!-------------------------------------- LICENCE BEGIN ------------------------------------
!Environment Canada - Atmospheric Science and Technology License/Disclaimer,
! version 3; Last Modified: May 7, 2008.
!This is free but copyrighted software; you can use/redistribute/modify it under the terms
!of the Environment Canada - Atmospheric Science and Technology License/Disclaimer
!version 3 or (at your option) any later version that should be found at:
!http://collaboration.cmc.ec.gc.ca/science/rpn.comm/license.html
!
!This software is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY;
!without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
!See the above mentioned License/Disclaimer for more details.
!You should have received a copy of the License/Disclaimer along with this software;
!if not, you can write to: EC-RPN COMM Group, 2121 TransCanada, suite 500, Dorval (Quebec),
!CANADA, H9P 1J3; or send e-mail to service.rpn@ec.gc.ca
!-------------------------------------- LICENCE END --------------------------------------
! ##################
MODULE MODE_SNOW3L 5,9
! ##################
!
!!**** *MODE_SNOW * - contains explicit snow (ISBA-ES) characteristics functions
!! for total liquid water holding capacity of a snow layer (m)
!! and the thermal heat capacity of a layer (J K-1 m-3)
!!
!! PURPOSE
!! -------
!
!!** METHOD
!! ------
!! direct calculation
!!
!! EXTERNAL
!! --------
!!
!! IMPLICIT ARGUMENTS
!! ------------------
!!
!! REFERENCE
!! ---------
!! Boone and Etchevers, J. HydroMeteor., 2001
!!
!!
!! AUTHOR
!! ------
!! A. Boone * Meteo France *
!!
!! MODIFICATIONS
!! -------------
!! Original 01/08/02
!! V. Masson 01/2004 add snow grid computations
!-----------------------------------------------------------------------------
!
!* 0. DECLARATIONS
!
!
INTERFACE SNOW3LSCAP
MODULE PROCEDURE SNOW3LSCAP_3D
MODULE PROCEDURE SNOW3LSCAP_2D
MODULE PROCEDURE SNOW3LSCAP_1D
END INTERFACE
INTERFACE SNOW3LHOLD
MODULE PROCEDURE SNOW3LHOLD_3D
MODULE PROCEDURE SNOW3LHOLD_2D
MODULE PROCEDURE SNOW3LHOLD_1D
END INTERFACE
INTERFACE SNOW3LWLIQMAX
MODULE PROCEDURE SNOW3LWLIQMAX_3D
MODULE PROCEDURE SNOW3LWLIQMAX_2D
MODULE PROCEDURE SNOW3LWLIQMAX_1D
END INTERFACE
!
!-------------------------------------------------------------------------------
CONTAINS
!
!####################################################################
!####################################################################
!####################################################################
FUNCTION SNOW3LWLIQMAX_3D(PSNOWRHO) RESULT(PWLIQMAX) 1,2
!
!! PURPOSE
!! -------
! Calculate the maximum liquid water holding capacity of
! snow layer(s).
!
!
USE MODD_CSTS, ONLY : XRHOLW
USE MODD_SNOW_PAR, ONLY : XRHOSMAX_ES, XSNOWRHOHOLD, &
XWSNOWHOLDMAX2, XWSNOWHOLDMAX1
!
IMPLICIT NONE
!
!* 0.1 declarations of arguments
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSNOWRHO ! (kg/m3)
!
REAL, DIMENSION(SIZE(PSNOWRHO,1),SIZE(PSNOWRHO,2),SIZE(PSNOWRHO,3)) :: PWLIQMAX ! (kg/m3)
!
!* 0.2 declarations of local variables
!
REAL, DIMENSION(SIZE(PSNOWRHO,1),SIZE(PSNOWRHO,2),SIZE(PSNOWRHO,3)) :: ZHOLDMAXR, ZSNOWRHO
!
!-------------------------------------------------------------------------------
!
! Evaluate capacity using upper density limit:
!
ZSNOWRHO(:,:,:) = MIN(XRHOSMAX_ES, PSNOWRHO(:,:,:))
!
! Maximum ratio of liquid to SWE:
!
ZHOLDMAXR(:,:,:) = XWSNOWHOLDMAX1 + (XWSNOWHOLDMAX2-XWSNOWHOLDMAX1)* &
MAX(0.,XSNOWRHOHOLD-ZSNOWRHO(:,:,:))/XSNOWRHOHOLD
!
!
! Maximum liquid water holding capacity of the snow (kg/m3):
!
PWLIQMAX(:,:,:) = ZHOLDMAXR(:,:,:)*ZSNOWRHO(:,:,:)
!
!
END FUNCTION SNOW3LWLIQMAX_3D
!####################################################################
!####################################################################
!####################################################################
FUNCTION SNOW3LWLIQMAX_2D(PSNOWRHO) RESULT(PWLIQMAX) 1,2
!
!! PURPOSE
!! -------
! Calculate the maximum liquid water holding capacity of
! snow layer(s).
!
!
USE MODD_CSTS, ONLY : XRHOLW
USE MODD_SNOW_PAR, ONLY : XRHOSMAX_ES, XSNOWRHOHOLD, &
XWSNOWHOLDMAX2, XWSNOWHOLDMAX1
!
IMPLICIT NONE
!
!* 0.1 declarations of arguments
!
REAL, DIMENSION(:,:), INTENT(IN) :: PSNOWRHO ! (kg/m3)
!
REAL, DIMENSION(SIZE(PSNOWRHO,1),SIZE(PSNOWRHO,2)) :: PWLIQMAX ! (kg/m3)
!
!* 0.2 declarations of local variables
!
REAL, DIMENSION(SIZE(PSNOWRHO,1),SIZE(PSNOWRHO,2)) :: ZHOLDMAXR, ZSNOWRHO
!
!-------------------------------------------------------------------------------
!
! Evaluate capacity using upper density limit:
!
ZSNOWRHO(:,:) = MIN(XRHOSMAX_ES, PSNOWRHO(:,:))
!
! Maximum ratio of liquid to SWE:
!
ZHOLDMAXR(:,:) = XWSNOWHOLDMAX1 + (XWSNOWHOLDMAX2-XWSNOWHOLDMAX1)* &
MAX(0.,XSNOWRHOHOLD-ZSNOWRHO(:,:))/XSNOWRHOHOLD
!
!
! Maximum liquid water holding capacity of the snow (kg/m3):
!
PWLIQMAX(:,:) = ZHOLDMAXR(:,:)*ZSNOWRHO(:,:)
!
!
END FUNCTION SNOW3LWLIQMAX_2D
!####################################################################
!####################################################################
!####################################################################
FUNCTION SNOW3LWLIQMAX_1D(PSNOWRHO) RESULT(PWLIQMAX) 1,2
!
!! PURPOSE
!! -------
! Calculate the maximum liquid water holding capacity of
! snow layer(s).
!
!
USE MODD_CSTS, ONLY : XRHOLW
USE MODD_SNOW_PAR, ONLY : XRHOSMAX_ES, XSNOWRHOHOLD, &
XWSNOWHOLDMAX2, XWSNOWHOLDMAX1
!
IMPLICIT NONE
!
!* 0.1 declarations of arguments
!
REAL, DIMENSION(:), INTENT(IN) :: PSNOWRHO ! (kg/m3)
!
REAL, DIMENSION(SIZE(PSNOWRHO)) :: PWLIQMAX ! (kg/m3)
!
!* 0.2 declarations of local variables
!
REAL, DIMENSION(SIZE(PSNOWRHO)) :: ZHOLDMAXR, ZSNOWRHO
!
!-------------------------------------------------------------------------------
!
! Evaluate capacity using upper density limit:
!
ZSNOWRHO(:) = MIN(XRHOSMAX_ES, PSNOWRHO(:))
!
! Maximum ratio of liquid to SWE:
!
ZHOLDMAXR(:) = XWSNOWHOLDMAX1 + (XWSNOWHOLDMAX2-XWSNOWHOLDMAX1)* &
MAX(0.,XSNOWRHOHOLD-ZSNOWRHO(:))/XSNOWRHOHOLD
!
!
! Maximum liquid water holding capacity of the snow (kg/m3):
!
PWLIQMAX(:) = ZHOLDMAXR(:)*ZSNOWRHO(:)
!
!
END FUNCTION SNOW3LWLIQMAX_1D
!####################################################################
!####################################################################
!####################################################################
FUNCTION SNOW3LHOLD_3D(PSNOWRHO,PSNOWDZ) RESULT(PWHOLDMAX) 1,2
!
!! PURPOSE
!! -------
! Calculate the maximum liquid water holding capacity of
! snow layer(s).
!
!
USE MODD_CSTS, ONLY : XRHOLW
USE MODD_SNOW_PAR, ONLY : XRHOSMAX_ES, XSNOWRHOHOLD, &
XWSNOWHOLDMAX2, XWSNOWHOLDMAX1
!
IMPLICIT NONE
!
!* 0.1 declarations of arguments
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSNOWDZ, PSNOWRHO
!
REAL, DIMENSION(SIZE(PSNOWRHO,1),SIZE(PSNOWRHO,2),SIZE(PSNOWRHO,3)) :: PWHOLDMAX
!
!* 0.2 declarations of local variables
!
REAL, DIMENSION(SIZE(PSNOWRHO,1),SIZE(PSNOWRHO,2),SIZE(PSNOWRHO,3)) :: ZHOLDMAXR, ZSNOWRHO
!
!-------------------------------------------------------------------------------
!
! Evaluate capacity using upper density limit:
!
ZSNOWRHO(:,:,:) = MIN(XRHOSMAX_ES, PSNOWRHO(:,:,:))
!
!
! Maximum ratio of liquid to SWE:
!
ZHOLDMAXR(:,:,:) = XWSNOWHOLDMAX1 + (XWSNOWHOLDMAX2-XWSNOWHOLDMAX1)* &
MAX(0.,XSNOWRHOHOLD-ZSNOWRHO(:,:,:))/XSNOWRHOHOLD
!
!
! Maximum liquid water holding capacity of the snow (m):
!
PWHOLDMAX(:,:,:) = ZHOLDMAXR(:,:,:)*PSNOWDZ(:,:,:)*ZSNOWRHO(:,:,:)/XRHOLW
!
!
!-------------------------------------------------------------------------------
!
END FUNCTION SNOW3LHOLD_3D
!####################################################################
!####################################################################
!####################################################################
!####################################################################
!####################################################################
!####################################################################
FUNCTION SNOW3LHOLD_2D(PSNOWRHO,PSNOWDZ) RESULT(PWHOLDMAX) 1,2
!
!! PURPOSE
!! -------
! Calculate the maximum liquid water holding capacity of
! snow layer(s).
!
!
USE MODD_CSTS, ONLY : XRHOLW
USE MODD_SNOW_PAR, ONLY : XRHOSMAX_ES, XSNOWRHOHOLD, &
XWSNOWHOLDMAX2, XWSNOWHOLDMAX1
!
IMPLICIT NONE
!
!* 0.1 declarations of arguments
!
REAL, DIMENSION(:,:), INTENT(IN) :: PSNOWDZ, PSNOWRHO
!
REAL, DIMENSION(SIZE(PSNOWRHO,1),SIZE(PSNOWRHO,2)) :: PWHOLDMAX
!
!* 0.2 declarations of local variables
!
REAL, DIMENSION(SIZE(PSNOWRHO,1),SIZE(PSNOWRHO,2)) :: ZHOLDMAXR, ZSNOWRHO
!
!-------------------------------------------------------------------------------
!
! Evaluate capacity using upper density limit:
!
ZSNOWRHO(:,:) = MIN(XRHOSMAX_ES, PSNOWRHO(:,:))
!
!
! Maximum ratio of liquid to SWE:
!
ZHOLDMAXR(:,:) = XWSNOWHOLDMAX1 + (XWSNOWHOLDMAX2-XWSNOWHOLDMAX1)* &
MAX(0.,XSNOWRHOHOLD-ZSNOWRHO(:,:))/XSNOWRHOHOLD
!
!
! Maximum liquid water holding capacity of the snow (m):
!
PWHOLDMAX(:,:) = ZHOLDMAXR(:,:)*PSNOWDZ(:,:)*ZSNOWRHO(:,:)/XRHOLW
!
!
!-------------------------------------------------------------------------------
!
END FUNCTION SNOW3LHOLD_2D
!####################################################################
!####################################################################
!####################################################################
FUNCTION SNOW3LHOLD_1D(PSNOWRHO,PSNOWDZ) RESULT(PWHOLDMAX) 1,2
!
!! PURPOSE
!! -------
! Calculate the maximum liquid water holding capacity of
! snow layer(s).
!
!
USE MODD_CSTS, ONLY : XRHOLW
USE MODD_SNOW_PAR, ONLY : XRHOSMAX_ES, XSNOWRHOHOLD, &
XWSNOWHOLDMAX2, XWSNOWHOLDMAX1
!
IMPLICIT NONE
!
!* 0.1 declarations of arguments
!
REAL, DIMENSION(:), INTENT(IN) :: PSNOWDZ, PSNOWRHO
!
REAL, DIMENSION(SIZE(PSNOWRHO)) :: PWHOLDMAX
!
!* 0.2 declarations of local variables
!
REAL, DIMENSION(SIZE(PSNOWRHO)) :: ZHOLDMAXR, ZSNOWRHO
!
!-------------------------------------------------------------------------------
!
! Evaluate capacity using upper density limit:
!
ZSNOWRHO(:) = MIN(XRHOSMAX_ES, PSNOWRHO(:))
!
!
! Maximum ratio of liquid to SWE:
!
ZHOLDMAXR(:) = XWSNOWHOLDMAX1 + (XWSNOWHOLDMAX2-XWSNOWHOLDMAX1)* &
MAX(0.,XSNOWRHOHOLD-ZSNOWRHO(:))/XSNOWRHOHOLD
!
!
! Maximum liquid water holding capacity of the snow (m):
!
PWHOLDMAX(:) = ZHOLDMAXR(:)*PSNOWDZ(:)*ZSNOWRHO(:)/XRHOLW
!
!
!-------------------------------------------------------------------------------
!
END FUNCTION SNOW3LHOLD_1D
!####################################################################
!####################################################################
!####################################################################
FUNCTION SNOW3LSCAP_3D(PSNOWRHO) RESULT(PSCAP) 1,1
!
!! PURPOSE
!! -------
! Calculate the heat capacity of a snow layer.
!
USE MODD_CSTS, ONLY : XCI
!
IMPLICIT NONE
!
!* 0.1 declarations of arguments
!
REAL, DIMENSION(:,:,:), INTENT(IN) :: PSNOWRHO
!
REAL, DIMENSION(SIZE(PSNOWRHO,1),SIZE(PSNOWRHO,2),SIZE(PSNOWRHO,3)) :: PSCAP
!
!-------------------------------------------------------------------------------
!
! The method of Verseghy (1991), Int. J. Climat., 11, 111-133.
!
PSCAP(:,:,:) = PSNOWRHO(:,:,:)*XCI ! (J K-1 m-3)
!
!-------------------------------------------------------------------------------
!
END FUNCTION SNOW3LSCAP_3D
!####################################################################
!####################################################################
!####################################################################
FUNCTION SNOW3LSCAP_2D(PSNOWRHO) RESULT(PSCAP) 1,1
!
!! PURPOSE
!! -------
! Calculate the heat capacity of a snow layer.
!
USE MODD_CSTS, ONLY : XCI
!
IMPLICIT NONE
!
!* 0.1 declarations of arguments
!
REAL, DIMENSION(:,:), INTENT(IN) :: PSNOWRHO
!
REAL, DIMENSION(SIZE(PSNOWRHO,1),SIZE(PSNOWRHO,2)) :: PSCAP
!
!-------------------------------------------------------------------------------
!
! The method of Verseghy (1991), Int. J. Climat., 11, 111-133.
!
PSCAP(:,:) = PSNOWRHO(:,:)*XCI ! (J K-1 m-3)
!
!-------------------------------------------------------------------------------
!
END FUNCTION SNOW3LSCAP_2D
!####################################################################
!####################################################################
!####################################################################
FUNCTION SNOW3LSCAP_1D(PSNOWRHO) RESULT(PSCAP) 1,1
!
!! PURPOSE
!! -------
! Calculate the heat capacity of a snow layer.
!
USE MODD_CSTS, ONLY : XCI
!
IMPLICIT NONE
!
!* 0.1 declarations of arguments
!
REAL, DIMENSION(:), INTENT(IN) :: PSNOWRHO
!
REAL, DIMENSION(SIZE(PSNOWRHO)) :: PSCAP
!
!-------------------------------------------------------------------------------
!
! The method of Verseghy (1991), Int. J. Climat., 11, 111-133.
!
PSCAP(:) = PSNOWRHO(:)*XCI ! (J K-1 m-3)
!
!-------------------------------------------------------------------------------
!
END FUNCTION SNOW3LSCAP_1D
!####################################################################
!####################################################################
!####################################################################
SUBROUTINE SNOW3LGRID(PSNOWDZ,PSNOW) 1,2
!
!! PURPOSE
!! -------
! Once during each time step, update grid to maintain
! grid proportions. Similar to approach of Lynch-Steiglitz,
! 1994, J. Clim., 7, 1842-1855. Corresponding mass and
! heat adjustments made directly after the call to this
! routine. 3 grid configurations:
! 1) for very thin snow, constant grid spacing
! 2) for intermediate thicknesses, highest resolution at soil/snow
! interface and at the snow/atmosphere interface
! 3) for deep snow, vertical resoution finest at snow/atmosphere
! interface (set to a constant value) and increases with snow depth.
! Second layer can't be more than an order of magnitude thicker
! than surface layer.
!
!
USE MODD_SURF_PAR, ONLY : XUNDEF
USE MODD_SNOW_PAR, ONLY : XSNOWCRITD
!
IMPLICIT NONE
!
!* 0.1 declarations of arguments
!
REAL, DIMENSION(:), INTENT(IN) :: PSNOW
!
REAL, DIMENSION(:,:), INTENT(OUT) :: PSNOWDZ
!
!* 0.1 declarations of local variables
!
INTEGER JJ
!
INTEGER :: INLVLS
!
! ISBA-ES snow grid parameters
!
REAL, PARAMETER, DIMENSION(3) :: ZSGCOEF1 = (/0.25, 0.50, 0.25/)
REAL, PARAMETER, DIMENSION(2) :: ZSGCOEF2 = (/0.05, 0.34/)
!
! Minimum total snow depth at which surface layer thickness is constant:
!
REAL, PARAMETER :: ZSNOWTRANS = 0.20 ! (m)
!
!-------------------------------------------------------------------------------
!
! 0. Initialization:
! ------------------
!
INLVLS = SIZE(PSNOWDZ(:,:),2)
!
! 1. Calculate current grid for 3-layer (default) configuration):
! ---------------------------------------------------------------
! Based on formulation of Lynch-Stieglitz (1994)
! except for 3 modifications:
! i) smooth transition here at ZSNOWTRANS
! ii) constant ratio for very thin snow:
! iii) ratio of layer 2 to surface layer <= 10
!
IF(INLVLS == 3)THEN
!
WHERE(PSNOW <= XSNOWCRITD+0.01)
PSNOWDZ(:,1) = MIN(0.01, PSNOW(:)/INLVLS)
PSNOWDZ(:,3) = MIN(0.01, PSNOW(:)/INLVLS)
PSNOWDZ(:,2) = PSNOW(:) - PSNOWDZ(:,1) - PSNOWDZ(:,3)
END WHERE
!
WHERE(PSNOW <= ZSNOWTRANS .AND. PSNOW > XSNOWCRITD+0.01)
PSNOWDZ(:,1) = PSNOW(:)*ZSGCOEF1(1)
PSNOWDZ(:,2) = PSNOW(:)*ZSGCOEF1(2)
PSNOWDZ(:,3) = PSNOW(:)*ZSGCOEF1(3)
END WHERE
!
WHERE(PSNOW > ZSNOWTRANS)
PSNOWDZ(:,1) = ZSGCOEF2(1)
PSNOWDZ(:,2) = (PSNOW(:)-ZSGCOEF2(1))*ZSGCOEF2(2) + ZSGCOEF2(1)
!
! When using simple finite differences, limit the thickness
! factor between the top and 2nd layers to at most 10
!
PSNOWDZ(:,2) = MIN(10*ZSGCOEF2(1), PSNOWDZ(:,2))
PSNOWDZ(:,3) = PSNOW(:) - PSNOWDZ(:,2) - PSNOWDZ(:,1)
END WHERE
!
ELSE
!
!
! 2. For more than 3-layers:
! --------------------------
! For the case when more than 3 layers are to be used, specifiy how
! grid should be defined here. For now, a very simple arbitrary method
! herein. WARNING: Detailed testing using more than 3-layers has not been done
! to date, only minor tests.
!
DO JJ=1,INLVLS
PSNOWDZ(:,JJ) = PSNOW(:)/INLVLS
ENDDO
!
PSNOWDZ(:,INLVLS) = PSNOWDZ(:,INLVLS) + (PSNOWDZ(:,1) - MIN(0.05, PSNOWDZ(:,1)))
PSNOWDZ(:,1) = MIN(0.05, PSNOWDZ(:,1))
!
ENDIF
!
DO JJ=1,INLVLS
WHERE(PSNOW(:)==XUNDEF)
PSNOWDZ(:,JJ) = XUNDEF
END WHERE
END DO
!
END SUBROUTINE SNOW3LGRID
!####################################################################
!####################################################################
!####################################################################
END MODULE MODE_SNOW3L