vars_pids, 'bad' ) )  THEN
                   basal_area_density_f%from_file = .TRUE.
                   CALL get_attribute( pids_id, char_fill,                     &
                                       basal_area_density_f%fill,              &
                                       .FALSE., 'bad' )
!
!--                Inquire number of vertical vegetation layer
                   CALL get_dimension_length( pids_id,                         &
                                              basal_area_density_f%nz,         & 
                                              'zlad' )
!
!--                Allocate variable
                   ALLOCATE( basal_area_density_f%var                          &
                                              (0:basal_area_density_f%nz-1,    &
                                               nys:nyn,nxl:nxr) )

                   CALL get_variable( pids_id, 'bad', basal_area_density_f%var,&
                                      nxl, nxr, nys, nyn,                      &
                                      0,  basal_area_density_f%nz-1 )
                ELSE
                   basal_area_density_f%from_file = .FALSE.
                ENDIF
!
!--             Read root area density - resolved vegetation
                IF ( check_existence( vars_pids, 'root_area_dens_r' ) )  THEN
                   root_area_density_lad_f%from_file = .TRUE.
                   CALL get_attribute( pids_id, char_fill,                     &
                                       root_area_density_lad_f%fill,           &
                                       .FALSE., 'root_area_dens_r' )
!
!--                Inquire number of vertical soil layers
                   CALL get_dimension_length( pids_id,                         &
                                              root_area_density_lad_f%nz,      &
                                              'zsoil' )
!
!--                Allocate variable
                   ALLOCATE( root_area_density_lad_f%var                       &
                                               (0:root_area_density_lad_f%nz-1,&
                                                nys:nyn,nxl:nxr) )

                   CALL get_variable( pids_id, 'root_area_dens_r',             &
                                      root_area_density_lad_f%var,             &
                                      nxl, nxr, nys, nyn,                      &
                                      0,  root_area_density_lad_f%nz-1 )
                ELSE
                   root_area_density_lad_f%from_file = .FALSE.
                ENDIF

                DEALLOCATE( vars_pids )
!
!--             Finally, close the input file and deallocate temporary array
                CALL close_input_file( pids_id )
#endif
             ENDIF

!
!--          Initialize LAD with data from file. If LAD is given in NetCDF file,
!--          use these values, else take LAD profiles from ASCII file. 
!--          Please note, in NetCDF file LAD is only given up to the maximum 
!--          canopy top, indicated by leaf_area_density_f%nz.  
             lad_s = 0.0_wp
             IF ( leaf_area_density_f%from_file )  THEN
!
!--             Set also pch_index, used to be the upper bound of the vertical 
!--             loops. Therefore, use the global top of the canopy layer. 
                pch_index = leaf_area_density_f%nz - 1

                DO  i = nxl, nxr
                   DO  j = nys, nyn
                      DO  k = 0, leaf_area_density_f%nz - 1
                         IF ( leaf_area_density_f%var(k,j,i) /=                &
                              leaf_area_density_f%fill )                       &
                         lad_s(k,j,i) = leaf_area_density_f%var(k,j,i)
                      ENDDO
!
!--                   Check if resolved vegetation is mapped onto buildings.
!--                   In general, this is allowed and also meaningful, e.g. 
!--                   when trees carry across roofs. However, due to the 
!--                   topography filtering, new building grid points can emerge
!--                   at location where also plant canopy is defined. As a 
!--                   result, plant canopy is mapped on top of roofs, with
!--                   siginficant impact on the downstream flow field and the
!--                   nearby surface radiation. In order to avoid that 
!--                   plant canopy is mistakenly mapped onto building roofs, 
!--                   check for building grid points (bit 6) that emerge from 
!--                   the filtering (bit 4) and set LAD to zero at these
!--                   artificially  created building grid points. This case, 
!--                   an informative message is given.
                      IF ( ANY( lad_s(:,j,i) /= 0.0_wp )  .AND.                &
                           ANY( BTEST( wall_flags_total_0(:,j,i), 6 ) ) .AND.  &
                           ANY( BTEST( wall_flags_total_0(:,j,i), 4 ) ) )  THEN
                         lad_s(:,j,i) = 0.0_wp
                         WRITE( message_string, * )                            &
                                        'Resolved plant-canopy is ' //         &
                                        'defined on top of an artificially '// &
                                        'created building grid point ' //      &
                                        '(emerged from the filtering) - ' //   &
                                        'LAD profile is omitted at this ' //   &
                                        'grid point: (i,j) = ', i, j
                         CALL message( 'pcm_init', 'PA0313', 0, 0, myid, 6, 0 )
                      ENDIF
                   ENDDO
                ENDDO
                CALL exchange_horiz( lad_s, nbgp )
!
!            ASCII file
!--          Initialize canopy parameters canopy_drag_coeff,
!--          leaf_scalar_exch_coeff, leaf_surface_conc
!--          from file which contains complete 3D data (separate vertical profiles for
!--          each location).
             ELSE
                CALL pcm_read_plant_canopy_3d
             ENDIF

          CASE DEFAULT
!
!--          The DEFAULT case is reached either if the parameter 
!--          canopy mode contains a wrong character string or if the 
!--          user has coded a special case in the user interface. 
!--          There, the subroutine user_init_plant_canopy checks 
!--          which of these two conditions applies.
             CALL user_init_plant_canopy
 
       END SELECT
!
!--    Check that at least one grid point has an LAD /= 0, else this may 
!--    cause errors in the radiation model. 
       lad_max = MAXVAL( lad_s )
#if defined( __parallel )
       CALL MPI_ALLREDUCE( MPI_IN_PLACE, lad_max, 1, MPI_REAL, MPI_MAX,        &
                           comm2d, ierr)
#endif
       IF ( lad_max <= 0.0_wp )  THEN
          message_string = 'Plant-canopy model is switched-on but no ' //      &
                           'plant canopy is present in the model domain.'
          CALL message( 'pcm_init', 'PA0685', 1, 2, 0, 6, 0 )
       ENDIF
    
!
!--    Initialize 2D index array indicating canopy top index. 
       ALLOCATE( pch_index_ji(nysg:nyng,nxlg:nxrg) )
       pch_index_ji = 0
       
       DO  i = nxlg, nxrg
          DO  j = nysg, nyng
             DO  k = 0, pch_index
                IF ( lad_s(k,j,i) /= 0 )  pch_index_ji(j,i) = k
             ENDDO
!
!--          Check whether topography and local vegetation on top exceed 
!--          height of the model domain.
             IF ( topo_top_ind(j,i,0) + pch_index_ji(j,i) >= nzt + 1 )  THEN
                message_string =  'Local vegetation height on top of ' //      &
                                  'topography exceeds height of model domain.'
                CALL message( 'pcm_init', 'PA0674', 2, 2, myid, 6, 0 )
             ENDIF

          ENDDO
       ENDDO
!
!--    Calculate global pch_index value (index of top of plant canopy from ground)
       pch_index = MAXVAL( pch_index_ji )
!
!--    Exchange pch_index from all processors
#if defined( __parallel )
       CALL MPI_ALLREDUCE( MPI_IN_PLACE, pch_index, 1, MPI_INTEGER,            &
                           MPI_MAX, comm2d, ierr)
#endif
!
!--    Allocation of arrays pcm_heating_rate, pcm_transpiration_rate and pcm_latent_rate
       ALLOCATE( pcm_heating_rate(0:pch_index,nysg:nyng,nxlg:nxrg) )
       pcm_heating_rate = 0.0_wp
       
       IF ( humidity )  THEN
          ALLOCATE( pcm_transpiration_rate(0:pch_index,nysg:nyng,nxlg:nxrg) )
          pcm_transpiration_rate = 0.0_wp
          ALLOCATE( pcm_latent_rate(0:pch_index,nysg:nyng,nxlg:nxrg) )
          pcm_latent_rate = 0.0_wp
       ENDIF
!
!--    Initialization of the canopy heat source distribution due to heating
!--    of the canopy layers by incoming solar radiation, in case that a non-zero
!--    value is set for the canopy top heat flux (cthf), which equals the
!--    available net radiation at canopy top.
!--    The heat source distribution is calculated by a decaying exponential 
!--    function of the downward cumulative leaf area index (cum_lai_hf), 
!--    assuming that the foliage inside the plant canopy is heated by solar
!--    radiation penetrating the canopy layers according to the distribution
!--    of net radiation as suggested by Brown & Covey (1966; Agric. Meteorol. 3, 
!--    73–96). This approach has been applied e.g. by Shaw & Schumann (1992;
!--    Bound.-Layer Meteorol. 61, 47–64).
!--    When using the radiation_interactions, canopy heating (pcm_heating_rate)
!--    and plant canopy transpiration (pcm_transpiration_rate, pcm_latent_rate)
!--    are calculated in the RTM after the calculation of radiation.
       IF ( cthf /= 0.0_wp )  THEN

          ALLOCATE( cum_lai_hf(nzb:nzt+1,nysg:nyng,nxlg:nxrg) )
!
!--       Piecewise calculation of the cumulative leaf area index by vertical
!--       integration of the leaf area density
          cum_lai_hf(:,:,:) = 0.0_wp
          DO  i = nxlg, nxrg
             DO  j = nysg, nyng
                DO  k = pch_index_ji(j,i)-1, 0, -1
                   IF ( k == pch_index_ji(j,i)-1 )  THEN
                      cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) +                &
                         ( 0.5_wp * lad_s(k+1,j,i) *                           &
                           ( zw(k+1) - zu(k+1) ) )  +                          &
                         ( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) +              &
                                                 lad_s(k,j,i) ) +              &
                                      lad_s(k+1,j,i) ) *                       &
                           ( zu(k+1) - zw(k) ) ) 
                   ELSE
                      cum_lai_hf(k,j,i) = cum_lai_hf(k+1,j,i) +                &
                         ( 0.5_wp * ( 0.5_wp * ( lad_s(k+2,j,i) +              &
                                                 lad_s(k+1,j,i) ) +            &
                                      lad_s(k+1,j,i) ) *                       &
                           ( zw(k+1) - zu(k+1) ) )  +                          &
                         ( 0.5_wp * ( 0.5_wp * ( lad_s(k+1,j,i) +              &
                                                 lad_s(k,j,i) ) +              &
                                      lad_s(k+1,j,i) ) *                       &
                           ( zu(k+1) - zw(k) ) )
                   ENDIF
                ENDDO
             ENDDO
          ENDDO

!
!--       In areas with canopy the surface value of the canopy heat 
!--       flux distribution overrides the surface heat flux (shf) 
!--       Start with default surface type
          DO  m = 1, surf_def_h(0)%ns
             i = surf_def_h(0)%i(m)
             j = surf_def_h(0)%j(m)
             IF ( cum_lai_hf(0,j,i) /= 0.0_wp )                                &
                surf_def_h(0)%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
          ENDDO
!
!--       Natural surfaces
          DO  m = 1, surf_lsm_h%ns
             i = surf_lsm_h%i(m)
             j = surf_lsm_h%j(m)
             IF ( cum_lai_hf(0,j,i) /= 0.0_wp )                                &
                surf_lsm_h%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
          ENDDO
!
!--       Urban surfaces
          DO  m = 1, surf_usm_h%ns
             i = surf_usm_h%i(m)
             j = surf_usm_h%j(m)
             IF ( cum_lai_hf(0,j,i) /= 0.0_wp )                                &
                surf_usm_h%shf(m) = cthf * exp( -ext_coef * cum_lai_hf(0,j,i) )
          ENDDO
!
!
!--       Calculation of the heating rate (K/s) within the different layers of 
!--       the plant canopy. Calculation is only necessary in areas covered with
!--       canopy. 
!--       Within the different canopy layers the plant-canopy heating
!--       rate (pcm_heating_rate) is calculated as the vertical 
!--       divergence of the canopy heat fluxes at the top and bottom
!--       of the respective layer
          DO  i = nxlg, nxrg
             DO  j = nysg, nyng
                DO  k = 1, pch_index_ji(j,i)
                   IF ( cum_lai_hf(0,j,i) /= 0.0_wp )  THEN
                      pcm_heating_rate(k,j,i) = cthf *                          &
                                ( exp(-ext_coef*cum_lai_hf(k,j,i)) -           &
                                  exp(-ext_coef*cum_lai_hf(k-1,j,i) ) ) / dzw(k)
                   ENDIF
                ENDDO
             ENDDO
          ENDDO

       ENDIF

       IF ( debug_output )  CALL debug_message( 'pcm_init', 'end' )

    END SUBROUTINE pcm_init


!------------------------------------------------------------------------------!
! Description:
! ------------
!> Parin for &plant_canopy_parameters for plant canopy model
!------------------------------------------------------------------------------!
    SUBROUTINE pcm_parin

       CHARACTER (LEN=80) ::  line  !< dummy string that contains the current line of the parameter file 
       
       NAMELIST /plant_canopy_parameters/                                      &
                                  alpha_lad, beta_lad, canopy_drag_coeff,      &
                                  canopy_mode, cthf,                           &
                                  lad_surface, lad_type_coef,                  & 
                                  lad_vertical_gradient,                       &
                                  lad_vertical_gradient_level,                 &
                                  lai_beta,                                    &
                                  leaf_scalar_exch_coeff,                      &
                                  leaf_surface_conc, pch_index,                &
                                  plant_canopy_transpiration

       NAMELIST /canopy_par/      alpha_lad, beta_lad, canopy_drag_coeff,      &
                                  canopy_mode, cthf,                           &
                                  lad_surface, lad_type_coef,                  & 
                                  lad_vertical_gradient,                       &
                                  lad_vertical_gradient_level,                 &
                                  lai_beta,                                    &
                                  leaf_scalar_exch_coeff,                      &
                                  leaf_surface_conc, pch_index,                &
                                  plant_canopy_transpiration

       line = ' '

!
!--    Try to find plant-canopy model package
       REWIND ( 11 )
       line = ' '
       DO WHILE ( INDEX( line, '&plant_canopy_parameters' ) == 0 )
          READ ( 11, '(A)', END=12 )  line
       ENDDO
       BACKSPACE ( 11 )

!
!--    Read user-defined namelist
       READ ( 11, plant_canopy_parameters, ERR = 10 )

!
!--    Set flag that indicates that the plant-canopy model is switched on
       plant_canopy = .TRUE.

       GOTO 14

 10    BACKSPACE( 11 )
       READ( 11 , '(A)') line
       CALL parin_fail_message( 'plant_canopy_parameters', line )
!
!--    Try to find old namelist
 12    REWIND ( 11 )
       line = ' '
       DO WHILE ( INDEX( line, '&canopy_par' ) == 0 )
          READ ( 11, '(A)', END=14 )  line
       ENDDO
       BACKSPACE ( 11 )

!
!--    Read user-defined namelist
       READ ( 11, canopy_par, ERR = 13, END = 14 )

       message_string = 'namelist canopy_par is deprecated and will be ' // &
                     'removed in near future. Please use namelist ' //      &
                     'plant_canopy_parameters instead'
       CALL message( 'pcm_parin', 'PA0487', 0, 1, 0, 6, 0 )

!
!--    Set flag that indicates that the plant-canopy model is switched on
       plant_canopy = .TRUE.

       GOTO 14

 13    BACKSPACE( 11 )
       READ( 11 , '(A)') line
       CALL parin_fail_message( 'canopy_par', line )

 14    CONTINUE

    END SUBROUTINE pcm_parin


!------------------------------------------------------------------------------!
! Description:
! ------------
!
!> Loads 3D plant canopy data from file. File format is as follows:
!>
!> num_levels
!> dtype,x,y,pctype,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
!> dtype,x,y,pctype,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
!> dtype,x,y,pctype,value(nzb),value(nzb+1), ... ,value(nzb+num_levels-1)
!> ...
!>
!> i.e. first line determines number of levels and further lines represent plant
!> canopy data, one line per column and variable. In each data line,
!> dtype represents variable to be set:
!>
!> dtype=1: leaf area density (lad_s)
!> dtype=2....n: some additional plant canopy input data quantity
!>
!> Zeros are added automatically above num_levels until top of domain.  Any
!> non-specified (x,y) columns have zero values as default.
!------------------------------------------------------------------------------!
    SUBROUTINE pcm_read_plant_canopy_3d

       INTEGER(iwp)                        ::  dtype     !< type of input data (1=lad)
       INTEGER(iwp)                        ::  pctype    !< type of plant canopy (deciduous,non-deciduous,...)
       INTEGER(iwp)                        ::  i, j      !< running index
       INTEGER(iwp)                        ::  nzp       !< number of vertical layers of plant canopy
       INTEGER(iwp)                        ::  nzpltop   !<
       INTEGER(iwp)                        ::  nzpl      !<
       INTEGER(iwp)                        ::  kk        !<
       
       REAL(wp), DIMENSION(:), ALLOCATABLE ::  col   !< vertical column of input data

!
!--    Initialize lad_s array
       lad_s = 0.0_wp
       
!
!--    Open and read plant canopy input data
       OPEN(152, FILE='PLANT_CANOPY_DATA_3D' // TRIM( coupling_char ),         &
                 ACCESS='SEQUENTIAL', ACTION='READ', STATUS='OLD',             &
                 FORM='FORMATTED', ERR=515)
       READ(152, *, ERR=516, END=517)  nzp   !< read first line = number of vertical layers
       nzpltop = MIN(nzt+1, nzb+nzp-1)
       nzpl = nzpltop - nzb + 1    !< no. of layers to assign
       ALLOCATE( col(0:nzp-1) )

       DO
          READ(152, *, ERR=516, END=517) dtype, i, j, pctype, col(:)
          IF ( i < nxlg  .OR.  i > nxrg  .OR.  j < nysg  .OR.  j > nyng )  CYCLE
          
          SELECT CASE (dtype)
             CASE( 1 )   !< leaf area density
!
!--             This is just the pure canopy layer assumed to be grounded to
!--             a flat domain surface. At locations where plant canopy sits 
!--             on top of any kind of topography, the vertical plant column 
!--             must be "lifted", which is done in SUBROUTINE pcm_tendency.           
                IF ( pctype < 0  .OR.  pctype > 10 )  THEN   !< incorrect plant canopy type
                   WRITE( message_string, * ) 'Incorrect type of plant canopy. '   //  &
                                              'Allowed values 0 <= pctype <= 10, ' //  &
                                              'but pctype is ', pctype
                   CALL message( 'pcm_read_plant_canopy_3d', 'PA0349', 1, 2, 0, 6, 0 )
                ENDIF
                kk = topo_top_ind(j,i,0)
                lad_s(nzb:nzpltop-kk, j, i) = col(kk:nzpl-1)*lad_type_coef(pctype)
             CASE DEFAULT
                WRITE(message_string, '(a,i2,a)')   &
                     'Unknown record type in file PLANT_CANOPY_DATA_3D: "', dtype, '"'
                CALL message( 'pcm_read_plant_canopy_3d', 'PA0530', 1, 2, 0, 6, 0 )
          END SELECT
       ENDDO

515    message_string = 'error opening file PLANT_CANOPY_DATA_3D'
       CALL message( 'pcm_read_plant_canopy_3d', 'PA0531', 1, 2, 0, 6, 0 )

516    message_string = 'error reading file PLANT_CANOPY_DATA_3D'
       CALL message( 'pcm_read_plant_canopy_3d', 'PA0532', 1, 2, 0, 6, 0 )

517    CLOSE(152)
       DEALLOCATE( col )
       
       CALL exchange_horiz( lad_s, nbgp )
        
    END SUBROUTINE pcm_read_plant_canopy_3d

!------------------------------------------------------------------------------!
! Description:
! ------------
!> Subroutine reads local (subdomain) restart data
!------------------------------------------------------------------------------!
    SUBROUTINE pcm_rrd_local( k, nxlf, nxlc, nxl_on_file, nxrf, nxrc,          &
                              nxr_on_file, nynf, nync, nyn_on_file, nysf,      &
                              nysc, nys_on_file, found )

       INTEGER(iwp) ::  k               !< 
       INTEGER(iwp) ::  nxlc            !< 
       INTEGER(iwp) ::  nxlf            !< 
       INTEGER(iwp) ::  nxl_on_file     !< 
       INTEGER(iwp) ::  nxrc            !< 
       INTEGER(iwp) ::  nxrf            !< 
       INTEGER(iwp) ::  nxr_on_file     !< 
       INTEGER(iwp) ::  nync            !< 
       INTEGER(iwp) ::  nynf            !< 
       INTEGER(iwp) ::  nyn_on_file     !< 
       INTEGER(iwp) ::  nysc            !< 
       INTEGER(iwp) ::  nysf            !< 
       INTEGER(iwp) ::  nys_on_file     !< 

       LOGICAL, INTENT(OUT)  :: found

       REAL(wp), DIMENSION(0:pch_index,                                        &
                           nys_on_file-nbgp:nyn_on_file+nbgp,                  &
                           nxl_on_file-nbgp:nxr_on_file+nbgp) :: tmp_3d2  !< temporary 3D array for entire vertical 
                                                                          !< extension of canopy layer
       found = .TRUE.

       SELECT CASE ( restart_string(1:length) )

          CASE ( 'pcm_heatrate_av' )
             IF ( .NOT. ALLOCATED( pcm_heatrate_av ) )  THEN
                ALLOCATE( pcm_heatrate_av(0:pch_index,nysg:nyng,nxlg:nxrg) )
                pcm_heatrate_av = 0.0_wp
             ENDIF  
             IF ( k == 1 )  READ ( 13 )  tmp_3d2
             pcm_heatrate_av(0:pch_index,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
                        tmp_3d2(0:pch_index,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)

          CASE ( 'pcm_latentrate_av' )
             IF ( .NOT. ALLOCATED( pcm_latentrate_av ) )  THEN
                ALLOCATE( pcm_latentrate_av(0:pch_index,nysg:nyng,nxlg:nxrg) )
                pcm_latentrate_av = 0.0_wp
             ENDIF  
             IF ( k == 1 )  READ ( 13 )  tmp_3d2
             pcm_latentrate_av(0:pch_index,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
                        tmp_3d2(0:pch_index,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)

          CASE ( 'pcm_transpirationrate_av' )
             IF ( .NOT. ALLOCATED( pcm_transpirationrate_av ) )  THEN
                ALLOCATE( pcm_transpirationrate_av(0:pch_index,nysg:nyng,nxlg:nxrg) )
                pcm_transpirationrate_av = 0.0_wp
             ENDIF  
             IF ( k == 1 )  READ ( 13 )  tmp_3d2
             pcm_transpirationrate_av(0:pch_index,nysc-nbgp:nync+nbgp,nxlc-nbgp:nxrc+nbgp) = &
                        tmp_3d2(0:pch_index,nysf-nbgp:nynf+nbgp,nxlf-nbgp:nxrf+nbgp)

          CASE DEFAULT

             found = .FALSE.

       END SELECT

    END SUBROUTINE pcm_rrd_local

!------------------------------------------------------------------------------!
! Description:
! ------------
!> Calculation of the tendency terms, accounting for the effect of the plant
!> canopy on momentum and scalar quantities.
!>
!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0 
!> (defined on scalar grid), as initialized in subroutine pcm_init. 
!> The lad on the w-grid is vertically interpolated from the surrounding
!> lad_s. The upper boundary of the canopy is defined on the w-grid at 
!> k = pch_index. Here, the lad is zero.
!>
!> The canopy drag must be limited (previously accounted for by calculation of 
!> a limiting canopy timestep for the determination of the maximum LES timestep
!> in subroutine timestep), since it is physically impossible that the canopy
!> drag alone can locally change the sign of a velocity component. This 
!> limitation is realized by calculating preliminary tendencies and velocities.
!> It is subsequently checked if the preliminary new velocity has a different
!> sign than the current velocity. If so, the tendency is limited in a way that
!> the velocity can at maximum be reduced to zero by the canopy drag. 
!>
!>
!> Call for all grid points
!------------------------------------------------------------------------------!
    SUBROUTINE pcm_tendency( component )

       INTEGER(iwp) ::  component !< prognostic variable (u,v,w,pt,q,e)
       INTEGER(iwp) ::  i         !< running index
       INTEGER(iwp) ::  j         !< running index
       INTEGER(iwp) ::  k         !< running index
       INTEGER(iwp) ::  kk        !< running index for flat lad arrays

       LOGICAL ::  building_edge_e !< control flag indicating an eastward-facing building edge
       LOGICAL ::  building_edge_n !< control flag indicating a north-facing building edge
       LOGICAL ::  building_edge_s !< control flag indicating a south-facing building edge
       LOGICAL ::  building_edge_w !< control flag indicating a westward-facing building edge

       REAL(wp) ::  ddt_3d    !< inverse of the LES timestep (dt_3d)
       REAL(wp) ::  lad_local !< local lad value
       REAL(wp) ::  pre_tend  !< preliminary tendency
       REAL(wp) ::  pre_u     !< preliminary u-value 
       REAL(wp) ::  pre_v     !< preliminary v-value 
       REAL(wp) ::  pre_w     !< preliminary w-value 


       ddt_3d = 1.0_wp / dt_3d
 
!
!--    Compute drag for the three velocity components and the SGS-TKE:
       SELECT CASE ( component )

!
!--       u-component
          CASE ( 1 )
             DO  i = nxlu, nxr
                DO  j = nys, nyn
!
!--                Set control flags indicating east- and westward-orientated 
!--                building edges. Note, building_egde_w is set from the perspective
!--                of the potential rooftop grid point, while building_edge_e is
!--                is set from the perspective of the non-building grid point.
                   building_edge_w = ANY( BTEST( wall_flags_total_0(:,j,i),   6 ) )&
                        .AND.  .NOT. ANY( BTEST( wall_flags_total_0(:,j,i-1), 6 ) )
                   building_edge_e = ANY( BTEST( wall_flags_total_0(:,j,i-1), 6 ) )&
                        .AND.  .NOT. ANY( BTEST( wall_flags_total_0(:,j,i),   6 ) )
!
!--                Determine topography-top index on u-grid
                   DO  k = topo_top_ind(j,i,1)+1, topo_top_ind(j,i,1) + pch_index_ji(j,i)

                      kk = k - topo_top_ind(j,i,1)   !- lad arrays are defined flat
!
!--                   In order to create sharp boundaries of the plant canopy, 
!--                   the lad on the u-grid at index (k,j,i) is equal to lad_s(k,j,i),
!--                   rather than being interpolated from the surrounding lad_s, 
!--                   because this would yield smaller lad at the canopy boundaries 
!--                   than inside of the canopy.
!--                   For the same reason, the lad at the rightmost(i+1)canopy 
!--                   boundary on the u-grid equals lad_s(k,j,i), which is considered
!--                   in the next if-statement. Note, at left-sided building edges 
!--                   this is not applied, here the LAD is equals the LAD at grid
!--                   point (k,j,i), in order to avoid that LAD is mistakenly mapped 
!--                   on top of a roof where (usually) is no LAD is defined. 
                      lad_local = lad_s(kk,j,i)
                      IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp  &
                           .AND.  .NOT. building_edge_w )  lad_local = lad_s(kk,j,i-1)
!
!--                   In order to avoid that LAD is mistakenly considered at right-
!--                   sided building edges (here the topography-top index for the
!--                   u-component at index j,i is still on the building while the
!--                   topography top for the scalar isn't), LAD is taken from grid
!--                   point (j,i-1).
                      IF ( lad_local > 0.0_wp .AND. lad_s(kk,j,i-1) == 0.0_wp  &
                           .AND.  building_edge_e )  lad_local = lad_s(kk,j,i-1)

                      pre_tend = 0.0_wp
                      pre_u = 0.0_wp
!
!--                   Calculate preliminary value (pre_tend) of the tendency
                      pre_tend = - canopy_drag_coeff *                         &
                                   lad_local *                                 &
                                   SQRT( u(k,j,i)**2 +                         &
                                         ( 0.25_wp * ( v(k,j,i-1) +            &
                                                       v(k,j,i)   +            &
                                                       v(k,j+1,i) +            &
                                                       v(k,j+1,i-1) )          &
                                         )**2 +                                &
                                         ( 0.25_wp * ( w(k-1,j,i-1) +          &
                                                       w(k-1,j,i)   +          &
                                                       w(k,j,i-1)   +          &
                                                       w(k,j,i) )              &
                                         )**2                                  &
                                       ) *                                     &
                                   u(k,j,i)

!
!--                   Calculate preliminary new velocity, based on pre_tend
                      pre_u = u(k,j,i) + dt_3d * pre_tend
!
!--                   Compare sign of old velocity and new preliminary velocity,
!--                   and in case the signs are different, limit the tendency
                      IF ( SIGN(pre_u,u(k,j,i)) /= pre_u )  THEN
                         pre_tend = - u(k,j,i) * ddt_3d
                      ENDIF
!
!--                   Calculate final tendency
                      tend(k,j,i) = tend(k,j,i) + pre_tend

                   ENDDO
                ENDDO
             ENDDO

!
!--       v-component
          CASE ( 2 )
             DO  i = nxl, nxr
                DO  j = nysv, nyn
!
!--                Set control flags indicating north- and southward-orientated 
!--                building edges. Note, building_egde_s is set from the perspective
!--                of the potential rooftop grid point, while building_edge_n is
!--                is set from the perspective of the non-building grid point.
                   building_edge_s = ANY( BTEST( wall_flags_total_0(:,j,i),   6 ) )&
                        .AND.  .NOT. ANY( BTEST( wall_flags_total_0(:,j-1,i), 6 ) )
                   building_edge_n = ANY( BTEST( wall_flags_total_0(:,j-1,i), 6 ) )&
                        .AND.  .NOT. ANY( BTEST( wall_flags_total_0(:,j,i),   6 ) )
!
!--                Determine topography-top index on v-grid
                   DO  k = topo_top_ind(j,i,2)+1, topo_top_ind(j,i,2) + pch_index_ji(j,i)

                      kk = k - topo_top_ind(j,i,2)   !- lad arrays are defined flat
!
!--                   In order to create sharp boundaries of the plant canopy, 
!--                   the lad on the v-grid at index (k,j,i) is equal to lad_s(k,j,i),
!--                   rather than being interpolated from the surrounding lad_s, 
!--                   because this would yield smaller lad at the canopy boundaries 
!--                   than inside of the canopy.
!--                   For the same reason, the lad at the northmost(j+1)canopy 
!--                   boundary on the v-grid equals lad_s(k,j,i), which is considered
!--                   in the next if-statement. Note, at left-sided building edges 
!--                   this is not applied, here the LAD is equals the LAD at grid
!--                   point (k,j,i), in order to avoid that LAD is mistakenly mapped 
!--                   on top of a roof where (usually) is no LAD is defined. 
                      lad_local = lad_s(kk,j,i)
                      IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp &
                       .AND.  .NOT. building_edge_s )  lad_local = lad_s(kk,j-1,i)
!
!--                   In order to avoid that LAD is mistakenly considered at right-
!--                   sided building edges (here the topography-top index for the
!--                   u-component at index j,i is still on the building while the
!--                   topography top for the scalar isn't), LAD is taken from grid
!--                   point (j,i-1). 
                      IF ( lad_local > 0.0_wp .AND. lad_s(kk,j-1,i) == 0.0_wp  &
                       .AND.  building_edge_n )  lad_local = lad_s(kk,j-1,i)

                      pre_tend = 0.0_wp
                      pre_v = 0.0_wp
!
!--                   Calculate preliminary value (pre_tend) of the tendency
                      pre_tend = - canopy_drag_coeff *                         &
                                   lad_local *                                 &
                                   SQRT( ( 0.25_wp * ( u(k,j-1,i)   +          &
                                                       u(k,j-1,i+1) +          &
                                                       u(k,j,i)     +          &
                                                       u(k,j,i+1) )            &
                                         )**2 +                                &
                                         v(k,j,i)**2 +                         &
                                         ( 0.25_wp * ( w(k-1,j-1,i) +          &
                                                       w(k-1,j,i)   +          &
                                                       w(k,j-1,i)   +          &
                                                       w(k,j,i) )              &
                                         )**2                                  &
                                       ) *                                     &
                                   v(k,j,i)

!
!--                   Calculate preliminary new velocity, based on pre_tend
                      pre_v = v(k,j,i) + dt_3d * pre_tend
!
!--                   Compare sign of old velocity and new preliminary velocity,
!--                   and in case the signs are different, limit the tendency
                      IF ( SIGN(pre_v,v(k,j,i)) /= pre_v )  THEN
                         pre_tend = - v(k,j,i) * ddt_3d
                      ELSE
                         pre_tend = pre_tend
                      ENDIF
!
!--                   Calculate final tendency
                      tend(k,j,i) = tend(k,j,i) + pre_tend

                   ENDDO
                ENDDO
             ENDDO

!
!--       w-component
          CASE ( 3 )
             DO  i = nxl, nxr
                DO  j = nys, nyn
!
!--                Determine topography-top index on w-grid
                   DO  k = topo_top_ind(j,i,3)+1, topo_top_ind(j,i,3) + pch_index_ji(j,i) - 1

                      kk = k - topo_top_ind(j,i,3)   !- lad arrays are defined flat

                      pre_tend = 0.0_wp
                      pre_w = 0.0_wp
!
!--                   Calculate preliminary value (pre_tend) of the tendency
                      pre_tend = - canopy_drag_coeff *                         &
                                   (0.5_wp *                                   &
                                      ( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) *   &
                                   SQRT( ( 0.25_wp * ( u(k,j,i)   +            &
                                                       u(k,j,i+1) +            &
                                                       u(k+1,j,i) +            &
                                                       u(k+1,j,i+1) )          &
                                         )**2 +                                &
                                         ( 0.25_wp * ( v(k,j,i)   +            &
                                                       v(k,j+1,i) +            &
                                                       v(k+1,j,i) +            &
                                                       v(k+1,j+1,i) )          &
                                         )**2 +                                &
                                         w(k,j,i)**2                           &
                                       ) *                                     &
                                   w(k,j,i)
!
!--                   Calculate preliminary new velocity, based on pre_tend
                      pre_w = w(k,j,i) + dt_3d * pre_tend
!
!--                   Compare sign of old velocity and new preliminary velocity,
!--                   and in case the signs are different, limit the tendency
                      IF ( SIGN(pre_w,w(k,j,i)) /= pre_w )  THEN
                         pre_tend = - w(k,j,i) * ddt_3d
                      ELSE
                         pre_tend = pre_tend
                      ENDIF
!
!--                   Calculate final tendency
                      tend(k,j,i) = tend(k,j,i) + pre_tend

                   ENDDO
                ENDDO
             ENDDO

!
!--       potential temperature
          CASE ( 4 )
             IF ( humidity ) THEN
                DO  i = nxl, nxr
                   DO  j = nys, nyn
!--                   Determine topography-top index on scalar-grid
                      DO  k = topo_top_ind(j,i,0)+1, topo_top_ind(j,i,0) + pch_index_ji(j,i)
                         kk = k - topo_top_ind(j,i,0)   !- lad arrays are defined flat
                         tend(k,j,i) = tend(k,j,i) + pcm_heating_rate(kk,j,i) - pcm_latent_rate(kk,j,i)
                      ENDDO
                   ENDDO
                ENDDO
             ELSE
                DO  i = nxl, nxr
                   DO  j = nys, nyn
!--                   Determine topography-top index on scalar-grid
                      DO  k = topo_top_ind(j,i,0)+1, topo_top_ind(j,i,0) + pch_index_ji(j,i)
                         kk = k - topo_top_ind(j,i,0)   !- lad arrays are defined flat
                         tend(k,j,i) = tend(k,j,i) + pcm_heating_rate(kk,j,i)
                      ENDDO
                   ENDDO
                ENDDO
             ENDIF

!
!--       humidity
          CASE ( 5 )
             DO  i = nxl, nxr
                DO  j = nys, nyn
!
!--                Determine topography-top index on scalar-grid
                   DO  k = topo_top_ind(j,i,0)+1, topo_top_ind(j,i,0) + pch_index_ji(j,i)

                      kk = k - topo_top_ind(j,i,0)   !- lad arrays are defined flat

                      IF ( .NOT. plant_canopy_transpiration ) THEN
                         ! pcm_transpiration_rate is calculated in radiation model
                         ! in case of plant_canopy_transpiration = .T.
                         ! to include also the dependecy to the radiation
                         ! in the plant canopy box
                         pcm_transpiration_rate(kk,j,i) =  - leaf_scalar_exch_coeff &
                                          * lad_s(kk,j,i) *                         &
                                          SQRT( ( 0.5_wp * ( u(k,j,i) +             &
                                                             u(k,j,i+1) )           &
                                                )**2 +                              &
                                                ( 0.5_wp * ( v(k,j,i) +             &
                                                             v(k,j+1,i) )           &
                                                )**2 +                              &
                                                ( 0.5_wp * ( w(k-1,j,i) +           &
                                                             w(k,j,i) )             &
                                                )**2                                &
                                              ) *                                   &
                                          ( q(k,j,i) - leaf_surface_conc )
                      ENDIF

                      tend(k,j,i) = tend(k,j,i) + pcm_transpiration_rate(kk,j,i)
                   ENDDO
                ENDDO
             ENDDO

!
!--       sgs-tke
          CASE ( 6 )
             DO  i = nxl, nxr
                DO  j = nys, nyn
!
!--                Determine topography-top index on scalar-grid
                   DO  k = topo_top_ind(j,i,0)+1, topo_top_ind(j,i,0) + pch_index_ji(j,i)

                      kk = k - topo_top_ind(j,i,0)   !- lad arrays are defined flat
                      tend(k,j,i) = tend(k,j,i) -                              &
                                       2.0_wp * canopy_drag_coeff *            &
                                       lad_s(kk,j,i) *                         &
                                       SQRT( ( 0.5_wp * ( u(k,j,i) +           &
                                                          u(k,j,i+1) )         &
                                             )**2 +                            &
                                             ( 0.5_wp * ( v(k,j,i) +           &
                                                          v(k,j+1,i) )         &
                                             )**2 +                            &
                                             ( 0.5_wp * ( w(k,j,i) +           &
                                                          w(k+1,j,i) )         &
                                             )**2                              &
                                           ) *                                 &
                                       e(k,j,i)
                   ENDDO
                ENDDO
             ENDDO 
!
!--       scalar concentration
          CASE ( 7 )
             DO  i = nxl, nxr
                DO  j = nys, nyn
!
!--                Determine topography-top index on scalar-grid
                   DO  k = topo_top_ind(j,i,0)+1, topo_top_ind(j,i,0) + pch_index_ji(j,i)

                      kk = k - topo_top_ind(j,i,0)   !- lad arrays are defined flat
                      tend(k,j,i) = tend(k,j,i) -                              &
                                       leaf_scalar_exch_coeff *                &
                                       lad_s(kk,j,i) *                         &
                                       SQRT( ( 0.5_wp * ( u(k,j,i) +           &
                                                          u(k,j,i+1) )         &
                                             )**2 +                            &
                                             ( 0.5_wp * ( v(k,j,i) +           &
                                                          v(k,j+1,i) )         &
                                             )**2 +                            &
                                             ( 0.5_wp * ( w(k-1,j,i) +         & 
                                                          w(k,j,i) )           &
                                             )**2                              &
                                           ) *                                 &
                                       ( s(k,j,i) - leaf_surface_conc )
                   ENDDO
                ENDDO
             ENDDO    



          CASE DEFAULT

             WRITE( message_string, * ) 'wrong component: ', component
             CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 ) 

       END SELECT

    END SUBROUTINE pcm_tendency


!------------------------------------------------------------------------------!
! Description:
! ------------
!> Calculation of the tendency terms, accounting for the effect of the plant
!> canopy on momentum and scalar quantities.
!>
!> The canopy is located where the leaf area density lad_s(k,j,i) > 0.0 
!> (defined on scalar grid), as initialized in subroutine pcm_init. 
!> The lad on the w-grid is vertically interpolated from the surrounding
!> lad_s. The upper boundary of the canopy is defined on the w-grid at 
!> k = pch_index. Here, the lad is zero.
!>
!> The canopy drag must be limited (previously accounted for by calculation of 
!> a limiting canopy timestep for the determination of the maximum LES timestep
!> in subroutine timestep), since it is physically impossible that the canopy
!> drag alone can locally change the sign of a velocity component. This 
!> limitation is realized by calculating preliminary tendencies and velocities.
!> It is subsequently checked if the preliminary new velocity has a different
!> sign than the current velocity. If so, the tendency is limited in a way that
!> the velocity can at maximum be reduced to zero by the canopy drag. 
!>
!>
!> Call for grid point i,j
!------------------------------------------------------------------------------!
    SUBROUTINE pcm_tendency_ij( i, j, component )

       INTEGER(iwp) ::  component !< prognostic variable (u,v,w,pt,q,e)
       INTEGER(iwp) ::  i         !< running index
       INTEGER(iwp) ::  j         !< running index
       INTEGER(iwp) ::  k         !< running index
       INTEGER(iwp) ::  kk        !< running index for flat lad arrays

       LOGICAL ::  building_edge_e !< control flag indicating an eastward-facing building edge
       LOGICAL ::  building_edge_n !< control flag indicating a north-facing building edge
       LOGICAL ::  building_edge_s !< control flag indicating a south-facing building edge
       LOGICAL ::  building_edge_w !< control flag indicating a westward-facing building edge

       REAL(wp) ::  ddt_3d    !< inverse of the LES timestep (dt_3d)
       REAL(wp) ::  lad_local !< local lad value
       REAL(wp) ::  pre_tend  !< preliminary tendency
       REAL(wp) ::  pre_u     !< preliminary u-value 
       REAL(wp) ::  pre_v     !< preliminary v-value 
       REAL(wp) ::  pre_w     !< preliminary w-value 


       ddt_3d = 1.0_wp / dt_3d
!
!--    Compute drag for the three velocity components and the SGS-TKE
       SELECT CASE ( component )

!
!--       u-component
          CASE ( 1 )
!
!--          Set control flags indicating east- and westward-orientated 
!--          building edges. Note, building_egde_w is set from the perspective
!--          of the potential rooftop grid point, while building_edge_e is
!--          is set from the perspective of the non-building grid point.
             building_edge_w = ANY( BTEST( wall_flags_total_0(:,j,i),   6 ) )  .AND. &
                         .NOT. ANY( BTEST( wall_flags_total_0(:,j,i-1), 6 ) )
             building_edge_e = ANY( BTEST( wall_flags_total_0(:,j,i-1), 6 ) )  .AND. &
                         .NOT. ANY( BTEST( wall_flags_total_0(:,j,i),   6 ) )
!
!--          Determine topography-top index on u-grid
             DO  k = topo_top_ind(j,i,1) + 1, topo_top_ind(j,i,1) + pch_index_ji(j,i)

                kk = k - topo_top_ind(j,i,1)  !- lad arrays are defined flat

!
!--             In order to create sharp boundaries of the plant canopy, 
!--             the lad on the u-grid at index (k,j,i) is equal to lad_s(k,j,i),
!--             rather than being interpolated from the surrounding lad_s, 
!--             because this would yield smaller lad at the canopy boundaries 
!--             than inside of the canopy.
!--             For the same reason, the lad at the rightmost(i+1)canopy 
!--             boundary on the u-grid equals lad_s(k,j,i), which is considered
!--             in the next if-statement. Note, at left-sided building edges 
!--             this is not applied, here the LAD is equals the LAD at grid
!--             point (k,j,i), in order to avoid that LAD is mistakenly mapped 
!--             on top of a roof where (usually) is no LAD is defined. 
                lad_local = lad_s(kk,j,i)
                IF ( lad_local == 0.0_wp .AND. lad_s(kk,j,i-1) > 0.0_wp  .AND. &
                     .NOT. building_edge_w )  lad_local = lad_s(kk,j,i-1)
!
!--             In order to avoid that LAD is mistakenly considered at right-
!--             sided building edges (here the topography-top index for the
!--             u-component at index j,i is still on the building while the
!--             topography top for the scalar isn't), LAD is taken from grid
!--             point (j,i-1). 
                IF ( lad_local > 0.0_wp .AND. lad_s(kk,j,i-1) == 0.0_wp  .AND. &
                     building_edge_e )  lad_local = lad_s(kk,j,i-1)

                pre_tend = 0.0_wp
                pre_u = 0.0_wp
!
!--             Calculate preliminary value (pre_tend) of the tendency
                pre_tend = - canopy_drag_coeff *                               &
                             lad_local *                                       &   
                             SQRT( u(k,j,i)**2 +                               &
                                   ( 0.25_wp * ( v(k,j,i-1)  +                 &
                                                 v(k,j,i)    +                 &
                                                 v(k,j+1,i)  +                 &
                                                 v(k,j+1,i-1) )                &
                                   )**2 +                                      &
                                   ( 0.25_wp * ( w(k-1,j,i-1) +                &
                                                 w(k-1,j,i)   +                &
                                                 w(k,j,i-1)   +                &
                                                 w(k,j,i) )                    &
                                   )**2                                        &
                                 ) *                                           &
                             u(k,j,i)

!
!--             Calculate preliminary new velocity, based on pre_tend
                pre_u = u(k,j,i) + dt_3d * pre_tend
!
!--             Compare sign of old velocity and new preliminary velocity,
!--             and in case the signs are different, limit the tendency
                IF ( SIGN(pre_u,u(k,j,i)) /= pre_u )  THEN
                   pre_tend = - u(k,j,i) * ddt_3d
                ELSE
                   pre_tend = pre_tend
                ENDIF
!
!--             Calculate final tendency
                tend(k,j,i) = tend(k,j,i) + pre_tend
             ENDDO


!
!--       v-component
          CASE ( 2 )
!
!--          Set control flags indicating north- and southward-orientated 
!--          building edges. Note, building_egde_s is set from the perspective
!--          of the potential rooftop grid point, while building_edge_n is
!--          is set from the perspective of the non-building grid point.
             building_edge_s = ANY( BTEST( wall_flags_total_0(:,j,i),   6 ) )  .AND. &
                         .NOT. ANY( BTEST( wall_flags_total_0(:,j-1,i), 6 ) )
             building_edge_n = ANY( BTEST( wall_flags_total_0(:,j-1,i), 6 ) )  .AND. &
                         .NOT. ANY( BTEST( wall_flags_total_0(:,j,i),   6 ) )
!
!--          Determine topography-top index on v-grid
             DO  k = topo_top_ind(j,i,2) + 1, topo_top_ind(j,i,2) + pch_index_ji(j,i)

                kk = k - topo_top_ind(j,i,2)  !- lad arrays are defined flat
!
!--             In order to create sharp boundaries of the plant canopy, 
!--             the lad on the v-grid at index (k,j,i) is equal to lad_s(k,j,i),
!--             rather than being interpolated from the surrounding lad_s, 
!--             because this would yield smaller lad at the canopy boundaries 
!--             than inside of the canopy.
!--             For the same reason, the lad at the northmost(j+1)canopy 
!--             boundary on the v-grid equals lad_s(k,j,i), which is considered
!--             in the next if-statement. Note, at left-sided building edges 
!--             this is not applied, here the LAD is equals the LAD at grid
!--             point (k,j,i), in order to avoid that LAD is mistakenly mapped 
!--             on top of a roof where (usually) is no LAD is defined. 
                lad_local = lad_s(kk,j,i)
                IF ( lad_local == 0.0_wp .AND. lad_s(kk,j-1,i) > 0.0_wp  .AND. &
                     .NOT. building_edge_s )  lad_local = lad_s(kk,j-1,i)
!
!--             In order to avoid that LAD is mistakenly considered at right-
!--             sided building edges (here the topography-top index for the
!--             u-component at index j,i is still on the building while the
!--             topography top for the scalar isn't), LAD is taken from grid
!--             point (j,i-1). 
                IF ( lad_local > 0.0_wp .AND. lad_s(kk,j-1,i) == 0.0_wp  .AND. &
                     building_edge_n )  lad_local = lad_s(kk,j-1,i)

                pre_tend = 0.0_wp
                pre_v = 0.0_wp
!
!--             Calculate preliminary value (pre_tend) of the tendency
                pre_tend = - canopy_drag_coeff *                               &
                             lad_local *                                       &
                             SQRT( ( 0.25_wp * ( u(k,j-1,i)   +                &
                                                 u(k,j-1,i+1) +                &
                                                 u(k,j,i)     +                &
                                                 u(k,j,i+1) )                  &
                                   )**2 +                                      &
                                   v(k,j,i)**2 +                               &
                                   ( 0.25_wp * ( w(k-1,j-1,i) +                &
                                                 w(k-1,j,i)   +                &
                                                 w(k,j-1,i)   +                &
                                                 w(k,j,i) )                    &
                                   )**2                                        &
                                 ) *                                           &
                             v(k,j,i)

!
!--             Calculate preliminary new velocity, based on pre_tend
                pre_v = v(k,j,i) + dt_3d * pre_tend
!
!--             Compare sign of old velocity and new preliminary velocity,
!--             and in case the signs are different, limit the tendency
                IF ( SIGN(pre_v,v(k,j,i)) /= pre_v )  THEN
                   pre_tend = - v(k,j,i) * ddt_3d
                ELSE
                   pre_tend = pre_tend
                ENDIF
!
!--             Calculate final tendency
                tend(k,j,i) = tend(k,j,i) + pre_tend
             ENDDO


!
!--       w-component
          CASE ( 3 )
!
!--          Determine topography-top index on w-grid
             DO  k = topo_top_ind(j,i,3) + 1, topo_top_ind(j,i,3) + pch_index_ji(j,i) - 1

                kk = k - topo_top_ind(j,i,3)  !- lad arrays are defined flat

                pre_tend = 0.0_wp
                pre_w = 0.0_wp
!
!--             Calculate preliminary value (pre_tend) of the tendency
                pre_tend = - canopy_drag_coeff *                               &
                             (0.5_wp *                                         &
                                ( lad_s(kk+1,j,i) + lad_s(kk,j,i) )) *         &
                             SQRT( ( 0.25_wp * ( u(k,j,i)    +                 &  
                                                 u(k,j,i+1)  +                 &
                                                 u(k+1,j,i)  +                 &
                                                 u(k+1,j,i+1) )                &
                                   )**2 +                                      &
                                   ( 0.25_wp * ( v(k,j,i)    +                 &
                                                 v(k,j+1,i)  +                 &
                                                 v(k+1,j,i)  +                 &
                                                 v(k+1,j+1,i) )                &
                                   )**2 +                                      &
                                   w(k,j,i)**2                                 &
                                 ) *                                           &
                             w(k,j,i)
!
!--             Calculate preliminary new velocity, based on pre_tend
                pre_w = w(k,j,i) + dt_3d * pre_tend
!
!--             Compare sign of old velocity and new preliminary velocity,
!--             and in case the signs are different, limit the tendency
                IF ( SIGN(pre_w,w(k,j,i)) /= pre_w )  THEN
                   pre_tend = - w(k,j,i) * ddt_3d
                ELSE
                   pre_tend = pre_tend
                ENDIF
!
!--             Calculate final tendency
                tend(k,j,i) = tend(k,j,i) + pre_tend
             ENDDO

!
!--       potential temperature
          CASE ( 4 )
!
!--          Determine topography-top index on scalar grid
             IF ( humidity ) THEN
                DO  k = topo_top_ind(j,i,0) + 1, topo_top_ind(j,i,0) + pch_index_ji(j,i)
                   kk = k - topo_top_ind(j,i,0)  !- lad arrays are defined flat
                   tend(k,j,i) = tend(k,j,i) + pcm_heating_rate(kk,j,i) -       &
                                 pcm_latent_rate(kk,j,i)
                ENDDO
             ELSE
                DO  k = topo_top_ind(j,i,0) + 1, topo_top_ind(j,i,0) + pch_index_ji(j,i)
                   kk = k - topo_top_ind(j,i,0)  !- lad arrays are defined flat
                   tend(k,j,i) = tend(k,j,i) + pcm_heating_rate(kk,j,i)
                ENDDO
             ENDIF

!
!--       humidity
          CASE ( 5 )
!
!--          Determine topography-top index on scalar grid
             DO  k = topo_top_ind(j,i,0) + 1, topo_top_ind(j,i,0) + pch_index_ji(j,i)
                kk = k - topo_top_ind(j,i,0)  !- lad arrays are defined flat
                IF ( .NOT. plant_canopy_transpiration ) THEN
                   ! pcm_transpiration_rate is calculated in radiation model
                   ! in case of plant_canopy_transpiration = .T.
                   ! to include also the dependecy to the radiation
                   ! in the plant canopy box
                   pcm_transpiration_rate(kk,j,i) = - leaf_scalar_exch_coeff   &
                                    * lad_s(kk,j,i) *                          &
                                    SQRT( ( 0.5_wp * ( u(k,j,i) +              &
                                                       u(k,j,i+1) )            &
                                          )**2  +                              &
                                          ( 0.5_wp * ( v(k,j,i) +              &
                                                       v(k,j+1,i) )            &
                                          )**2 +                               &
                                          ( 0.5_wp * ( w(k-1,j,i) +            &
                                                       w(k,j,i) )              &
                                          )**2                                 &
                                        ) *                                    &
                                    ( q(k,j,i) - leaf_surface_conc )
                ENDIF

                tend(k,j,i) = tend(k,j,i) + pcm_transpiration_rate(kk,j,i)

             ENDDO   

!
!--       sgs-tke
          CASE ( 6 )
!
!--          Determine topography-top index on scalar grid
             DO  k = topo_top_ind(j,i,0) + 1, topo_top_ind(j,i,0) + pch_index_ji(j,i)

                kk = k - topo_top_ind(j,i,0)
                tend(k,j,i) = tend(k,j,i) -                                    &
                                 2.0_wp * canopy_drag_coeff *                  &
                                 lad_s(kk,j,i) *                               &
                                 SQRT( ( 0.5_wp * ( u(k,j,i) +                 &
                                                    u(k,j,i+1) )               &
                                       )**2 +                                  &  
                                       ( 0.5_wp * ( v(k,j,i) +                 &
                                                    v(k,j+1,i) )               &
                                       )**2 +                                  &
                                       ( 0.5_wp * ( w(k,j,i) +                 &
                                                    w(k+1,j,i) )               &
                                       )**2                                    &
                                     ) *                                       &
                                 e(k,j,i)
             ENDDO
             
!
!--       scalar concentration 
          CASE ( 7 )
!
!--          Determine topography-top index on scalar grid
             DO  k = topo_top_ind(j,i,0) + 1, topo_top_ind(j,i,0) + pch_index_ji(j,i)

                kk = k - topo_top_ind(j,i,0)
                tend(k,j,i) = tend(k,j,i) -                                    &
                                 leaf_scalar_exch_coeff *                      &
                                 lad_s(kk,j,i) *                               &
                                 SQRT( ( 0.5_wp * ( u(k,j,i) +                 &
                                                    u(k,j,i+1) )               &
                                       )**2  +                                 &
                                       ( 0.5_wp * ( v(k,j,i) +                 &
                                                    v(k,j+1,i) )               &
                                       )**2 +                                  &
                                       ( 0.5_wp * ( w(k-1,j,i) +               &
                                                    w(k,j,i) )                 &
                                       )**2                                    &
                                     ) *                                       &
                                 ( s(k,j,i) - leaf_surface_conc )
             ENDDO                

       CASE DEFAULT

          WRITE( message_string, * ) 'wrong component: ', component
          CALL message( 'pcm_tendency', 'PA0279', 1, 2, 0, 6, 0 ) 

       END SELECT

    END SUBROUTINE pcm_tendency_ij

!------------------------------------------------------------------------------!
! Description:
! ------------
!> Subroutine writes local (subdomain) restart data
!------------------------------------------------------------------------------!
    SUBROUTINE pcm_wrd_local

       IF ( ALLOCATED( pcm_heatrate_av ) )  THEN
          CALL wrd_write_string( 'pcm_heatrate_av' )
          WRITE ( 14 )  pcm_heatrate_av
       ENDIF

       IF ( ALLOCATED( pcm_latentrate_av ) )  THEN
          CALL wrd_write_string( 'pcm_latentrate_av' )
          WRITE ( 14 )  pcm_latentrate_av
       ENDIF

       IF ( ALLOCATED( pcm_transpirationrate_av ) )  THEN
          CALL wrd_write_string( 'pcm_transpirationrate_av' )
          WRITE ( 14 )  pcm_transpirationrate_av
       ENDIF

    END SUBROUTINE pcm_wrd_local


 END MODULE plant_canopy_model_mod