!
! Fresnel
!
! Module containing routines to compute Fresnel reflectivities.
!
!
! CREATION HISTORY:
! Written by: Masahiro Kazumori, JCSDA
! Masahiro.Kazumori@noaa.gov
! Modified by: Paul van Delst, CIMSS/SSEC 11-Apr-2007
! paul.vandelst@noaa.gov
MODULE Fresnel
! -----------------
! Environment setup
! -----------------
! Module use
USE Type_Kinds, ONLY: fp
! Disable implicit typing
IMPLICIT NONE
! ------------
! Visibilities
! ------------
PRIVATE
PUBLIC :: iVar_type
PUBLIC :: Fresnel_Reflectivity
PUBLIC :: Fresnel_Reflectivity_TL
PUBLIC :: Fresnel_Reflectivity_AD
! -----------------
! Module parameters
! -----------------
! RCS Id for the module
CHARACTER(*), PARAMETER :: MODULE_RCS_ID = &
'$Id: Fresnel.f90 99117 2017-11-27 18:37:14Z tong.zhu@noaa.gov $'
REAL(fp), PARAMETER :: ZERO = 0.0_fp
REAL(fp), PARAMETER :: POINT5 = 0.5_fp
REAL(fp), PARAMETER :: ONE = 1.0_fp
REAL(fp), PARAMETER :: TWO = 2.0_fp
! --------------------------------------
! Structure definition to hold forward
! variables across FWD, TL, and AD calls
! --------------------------------------
TYPE :: iVar_type
PRIVATE
! The intermediate terms
COMPLEX(fp) :: z1, z2
! The real and imaginary components
REAL(fp) :: rzRv,izRv ! Vertical
REAL(fp) :: rzRh,izRh ! Horizontal
END TYPE iVar_type
CONTAINS
!--------------------------------------------------------------------------------
!
! NAME:
! Fresnel_Reflectivity
!
! PURPOSE:
! Subroutine to compute Fresnel reflectivities
!
! CALLING SEQUENCE:
! CALL Fresnel_Reflectivity( permittivity, & ! Input
! cos_i , & ! Input
! Rv , & ! Output
! Rh , & ! Output
! iVar ) ! Internal variable output
!
! INPUT ARGUMENTS:
! permittivity: Permittivity of medium
! UNITS: Farads per metre (F.m^-1)
! TYPE: COMPLEX(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! cos_i: Cosine of incidence angle
! UNITS: N/A
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! OUTPUT ARGUMENTS:
! Rv: Reflectivity for polarisation parallel to the
! plane of incidence (i.e. vertical polarization)
! UNITS: N/A
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!
! Rh: Reflectivity for polarisation perpendicular to the
! plane of incidence (i.e. horizontal polarization)
! UNITS: N/A
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!
! iVar: Structure containing internal variables required for
! subsequent tangent-linear or adjoint model calls.
! The contents of this structure are NOT accessible
! outside of the Fresnel module.
! UNITS: N/A
! TYPE: TYPE(iVar_type)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!
! CREATION HISTORY:
! Written by: Masahiro Kazumori, JCSDA
! Masahiro.Kazumori@noaa.gov
! Modified by: Paul van Delst, CIMSS/SSEC 11-Apr-2007
! paul.vandelst@noaa.gov
!
!--------------------------------------------------------------------------------
SUBROUTINE Fresnel_Reflectivity( permittivity, & ! Input
cos_i , & ! Input
Rv , & ! Output
Rh , & ! Output
iVar ) ! Internal variable output
! Arguments
COMPLEX(fp), INTENT(IN) :: permittivity
REAL(fp), INTENT(IN) :: cos_i
REAL(fp), INTENT(OUT) :: Rv
REAL(fp), INTENT(OUT) :: Rh
TYPE(iVar_type), INTENT(IN OUT) :: iVar
! Local variables
COMPLEX(fp) :: zRv ! Vertical
COMPLEX(fp) :: zRh ! Horizontal
! Compute the complex reflectivity components
iVar%z1 = SQRT(permittivity - ONE + (cos_i*cos_i))
iVar%z2 = permittivity * cos_i
zRh = (cos_i -iVar%z1) / (cos_i +iVar%z1)
zRv = (iVar%z2-iVar%z1) / (iVar%z2+iVar%z1)
! The square of the vertical abs value
iVar%rzRv = REAL(zRv,fp)
iVar%izRv = AIMAG(zRv)
Rv = iVar%rzRv**2 + iVar%izRv**2
! The square of the horizontal abs value
iVar%rzRh = REAL(zRh,fp)
iVar%izRh = AIMAG(zRh)
Rh = iVar%rzRh**2 + iVar%izRh**2
END SUBROUTINE Fresnel_Reflectivity
!--------------------------------------------------------------------------------
!
! NAME:
! Fresnel_Reflectivity_TL
!
! PURPOSE:
! Subroutine to compute tangent-linear Fresnel reflectivities
!
! CALLING SEQUENCE:
! CALL Fresnel_Reflectivity_TL( permittivity_TL, & ! Input
! cos_i , & ! Input
! Rv_TL , & ! Output
! Rh_TL , & ! Output
! iVar ) ! Internal variable input
!
! INPUT ARGUMENTS:
! permittivity_TL: Tangent-linear permittivity of medium
! UNITS: Farads per metre (F.m^-1)
! TYPE: COMPLEX(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! cos_i Cosine of incidence angle
! UNITS: N/A
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! iVar: Structure containing internal variables required for
! subsequent tangent-linear or adjoint model calls.
! The contents of this structure are NOT accessible
! outside of the Fresnel module.
! UNITS: N/A
! TYPE: TYPE(iVar_type)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! OUTPUT ARGUMENTS:
! Rv_TL Tangent-linear reflectivity for polarisation parallel
! to the plane of incidence (i.e. vertical polarization)
! UNITS: N/A
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!
! Rh_TL Tangent-linear reflectivity for polarisation
! perpendicular to the plane of incidence
! (i.e. horizontal polarization)
! UNITS: N/A
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!
! CREATION HISTORY:
! Written by: Masahiro Kazumori, JCSDA
! Masahiro.Kazumori@noaa.gov
! Modified by: Paul van Delst, CIMSS/SSEC 11-Apr-2007
! paul.vandelst@noaa.gov
!
!--------------------------------------------------------------------------------
SUBROUTINE Fresnel_Reflectivity_TL( permittivity_TL, & ! Input
cos_i , & ! Input
Rv_TL , & ! Output
Rh_TL , & ! Output
iVar ) ! Internal variable input
! Arguments
COMPLEX(fp), INTENT(IN) :: permittivity_TL
REAL(fp), INTENT(IN) :: cos_i
REAL(fp), INTENT(OUT) :: Rv_TL
REAL(fp), INTENT(OUT) :: Rh_TL
TYPE(iVar_type), INTENT(IN) :: iVar
! Local variables
COMPLEX(fp) :: z1_TL, z2_TL
COMPLEX(fp) :: zRv_TL ! Vertical
COMPLEX(fp) :: zRh_TL ! Horizontal
REAL(fp) :: rzRv_TL,izRv_TL ! Vertical
REAL(fp) :: rzRh_TL,izRh_TL ! Horizontal
! Compute the tangent-linear complex reflectivity components
z1_TL = POINT5 * permittivity_TL / iVar%z1
z2_TL = cos_i * permittivity_TL
zRh_TL = -TWO * cos_i * z1_TL / (cos_i+iVar%z1)**2
zRv_TL = TWO * (iVar%z1*z2_TL - iVar%z2*z1_TL) / (iVar%z2+iVar%z1)**2
! The square of the tangent-linear vertical abs value
rzRv_TL = REAL(zRv_TL,fp)
izRv_TL = AIMAG(zRv_TL)
Rv_TL = TWO * (iVar%rzRv*rzRv_TL + iVar%izRv*izRv_TL)
! The square of the tangent-linear horizontal abs value
rzRh_TL = REAL(zRh_TL,fp)
izRh_TL = AIMAG(zRh_TL)
Rh_TL = TWO * (iVar%rzRh*rzRh_TL + iVar%izRh*izRh_TL)
END SUBROUTINE Fresnel_Reflectivity_TL
!--------------------------------------------------------------------------------
!
! NAME:
! Fresnel_Reflectivity_AD
!
! PURPOSE:
! Subroutine to compute Fresnel reflectivity adjoints
!
! CALLING SEQUENCE:
! CALL Fresnel_Reflectivity_AD( Rv_AD , & ! Input
! Rh_AD , & ! Input
! cos_i , & ! Input
! permittivity_AD, & ! Output
! iVar ) ! Internal variable input
!
! INPUT ARGUMENTS:
! Rv_AD Adjoint reflectivity for polarisation parallel
! to the plane of incidence (i.e. vertical polarization)
! ** Set to ZERO on exit **
! UNITS: N/A
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN OUT)
!
! Rh_AD Adjoint reflectivity for polarisation
! perpendicular to the plane of incidence
! (i.e. horizontal polarization)
! ** Set to ZERO on exit **
! UNITS: N/A
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN OUT)
!
! cos_i Cosine of incidence angle
! UNITS: N/A
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! iVar: Structure containing internal variables required for
! subsequent tangent-linear or adjoint model calls.
! The contents of this structure are NOT accessible
! outside of the Fresnel module.
! UNITS: N/A
! TYPE: TYPE(iVar_type)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! OUTPUT ARGUMENTS:
! permittivity_AD: Adjoint permittivity of medium, dR/de,
! where R == reflectivity
! e == permittivity
! UNITS: inverse Farads per metre (F.m^-1)^-1
! TYPE: COMPLEX(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN OUT)
!
! CREATION HISTORY:
! Written by: Masahiro Kazumori, JCSDA
! Masahiro.Kazumori@noaa.gov
! Modified by: Paul van Delst, CIMSS/SSEC 11-Apr-2007
! paul.vandelst@noaa.gov
!
!--------------------------------------------------------------------------------
SUBROUTINE Fresnel_Reflectivity_AD( Rv_AD , & ! Input
Rh_AD , & ! Input
cos_i , & ! Input
permittivity_AD, & ! Output
iVar ) ! Internal variable input
! Arguments
REAL(fp), INTENT(IN OUT) :: Rv_AD
REAL(fp), INTENT(IN OUT) :: Rh_AD
REAL(fp), INTENT(IN) :: cos_i
COMPLEX(fp), INTENT(IN OUT) :: permittivity_AD
TYPE(iVar_type), INTENT(IN) :: iVar
! Local variables
COMPLEX(fp) :: z1_AD, z2_AD
COMPLEX(fp) :: zRv_AD ! Vertical
COMPLEX(fp) :: zRh_AD ! Horizontal
REAL(fp) :: rzRv_AD,izRv_AD ! Vertical
REAL(fp) :: rzRh_AD,izRh_AD ! Horizontal
COMPLEX(fp) :: denom
! The adjoint of the horizontal reflectivity
izRh_AD = TWO*iVar%izRh*Rh_AD
rzRh_AD = TWO*iVar%rzRh*Rh_AD
Rh_AD = ZERO
zRh_AD = CMPLX(rzRh_AD, -izRh_AD, fp) ! complex conjugate
! The adjoint of the vertical reflectivity
izRv_AD = TWO*iVar%izRv*Rv_AD
rzRv_AD = TWO*iVar%rzRv*Rv_AD
Rv_AD = ZERO
zRv_AD = CMPLX(rzRv_AD, -izRv_AD, fp) ! complex conjugate
! The adjoint of the complex vertical polarised component
denom = (iVar%z2+iVar%z1)**2
z1_AD = -TWO*iVar%z2*zRv_AD / denom
z2_AD = TWO*iVar%z1*zRv_AD / denom
! The adjoint of the complex horizontal polarised component
z1_AD = z1_AD - ( TWO*cos_i*zRh_AD / (cos_i+iVar%z1)**2 )
! The adjoint of the preserved variables
permittivity_AD = permittivity_AD + CONJG(cos_i*z2_AD)
permittivity_AD = permittivity_AD + CONJG(POINT5*z1_AD/iVar%z1)
END SUBROUTINE Fresnel_Reflectivity_AD
END MODULE Fresnel