Class vdiffusion_my
In: vdiffusion/vdiffusion_my.f90

���´æ�¡æ�£ã���������� (Mellor and Yamada, 1974, 1982)

Vertical diffusion flux (Mellor and Yamada, 1974, 1982)

Note that Japanese and English are described in parallel.

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Vertical diffusion flux is calculated.

Procedures List

VDiffusion :���´æ�¡æ�£ã���������¹ã���ç®�
VDiffusionOutPut :���������¹ã���ºå��
———— :————
VDiffusion :Calculate vertical diffusion fluxes
VDiffusionOutPut :Output fluxes

NAMELIST

NAMELIST#vdiffusion_my_nml

Methods

Included Modules

gridset composition dc_types dc_message constants timeset gtool_historyauto mpi_wrapper phy_implicit_utils namelist_util dc_iounit dc_string axesset

Public Instance methods

Subroutine :
xyz_U(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ u $ . �±è¥¿é¢���. Eastward wind
xyz_V(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ v $ . �������. Northward wind
xyzf_QMix(0:imax-1, 1:jmax, 1:kmax, 1:ncmax) :real(DP), intent(in)
: $ q $ . è³��闋·å��æ¯�. Mass mixing ratio
xyz_Temp(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ T $ . æ¸�º¦. Temperature
xyr_Temp(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{T} $ . æ¸�º¦ (���´æ�°ã������). Temperature (half level)
xyz_VirTemp(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ T_v $ . ä»�¸©åº�. Virtual temperature
xyr_VirTemp(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). Virtual temperature (half level)
xyr_Press(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{p} $ . æ°��� (���´æ�°ã������). Air pressure (half level)
xy_SurfHeight(0:imax-1,1:jmax) :real(DP), intent(in)
: $ z_s $ . �°è¡¨�¢é�åº�. Surface height.
xyz_Height(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: é«�åº� (�´æ�°ã������). Height (full level)
xyr_Height(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: é«�åº� (���´æ�°ã������). Height (half level)
xyz_Exner(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: Exner �¢æ�� (�´æ�°ã������). Exner function (full level)
xyr_Exner(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: Exner �¢æ�� (���´æ�°ã������). Exner function (half level)
xyr_MomFluxX(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �±è¥¿�¹å�����������������. Eastward momentum flux
xyr_MomFluxY(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �����¹å�����������������. Northward momentum flux
xyr_HeatFlux(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �±ã����������. Heat flux
xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax) :real(DP), intent(out)
: ������������. Mass flux of compositions
xyr_VelDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�������. Diffusion coefficient: velocity
xyr_TempDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�æ¸�º¦. Transfer coefficient: temperature
xyr_QMixDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�æ¯�æ¹�. Diffusion coefficient: specific humidity

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Vertical diffusion flux is calculated by use of MY2 model.

[Source]

  subroutine VDiffusion( xyz_U, xyz_V, xyzf_QMix, xyz_Temp, xyr_Temp, xyz_VirTemp, xyr_VirTemp, xyr_Press, xy_SurfHeight, xyz_Height, xyr_Height, xyz_Exner, xyr_Exner, xyr_MomFluxX,  xyr_MomFluxY,  xyr_HeatFlux, xyrf_QMixFlux, xyr_VelDiffCoef, xyr_TempDiffCoef, xyr_QMixDiffCoef )
    !
    ! ���´æ�¡æ�£ã���������¹ã��è¨�ç®����¾ã��. 
    !
    ! Vertical diffusion flux is calculated by use of MY2 model.
    !

    ! �¢ã�¸ã�¥ã�¼ã����� ; USE statements
    !

    ! ����å®��°è¨­å®�
    ! Physical constants settings
    !
    use constants, only: FKarm, Grav
                              ! $ g $ [m s-2]. 
                              ! ���������. 
                              ! Gravitational acceleration

    ! ���»ç���
    ! Time control
    !
    use timeset, only: TimeN, TimesetClockStart, TimesetClockStop

    ! ���¹ã�������¼ã�¿å�ºå��
    ! History data output
    !
    use gtool_historyauto, only: HistoryAutoPut

    ! 宣�� ; Declaration statements
    !
    implicit none

    real(DP), intent(in):: xyz_U (0:imax-1, 1:jmax, 1:kmax)
                              ! $ u $ .   �±è¥¿é¢���. Eastward wind
    real(DP), intent(in):: xyz_V (0:imax-1, 1:jmax, 1:kmax)
                              ! $ v $ .   �������. Northward wind
    real(DP), intent(in):: xyzf_QMix(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
                              ! $ q $ .   è³��闋·å��æ¯�. Mass mixing ratio
    real(DP), intent(in):: xyz_Temp (0:imax-1, 1:jmax, 1:kmax)
                              ! $ T $ .   æ¸�º¦. Temperature
    real(DP), intent(in):: xyr_Temp (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{T} $ . æ¸�º¦ (���´æ�°ã������). 
                              ! Temperature (half level)
    real(DP), intent(in):: xyz_VirTemp (0:imax-1, 1:jmax, 1:kmax)
                              ! $ T_v $ .   ä»�¸©åº�. Virtual temperature
    real(DP), intent(in):: xyr_VirTemp (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). 
                              ! Virtual temperature (half level)
    real(DP), intent(in):: xyr_Press  (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{p} $ . æ°��� (���´æ�°ã������). 
                              ! Air pressure (half level)
    real(DP), intent(in):: xy_SurfHeight (0:imax-1,1:jmax)
                              ! $ z_s $ . �°è¡¨�¢é�åº�. 
                              ! Surface height. 
    real(DP), intent(in):: xyz_Height (0:imax-1, 1:jmax, 1:kmax)
                              ! é«�åº� (�´æ�°ã������). 
                              ! Height (full level)
    real(DP), intent(in):: xyr_Height (0:imax-1, 1:jmax, 0:kmax)
                              ! é«�åº� (���´æ�°ã������). 
                              ! Height (half level)
    real(DP), intent(in):: xyz_Exner (0:imax-1, 1:jmax, 1:kmax)
                              ! Exner �¢æ�� (�´æ�°ã������). 
                              ! Exner function (full level)
    real(DP), intent(in):: xyr_Exner (0:imax-1, 1:jmax, 0:kmax)
                              ! Exner �¢æ�� (���´æ�°ã������). 
                              ! Exner function (half level)

    real(DP), intent(out):: xyr_MomFluxX (0:imax-1, 1:jmax, 0:kmax)
                              ! �±è¥¿�¹å�����������������. 
                              ! Eastward momentum flux
    real(DP), intent(out):: xyr_MomFluxY (0:imax-1, 1:jmax, 0:kmax)
                              ! �����¹å�����������������. 
                              ! Northward momentum flux
    real(DP), intent(out):: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! �±ã����������. 
                              ! Heat flux
    real(DP), intent(out):: xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax)
                              ! ������������. 
                              ! Mass flux of compositions
    real(DP), intent(out):: xyr_VelDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�������. 
                              ! Diffusion coefficient: velocity
    real(DP), intent(out):: xyr_TempDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�æ¸�º¦. 
                              ! Transfer coefficient: temperature
    real(DP), intent(out):: xyr_QMixDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�æ¯�æ¹�. 
                              ! Diffusion coefficient: specific humidity

    ! �業��
    ! Work variables
    !
    real(DP) :: xyr_DVelDz (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \DD{|\Dvect{v}|}{z} $
    real(DP) :: xyr_BulkRiNum (0:imax-1, 1:jmax, 0:kmax)
                              ! ������ $ R_i $ ��. 
                              ! Bulk $ R_i $

    integer:: k               ! ���´æ�¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in vertical direction

    integer:: n               ! çµ����¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in dimension of constituents

    ! ���� ; Executable statement
    !

    ! ������確è�
    ! Initialization check
    !
    if ( .not. vdiffusion_my_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


    ! �����������
    ! Start measurement of computation time
    !
    call TimesetClockStart( module_name )


    ! �¡æ�£ä��°ã���ç®�
    ! Calculation of diffusion coefficient
    !
    if ( FlagConstDiffCoef ) then

      xyr_VelDiffCoef (:,:,0       ) = 0.0_DP
      xyr_VelDiffCoef (:,:,1:kmax-1) = ConstDiffCoefM
      xyr_VelDiffCoef (:,:,kmax    ) = 0.0_DP

      xyr_TempDiffCoef(:,:,0       ) = 0.0_DP
      xyr_TempDiffCoef(:,:,1:kmax-1) = ConstDiffCoefH
      xyr_TempDiffCoef(:,:,kmax    ) = 0.0_DP

      xyr_QMixDiffCoef(:,:,0       ) = 0.0_DP
      xyr_QMixDiffCoef(:,:,1:kmax-1) = ConstDiffCoefH
      xyr_QMixDiffCoef(:,:,kmax    ) = 0.0_DP

    else

      ! ������ $ R_i $ �°ç���
      ! Calculate bulk $ R_i $
      !
      xyr_DVelDz(:,:,0)       = 0.0_DP
      xyr_DVelDz(:,:,kmax)    = 0.0_DP
      xyr_BulkRiNum(:,:,0)    = 0.0_DP
      xyr_BulkRiNum(:,:,kmax) = 0.0_DP

      do k = 1, kmax-1
        xyr_DVelDz(:,:,k) = sqrt( max( SquareVelMin , ( xyz_U(:,:,k+1) - xyz_U(:,:,k) )**2 + ( xyz_V(:,:,k+1) - xyz_V(:,:,k) )**2 ) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k) )

        xyr_BulkRiNum(:,:,k) = Grav / ( xyr_VirTemp(:,:,k) / xyr_Exner(:,:,k) ) * (   xyz_VirTemp(:,:,k+1) / xyz_Exner(:,:,k+1) - xyz_VirTemp(:,:,k  ) / xyz_Exner(:,:,k  ) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k) ) / xyr_DVelDz(:,:,k)**2

        xyr_BulkRiNum(:,:,k) = max( xyr_BulkRiNum(:,:,k) , BulkRiNumMin )
      end do

      ! �¡æ�£ä��°ã���ç®�
      ! Calculate diffusion coefficients
      !
      call VDiffCoefficient( xy_SurfHeight, xyr_Height, xyr_DVelDz, xyr_BulkRiNum, xyr_VelDiffCoef, xyr_TempDiffCoef, xyr_QMixDiffCoef )

    end if

    ! æµ���ç©��²å�æµ�
    ! Shallow cumulus convection
    !
    ! (AGCM5 ����å°��¥ä�å®�)


    ! �¡æ�£ä��°ã���ºå��
    ! Output diffusion coefficients
    !
    ! (ä¸�è¨�����æµ���ç©��²å�æµ���å°��¥å������)

    ! �¡æ�£ä��°å�ºå��
    ! Diffusion coeffficients output
    !
    call HistoryAutoPut( TimeN, 'VelDiffCoef',  xyr_VelDiffCoef  )
    call HistoryAutoPut( TimeN, 'TempDiffCoef', xyr_TempDiffCoef )
    call HistoryAutoPut( TimeN, 'QVapDiffCoef', xyr_QMixDiffCoef )


    ! 輸é��ä¿��°ã�����������¹ã���ç®�
    ! Calculate transfer coefficient and flux
    !
    call VDiffusionCalcFlux( xyz_U, xyz_V, xyzf_QMix, xyz_Temp, xyr_VirTemp, xyr_Press, xyz_Height, xyz_Exner, xyr_Exner, xyr_VelDiffCoef, xyr_TempDiffCoef, xyr_QMixDiffCoef, xyr_MomFluxX,  xyr_MomFluxY,  xyr_HeatFlux, xyrf_QMixFlux )

    ! ��������������
    ! Pause measurement of computation time
    !
    call TimesetClockStop( module_name )

  end subroutine VDiffusion
Subroutine :
xyr_Press(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in )
: $ hat{p} $ . æ°��� (���´æ�°ã������). Air pressure (half level)
xyr_MomFluxX(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in ), optional
: �±è¥¿�¹å�����������������. Eastward momentum flux
xyr_MomFluxY(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in ), optional
: �����¹å�����������������. Northward momentum flux
xyr_HeatFlux(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in ), optional
: �±ã����������. Heat flux
xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax) :real(DP), intent(in ), optional
: �湿���������. Specific humidity flux
xyz_DUDt(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(out), optional
: $ DP{u}{t} $ . �±è¥¿é¢���å¤���. Eastward wind tendency
xyz_DVDt(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(out), optional
: $ DP{v}{t} $ . ����������. Northward wind tendency
xyz_DTempDt(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(out), optional
: $ DP{T}{t} $ . æ¸�º¦å¤���. Temperature tendency
xyzf_DQMixDt(0:imax-1, 1:jmax, 1:kmax, 1:ncmax) :real(DP), intent(out), optional
: $ DP{q}{t} $ . è³��闋·å��æ¯�å¤���. Mass mixing ratio tendency

����å¤��������ç®���è¡����¾ã��.

Calculate tendencies.

[Source]

  subroutine VDiffusionExpTendency( xyr_Press, xyr_MomFluxX, xyr_MomFluxY, xyr_HeatFlux, xyrf_QMixFlux, xyz_DUDt, xyz_DVDt, xyz_DTempDt, xyzf_DQMixDt )
    !
    ! ����å¤��������ç®���è¡����¾ã��.
    !
    ! Calculate tendencies.
    !

    ! �¢ã�¸ã�¥ã�¼ã����� ; USE statements
    !

    ! ����å®��°è¨­å®�
    ! Physical constants settings
    !
    use constants, only: Grav, CpDry
                              ! $ C_p $ [J kg-1 K-1].
                              ! ä¹¾ç�¥å¤§æ°�����§æ���.
                              ! Specific heat of air at constant pressure

    ! 宣�� ; Declaration statements
    !
    implicit none

    real(DP), intent(in ):: xyr_Press (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{p} $ . æ°��� (���´æ�°ã������).
                              ! Air pressure (half level)
    real(DP), intent(in ), optional :: xyr_MomFluxX (0:imax-1, 1:jmax, 0:kmax)
                              ! �±è¥¿�¹å�����������������.
                              ! Eastward momentum flux
    real(DP), intent(in ), optional :: xyr_MomFluxY (0:imax-1, 1:jmax, 0:kmax)
                              ! �����¹å�����������������.
                              ! Northward momentum flux
    real(DP), intent(in ), optional :: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! �±ã����������.
                              ! Heat flux
    real(DP), intent(in ), optional :: xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax)
                              ! �湿���������.
                              ! Specific humidity flux
    real(DP), intent(out), optional :: xyz_DUDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{u}{t} $ . �±è¥¿é¢���å¤���.
                              ! Eastward wind tendency
    real(DP), intent(out), optional :: xyz_DVDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{v}{t} $ . ����������.
                              ! Northward wind tendency
    real(DP), intent(out), optional :: xyz_DTempDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{T}{t} $ . æ¸�º¦å¤���.
                              ! Temperature tendency
    real(DP), intent(out), optional :: xyzf_DQMixDt(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
                              ! $ \DP{q}{t} $ . è³��闋·å��æ¯�å¤���.
                              ! Mass mixing ratio tendency

    ! �業��
    ! Work variables
    !
    integer:: k               ! ���´æ�¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in vertical direction
    integer:: n               ! çµ����¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in dimension of constituents

    ! ���� ; Executable statement
    !

    ! ������確è�
    ! Initialization check
    !
    if ( .not. vdiffusion_my_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


    ! Check arguments
    !
    if ( present( xyz_DUDt ) ) then
      if ( .not. present( xyr_MomFluxX ) ) then
        call MessageNotify( 'E', module_name, 'xyr_MomFluxX has to be present.' )
      end if
    end if
    if ( present( xyz_DVDt ) ) then
      if ( .not. present( xyr_MomFluxY ) ) then
        call MessageNotify( 'E', module_name, 'xyr_MomFluxY has to be present.' )
      end if
    end if
    if ( present( xyz_DTempDt ) ) then
      if ( .not. present( xyr_HeatFlux ) ) then
        call MessageNotify( 'E', module_name, 'xyr_HeatFlux has to be present.' )
      end if
    end if
    if ( present( xyzf_DQMixDt ) ) then
      if ( .not. present( xyrf_QMixFlux ) ) then
        call MessageNotify( 'E', module_name, 'xyrf_QMixFlux has to be present.' )
      end if
    end if


    if ( present( xyz_DUDt ) ) then
      do k = 1, kmax
        xyz_DUDt(:,:,k) = + Grav * ( xyr_MomFluxX(:,:,k) - xyr_MomFluxX(:,:,k-1) ) / ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) )
      end do
    end if
    if ( present( xyz_DVDt ) ) then
      do k = 1, kmax
        xyz_DVDt(:,:,k) = + Grav * ( xyr_MomFluxY(:,:,k) - xyr_MomFluxY(:,:,k-1) ) / ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) )
      end do
    end if
    if ( present( xyz_DTempDt ) ) then
      do k = 1, kmax
        xyz_DTempDt(:,:,k) = + Grav / CpDry * ( xyr_HeatFlux(:,:,k) - xyr_HeatFlux(:,:,k-1) ) / ( xyr_Press   (:,:,k) - xyr_Press   (:,:,k-1) )
      end do
    end if

    if ( present( xyzf_DQMixDt ) ) then
      do n = 1, ncmax
        do k = 1, kmax
          xyzf_DQMixDt(:,:,k,n) = + Grav * ( xyrf_QMixFlux(:,:,k,n) - xyrf_QMixFlux(:,:,k-1,n) ) / ( xyr_Press    (:,:,k)   - xyr_Press    (:,:,k-1)   )
        end do
      end do
    end if


  end subroutine VDiffusionExpTendency
Subroutine :

vdiffusion_my �¢ã�¸ã�¥ã�¼ã������������è¡����¾ã��. NAMELIST#vdiffusion_my_nml ����¿è¾¼�¿ã��������ç¶����§è�����¾ã��.

"vdiffusion_my" module is initialized. "NAMELIST#vdiffusion_my_nml" is loaded in this procedure.

This procedure input/output NAMELIST#vdiffusion_my_nml .

[Source]

  subroutine VDiffusionInit
    !
    ! vdiffusion_my �¢ã�¸ã�¥ã�¼ã������������è¡����¾ã��. 
    ! NAMELIST#vdiffusion_my_nml ����¿è¾¼�¿ã��������ç¶����§è�����¾ã��. 
    !
    ! "vdiffusion_my" module is initialized. 
    ! "NAMELIST#vdiffusion_my_nml" is loaded in this procedure. 
    !

    ! �¢ã�¸ã�¥ã�¼ã����� ; USE statements
    !

    ! NAMELIST ���¡ã�¤ã���¥å�����¢ã�������¼ã���£ã������
    ! Utilities for NAMELIST file input
    !
    use namelist_util, only: namelist_filename, NmlutilMsg, NmlutilAryValid

    ! ���¡ã�¤ã���¥å�ºå��è£���
    ! File I/O support
    !
    use dc_iounit, only: FileOpen

    ! ç¨��¥å�������¡ã��
    ! Kind type parameter
    !
    use dc_types, only: STDOUT ! æ¨�æº��ºå�����ç½����. Unit number of standard output

    ! ��������
    ! Character handling
    !
    use dc_string, only: StoA

    ! ���¹ã�������¼ã�¿å�ºå��
    ! History data output
    !
    use gtool_historyauto, only: HistoryAutoAddVariable

    ! 座æ����¼ã�¿è¨­å®�
    ! Axes data settings
    !
    use axesset, only: AxnameX, AxnameY, AxnameZ, AxnameR, AxnameT

    ! 宣�� ; Declaration statements
    !
    implicit none

    integer:: unit_nml        ! NAMELIST ���¡ã�¤ã�����¼ã���³ç���ç½����. 
                              ! Unit number for NAMELIST file open
    integer:: iostat_nml      ! NAMELIST 読ã�¿è¾¼�¿æ���� IOSTAT. 
                              ! IOSTAT of NAMELIST read

    ! NAMELIST å¤��°ç¾¤
    ! NAMELIST group name
    !
    namelist /vdiffusion_my_nml/ FlagConstDiffCoef, ConstDiffCoefM, ConstDiffCoefH, SquareVelMin, BulkRiNumMin, MixLengthMax, ShMin, SmMin, VelDiffCoefMin, TempDiffCoefMin, VelDiffCoefMax, TempDiffCoefMax, MYConstA1, MYConstB1, MYConstA2, MYConstB2, MYConstC1
          !
          ! �����������¤ã���¤ã��������������ç¶� "vdiffusion_my#VDiffInit" 
          ! ���½ã�¼ã�¹ã�³ã�¼ã�������§ã������. 
          !
          ! Refer to source codes in the initialization procedure
          ! "vdiffusion_my#VDiffInit" for the default values. 
          !

    ! ���� ; Executable statement
    !

    if ( vdiffusion_my_inited ) return


    ! �����������¤ã��¨­å®�
    ! Default values settings
    !
    FlagConstDiffCoef = .false.
    ConstDiffCoefM    = 0.0_DP
    ConstDiffCoefH    = 0.0_DP

    SquareVelMin    =     0.1_DP
    BulkRiNumMin    = - 100.0_DP

    MixLengthMax    = 300.0_DP
    ShMin           =   0.0_DP
    SmMin           =   0.0_DP
    VelDiffCoefMin  =   0.1_DP
    TempDiffCoefMin =   0.1_DP
    VelDiffCoefMax  = 10000.0_DP
    TempDiffCoefMax = 10000.0_DP

    ! Parameters proposed by Mellor and Yamada (1982).
    !
    MYConstA1 =  0.92_DP
    MYConstB1 = 16.6_DP
    MYConstA2 =  0.74_DP
    MYConstB2 = 10.1_DP
    MYConstC1 =  0.08_DP


    ! NAMELIST ����¿è¾¼��
    ! NAMELIST is input
    !
    if ( trim(namelist_filename) /= '' ) then
      call FileOpen( unit_nml, namelist_filename, mode = 'r' ) ! (in)

      rewind( unit_nml )
      read( unit_nml, nml = vdiffusion_my_nml, iostat = iostat_nml )           ! (out)
      close( unit_nml )

      call NmlutilMsg( iostat_nml, module_name ) ! (in)
      if ( iostat_nml == 0 ) write( STDOUT, nml = vdiffusion_my_nml )
    end if


    ! ���¹ã�������¼ã�¿å�ºå�����������¸ã����°ç�»é��
    ! Register of variables for history data output
    !
    call HistoryAutoAddVariable( 'VelDiffCoef', (/ AxNameX, AxNameY, AxNameR, AxNameT /), 'diffusion coef. momentum', 'm2 s-1' )
    call HistoryAutoAddVariable( 'TempDiffCoef', (/ AxNameX, AxNameY, AxNameR, AxNameT /), 'diffusion coef. heat    ', 'm2 s-1' )
    call HistoryAutoAddVariable( 'QVapDiffCoef', (/ AxNameX, AxNameY, AxNameR, AxNameT /), 'diffusion coef. moisture', 'm2 s-1' )

    call HistoryAutoAddVariable( 'MomFluxX', (/ AxNameX, AxNameY, AxNameR, AxNameT /), 'eastward momentum flux', 'N m-2' )
    call HistoryAutoAddVariable( 'MomFluxY', (/ AxNameX, AxNameY, AxNameR, AxNameT /), 'northward momentum flux', 'N m-2' )
    call HistoryAutoAddVariable( 'HeatFlux', (/ AxNameX, AxNameY, AxNameR, AxNameT /), 'heat flux', 'W m-2' )
    call HistoryAutoAddVariable( 'QVapFlux', (/ AxNameX, AxNameY, AxNameR, AxNameT /), 'moisture flux', 'W m-2' )

    call HistoryAutoAddVariable( 'DUDtVDiff', (/ AxNameX, AxNameY, AxNameZ, AxNameT /), 'tendency of zonal wind by vertical diffusion', 'm s-2' )
    call HistoryAutoAddVariable( 'DVDtVDiff', (/ AxNameX, AxNameY, AxNameZ, AxNameT /), 'tendency of meridional wind by vertical diffusion', 'm s-2' )
    call HistoryAutoAddVariable( 'DTempDtVDiff', (/ AxNameX, AxNameY, AxNameZ, AxNameT /), 'tendency of temperature by vertical diffusion', 'K s-1' )
    call HistoryAutoAddVariable( 'DQVapDtVDiff', (/ AxNameX, AxNameY, AxNameZ, AxNameT /), 'tendency of specific humidity by vertical diffusion', 's-1' )

    call HistoryAutoAddVariable( 'TurKinEne', (/ AxNameX, AxNameY, AxNameR, AxNameT /), 'turbulent kinetic energy', 'm2 s-2' )

    call HistoryAutoAddVariable( 'TKEPShear', (/ AxNameX, AxNameY, AxNameZ, AxNameT /), 'turbulent kinetic energy production rate by shear', 'm2 s-3' )
    call HistoryAutoAddVariable( 'TKEPBuoy', (/ AxNameX, AxNameY, AxNameZ, AxNameT /), 'turbulent kinetic energy production rate by buoyancy', 'm2 s-3' )
    call HistoryAutoAddVariable( 'TKEDiss', (/ AxNameX, AxNameY, AxNameZ, AxNameT /), 'turbulent kinetic energy dissipation rate', 'm2 s-3' )
    call HistoryAutoAddVariable( 'MixLength', (/ AxNameX, AxNameY, AxNameZ, AxNameT /), 'mixing length', 'm' )

    ! �°å� ; Print
    !
    call MessageNotify( 'M', module_name, '----- Initialization Messages -----' )
    call MessageNotify( 'M', module_name, 'For vertical diffusion flux:' )
    call MessageNotify( 'M', module_name, '  FlagConstDiffCoef = %b', l = (/ FlagConstDiffCoef /) )
    call MessageNotify( 'M', module_name, '  ConstDiffCoefM    = %f', d = (/ ConstDiffCoefM /) )
    call MessageNotify( 'M', module_name, '  ConstDiffCoefH    = %f', d = (/ ConstDiffCoefH /) )
    call MessageNotify( 'M', module_name, '  SquareVelMin = %f', d = (/ SquareVelMin /) )
    call MessageNotify( 'M', module_name, '  BulkRiNumMin = %f', d = (/ BulkRiNumMin /) )
    call MessageNotify( 'M', module_name, 'For diffusion coefficients:' )
    call MessageNotify( 'M', module_name, '  MixLengthMax      = %f', d = (/ MixLengthMax     /) )
    call MessageNotify( 'M', module_name, '  ShMin             = %f', d = (/ ShMin       /) )
    call MessageNotify( 'M', module_name, '  SmMin             = %f', d = (/ SmMin       /) )
    call MessageNotify( 'M', module_name, '  VelDiffCoefMin    = %f', d = (/ VelDiffCoefMin  /) )
    call MessageNotify( 'M', module_name, '  TempDiffCoefMin   = %f', d = (/ TempDiffCoefMin /) )
    call MessageNotify( 'M', module_name, '  VelDiffCoefMax    = %f', d = (/ VelDiffCoefMax  /) )
    call MessageNotify( 'M', module_name, '  TempDiffCoefMax   = %f', d = (/ TempDiffCoefMax /) )
    call MessageNotify( 'M', module_name, '  MYConstA1         = %f', d = (/ MYConstA1     /) )
    call MessageNotify( 'M', module_name, '  MYConstB1         = %f', d = (/ MYConstB1     /) )
    call MessageNotify( 'M', module_name, '  MYConstA2         = %f', d = (/ MYConstA2     /) )
    call MessageNotify( 'M', module_name, '  MYConstB2         = %f', d = (/ MYConstB2     /) )
    call MessageNotify( 'M', module_name, '  MYConstC1         = %f', d = (/ MYConstC1     /) )
    call MessageNotify( 'M', module_name, '-- version = %c', c1 = trim(version) )

    vdiffusion_my_inited = .true.

  end subroutine VDiffusionInit
Subroutine :
xyz_U(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ u $ . �±è¥¿é¢���. Eastward wind
xyz_V(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ v $ . �������. Northward wind
xyzf_QMix(0:imax-1, 1:jmax, 1:kmax, 1:ncmax) :real(DP), intent(in)
: $ q $ . è³��闋·å��æ¯�. Mass mixing ratio
xyz_Temp(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ T $ . æ¸�º¦. Temperature
xyr_Temp(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{T} $ . æ¸�º¦ (���´æ�°ã������). Temperature (half level)
xyz_VirTemp(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ T_v $ . ä»�¸©åº�. Virtual temperature
xyr_VirTemp(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). Virtual temperature (half level)
xyr_Press(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{p} $ . æ°��� (���´æ�°ã������). Air pressure (half level)
xy_SurfHeight(0:imax-1,1:jmax) :real(DP), intent(in)
: $ z_s $ . �°è¡¨�¢é�åº�. Surface height.
xyz_Height(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: é«�åº� (�´æ�°ã������). Height (full level)
xyr_Height(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: é«�åº� (���´æ�°ã������). Height (half level)
xyz_Exner(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: Exner �¢æ�� (�´æ�°ã������). Exner function (full level)
xyr_Exner(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: Exner �¢æ�� (���´æ�°ã������). Exner function (half level)
xyz_TurKinEne(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: Turbulent kinetic energy (m2 s-2)
xy_SurfMomFluxX(0:imax-1, 1:jmax) :real(DP), intent(in)
: Eastward momentum flux at surface
xy_SurfMomFluxY(0:imax-1, 1:jmax) :real(DP), intent(in)
: Northward momentum flux at surface
xyr_MomFluxX(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �±è¥¿�¹å�����������������. Eastward momentum flux
xyr_MomFluxY(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �����¹å�����������������. Northward momentum flux
xyr_HeatFlux(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �±ã����������. Heat flux
xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax) :real(DP), intent(out)
: ������������. Mass flux of compositions
xyr_VelDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�������. Diffusion coefficient: velocity
xyr_TempDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�æ¸�º¦. Diffusion coefficient: temperature
xyr_QMixDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�æ¯�æ¹�. Diffusion coefficient: specific humidity
xyz_DTurKinEneDt(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(out)
: Tendency of turbulent kinetic energy

���´æ�¡æ�£ã���������¹ã��è¨�ç®����¾ã��.

Vertical diffusion flux is calculated by use of MY2.5 model.

[Source]

  subroutine VDiffusionMY25( xyz_U, xyz_V, xyzf_QMix, xyz_Temp, xyr_Temp, xyz_VirTemp, xyr_VirTemp, xyr_Press, xy_SurfHeight, xyz_Height, xyr_Height, xyz_Exner, xyr_Exner, xyz_TurKinEne, xy_SurfMomFluxX, xy_SurfMomFluxY, xyr_MomFluxX,  xyr_MomFluxY,  xyr_HeatFlux, xyrf_QMixFlux, xyr_VelDiffCoef, xyr_TempDiffCoef, xyr_QMixDiffCoef, xyz_DTurKinEneDt )
    !
    ! ���´æ�¡æ�£ã���������¹ã��è¨�ç®����¾ã��. 
    !
    ! Vertical diffusion flux is calculated by use of MY2.5 model.
    !

    ! �¢ã�¸ã�¥ã�¼ã����� ; USE statements
    !

    ! ����å®��°è¨­å®�
    ! Physical constants settings
    !
    use constants, only: FKarm, Grav, GasRDry, CpDry
                              ! $ C_p $ [J kg-1 K-1]. 
                              ! ä¹¾ç�¥å¤§æ°�����§æ���. 
                              ! Specific heat of air at constant pressure

    ! ���»ç���
    ! Time control
    !
    use timeset, only: DelTime, TimeN, TimesetClockStart, TimesetClockStop

    ! ���¹ã�������¼ã�¿å�ºå��
    ! History data output
    !
    use gtool_historyauto, only: HistoryAutoPut

    ! MPI �¢é�£ã���¼ã����
    ! MPI related routines
    !
    use mpi_wrapper, only : MPIWrapperChkTrue

    ! �°è§£æ³�����������ç©��������������¼ã����
    ! Routines for time integration with implicit scheme
    !
    use phy_implicit_utils, only : PhyImplLUDecomp3, PhyImplLUSolve3

    ! 宣�� ; Declaration statements
    !
    implicit none

    real(DP), intent(in):: xyz_U (0:imax-1, 1:jmax, 1:kmax)
                              ! $ u $ .   �±è¥¿é¢���. Eastward wind
    real(DP), intent(in):: xyz_V (0:imax-1, 1:jmax, 1:kmax)
                              ! $ v $ .   �������. Northward wind
    real(DP), intent(in):: xyzf_QMix(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
                              ! $ q $ .   è³��闋·å��æ¯�. Mass mixing ratio
    real(DP), intent(in):: xyz_Temp (0:imax-1, 1:jmax, 1:kmax)
                              ! $ T $ .   æ¸�º¦. Temperature
    real(DP), intent(in):: xyr_Temp (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{T} $ . æ¸�º¦ (���´æ�°ã������). 
                              ! Temperature (half level)
    real(DP), intent(in):: xyz_VirTemp (0:imax-1, 1:jmax, 1:kmax)
                              ! $ T_v $ .   ä»�¸©åº�. Virtual temperature
    real(DP), intent(in):: xyr_VirTemp (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). 
                              ! Virtual temperature (half level)
    real(DP), intent(in):: xyr_Press  (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{p} $ . æ°��� (���´æ�°ã������). 
                              ! Air pressure (half level)
    real(DP), intent(in):: xy_SurfHeight (0:imax-1,1:jmax)
                              ! $ z_s $ . �°è¡¨�¢é�åº�. 
                              ! Surface height. 
    real(DP), intent(in):: xyz_Height (0:imax-1, 1:jmax, 1:kmax)
                              ! é«�åº� (�´æ�°ã������). 
                              ! Height (full level)
    real(DP), intent(in):: xyr_Height (0:imax-1, 1:jmax, 0:kmax)
                              ! é«�åº� (���´æ�°ã������). 
                              ! Height (half level)
    real(DP), intent(in):: xyz_Exner (0:imax-1, 1:jmax, 1:kmax)
                              ! Exner �¢æ�� (�´æ�°ã������). 
                              ! Exner function (full level)
    real(DP), intent(in):: xyr_Exner (0:imax-1, 1:jmax, 0:kmax)
                              ! Exner �¢æ�� (���´æ�°ã������). 
                              ! Exner function (half level)

    real(DP), intent(in):: xyz_TurKinEne(0:imax-1, 1:jmax, 1:kmax)
                              ! 
                              ! Turbulent kinetic energy (m2 s-2)
    real(DP), intent(in):: xy_SurfMomFluxX (0:imax-1, 1:jmax)
                              ! 
                              ! Eastward momentum flux at surface
    real(DP), intent(in):: xy_SurfMomFluxY (0:imax-1, 1:jmax)
                              ! 
                              ! Northward momentum flux at surface

    real(DP), intent(out):: xyr_MomFluxX (0:imax-1, 1:jmax, 0:kmax)
                              ! �±è¥¿�¹å�����������������. 
                              ! Eastward momentum flux
    real(DP), intent(out):: xyr_MomFluxY (0:imax-1, 1:jmax, 0:kmax)
                              ! �����¹å�����������������. 
                              ! Northward momentum flux
    real(DP), intent(out):: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! �±ã����������. 
                              ! Heat flux
    real(DP), intent(out):: xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax)
                              ! ������������. 
                              ! Mass flux of compositions

    real(DP), intent(out):: xyr_VelDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�������. 
                              ! Diffusion coefficient: velocity
    real(DP), intent(out):: xyr_TempDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�æ¸�º¦. 
                              ! Diffusion coefficient: temperature
    real(DP), intent(out):: xyr_QMixDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�æ¯�æ¹�. 
                              ! Diffusion coefficient: specific humidity

    real(DP), intent(out):: xyz_DTurKinEneDt (0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! Tendency of turbulent kinetic energy

    ! �業��
    ! Work variables
    !

    real(DP) :: xyz_MixLength(0:imax-1, 1:jmax, 1:kmax)
                              ! 混����. 
                              ! Mixing length
    real(DP) :: xyz_DVelDzSq(0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! Vertical shear squared (s-2)
    real(DP) :: xyz_StatStab(0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! Static stability (s-2)
    real(DP) :: GhMin
                              !
                              ! Minimum of G_h
    real(DP) :: GhMax
                              !
                              ! Maximum of G_h
    real(DP) :: xyz_Gm(0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! G_m
    real(DP) :: xyz_Gh(0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! G_h
!!$    real(DP) :: xyz_SmHat(0:imax-1, 1:jmax, 1:kmax)
!!$                              !
!!$                              ! \hat{S}_M
!!$    real(DP) :: xyz_ShHat(0:imax-1, 1:jmax, 1:kmax)
!!$                              !
!!$                              ! \hat{S}_h
!!$    real(DP) :: xyz_DSmHatDTKE(0:imax-1, 1:jmax, 1:kmax)
!!$                              !
!!$                              ! derivative of \hat{S}_M
!!$    real(DP) :: xyz_DShHatDTKE(0:imax-1, 1:jmax, 1:kmax)
!!$                              !
!!$                              ! derivative of \hat{S}_h
    real(DP) :: xyz_Sm(0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! S_M
    real(DP) :: xyz_Sh(0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! S_h

    real(DP), parameter :: Stke = 0.2_DP
                              !
                              ! S_{TKE} = 0.2

    real(DP) :: xyz_VelDiffCoef (0:imax-1, 1:jmax, 1:kmax)
                              ! �¡æ�£ä��°ï�������. 
                              ! Diffusion coefficient: velocity
    real(DP) :: xyz_TempDiffCoef (0:imax-1, 1:jmax, 1:kmax)
                              ! �¡æ�£ä��°ï�æ¸�º¦. 
                              ! Transfer coefficient: temperature

    real(DP) :: xyr_TurKinEneDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! 
                              ! Diffusion coefficient: turbulent kinetic energy
    real(DP) :: xyz_TurKinEneDiffCoef (0:imax-1, 1:jmax, 1:kmax)
                              ! 
                              ! Diffusion coefficient: turbulent kinetic energy
    real(DP) :: xyr_TurKinEneTransCoef(0:imax-1, 1:jmax, 0:kmax)
                              ! 
                              ! Transfer coefficient: turbulent kinetic energy

    real(DP) :: xyr_TurKinEneFlux(0:imax-1, 1:jmax, 0:kmax)
                              ! 
                              ! Turbulent energy flux

    real(DP) :: xyz_CShe1(0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_CShe2(0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_CBuo1(0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_CBuo2(0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_CDis1(0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_CDis2(0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_TurKinEneProShear(0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_TurKinEneProBuoya(0:imax-1, 1:jmax, 1:kmax)

    real(DP) :: xy_FricVelSq    (0:imax-1, 1:jmax)
    real(DP) :: xy_TurKinEneAtLB(0:imax-1, 1:jmax)

    real(DP) :: xyza_TurKinEneMtx(0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 
                              ! Implicit matrix for turbulent kinetic energy
    real(DP) :: xyz_TurKinEneVec(0:imax-1, 1:jmax, 1:kmax)
                              ! 
                              ! Implicit vector for turbulent kinetic energy

    real(DP) :: xyza_TurKinEneLUMtx  (0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! LU ���.
                              ! LU matrix
    real(DP) :: xyz_DelTurKinEneLUVec(0:imax-1, 1:jmax, 1:kmax)
                              ! 
                              ! Tendency of turbulent kinetic energy

    real(DP) :: xyz_TurKinEneDiss(0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! Dissipation rate of turbulent kinetic energy (m2 s-3)

    real(DP) :: xyz_TurKinEneNonZero(0:imax-1, 1:jmax, 1:kmax)
                              ! 
                              ! Turbulent kinetic energy with offset (m2 s-2)

    real(DP), parameter :: TurKinEneOffset  = ( 1.0e-3_DP )**2 / 2.0_DP

    logical :: FlagReCalc
                              !
                              ! Flag for recalculation
    logical :: a_FlagReCalcLocal (1)
    logical :: a_FlagReCalcGlobal(1)
    integer :: iloop
    integer :: nloop

    integer:: i               ! çµ�åº��¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in longitude
    integer:: j               ! ç·�º¦�¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in latitude
    integer:: k               ! ���´æ�¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in vertical direction

    integer:: n               ! çµ����¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in dimension of constituents

    ! ���� ; Executable statement
    !

    ! ������確è�
    ! Initialization check
    !
    if ( .not. vdiffusion_my_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


    ! �����������
    ! Start measurement of computation time
    !
    call TimesetClockStart( module_name )


    ! Calculate turbulent kinetic energy with offset
    !
    xyz_TurKinEneNonZero = xyz_TurKinEne + TurKinEneOffset

    !
    ! Calculation of vertical shear squared
    do k = 1, kmax
      if ( k == 1 ) then
        xyz_DVelDzSq(:,:,k) = (   ( xyz_U(:,:,k+1) - xyz_U(:,:,k  ) )**2 + ( xyz_V(:,:,k+1) - xyz_V(:,:,k  ) )**2 ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k  ) )**2
!!$        xyz_DVelDzSq(:,:,k) =                              &
!!$          &   (   ( xyz_U(:,:,k+1) - 0.0_DP )**2   &
!!$          &     + ( xyz_V(:,:,k+1) - 0.0_DP )**2 ) &
!!$          & / ( xyz_Height(:,:,k+1) - xy_SurfHeight )**2
      else if ( k == kmax ) then
        xyz_DVelDzSq(:,:,k) = (   ( xyz_U(:,:,k  ) - xyz_U(:,:,k-1) )**2 + ( xyz_V(:,:,k  ) - xyz_V(:,:,k-1) )**2 ) / ( xyz_Height(:,:,k  ) - xyz_Height(:,:,k-1) )**2
      else
        xyz_DVelDzSq(:,:,k) = (   ( xyz_U(:,:,k+1) - xyz_U(:,:,k-1) )**2 + ( xyz_V(:,:,k+1) - xyz_V(:,:,k-1) )**2 ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k-1) )**2
      end if
    end do
    ! Calculation of static stability
    do k = 1, kmax
      if ( k == 1 ) then
        xyz_StatStab(:,:,k) = Grav / ( xyz_VirTemp(:,:,k) / xyz_Exner(:,:,k) ) * (   xyz_VirTemp(:,:,k+1) / xyz_Exner(:,:,k+1) - xyz_VirTemp(:,:,k  ) / xyz_Exner(:,:,k  ) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k  ) )
      else if ( k == kmax ) then
        xyz_StatStab(:,:,k) = Grav / ( xyz_VirTemp(:,:,k) / xyz_Exner(:,:,k) ) * (   xyz_VirTemp(:,:,k  ) / xyz_Exner(:,:,k  ) - xyz_VirTemp(:,:,k-1) / xyz_Exner(:,:,k-1) ) / ( xyz_Height(:,:,k  ) - xyz_Height(:,:,k-1) )
      else
        xyz_StatStab(:,:,k) = Grav / ( xyz_VirTemp(:,:,k) / xyz_Exner(:,:,k) ) * (   xyz_VirTemp(:,:,k+1) / xyz_Exner(:,:,k+1) - xyz_VirTemp(:,:,k-1) / xyz_Exner(:,:,k-1) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k-1) )
      end if
    end do

    ! æ··å��è·��¢ã�����
    ! Calculate mixing length
    !
    do k = 1, kmax
      xyz_MixLength(:,:,k) = FKarm * ( xyz_Height(:,:,k) - xy_SurfHeight ) / (1.0_DP + FKarm * ( xyz_Height(:,:,k) - xy_SurfHeight ) / MixLengthMax )
    end do
    !   Limit mixing length (Galperin et al., 1988) and avoid zero
    xyz_MixLength = min( xyz_MixLength, 0.53_DP * sqrt( 2.0_DP * xyz_TurKinEneNonZero / max( xyz_StatStab, 1.0e-10_DP ) ) ) + 1.0e-10_DP

    xyz_Gh = - xyz_MixLength**2 / ( 2.0_DP * xyz_TurKinEneNonZero ) * xyz_StatStab
    ! Actually, xyz_Gm is not used below.
    xyz_Gm =   xyz_MixLength**2 / ( 2.0_DP * xyz_TurKinEneNonZero ) * xyz_DVelDzSq


    ! Limit Gh (Galperin et al., 1988)
    GhMin = - 0.53_DP**2
    GhMax = 1.0_DP / ( MYConstA2 * (  12.0_DP * MYConstA1 + MYConstB1 + 3.0_DP * MYConstB2 ) )
    xyz_Gh = max( GhMin, min( xyz_Gh, GhMax ) )


    xyz_Sh = MYConstA2 * ( 1.0_DP - 6.0_DP * MYConstA1 / MYConstB1 ) / (   1.0_DP - 3.0_DP * MYConstA2 * ( 6.0_DP * MYConstA1 + MYConstB2 ) * xyz_Gh )

    xyz_Sm = ( MYConstA1 * (   1.0_DP - 3.0_DP * MYConstC1 - 6.0_DP * MYConstA1 / MYConstB1 ) + 9.0_DP * MYConstA1 * ( 2.0_DP * MYConstA1 + MYConstA2 ) * xyz_Gh * xyz_Sh ) / (   1.0_DP - 9.0_DP * MYConstA1 * MYConstA2 * xyz_Gh )


!!$    xyz_DShHatDTKE =                                                       &
!!$      & - 2.0_DP * MYConstA2 * ( 1.0_DP - 6.0_DP * MYConstA1 / MYConstB1 ) &
!!$      & / (   2.0_DP * xyz_TurKinEneNonZero                                &
!!$      &     - 3.0_DP * MYConstA2 * ( 6.0_DP * MYConstA1 + MYConstB2 ) * xyz_GhPrime )**2
!!$    xyz_DSmHatDTKE =                                                &
!!$      & (                                                           &
!!$      &     9.0_DP * MYConstA1 * ( 2.0_DP * MYConstA1 + MYConstA2 ) &
!!$      &     * xyz_GhPrime * xyz_DShHatDTKE                          &
!!$      &     * (   2.0_DP * xyz_TurKinEneNonZero                     &
!!$      &         - 9.0_DP * MYConstA1 * MYConstA2 * xyz_GhPrime )    &
!!$      &   - 2.0_DP                                                        &
!!$      &     * (                                                           &
!!$      &           MYConstA1 * (   1.0_DP - 3.0_DP * MYConstC1             &
!!$      &                         - 6.0_DP * MYConstA1 / MYConstB1 )        &
!!$      &         + 9.0_DP * MYConstA1 * ( 2.0_DP * MYConstA1 + MYConstA2 ) &
!!$      &           * xyz_GhPrime * xyz_ShHat                               &
!!$      &       )                                                           &
!!$      & )                                                                 &
!!$      & / (   2.0_DP * xyz_TurKinEneNonZero                               &
!!$      &     - 9.0_DP * MYConstA1 * MYConstA2 * xyz_GhPrime )**2


    ! �¡æ�£ä��°ã���ç®�
    ! Calculation of diffusion coefficient
    !
    xyz_VelDiffCoef  = xyz_MixLength * sqrt( 2.0_DP * xyz_TurKinEneNonZero ) * xyz_Sm
    xyz_TempDiffCoef = xyz_MixLength * sqrt( 2.0_DP * xyz_TurKinEneNonZero ) * xyz_Sh
    !
    do k = 0, kmax
      if ( ( k == 0 ) .or. ( k == kmax ) ) then
        xyr_VelDiffCoef (:,:,k) = 0.0_DP
        xyr_TempDiffCoef(:,:,k) = 0.0_DP
      else
        xyr_VelDiffCoef (:,:,k) = ( xyz_VelDiffCoef (:,:,k) + xyz_VelDiffCoef (:,:,k+1) ) / 2.0_DP
        xyr_TempDiffCoef(:,:,k) = ( xyz_TempDiffCoef(:,:,k) + xyz_TempDiffCoef(:,:,k+1) ) / 2.0_DP
      end if
    end do
    !
    do k = 1, kmax-1
      do j = 1, jmax
        do i = 0, imax-1
          xyr_VelDiffCoef(i,j,k) = max( min( xyr_VelDiffCoef(i,j,k), VelDiffCoefMax ), VelDiffCoefMin )
          xyr_TempDiffCoef(i,j,k) = max( min( xyr_TempDiffCoef(i,j,k), TempDiffCoefMax ), TempDiffCoefMin )
        end do
      end do
    end do
    !
    xyr_QMixDiffCoef      = xyr_TempDiffCoef


    ! 輸é��ä¿��°ã�����������¹ã���ç®�
    ! Calculate transfer coefficient and flux
    !
    call VDiffusionCalcFlux( xyz_U, xyz_V, xyzf_QMix, xyz_Temp, xyr_VirTemp, xyr_Press, xyz_Height, xyz_Exner, xyr_Exner, xyr_VelDiffCoef, xyr_TempDiffCoef, xyr_QMixDiffCoef, xyr_MomFluxX,  xyr_MomFluxY,  xyr_HeatFlux, xyrf_QMixFlux )


    ! Calculate tendency of turbulent kinetic energy

    !   Set diffusion coefficient for turbulent kinetic energy
    xyz_TurKinEneDiffCoef = xyz_MixLength * sqrt( 2.0_DP * xyz_TurKinEneNonZero ) * Stke
    !
    do k = 0, kmax
      if ( k == 0 ) then
        xyr_TurKinEneDiffCoef(:,:,k) = xyz_TurKinEneDiffCoef(:,:,1)
      else if ( k == kmax ) then
        xyr_TurKinEneDiffCoef(:,:,k) = xyz_TurKinEneDiffCoef(:,:,kmax)
      else
        xyr_TurKinEneDiffCoef(:,:,k) = ( xyz_TurKinEneDiffCoef(:,:,k) + xyz_TurKinEneDiffCoef(:,:,k+1) ) / 2.0_DP
      end if
    end do

    !   Calculate turbulent kinetic energy at lower boundary
    !
    xy_FricVelSq = sqrt( xy_SurfMomFluxX**2 + xy_SurfMomFluxY**2 ) / ( xyr_Press(:,:,0) / ( GasRDry * xyr_VirTemp(:,:,0) ) )
    xy_TurKinEneAtLB = MYConstB1**(2.0_DP/3.0_DP) / 2.0_DP * xy_FricVelSq
    xy_TurKinEneAtLB = xy_TurKinEneAtLB + TurKinEneOffset

    !   Calculate transfer coefficient and flux of turbulent kinetic energy
    !
    !    When transfer coefficient at lower boundary is calculated, 
    !    diffusion coefficient at mid-point of 1st layer is used. 
    !    In addition, transfer coefficient at upper boundary is assumed 
    !    to be zero.
    k = 0
    xyr_TurKinEneTransCoef(:,:,k) = xyz_TurKinEneDiffCoef(:,:,1) * xyr_Press(:,:,k) / ( GasRDry * xyr_VirTemp(:,:,k) ) / ( xyz_Height(:,:,1) - xy_SurfHeight )
    do k = 1, kmax-1
      xyr_TurKinEneTransCoef(:,:,k) = xyr_TurKinEneDiffCoef(:,:,k) * xyr_Press(:,:,k) / ( GasRDry * xyr_VirTemp(:,:,k) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k) )
    end do
    k = kmax
    xyr_TurKinEneTransCoef(:,:,k) = 0.0_DP
    !
    do k = 1, kmax-1
      xyr_TurKinEneFlux(:,:,k) = - xyr_TurKinEneTransCoef(:,:,k) * ( xyz_TurKinEneNonZero(:,:,k+1) - xyz_TurKinEneNonZero(:,:,k) )
    end do
    k = 0
    xyr_TurKinEneFlux(:,:,k) = - xyr_TurKinEneTransCoef(:,:,k) * ( xyz_TurKinEneNonZero(:,:,k+1) - xy_TurKinEneAtLB )
    k = kmax
    xyr_TurKinEneFlux(:,:,k) = 0.0_DP


!!$    xyz_CShe1 =          2.0d0**1.5 * xyz_MixLength * xyz_SmHat &
!!$      & * xyz_DVelDzSq                                          &
!!$!      & * xyz_TurKinEne**1.5
!!$      & * ( xyz_TurKinEne + TurKinEneNonZero )**1.5
!!$    xyz_CShe2 = 1.5_DP * 2.0d0**1.5 * xyz_MixLength * xyz_SmHat &
!!$      & * xyz_DVelDzSq                                          &
!!$!      & * xyz_TurKinEne**0.5
!!$      & * ( xyz_TurKinEne + TurKinEneNonZero )**0.5
!!$    xyz_CBuo1 = -          2.0d0**1.5 * xyz_MixLength * xyz_ShHat &
!!$      & * xyz_StatStab                                            &
!!$!      & * xyz_TurKinEne**1.5
!!$      & * ( xyz_TurKinEne + TurKinEneNonZero )**1.5
!!$    xyz_CBuo2 = - 1.5_DP * 2.0d0**1.5 * xyz_MixLength * xyz_ShHat &
!!$      & * xyz_StatStab                                            &
!!$!      & * xyz_TurKinEne**0.5
!!$      & * ( xyz_TurKinEne + TurKinEneNonZero )**0.5
!!$    xyz_CDis1 =          2.0_DP**1.5 / ( MYConstB1 * xyz_MixLength ) &
!!$!      & * xyz_TurKinEne**1.5
!!$      & * ( xyz_TurKinEne + TurKinEneNonZero )**1.5
!!$    xyz_CDis2 = 1.5_DP * 2.0_DP**1.5 / ( MYConstB1 * xyz_MixLength ) &
!!$!      & * xyz_TurKinEne**0.5
!!$      & * ( xyz_TurKinEne + TurKinEneNonZero )**0.5


!!$!    xyz_CShe1 =          2.0d0**1.5 * xyz_MixLength * xyz_SmHat &
!!$!      & * xyz_DVelDzSq                                          &
!!$!!      & * xyz_TurKinEne**1.5
!!$!      & * ( xyz_TurKinEne + TurKinEneNonZero )**1.5
!!$    xyz_CShe1 =          2.0d0**1.5 * xyz_MixLength * xyz_Sm &
!!$      & * xyz_DVelDzSq                                       &
!!$!      & * xyz_TurKinEne**1.5
!!$      & * ( xyz_TurKinEne + TurKinEneNonZero )**0.5
!!$    xyz_CShe2 = 0.0_DP
!!$!    xyz_CBuo1 = -          2.0d0**1.5 * xyz_MixLength * xyz_ShHat &
!!$!      & * xyz_StatStab                                            &
!!$!!      & * xyz_TurKinEne**1.5
!!$!      & * ( xyz_TurKinEne + TurKinEneNonZero )**1.5
!!$    xyz_CBuo1 = -          2.0d0**1.5 * xyz_MixLength * xyz_Sh &
!!$      & * xyz_StatStab                                         &
!!$!      & * xyz_TurKinEne**1.5
!!$      & * ( xyz_TurKinEne + TurKinEneNonZero )**0.5
!!$    xyz_CBuo2 = 0.0_DP
!!$    xyz_CDis1 =          2.0_DP**1.5 / ( MYConstB1 * xyz_MixLength ) &
!!$      & * xyz_TurKinEne**1.5
!!$!      & * ( xyz_TurKinEne + TurKinEneNonZero )**1.5
!!$    xyz_CDis2 = 1.5_DP * 2.0_DP**1.5 / ( MYConstB1 * xyz_MixLength ) &
!!$      & * xyz_TurKinEne**0.5
!!$!      & * ( xyz_TurKinEne + TurKinEneNonZero )**0.5


!!$    xyz_CShe1 = 2.0d0**1.5 * xyz_MixLength * xyz_DVelDzSq       &
!!$      & * xyz_SmHat                                             &
!!$      & * xyz_TurKinEneNonZero**1.5
!!$    xyz_CShe2 = 2.0d0**1.5 * xyz_MixLength * xyz_DVelDzSq       &
!!$      & * (   xyz_DSmHatDTKE                                    &
!!$      &         * xyz_TurKinEneNonZero**1.5                     &
!!$      &     + 1.5_DP * xyz_SmHat                                &
!!$      &         * xyz_TurKinEneNonZero**0.5                     &
!!$      &   )
!!$    xyz_CBuo1 = - 2.0d0**1.5 * xyz_MixLength * xyz_StatStab     &
!!$      & * xyz_ShHat                                             &
!!$      & * xyz_TurKinEneNonZero**1.5
!!$    xyz_CBuo2 = - 2.0d0**1.5 * xyz_MixLength * xyz_StatStab     &
!!$      & * (   xyz_DShHatDTKE                                    &
!!$      &         * xyz_TurKinEneNonZero**1.5                     &
!!$      &     + 1.5_DP * xyz_ShHat                                &
!!$      &         * xyz_TurKinEneNonZero**0.5                     &
!!$      &   )
!!$    xyz_CDis1 =          2.0_DP**1.5 / ( MYConstB1 * xyz_MixLength ) &
!!$      & * xyz_TurKinEneNonZero**1.5
!!$    xyz_CDis2 = 1.5_DP * 2.0_DP**1.5 / ( MYConstB1 * xyz_MixLength ) &
!!$      & * xyz_TurKinEneNonZero**0.5


    xyz_CShe1 =            sqrt( 2.0_DP ) * xyz_MixLength * xyz_DVelDzSq * xyz_Sm * sqrt( xyz_TurKinEneNonZero )
!!$    xyz_CShe2 =   0.5_DP * sqrt( 2.0_DP ) * xyz_MixLength * xyz_DVelDzSq  &
!!$      & * xyz_Sm                                                          &
!!$      & / sqrt( xyz_TurKinEneNonZero )
    xyz_CShe2 = 0.0_DP
    xyz_CBuo1 = -          sqrt( 2.0_DP ) * xyz_MixLength * xyz_StatStab * xyz_Sh * sqrt( xyz_TurKinEneNonZero )
!!$    xyz_CBuo2 = - 0.5_DP * sqrt( 2.0_DP ) * xyz_MixLength * xyz_StatStab  &
!!$      & * xyz_Sh                                                          &
!!$      & / sqrt( xyz_TurKinEneNonZero )
    xyz_CBuo2 = 0.0_DP
    xyz_CDis1 =          2.0_DP**1.5_DP / ( MYConstB1 * xyz_MixLength ) * xyz_TurKinEneNonZero**1.5_DP
    xyz_CDis2 = 1.5_DP * 2.0_DP**1.5_DP / ( MYConstB1 * xyz_MixLength ) * xyz_TurKinEneNonZero**0.5_DP


    nloop = kmax
    loop_solve : do iloop = 1, nloop

      !
      ! Construct implicit matrix from transfer coefficient of vertical 
      ! diffusion scheme (turbulent kinetic energy)
      !
      k = 1
      xyza_TurKinEneMtx(:,:,k,-1) = 0.0_DP
      xyza_TurKinEneMtx(:,:,k, 0) = - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + xyr_TurKinEneTransCoef(:,:,k-1) + xyr_TurKinEneTransCoef(:,:,k  ) + ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav * ( xyz_CShe2(:,:,k) + xyz_CBuo2(:,:,k) - xyz_CDis2(:,:,k) )
      xyza_TurKinEneMtx(:,:,k, 1) = - xyr_TurKinEneTransCoef(:,:,k  )
      !
      do k = 2, kmax-1
        xyza_TurKinEneMtx(:,:,k,-1) = - xyr_TurKinEneTransCoef(:,:,k-1)
        xyza_TurKinEneMtx(:,:,k, 0) = - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + xyr_TurKinEneTransCoef(:,:,k-1) + xyr_TurKinEneTransCoef(:,:,k  ) + ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav * ( xyz_CShe2(:,:,k) + xyz_CBuo2(:,:,k) - xyz_CDis2(:,:,k) )
        xyza_TurKinEneMtx(:,:,k, 1) = - xyr_TurKinEneTransCoef(:,:,k  )
      end do
      !
      k = kmax
      xyza_TurKinEneMtx(:,:,k,-1) = - xyr_TurKinEneTransCoef(:,:,k-1)
      xyza_TurKinEneMtx(:,:,k, 0) = - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + xyr_TurKinEneTransCoef(:,:,k-1) + xyr_TurKinEneTransCoef(:,:,k  ) + ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav * ( xyz_CShe2(:,:,k) + xyz_CBuo2(:,:,k) - xyz_CDis2(:,:,k) )
      xyza_TurKinEneMtx(:,:,k, 1) = 0.0_DP

      do k = 1, kmax
        xyz_TurKinEneVec(:,:,k) = - ( xyr_TurKinEneFlux(:,:,k) - xyr_TurKinEneFlux(:,:,k-1) ) - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav * ( xyz_CShe1(:,:,k) + xyz_CBuo1(:,:,k) - xyz_CDis1(:,:,k) )
      end do


      !
      ! Solve simultaneous linear equations by use of LU decomposition technique
      !
      xyza_TurKinEneLUMtx = xyza_TurKinEneMtx
      !
      call PhyImplLUDecomp3( xyza_TurKinEneLUMtx, imax * jmax, kmax )

      xyz_DelTurKinEneLUVec = xyz_TurKinEneVec
      !
      call PhyImplLUSolve3( xyz_DelTurKinEneLUVec, xyza_TurKinEneLUMtx, 1, imax * jmax , kmax )

      xyz_DTurKinEneDt = xyz_DelTurKinEneLUVec / ( 2.0_DP * DelTime )


      ! Calculation of dissipation rate of turbulent kinetic energy
      !
      ! Calculate production rate of turbulent kinetic energy
      ! by shear and buoyancy
      xyz_TurKinEneProShear = xyz_CShe1 + xyz_CShe2 * xyz_DTurKinEneDt * 2.0_DP * DelTime
      xyz_TurKinEneProBuoya = xyz_CBuo1 + xyz_CBuo2 * xyz_DTurKinEneDt * 2.0_DP * DelTime
      xyz_TurKinEneDiss     = xyz_CDis1 + xyz_CDis2 * xyz_DTurKinEneDt * 2.0_DP * DelTime

      ! Check of turbulent kinetic energy dissipation rate
      ! If it is negative, tendency is recalculated without dissipation.
      !
      FlagReCalc = .false.
      do k = 1, kmax
        do j = 1, jmax
          do i = 0, imax-1
            if ( xyz_TurKinEneDiss(i,j,k) < 0.0_DP ) then
              xyz_CDis1(i,j,k) = 0.0_DP
              xyz_CDis2(i,j,k) = 0.0_DP
              FlagReCalc = .true.
            end if
          end do
        end do
      end do

      ! Check convergence
      a_FlagReCalcLocal = FlagReCalc
      call MPIWrapperChkTrue( 1, a_FlagReCalcLocal, a_FlagReCalcGlobal )
      if ( .not. a_FlagReCalcGlobal(1) ) exit loop_solve

    end do loop_solve


!!$    write( 6, * ) TimeN, iloop
!!$    write( 6, * ) xyz_TurKinEne(0,jmax/2+1,1:4)
!!$    write( 6, * ) xyz_TempDiffCoef(0,jmax/2+1,1:4)
!!$    write( 6, * ) xyz_TurKinEneProShear(0,jmax/2+1,1:4)
!!$    write( 6, * ) xyz_TurKinEneProBuoya(0,jmax/2+1,1:4)
!!$    write( 6, * ) xyz_TurKinEneDiss(0,jmax/2+1,1:4)
!!$    write( 6, * ) xyz_DTurKinEneDt(0,jmax/2+1,1:4)



    ! �¡æ�£ä��°ã���ºå��
    ! Output diffusion coefficients
    !

    ! �¡æ�£ä��°å�ºå��
    ! Diffusion coeffficients output
    !
    call HistoryAutoPut( TimeN, 'VelDiffCoef',  xyr_VelDiffCoef  )
    call HistoryAutoPut( TimeN, 'TempDiffCoef', xyr_TempDiffCoef )
    call HistoryAutoPut( TimeN, 'QVapDiffCoef', xyr_QMixDiffCoef )

    call HistoryAutoPut( TimeN, 'TKEPShear', xyz_TurKinEneProShear )
    call HistoryAutoPut( TimeN, 'TKEPBuoy' , xyz_TurKinEneProBuoya )
    call HistoryAutoPut( TimeN, 'TKEDiss'  , xyz_TurKinEneDiss     )

    call HistoryAutoPut( TimeN, 'MixLength' , xyz_MixLength )



    ! ��������������
    ! Pause measurement of computation time
    !
    call TimesetClockStop( module_name )

  end subroutine VDiffusionMY25
Subroutine :
xyz_U(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ u $ . �±è¥¿é¢���. Eastward wind
xyz_V(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ v $ . �������. Northward wind
xyzf_QMix(0:imax-1, 1:jmax, 1:kmax, 1:ncmax) :real(DP), intent(in)
: $ q $ . è³��闋·å��æ¯�. Mass mixing ratio
xyz_Temp(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ T $ . æ¸�º¦. Temperature
xyr_Temp(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{T} $ . æ¸�º¦ (���´æ�°ã������). Temperature (half level)
xyz_VirTemp(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ T_v $ . ä»�¸©åº�. Virtual temperature
xyr_VirTemp(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). Virtual temperature (half level)
xyr_Press(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{p} $ . æ°��� (���´æ�°ã������). Air pressure (half level)
xy_SurfHeight(0:imax-1,1:jmax) :real(DP), intent(in)
: $ z_s $ . �°è¡¨�¢é�åº�. Surface height.
xyz_Height(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: é«�åº� (�´æ�°ã������). Height (full level)
xyr_Height(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: é«�åº� (���´æ�°ã������). Height (half level)
xyz_Exner(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: Exner �¢æ�� (�´æ�°ã������). Exner function (full level)
xyr_Exner(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: Exner �¢æ�� (���´æ�°ã������). Exner function (half level)
xyz_TurKinEne(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: Turbulent kinetic energy (m2 s-2)
xy_SurfMomFluxX(0:imax-1, 1:jmax) :real(DP), intent(in)
: Eastward momentum flux at surface
xy_SurfMomFluxY(0:imax-1, 1:jmax) :real(DP), intent(in)
: Northward momentum flux at surface
xyr_MomFluxX(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �±è¥¿�¹å�����������������. Eastward momentum flux
xyr_MomFluxY(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �����¹å�����������������. Northward momentum flux
xyr_HeatFlux(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �±ã����������. Heat flux
xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax) :real(DP), intent(out)
: ������������. Mass flux of compositions
xyr_VelDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�������. Diffusion coefficient: velocity
xyr_TempDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�æ¸�º¦. Diffusion coefficient: temperature
xyr_QMixDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�æ¯�æ¹�. Diffusion coefficient: specific humidity
xyz_DTurKinEneDt(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(out)
: Tendency of turbulent kinetic energy

���´æ�¡æ�£ã���������¹ã��è¨�ç®����¾ã��.

Vertical diffusion flux is calculated by use of MY2.5 model.

[Source]

  subroutine VDiffusionMY251DWrapper3D( xyz_U, xyz_V, xyzf_QMix, xyz_Temp, xyr_Temp, xyz_VirTemp, xyr_VirTemp, xyr_Press, xy_SurfHeight, xyz_Height, xyr_Height, xyz_Exner, xyr_Exner, xyz_TurKinEne, xy_SurfMomFluxX, xy_SurfMomFluxY, xyr_MomFluxX,  xyr_MomFluxY,  xyr_HeatFlux, xyrf_QMixFlux, xyr_VelDiffCoef, xyr_TempDiffCoef, xyr_QMixDiffCoef, xyz_DTurKinEneDt )
    !
    ! ���´æ�¡æ�£ã���������¹ã��è¨�ç®����¾ã��. 
    !
    ! Vertical diffusion flux is calculated by use of MY2.5 model.
    !

    ! �¢ã�¸ã�¥ã�¼ã����� ; USE statements
    !

    ! ����å®��°è¨­å®�
    ! Physical constants settings
    !
    use constants, only: FKarm, Grav, GasRDry, CpDry
                              ! $ C_p $ [J kg-1 K-1]. 
                              ! ä¹¾ç�¥å¤§æ°�����§æ���. 
                              ! Specific heat of air at constant pressure

    ! ���»ç���
    ! Time control
    !
    use timeset, only: DelTime, TimeN, TimesetClockStart, TimesetClockStop

    ! ���¹ã�������¼ã�¿å�ºå��
    ! History data output
    !
    use gtool_historyauto, only: HistoryAutoPut

    ! �°è§£æ³�����������ç©��������������¼ã����
    ! Routines for time integration with implicit scheme
    !
    use phy_implicit_utils, only : PhyImplLUDecomp3, PhyImplLUSolve3

    ! 宣�� ; Declaration statements
    !
    implicit none

    real(DP), intent(in):: xyz_U (0:imax-1, 1:jmax, 1:kmax)
                              ! $ u $ .   �±è¥¿é¢���. Eastward wind
    real(DP), intent(in):: xyz_V (0:imax-1, 1:jmax, 1:kmax)
                              ! $ v $ .   �������. Northward wind
    real(DP), intent(in):: xyzf_QMix(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
                              ! $ q $ .   è³��闋·å��æ¯�. Mass mixing ratio
    real(DP), intent(in):: xyz_Temp (0:imax-1, 1:jmax, 1:kmax)
                              ! $ T $ .   æ¸�º¦. Temperature
    real(DP), intent(in):: xyr_Temp (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{T} $ . æ¸�º¦ (���´æ�°ã������). 
                              ! Temperature (half level)
    real(DP), intent(in):: xyz_VirTemp (0:imax-1, 1:jmax, 1:kmax)
                              ! $ T_v $ .   ä»�¸©åº�. Virtual temperature
    real(DP), intent(in):: xyr_VirTemp (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). 
                              ! Virtual temperature (half level)
    real(DP), intent(in):: xyr_Press  (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{p} $ . æ°��� (���´æ�°ã������). 
                              ! Air pressure (half level)
    real(DP), intent(in):: xy_SurfHeight (0:imax-1,1:jmax)
                              ! $ z_s $ . �°è¡¨�¢é�åº�. 
                              ! Surface height. 
    real(DP), intent(in):: xyz_Height (0:imax-1, 1:jmax, 1:kmax)
                              ! é«�åº� (�´æ�°ã������). 
                              ! Height (full level)
    real(DP), intent(in):: xyr_Height (0:imax-1, 1:jmax, 0:kmax)
                              ! é«�åº� (���´æ�°ã������). 
                              ! Height (half level)
    real(DP), intent(in):: xyz_Exner (0:imax-1, 1:jmax, 1:kmax)
                              ! Exner �¢æ�� (�´æ�°ã������). 
                              ! Exner function (full level)
    real(DP), intent(in):: xyr_Exner (0:imax-1, 1:jmax, 0:kmax)
                              ! Exner �¢æ�� (���´æ�°ã������). 
                              ! Exner function (half level)

    real(DP), intent(in):: xyz_TurKinEne(0:imax-1, 1:jmax, 1:kmax)
                              ! 
                              ! Turbulent kinetic energy (m2 s-2)
    real(DP), intent(in):: xy_SurfMomFluxX (0:imax-1, 1:jmax)
                              ! 
                              ! Eastward momentum flux at surface
    real(DP), intent(in):: xy_SurfMomFluxY (0:imax-1, 1:jmax)
                              ! 
                              ! Northward momentum flux at surface

    real(DP), intent(out):: xyr_MomFluxX (0:imax-1, 1:jmax, 0:kmax)
                              ! �±è¥¿�¹å�����������������. 
                              ! Eastward momentum flux
    real(DP), intent(out):: xyr_MomFluxY (0:imax-1, 1:jmax, 0:kmax)
                              ! �����¹å�����������������. 
                              ! Northward momentum flux
    real(DP), intent(out):: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! �±ã����������. 
                              ! Heat flux
    real(DP), intent(out):: xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax)
                              ! ������������. 
                              ! Mass flux of compositions
    real(DP), intent(out):: xyr_VelDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�������. 
                              ! Diffusion coefficient: velocity
    real(DP), intent(out):: xyr_TempDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�æ¸�º¦. 
                              ! Diffusion coefficient: temperature
    real(DP), intent(out):: xyr_QMixDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�æ¯�æ¹�. 
                              ! Diffusion coefficient: specific humidity
    real(DP), intent(out):: xyz_DTurKinEneDt (0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! Tendency of turbulent kinetic energy

    ! �業��
    ! Work variables
    !
    real(DP) :: z_U (1:kmax)
    real(DP) :: z_V (1:kmax)
    real(DP) :: zf_QMix(1:kmax, 1:ncmax)
    real(DP) :: z_Temp (1:kmax)
    real(DP) :: r_Temp (0:kmax)
    real(DP) :: z_VirTemp (1:kmax)
    real(DP) :: r_VirTemp (0:kmax)
    real(DP) :: r_Press  (0:kmax)
    real(DP) :: SurfHeight
    real(DP) :: z_Height (1:kmax)
    real(DP) :: r_Height (0:kmax)
    real(DP) :: z_Exner (1:kmax)
    real(DP) :: r_Exner (0:kmax)
    real(DP) :: z_TurKinEne(1:kmax)
    real(DP) :: SurfMomFluxX
    real(DP) :: SurfMomFluxY
    real(DP) :: r_MomFluxX (0:kmax)
    real(DP) :: r_MomFluxY (0:kmax)
    real(DP) :: r_HeatFlux (0:kmax)
    real(DP) :: rf_QMixFlux(0:kmax, 1:ncmax)
    real(DP) :: r_VelDiffCoef (0:kmax)
    real(DP) :: r_TempDiffCoef(0:kmax)
    real(DP) :: r_QMixDiffCoef(0:kmax)
    real(DP) :: z_DTurKinEneDt (1:kmax)
                              !
                              ! Tendency of turbulent kinetic energy


    integer:: i               ! çµ�åº��¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in longitude
    integer:: j               ! ç·�º¦�¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in latitude


    ! ���� ; Executable statement
    !

    ! ������確è�
    ! Initialization check
    !
    if ( .not. vdiffusion_my_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


    ! �����������
    ! Start measurement of computation time
    !
    call TimesetClockStart( module_name )


    do j = 1, jmax
      do i = 0, imax-1

        z_U          = xyz_U          (i,j,:)
        z_V          = xyz_V          (i,j,:)
        zf_QMix      = xyzf_QMix      (i,j,:,:)
        z_Temp       = xyz_Temp       (i,j,:)
        r_Temp       = xyr_Temp       (i,j,:)
        z_VirTemp    = xyz_VirTemp    (i,j,:)
        r_VirTemp    = xyr_VirTemp    (i,j,:)
        r_Press      = xyr_Press      (i,j,:)
        SurfHeight   = xy_SurfHeight  (i,j)
        z_Height     = xyz_Height     (i,j,:)
        r_Height     = xyr_Height     (i,j,:)
        z_Exner      = xyz_Exner      (i,j,:)
        r_Exner      = xyr_Exner      (i,j,:)
        z_TurKinEne  = xyz_TurKinEne  (i,j,:)
        SurfMomFluxX = xy_SurfMomFluxX(i,j)
        SurfMomFluxY = xy_SurfMomFluxY(i,j)


        call VDiffusionMY251D( z_U, z_V, zf_QMix, z_Temp, r_Temp, z_VirTemp, r_VirTemp, r_Press, SurfHeight, z_Height, r_Height, z_Exner, r_Exner, z_TurKinEne, SurfMomFluxX, SurfMomFluxY, r_MomFluxX, r_MomFluxY, r_HeatFlux, rf_QMixFlux, r_VelDiffCoef, r_TempDiffCoef, r_QMixDiffCoef, z_DTurKinEneDt )

        xyr_MomFluxX     (i,j,:)   = r_MomFluxX
        xyr_MomFluxY     (i,j,:)   = r_MomFluxY
        xyr_HeatFlux     (i,j,:)   = r_HeatFlux
        xyrf_QMixFlux    (i,j,:,:) = rf_QMixFlux
        xyr_VelDiffCoef (i,j,:) = r_VelDiffCoef
        xyr_TempDiffCoef(i,j,:) = r_TempDiffCoef
        xyr_QMixDiffCoef(i,j,:) = r_QMixDiffCoef
        xyz_DTurKinEneDt (i,j,:)   = z_DTurKinEneDt

      end do
    end do



!!$    ! �¡æ�£ä��°ã���ºå��
!!$    ! Output diffusion coefficients
!!$    !
!!$
!!$    ! �¡æ�£ä��°å�ºå��
!!$    ! Diffusion coeffficients output
!!$    !
!!$    call HistoryAutoPut( TimeN, 'VelDiffCoef',  xyr_VelDiffCoef  )
!!$    call HistoryAutoPut( TimeN, 'TempDiffCoef', xyr_TempDiffCoef )
!!$    call HistoryAutoPut( TimeN, 'QVapDiffCoef', xyr_QMixDiffCoef )
!!$
!!$    call HistoryAutoPut( TimeN, 'TKEPShear', xyz_TurKinEneProShear )
!!$    call HistoryAutoPut( TimeN, 'TKEPBuoy' , xyz_TurKinEneProBuoya )
!!$    call HistoryAutoPut( TimeN, 'TKEDiss'  , xyz_TurKinEneDiss     )
!!$
!!$    call HistoryAutoPut( TimeN, 'MixLength' , xyz_MixLength )



    ! ��������������
    ! Pause measurement of computation time
    !
    call TimesetClockStop( module_name )

  end subroutine VDiffusionMY251DWrapper3D
Subroutine :
xyz_U(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ u $ . �±è¥¿é¢���. Eastward wind
xyz_V(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ v $ . �������. Northward wind
xyzf_QMix(0:imax-1, 1:jmax, 1:kmax, 1:ncmax) :real(DP), intent(in)
: $ q $ . è³��闋·å��æ¯�. Mass mixing ratio
xyz_Temp(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ T $ . æ¸�º¦. Temperature
xyr_Temp(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{T} $ . æ¸�º¦ (���´æ�°ã������). Temperature (half level)
xyz_VirTemp(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ T_v $ . ä»�¸©åº�. Virtual temperature
xyr_VirTemp(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). Virtual temperature (half level)
xyr_Press(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{p} $ . æ°��� (���´æ�°ã������). Air pressure (half level)
xy_SurfHeight(0:imax-1,1:jmax) :real(DP), intent(in)
: $ z_s $ . �°è¡¨�¢é�åº�. Surface height.
xyz_Height(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: é«�åº� (�´æ�°ã������). Height (full level)
xyr_Height(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: é«�åº� (���´æ�°ã������). Height (half level)
xyz_Exner(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: Exner �¢æ�� (�´æ�°ã������). Exner function (full level)
xyr_Exner(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: Exner �¢æ�� (���´æ�°ã������). Exner function (half level)
xyz_TurKinEne(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: Turbulent kinetic energy (m2 s-2)
xy_SurfMomFluxX(0:imax-1, 1:jmax) :real(DP), intent(in)
: Eastward momentum flux at surface
xy_SurfMomFluxY(0:imax-1, 1:jmax) :real(DP), intent(in)
: Northward momentum flux at surface
xyr_MomFluxX(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �±è¥¿�¹å�����������������. Eastward momentum flux
xyr_MomFluxY(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �����¹å�����������������. Northward momentum flux
xyr_HeatFlux(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �±ã����������. Heat flux
xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax) :real(DP), intent(out)
: ������������. Mass flux of compositions
xyr_VelDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�������. Diffusion coefficient: velocity
xyr_TempDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�æ¸�º¦. Diffusion coefficient: temperature
xyr_QMixDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�æ¯�æ¹�. Diffusion coefficient: specific humidity
xyz_DTurKinEneDt(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(out)
: Tendency of turbulent kinetic energy

���´æ�¡æ�£ã���������¹ã��è¨�ç®����¾ã��.

Vertical diffusion flux is calculated by use of MY2.5 model.

[Source]

  subroutine VDiffusionMY25GBT94( xyz_U, xyz_V, xyzf_QMix, xyz_Temp, xyr_Temp, xyz_VirTemp, xyr_VirTemp, xyr_Press, xy_SurfHeight, xyz_Height, xyr_Height, xyz_Exner, xyr_Exner, xyz_TurKinEne, xy_SurfMomFluxX, xy_SurfMomFluxY, xyr_MomFluxX,  xyr_MomFluxY,  xyr_HeatFlux, xyrf_QMixFlux, xyr_VelDiffCoef, xyr_TempDiffCoef, xyr_QMixDiffCoef, xyz_DTurKinEneDt )
    !
    ! ���´æ�¡æ�£ã���������¹ã��è¨�ç®����¾ã��. 
    !
    ! Vertical diffusion flux is calculated by use of MY2.5 model.
    !

    ! �¢ã�¸ã�¥ã�¼ã����� ; USE statements
    !

    ! ����å®��°è¨­å®�
    ! Physical constants settings
    !
    use constants, only: FKarm, Grav, GasRDry, CpDry
                              ! $ C_p $ [J kg-1 K-1]. 
                              ! ä¹¾ç�¥å¤§æ°�����§æ���. 
                              ! Specific heat of air at constant pressure

    ! ���»ç���
    ! Time control
    !
    use timeset, only: DelTime, TimeN, TimesetClockStart, TimesetClockStop

    ! ���¹ã�������¼ã�¿å�ºå��
    ! History data output
    !
    use gtool_historyauto, only: HistoryAutoPut

    ! MPI �¢é�£ã���¼ã����
    ! MPI related routines
    !
    use mpi_wrapper, only : MPIWrapperChkTrue

    ! �°è§£æ³�����������ç©��������������¼ã����
    ! Routines for time integration with implicit scheme
    !
    use phy_implicit_utils, only : PhyImplLUDecomp3, PhyImplLUSolve3

    ! 宣�� ; Declaration statements
    !
    implicit none

    real(DP), intent(in):: xyz_U (0:imax-1, 1:jmax, 1:kmax)
                              ! $ u $ .   �±è¥¿é¢���. Eastward wind
    real(DP), intent(in):: xyz_V (0:imax-1, 1:jmax, 1:kmax)
                              ! $ v $ .   �������. Northward wind
    real(DP), intent(in):: xyzf_QMix(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
                              ! $ q $ .   è³��闋·å��æ¯�. Mass mixing ratio
    real(DP), intent(in):: xyz_Temp (0:imax-1, 1:jmax, 1:kmax)
                              ! $ T $ .   æ¸�º¦. Temperature
    real(DP), intent(in):: xyr_Temp (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{T} $ . æ¸�º¦ (���´æ�°ã������). 
                              ! Temperature (half level)
    real(DP), intent(in):: xyz_VirTemp (0:imax-1, 1:jmax, 1:kmax)
                              ! $ T_v $ .   ä»�¸©åº�. Virtual temperature
    real(DP), intent(in):: xyr_VirTemp (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). 
                              ! Virtual temperature (half level)
    real(DP), intent(in):: xyr_Press  (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{p} $ . æ°��� (���´æ�°ã������). 
                              ! Air pressure (half level)
    real(DP), intent(in):: xy_SurfHeight (0:imax-1,1:jmax)
                              ! $ z_s $ . �°è¡¨�¢é�åº�. 
                              ! Surface height. 
    real(DP), intent(in):: xyz_Height (0:imax-1, 1:jmax, 1:kmax)
                              ! é«�åº� (�´æ�°ã������). 
                              ! Height (full level)
    real(DP), intent(in):: xyr_Height (0:imax-1, 1:jmax, 0:kmax)
                              ! é«�åº� (���´æ�°ã������). 
                              ! Height (half level)
    real(DP), intent(in):: xyz_Exner (0:imax-1, 1:jmax, 1:kmax)
                              ! Exner �¢æ�� (�´æ�°ã������). 
                              ! Exner function (full level)
    real(DP), intent(in):: xyr_Exner (0:imax-1, 1:jmax, 0:kmax)
                              ! Exner �¢æ�� (���´æ�°ã������). 
                              ! Exner function (half level)

    real(DP), intent(in):: xyz_TurKinEne(0:imax-1, 1:jmax, 1:kmax)
                              ! 
                              ! Turbulent kinetic energy (m2 s-2)
    real(DP), intent(in):: xy_SurfMomFluxX (0:imax-1, 1:jmax)
                              ! 
                              ! Eastward momentum flux at surface
    real(DP), intent(in):: xy_SurfMomFluxY (0:imax-1, 1:jmax)
                              ! 
                              ! Northward momentum flux at surface

    real(DP), intent(out):: xyr_MomFluxX (0:imax-1, 1:jmax, 0:kmax)
                              ! �±è¥¿�¹å�����������������. 
                              ! Eastward momentum flux
    real(DP), intent(out):: xyr_MomFluxY (0:imax-1, 1:jmax, 0:kmax)
                              ! �����¹å�����������������. 
                              ! Northward momentum flux
    real(DP), intent(out):: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! �±ã����������. 
                              ! Heat flux
    real(DP), intent(out):: xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax)
                              ! ������������. 
                              ! Mass flux of compositions

    real(DP), intent(out):: xyr_VelDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�������. 
                              ! Diffusion coefficient: velocity
    real(DP), intent(out):: xyr_TempDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�æ¸�º¦. 
                              ! Diffusion coefficient: temperature
    real(DP), intent(out):: xyr_QMixDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�æ¯�æ¹�. 
                              ! Diffusion coefficient: specific humidity

    real(DP), intent(out):: xyz_DTurKinEneDt (0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! Tendency of turbulent kinetic energy

    ! �業��
    ! Work variables
    !

    real(DP) :: xyz_MixLength(0:imax-1, 1:jmax, 1:kmax)
                              ! 混����. 
                              ! Mixing length
    real(DP) :: xyz_DVelDzSq(0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! Vertical shear squared (s-2)
    real(DP) :: xyz_StatStab(0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! Static stability (s-2)
!!$    real(DP) :: GhMin
!!$                              !
!!$                              ! Minimum of G_h
!!$    real(DP) :: GhMax
!!$                              !
!!$                              ! Maximum of G_h
    real(DP) :: xyz_Gm(0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! G_m
    real(DP) :: xyz_Gh(0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! G_h
!!$    real(DP) :: xyz_SmHat(0:imax-1, 1:jmax, 1:kmax)
!!$                              !
!!$                              ! \hat{S}_M
!!$    real(DP) :: xyz_ShHat(0:imax-1, 1:jmax, 1:kmax)
!!$                              !
!!$                              ! \hat{S}_h
!!$    real(DP) :: xyz_DSmHatDTKE(0:imax-1, 1:jmax, 1:kmax)
!!$                              !
!!$                              ! derivative of \hat{S}_M
!!$    real(DP) :: xyz_DShHatDTKE(0:imax-1, 1:jmax, 1:kmax)
!!$                              !
!!$                              ! derivative of \hat{S}_h
    real(DP) :: xyz_Sm(0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! S_M
    real(DP) :: xyz_Sh(0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! S_h

    real(DP), parameter :: Stke = 0.2_DP
                              !
                              ! S_{TKE} = 0.2

    real(DP) :: xyz_VelDiffCoef (0:imax-1, 1:jmax, 1:kmax)
                              ! �¡æ�£ä��°ï�������. 
                              ! Diffusion coefficient: velocity
    real(DP) :: xyz_TempDiffCoef (0:imax-1, 1:jmax, 1:kmax)
                              ! �¡æ�£ä��°ï�æ¸�º¦. 
                              ! Transfer coefficient: temperature

    real(DP) :: xyr_TurKinEneDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! 
                              ! Diffusion coefficient: turbulent kinetic energy
    real(DP) :: xyz_TurKinEneDiffCoef (0:imax-1, 1:jmax, 1:kmax)
                              ! 
                              ! Diffusion coefficient: turbulent kinetic energy
    real(DP) :: xyr_TurKinEneTransCoef(0:imax-1, 1:jmax, 0:kmax)
                              ! 
                              ! Transfer coefficient: turbulent kinetic energy

    real(DP) :: xyr_TurKinEneFlux(0:imax-1, 1:jmax, 0:kmax)
                              ! 
                              ! Turbulent energy flux

    real(DP) :: xy_FricVelSq    (0:imax-1, 1:jmax)
    real(DP) :: xy_TurKinEneAtLB(0:imax-1, 1:jmax)

    real(DP) :: xyza_TurKinEneMtx(0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! 
                              ! Implicit matrix for turbulent kinetic energy
    real(DP) :: xyz_TurKinEneVec(0:imax-1, 1:jmax, 1:kmax)
                              ! 
                              ! Implicit vector for turbulent kinetic energy

    real(DP) :: xyza_TurKinEneLUMtx  (0:imax-1, 1:jmax, 1:kmax, -1:1)
                              ! LU ���.
                              ! LU matrix
    real(DP) :: xyz_DelTurKinEneLUVec(0:imax-1, 1:jmax, 1:kmax)
                              ! 
                              ! Tendency of turbulent kinetic energy

    real(DP) :: xyz_TurKinEneDiss(0:imax-1, 1:jmax, 1:kmax)
                              !
                              ! Dissipation rate of turbulent kinetic energy (m2 s-3)

    real(DP) :: xyz_TurKinEneNonZero(0:imax-1, 1:jmax, 1:kmax)
                              ! 
                              ! Turbulent kinetic energy with offset (m2 s-2)

    real(DP), parameter :: TurKinEneOffset  = ( 1.0e-3_DP )**2 / 2.0_DP


    logical :: xyz_FlagUseRiNum       (0:imax-1, 1:jmax, 1:kmax)
    logical :: xyz_FlagTKEAsymptToZero(0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_RiNum(0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: Beta1
    real(DP) :: Beta2
    real(DP) :: Beta3
    real(DP) :: Beta4
    real(DP) :: MixLength
    real(DP) :: xyz_A1    (0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_A2    (0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_R1    (0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_R2    (0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_SqrtA1(0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_TKEInit     (0:imax-1, 1:jmax, 1:kmax)
                              ! 
                              ! Turbulent kinetic energy for current time step
                              ! with offset (m2 s-2)
    real(DP) :: xyz_TKEx2       (0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_SqrtTKEx2   (0:imax-1, 1:jmax, 1:kmax)
    real(DP) :: xyz_TKETentative(0:imax-1, 1:jmax, 1:kmax)

    real(DP) :: Alpha
    real(DP) :: BetaSq
    real(DP) :: StatStab
    real(DP) :: RiNum
    real(DP) :: DVelDzSq

    real(DP), parameter :: Epsilon   = 1.0e-10_DP
    real(DP), parameter :: CrtlRiNum = 0.195_DP
    real(DP), parameter :: CrtlShear = 0.001_DP / 1000.0_DP

!!$    logical :: FlagReCalc
!!$                              !
!!$                              ! Flag for recalculation
!!$    logical :: a_FlagReCalcLocal (1)
!!$    logical :: a_FlagReCalcGlobal(1)
!!$    integer :: iloop
!!$    integer :: nloop

    integer:: i               ! çµ�åº��¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in longitude
    integer:: j               ! ç·�º¦�¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in latitude
    integer:: k               ! ���´æ�¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in vertical direction

!!$    integer:: n               ! çµ����¹å�������� DO ���¼ã�����業å���
!!$                              ! Work variables for DO loop in dimension of constituents

    ! ���� ; Executable statement
    !

    ! ������確è�
    ! Initialization check
    !
    if ( .not. vdiffusion_my_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


    ! �����������
    ! Start measurement of computation time
    !
    call TimesetClockStart( module_name )


    !
    ! Calculation of vertical shear squared
    do k = 1, kmax
      if ( k == 1 ) then
        xyz_DVelDzSq(:,:,k) = (   ( xyz_U(:,:,k+1) - xyz_U(:,:,k  ) )**2 + ( xyz_V(:,:,k+1) - xyz_V(:,:,k  ) )**2 ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k  ) )**2
!!$        xyz_DVelDzSq(:,:,k) =                              &
!!$          &   (   ( xyz_U(:,:,k+1) - 0.0_DP )**2   &
!!$          &     + ( xyz_V(:,:,k+1) - 0.0_DP )**2 ) &
!!$          & / ( xyz_Height(:,:,k+1) - xy_SurfHeight )**2
      else if ( k == kmax ) then
        xyz_DVelDzSq(:,:,k) = (   ( xyz_U(:,:,k  ) - xyz_U(:,:,k-1) )**2 + ( xyz_V(:,:,k  ) - xyz_V(:,:,k-1) )**2 ) / ( xyz_Height(:,:,k  ) - xyz_Height(:,:,k-1) )**2
      else
        xyz_DVelDzSq(:,:,k) = (   ( xyz_U(:,:,k+1) - xyz_U(:,:,k-1) )**2 + ( xyz_V(:,:,k+1) - xyz_V(:,:,k-1) )**2 ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k-1) )**2
      end if
    end do
    ! Calculation of static stability
    do k = 1, kmax
      if ( k == 1 ) then
        xyz_StatStab(:,:,k) = Grav / ( xyz_VirTemp(:,:,k) / xyz_Exner(:,:,k) ) * (   xyz_VirTemp(:,:,k+1) / xyz_Exner(:,:,k+1) - xyz_VirTemp(:,:,k  ) / xyz_Exner(:,:,k  ) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k  ) )
      else if ( k == kmax ) then
        xyz_StatStab(:,:,k) = Grav / ( xyz_VirTemp(:,:,k) / xyz_Exner(:,:,k) ) * (   xyz_VirTemp(:,:,k  ) / xyz_Exner(:,:,k  ) - xyz_VirTemp(:,:,k-1) / xyz_Exner(:,:,k-1) ) / ( xyz_Height(:,:,k  ) - xyz_Height(:,:,k-1) )
      else
        xyz_StatStab(:,:,k) = Grav / ( xyz_VirTemp(:,:,k) / xyz_Exner(:,:,k) ) * (   xyz_VirTemp(:,:,k+1) / xyz_Exner(:,:,k+1) - xyz_VirTemp(:,:,k-1) / xyz_Exner(:,:,k-1) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k-1) )
      end if
    end do


    ! æ··å��è·��¢ã�����
    ! Calculate mixing length
    !
    do k = 1, kmax
      xyz_MixLength(:,:,k) = FKarm * ( xyz_Height(:,:,k) - xy_SurfHeight ) / (1.0_DP + FKarm * ( xyz_Height(:,:,k) - xy_SurfHeight ) / MixLengthMax )
    end do
!!$    !   Limit mixing length (Galperin et al., 1988) and avoid zero
!!$    xyz_MixLength = &
!!$      &   min( xyz_MixLength, &
!!$      &        0.53_DP &
!!$      &          * sqrt( 2.0_DP * xyz_TurKinEneNonZero / max( xyz_StatStab, 1.0d-10 ) ) ) &
!!$      & + 1.0d-10

    !********************************************************************
    ! Gerrity et al. (1994)

    ! Set flag for using Richardson number
    do k = 1, kmax
      do j = 1, jmax
        do i = 0, imax-1
          if ( xyz_DVelDzSq(i,j,k) < CrtlShear**2 ) then
            xyz_FlagUseRiNum(i,j,k) = .false.
          else
            xyz_FlagUseRiNum(i,j,k) = .true.
          end if
        end do
      end do
    end do
    ! Calculation of Richardson number
    do k = 1, kmax
      do j = 1, jmax
        do i = 0, imax-1
          if ( xyz_FlagUseRiNum(i,j,k) ) then
            xyz_RiNum(i,j,k) = xyz_StatStab(i,j,k) / xyz_DVelDzSq(i,j,k)
          else
            xyz_RiNum(i,j,k) = - 1.0e100_DP
          end if
        end do
      end do
    end do

    ! Set flag for selecting an asymptotic equation
    do k = 1, kmax
      do j = 1, jmax
        do i = 0, imax-1
          if ( xyz_FlagUseRiNum(i,j,k) ) then
            if ( CrtlRiNum <= xyz_RiNum(i,j,k) ) then
              ! Ric <= Ri
              xyz_FlagTKEAsymptToZero = .true.
            else
              ! Ri  <  Ric
              xyz_FlagTKEAsymptToZero = .false.
            end if
          else
            if ( xyz_StatStab(i,j,k) > 0.0_DP ) then
              xyz_FlagTKEAsymptToZero = .true.
            else
              xyz_FlagTKEAsymptToZero = .false.
            end if
          end if
        end do
      end do
    end do

    ! Calculation of roos for equations for steady state
    do k = 1, kmax
      do j = 1, jmax
        do i = 0, imax-1
          if ( xyz_FlagUseRiNum(i,j,k) ) then
            ! Calculation with Richardson number
            MixLength = xyz_MixLength(i,j,k)
            DVelDzSq  = xyz_DVelDzSq (i,j,k)
            RiNum     = xyz_RiNum    (i,j,k)
            !
            Beta1 = - MixLength**2 * DVelDzSq * (  6.53_DP - 49.0_DP  * RiNum )
            Beta2 = - MixLength**4 * DVelDzSq**2 * ( 51.2_DP  - 262.7_DP * RiNum ) * RiNum
            Beta3 = MixLength**2 * DVelDzSq * (  5.08_DP + 36.7_DP  * RiNum )
            Beta4 = MixLength**4 * DVelDzSq**2 * ( 88.8_DP  + 187.4_DP * RiNum ) * RiNum
            !
            xyz_A1(i,j,k) = - Beta1 / 2.0_DP + sqrt( Beta1**2 - 4.0_DP * Beta2 ) / 2.0_DP
            xyz_A2(i,j,k) = - Beta1 / 2.0_DP - sqrt( Beta1**2 - 4.0_DP * Beta2 ) / 2.0_DP
            xyz_R1(i,j,k) = - Beta3 / 2.0_DP + sqrt( Beta3**2 - 4.0_DP * Beta4 ) / 2.0_DP
            xyz_R2(i,j,k) = - Beta3 / 2.0_DP - sqrt( Beta3**2 - 4.0_DP * Beta4 ) / 2.0_DP
          else
            ! Calculation without Richardson number
            MixLength = xyz_MixLength(i,j,k)
            StatStab  = xyz_StatStab (i,j,k)
            !
            xyz_A1(i,j,k) = 24.49_DP * MixLength**2 *    ( - StatStab ) + 18.36_DP * MixLength**2 * abs( - StatStab )
            xyz_A2(i,j,k) = 24.49_DP * MixLength**2 *    ( - StatStab ) - 18.36_DP * MixLength**2 * abs( - StatStab )
            xyz_R1(i,j,k) = 18.35_DP * MixLength**2 *    ( - StatStab ) + 12.22_DP * MixLength**2 * abs( - StatStab )
            xyz_R2(i,j,k) = 18.35_DP * MixLength**2 *    ( - StatStab ) - 12.22_DP * MixLength**2 * abs( - StatStab )
          end if
        end do
      end do
    end do

    ! Set turbulent kinetic energy at current time step
    !
    do k = 1, kmax
      do j = 1, jmax
        do i = 0, imax-1
          if ( xyz_FlagUseRiNum(i,j,k) ) then
            if ( xyz_RiNum(i,j,k) < 0.0_DP ) then
              ! Ri < 0 (or CT > 0)
              xyz_TKEInit(i,j,k) = max( xyz_TurKinEne(i,j,k), xyz_R1(i,j,k) / 2.0_DP )
            else if ( xyz_RiNum(i,j,k) < CrtlRiNum ) then
              ! 0 <= Ri < Ric
              xyz_TKEInit(i,j,k) = xyz_TurKinEne(i,j,k)
            else
              ! Ric <= Ri
              xyz_TKEInit(i,j,k) = xyz_TurKinEne(i,j,k)
            end if
          else
            if ( xyz_StatStab(i,j,k) < 0.0_DP ) then
              ! CT >  0
              xyz_TKEInit(i,j,k) = max( xyz_TurKinEne(i,j,k), xyz_R1(i,j,k) / 2.0_DP )
            else
              ! CT <= 0
              xyz_TKEInit(i,j,k) = xyz_TurKinEne(i,j,k)
            end if
          end if
          xyz_TKEInit(i,j,k) = xyz_TKEInit(i,j,k) + TurKinEneOffset
        end do
      end do
    end do
    !
    xyz_TKEx2     = 2.0_DP * xyz_TKEInit
    xyz_SqrtTKEx2 = sqrt( xyz_TKEx2 )
    do k = 1, kmax
      do j = 1, jmax
        do i = 0, imax-1
          if ( xyz_FlagTKEAsymptToZero(i,j,k) ) then
            xyz_SqrtA1(i,j,k) = 1.0e100_DP
          else
            xyz_SqrtA1(i,j,k) = sqrt( xyz_A1(i,j,k) )
          end if
        end do
      end do
    end do
    !
    do k = 1, kmax
      do j = 1, jmax
        do i = 0, imax-1
          if ( xyz_FlagTKEAsymptToZero(i,j,k) ) then
            ! Use equations asymptotic to zero TKE, Eq. (10)
            ! Eq. (11)
            BetaSq = ( xyz_TKEx2(i,j,k) - xyz_A1(i,j,k)**2 ) * ( xyz_TKEx2(i,j,k) - xyz_A2(i,j,k)**2 ) / ( MYConstB1 * xyz_MixLength(i,j,k) * ( xyz_TKEx2(i,j,k) - xyz_R1(i,j,k) ) * ( xyz_TKEx2(i,j,k) - xyz_R2(i,j,k) ) )
            ! Eq. (10)
            xyz_TKETentative(i,j,k) = xyz_TKEInit(i,j,k) / 2.0_DP / ( 1.0_DP + xyz_SqrtTKEx2(i,j,k) * BetaSq * ( 2.0_DP * DelTime ) )**2
          else
            ! Use equations asymptotic to certain TKE, Eq. (8)
            ! Eq. (7b)
            BetaSq = xyz_TKEx2(i,j,k) * ( xyz_TKEx2(i,j,k) - xyz_A2(i,j,k)**2 ) / ( MYConstB1 * xyz_MixLength(i,j,k) * ( xyz_TKEx2(i,j,k) - xyz_R1(i,j,k) ) * ( xyz_TKEx2(i,j,k) - xyz_R2(i,j,k) ) )
            ! Eq. (9)
            Alpha = ( xyz_SqrtTKEx2(i,j,k) - xyz_SqrtA1(i,j,k) ) / ( xyz_SqrtTKEx2(i,j,k) + xyz_SqrtA1(i,j,k) ) * exp( - 2.0_DP * xyz_SqrtA1(i,j,k) * BetaSq * ( 2.0_DP * DelTime ) )
            Alpha = max( min( Alpha, 1.0_DP - Epsilon ), -1.0_DP )
            ! Eq. (8)
            xyz_TKETentative(i,j,k) = xyz_A1(i,j,k) / 2.0_DP * ( ( 1.0_DP + Alpha ) / ( 1.0_DP - Alpha ) )**2
          end if
        end do
      end do
    end do


    !********************************************************************

    ! Set turbulent kinetic energy for diffusion calculation
    !
!!$    xyz_TurKinEneNonZero = xyz_TurKinEne + TurKinEneOffset
    xyz_TurKinEneNonZero = xyz_TKETentative + TurKinEneOffset


    xyz_Gh = - xyz_MixLength**2 / ( 2.0_DP * xyz_TurKinEneNonZero ) * xyz_StatStab
    ! Actually, xyz_Gm is not used below.
    xyz_Gm =   xyz_MixLength**2 / ( 2.0_DP * xyz_TurKinEneNonZero ) * xyz_DVelDzSq


    ! Limit Gh (Galperin et al., 1988)
!!$    GhMin = - 0.53d0**2
!!$    GhMax = 1.0_DP                                         &
!!$      & / ( MYConstA2                                      &
!!$      &     * (  12.0_DP * MYConstA1 + MYConstB1 + 3.0_DP * MYConstB2 ) )
!!$    xyz_Gh = max( GhMin, min( xyz_Gh, GhMax ) )


    xyz_Sh = MYConstA2 * ( 1.0_DP - 6.0_DP * MYConstA1 / MYConstB1 ) / (   1.0_DP - 3.0_DP * MYConstA2 * ( 6.0_DP * MYConstA1 + MYConstB2 ) * xyz_Gh )

    xyz_Sm = ( MYConstA1 * (   1.0_DP - 3.0_DP * MYConstC1 - 6.0_DP * MYConstA1 / MYConstB1 ) + 9.0_DP * MYConstA1 * ( 2.0_DP * MYConstA1 + MYConstA2 ) * xyz_Gh * xyz_Sh ) / (   1.0_DP - 9.0_DP * MYConstA1 * MYConstA2 * xyz_Gh )


    ! �¡æ�£ä��°ã���ç®�
    ! Calculation of diffusion coefficient
    !
    xyz_VelDiffCoef  = xyz_MixLength * sqrt( 2.0_DP * xyz_TurKinEneNonZero ) * xyz_Sm
    xyz_TempDiffCoef = xyz_MixLength * sqrt( 2.0_DP * xyz_TurKinEneNonZero ) * xyz_Sh
    !
    do k = 0, kmax
      if ( ( k == 0 ) .or. ( k == kmax ) ) then
        xyr_VelDiffCoef (:,:,k) = 0.0_DP
        xyr_TempDiffCoef(:,:,k) = 0.0_DP
      else
        xyr_VelDiffCoef (:,:,k) = ( xyz_VelDiffCoef (:,:,k) + xyz_VelDiffCoef (:,:,k+1) ) / 2.0_DP
        xyr_TempDiffCoef(:,:,k) = ( xyz_TempDiffCoef(:,:,k) + xyz_TempDiffCoef(:,:,k+1) ) / 2.0_DP
      end if
    end do
    !
    do k = 1, kmax-1
      do j = 1, jmax
        do i = 0, imax-1
          xyr_VelDiffCoef(i,j,k) = max( min( xyr_VelDiffCoef(i,j,k), VelDiffCoefMax ), VelDiffCoefMin )
          xyr_TempDiffCoef(i,j,k) = max( min( xyr_TempDiffCoef(i,j,k), TempDiffCoefMax ), TempDiffCoefMin )
        end do
      end do
    end do
    !
    xyr_QMixDiffCoef      = xyr_TempDiffCoef


    ! 輸é��ä¿��°ã�����������¹ã���ç®�
    ! Calculate transfer coefficient and flux
    !
    call VDiffusionCalcFlux( xyz_U, xyz_V, xyzf_QMix, xyz_Temp, xyr_VirTemp, xyr_Press, xyz_Height, xyz_Exner, xyr_Exner, xyr_VelDiffCoef, xyr_TempDiffCoef, xyr_QMixDiffCoef, xyr_MomFluxX,  xyr_MomFluxY,  xyr_HeatFlux, xyrf_QMixFlux )


    ! Calculate tendency of turbulent kinetic energy

    !   Set diffusion coefficient for turbulent kinetic energy
    xyz_TurKinEneDiffCoef = xyz_MixLength * sqrt( 2.0_DP * xyz_TurKinEneNonZero ) * Stke
    !
    do k = 0, kmax
      if ( k == 0 ) then
        xyr_TurKinEneDiffCoef(:,:,k) = xyz_TurKinEneDiffCoef(:,:,1)
      else if ( k == kmax ) then
        xyr_TurKinEneDiffCoef(:,:,k) = xyz_TurKinEneDiffCoef(:,:,kmax)
      else
        xyr_TurKinEneDiffCoef(:,:,k) = ( xyz_TurKinEneDiffCoef(:,:,k) + xyz_TurKinEneDiffCoef(:,:,k+1) ) / 2.0_DP
      end if
    end do

    !   Calculate turbulent kinetic energy at lower boundary
    !
    xy_FricVelSq = sqrt( xy_SurfMomFluxX**2 + xy_SurfMomFluxY**2 ) / ( xyr_Press(:,:,0) / ( GasRDry * xyr_VirTemp(:,:,0) ) )
    xy_TurKinEneAtLB = MYConstB1**(2.0_DP/3.0_DP) / 2.0_DP * xy_FricVelSq
    xy_TurKinEneAtLB = xy_TurKinEneAtLB + TurKinEneOffset

    !   Calculate transfer coefficient and flux of turbulent kinetic energy
    !
    !    When transfer coefficient at lower boundary is calculated, 
    !    diffusion coefficient at mid-point of 1st layer is used. 
    !    In addition, transfer coefficient at upper boundary is assumed 
    !    to be zero.
    k = 0
    xyr_TurKinEneTransCoef(:,:,k) = xyz_TurKinEneDiffCoef(:,:,1) * xyr_Press(:,:,k) / ( GasRDry * xyr_VirTemp(:,:,k) ) / ( xyz_Height(:,:,1) - xy_SurfHeight )
    do k = 1, kmax-1
      xyr_TurKinEneTransCoef(:,:,k) = xyr_TurKinEneDiffCoef(:,:,k) * xyr_Press(:,:,k) / ( GasRDry * xyr_VirTemp(:,:,k) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k) )
    end do
    k = kmax
    xyr_TurKinEneTransCoef(:,:,k) = 0.0_DP
    !
    do k = 1, kmax-1
      xyr_TurKinEneFlux(:,:,k) = - xyr_TurKinEneTransCoef(:,:,k) * ( xyz_TurKinEneNonZero(:,:,k+1) - xyz_TurKinEneNonZero(:,:,k) )
    end do
    k = 0
    xyr_TurKinEneFlux(:,:,k) = - xyr_TurKinEneTransCoef(:,:,k) * ( xyz_TurKinEneNonZero(:,:,k+1) - xy_TurKinEneAtLB )
    k = kmax
    xyr_TurKinEneFlux(:,:,k) = 0.0_DP


    !
    ! Construct implicit matrix from transfer coefficient of vertical 
    ! diffusion scheme (turbulent kinetic energy)
    !
    k = 1
    xyza_TurKinEneMtx(:,:,k,-1) = 0.0_DP
    xyza_TurKinEneMtx(:,:,k, 0) = - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + xyr_TurKinEneTransCoef(:,:,k-1) + xyr_TurKinEneTransCoef(:,:,k  )
    xyza_TurKinEneMtx(:,:,k, 1) = - xyr_TurKinEneTransCoef(:,:,k  )
    !
    do k = 2, kmax-1
      xyza_TurKinEneMtx(:,:,k,-1) = - xyr_TurKinEneTransCoef(:,:,k-1)
      xyza_TurKinEneMtx(:,:,k, 0) = - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + xyr_TurKinEneTransCoef(:,:,k-1) + xyr_TurKinEneTransCoef(:,:,k  )
      xyza_TurKinEneMtx(:,:,k, 1) = - xyr_TurKinEneTransCoef(:,:,k  )
    end do
    !
    k = kmax
    xyza_TurKinEneMtx(:,:,k,-1) = - xyr_TurKinEneTransCoef(:,:,k-1)
    xyza_TurKinEneMtx(:,:,k, 0) = - ( xyr_Press(:,:,k) - xyr_Press(:,:,k-1) ) / Grav / ( 2.0_DP * DelTime ) + xyr_TurKinEneTransCoef(:,:,k-1) + xyr_TurKinEneTransCoef(:,:,k  )
    xyza_TurKinEneMtx(:,:,k, 1) = 0.0_DP

    do k = 1, kmax
      xyz_TurKinEneVec(:,:,k) = - ( xyr_TurKinEneFlux(:,:,k) - xyr_TurKinEneFlux(:,:,k-1) )
    end do


    !
    ! Solve simultaneous linear equations by use of LU decomposition technique
    !
    xyza_TurKinEneLUMtx = xyza_TurKinEneMtx
    !
    call PhyImplLUDecomp3( xyza_TurKinEneLUMtx, imax * jmax, kmax )

    xyz_DelTurKinEneLUVec = xyz_TurKinEneVec
    !
    call PhyImplLUSolve3( xyz_DelTurKinEneLUVec, xyza_TurKinEneLUMtx, 1, imax * jmax , kmax )

!!$    xyz_DTurKinEneDt = xyz_DelTurKinEneLUVec / ( 2.0_DP * DelTime )

    xyz_TKETentative = xyz_TKETentative + xyz_DelTurKinEneLUVec
    xyz_DTurKinEneDt = ( xyz_TKETentative - xyz_TurKinEne ) / ( 2.0_DP * DelTime )


!!$    write( 6, * ) TimeN, iloop
!!$    write( 6, * ) xyz_TurKinEne(0,jmax/2+1,1:4)
!!$    write( 6, * ) xyz_TempDiffCoef(0,jmax/2+1,1:4)
!!$    write( 6, * ) xyz_DTurKinEneDt(0,jmax/2+1,1:4)



    ! �¡æ�£ä��°ã���ºå��
    ! Output diffusion coefficients
    !

    ! �¡æ�£ä��°å�ºå��
    ! Diffusion coeffficients output
    !
    call HistoryAutoPut( TimeN, 'VelDiffCoef',  xyr_VelDiffCoef  )
    call HistoryAutoPut( TimeN, 'TempDiffCoef', xyr_TempDiffCoef )
    call HistoryAutoPut( TimeN, 'QVapDiffCoef', xyr_QMixDiffCoef )

    call HistoryAutoPut( TimeN, 'MixLength' , xyz_MixLength )



    ! ��������������
    ! Pause measurement of computation time
    !
    call TimesetClockStop( module_name )

  end subroutine VDiffusionMY25GBT94
Subroutine :
xyr_MomFluxX(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: �±è¥¿�¹å�����������������. Eastward wind flux
xyr_MomFluxY(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: �����¹å�����������������. Northward momentum flux
xyr_HeatFlux(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: �±ã����������. Heat flux
xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax) :real(DP), intent(in)
: ������������. Mass flux of constituents
xyz_DUDt(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ DP{u}{t} $ . �±è¥¿é¢���å¤���. Eastward wind tendency
xyz_DVDt(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ DP{v}{t} $ . ����������. Northward wind tendency
xyz_DTempDt(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ DP{T}{t} $ . æ¸�º¦å¤���. Temperature tendency
xyzf_DQMixDt(0:imax-1, 1:jmax, 1:kmax, 1:ncmax) :real(DP), intent(in)
: $ DP{q}{t} $ . 混�����. Mass mixing ratio tendency
xyr_Press(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{p} $ . æ°��� (���´æ�°ã������). Air pressure (half level)
xyz_Exner(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: Exner �¢æ�� (�´æ�°ã������). Exner function (full level)
xyr_Exner(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: Exner �¢æ�� (���´æ�°ã������). Exner function (half level)
xyr_VirTemp(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). Virtual temperature (half level)
xyz_Height(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: é«�åº� (�´æ�°ã������). Height (full level)
xyr_VelDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: �¡æ�£ä��°ï�������. Diffusion coefficient: velocity
xyr_TempDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: �¡æ�£ä��°ï�æ¸�º¦. Transfer coefficient: temperature
xyr_QMixDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: �¡æ�£ä��°ï�æ¯�æ¹�. Diffusion coefficient: specific humidity

���������� (xyr_MomFluxX, xyr_MomFluxY, xyr_HeatFlux, xyrf_QMixFlux). ���¤ã����, ���������°ã���������æ­£ã��, �ºå����è¡���.

Fluxes (xyr_MomFluxX, xyr_MomFluxY, xyr_HeatFlux, xyrf_QMixFlux) are corrected by using other arguments, and the corrected values are output.

[Source]

  subroutine VDiffusionOutPut( xyr_MomFluxX, xyr_MomFluxY, xyr_HeatFlux, xyrf_QMixFlux, xyz_DUDt,  xyz_DVDt,  xyz_DTempDt,  xyzf_DQMixDt, xyr_Press, xyz_Exner, xyr_Exner, xyr_VirTemp, xyz_Height, xyr_VelDiffCoef, xyr_TempDiffCoef, xyr_QMixDiffCoef )
    !
    ! ���������� (xyr_MomFluxX, xyr_MomFluxY, xyr_HeatFlux, xyrf_QMixFlux). 
    ! ���¤ã����, ���������°ã���������æ­£ã��, �ºå����è¡���. 
    !
    ! Fluxes (xyr_MomFluxX, xyr_MomFluxY, xyr_HeatFlux, xyrf_QMixFlux) are
    ! corrected by using other arguments, and the corrected values are output.
    !

    ! �¢ã�¸ã�¥ã�¼ã����� ; USE statements
    !

    ! ����å®��°è¨­å®�
    ! Physical constants settings
    !
    use constants, only: CpDry, LatentHeat, GasRDry
                              ! $ R $ [J kg-1 K-1]. 
                              ! 乾�大��������. 
                              ! Gas constant of air

    ! ���»ç���
    ! Time control
    !
    use timeset, only: DelTime, TimeN, TimesetClockStart, TimesetClockStop

    ! ���¹ã�������¼ã�¿å�ºå��
    ! History data output
    !
    use gtool_historyauto, only: HistoryAutoPut

    ! 宣�� ; Declaration statements
    !
    implicit none
    real(DP), intent(in):: xyr_MomFluxX (0:imax-1, 1:jmax, 0:kmax)
                              ! �±è¥¿�¹å�����������������. 
                              ! Eastward wind flux
    real(DP), intent(in):: xyr_MomFluxY (0:imax-1, 1:jmax, 0:kmax)
                              ! �����¹å�����������������. 
                              ! Northward momentum flux
    real(DP), intent(in):: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! �±ã����������. 
                              ! Heat flux
    real(DP), intent(in):: xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax)
                              ! ������������. 
                              ! Mass flux of constituents
    real(DP), intent(in):: xyz_DUDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{u}{t} $ . �±è¥¿é¢���å¤���. 
                              ! Eastward wind tendency
    real(DP), intent(in):: xyz_DVDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{v}{t} $ . ����������. 
                              ! Northward wind tendency
    real(DP), intent(in):: xyz_DTempDt (0:imax-1, 1:jmax, 1:kmax)
                              ! $ \DP{T}{t} $ . æ¸�º¦å¤���. 
                              ! Temperature tendency
    real(DP), intent(in):: xyzf_DQMixDt(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
                              ! $ \DP{q}{t} $ . 混�����. 
                              ! Mass mixing ratio tendency
    real(DP), intent(in):: xyr_Press (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{p} $ . æ°��� (���´æ�°ã������). 
                              ! Air pressure (half level)
    real(DP), intent(in):: xyz_Exner (0:imax-1, 1:jmax, 1:kmax)
                              ! Exner �¢æ�� (�´æ�°ã������). 
                              ! Exner function (full level)
    real(DP), intent(in):: xyr_Exner (0:imax-1, 1:jmax, 0:kmax)
                              ! Exner �¢æ�� (���´æ�°ã������). 
                              ! Exner function (half level)

    real(DP), intent(in):: xyr_VirTemp (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). 
                              ! Virtual temperature (half level)
    real(DP), intent(in):: xyz_Height (0:imax-1, 1:jmax, 1:kmax)
                              ! é«�åº� (�´æ�°ã������). 
                              ! Height (full level)

    real(DP), intent(in):: xyr_VelDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�������. 
                              ! Diffusion coefficient: velocity
    real(DP), intent(in):: xyr_TempDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�æ¸�º¦. 
                              ! Transfer coefficient: temperature
    real(DP), intent(in):: xyr_QMixDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�æ¯�æ¹�. 
                              ! Diffusion coefficient: specific humidity

    ! �ºå�����������業å���
    ! Work variables for output
    !
    real(DP):: xyr_MomFluxXCor (0:imax-1, 1:jmax, 0:kmax)
                              ! �±è¥¿�¹å�����������������. 
                              ! Eastward momentum flux
    real(DP):: xyr_MomFluxYCor (0:imax-1, 1:jmax, 0:kmax)
                              ! �����¹å�����������������. 
                              ! Northward momentum flux
    real(DP):: xyr_HeatFluxCor (0:imax-1, 1:jmax, 0:kmax)
                              ! �±ã����������. 
                              ! Heat flux
    real(DP):: xyrf_QMixFluxCor(0:imax-1, 1:jmax, 0:kmax, 1:ncmax)
                              ! ������������. 
                              ! Mass flux of constituents


    ! �業��
    ! Work variables
    !
    real(DP) :: xyr_VelTransCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! 輸é��ä¿��°ï�������. 
                              ! Transfer coefficient: velocity
    real(DP) :: xyr_TempTransCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! 輸é��ä¿��°ï�æ¸�º¦. 
                              ! Transfer coefficient: temperature
    real(DP) :: xyr_QMixTransCoef(0:imax-1, 1:jmax, 0:kmax)
                              ! 輸é��ä¿��°ï�è³���. 
                              ! Transfer coefficient: mass of constituents

    integer:: i               ! çµ�åº��¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in longitude
    integer:: j               ! ç·�º¦�¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in latitude
    integer:: k               ! ���´æ�¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in vertical direction
    integer:: n               ! çµ����¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in dimension of constituents
    real(DP):: LCp
                              ! $ L / C_p $ [K]. 

    ! ���� ; Executable statement
    !

    ! ������確è�
    ! Initialization check
    !
    if ( .not. vdiffusion_my_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


    ! �����������
    ! Start measurement of computation time
    !
    call TimesetClockStart( module_name )


    ! 輸é��ä¿��°ã���ç®�
    ! Calculate transfer coefficient
    !
    xyr_VelTransCoef (:,:,0)    = 0.0_DP
    xyr_VelTransCoef (:,:,kmax) = 0.0_DP
    xyr_TempTransCoef(:,:,0)    = 0.0_DP
    xyr_TempTransCoef(:,:,kmax) = 0.0_DP
    xyr_QMixTransCoef(:,:,0)    = 0.0_DP
    xyr_QMixTransCoef(:,:,kmax) = 0.0_DP

    do k = 1, kmax-1
      xyr_VelTransCoef(:,:,k) = xyr_VelDiffCoef(:,:,k) * xyr_Press(:,:,k) / ( GasRDry * xyr_VirTemp(:,:,k) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k) )

      xyr_TempTransCoef(:,:,k) = xyr_TempDiffCoef(:,:,k) * xyr_Press(:,:,k) / ( GasRDry * xyr_VirTemp(:,:,k) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k) )

      xyr_QMixTransCoef(:,:,k) = xyr_QMixDiffCoef(:,:,k) * xyr_Press(:,:,k) / ( GasRDry * xyr_VirTemp(:,:,k) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k) )
    end do


    ! é¢���, æ¸�º¦, æ¯�湿ã���������¹è�æ­�
    ! Correct fluxes of wind, temperature, specific humidity
    !
    LCp = LatentHeat / CpDry

    do k = 1, kmax-1
      do j = 1, jmax
        do i = 0, imax-1

          xyr_MomFluxXCor( i,j,k ) = xyr_MomFluxX( i,j,k ) + ( xyz_DUDt( i,j,k ) - xyz_DUDt( i,j,k+1 ) ) * xyr_VelTransCoef( i,j,k ) * DelTime

          xyr_MomFluxYCor( i,j,k ) = xyr_MomFluxY( i,j,k ) + ( xyz_DVDt( i,j,k ) - xyz_DVDt( i,j,k+1 ) ) * xyr_VelTransCoef( i,j,k ) * DelTime

          xyr_HeatFluxCor( i,j,k ) = xyr_HeatFlux( i,j,k ) + (   xyz_DTempDt( i,j,k   ) / xyz_Exner( i,j,k   ) - xyz_DTempDt( i,j,k+1 ) / xyz_Exner( i,j,k+1 ) ) * CpDry * xyr_TempTransCoef( i,j,k ) * xyr_Exner( i,j,k ) * DelTime
        end do
      end do
    end do

    do n = 1, ncmax
      do k = 1, kmax-1
        do j = 1, jmax
          do i = 0, imax-1
            xyrf_QMixFluxCor( i,j,k,n ) = xyrf_QMixFlux( i,j,k,n ) + ( xyzf_DQMixDt( i,j,k,n ) - xyzf_DQMixDt( i,j,k+1,n ) ) * CpDry * xyr_QMixTransCoef( i,j,k ) * LCp * DelTime
          end do
        end do
      end do
    end do

    xyr_MomFluxXCor   (:,:,0)    = 0.0_DP
    xyr_MomFluxXCor   (:,:,kmax) = 0.0_DP
    xyr_MomFluxYCor   (:,:,0)    = 0.0_DP
    xyr_MomFluxYCor   (:,:,kmax) = 0.0_DP
    xyr_HeatFluxCor   (:,:,0)    = 0.0_DP
    xyr_HeatFluxCor   (:,:,kmax) = 0.0_DP
    do n = 1, ncmax
      xyrf_QMixFluxCor(:,:,0,n)    = 0.0_DP
      xyrf_QMixFluxCor(:,:,kmax,n) = 0.0_DP
    end do

    ! MEMO
    ! Output values of surface fluxes in MomFluxX, MomFluxY, HeatFlux, and QVapFlux 
    ! are not correct. (YOT, 2009/08/14)
    ! Please refer to output variables, 'TauX', 'TauY', 'Sens', and 'Evap' for those 
    ! values.  (YOT, 2011/05/28)

    ! ���¹ã�������¼ã�¿å�ºå��
    ! History data output
    !
    call HistoryAutoPut( TimeN, 'MomFluxX', xyr_MomFluxXCor  )
    call HistoryAutoPut( TimeN, 'MomFluxY', xyr_MomFluxYCor  )
    call HistoryAutoPut( TimeN, 'HeatFlux', xyr_HeatFluxCor  )
    call HistoryAutoPut( TimeN, 'QVapFlux', xyrf_QMixFluxCor )

    call HistoryAutoPut( TimeN, 'DUDtVDiff'   , xyz_DUDt                        )
    call HistoryAutoPut( TimeN, 'DVDtVDiff'   , xyz_DVDt                        )
    call HistoryAutoPut( TimeN, 'DTempDtVDiff', xyz_DTempDt                     )
    call HistoryAutoPut( TimeN, 'DQVapDtVDiff', xyzf_DQMixDt(:,:,:,IndexH2OVap) )

    ! ��������������
    ! Pause measurement of computation time
    !
    call TimesetClockStop( module_name )

  end subroutine VDiffusionOutPut

Private Instance methods

BulkRiNumMin
Variable :
BulkRiNumMin :real(DP), save
: ������ $ R_i $ �°æ��å°��. Minimum value of bulk $ R_i $
ConstDiffCoefH
Variable :
ConstDiffCoefH :real(DP), save
: Diffusion coefficient for heat that is used in the case of FlagConstDiffCoef == .true.
ConstDiffCoefM
Variable :
ConstDiffCoefM :real(DP), save
: Diffusion coefficient for momentum that is used in the case of FlagConstDiffCoef == .true.
FlagConstDiffCoef
Variable :
FlagConstDiffCoef :logical , save
: Flag for use of constant diffusion coefficient
MYConstA1
Variable :
MYConstA1 :real(DP), save
MYConstA2
Variable :
MYConstA2 :real(DP), save
MYConstB1
Variable :
MYConstB1 :real(DP), save
MYConstB2
Variable :
MYConstB2 :real(DP), save
MYConstC1
Variable :
MYConstC1 :real(DP), save
MixLengthMax
Variable :
MixLengthMax :real(DP), save
: ��大混�����. Maximum mixing length
ShMin
Variable :
ShMin :real(DP), save
: $ S_h $ ����. Minimum $ S_h $
SmMin
Variable :
SmMin :real(DP), save
: $ S_m $ ����. Minimum $ S_m $
SquareVelMin
Variable :
SquareVelMin :real(DP), save
: ��������. Minimum value of square of velocity
TempDiffCoefMax
Variable :
TempDiffCoefMax :real(DP), save
: $ T $ �¡æ�£ä��°æ��大å��. Maximum diffusion coefficient of $ T $
TempDiffCoefMin
Variable :
TempDiffCoefMin :real(DP), save
: $ T $ �¡æ�£ä��°æ��å°��. Minimum diffusion coefficient of $ T $
Subroutine :
xy_SurfHeight(0:imax-1,1:jmax) :real(DP), intent(in)
: $ z_s $ . �°è¡¨�¢é�åº�. Surface height.
xyr_Height(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: é«�åº� (���´æ�°ã������). Height (half level)
xyr_DVelDz(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ DD{|Dvect{v}|}{z} $
xyr_BulkRiNum(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: ������ $ R_i $ ��. Bulk $ R_i $
xyr_VelDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�������. Diffusion coefficient: velocity
xyr_TempDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�æ¸�º¦. Transfer coefficient: temperature
xyr_QMixDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�è³��� Diffusion coefficient: mass of constituents

���´æ�¡æ�£ã���������¹ã��è¨�ç®����¾ã��.

Vertical diffusion flux is calculated.

[Source]

  subroutine VDiffCoefficient( xy_SurfHeight, xyr_Height, xyr_DVelDz, xyr_BulkRiNum, xyr_VelDiffCoef, xyr_TempDiffCoef, xyr_QMixDiffCoef )
    !
    ! ���´æ�¡æ�£ã���������¹ã��è¨�ç®����¾ã��. 
    !
    ! Vertical diffusion flux is calculated. 
    !

    ! �¢ã�¸ã�¥ã�¼ã����� ; USE statements
    !

    ! ���»ç���
    ! Time control
    !
    use timeset, only: TimeN, TimesetClockStart, TimesetClockStop

    ! ����å®��°è¨­å®�
    ! Physical constants settings
    !
    use constants, only: FKarm
                              ! $ k $ .
                              ! �������³å���. 
                              ! Karman constant

    ! ���¹ã�������¼ã�¿å�ºå��
    ! History data output
    !
    use gtool_historyauto, only: HistoryAutoPut

    ! 宣�� ; Declaration statements
    !
    implicit none
    real(DP), intent(in):: xy_SurfHeight (0:imax-1,1:jmax)
                              ! $ z_s $ . �°è¡¨�¢é�åº�. 
                              ! Surface height. 
    real(DP), intent(in):: xyr_Height (0:imax-1, 1:jmax, 0:kmax)
                              ! é«�åº� (���´æ�°ã������). 
                              ! Height (half level)
    real(DP), intent(in):: xyr_DVelDz (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \DD{|\Dvect{v}|}{z} $
    real(DP), intent(in):: xyr_BulkRiNum (0:imax-1, 1:jmax, 0:kmax)
                              ! ������ $ R_i $ ��. 
                              ! Bulk $ R_i $
    real(DP), intent(out):: xyr_VelDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�������. 
                              ! Diffusion coefficient: velocity
    real(DP), intent(out):: xyr_TempDiffCoef(0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�æ¸�º¦. 
                              ! Transfer coefficient: temperature
    real(DP), intent(out):: xyr_QMixDiffCoef(0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�è³���
                              ! Diffusion coefficient: mass of constituents



    ! �業��
    ! Work variables
    !
    real(DP):: xyr_FluxRiNum (0:imax-1, 1:jmax, 0:kmax)
                              ! ���������� $ R_i $ ��. 
                              ! Flux $ R_i $ number
    real(DP):: xyr_Sh (0:imax-1, 1:jmax, 0:kmax)
                              ! $ S_h $ (æ¸�º¦, æ¯�æ¹�). 
                              ! $ S_h $ (temperature, specific humidity)
    real(DP):: xyr_Sm (0:imax-1, 1:jmax, 0:kmax)
                              ! $ S_m $ (������). 
                              ! $ S_m $ (momentum)
    real(DP):: xyr_MixLength (0:imax-1, 1:jmax, 0:kmax)
                              ! 混����. 
                              ! Mixing length

    real(DP):: Alpha1, Alpha2
    real(DP):: Beta1, Beta2, Beta3, Beta4
    real(DP):: Gamma1, Gamma2
    real(DP):: CrtlFluxRiNum

    real(DP):: xyr_TurKinEne(0:imax-1, 1:jmax, 0:kmax)
                              ! 
                              ! Turbulent kinetic energy

    integer:: i               ! çµ�åº��¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in longitude
    integer:: j               ! ç·�º¦�¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in latitude
    integer:: k               ! ���´æ�¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in vertical direction

    ! ���� ; Executable statement
    !

    ! ������確è�
    ! Initialization check
    !
    if ( .not. vdiffusion_my_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


    ! å®��°è�ç®�
    ! Calculate constants
    !
    Gamma1 = ( 1.0_DP / 3.0_DP ) - ( 2.0_DP * MYConstA1 / MYConstB1 )
    Gamma2 =   ( MYConstB2 / MYConstB1 ) + ( 6.0_DP * MYConstA1 / MYConstB1 )
    Alpha1 = 3.0_DP  * MYConstA2 * Gamma1
    Alpha2 = 3.0_DP  * MYConstA2 * ( Gamma1 + Gamma2 )
    Beta1  = MYConstA1 * MYConstB1 * ( Gamma1 - MYConstC1 )
    Beta2  = MYConstA1 * (   MYConstB1 * ( Gamma1 - MYConstC1 ) + 6.0_DP * MYConstA1 + 3.0_DP * MYConstA2 )
    Beta3  = MYConstA2 * MYConstB1 * Gamma1
    Beta4  = MYConstA2 * (   MYConstB1 * ( Gamma1 + Gamma2 ) - 3.0_DP * MYConstA1 )
    CrtlFluxRiNum = Gamma1 / ( Gamma1 + Gamma2 )

    ! ���������� $ R_i $ �°ã�����
    ! Calculate flux $ R_i $ number
    !
    xyr_FluxRiNum = (   Beta1 + Beta4 * xyr_BulkRiNum - sqrt(   ( Beta1 + Beta4 * xyr_BulkRiNum )**2 - 4.0_DP * Beta2 * Beta3 * xyr_BulkRiNum ) ) / ( 2.0_DP * Beta2 )

    ! $ \tilde{S_h} $ �� $ \tilde{S_m} $ �����
    ! Calculate $ \tilde{S_h} $ and $ \tilde{S_m} $
    !
    xyr_Sh(:,:,kmax) = 0.0_DP
    xyr_Sm(:,:,kmax) = 0.0_DP

    do k = 0, kmax-1
      do i = 0, imax-1
        do j = 1, jmax

          if ( xyr_FluxRiNum(i,j,k) < CrtlFluxRiNum ) then 

            xyr_Sh(i,j,k) = (   Alpha1 - Alpha2 * xyr_FluxRiNum(i,j,k) ) / ( 1.0_DP - 1.0_DP * xyr_FluxRiNum(i,j,k) )

            xyr_Sm(i,j,k) = (   Beta1 - Beta2 * xyr_FluxRiNum(i,j,k) ) / ( Beta3 - Beta4 * xyr_FluxRiNum(i,j,k) ) * xyr_Sh(i,j,k)

            xyr_Sh(i,j,k) = max( xyr_Sh(i,j,k), ShMin )
            xyr_Sm(i,j,k) = max( xyr_Sm(i,j,k), SmMin )

          else

            xyr_Sh(i,j,k) = ShMin
            xyr_Sm(i,j,k) = SmMin

          end if

        end do
      end do
    end do


    ! æ··å��è·��¢ã�����
    ! Calculate mixing length
    !
    do k = 0, kmax
      xyr_MixLength(:,:,k) = FKarm * ( xyr_Height(:,:,k) - xy_SurfHeight(:,:) ) / (1.0_DP + FKarm * ( xyr_Height(:,:,k) - xy_SurfHeight(:,:) ) / MixLengthMax )
    end do

    ! �¡æ�£ä��°ã�����
    ! Calculate diffusion constants
    !
    xyr_VelDiffCoef = xyr_MixLength**2 * xyr_DVelDz * sqrt ( MYConstB1 * ( 1.0_DP - xyr_FluxRiNum ) * xyr_Sm ) * xyr_Sm

    xyr_TempDiffCoef = xyr_MixLength ** 2 * xyr_DVelDz * sqrt ( MYConstB1 * ( 1.0_DP - xyr_FluxRiNum ) * xyr_Sm ) * xyr_Sh

    do k = 0, kmax-1
      do i = 0, imax-1
        do j = 1, jmax
          xyr_VelDiffCoef(i,j,k) = max( min( xyr_VelDiffCoef(i,j,k), VelDiffCoefMax ), VelDiffCoefMin )
          xyr_TempDiffCoef(i,j,k) = max( min( xyr_TempDiffCoef(i,j,k), TempDiffCoefMax ), TempDiffCoefMin )
        end do
      end do
    end do

    xyr_QMixDiffCoef = xyr_TempDiffCoef

    xyr_VelDiffCoef (:,:,0)    = 0.0_DP
    xyr_VelDiffCoef (:,:,kmax) = 0.0_DP
    xyr_TempDiffCoef(:,:,0)    = 0.0_DP
    xyr_TempDiffCoef(:,:,kmax) = 0.0_DP
    xyr_QMixDiffCoef(:,:,0)    = 0.0_DP
    xyr_QMixDiffCoef(:,:,kmax) = 0.0_DP


    ! Calculation of turbulent kinetic energy
    ! Turbulent kinetic energy is diagnosed.
    xyr_TurKinEne = MYConstB1 * xyr_MixLength**2 * ( 1.0_DP - xyr_FluxRiNum ) * xyr_Sm * xyr_DVelDz**2 / 2.0_DP
    xyr_TurKinEne(:,:,0   ) = 0.0_DP
    xyr_TurKinEne(:,:,kmax) = 0.0_DP

    ! ���¹ã�������¼ã�¿å�ºå��
    ! History data output
    !
    call HistoryAutoPut( TimeN, 'TurKinEne', xyr_TurKinEne )


  end subroutine VDiffCoefficient
Subroutine :
xyz_U(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ u $ . �±è¥¿é¢���. Eastward wind
xyz_V(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ v $ . �������. Northward wind
xyzf_QMix(0:imax-1, 1:jmax, 1:kmax, 1:ncmax) :real(DP), intent(in)
: $ q $ . è³��闋·å��æ¯�. Mass mixing ratio
xyz_Temp(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: $ T $ . æ¸�º¦. Temperature
xyr_VirTemp(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). Virtual temperature (half level)
xyr_Press(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: $ hat{p} $ . æ°��� (���´æ�°ã������). Air pressure (half level)
xyz_Height(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: é«�åº� (�´æ�°ã������). Height (full level)
xyz_Exner(0:imax-1, 1:jmax, 1:kmax) :real(DP), intent(in)
: Exner �¢æ�� (�´æ�°ã������). Exner function (full level)
xyr_Exner(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: Exner �¢æ�� (���´æ�°ã������). Exner function (half level)
xyr_VelDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: �¡æ�£ä��°ï�������. Diffusion coefficient: velocity
xyr_TempDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: �¡æ�£ä��°ï�æ¸�º¦. Transfer coefficient: temperature
xyr_QMixDiffCoef(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(in)
: �¡æ�£ä��°ï�æ¯�æ¹�. Diffusion coefficient: specific humidity
xyr_MomFluxX(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �±è¥¿�¹å�����������������. Eastward momentum flux
xyr_MomFluxY(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �����¹å�����������������. Northward momentum flux
xyr_HeatFlux(0:imax-1, 1:jmax, 0:kmax) :real(DP), intent(out)
: �±ã����������. Heat flux
xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax) :real(DP), intent(out)
: ������������. Mass flux of compositions

���´æ�¡æ�£ã���������¹ã��è¨�ç®����¾ã��.

Vertical diffusion flux is calculated.

[Source]

  subroutine VDiffusionCalcFlux( xyz_U, xyz_V, xyzf_QMix, xyz_Temp, xyr_VirTemp, xyr_Press, xyz_Height, xyz_Exner, xyr_Exner, xyr_VelDiffCoef, xyr_TempDiffCoef, xyr_QMixDiffCoef, xyr_MomFluxX,  xyr_MomFluxY,  xyr_HeatFlux, xyrf_QMixFlux )
    !
    ! ���´æ�¡æ�£ã���������¹ã��è¨�ç®����¾ã��. 
    !
    ! Vertical diffusion flux is calculated. 
    !

    ! �¢ã�¸ã�¥ã�¼ã����� ; USE statements
    !

    ! ����å®��°è¨­å®�
    ! Physical constants settings
    !
    use constants, only: FKarm, GasRDry, CpDry
                              ! $ C_p $ [J kg-1 K-1]. 
                              ! ä¹¾ç�¥å¤§æ°�����§æ���. 
                              ! Specific heat of air at constant pressure

    ! ���»ç���
    ! Time control
    !
    use timeset, only: TimeN, TimesetClockStart, TimesetClockStop

    ! ���¹ã�������¼ã�¿å�ºå��
    ! History data output
    !
    use gtool_historyauto, only: HistoryAutoPut

    ! 宣�� ; Declaration statements
    !
    implicit none

    real(DP), intent(in):: xyz_U (0:imax-1, 1:jmax, 1:kmax)
                              ! $ u $ .   �±è¥¿é¢���. Eastward wind
    real(DP), intent(in):: xyz_V (0:imax-1, 1:jmax, 1:kmax)
                              ! $ v $ .   �������. Northward wind
    real(DP), intent(in):: xyzf_QMix(0:imax-1, 1:jmax, 1:kmax, 1:ncmax)
                              ! $ q $ .   è³��闋·å��æ¯�. Mass mixing ratio
    real(DP), intent(in):: xyz_Temp (0:imax-1, 1:jmax, 1:kmax)
                              ! $ T $ .   æ¸�º¦. Temperature
    real(DP), intent(in):: xyr_VirTemp (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). 
                              ! Virtual temperature (half level)
    real(DP), intent(in):: xyr_Press  (0:imax-1, 1:jmax, 0:kmax)
                              ! $ \hat{p} $ . æ°��� (���´æ�°ã������). 
                              ! Air pressure (half level)
    real(DP), intent(in):: xyz_Height (0:imax-1, 1:jmax, 1:kmax)
                              ! é«�åº� (�´æ�°ã������). 
                              ! Height (full level)
    real(DP), intent(in):: xyz_Exner (0:imax-1, 1:jmax, 1:kmax)
                              ! Exner �¢æ�� (�´æ�°ã������). 
                              ! Exner function (full level)
    real(DP), intent(in):: xyr_Exner (0:imax-1, 1:jmax, 0:kmax)
                              ! Exner �¢æ�� (���´æ�°ã������). 
                              ! Exner function (half level)

    real(DP), intent(in):: xyr_VelDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�������. 
                              ! Diffusion coefficient: velocity
    real(DP), intent(in):: xyr_TempDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�æ¸�º¦. 
                              ! Transfer coefficient: temperature
    real(DP), intent(in):: xyr_QMixDiffCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! �¡æ�£ä��°ï�æ¯�æ¹�. 
                              ! Diffusion coefficient: specific humidity

    real(DP), intent(out):: xyr_MomFluxX (0:imax-1, 1:jmax, 0:kmax)
                              ! �±è¥¿�¹å�����������������. 
                              ! Eastward momentum flux
    real(DP), intent(out):: xyr_MomFluxY (0:imax-1, 1:jmax, 0:kmax)
                              ! �����¹å�����������������. 
                              ! Northward momentum flux
    real(DP), intent(out):: xyr_HeatFlux (0:imax-1, 1:jmax, 0:kmax)
                              ! �±ã����������. 
                              ! Heat flux
    real(DP), intent(out):: xyrf_QMixFlux(0:imax-1, 1:jmax, 0:kmax, 1:ncmax)
                              ! ������������. 
                              ! Mass flux of compositions

    ! �業��
    ! Work variables
    !
    real(DP) :: xyr_VelTransCoef (0:imax-1, 1:jmax, 0:kmax)
                              ! 輸é��ä¿��°ï�������. 
                              ! Transfer coefficient: velocity
    real(DP) :: xyr_TempTransCoef(0:imax-1, 1:jmax, 0:kmax)
                              ! 輸é��ä¿��°ï�æ¸�º¦. 
                              ! Transfer coefficient: temperature
    real(DP) :: xyr_QMixTransCoef(0:imax-1, 1:jmax, 0:kmax)
                              ! 輸é��ä¿��°ï�è³���. 
                              ! Transfer coefficient: mass (composition)

    integer:: k               ! ���´æ�¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in vertical direction

    integer:: n               ! çµ����¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in dimension of constituents

    ! ���� ; Executable statement
    !

    ! ������確è�
    ! Initialization check
    !
    if ( .not. vdiffusion_my_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


    ! 輸é��ä¿��°ã���ç®�
    ! Calculate transfer coefficient
    !
    xyr_VelTransCoef (:,:,0)    = 0.0_DP
    xyr_VelTransCoef (:,:,kmax) = 0.0_DP
    xyr_TempTransCoef(:,:,0)    = 0.0_DP
    xyr_TempTransCoef(:,:,kmax) = 0.0_DP
    xyr_QMixTransCoef(:,:,0)    = 0.0_DP
    xyr_QMixTransCoef(:,:,kmax) = 0.0_DP

    do k = 1, kmax-1
      xyr_VelTransCoef(:,:,k) = xyr_VelDiffCoef(:,:,k) * xyr_Press(:,:,k) / ( GasRDry * xyr_VirTemp(:,:,k) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k) )

      xyr_TempTransCoef(:,:,k) = xyr_TempDiffCoef(:,:,k) * xyr_Press(:,:,k) / ( GasRDry * xyr_VirTemp(:,:,k) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k) )

      xyr_QMixTransCoef(:,:,k) = xyr_QMixDiffCoef(:,:,k) * xyr_Press(:,:,k) / ( GasRDry * xyr_VirTemp(:,:,k) ) / ( xyz_Height(:,:,k+1) - xyz_Height(:,:,k) )
    end do

    ! ���������¹ã���ç®�
    ! Calculate fluxes
    !
    xyr_MomFluxX(:,:,0)    = 0.0_DP
    xyr_MomFluxX(:,:,kmax) = 0.0_DP
    xyr_MomFluxY(:,:,0)    = 0.0_DP
    xyr_MomFluxY(:,:,kmax) = 0.0_DP
    xyr_HeatFlux(:,:,0)    = 0.0_DP
    xyr_HeatFlux(:,:,kmax) = 0.0_DP
    do n = 1, ncmax
      xyrf_QMixFlux(:,:,0,n)    = 0.0_DP
      xyrf_QMixFlux(:,:,kmax,n) = 0.0_DP
    end do

    do k = 1, kmax-1
      xyr_MomFluxX(:,:,k) = - xyr_VelTransCoef(:,:,k) * ( xyz_U(:,:,k+1) - xyz_U(:,:,k) )

      xyr_MomFluxY(:,:,k) = - xyr_VelTransCoef(:,:,k) * ( xyz_V(:,:,k+1) - xyz_V(:,:,k) )

      xyr_HeatFlux(:,:,k) = - CpDry * xyr_TempTransCoef(:,:,k) * xyr_Exner(:,:,k) * (   xyz_Temp(:,:,k+1) / xyz_Exner(:,:,k+1) - xyz_Temp(:,:,k)   / xyz_Exner(:,:,k)     )
    end do

    do n = 1, ncmax
      do k = 1, kmax-1
        xyrf_QMixFlux(:,:,k,n) = - xyr_QMixTransCoef(:,:,k) * ( xyzf_QMix(:,:,k+1,n) - xyzf_QMix(:,:,k,n)  )
      end do
    end do


  end subroutine VDiffusionCalcFlux
Subroutine :
z_U(1:kmax) :real(DP), intent(in)
: $ u $ . �±è¥¿é¢���. Eastward wind
z_V(1:kmax) :real(DP), intent(in)
: $ v $ . �������. Northward wind
zf_QMix(1:kmax, 1:ncmax) :real(DP), intent(in)
: $ q $ . è³��闋·å��æ¯�. Mass mixing ratio
z_Temp(1:kmax) :real(DP), intent(in)
: $ T $ . æ¸�º¦. Temperature
r_VirTemp(0:kmax) :real(DP), intent(in)
: $ hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). Virtual temperature (half level)
r_Press(0:kmax) :real(DP), intent(in)
: $ hat{p} $ . æ°��� (���´æ�°ã������). Air pressure (half level)
z_Height(1:kmax) :real(DP), intent(in)
: é«�åº� (�´æ�°ã������). Height (full level)
z_Exner(1:kmax) :real(DP), intent(in)
: Exner �¢æ�� (�´æ�°ã������). Exner function (full level)
r_Exner(0:kmax) :real(DP), intent(in)
: Exner �¢æ�� (���´æ�°ã������). Exner function (half level)
r_VelDiffCoef(0:kmax) :real(DP), intent(in)
: �¡æ�£ä��°ï�������. Diffusion coefficient: velocity
r_TempDiffCoef(0:kmax) :real(DP), intent(in)
: �¡æ�£ä��°ï�æ¸�º¦. Transfer coefficient: temperature
r_QMixDiffCoef(0:kmax) :real(DP), intent(in)
: �¡æ�£ä��°ï�æ¯�æ¹�. Diffusion coefficient: specific humidity
r_MomFluxX(0:kmax) :real(DP), intent(out)
: �±è¥¿�¹å�����������������. Eastward momentum flux
r_MomFluxY(0:kmax) :real(DP), intent(out)
: �����¹å�����������������. Northward momentum flux
r_HeatFlux(0:kmax) :real(DP), intent(out)
: �±ã����������. Heat flux
rf_QMixFlux(0:kmax, 1:ncmax) :real(DP), intent(out)
: ������������. Mass flux of compositions

���´æ�¡æ�£ã���������¹ã��è¨�ç®����¾ã��.

Vertical diffusion flux is calculated.

[Source]

  subroutine VDiffusionCalcFlux1D( z_U, z_V, zf_QMix, z_Temp, r_VirTemp, r_Press, z_Height, z_Exner, r_Exner, r_VelDiffCoef, r_TempDiffCoef, r_QMixDiffCoef, r_MomFluxX, r_MomFluxY, r_HeatFlux, rf_QMixFlux )
    !
    ! ���´æ�¡æ�£ã���������¹ã��è¨�ç®����¾ã��. 
    !
    ! Vertical diffusion flux is calculated. 
    !

    ! �¢ã�¸ã�¥ã�¼ã����� ; USE statements
    !

    ! ����å®��°è¨­å®�
    ! Physical constants settings
    !
    use constants, only: FKarm, GasRDry, CpDry
                              ! $ C_p $ [J kg-1 K-1]. 
                              ! ä¹¾ç�¥å¤§æ°�����§æ���. 
                              ! Specific heat of air at constant pressure

    ! ���»ç���
    ! Time control
    !
    use timeset, only: TimeN, TimesetClockStart, TimesetClockStop

    ! ���¹ã�������¼ã�¿å�ºå��
    ! History data output
    !
    use gtool_historyauto, only: HistoryAutoPut

    ! 宣�� ; Declaration statements
    !
    implicit none

    real(DP), intent(in):: z_U (1:kmax)
                              ! $ u $ .   �±è¥¿é¢���. Eastward wind
    real(DP), intent(in):: z_V (1:kmax)
                              ! $ v $ .   �������. Northward wind
    real(DP), intent(in):: zf_QMix(1:kmax, 1:ncmax)
                              ! $ q $ .   è³��闋·å��æ¯�. Mass mixing ratio
    real(DP), intent(in):: z_Temp (1:kmax)
                              ! $ T $ .   æ¸�º¦. Temperature
    real(DP), intent(in):: r_VirTemp (0:kmax)
                              ! $ \hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). 
                              ! Virtual temperature (half level)
    real(DP), intent(in):: r_Press  (0:kmax)
                              ! $ \hat{p} $ . æ°��� (���´æ�°ã������). 
                              ! Air pressure (half level)
    real(DP), intent(in):: z_Height (1:kmax)
                              ! é«�åº� (�´æ�°ã������). 
                              ! Height (full level)
    real(DP), intent(in):: z_Exner (1:kmax)
                              ! Exner �¢æ�� (�´æ�°ã������). 
                              ! Exner function (full level)
    real(DP), intent(in):: r_Exner (0:kmax)
                              ! Exner �¢æ�� (���´æ�°ã������). 
                              ! Exner function (half level)

    real(DP), intent(in):: r_VelDiffCoef (0:kmax)
                              ! �¡æ�£ä��°ï�������. 
                              ! Diffusion coefficient: velocity
    real(DP), intent(in):: r_TempDiffCoef (0:kmax)
                              ! �¡æ�£ä��°ï�æ¸�º¦. 
                              ! Transfer coefficient: temperature
    real(DP), intent(in):: r_QMixDiffCoef (0:kmax)
                              ! �¡æ�£ä��°ï�æ¯�æ¹�. 
                              ! Diffusion coefficient: specific humidity

    real(DP), intent(out):: r_MomFluxX (0:kmax)
                              ! �±è¥¿�¹å�����������������. 
                              ! Eastward momentum flux
    real(DP), intent(out):: r_MomFluxY (0:kmax)
                              ! �����¹å�����������������. 
                              ! Northward momentum flux
    real(DP), intent(out):: r_HeatFlux (0:kmax)
                              ! �±ã����������. 
                              ! Heat flux
    real(DP), intent(out):: rf_QMixFlux(0:kmax, 1:ncmax)
                              ! ������������. 
                              ! Mass flux of compositions

    ! �業��
    ! Work variables
    !
    real(DP) :: r_VelTransCoef (0:kmax)
                              ! 輸é��ä¿��°ï�������. 
                              ! Transfer coefficient: velocity
    real(DP) :: r_TempTransCoef(0:kmax)
                              ! 輸é��ä¿��°ï�æ¸�º¦. 
                              ! Transfer coefficient: temperature
    real(DP) :: r_QMixTransCoef(0:kmax)
                              ! 輸é��ä¿��°ï�è³���. 
                              ! Transfer coefficient: mass (composition)

    integer:: k               ! ���´æ�¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in vertical direction

    integer:: n               ! çµ����¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in dimension of constituents

    ! ���� ; Executable statement
    !

    ! ������確è�
    ! Initialization check
    !
    if ( .not. vdiffusion_my_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


    ! 輸é��ä¿��°ã���ç®�
    ! Calculate transfer coefficient
    !
    r_VelTransCoef (0)    = 0.0_DP
    r_VelTransCoef (kmax) = 0.0_DP
    r_TempTransCoef(0)    = 0.0_DP
    r_TempTransCoef(kmax) = 0.0_DP
    r_QMixTransCoef(0)    = 0.0_DP
    r_QMixTransCoef(kmax) = 0.0_DP

    do k = 1, kmax-1
      r_VelTransCoef(k) = r_VelDiffCoef(k) * r_Press(k) / ( GasRDry * r_VirTemp(k) ) / ( z_Height(k+1) - z_Height(k) )

      r_TempTransCoef(k) = r_TempDiffCoef(k) * r_Press(k) / ( GasRDry * r_VirTemp(k) ) / ( z_Height(k+1) - z_Height(k) )

      r_QMixTransCoef(k) = r_QMixDiffCoef(k) * r_Press(k) / ( GasRDry * r_VirTemp(k) ) / ( z_Height(k+1) - z_Height(k) )
    end do

    ! ���������¹ã���ç®�
    ! Calculate fluxes
    !
    r_MomFluxX(0)    = 0.0_DP
    r_MomFluxX(kmax) = 0.0_DP
    r_MomFluxY(0)    = 0.0_DP
    r_MomFluxY(kmax) = 0.0_DP
    r_HeatFlux(0)    = 0.0_DP
    r_HeatFlux(kmax) = 0.0_DP
    do n = 1, ncmax
      rf_QMixFlux(0,n)    = 0.0_DP
      rf_QMixFlux(kmax,n) = 0.0_DP
    end do

    do k = 1, kmax-1
      r_MomFluxX(k) = - r_VelTransCoef(k) * ( z_U(k+1) - z_U(k) )

      r_MomFluxY(k) = - r_VelTransCoef(k) * ( z_V(k+1) - z_V(k) )

      r_HeatFlux(k) = - CpDry * r_TempTransCoef(k) * r_Exner(k) * (   z_Temp(k+1) / z_Exner(k+1) - z_Temp(k)   / z_Exner(k)     )
    end do

    do n = 1, ncmax
      do k = 1, kmax-1
        rf_QMixFlux(k,n) = - r_QMixTransCoef(k) * ( zf_QMix(k+1,n) - zf_QMix(k,n)  )
      end do
    end do


  end subroutine VDiffusionCalcFlux1D
Subroutine :
z_U(1:kmax) :real(DP), intent(in)
: $ u $ . �±è¥¿é¢���. Eastward wind
z_V(1:kmax) :real(DP), intent(in)
: $ v $ . �������. Northward wind
zf_QMix(1:kmax, 1:ncmax) :real(DP), intent(in)
: $ q $ . è³��闋·å��æ¯�. Mass mixing ratio
z_Temp(1:kmax) :real(DP), intent(in)
: $ T $ . æ¸�º¦. Temperature
r_Temp(0:kmax) :real(DP), intent(in)
: $ hat{T} $ . æ¸�º¦ (���´æ�°ã������). Temperature (half level)
z_VirTemp(1:kmax) :real(DP), intent(in)
: $ T_v $ . ä»�¸©åº�. Virtual temperature
r_VirTemp(0:kmax) :real(DP), intent(in)
: $ hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). Virtual temperature (half level)
r_Press(0:kmax) :real(DP), intent(in)
: $ hat{p} $ . æ°��� (���´æ�°ã������). Air pressure (half level)
SurfHeight :real(DP), intent(in)
: $ z_s $ . �°è¡¨�¢é�åº�. Surface height.
z_Height(1:kmax) :real(DP), intent(in)
: é«�åº� (�´æ�°ã������). Height (full level)
r_Height(0:kmax) :real(DP), intent(in)
: é«�åº� (���´æ�°ã������). Height (half level)
z_Exner(1:kmax) :real(DP), intent(in)
: Exner �¢æ�� (�´æ�°ã������). Exner function (full level)
r_Exner(0:kmax) :real(DP), intent(in)
: Exner �¢æ�� (���´æ�°ã������). Exner function (half level)
z_TurKinEne(1:kmax) :real(DP), intent(in)
: Turbulent kinetic energy (m2 s-2)
SurfMomFluxX :real(DP), intent(in)
: Eastward momentum flux at surface
SurfMomFluxY :real(DP), intent(in)
: Northward momentum flux at surface
r_MomFluxX(0:kmax) :real(DP), intent(out)
: �±è¥¿�¹å�����������������. Eastward momentum flux
r_MomFluxY(0:kmax) :real(DP), intent(out)
: �����¹å�����������������. Northward momentum flux
r_HeatFlux(0:kmax) :real(DP), intent(out)
: �±ã����������. Heat flux
rf_QMixFlux(0:kmax, 1:ncmax) :real(DP), intent(out)
: ������������. Mass flux of compositions
r_VelDiffCoef(0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�������. Diffusion coefficient: velocity
r_TempDiffCoef(0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�æ¸�º¦. Diffusion coefficient: temperature
r_QMixDiffCoef(0:kmax) :real(DP), intent(out)
: �¡æ�£ä��°ï�æ¯�æ¹�. Diffusion coefficient: specific humidity
z_DTurKinEneDt(1:kmax) :real(DP), intent(out)
: Tendency of turbulent kinetic energy

���´æ�¡æ�£ã���������¹ã��è¨�ç®����¾ã��.

Vertical diffusion flux is calculated by use of MY2.5 model.

[Source]

  subroutine VDiffusionMY251D( z_U, z_V, zf_QMix, z_Temp, r_Temp, z_VirTemp, r_VirTemp, r_Press, SurfHeight, z_Height, r_Height, z_Exner, r_Exner, z_TurKinEne, SurfMomFluxX, SurfMomFluxY, r_MomFluxX, r_MomFluxY, r_HeatFlux, rf_QMixFlux, r_VelDiffCoef, r_TempDiffCoef, r_QMixDiffCoef, z_DTurKinEneDt )
    !
    ! ���´æ�¡æ�£ã���������¹ã��è¨�ç®����¾ã��. 
    !
    ! Vertical diffusion flux is calculated by use of MY2.5 model.
    !

    ! �¢ã�¸ã�¥ã�¼ã����� ; USE statements
    !

    ! ����å®��°è¨­å®�
    ! Physical constants settings
    !
    use constants, only: FKarm, Grav, GasRDry, CpDry
                              ! $ C_p $ [J kg-1 K-1]. 
                              ! ä¹¾ç�¥å¤§æ°�����§æ���. 
                              ! Specific heat of air at constant pressure

    ! ���»ç���
    ! Time control
    !
    use timeset, only: DelTime, TimeN, TimesetClockStart, TimesetClockStop

    ! ���¹ã�������¼ã�¿å�ºå��
    ! History data output
    !
    use gtool_historyauto, only: HistoryAutoPut

    ! �°è§£æ³�����������ç©��������������¼ã����
    ! Routines for time integration with implicit scheme
    !
    use phy_implicit_utils, only : PhyImplLUDecomp3, PhyImplLUSolve3

    ! 宣�� ; Declaration statements
    !
    implicit none

    real(DP), intent(in):: z_U (1:kmax)
                              ! $ u $ .   �±è¥¿é¢���. Eastward wind
    real(DP), intent(in):: z_V (1:kmax)
                              ! $ v $ .   �������. Northward wind
    real(DP), intent(in):: zf_QMix(1:kmax, 1:ncmax)
                              ! $ q $ .   è³��闋·å��æ¯�. Mass mixing ratio
    real(DP), intent(in):: z_Temp (1:kmax)
                              ! $ T $ .   æ¸�º¦. Temperature
    real(DP), intent(in):: r_Temp (0:kmax)
                              ! $ \hat{T} $ . æ¸�º¦ (���´æ�°ã������). 
                              ! Temperature (half level)
    real(DP), intent(in):: z_VirTemp (1:kmax)
                              ! $ T_v $ .   ä»�¸©åº�. Virtual temperature
    real(DP), intent(in):: r_VirTemp (0:kmax)
                              ! $ \hat{T}_v $ . ä»�¸©åº� (���´æ�°ã������). 
                              ! Virtual temperature (half level)
    real(DP), intent(in):: r_Press  (0:kmax)
                              ! $ \hat{p} $ . æ°��� (���´æ�°ã������). 
                              ! Air pressure (half level)
    real(DP), intent(in):: SurfHeight
                              ! $ z_s $ . �°è¡¨�¢é�åº�. 
                              ! Surface height. 
    real(DP), intent(in):: z_Height (1:kmax)
                              ! é«�åº� (�´æ�°ã������). 
                              ! Height (full level)
    real(DP), intent(in):: r_Height (0:kmax)
                              ! é«�åº� (���´æ�°ã������). 
                              ! Height (half level)
    real(DP), intent(in):: z_Exner (1:kmax)
                              ! Exner �¢æ�� (�´æ�°ã������). 
                              ! Exner function (full level)
    real(DP), intent(in):: r_Exner (0:kmax)
                              ! Exner �¢æ�� (���´æ�°ã������). 
                              ! Exner function (half level)

    real(DP), intent(in):: z_TurKinEne(1:kmax)
                              ! 
                              ! Turbulent kinetic energy (m2 s-2)
    real(DP), intent(in):: SurfMomFluxX
                              ! 
                              ! Eastward momentum flux at surface
    real(DP), intent(in):: SurfMomFluxY
                              ! 
                              ! Northward momentum flux at surface

    real(DP), intent(out):: r_MomFluxX (0:kmax)
                              ! �±è¥¿�¹å�����������������. 
                              ! Eastward momentum flux
    real(DP), intent(out):: r_MomFluxY (0:kmax)
                              ! �����¹å�����������������. 
                              ! Northward momentum flux
    real(DP), intent(out):: r_HeatFlux (0:kmax)
                              ! �±ã����������. 
                              ! Heat flux
    real(DP), intent(out):: rf_QMixFlux(0:kmax, 1:ncmax)
                              ! ������������. 
                              ! Mass flux of compositions
    real(DP), intent(out):: r_VelDiffCoef (0:kmax)
                              ! �¡æ�£ä��°ï�������. 
                              ! Diffusion coefficient: velocity
    real(DP), intent(out):: r_TempDiffCoef(0:kmax)
                              ! �¡æ�£ä��°ï�æ¸�º¦. 
                              ! Diffusion coefficient: temperature
    real(DP), intent(out):: r_QMixDiffCoef(0:kmax)
                              ! �¡æ�£ä��°ï�æ¯�æ¹�. 
                              ! Diffusion coefficient: specific humidity
    real(DP), intent(out):: z_DTurKinEneDt (1:kmax)
                              !
                              ! Tendency of turbulent kinetic energy

    ! �業��
    ! Work variables
    !

    real(DP) :: z_MixLength(1:kmax)
                              ! 混����. 
                              ! Mixing length
    real(DP) :: z_DVelDzSq(1:kmax)
                              !
                              ! Vertical shear squared (s-2)
    real(DP) :: z_StatStab(1:kmax)
                              !
                              ! Static stability (s-2)
    real(DP) :: GhMin
                              !
                              ! Minimum of G_h
    real(DP) :: GhMax
                              !
                              ! Maximum of G_h
    real(DP) :: z_Gm(1:kmax)
                              !
                              ! G_m
    real(DP) :: z_Gh(1:kmax)
                              !
                              ! G_h
    real(DP) :: z_Sm(1:kmax)
                              !
                              ! S_M
    real(DP) :: z_Sh(1:kmax)
                              !
                              ! S_h

    real(DP), parameter :: Stke = 0.2_DP
                              !
                              ! S_{TKE} = 0.2

    real(DP) :: z_VelDiffCoef (1:kmax)
                              ! �¡æ�£ä��°ï�������. 
                              ! Diffusion coefficient: velocity
    real(DP) :: z_TempDiffCoef (1:kmax)
                              ! �¡æ�£ä��°ï�æ¸�º¦. 
                              ! Transfer coefficient: temperature

    real(DP) :: r_TurKinEneDiffCoef (0:kmax)
                              ! 
                              ! Diffusion coefficient: turbulent kinetic energy
    real(DP) :: z_TurKinEneDiffCoef (1:kmax)
                              ! 
                              ! Diffusion coefficient: turbulent kinetic energy
    real(DP) :: r_TurKinEneTransCoef(0:kmax)
                              ! 
                              ! Transfer coefficient: turbulent kinetic energy

    real(DP) :: r_TurKinEneFlux(0:kmax)
                              ! 
                              ! Turbulent energy flux

    real(DP) :: z_CShe1(1:kmax)
    real(DP) :: z_CShe2(1:kmax)
    real(DP) :: z_CBuo1(1:kmax)
    real(DP) :: z_CBuo2(1:kmax)
    real(DP) :: z_CDis1(1:kmax)
    real(DP) :: z_CDis2(1:kmax)
    real(DP) :: z_TurKinEneProShear(1:kmax)
    real(DP) :: z_TurKinEneProBuoya(1:kmax)

    real(DP) :: FricVelSq
    real(DP) :: TurKinEneAtLB

    real(DP) :: za_TurKinEneMtx(1:kmax, -1:1)
                              ! 
                              ! Implicit matrix for turbulent kinetic energy
    real(DP) :: z_TurKinEneVec(1:kmax)
                              ! 
                              ! Implicit vector for turbulent kinetic energy

    real(DP) :: aaza_TurKinEneLUMtx  (1:1, 1:1, 1:kmax, -1:1)
                              ! LU ���.
                              ! LU matrix
    real(DP) :: aaz_DelTurKinEneLUVec(1:1, 1:1, 1:kmax)
                              ! 
                              ! Tendency of turbulent kinetic energy

    real(DP) :: z_TurKinEneDiss(1:kmax)
                              !
                              ! Dissipation rate of turbulent kinetic energy (m2 s-3)

    real(DP) :: z_TurKinEneNonZero(1:kmax)
                              ! 
                              ! Turbulent kinetic energy with offset (m2 s-2)

    real(DP), parameter :: TurKinEneOffset  = ( 1.0e-3_DP )**2 / 2.0_DP

    logical :: FlagReCalc
                              !
                              ! Flag for recalculation
    logical :: a_FlagReCalcLocal (1)
    logical :: a_FlagReCalcGlobal(1)
    integer :: iloop
    integer :: nloop

    integer:: k               ! ���´æ�¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in vertical direction

    integer:: n               ! çµ����¹å�������� DO ���¼ã�����業å���
                              ! Work variables for DO loop in dimension of constituents

    ! ���� ; Executable statement
    !

    ! ������確è�
    ! Initialization check
    !
    if ( .not. vdiffusion_my_inited ) then
      call MessageNotify( 'E', module_name, 'This module has not been initialized.' )
    end if


!!$    ! �����������
!!$    ! Start measurement of computation time
!!$    !
!!$    call TimesetClockStart( module_name )


    ! Calculate turbulent kinetic energy with offset
    !
    z_TurKinEneNonZero = z_TurKinEne + TurKinEneOffset

    !
    ! Calculation of vertical shear squared
    do k = 1, kmax
      if ( k == 1 ) then
        z_DVelDzSq(k) = (   ( z_U(k+1) - z_U(k  ) )**2 + ( z_V(k+1) - z_V(k  ) )**2 ) / ( z_Height(k+1) - z_Height(k  ) )**2
      else if ( k == kmax ) then
        z_DVelDzSq(k) = (   ( z_U(k  ) - z_U(k-1) )**2 + ( z_V(k  ) - z_V(k-1) )**2 ) / ( z_Height(k  ) - z_Height(k-1) )**2
      else
        z_DVelDzSq(k) = (   ( z_U(k+1) - z_U(k-1) )**2 + ( z_V(k+1) - z_V(k-1) )**2 ) / ( z_Height(k+1) - z_Height(k-1) )**2
      end if
    end do
    ! Calculation of static stability
    do k = 1, kmax
      if ( k == 1 ) then
        z_StatStab(k) = Grav / ( z_VirTemp(k) / z_Exner(k) ) * (   z_VirTemp(k+1) / z_Exner(k+1) - z_VirTemp(k  ) / z_Exner(k  ) ) / ( z_Height(k+1) - z_Height(k  ) )
      else if ( k == kmax ) then
        z_StatStab(k) = Grav / ( z_VirTemp(k) / z_Exner(k) ) * (   z_VirTemp(k  ) / z_Exner(k  ) - z_VirTemp(k-1) / z_Exner(k-1) ) / ( z_Height(k  ) - z_Height(k-1) )
      else
        z_StatStab(k) = Grav / ( z_VirTemp(k) / z_Exner(k) ) * (   z_VirTemp(k+1) / z_Exner(k+1) - z_VirTemp(k-1) / z_Exner(k-1) ) / ( z_Height(k+1) - z_Height(k-1) )
      end if
    end do

    ! æ··å��è·��¢ã�����
    ! Calculate mixing length
    !
    do k = 1, kmax
      z_MixLength(k) = FKarm * ( z_Height(k) - SurfHeight ) / (1.0_DP + FKarm * ( z_Height(k) - SurfHeight ) / MixLengthMax )
    end do
    !   Limit mixing length (Galperin et al., 1988) and avoid zero
    z_MixLength = min( z_MixLength, 0.53_DP * sqrt( 2.0_DP * z_TurKinEneNonZero / max( z_StatStab, 1.0e-10_DP ) ) ) + 1.0e-10_DP

    z_Gh = - z_MixLength**2 / ( 2.0_DP * z_TurKinEneNonZero ) * z_StatStab
    ! Actually, xyz_Gm is not used below.
    z_Gm =   z_MixLength**2 / ( 2.0_DP * z_TurKinEneNonZero ) * z_DVelDzSq


    ! Limit Gh (Galperin et al., 1988)
    GhMin = - 0.53_DP**2
    GhMax = 1.0_DP / ( MYConstA2 * (  12.0_DP * MYConstA1 + MYConstB1 + 3.0_DP * MYConstB2 ) )
    z_Gh = max( GhMin, min( z_Gh, GhMax ) )


    z_Sh = MYConstA2 * ( 1.0_DP - 6.0_DP * MYConstA1 / MYConstB1 ) / (   1.0_DP - 3.0_DP * MYConstA2 * ( 6.0_DP * MYConstA1 + MYConstB2 ) * z_Gh )

    z_Sm = ( MYConstA1 * (   1.0_DP - 3.0_DP * MYConstC1 - 6.0_DP * MYConstA1 / MYConstB1 ) + 9.0_DP * MYConstA1 * ( 2.0_DP * MYConstA1 + MYConstA2 ) * z_Gh * z_Sh ) / (   1.0_DP - 9.0_DP * MYConstA1 * MYConstA2 * z_Gh )



    ! �¡æ�£ä��°ã���ç®�
    ! Calculation of diffusion coefficient
    !
    z_VelDiffCoef  = z_MixLength * sqrt( 2.0_DP * z_TurKinEneNonZero ) * z_Sm
    z_TempDiffCoef = z_MixLength * sqrt( 2.0_DP * z_TurKinEneNonZero ) * z_Sh
    !
    do k = 0, kmax
      if ( ( k == 0 ) .or. ( k == kmax ) ) then
        r_VelDiffCoef (k) = 0.0_DP
        r_TempDiffCoef(k) = 0.0_DP
      else
        r_VelDiffCoef (k) = ( z_VelDiffCoef (k) + z_VelDiffCoef (k+1) ) / 2.0_DP
        r_TempDiffCoef(k) = ( z_TempDiffCoef(k) + z_TempDiffCoef(k+1) ) / 2.0_DP
      end if
    end do
    !
    do k = 1, kmax-1
      r_VelDiffCoef(k) = max( min( r_VelDiffCoef(k), VelDiffCoefMax ), VelDiffCoefMin )
      r_TempDiffCoef(k) = max( min( r_TempDiffCoef(k), TempDiffCoefMax ), TempDiffCoefMin )
    end do
    !
    r_QMixDiffCoef      = r_TempDiffCoef


    ! 輸é��ä¿��°ã�����������¹ã���ç®�
    ! Calculate transfer coefficient and flux
    !
    call VDiffusionCalcFlux1D( z_U, z_V, zf_QMix, z_Temp, r_VirTemp, r_Press, z_Height, z_Exner, r_Exner, r_VelDiffCoef, r_TempDiffCoef, r_QMixDiffCoef, r_MomFluxX, r_MomFluxY, r_HeatFlux, rf_QMixFlux )


    ! Calculate tendency of turbulent kinetic energy

    !   Set diffusion coefficient for turbulent kinetic energy
    z_TurKinEneDiffCoef = z_MixLength * sqrt( 2.0_DP * z_TurKinEneNonZero ) * Stke
    !
    do k = 0, kmax
      if ( k == 0 ) then
        r_TurKinEneDiffCoef(k) = z_TurKinEneDiffCoef(1)
      else if ( k == kmax ) then
        r_TurKinEneDiffCoef(k) = z_TurKinEneDiffCoef(kmax)
      else
        r_TurKinEneDiffCoef(k) = ( z_TurKinEneDiffCoef(k) + z_TurKinEneDiffCoef(k+1) ) / 2.0_DP
      end if
    end do

    !   Calculate turbulent kinetic energy at lower boundary
    !
    FricVelSq = sqrt( SurfMomFluxX**2 + SurfMomFluxY**2 ) / ( r_Press(0) / ( GasRDry * r_VirTemp(0) ) )
    TurKinEneAtLB = MYConstB1**(2.0_DP/3.0_DP) / 2.0_DP * FricVelSq
    TurKinEneAtLB = TurKinEneAtLB + TurKinEneOffset

    !   Calculate transfer coefficient and flux of turbulent kinetic energy
    !
    !    When transfer coefficient at lower boundary is calculated, 
    !    diffusion coefficient at mid-point of 1st layer is used. 
    !    In addition, transfer coefficient at upper boundary is assumed 
    !    to be zero.
    k = 0
    r_TurKinEneTransCoef(k) = z_TurKinEneDiffCoef(1) * r_Press(k) / ( GasRDry * r_VirTemp(k) ) / ( z_Height(1) - SurfHeight )
    do k = 1, kmax-1
      r_TurKinEneTransCoef(k) = r_TurKinEneDiffCoef(k) * r_Press(k) / ( GasRDry * r_VirTemp(k) ) / ( z_Height(k+1) - z_Height(k) )
    end do
    k = kmax
    r_TurKinEneTransCoef(k) = 0.0_DP
    !
    do k = 1, kmax-1
      r_TurKinEneFlux(k) = - r_TurKinEneTransCoef(k) * ( z_TurKinEneNonZero(k+1) - z_TurKinEneNonZero(k) )
    end do
    k = 0
    r_TurKinEneFlux(k) = - r_TurKinEneTransCoef(k) * ( z_TurKinEneNonZero(k+1) - TurKinEneAtLB )
    k = kmax
    r_TurKinEneFlux(k) = 0.0_DP


    z_CShe1 =            sqrt( 2.0_DP ) * z_MixLength * z_DVelDzSq * z_Sm * sqrt( z_TurKinEneNonZero )
    z_CShe2 = 0.0_DP
    z_CBuo1 = -          sqrt( 2.0_DP ) * z_MixLength * z_StatStab * z_Sh * sqrt( z_TurKinEneNonZero )
    z_CBuo2 = 0.0_DP
    z_CDis1 =          2.0_DP**1.5_DP / ( MYConstB1 * z_MixLength ) * z_TurKinEneNonZero**1.5_DP
    z_CDis2 = 1.5_DP * 2.0_DP**1.5_DP / ( MYConstB1 * z_MixLength ) * z_TurKinEneNonZero**0.5_DP


    nloop = kmax
    loop_solve : do iloop = 1, nloop

      !
      ! Construct implicit matrix from transfer coefficient of vertical 
      ! diffusion scheme (turbulent kinetic energy)
      !
      k = 1
      za_TurKinEneMtx(k,-1) = 0.0_DP
      za_TurKinEneMtx(k, 0) = - ( r_Press(k) - r_Press(k-1) ) / Grav / ( 2.0_DP * DelTime ) + r_TurKinEneTransCoef(k-1) + r_TurKinEneTransCoef(k  ) + ( r_Press(k) - r_Press(k-1) ) / Grav * ( z_CShe2(k) + z_CBuo2(k) - z_CDis2(k) )
      za_TurKinEneMtx(k, 1) = - r_TurKinEneTransCoef(k  )
      !
      do k = 2, kmax-1
        za_TurKinEneMtx(k,-1) = - r_TurKinEneTransCoef(k-1)
        za_TurKinEneMtx(k, 0) = - ( r_Press(k) - r_Press(k-1) ) / Grav / ( 2.0_DP * DelTime ) + r_TurKinEneTransCoef(k-1) + r_TurKinEneTransCoef(k  ) + ( r_Press(k) - r_Press(k-1) ) / Grav * ( z_CShe2(k) + z_CBuo2(k) - z_CDis2(k) )
        za_TurKinEneMtx(k, 1) = - r_TurKinEneTransCoef(k  )
      end do
      !
      k = kmax
      za_TurKinEneMtx(k,-1) = - r_TurKinEneTransCoef(k-1)
      za_TurKinEneMtx(k, 0) = - ( r_Press(k) - r_Press(k-1) ) / Grav / ( 2.0_DP * DelTime ) + r_TurKinEneTransCoef(k-1) + r_TurKinEneTransCoef(k  ) + ( r_Press(k) - r_Press(k-1) ) / Grav * ( z_CShe2(k) + z_CBuo2(k) - z_CDis2(k) )
      za_TurKinEneMtx(k, 1) = 0.0_DP

      do k = 1, kmax
        z_TurKinEneVec(k) = - ( r_TurKinEneFlux(k) - r_TurKinEneFlux(k-1) ) - ( r_Press(k) - r_Press(k-1) ) / Grav * ( z_CShe1(k) + z_CBuo1(k) - z_CDis1(k) )
      end do


      !
      ! Solve simultaneous linear equations by use of LU decomposition technique
      !
      aaza_TurKinEneLUMtx(1,1,:,:) = za_TurKinEneMtx
      !
      call PhyImplLUDecomp3( aaza_TurKinEneLUMtx, 1 * 1, kmax )

      aaz_DelTurKinEneLUVec(1,1,:) = z_TurKinEneVec
      !
      call PhyImplLUSolve3( aaz_DelTurKinEneLUVec, aaza_TurKinEneLUMtx, 1, 1 * 1 , kmax )

      z_DTurKinEneDt = aaz_DelTurKinEneLUVec(1,1,:) / ( 2.0_DP * DelTime )


      ! Calculation of dissipation rate of turbulent kinetic energy
      !
      ! Calculate production rate of turbulent kinetic energy
      ! by shear and buoyancy
      z_TurKinEneProShear = z_CShe1 + z_CShe2 * z_DTurKinEneDt * 2.0_DP * DelTime
      z_TurKinEneProBuoya = z_CBuo1 + z_CBuo2 * z_DTurKinEneDt * 2.0_DP * DelTime
      z_TurKinEneDiss     = z_CDis1 + z_CDis2 * z_DTurKinEneDt * 2.0_DP * DelTime

      ! Check of turbulent kinetic energy dissipation rate
      ! If it is negative, tendency is recalculated without dissipation.
      !
      FlagReCalc = .false.
      do k = 1, kmax
        if ( z_TurKinEneDiss(k) < 0.0_DP ) then
          z_CDis1(k) = 0.0_DP
          z_CDis2(k) = 0.0_DP
          FlagReCalc = .true.
        end if
      end do

      ! Check convergence
      a_FlagReCalcLocal = FlagReCalc
!!$      call MPIWrapperChkTrue(   &
!!$        & 1, a_FlagReCalcLocal, & ! (in)
!!$        & a_FlagReCalcGlobal    & ! (out)
!!$        & )
      a_FlagReCalcGlobal = a_FlagReCalcLocal
      if ( .not. a_FlagReCalcGlobal(1) ) exit loop_solve

    end do loop_solve



!!$    ! ��������������
!!$    ! Pause measurement of computation time
!!$    !
!!$    call TimesetClockStop( module_name )

  end subroutine VDiffusionMY251D
VelDiffCoefMax
Variable :
VelDiffCoefMax :real(DP), save
: $ Dvect{u} $ �¡æ�£ä��°æ��大å��. Maximum diffusion coefficient of $ Dvect{u} $
VelDiffCoefMin
Variable :
VelDiffCoefMin :real(DP), save
: $ Dvect{u} $ �¡æ�£ä��°æ��å°��. Minimum diffusion coefficient of $ Dvect{u} $
module_name
Constant :
module_name = ‘vdiffusion_my :character(*), parameter
: �¢ã�¸ã�¥ã�¼ã������ç§�. Module name
vdiffusion_my_inited
Variable :
vdiffusion_my_inited = .false. :logical, save
: ����設������. Initialization flag
version
Constant :
version = ’$Name: $’ // ’$Id: vdiffusion_my.f90,v 1.5 2015/01/29 12:09:17 yot Exp $’ :character(*), parameter
: �¢ã�¸ã�¥ã�¼ã�������¼ã�¸ã�§ã�� Module version