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msis_gfn.F90
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!#######################################################################
! MSIS® (NRL-SOF-014-1) SOFTWARE
! NRLMSIS® empirical atmospheric model software. Use is governed by the
! Open Source Academic Research License Agreement contained in the file
! nrlmsis2.1_license.txt, which is part of this software package. BY
! USING OR MODIFYING THIS SOFTWARE, YOU ARE AGREEING TO THE TERMS AND
! CONDITIONS OF THE LICENSE.
!#######################################################################
!!! ===========================================================================
!!! NRLMSIS 2.1:
!!! Neutral atmosphere empirical model from the surface to lower exosphere
!!! ===========================================================================
!**************************************************************************************************
! MSIS_GFN Module: Contains subroutines to calculate global (horizontal and time-dependent) model
! basis functions
!**************************************************************************************************
module msis_gfn
use msis_constants, only : rp, maxn
use msis_init, only : TN,PR,N2,O2,O1,HE,H1,AR,N1,OA,NO, swg
implicit none
real(kind=rp) :: plg(0:maxn,0:maxn)
real(kind=rp) :: cdoy(2), sdoy(2)
real(kind=rp) :: clst(3), slst(3)
real(kind=rp) :: clon(2), slon(2)
real(kind=rp) :: sfluxavgref = 150.0 ! Reference F10.7 value (=150 in NRLMSISE-00)
real(kind=rp) :: sfluxavg_quad_cutoff = 150.0 ! Cutoff F10.7 for truncated quadratic F10.7a function
real(kind=rp) :: lastlat = -999.9
real(kind=rp) :: lastdoy = -999.9
real(kind=rp) :: lastlst = -999.9
real(kind=rp) :: lastlon = -999.9
contains
!==================================================================================================
! GLOBE: Calculate horizontal and time-dependent basis functions
! (Same purpose as NRLMSISE-00 "GLOBE7" subroutine)
!==================================================================================================
subroutine globe(doy,utsec,lat,lon,sfluxavg,sflux,ap,bf)
use msis_constants, only : deg2rad, doy2rad, lst2rad, &
maxnbf, mbf, maxn, amaxn, amaxs, tmaxl, tmaxn, tmaxs, pmaxm, pmaxn, pmaxs, &
nsfx, nsfxmod, ctimeind, cintann, ctide, cspw, csfx, cextra, cnonlin, csfxmod, cmag, cut
implicit none
real(kind=rp), intent(in) :: doy ! Day of year
real(kind=rp), intent(in) :: utsec ! Universal time in seconds
real(kind=rp), intent(in) :: lat ! Latitude
real(kind=rp), intent(in) :: lon ! Longitdue
real(kind=rp), intent(in) :: sfluxavg ! 81-day average F10.7
real(kind=rp), intent(in) :: sflux ! Daily F10.7
real(kind=rp), intent(in) :: ap(1:7) ! Ap geomagnetic activity index history array
real(kind=rp), intent(out) :: bf(0:maxnbf-1) ! Output array of basis function terms
real(kind=rp) :: lst
real(kind=rp) :: slat, clat, clat2, clat4, slat2
real(kind=rp) :: cosdoy, sindoy
real(kind=rp) :: coslon, sinlon
real(kind=rp) :: pl
real(kind=rp) :: coslst, sinlst
real(kind=rp) :: dfa, df
real(kind=rp) :: theta
real(kind=rp) :: sza
integer :: n, m, l, s, c
! Associated Legendre polynomials
if (lat .ne. lastlat) then
clat = sin(lat*deg2rad) ! clat <=> sin, Legendre polyomial defined in colat
slat = cos(lat*deg2rad) ! slat <=> cos, Legendre polyomial defined in colat
clat2 = clat*clat
clat4 = clat2*clat2
slat2 = slat*slat
plg(0,0) = 1.0_rp
plg(1,0) = clat
plg(2,0) = 0.5_rp * (3.0_rp * clat2 - 1.0_rp)
plg(3,0) = 0.5_rp * (5.0_rp * clat * clat2 - 3.0_rp * clat)
plg(4,0) = (35.0_rp * clat4 - 30.0_rp * clat2 + 3.0_rp)/8.0_rp
plg(5,0) = (63.0_rp * clat2 * clat2 * clat - 70.0_rp * clat2 * clat + 15.0_rp * clat)/8.0_rp
plg(6,0) = (11.0_rp * clat * plg(5, 0) - 5.0_rp * plg(4, 0))/6.0_rp
plg(1,1) = slat
plg(2,1) = 3.0_rp * clat * slat
plg(3,1) = 1.5_rp * (5.0_rp * clat2 - 1.0_rp) * slat
plg(4,1) = 2.5_rp * (7.0_rp * clat2 * clat - 3.0_rp * clat) * slat
plg(5,1) = 1.875_rp * (21.0_rp * clat4 - 14.0_rp * clat2 + 1.0_rp) * slat
plg(6,1) = (11.0_rp * clat * plg(5, 1) - 6.0_rp * plg(4, 1))/5.0_rp
plg(2,2) = 3.0_rp * slat2
plg(3,2) = 15.0_rp * slat2 * clat
plg(4,2) = 7.5_rp * (7.0_rp * clat2 - 1.0_rp) * slat2
plg(5,2) = 3.0_rp * clat * plg(4, 2) - 2.0_rp * plg(3, 2)
plg(6,2) = (11.0_rp * clat * plg(5, 2) - 7.0_rp * plg(4, 2))/4.0_rp
plg(3,3) = 15.0_rp * slat2 * slat
plg(4,3) = 105.0_rp * slat2 * slat * clat
plg(5,3) = (9.0_rp * clat * plg(4, 3) - 7.0_rp * plg(3, 3))/2.0_rp
plg(6,3) = (11.0_rp * clat * plg(5, 3) - 8.0_rp * plg(4, 3))/3.0_rp
lastlat = lat
endif
! Fourier harmonics of day of year
if (doy .ne. lastdoy) then
cdoy(1) = cos(doy2rad*doy)
sdoy(1) = sin(doy2rad*doy)
cdoy(2) = cos(doy2rad*doy*2.0_rp)
sdoy(2) = sin(doy2rad*doy*2.0_rp)
lastdoy = doy
endif
! Fourier harmonics of local time
lst = mod(utsec/3600.0_rp + lon/15.0_rp + 24.0_rp, 24.0_rp)
if (lst .ne. lastlst) then
clst(1) = cos(lst2rad*lst)
slst(1) = sin(lst2rad*lst)
clst(2) = cos(lst2rad*lst*2.0_rp)
slst(2) = sin(lst2rad*lst*2.0_rp)
clst(3) = cos(lst2rad*lst*3.0_rp)
slst(3) = sin(lst2rad*lst*3.0_rp)
lastlst = lst
endif
! Fourier harmonics of longitude
if (lon .ne. lastlon) then
clon(1) = cos(deg2rad*lon)
slon(1) = sin(deg2rad*lon)
clon(2) = cos(deg2rad*lon*2.0_rp)
slon(2) = sin(deg2rad*lon*2.0_rp)
lastlon = lon
endif
!---------------------------------------------
! Coupled Linear Terms
!---------------------------------------------
! Reset basis functions
bf(:) = 0.0_rp
! Time-independent (pure latitude dependence)
c = ctimeind
do n = 0, amaxn
bf(c) = plg(n,0)
c = c + 1
enddo
! Intra-annual (annual and semiannual)
if (c .ne. cintann) stop 'problem with basis definitions'
do s = 1, amaxs
cosdoy = cdoy(s)
sindoy = sdoy(s)
do n = 0, amaxn
pl = plg(n,0)
bf(c) = pl*cosdoy
bf(c+1) = pl*sindoy
c = c + 2
enddo
enddo
! Migrating Tides (local time dependence)
if (c .ne. ctide) stop 'problem with basis definitions'
do l = 1, tmaxl
coslst = clst(l)
sinlst = slst(l)
do n = l, tmaxn
pl = plg(n,l)
bf(c) = pl*coslst
bf(c+1) = pl*sinlst
c = c + 2
enddo
! Intra-annual modulation of tides
do s = 1, tmaxs
cosdoy = cdoy(s)
sindoy = sdoy(s)
do n = l, tmaxn
pl = plg(n,l)
bf(c) = pl*coslst*cosdoy
bf(c+1) = pl*sinlst*cosdoy
bf(c+2) = pl*coslst*sindoy
bf(c+3) = pl*sinlst*sindoy
c = c + 4
enddo
enddo
enddo
! Stationary Planetary Waves (longitude dependence)
if (c .ne. cspw) stop 'problem with basis definitions'
do m = 1, pmaxm
coslon = clon(m)
sinlon = slon(m)
do n = m, pmaxn
pl = plg(n,m)
bf(c) = pl*coslon
bf(c+1) = pl*sinlon
c = c + 2
enddo
! Intra-annual modulation of SPWs
do s = 1, pmaxs
cosdoy = cdoy(s)
sindoy = sdoy(s)
do n = m, pmaxn
pl = plg(n,m)
bf(c) = pl*coslon*cosdoy
bf(c+1) = pl*sinlon*cosdoy
bf(c+2) = pl*coslon*sindoy
bf(c+3) = pl*sinlon*sindoy
c = c + 4
enddo
enddo
enddo
! Linear solar flux terms
if (c .ne. csfx) stop 'problem with basis definitions'
dfa = sfluxavg - sfluxavgref
df = sflux - sfluxavg
bf(c) = dfa
bf(c+1) = dfa*dfa
bf(c+2) = df
bf(c+3) = df*df
bf(c+4) = df*dfa
c = c + nsfx
! Additional linear terms
if (c .ne. cextra) stop 'problem with basis definitions'
sza = solzen(doy,lst,lat,lon)
bf(c) = -0.5_rp*tanh((sza-98.0_rp)/6.0_rp) !Solar zenith angle logistic function for O, H (transition width 3 deg, transition sza for horizon at ~65 km altitude)
bf(c+1) = -0.5_rp*tanh((sza-101.5_rp)/20.0_rp) !Solar zenith angle logistic function for NO (transition width 10 deg, transition sza for horizon at ~130 km altitude)
bf(c+2) = dfa*bf(c) !Solar flux modulation of logistic sza term
bf(c+3) = dfa*bf(c+1) !Solar flux modulation of logistic sza term
bf(c+4) = dfa*plg(2,0) !Solar flux modulation of P(2,0) term
bf(c+5) = dfa*plg(4,0) !Solar flux modulation of P(4,0) term
bf(c+6) = dfa*plg(0,0)*cdoy(1) !Solar flux modulation of global AO
bf(c+7) = dfa*plg(0,0)*sdoy(1) !Solar flux modulation of global AO
bf(c+8) = dfa*plg(0,0)*cdoy(2) !Solar flux modulation of global SAO
bf(c+9) = dfa*plg(0,0)*sdoy(2) !Solar flux modulation of global SAO
if (sfluxavg .le. sfluxavg_quad_cutoff) then !Quadratic F10.7a function with cutoff of quadratic term (for robust extrapolation)
bf(c+10) = dfa*dfa
else
bf(c+10) = (sfluxavg_quad_cutoff-sfluxavgref)*(2.0_rp*dfa - (sfluxavg_quad_cutoff-sfluxavgref))
endif
bf(c+11) = bf(c+10)*plg(2,0) !P(2,0) modulation of truncated quadratic F10.7a term
bf(c+12) = bf(c+10)*plg(4,0) !P(4,0) modulation of truncated quadratic F10.7a term
bf(c+13) = df*plg(2,0) !P(2,0) modulation of df --> (F10.7 - F10.7a)
bf(c+14) = df*plg(4,0) !P(4,0) modulation of df --> (F10.7 - F10.7a)
!---------------------------------------------
! Nonlinear Terms
!---------------------------------------------
c = cnonlin
! Solar flux modulation terms
if (c .ne. csfxmod) stop 'problem with basis definitions'
bf(c) = dfa
bf(c+1) = dfa*dfa
bf(c+2) = df
bf(c+3) = df*df
bf(c+4) = df*dfa
c = c + nsfxmod
! Terms needed for legacy geomagnetic activity dependence
if (c .ne. cmag) stop 'problem with basis set'
bf(c:c+6) = ap - 4.0
bf(c+8) = doy2rad*doy
bf(c+9) = lst2rad*lst
bf(c+10) = deg2rad*lon
bf(c+11) = lst2rad*utsec/3600.0
bf(c+12) = abs(lat)
c = c + 13
do m = 0,1
do n = 0,amaxn
bf(c) = plg(n,m)
c = c + 1
enddo
enddo
! Terms needed for legacy UT dependence
c = cut
bf(c) = lst2rad*utsec/3600.0
bf(c+1) = doy2rad*doy
bf(c+2) = dfa
bf(c+3) = deg2rad*lon
bf(c+4) = plg(1,0)
bf(c+5) = plg(3,0)
bf(c+6) = plg(5,0)
bf(c+7) = plg(3,2)
bf(c+8) = plg(5,2)
!---------------------------------------------
! Apply Switches
!---------------------------------------------
where(.not. swg(0:mbf)) bf(0:mbf) = 0.0_rp
return
end subroutine globe
!==================================================================================================
! SOLZEN: Calculate solar zenith angle (adapted from IRI subroutine)
!==================================================================================================
real(kind=rp) function solzen(ddd,lst,lat,lon)
use msis_constants, only : pi, deg2rad
implicit none
real(kind=rp), intent(in) :: ddd
real(kind=rp), intent(in) :: lst
real(kind=rp), intent(in) :: lat
real(kind=rp), intent(in) :: lon
real(kind=rp) :: wlon,dec
real(kind=rp) :: teqnx,tf,teqt
real(kind=rp) :: rlat,phi,cosx
real(kind=rp), parameter :: humr = pi/12.0_rp
real(kind=rp), parameter :: dumr = pi/182.5_rp
real(kind=rp), parameter :: p(5) = (/0.017203534,0.034407068,0.051610602,0.068814136,0.103221204/)
wlon = 360.0 - lon
teqnx = ddd + (lst + wlon / 15.0_rp) / 24.0_rp + 0.9369_rp
teqnx = ddd + 0.9369_rp
! Solar declination
dec = 23.256_rp * sin(p(1) * (teqnx - 82.242_rp)) + 0.381_rp * sin(p(2)*(teqnx - 44.855_rp)) &
+ 0.167_rp * sin(p(3) * (teqnx - 23.355_rp)) - 0.013_rp * sin(p(4)*(teqnx + 11.97_rp)) &
+ 0.011_rp * sin(p(5) * (teqnx - 10.410_rp)) + 0.339137_rp
dec = dec * deg2rad
! Equation of time
tf = teqnx - 0.5_rp
teqt = -7.38_rp * sin(p(1) * (tf - 4.0_rp)) - 9.87_rp * sin(p(2) * (tf + 9.0_rp)) &
+ 0.27_rp * sin(p(3) * (tf - 53.0_rp)) - 0.2_rp * cos(p(4) * (tf - 17.0_rp))
phi = humr * (lst - 12.0_rp) + teqt * deg2rad / 4.0_rp
rlat = lat * deg2rad
! Cosine of solar zenith angle
cosx = sin(rlat) * sin(dec) + cos(rlat) * cos(dec) * cos(phi)
if (abs(cosx) .gt. 1.0_rp) cosx = sign(1.0_rp,cosx)
solzen = acos(cosx) / deg2rad
return
end function solzen
!==================================================================================================
! SFLUXMOD: Legacy nonlinear modulation of intra-annual, tide, and SPW terms
!==================================================================================================
real(kind=rp) function sfluxmod(iz,gf,parmset,dffact)
use msis_constants, only : maxnbf, mbf, csfx, csfxmod
use msis_init, only : basissubset, zsfx, tsfx, psfx
implicit none
integer, intent(in) :: iz
real(kind=rp), intent(in) :: gf(0:maxnbf-1)
type(basissubset), intent(in) :: parmset
real(kind=rp), intent(in) :: dffact !Turns on or adjusts the delta-F terms added to F1 and F2 (eqns. A22b and A22c in Hedin (1987)).
real(kind=rp) :: f1, f2, f3, sum
integer :: j
! Intra-annual modulation factor
if (swg(csfxmod)) then
f1 = parmset%beta(csfxmod,iz) * gf(csfxmod) &
+ (parmset%beta(csfx+2,iz) * gf(csfxmod+2) + parmset%beta(csfx+3,iz) * gf(csfxmod+3) ) * dffact
else
f1 = 0.0_rp
endif
! Migrating tide (local time) modulation factor
if (swg(csfxmod+1)) then
f2 = parmset%beta(csfxmod+1,iz) * gf(csfxmod) &
+ (parmset%beta(csfx+2,iz) * gf(csfxmod+2) + parmset%beta(csfx+3,iz) * gf(csfxmod+3) ) * dffact
else
f2 = 0.0_rp
endif
! SPW (longitude) modulation factor
if (swg(csfxmod+2)) then
f3 = parmset%beta(csfxmod+2,iz) * gf(csfxmod)
else
f3 = 0.0_rp
endif
sum = 0.0
do j = 0, mbf
! Apply intra-annual modulation
if (zsfx(j)) then
sum = sum + parmset%beta(j,iz)*gf(j)*f1
cycle
endif
! Apply migrating tide modulation
if (tsfx(j)) then
sum = sum + parmset%beta(j,iz)*gf(j)*f2
cycle
endif
! Apply SPW modulation
if (psfx(j)) then
sum = sum + parmset%beta(j,iz)*gf(j)*f3
cycle
endif
enddo
sfluxmod = sum
return
end function sfluxmod
!==================================================================================================
! GEOMAG: Legacy nonlinear ap dependence (daily ap mode and ap history mode), including mixed
! ap/UT/Longitude terms.
! Master switch control is as follows:
! swg(cmag) .nor. swg(cmag+1) Do nothing: Return zero
! swg(cmag) .and. swg(cmag+1) Daily Ap mode
! swg(cmag) .neqv. swg(cmag+1) 3-hour ap history mode
!==================================================================================================
real(kind=rp) function geomag(p0,bf,plg)
use msis_constants, only : nmag, cmag
implicit none
real(kind=rp), intent(in) :: p0(0:nmag-1)
real(kind=rp), intent(in) :: bf(0:12)
real(kind=rp), intent(in) :: plg(0:6,0:1)
logical :: swg1(0:nmag-1) !Copy of switches
real(kind=rp) :: p(0:nmag-1) !Copy of parameters used to apply switches
real(kind=rp) :: delA, gbeta, ex, sumex, G(1:6)
integer(4) :: i
! Return zero if both master switches are off
if (.not. (swg(cmag) .or. swg(cmag+1))) then
geomag = 0.0_rp
return
endif
! Copy parameters
p = p0
swg1 = swg(cmag:cmag+nmag-1)
! Calculate function
if (swg1(0) .eqv. swg1(1)) then
! Daily Ap mode
if (p(1) .eq. 0) then !If k00s is zero, then cannot compute function
geomag = 0.0_rp
return
endif
where(.not. swg1(2:25)) p(2:25) = 0.0_rp !Apply switches
p(8) = p0(8) !Need doy phase term
delA = G0fn(bf(0),p(0),p(1))
geomag = ( p(2)*plg(0,0) + p(3)*plg(2,0) + p(4)*plg(4,0) & ! time independent
+ (p(5)*plg(1,0) + p(6)*plg(3,0) + p(7)*plg(5,0)) * cos(bf(8) - p(8)) & ! doy modulation
+ (p(9)*plg(1,1) + p(10)*plg(3,1) + p(11)*plg(5,1)) * cos(bf(9) - p(12)) & ! local time modulation
+ (1.0_rp + p(13)*plg(1,0)) * &
(p(14)*plg(2,1) + p(15)*plg(4,1) + p(16)*plg(6,1)) * cos(bf(10) - p(17)) & ! longitude effect
+ (p(18)*plg(1,1) + p(19)*plg(3,1) + p(20)*plg(5,1)) * cos(bf(10) - p(21)) * &
cos(bf(8) - p(8)) & ! longitude with doy modulaiton
+ (p(22)*plg(1,0) + p(23)*plg(3,0) + p(24)*plg(5,0)) * cos(bf(11) - p(25)) ) & ! universal time
*delA
else
! 3-hour ap history mode
if (p(28) .eq. 0) then !If beta00 is zero, then cannot compute function
geomag = 0.0
return
endif
where(.not. swg1(30:)) p(30:) = 0.0 !Apply switches
p(36) = p0(36) !Need doy phase term
gbeta = p(28)/(1 + p(29)*(45.0_rp - bf(12)))
ex = exp(-10800.0_rp*gbeta)
sumex = 1 + (1 - ex**19.0_rp) * ex**(0.5_rp) / (1 - ex)
do i = 1, 6
G(i) = G0fn(bf(i),p(26),p(27))
enddo
delA = ( G(1) &
+ ( G(2)*ex + G(3)*ex*ex + G(4)*ex**3.0_rp &
+(G(5)*ex**4.0_rp + G(6)*ex**12.0_rp)*(1-ex**8.0_rp)/(1-ex) ) ) / sumex
geomag = ( p(30)*plg(0,0) + p(31)*plg(2,0) + p(32)*plg(4,0) & ! time independent
+ (p(33)*plg(1,0) + p(34)*plg(3,0) + p(35)*plg(5,0)) * cos(bf(8) - p(36)) & ! doy modulation
+ (p(37)*plg(1,1) + p(38)*plg(3,1) + p(39)*plg(5,1)) * cos(bf(9) - p(40)) & ! local time modulation
+ (1.0_rp + p(41)*plg(1,0)) * &
(p(42)*plg(2,1) + p(43)*plg(4,1) + p(44)*plg(6,1)) * cos(bf(10) - p(45)) & ! longitude effect
+ (p(46)*plg(1,1) + p(47)*plg(3,1) + p(48)*plg(5,1)) * cos(bf(10) - p(49)) * &
cos(bf(8) - p(36)) & ! longitude with doy modulaiton
+ (p(50)*plg(1,0) + p(51)*plg(3,0) + p(52)*plg(5,0)) * cos(bf(11) - p(53)) ) & ! universal time
*delA
endif
return
contains
real(kind=rp) function G0fn(a,k00r,k00s)
real(kind=rp),intent(in) :: a, k00r, k00s
G0fn = a + (k00r - 1.0_rp) * (a + (exp(-a*k00s) - 1.0_rp)/k00s)
return
end function G0fn
end function geomag
!==================================================================================================
! UTDEP: Legacy nonlinear UT dependence
!==================================================================================================
real(kind=rp) function utdep(p0,bf)
use msis_constants, only : nut, cut
implicit none
real(kind=rp), intent(in) :: p0(0:nut-1)
real(kind=rp), intent(in) :: bf(0:8)
real(kind=rp) :: p(0:nut-1) !Copy of parameters used to apply switches
logical :: swg1(0:nut-1) !Copy of switches
!Copy parameters
p = p0
swg1 = swg(cut:cut+nut-1)
where(.not. swg1(3:nut-1)) p(3:nut-1) = 0.0 !Apply switches
! Calculate function
utdep = cos(bf(0)-p(0)) * &
(1 + p(3)*bf(4)*cos(bf(1)-p(1))) * &
(1 + p(4)*bf(2)) * (1 + p(5)*bf(4)) * &
(p(6)*bf(4) + p(7)*bf(5) + p(8)*bf(6)) + &
cos(bf(0)-p(2)+2*bf(3)) * (p(9)*bf(7) + p(10)*bf(8)) * (1 + p(11)*bf(2))
return
end function utdep
end module msis_gfn