! ! 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