!
! Guillou Ocean Permittivity module.
!
! Module containing routines to compute the complex permittivities for
! sea water based on
!
! Guillou, C. et al. (1998) Impact of new permittivity measurements
! on sea surface emissivity modeling in microwaves.
! Radio Science, Volume 33, Number 3, Pages 649-667
!
!
! CREATION HISTORY:
! Written by: Paul van Delst, 11-Apr-2007
! paul.vandelst@noaa.gov
!
MODULE Guillou
! -----------------
! Environment setup
! -----------------
! Module use
USE Type_Kinds, ONLY: fp
USE Fundamental_Constants, ONLY: PI, &
E0 => PERMITTIVITY, & ! Permittivity of vacuum (F/m)
K_TO_C => STANDARD_TEMPERATURE ! Temperature units conversion
! Disable implicit typing
IMPLICIT NONE
! ------------
! Visibilities
! ------------
PRIVATE
! ...Datatypes
PUBLIC :: iVar_type
! ...Procedures
PUBLIC :: Guillou_Ocean_Permittivity
PUBLIC :: Guillou_Ocean_Permittivity_TL
PUBLIC :: Guillou_Ocean_Permittivity_AD
! -----------------
! Module parameters
! -----------------
CHARACTER(*), PARAMETER :: MODULE_VERSION_ID = &
'$Id: Guillou.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
REAL(fp), PARAMETER :: THREE = 3.0_fp
REAL(fp), PARAMETER :: FOUR = 4.0_fp
REAL(fp), PARAMETER :: FIVE = 5.0_fp
REAL(fp), PARAMETER :: TWOPI = TWO*PI
! Scaling factors (used here for documenting the conversion
! to SI units of the double Debye model denominator)
! ---------------------------------------------------------
REAL(fp), PARAMETER :: PS_TO_S = 1.0e-12_fp ! Picoseconds -> Seconds
REAL(fp), PARAMETER :: GHZ_TO_HZ = 1.0e+09_fp ! Gigahertz -> Hertz
REAL(fp), PARAMETER :: SCALE_FACTOR = PS_TO_S * GHZ_TO_HZ
! Parameters for the Guillou et al (1998) permittivity model
! ----------------------------------------------------------
! The coefficients for the sea water conductivity temperature
! polynomials. Eqn.(1) in reference. Note that these values
! have more precision than is reported in the ref.
REAL(fp), PARAMETER :: D1_COEFF(0:2) = (/ 0.086374_fp, &
0.030606_fp, &
-0.0004121_fp /)
REAL(fp), PARAMETER :: D2_COEFF(0:2) = (/ 0.077454_fp, &
0.001687_fp, &
0.00001937_fp /)
! The coefficients for the static permittivity temperature
! polynomials. Eqn.(3) in reference. Note that these values
! have more precision than is reported in the ref.
REAL(fp), PARAMETER :: A1_COEFF(0:5) = (/ 81.820_fp, &
-6.0503E-02_fp, &
-3.1661E-02_fp, &
3.1097E-03_fp, &
-1.1791E-04_fp, &
1.4838E-06_fp /)
REAL(fp), PARAMETER :: A2_COEFF(0:5) = (/ 0.12544_fp, &
9.4037E-03_fp, &
-9.5551E-04_fp, &
9.0888E-05_fp, &
-3.6011E-06_fp, &
4.7130E-08_fp /)
! The coefficients for the high-frequency permittivity temperature
! polynomial. Eqn.(4) in reference. Note that these values
! have more precision than is reported in the ref.
REAL(fp), PARAMETER :: B1_COEFF(0:5) = (/ 6.4587_fp , &
-0.04203_fp , &
-0.0065881_fp , &
0.00064924_fp, &
-1.2328E-05_fp, &
5.0433E-08_fp /)
! The coefficients for the relaxation time temperature
! polynomial. Eqn.(5) in reference. Note that these values
! have more precision than is reported in the ref.
REAL(fp), PARAMETER :: C1_COEFF(0:5) = (/ 17.303_fp , &
-0.66651_fp , &
5.1482E-03_fp, &
1.2145E-03_fp, &
-5.0325E-05_fp, &
5.8272E-07_fp /)
REAL(fp), PARAMETER :: C2_COEFF(0:5) = (/-6.272E-03_fp , &
2.357E-04_fp , &
5.075E-04_fp , &
-6.3983E-05_fp, &
2.463E-06_fp , &
-3.0676E-08_fp /)
! --------------------------------------
! Structure definition to hold forward
! variables across FWD, TL, and AD calls
! --------------------------------------
TYPE :: iVar_type
PRIVATE
REAL(fp) :: t=ZERO, s=ZERO ! Temperature in degC; salinity
REAL(fp) :: f=ZERO, f2=ZERO, f0=ZERO, f2po=ZERO ! Frequency terms
REAL(fp) :: a1=ZERO, a2=ZERO, es=ZERO ! Static permittivity temperature polynomials
REAL(fp) :: einf=ZERO ! High-frequency permittivity temperature polynomial
REAL(fp) :: c1=ZERO, c2=ZERO ! Relaxation time temperature polynomial
REAL(fp) :: d1=ZERO, d2=ZERO ! Conductivity temperature polynomials
END TYPE iVar_type
CONTAINS
!################################################################################
!################################################################################
!## ##
!## ## PUBLIC MODULE ROUTINES ## ##
!## ##
!################################################################################
!################################################################################
!--------------------------------------------------------------------------------
!:sdoc+:
!
! NAME:
! Guillou_Ocean_Permittivity
!
! PURPOSE:
! Subroutine to compute ocean permittivity according to the reference,
! Guillou, C. et al. (1998) Impact of new permittivity measurements
! on sea surface emissivity modeling in microwaves.
! Radio Science, Volume 33, Number 3, Pages 649-667
!
! CALLING SEQUENCE:
! CALL Guillou_Ocean_Permittivity( Temperature , & ! Input
! Salinity , & ! Input
! Frequency , & ! Input
! Permittivity, & ! Output
! iVar ) ! Internal variable output
!
! INPUTS:
! Temperature: Sea surface temperature
! UNITS: Kelvin (K)
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! Salinity: Water salinity
! UNITS: ppt (parts per thousand)
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! Frequency: Frequency
! UNITS: GHz
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! OUTPUTS:
! Permittivity: Ocean permittivity
! UNITS: N/A
! TYPE: COMPLEX(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 this module.
! UNITS: N/A
! TYPE: TYPE(iVar_type)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!:sdoc-:
!--------------------------------------------------------------------------------
SUBROUTINE Guillou_Ocean_Permittivity( &
Temperature , & ! Input
Salinity , & ! Input
Frequency , & ! Input
Permittivity, & ! Output
iVar ) ! Internal variable output
! Arguments
REAL(fp), INTENT(IN) :: Temperature
REAL(fp), INTENT(IN) :: Salinity
REAL(fp), INTENT(IN) :: Frequency
COMPLEX(fp), INTENT(OUT) :: Permittivity
TYPE(iVar_type), INTENT(IN OUT) :: iVar
! Local variables
REAL(fp) :: sigma
REAL(fp) :: tau
REAL(fp) :: re, ie
! Save the inputs
! ---------------
iVar%t = Temperature - K_TO_C
iVar%s = Salinity
! Conductivity
! ------------
! Compute the conductivity temperature polynomials
! Eqn.(1) in reference
iVar%d1 = D1_COEFF(0) + iVar%t*(D1_COEFF(1) + iVar%t*D1_COEFF(2))
iVar%d2 = D2_COEFF(0) + iVar%t*(D2_COEFF(1) + iVar%t*D2_COEFF(2))
! Compute the salinity dependent conductivity
sigma = iVar%d1 + iVar%s*iVar%d2
! Static permittivity
! -------------------
! Compute the static permittivity temperature polynomials.
! Eqn.(3) in reference.
iVar%a1 = A1_COEFF(0) + iVar%t*(A1_COEFF(1) + &
iVar%t*(A1_COEFF(2) + &
iVar%t*(A1_COEFF(3) + &
iVar%t*(A1_COEFF(4) + &
iVar%t*A1_COEFF(5) ))))
iVar%a2 = A2_COEFF(0) + iVar%t*(A2_COEFF(1) + &
iVar%t*(A2_COEFF(2) + &
iVar%t*(A2_COEFF(3) + &
iVar%t*(A2_COEFF(4) + &
iVar%t*A2_COEFF(5) ))))
! Compute the salinity dependent static permittivity
iVar%es = iVar%a1 - iVar%s*iVar%a2
! High frequency permittivity
! ---------------------------
! Compute the high-frequency permittivity temperature polynomial
! Eqn.(4) in reference
iVar%einf = B1_COEFF(0) + iVar%t*(B1_COEFF(1) + &
iVar%t*(B1_COEFF(2) + &
iVar%t*(B1_COEFF(3) + &
iVar%t*(B1_COEFF(4) + &
iVar%t*B1_COEFF(5) ))))
! Relaxation time
! ---------------
! Compute the Debye relaxation time temperature polynomials
! Eqn.(5) in reference
iVar%c1 = C1_COEFF(0) + iVar%t*(C1_COEFF(1) + &
iVar%t*(C1_COEFF(2) + &
iVar%t*(C1_COEFF(3) + &
iVar%t*(C1_COEFF(4) + &
iVar%t*C1_COEFF(5) ))))
iVar%c2 = C2_COEFF(0) + iVar%t*(C2_COEFF(1) + &
iVar%t*(C2_COEFF(2) + &
iVar%t*(C2_COEFF(3) + &
iVar%t*(C2_COEFF(4) + &
iVar%t*C2_COEFF(5) ))))
! Compute the salinity dependent relaxation time in picoseconds
tau = iVar%c1 + iVar%s*iVar%c2
! Compute the complex permittivity
! --------------------------------
! The various frequency terms
iVar%f = TWOPI * Frequency * tau * SCALE_FACTOR
iVar%f2 = iVar%f**2
iVar%f0 = TWOPI * Frequency * GHZ_TO_HZ * E0
iVar%f2po = ONE+iVar%f2
! The real part
re = (iVar%es + iVar%einf*iVar%f2)/iVar%f2po
! The imaginary part
ie = iVar%f*(iVar%es - iVar%einf)/iVar%f2po + sigma/iVar%f0
! Combine them
Permittivity = CMPLX(re,-ie,fp)
END SUBROUTINE Guillou_Ocean_Permittivity
!--------------------------------------------------------------------------------
!:sdoc+:
!
! NAME:
! Guillou_Ocean_Permittivity_TL
!
! PURPOSE:
! Subroutine to compute the tangent-linear ocean permittivity according
! to the reference,
! Guillou, C. et al. (1998) Impact of new permittivity measurements
! on sea surface emissivity modeling in microwaves.
! Radio Science, Volume 33, Number 3, Pages 649-667
!
! CALLING SEQUENCE:
! CALL Guillou_Ocean_Permittivity_TL( Temperature_TL , & ! Input
! Salinity_TL , & ! Input
! Frequency , & ! Input
! Permittivity_TL, & ! Output
! iVar ) ! Internal variable input
!
! INPUTS:
! Temperature_TL: Tangent-linear sea surface temperature
! UNITS: Kelvin (K)
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! Salinity_TL: Tangent-linear water salinity
! UNITS: ppt (parts per thousand)
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN)
!
! Frequency: Frequency
! UNITS: GHz
! 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 this module.
! UNITS: N/A
! TYPE: TYPE(iVar_type)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!
! OUTPUTS:
! Permittivity_TL: Tangent-linear ocean permittivity
! UNITS: N/A
! TYPE: COMPLEX(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!:sdoc-:
!--------------------------------------------------------------------------------
SUBROUTINE Guillou_Ocean_Permittivity_TL( &
Temperature_TL , & ! Input
Salinity_TL , & ! Input
Frequency , & ! Input
Permittivity_TL, & ! Output
iVar ) ! Internal variable input
! Arguments
REAL(fp), INTENT(IN) :: Temperature_TL
REAL(fp), INTENT(IN) :: Salinity_TL
REAL(fp), INTENT(IN) :: Frequency
COMPLEX(fp), INTENT(OUT) :: Permittivity_TL
TYPE(iVar_type), INTENT(IN) :: iVar
! Local variables
REAL(fp) :: d1_TL, d2_TL, sigma_TL
REAL(fp) :: a1_TL, a2_TL, es_TL
REAL(fp) :: einf_TL
REAL(fp) :: c1_TL, c2_TL, tau_TL
REAL(fp) :: f_TL, f2_TL, f2po_TL
REAL(fp) :: inv_f2po
REAL(fp) :: re_TL, ie_TL
! Conductivity
! ------------
! Compute the tangent-linear conductivity
! temperature polynomials. Eqn.(1) in reference
d1_TL = (D1_COEFF(1) + iVar%t*TWO*D1_COEFF(2)) * Temperature_TL
d2_TL = (D2_COEFF(1) + iVar%t*TWO*D2_COEFF(2)) * Temperature_TL
! Compute the tangent-linear salinity
! dependent conductivity
sigma_TL = d1_TL + iVar%s*d2_TL + Salinity_TL*iVar%d2
! Static permittivity
! -------------------
! Compute the tangent-linear static permittivity
! temperature polynomials. Eqn.(3) in reference.
a1_TL = (A1_COEFF(1) + iVar%t*(TWO*A1_COEFF(2) + &
iVar%t*(THREE*A1_COEFF(3) + &
iVar%t*(FOUR*A1_COEFF(4) + &
iVar%t*FIVE*A1_COEFF(5)))) ) * Temperature_TL
a2_TL = (A2_COEFF(1) + iVar%t*(TWO*A2_COEFF(2) + &
iVar%t*(THREE*A2_COEFF(3) + &
iVar%t*(FOUR*A2_COEFF(4) + &
iVar%t*FIVE*A2_COEFF(5)))) ) * Temperature_TL
! Compute the tangent-linear salinity
! dependent static permittivity
es_TL = a1_TL - iVar%s*a2_TL - Salinity_TL*iVar%a2
! High frequency permittivity
! ---------------------------
! Compute the tangent-linear high-frequency permittivity
! temperature polynomial. Eqn.(4) in reference
einf_TL = (B1_COEFF(1) + iVar%t*(TWO*B1_COEFF(2) + &
iVar%t*(THREE*B1_COEFF(3) + &
iVar%t*(FOUR*B1_COEFF(4) + &
iVar%t*FIVE*B1_COEFF(5)))) ) * Temperature_TL
! Relaxation time
! ---------------
! Compute the tangent-linear Debye relaxation time
! temperature polynomials. Eqn.(5) in reference
c1_TL = (C1_COEFF(1) + iVar%t*(TWO*C1_COEFF(2) + &
iVar%t*(THREE*C1_COEFF(3) + &
iVar%t*(FOUR*C1_COEFF(4) + &
iVar%t*FIVE*C1_COEFF(5)))) ) * Temperature_TL
c2_TL = (C2_COEFF(1) + iVar%t*(TWO*C2_COEFF(2) + &
iVar%t*(THREE*C2_COEFF(3) + &
iVar%t*(FOUR*C2_COEFF(4) + &
iVar%t*FIVE*C2_COEFF(5)))) ) * Temperature_TL
! Compute the tangent-linear salinity
! dependent relaxation time in picoseconds
tau_TL = c1_TL + iVar%s*c2_TL + Salinity_TL*iVar%c2
! Compute the complex permittivity
! --------------------------------
! The tangent-linear of various frequency terms
f_TL = TWOPI * Frequency * tau_TL * SCALE_FACTOR
f2_TL = TWO * iVar%f * f_TL
f2po_TL = f2_TL
inv_f2po = ONE/iVar%f2po
! The real part
re_TL = inv_f2po*(iVar%f2*einf_TL + &
es_TL - &
inv_f2po*(iVar%es-iVar%einf)*f2po_TL)
! The imaginary part
ie_TL = inv_f2po*(iVar%f*es_TL - &
iVar%f*einf_TL +&
inv_f2po*(iVar%es-iVar%einf)*(ONE-iVar%f2)*f_TL) + &
sigma_TL/iVar%f0
! Combine them
Permittivity_tl = CMPLX(re_TL, -ie_TL, fp)
END SUBROUTINE Guillou_Ocean_Permittivity_TL
!--------------------------------------------------------------------------------
!:sdoc+:
!
! NAME:
! Guillou_Ocean_Permittivity_AD
!
! PURPOSE:
! Subroutine to compute the adjoint of the ocean permittivity according
! to the reference,
! Guillou, C. et al. (1998) Impact of new permittivity measurements
! on sea surface emissivity modeling in microwaves.
! Radio Science, Volume 33, Number 3, Pages 649-667
!
! CALLING SEQUENCE:
! CALL Guillou_Ocean_Permittivity_AD( Permittivity_AD, & ! Input
! Frequency , & ! Input
! Temperature_AD , & ! Output
! Salinity_AD , & ! Output
! iVar ) ! Internal variable input
!
! INPUTS:
! Permittivity_AD: Adjoint ocean permittivity
! UNITS: N/A
! TYPE: COMPLEX(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN OUT)
!
! Frequency: Frequency
! UNITS: GHz
! 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 this module.
! UNITS: N/A
! TYPE: TYPE(iVar_type)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(OUT)
!
! OUTPUTS:
! Temperature_AD: Adjoint sea surface temperature, de/dT.
! UNITS: per Kelvin (K^-1)
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN OUT)
!
! Salinity_AD: Adjoint water salinity, de/dS
! UNITS: per ppt (parts-per-thousand^-1)
! TYPE: REAL(fp)
! DIMENSION: Scalar
! ATTRIBUTES: INTENT(IN OUT)
!
! SIDE EFFECTS:
! The input adjoint variable, Permittivity_AD, is set to zero upon
! exiting this routine.
!
!:sdoc-:
!--------------------------------------------------------------------------------
SUBROUTINE Guillou_Ocean_Permittivity_AD( &
Permittivity_AD, & ! Input
Frequency , & ! Input
Temperature_AD , & ! Output
Salinity_AD , & ! Output
iVar ) ! Internal variable input
! Arguments
COMPLEX(fp), INTENT(IN OUT) :: Permittivity_AD
REAL(fp), INTENT(IN) :: Frequency
REAL(fp), INTENT(IN OUT) :: Temperature_AD
REAL(fp), INTENT(IN OUT) :: Salinity_AD
TYPE(iVar_type), INTENT(IN) :: iVar
! Local variables
REAL(fp) :: ie_AD, re_AD
REAL(fp) :: f2po2
REAL(fp) :: a1_AD, a2_AD, es_AD
REAL(fp) :: einf_AD
REAL(fp) :: c1_AD, c2_AD, tau_AD
REAL(fp) :: d1_AD, d2_AD, sigma_AD
REAL(fp) :: f2_AD, f_AD
! Complex permittivity
! --------------------
! Separate the real and imaginary parts
ie_AD = -AIMAG(Permittivity_AD)
re_AD = REAL(Permittivity_AD, fp)
Permittivity_AD = ZERO
! Adjoint of the imaginary part
f2po2 = iVar%f2po**2
sigma_AD = ie_AD/iVar%f0
f2_AD = -ie_AD*iVar%f*(iVar%es-iVar%einf)/f2po2
einf_AD = -ie_AD*iVar%f/iVar%f2po
es_AD = ie_AD*iVar%f/iVar%f2po
f_AD = ie_AD*(iVar%es-iVar%einf)/iVar%f2po
ie_AD = ZERO
! Adjoint of the real part
f2_AD = f2_AD - re_AD*(iVar%es-iVar%einf)/f2po2
einf_AD = einf_AD + re_AD*iVar%f2/iVar%f2po
es_AD = es_AD + re_AD/iVar%f2po
re_AD = ZERO
! Adjoint of the frequency terms
f_AD = f_AD + TWO*iVar%f*f2_AD
f2_AD = ZERO
tau_AD = TWOPI * Frequency * SCALE_FACTOR * f_AD
f_AD = ZERO
! Relaxation time
! ---------------
! Compute the adjoint of the salinity
! dependent relaxation time in picoseconds
Salinity_AD = Salinity_AD + iVar%c2*tau_AD
c2_AD = iVar%s * tau_AD
c1_AD = tau_AD
tau_AD = ZERO
! Compute the adjoint of the Debye relaxation time
! temperature polynomials. Eqn.(5) in reference
Temperature_AD = Temperature_AD + (C2_COEFF(1) + iVar%t*(TWO*C2_COEFF(2) + &
iVar%t*(THREE*C2_COEFF(3) + &
iVar%t*(FOUR*C2_COEFF(4) + &
iVar%t*FIVE*C2_COEFF(5)))) ) * c2_AD
Temperature_AD = Temperature_AD + (C1_COEFF(1) + iVar%t*(TWO*C1_COEFF(2) + &
iVar%t*(THREE*C1_COEFF(3) + &
iVar%t*(FOUR*C1_COEFF(4) + &
iVar%t*FIVE*C1_COEFF(5)))) ) * c1_AD
! High frequency permittivity
! ---------------------------
! Compute the adjoint of the high-frequency permittivity
! temperature polynomial. Eqn.(4) in reference
Temperature_AD = Temperature_AD + (B1_COEFF(1) + iVar%t*(TWO*B1_COEFF(2) + &
iVar%t*(THREE*B1_COEFF(3) + &
iVar%t*(FOUR*B1_COEFF(4) + &
iVar%t*FIVE*B1_COEFF(5)))) ) * einf_AD
! Static permittivity
! -------------------
! Compute the adjoint of the salinity
! dependent static permittivity
Salinity_AD = Salinity_AD - iVar%a2*es_AD
a2_AD = -iVar%s * es_AD
a1_AD = es_AD
es_AD = ZERO
! Compute the adjoint of the static permittivity
! temperature polynomials. Eqn.(3) in reference.
Temperature_AD = Temperature_AD + (A2_COEFF(1) + iVar%t*(TWO*A2_COEFF(2) + &
iVar%t*(THREE*A2_COEFF(3) + &
iVar%t*(FOUR*A2_COEFF(4) + &
iVar%t*FIVE*A2_COEFF(5)))) ) * a2_AD
Temperature_AD = Temperature_AD + (A1_COEFF(1) + iVar%t*(TWO*A1_COEFF(2) + &
iVar%t*(THREE*A1_COEFF(3) + &
iVar%t*(FOUR*A1_COEFF(4) + &
iVar%t*FIVE*A1_COEFF(5)))) ) * a1_AD
! Conductivity
! ------------
! Compute the adjoint of the salinity
! dependent conductivity
Salinity_AD = Salinity_AD + iVar%d2*sigma_AD
d2_AD = iVar%s * sigma_AD
d1_AD = sigma_AD
sigma_AD = ZERO
! Compute the adjoint of the conductivity
! temperature polynomials. Eqn.(1) in reference
Temperature_AD = Temperature_AD + (D2_COEFF(1) + iVar%t*TWO*D2_COEFF(2)) * d2_AD
Temperature_AD = Temperature_AD + (D1_COEFF(1) + iVar%t*TWO*D1_COEFF(2)) * d1_AD
END SUBROUTINE Guillou_Ocean_Permittivity_AD
END MODULE Guillou