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!MNH_LIC Copyright 1994-2020 CNRS, Meteo-France and Universite Paul Sabatier
!MNH_LIC This is part of the Meso-NH software governed by the CeCILL-C licence
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!MNH_LIC version 1. See LICENSE, CeCILL-C_V1-en.txt and CeCILL-C_V1-fr.txt
!MNH_LIC for details. version 1.
!-----------------------------------------------------------------
! ######################
MODULE MODI_GRADIENT_U
! ######################
!
INTERFACE
!
!
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FUNCTION GX_U_M(PA,PDXX,PDZZ,PDZX) RESULT(PGX_U_M)
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PA ! variable at the U point
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDXX ! metric coefficient dxx
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDZZ ! metric coefficient dzz
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDZX ! metric coefficient dzx
!
REAL, DIMENSION(SIZE(PA,1),SIZE(PA,2),SIZE(PA,3)) :: PGX_U_M ! result mass point
!
END FUNCTION GX_U_M
!
!
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FUNCTION GY_U_UV(PA,PDYY,PDZZ,PDZY) RESULT(PGY_U_UV)
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PA ! variable at the U point
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDYY ! metric coefficient dyy
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDZZ ! metric coefficient dzz
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDZY ! metric coefficient dzy
!
REAL, DIMENSION(SIZE(PA,1),SIZE(PA,2),SIZE(PA,3)) :: PGY_U_UV ! result UV point
!
END FUNCTION GY_U_UV
!
!
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FUNCTION GZ_U_UW(PA,PDZZ) RESULT(PGZ_U_UW)
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PA ! variable at the U point
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDZZ ! metric coefficient dzz
!
REAL, DIMENSION(SIZE(PA,1),SIZE(PA,2),SIZE(PA,3)) :: PGZ_U_UW ! result UW point
!
END FUNCTION GZ_U_UW
!
END INTERFACE
!
END MODULE MODI_GRADIENT_U
!
!
!
!
! #######################################################
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FUNCTION GX_U_M(PA,PDXX,PDZZ,PDZX) RESULT(PGX_U_M)
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! #######################################################
!
!!**** *GX_U_M* - Cartesian Gradient operator:
!! computes the gradient in the cartesian X
!! direction for a variable placed at the
!! U point and the result is placed at
!! the mass point.
!! PURPOSE
!! -------
! The purpose of this function is to compute the discrete gradient
! along the X cartesian direction for a field PA placed at the
! U point. The result is placed at the mass point.
!
!
! ( ______________z )
! ( (___________x ) )
! 1 ( (d*zx dzm(PA) ) )
! PGX_U_M = ---- (dxf(PA) - (------------)) )
! ___x ( ( ) )
! d*xx ( ( d*zz ) )
!
!
!
!!** METHOD
!! ------
!! The Chain rule of differencing is applied to variables expressed
!! in the Gal-Chen & Somerville coordinates to obtain the gradient in
!! the cartesian system
!!
!! EXTERNAL
!! --------
!! MXF,MZF : Shuman functions (mean operators)
!! DXF,DZF : Shuman functions (finite difference operators)
!!
!! IMPLICIT ARGUMENTS
!! ------------------
!! NONE
!!
!! REFERENCE
!! ---------
!! Book2 of documentation of Meso-NH (GRAD_CAR operators)
!! A Turbulence scheme for the Meso-NH model (Chapter 6)
!!
!! AUTHOR
!! ------
!! Joan Cuxart *INM and Meteo-France*
!!
!! MODIFICATIONS
!! -------------
!! Original 19/07/94
!! 18/10/00 (V.Masson) add LFLAT switch
!-------------------------------------------------------------------------
!
!* 0. DECLARATIONS
!
!
USE MODI_SHUMAN
USE MODD_CONF
!
IMPLICIT NONE
!
!
!* 0.1 declarations of arguments and result
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PA ! variable at the U point
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDXX ! metric coefficient dxx
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDZZ ! metric coefficient dzz
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDZX ! metric coefficient dzx
!
REAL, DIMENSION(SIZE(PA,1),SIZE(PA,2),SIZE(PA,3)) :: PGX_U_M ! result mass point
!
!
!* 0.2 declaration of local variables
!
! NONE
!
!----------------------------------------------------------------------------
!
!* 1. DEFINITION of GX_U_M
! --------------------
!
IF (.NOT. LFLAT) THEN
PGX_U_M(:,:,:)= ( DXF(PA) - &
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MZF(MXF(PDZX*DZM(PA)) / PDZZ ) &
) / MXF(PDXX)
ELSE
PGX_U_M(:,:,:)= DXF(PA) / MXF(PDXX)
END IF
!
!----------------------------------------------------------------------------
!
END FUNCTION GX_U_M
!
!
! #########################################################
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FUNCTION GY_U_UV(PA,PDYY,PDZZ,PDZY) RESULT(PGY_U_UV)
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! #########################################################
!
!!**** *GY_U_UV* - Cartesian Gradient operator:
!! computes the gradient in the cartesian Y
!! direction for a variable placed at the
!! U point and the result is placed at
!! the UV vorticity point.
!! PURPOSE
!! -------
! The purpose of this function is to compute the discrete gradient
! along the Y cartesian direction for a field PA placed at the
! U point. The result is placed at the UV vorticity point.
!
!
!
! ( _________________z )
! ( (___x _________y ) )
! 1 ( (d*zy (dzm(PA))) ) )
! PGY_U_UV= ---- (dym(PA) - ( (------ ) ) )
! ___x ( ( ( ___x ) ) )
! d*yy ( ( ( d*zz ) ) )
!
!
!
!!** METHOD
!! ------
!! The Chain rule of differencing is applied to variables expressed
!! in the Gal-Chen & Somerville coordinates to obtain the gradient in
!! the cartesian system
!!
!! EXTERNAL
!! --------
!! MXM,MYM,MZF : Shuman functions (mean operators)
!! DYM,DZM : Shuman functions (finite difference operators)
!!
!! IMPLICIT ARGUMENTS
!! ------------------
!! NONE
!!
!! REFERENCE
!! ---------
!! Book2 of documentation of Meso-NH (GRAD_CAR operators)
!! A Turbulence scheme for the Meso-NH model (Chapter 6)
!!
!! AUTHOR
!! ------
!! Joan Cuxart *INM and Meteo-France*
!!
!! MODIFICATIONS
!! -------------
!! Original 20/07/94
!! 18/10/00 (V.Masson) add LFLAT switch
!-------------------------------------------------------------------------
!
!* 0. DECLARATIONS
!
!
USE MODI_SHUMAN
USE MODD_CONF
!
IMPLICIT NONE
!
!
!* 0.1 declarations of arguments and result
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PA ! variable at the U point
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDYY ! metric coefficient dyy
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDZZ ! metric coefficient dzz
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDZY ! metric coefficient dzy
!
REAL, DIMENSION(SIZE(PA,1),SIZE(PA,2),SIZE(PA,3)) :: PGY_U_UV ! result UV point
!
!
!* 0.2 declaration of local variables
!
! NONE
!
!----------------------------------------------------------------------------
!
!* 1. DEFINITION of GY_U_UV
! ---------------------
!
IF (.NOT. LFLAT) THEN
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PGY_U_UV(:,:,:)= (DYM(PA)- MZF( MYM( DZM(PA)/&
MXM(PDZZ) ) *MXM(PDZY) ) ) / MXM(PDYY)
ELSE
PGY_U_UV(:,:,:)= DYM(PA) / MXM(PDYY)
END IF
!
!----------------------------------------------------------------------------
!
END FUNCTION GY_U_UV
!
!
! #######################################################
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FUNCTION GZ_U_UW(PA,PDZZ) RESULT(PGZ_U_UW)
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! #######################################################
!
!!**** *GZ_U_UW - Cartesian Gradient operator:
!! computes the gradient in the cartesian Z
!! direction for a variable placed at the
!! U point and the result is placed at
!! the UW vorticity point.
!! PURPOSE
!! -------
! The purpose of this function is to compute the discrete gradient
! along the Z cartesian direction for a field PA placed at the
! U point. The result is placed at the UW vorticity point.
!
! dzm(PA)
! PGZ_U_UW = ------
! ____x
! d*zz
!
!!** METHOD
!! ------
!! The Chain rule of differencing is applied to variables expressed
!! in the Gal-Chen & Somerville coordinates to obtain the gradient in
!! the cartesian system
!!
!! EXTERNAL
!! --------
!! MXM : Shuman functions (mean operators)
!! DZM : Shuman functions (finite difference operators)
!!
!! IMPLICIT ARGUMENTS
!! ------------------
!! NONE
!!
!! REFERENCE
!! ---------
!! Book2 of documentation of Meso-NH (GRAD_CAR operators)
!! A Turbulence scheme for the Meso-NH model (Chapter 6)
!!
!! AUTHOR
!! ------
!! Joan Cuxart *INM and Meteo-France*
!!
!! MODIFICATIONS
!! -------------
!! Original 20/07/94
!-------------------------------------------------------------------------
!
!* 0. DECLARATIONS
!
!
USE MODI_SHUMAN
!
IMPLICIT NONE
!
!
!* 0.1 declarations of arguments and result
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PA ! variable at the U point
REAL, DIMENSION(:,:,:), INTENT(IN) :: PDZZ ! metric coefficient dzz
!
REAL, DIMENSION(SIZE(PA,1),SIZE(PA,2),SIZE(PA,3)) :: PGZ_U_UW ! result UW point
!
!
!* 0.2 declaration of local variables
!
! NONE
!
!----------------------------------------------------------------------------
!
!* 1. DEFINITION of GZ_U_UW
! ---------------------
!
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PGZ_U_UW(:,:,:)= DZM(PA) / MXM(PDZZ)
!
!----------------------------------------------------------------------------
!
END FUNCTION GZ_U_UW