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L_Band_wind_emissivity_AQV5_module.f90
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L_Band_wind_emissivity_AQV5_module.f90
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! RSS L-band wind emissivity
! based on Aquarius V5 release
! written by T. Meissner, RSS, September 29, 2018
!
! References:
! 1. Meissner, T.; F. Wentz and D. Le Vine, Aquarius Salinity Retrieval Algorithm Theoretical Basis Document (ATBD),
! End of Mission Version; RSS Technical Report 120117; December 1, 2017;
! Available online at ftp://podaac-ftp.jpl.nasa.gov/allData/aquarius/docs/v5/AQ-014-PS-0017_Aquarius_ATBD-EndOfMission.pdf.
!
! 2. Meissner, T, F. Wentz, and D, Le Vine, 2018,
! The Salinity Retrieval Algorithms for the NASA Aquarius Version 5 and SMAP Version 3 Releases,
! Remote Sensing 10, 1121, doi:10.3390/rs10071121.
!
! 3. Meissner, T. and F. Wentz, The complex dielectric constant of pure and sea water from microwave satellite observations,
! IEEE TGRS, 2004, 42(9), 1836 – 1849, doi:10.1109/TGRS.2004.831888.
!
! 4. Meissner, T. and F. Wentz, The emissivity of the ocean surface between 6 and 90 GHz
! over a large range of wind speeds and Earth incidence angles,
! IEEE TGRS, 2012, 50(8), 3004 – 3026, doi: 10.1109/TGRS.2011.2179662.
!
! 5. Meissner, T., F. Wentz, F. and L. Ricciardulli, The emission and scattering of L-band microwave radiation
! from rough ocean surfaces and wind speed measurements from Aquarius,
! J. Geophys. Res. Oceans, 2014, 119, doi:10.1002/2014JC009837.
!
module L_Band_wind_emissivity_AQV5_module
implicit none
private
save
integer(4), parameter :: n_rad=3
real(4), parameter :: sst_ref0=20.0, sss_ref0=35.0, freq_aq=1.413, wcasp=11.0, wextrapol=17.0, teff=290.
real(4), parameter, dimension(n_rad) :: tht_ref = (/29.36, 38.44, 46.29/)
real(4), parameter :: kappascale=1.4 ! empirical scale factor for delta form factor
! input tables
character(len=200), parameter :: emiss_coeff_harm_file = &
'\\Thomas\C\AQUARIUS\surface_roughness\tables\V_may_2013\coeffs\deW_harm_coeffs_V9A_MI.dat'
character(len=200), parameter :: delta_file = '\\Thomas\C\AQUARIUS\V5.0\DTB_SST_WSPD\TABLES\delta_EW_V5_B.dat'
integer(4), parameter :: iu=3
public :: find_demiss_rough_LBAND
contains
subroutine find_demiss_rough_LBAND (wspd, sst, tht, demiss_rough)
! roughness correction
! Aquarius V5.0
! interpolate/extrapolate EIA
implicit none
real(4), intent(in) :: wspd ! [m/s]
real(4), intent(in) :: sst ! SST [Celsius]
real(4), intent(in) :: tht ! Earth Incidence Angle [deg]
real(4), intent(out), dimension(2) :: demiss_rough
! isotropic part of wind induced surface emissivity [*290K]
real(4), dimension(2) :: dew_0, dew_1
integer(4) :: irad_0,irad_1
real(4) :: brief
real(4), dimension(2) :: yy
real(4), dimension(0:n_rad) :: thtfix
thtfix(1:3) = tht_ref(1:3)
thtfix(0) = 0.0
if (tht<tht_ref(1)) then
irad_0 = 0
irad_1 = 1
call find_demiss_rough_wspd_AQV5 (1, wspd, sst, dew_1)
dew_0(1) = (dew_1(1)+dew_1(2))/2.0 ! (V+H)/2 at nadir
dew_0(2) = (dew_1(1)+dew_1(2))/2.0 ! (V+H)/2 at nadir
else if (tht>=tht_ref(1) .and. tht<tht_ref(2)) then
irad_0 = 1
irad_1 = 2
call find_demiss_rough_wspd_AQV5 (1, wspd, sst, dew_0)
call find_demiss_rough_wspd_AQV5 (2, wspd, sst, dew_1)
else
irad_0 = 2
irad_1 = 3
call find_demiss_rough_wspd_AQV5 (2, wspd, sst, dew_0)
call find_demiss_rough_wspd_AQV5 (3, wspd, sst, dew_1)
endif
brief = (tht-thtfix(irad_0))/(thtfix(irad_1)-thtfix(irad_0))
! linear interpolation/extrapolation to/form Aquarius EIA
yy = dew_0*(1.0-brief) + dew_1*brief
demiss_rough = yy
return
end subroutine find_demiss_rough_LBAND
! Aquarius V5.0
subroutine fd_TM_emiss_harmonics(irad,wspd, aharm, daharm)
implicit none
integer(4), intent(in) :: irad
real(4), intent(in) :: wspd
real(4), dimension(0:2,2), intent(out) :: aharm(0:2,2) !1=V, 2=H
real(4), dimension(0:2,2), intent(out), optional :: daharm(0:2,2) !1=V, 2=H
integer(4), parameter :: n_rad=3, npoly=5
real(4), dimension(2) :: A0, A1, A2 !1=V, 2=H
real(4), dimension(2) :: dA0, dA1, dA2 !1=V, 2=H
real(4) :: ww
integer(4) :: ipol, iharm
real(4) :: fval, dval
real(4) :: w0, w1, w2 ! linear extrapolation/cutoff points
integer(4), save :: istart=1
real(8), dimension(0:2,2,n_rad,npoly), save :: acoef ! harmonic coefficients for radiometer wind direction signal
real(8), dimension(0:2,2,n_rad), save :: wspd_max_a ! high wind speed for radiometer wind speed signal
if (istart==1) then
istart=0
open(unit=3,file=emiss_coeff_harm_file, form='binary', action='read', status='old')
read(3) acoef
read(3) wspd_max_a
! overwrite
wspd_max_a = wextrapol
close(3)
endif
A0=0.0
A1=0.0
A2=0.0
do ipol=1,2
! A0
iharm=0
w0 = wspd_max_a(iharm,ipol,irad)
ww = wspd
if (wspd >= w0) ww=w0 ! extrapolation at w0
fval = &
ww*acoef(iharm,ipol,irad,1) + (ww**2)*acoef(iharm,ipol,irad,2) + (ww**3)*acoef(iharm,ipol,irad,3) + (ww**4)*acoef(iharm,ipol,irad,4) + (ww**5)*acoef(iharm,ipol,irad,5)
dval = &
acoef(iharm,ipol,irad,1) + (2.0*ww)*acoef(iharm,ipol,irad,2) + (3.0*(ww**2))*acoef(iharm,ipol,irad,3) + (4.0*(ww**3))*acoef(iharm,ipol,irad,4) + (5.0*(ww**4))*acoef(iharm,ipol,irad,5)
if (wspd<=w0) then
A0(ipol) = fval
else
A0(ipol) = fval + dval*(wspd-w0)
endif
dA0(ipol) = dval
! A1
iharm=1
w1 = wspd_max_a(iharm,ipol,irad)
ww = wspd
if (wspd >= w1) ww=w1 ! cutoff at w1
fval = ww*acoef(iharm,ipol,irad,1) + (ww**2) *acoef(iharm,ipol,irad,2) + (ww**3)*acoef(iharm,ipol,irad,3) + (ww**4)*acoef(iharm,ipol,irad,4) + (ww**5)*acoef(iharm,ipol,irad,5)
dval = acoef(iharm,ipol,irad,1) + (2.0*ww)*acoef(iharm,ipol,irad,2) + (3.0*(ww**2))*acoef(iharm,ipol,irad,3) + (4.0*(ww**3))*acoef(iharm,ipol,irad,4) + (5.0*(ww**4))*acoef(iharm,ipol,irad,5)
A1(ipol) = fval
dA1(ipol) = dval
! A2
iharm=2
w2 = wspd_max_a(iharm,ipol,irad)
ww = wspd
if (wspd >= w2) ww=w2 ! cutoff at w2
fval = ww*acoef(iharm,ipol,irad,1) + (ww**2) *acoef(iharm,ipol,irad,2) + (ww**3)*acoef(iharm,ipol,irad,3) + (ww**4)*acoef(iharm,ipol,irad,4) + (ww**5)*acoef(iharm,ipol,irad,5)
dval = acoef(iharm,ipol,irad,1) + (2.0*ww) *acoef(iharm,ipol,irad,2) + (3.0*(ww**2))*acoef(iharm,ipol,irad,3) + (4.0*(ww**3))*acoef(iharm,ipol,irad,4) + (5.0*(ww**4))*acoef(iharm,ipol,irad,5)
A2(ipol) = fval
dA2(ipol) = dval
enddo !ipol
do ipol=1,2
aharm(0,ipol) = A0(ipol)
aharm(1,ipol) = A1(ipol)
aharm(2,ipol) = A2(ipol)
enddo
if (present(daharm)) then
do ipol=1,2
daharm(0,ipol) = dA0(ipol)
daharm(1,ipol) = dA1(ipol)
daharm(2,ipol) = dA2(ipol)
enddo
endif
return
end subroutine fd_TM_emiss_harmonics
subroutine find_demiss_rough_AQV5 (irad, wspd, phir, sst, demiss_rough)
! full roughness correction
implicit none
integer(4), intent(in) :: irad
real(4), intent(in) :: wspd ! [m/s]
real(4), intent(in) :: phir ! [deg] relative wind direction
real(4), intent(in) :: sst ! Celsius
real(4), intent(out), dimension(2) :: demiss_rough ! [*290K]
real(4) :: xsst, xwspd, xtht
real(4), dimension(2) :: dew_1, dew_2, xem0, yem0
real(4), dimension(0:2,2) :: aharm !1=V, 2=H
real(4), dimension(0:2,2) :: daharm !1=V, 2=H
real(4), dimension(2) :: delta
integer(4) :: ipol
integer(4) :: ksst1, ksst2
real(4) :: x1, x2, brief, y1, y2
integer(4), parameter :: msst=35, n_rad=3
integer(4), save :: istart=1
real(4), dimension(2,msst,n_rad), save :: dtab
real(4), parameter :: sst_step=1.0, sst0=0.0, sstmax=30.0, wmax=wcasp
if (istart==1) then
istart=0
open(unit=3,form='binary',file=delta_file,action='read',status='old')
read(3) dtab
close(3)
endif
call fd_TM_emiss_harmonics(irad,wspd, aharm, daharm)
if (phir > -900.) then
dew_1(1:2) = aharm(0,1:2) + aharm(1,1:2)*cosd(phir) + aharm(2,1:2)*cosd(2.0*phir) ! *290K
else
dew_1(1:2) = aharm(0,1:2)
endif
xtht=tht_ref(irad)
call fdem0_meissner_wentz(freq_aq,xtht,sst, sss_ref0, xem0)
call fdem0_meissner_wentz(freq_aq,xtht,sst_ref0,sss_ref0, yem0)
! sst adjustment
xsst=sst
if (xsst<sst0+sst_step/2) xsst=sst0+sst_step/2
if (xsst>sstmax) xsst=sstmax
xwspd=wspd
if (xwspd<0.0) xwspd=0.0
if (xwspd>wmax) xwspd=wmax
call fd_TM_emiss_harmonics(irad,xwspd, aharm, daharm)
if (phir > -900.) then
dew_2(1:2) = aharm(0,1:2) + aharm(1,1:2)*cosd(phir) + aharm(2,1:2)*cosd(2.0*phir) ! *290K
else
dew_2(1:2) = aharm(0,1:2)
endif
! *290K dew_2 = dew_1 below wmax. above wmax it is kept constant
ksst1 = floor((xsst - (sst0+sst_step/2))/sst_step) + 1
if (ksst1< 1) ksst1 = 1
if (ksst1> msst-1) ksst1 = msst-1
ksst2 = ksst1 + 1
do ipol=1,2
x1 = sst0 + (ksst1-1)*sst_step + sst_step/2
x2 = x1 + sst_step
brief = (xsst-x1)/sst_step
y1 = dtab(ipol,ksst1,irad)
y2 = dtab(ipol,ksst2,irad)
delta(ipol) = y1*(1.0-brief) + y2*brief
enddo ! ipol
! total roughness correction
do ipol=1,2
demiss_rough(ipol) = dew_1(ipol)*(xem0(ipol)/yem0(ipol)) + kappascale*delta(ipol)*dew_2(ipol)
enddo
return
end subroutine find_demiss_rough_AQV5
subroutine find_demiss_rough_wspd_AQV5 (irad, wspd, sst, demiss_rough)
! isotropic part of roughness correction
implicit none
integer(4), intent(in) :: irad
real(4), intent(in) :: wspd ! [m/s]
real(4), intent(in) :: sst ! Celsius
real(4), intent(out), dimension(2) :: demiss_rough ! [*290K]
real(4) :: xsst, xwspd, xtht
real(4), dimension(2) :: dew_1, dew_2, xem0, yem0
real(4), dimension(0:2,2) :: aharm !1=V, 2=H
real(4), dimension(0:2,2) :: daharm !1=V, 2=H
real(4), dimension(2) :: delta
integer(4) :: ipol
integer(4) :: ksst1, ksst2
real(4) :: x1, x2, brief, y1, y2
integer(4), parameter :: msst=35, n_rad=3
integer(4), save :: istart=1
real(4), dimension(2,msst,n_rad), save :: dtab
real(4), parameter :: sst_step=1.0, sst0=0.0, sstmax=30.0, wmax=wcasp
if (istart==1) then
istart=0
open(unit=3,form='binary',file=delta_file,action='read',status='old')
read(3) dtab
close(3)
endif
call fd_TM_emiss_harmonics(irad,wspd, aharm, daharm)
dew_1(1:2) = aharm(0,1:2) ! *290K
xtht=tht_ref(irad)
call fdem0_meissner_wentz(freq_aq,xtht,sst, sss_ref0, xem0)
call fdem0_meissner_wentz(freq_aq,xtht,sst_ref0,sss_ref0, yem0)
! sst adjustment
xsst=sst
if (xsst<sst0+sst_step/2) xsst=sst0+sst_step/2
if (xsst>sstmax) xsst=sstmax
xwspd=wspd
if (xwspd<0.0) xwspd=0.0
if (xwspd>wmax) xwspd=wmax
call fd_TM_emiss_harmonics(irad,xwspd, aharm, daharm)
dew_2(1:2) = aharm(0,1:2) ! *290K
! *290K dew_2 = dew_1 below wmax. above wmax it is kept constant
ksst1 = floor((xsst - (sst0+sst_step/2))/sst_step) + 1
if (ksst1< 1) ksst1 = 1
if (ksst1> msst-1) ksst1 = msst-1
ksst2 = ksst1 + 1
do ipol=1,2
x1 = sst0 + (ksst1-1)*sst_step + sst_step/2
x2 = x1 + sst_step
brief = (xsst-x1)/sst_step
y1 = dtab(ipol,ksst1,irad)
y2 = dtab(ipol,ksst2,irad)
delta(ipol) = y1*(1.0-brief) + y2*brief
enddo ! ipol
! total roughness correction
do ipol=1,2
demiss_rough(ipol) = dew_1(ipol)*(xem0(ipol)/yem0(ipol)) + kappascale*delta(ipol)*dew_2(ipol)
enddo
return
end subroutine find_demiss_rough_wspd_AQV5
subroutine fdem0_meissner_wentz(freq,tht,sst,salinity, em0)
! input:
! name parameter unit range
!
! freq frequency [GHz] >0
! tht EIA [deg] [0, 90[
! sst SST [C] -25 c to 40 c for pure water
! -2 c to 34 c for saline water
! salinity salinity [ppt] 0 to 40
!
! output:
! EM0 specular emissivity [0,1]
! 2-dimesnional vector, 1=v-pol, 2=h-pol
implicit none
real(4), intent(in) :: freq,tht,sst,salinity
real(4), dimension(2), intent(out) :: em0
real(4), parameter :: f0=17.97510
real(4) :: costht,sinsqtht
real(4) :: e0s,e1s,e2s,n1s,n2s,sig
complex(4) :: permit,esqrt,rh,rv
complex(4), parameter :: j=(0.,1.)
call dielectric_meissner_wentz(sst,salinity, e0s,e1s,e2s,n1s,n2s,sig)
costht=cosd(tht)
sinsqtht=1.-costht*costht
! debye law (2 relaxation wavelengths)
permit = (e0s - e1s)/(1.0 - j*(freq/n1s)) + (e1s - e2s)/(1.0 - j*(freq/n2s)) + e2s + j*sig*f0/freq
permit = conjg(permit)
esqrt=csqrt(permit-sinsqtht)
rh=(costht-esqrt)/(costht+esqrt)
rv=(permit*costht-esqrt)/(permit*costht+esqrt)
em0(1) =1.-rv*conjg(rv)
em0(2) =1.-rh*conjg(rh)
return
end subroutine fdem0_meissner_wentz
subroutine fdpermit_meissner_wentz(freq,sst,salinity, permit)
! input:
! name parameter unit range
!
! freq frequency [GHz] >0
! tht EIA [deg] [0, 90[
! sst SST [C] -25 c to 40 c for pure water
! -2 c to 34 c for saline water
! salinity salinity [ppt] 0 to 40
!
! output:
! permit permittivity
! (negative imaginary part to be consistent with wentz1 convention)
implicit none
real(4), intent(in) :: freq,sst,salinity
complex(4), intent(out) :: permit
real(4), parameter :: f0=17.97510
real(4) :: e0s,e1s,e2s,n1s,n2s,sig
complex(4), parameter :: j=(0.,1.)
call dielectric_meissner_wentz(sst,salinity, e0s,e1s,e2s,n1s,n2s,sig)
! debye law (2 relaxation wavelengths)
permit = (e0s - e1s)/(1.0 - j*(freq/n1s)) + (e1s - e2s)/(1.0 - j*(freq/n2s)) + e2s + j*sig*f0/freq
permit = conjg(permit)
return
end subroutine fdpermit_meissner_wentz
subroutine dielectric_meissner_wentz(sst_in,s, e0s,e1s,e2s,n1s,n2s,sig)
!
! complex dielectric constant: eps
! [MW 2004, MW 2012].
! References:
! [MW 2004]: T. Meissner and F. J. Wentz,
! "The complex dielectric constant of pure and sea water from microwave satellite observations,"
! IEEE Trans. Geosci. Remote Sens., vol. 42, no.9, pp 1836 – 1849, 2004.
!
! [MW 2012]: T. Meissner and F. J. Wentz,
! "The Emissivity of the Ocean Surface between 6 – 90 GHz over a Large Range of Wind Speeds and Earth Incidence Angles,"
! IEEE Trans. Geosci. Remote Sens., vol. 50, no.8, pp 3004 - 3026, 2012.
!
! Changes from [MW 2012]:
! 1. Typo (sign) in the printed version of coefficient d3 in Table 7. Its value should be -0.35594E-06.
! 2. Changed SST behavior of coefficient b2 from:
! b2 = 1.0 + s*(z(10) + z(11)*sst) to
! b2 = 1.0 + s*(z(10) + 0.5*z(11)*(sst + 30))
!
!!
! input:
! name parameter unit range
! sst sst [c] -25 c to 40 c for pure water
! -2 c to 34 c for saline water
! s salinity [ppt] 0 to 40
!
! output:
! Debye pparameters: e0s,e1s,e2s,n1s,n2s,sig
! The permittivity can be calculated in the subroutine: fdpermit_meissner_wentz
implicit none
real(4), intent(in) :: sst_in,s
real(4), intent(out) :: e0s,e1s,e2s,n1s,n2s,sig
real(4), dimension(11), parameter :: &
x=(/ 5.7230e+00, 2.2379e-02, -7.1237e-04, 5.0478e+00, -7.0315e-02, 6.0059e-04, 3.6143e+00, &
2.8841e-02, 1.3652e-01, 1.4825e-03, 2.4166e-04 /)
real(4), dimension(13), parameter :: &
z=(/ -3.56417e-03, 4.74868e-06, 1.15574e-05, 2.39357e-03, -3.13530e-05, &
2.52477e-07, -6.28908e-03, 1.76032e-04, -9.22144e-05, -1.99723e-02, &
1.81176e-04, -2.04265e-03, 1.57883e-04 /) ! 2004
real(4), dimension(3), parameter :: a0coef=(/ -0.33330E-02, 4.74868e-06, 0.0e+00/)
real(4), dimension(5), parameter :: b1coef=(/0.23232E-02, -0.79208E-04, 0.36764E-05, -0.35594E-06, 0.89795E-08/)
real(4) :: e0,e1,e2,n1,n2
real(4) :: a0,a1,a2,b1,b2
real(4) :: sig35,r15,rtr15,alpha0,alpha1
real(4) :: sst,sst2,sst3,sst4,s2
sst=sst_in
if(sst.lt.-30.16) sst=-30.16 !protects against n1 and n2 going zero for very cold water
sst2=sst*sst
sst3=sst2*sst
sst4=sst3*sst
s2=s*s
! pure water
e0 = (3.70886e4 - 8.2168e1*sst)/(4.21854e2 + sst) ! stogryn et al.
e1 = x(1) + x(2)*sst + x(3)*sst2
n1 = (45.00 + sst)/(x(4) + x(5)*sst + x(6)*sst2)
e2 = x(7) + x(8)*sst
n2 = (45.00 + sst)/(x(9) + x(10)*sst + x(11)*sst2)
! saline water
! conductivity [s/m] taken from stogryn et al.
sig35 = 2.903602 + 8.60700e-2*sst + 4.738817e-4*sst2 - 2.9910e-6*sst3 + 4.3047e-9*sst4
r15 = s*(37.5109+5.45216*s+1.4409e-2*s2)/(1004.75+182.283*s+s2)
alpha0 = (6.9431+3.2841*s-9.9486e-2*s2)/(84.850+69.024*s+s2)
alpha1 = 49.843 - 0.2276*s + 0.198e-2*s2
rtr15 = 1.0 + (sst-15.0)*alpha0/(alpha1+sst)
sig = sig35*r15*rtr15
! permittivity
a0 = exp(a0coef(1)*s + a0coef(2)*s2 + a0coef(3)*s*sst)
e0s = a0*e0
if(sst.le.30) then
b1 = 1.0 + s*(b1coef(1) + b1coef(2)*sst + b1coef(3)*sst2 + b1coef(4)*sst3 + b1coef(5)*sst4)
else
b1 = 1.0 + s*(9.1873715e-04 + 1.5012396e-04*(sst-30))
endif
n1s = n1*b1
a1 = exp(z(7)*s + z(8)*s2 + z(9)*s*sst)
e1s = e1*a1
! b2 = 1.0 + s*(z(10) + z(11)*sst)
b2 = 1.0 + s*(z(10) + 0.5*z(11)*(sst + 30))
n2s = n2*b2
a2 = 1.0 + s*(z(12) + z(13)*sst)
e2s = e2*a2
return
end subroutine dielectric_meissner_wentz
end module L_Band_wind_emissivity_AQV5_module