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*** Solid Earth tides (SET) prediction (section 7.1.2 in the 2003 IERS Conventions).
*** The used syntax is mainly f77 with MIL-STD-1753 extension.
*** Author: Dennis Milbert, 2018-06-01. The code is available at:
*** http://geodesyworld.github.io/SOFTS/solid.htm and can be downloaded as:
*** wget http://geodesyworld.github.io/SOFTS/solid.for.txt -O solid.for
*** The code is based on dehanttideinel.f provided by V. Dehant, S. Mathews,
*** J. Gipson and C. Bruyninx. The latest version of dehanttideinel.f and its
*** dependent subroutines can be download from IERS conventions website as:
*** wget -r -l1 --no-parent -R "index.html*" -nH --cut-dirs=3 https://iers-conventions.obspm.fr/content/chapter7/software/dehanttideinel
*** Z. Yunjun and S. Sangha, Sep 2020: modify solid() to solid_point/grid() as subroutines.
subroutine solid_grid(iyr,imo,idy,ihh,imm,iss,
* glad0,steplat,nlat,
* glod0,steplon,nlon)
*** calculate solid earth tides (SET) for one spatial grid given the date/time
*** Arguments: iyr/imo/idy/ihh/imm/iss - int, date/time for YYYY/MM/DD/HH/MM/SS
*** glad0/glad1/steplat - float, north(Y_FIRST)/south/step(negative) in deg
*** glod0/glod1/steplon - float, west(X_FIRST) /east /step(positive) in deg
*** Returns: latitude, longitude, SET_east, SET_north, SET_up
implicit double precision(a-h,o-z)
dimension rsun(3),rmoon(3),etide(3),xsta(3)
integer iyr,imo,idy,ihh,imm,iss
integer nlat,nlon
double precision glad0,steplat
double precision glod0,steplon
!***^ leap second table limit flag
logical lflag
common/stuff/rad,pi,pi2
common/comgrs/a,e2
*** open output file
lout=1
open(lout,file='solid.txt',form='formatted',status='unknown')
write(lout,'(a)') '# program solid -- UTC version -- 2018jun01'
*** constants
pi=4.d0*datan(1.d0)
pi2=pi+pi
rad=180.d0/pi
*** grs80
a=6378137.d0
e2=6.69438002290341574957d-03
*** input section
if(iyr.lt.1901.or.iyr.gt.2099) then
write(lout,'(a,i5)') 'ERROR: year NOT in [1901-2099]:',iyr
go to 98
endif
if(imo.lt.1.or.imo.gt.12) then
write(lout,'(a,i3)') 'ERROR: month NOT in [1-12]:',imo
go to 98
endif
if(idy.lt.1.or.idy.gt.31) then
write(lout,'(a,i3)') 'ERROR: day NOT in [1-31]:',idy
go to 98
endif
if(ihh.lt.0.or.ihh.gt.23) then
write(lout,'(a,i3)') 'ERROR: hour NOT in [0-23]:',ihh
go to 98
endif
if(imm.lt.0.or.imm.gt.59) then
write(lout,'(a,i3)') 'ERROR: minute NOT in [0-59]:',imm
go to 98
endif
if(iss.lt.0.or.iss.gt.59) then
write(lout,'(a,i3)') 'ERROR: second NOT in [0-59]:',iss
go to 98
endif
if(glad0.lt.-90.d0.or.glad0.gt.90.d0) then
write(lout,'(a,G0.9)') 'ERROR: lat0 NOT in [-90,+90]:',glad0
go to 98
endif
if(glod0.lt.-360.d0.or.glod0.gt.360.d0) then
write(lout,'(a,G0.9)') 'ERROR: lon0 NOT in [-360,+360]',glod0
go to 98
endif
*** output header
glad1=glad0+nlat*steplat
glod1=glod0+nlon*steplon
write(lout,'(a,i5,2i3)') '# year, month, day =',iyr,imo,idy
write(lout,'(a,3i3)') '# hour, minute, second =',ihh,imm,iss
write(lout,'(a,4f15.9)') '# S, N, W, E =',glad1,glad0,glod0,glod1
write(lout,'(a,f15.9,i6)') '# step_lat, num_lat =',steplat,nlat
write(lout,'(a,f15.9,i6)') '# step_lon, num_lon =',steplon,nlon
*** loop over the grid
do ilat=0,nlat
do ilon=0,nlon
glad=glad0+ilat*steplat
glod=glod0+ilon*steplon
*** position of observing point (positive East)
if(glod.lt. 0.d0) glod=glod+360.d0
if(glod.ge.360.d0) glod=glod-360.d0
gla0=glad/rad
glo0=glod/rad
eht0=0.d0
call geoxyz(gla0,glo0,eht0,x0,y0,z0)
xsta(1)=x0
xsta(2)=y0
xsta(3)=z0
*** here comes the sun (and the moon) (go, tide!)
!***^ UTC time system
ihr= ihh
imn= imm
sec= iss
call civmjd(iyr,imo,idy,ihr,imn,sec,mjd,fmjd)
!***^ normalize civil time
call mjdciv(mjd,fmjd,iyr,imo,idy,ihr,imn,sec)
call setjd0(iyr,imo,idy)
!***^ false means flag not raised
!***^ mjd/fmjd in UTC
!***^ mjd/fmjd in UTC
!***^ mjd/fmjd in UTC
lflag=.false.
call sunxyz (mjd,fmjd,rsun,lflag)
call moonxyz(mjd,fmjd,rmoon,lflag)
call detide (xsta,mjd,fmjd,rsun,rmoon,etide,lflag)
xt = etide(1)
yt = etide(2)
zt = etide(3)
*** determine local geodetic horizon components (topocentric)
!***^ tide vector
call rge(gla0,glo0,ut,vt,wt,xt, yt, zt)
call mjdciv(mjd,fmjd +0.001d0/86400.d0,
* iyr,imo,idy,ihr,imn,sec-0.001d0)
!*** write output to file
write(lout,'(*(G0.9,:,", "))') glad,glod,vt,ut,wt
enddo
enddo
*** end of processing and flag for leap second
if(lflag) then
write(*,'(a)') 'Mild Warning -- time crossed leap second table'
write(*,'(a)') ' boundaries. Boundary edge value used instead'
endif
close(lout)
go to 99
98 write(*,'(a)') 'Check arguments.'
return
99 end
*-----------------------------------------------------------------------
subroutine solid_point(glad,glod,iyr,imo,idy,step_sec)
*** calculate SET at given location for one day with step_sec seconds resolution
*** Arguments: glad/glod - float, latitude/longitude in deg
*** iyr/imo/idy - int, start date/time in UTC
*** step_sec - int, time step in seconds
*** Returns: seconds, SET_east, SET_north, SET_up
implicit double precision(a-h,o-z)
dimension rsun(3),rmoon(3),etide(3),xsta(3)
double precision glad,glod
integer iyr,imo,idy
integer nloop, step_sec
double precision tdel2
!*** leap second table limit flag
logical lflag
common/stuff/rad,pi,pi2
common/comgrs/a,e2
*** open output file
lout=1
open(lout,file='solid.txt',form='formatted',status='unknown')
write(lout,'(a)') '# program solid -- UTC version -- 2018jun01'
*** constants
pi=4.d0*datan(1.d0)
pi2=pi+pi
rad=180.d0/pi
*** grs80
a=6378137.d0
e2=6.69438002290341574957d-03
*** check inputs section
if(glad.lt.-90.d0.or.glad.gt.90.d0) then
write(lout,'(a,G0.9)') 'ERROR: lat NOT in [-90,+90]:',glad
go to 98
endif
if(glod.lt.-360.d0.or.glod.gt.360.d0) then
write(lout,'(a,G0.9)') 'ERROR: lon NOT in [-360,+360]:',glod
go to 98
endif
if(iyr.lt.1901.or.iyr.gt.2099) then
write(lout,'(a,i5)') 'ERROR: year NOT in [1901-2099]:',iyr
go to 98
endif
if(imo.lt.1.or.imo.gt.12) then
write(lout,'(a,i3)') 'ERROR: month NOT in [1-12]:',imo
go to 98
endif
if(idy.lt.1.or.idy.gt.31) then
write(lout,'(a,i3)') 'ERROR: day NOT in [1-31]:',idy
go to 98
endif
*** output header
write(lout,'(a,i5,2i3)') '# year, month, day =',iyr,imo,idy
write(lout,'(a,2f15.9)') '# lat, lon =',glad,glod
*** position of observing point (positive East)
if(glod.lt. 0.d0) glod=glod+360.d0
if(glod.ge.360.d0) glod=glod-360.d0
gla0=glad/rad
glo0=glod/rad
eht0=0.d0
call geoxyz(gla0,glo0,eht0,x0,y0,z0)
xsta(1)=x0
xsta(2)=y0
xsta(3)=z0
*** here comes the sun (and the moon) (go, tide!)
!*** UTC time system
ihr= 0
imn= 0
sec=0.d0
call civmjd(iyr,imo,idy,ihr,imn,sec,mjd,fmjd)
!*** normalize civil time
call mjdciv(mjd,fmjd,iyr,imo,idy,ihr,imn,sec)
call setjd0(iyr,imo,idy)
*** loop over time
!*** tdel2=1.d0/60.d0/24.d0
!*** do iloop=0,60*24
nloop=60*60*24/step_sec
tdel2=1.d0/DFLOAT(nloop)
do iloop=0,nloop
!*** false means flag not raised
!*** mjd/fmjd in UTC
!*** mjd/fmjd in UTC
!*** mjd/fmjd in UTC
lflag=.false.
call sunxyz (mjd,fmjd,rsun,lflag)
call moonxyz(mjd,fmjd,rmoon,lflag)
call detide (xsta,mjd,fmjd,rsun,rmoon,etide,lflag)
xt = etide(1)
yt = etide(2)
zt = etide(3)
*** determine local geodetic horizon components (topocentric)
!*** tide vector
call rge(gla0,glo0,ut,vt,wt,xt, yt, zt)
call mjdciv(mjd,fmjd,iyr,imo,idy,ihr,imn,sec)
!*** write output to file
tsec=ihr*3600.d0+imn*60.d0+sec
write(lout,'((f8.1,:,", "),*(f10.6,:,", "))') tsec,vt,ut,wt
!*** update fmjd for the next round
fmjd=fmjd+tdel2
!*** force 1 sec. granularity
fmjd=(idnint(fmjd*86400.d0))/86400.d0
enddo
*** end of processing and flag of leap second
if(lflag) then
write(*,'(a)') 'Mild Warning -- time crossed leap second table'
write(*,'(a)') ' boundaries. Boundary edge value used instead'
endif
close(lout)
go to 99
98 write(*,'(a)') 'Check arguments.'
return
99 end
*@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
subroutine detide(xsta,mjd,fmjd,xsun,xmon,dxtide,lflag)
*** computation of tidal corrections of station displacements caused
*** by lunar and solar gravitational attraction
*** UTC version
*** step 1 (here general degree 2 and 3 corrections +
*** call st1idiu + call st1isem + call st1l1)
*** + step 2 (call step2diu + call step2lon + call step2idiu)
*** it has been decided that the step 3 un-correction for permanent tide
*** would *not* be applied in order to avoid jump in the reference frame
*** (this step 3 must added in order to get the mean tide station position
*** and to be conformed with the iag resolution.)
*** inputs
*** xsta(i),i=1,2,3 -- geocentric position of the station (ITRF/ECEF)
*** xsun(i),i=1,2,3 -- geoc. position of the sun (ECEF)
*** xmon(i),i=1,2,3 -- geoc. position of the moon (ECEF)
*** mjd,fmjd -- modified julian day (and fraction) (in UTC time)
****old calling sequence*****************************************************
*** dmjd -- time in mean julian date (including day fraction)
*** fhr=hr+zmin/60.+sec/3600. -- hr in the day
*** outputs
*** dxtide(i),i=1,2,3 -- displacement vector (ITRF)
*** lflag -- leap second table limit flag, false:flag not raised
*** author iers 1996 : v. dehant, s. mathews and j. gipson
*** (test between two subroutines)
*** author iers 2000 : v. dehant, c. bruyninx and s. mathews
*** (test in the bernese program by c. bruyninx)
*** created: 96/03/23 (see above)
*** modified from dehanttideinelMJD.f by Dennis Milbert 2006sep10
*** bug fix regarding fhr (changed calling sequence, too)
*** modified to reflect table 7.5a and b IERS Conventions 2003
*** modified to use TT time system to call step 2 functions
*** sign correction by V.Dehant to match eq.16b, p.81, Conventions
*** applied by Dennis Milbert 2007may05
*** UTC version by Dennis Milbert 2018june01
implicit double precision(a-h,o-z)
double precision xsta(3),xsun(3),xmon(3),dxtide(3),xcorsta(3)
double precision h20,l20,h3,l3,h2,l2
double precision mass_ratio_sun,mass_ratio_moon
logical lflag,leapflag
!*** leap second table limit flag
!*** leap second table limit flag
save /limitflag/
common/limitflag/leapflag
*** nominal second degree and third degree love numbers and shida numbers
data h20/0.6078d0/,l20/0.0847d0/,h3/0.292d0/,l3/0.015d0/
*** internal support for new calling sequence
*** first, convert UTC time into TT time (and, bring leapflag into variable)
leapflag=lflag
!*** UTC time (sec of day)
!*** TT time (sec of day)
!*** TT time (fract. day)
tsecutc =fmjd*86400.d0
tsectt =utc2ttt(tsecutc)
fmjdtt =tsectt/86400.d0
lflag = leapflag
!*** float MJD in TT
dmjdtt=mjd+fmjdtt
*** commented line was live code in dehanttideinelMJD.f
*** changed on the suggestion of Dr. Don Kim, UNB -- 09mar21
*** Julian date for 2000 January 1 00:00:00.0 UT is JD 2451544.5
*** MJD for 2000 January 1 00:00:00.0 UT is MJD 51544.0
***** t=(dmjdtt-51545.d0)/36525.d0
!*** days to centuries, TT
!*** days to centuries, TT
t=(dmjdtt-51544.d0)/36525.d0
!*** hours in the day, TT
fhr=(dmjdtt-int(dmjdtt))*24.d0
*** scalar product of station vector with sun/moon vector
call sprod(xsta,xsun,scs,rsta,rsun)
call sprod(xsta,xmon,scm,rsta,rmon)
scsun=scs/rsta/rsun
scmon=scm/rsta/rmon
*** computation of new h2 and l2
cosphi=dsqrt(xsta(1)*xsta(1) + xsta(2)*xsta(2))/rsta
h2=h20-0.0006d0*(1.d0-3.d0/2.d0*cosphi*cosphi)
l2=l20+0.0002d0*(1.d0-3.d0/2.d0*cosphi*cosphi)
*** p2-term
p2sun=3.d0*(h2/2.d0-l2)*scsun*scsun-h2/2.d0
p2mon=3.d0*(h2/2.d0-l2)*scmon*scmon-h2/2.d0
*** p3-term
p3sun=5.d0/2.d0*(h3-3.d0*l3)*scsun**3+3.d0/2.d0*(l3-h3)*scsun
p3mon=5.d0/2.d0*(h3-3.d0*l3)*scmon**3+3.d0/2.d0*(l3-h3)*scmon
*** term in direction of sun/moon vector
x2sun=3.d0*l2*scsun
x2mon=3.d0*l2*scmon
x3sun=3.d0*l3/2.d0*(5.d0*scsun*scsun-1.d0)
x3mon=3.d0*l3/2.d0*(5.d0*scmon*scmon-1.d0)
*** factors for sun/moon
mass_ratio_sun=332945.943062d0
mass_ratio_moon=0.012300034d0
re =6378136.55d0
fac2sun=mass_ratio_sun*re*(re/rsun)**3
fac2mon=mass_ratio_moon*re*(re/rmon)**3
fac3sun=fac2sun*(re/rsun)
fac3mon=fac2mon*(re/rmon)
*** total displacement
do i=1,3
dxtide(i)=fac2sun*( x2sun*xsun(i)/rsun + p2sun*xsta(i)/rsta ) +
* fac2mon*( x2mon*xmon(i)/rmon + p2mon*xsta(i)/rsta ) +
* fac3sun*( x3sun*xsun(i)/rsun + p3sun*xsta(i)/rsta ) +
* fac3mon*( x3mon*xmon(i)/rmon + p3mon*xsta(i)/rsta )
enddo
call zero_vec8(xcorsta)
*** corrections for the out-of-phase part of love numbers
*** (part h_2^(0)i and l_2^(0)i )
*** first, for the diurnal band
call st1idiu(xsta,xsun,xmon,fac2sun,fac2mon,xcorsta)
dxtide(1)=dxtide(1)+xcorsta(1)
dxtide(2)=dxtide(2)+xcorsta(2)
dxtide(3)=dxtide(3)+xcorsta(3)
*** second, for the semi-diurnal band
call st1isem(xsta,xsun,xmon,fac2sun,fac2mon,xcorsta)
dxtide(1)=dxtide(1)+xcorsta(1)
dxtide(2)=dxtide(2)+xcorsta(2)
dxtide(3)=dxtide(3)+xcorsta(3)
*** corrections for the latitude dependence of love numbers (part l^(1) )
call st1l1(xsta,xsun,xmon,fac2sun,fac2mon,xcorsta)
dxtide(1)=dxtide(1)+xcorsta(1)
dxtide(2)=dxtide(2)+xcorsta(2)
dxtide(3)=dxtide(3)+xcorsta(3)
*** consider corrections for step 2
*** corrections for the diurnal band:
*** first, we need to know the date converted in julian centuries
*** this is now handled at top of code (also convert to TT time system)
***** t=(dmjd-51545.)/36525.
***** fhr=dmjd-int(dmjd) !*** this is/was a buggy line (day vs. hr)
*** second, the diurnal band corrections,
*** (in-phase and out-of-phase frequency dependence):
call step2diu(xsta,fhr,t,xcorsta)
dxtide(1)=dxtide(1)+xcorsta(1)
dxtide(2)=dxtide(2)+xcorsta(2)
dxtide(3)=dxtide(3)+xcorsta(3)
*** corrections for the long-period band,
*** (in-phase and out-of-phase frequency dependence):
call step2lon(xsta,fhr,t,xcorsta)
dxtide(1)=dxtide(1)+xcorsta(1)
dxtide(2)=dxtide(2)+xcorsta(2)
dxtide(3)=dxtide(3)+xcorsta(3)
*** consider corrections for step 3
*-----------------------------------------------------------------------
* The code below is commented to prevent restoring deformation
* due to permanent tide. All the code above removes
* total tidal deformation with conventional Love numbers.
* The code above realizes a conventional tide free crust (i.e. ITRF).
* This does NOT conform to Resolution 16 of the 18th General Assembly
* of the IAG (1983). This resolution has not been implemented by
* the space geodesy community in general (c.f. IERS Conventions 2003).
*-----------------------------------------------------------------------
*** uncorrect for the permanent tide (only if you want mean tide system)
*** pi=3.141592654
*** sinphi=xsta(3)/rsta
*** cosphi=dsqrt(xsta(1)**2+xsta(2)**2)/rsta
*** cosla=xsta(1)/cosphi/rsta
*** sinla=xsta(2)/cosphi/rsta
*** dr=-dsqrt(5./4./pi)*h2*0.31460*(3./2.*sinphi**2-0.5)
*** dn=-dsqrt(5./4./pi)*l2*0.31460*3.*cosphi*sinphi
*** dxtide(1)=dxtide(1)-dr*cosla*cosphi+dn*cosla*sinphi
*** dxtide(2)=dxtide(2)-dr*sinla*cosphi+dn*sinla*sinphi
*** dxtide(3)=dxtide(3)-dr*sinphi -dn*cosphi
return
end
*-----------------------------------------------------------------------
subroutine st1l1(xsta,xsun,xmon,fac2sun,fac2mon,xcorsta)
*** this subroutine gives the corrections induced by the latitude dependence
*** given by l^(1) in mahtews et al (1991)
*** input: xsta,xsun,xmon,fac3sun,fac3mon
*** output: xcorsta
implicit double precision (a-h,o-z)
dimension xsta(3),xsun(3),xmon(3),xcorsta(3)
double precision l1,l1d,l1sd
data l1d/0.0012d0/,l1sd/0.0024d0/
rsta=enorm8(xsta)
sinphi=xsta(3)/rsta
cosphi=dsqrt(xsta(1)**2+xsta(2)**2)/rsta
sinla=xsta(2)/cosphi/rsta
cosla=xsta(1)/cosphi/rsta
rmon=enorm8(xmon)
rsun=enorm8(xsun)
*** for the diurnal band
l1=l1d
dnsun=-l1*sinphi**2*fac2sun*xsun(3)*(xsun(1)*cosla+xsun(2)*sinla)
* /rsun**2
dnmon=-l1*sinphi**2*fac2mon*xmon(3)*(xmon(1)*cosla+xmon(2)*sinla)
* /rmon**2
desun=l1*sinphi*(cosphi**2-sinphi**2)*fac2sun*xsun(3)*
* (xsun(1)*sinla-xsun(2)*cosla)/rsun**2
demon=l1*sinphi*(cosphi**2-sinphi**2)*fac2mon*xmon(3)*
* (xmon(1)*sinla-xmon(2)*cosla)/rmon**2
de=3.d0*(desun+demon)
dn=3.d0*(dnsun+dnmon)
xcorsta(1)=-de*sinla-dn*sinphi*cosla
xcorsta(2)= de*cosla-dn*sinphi*sinla
xcorsta(3)= dn*cosphi
*** for the semi-diurnal band
l1=l1sd
costwola=cosla**2-sinla**2
sintwola=2.d0*cosla*sinla
dnsun=-l1/2.d0*sinphi*cosphi*fac2sun*((xsun(1)**2-xsun(2)**2)*
* costwola+2.d0*xsun(1)*xsun(2)*sintwola)/rsun**2
dnmon=-l1/2.d0*sinphi*cosphi*fac2mon*((xmon(1)**2-xmon(2)**2)*
* costwola+2.d0*xmon(1)*xmon(2)*sintwola)/rmon**2
desun=-l1/2.d0*sinphi**2*cosphi*fac2sun*((xsun(1)**2-xsun(2)**2)*
* sintwola-2.d0*xsun(1)*xsun(2)*costwola)/rsun**2
demon=-l1/2.d0*sinphi**2*cosphi*fac2mon*((xmon(1)**2-xmon(2)**2)*
* sintwola-2.d0*xmon(1)*xmon(2)*costwola)/rmon**2
de=3.d0*(desun+demon)
dn=3.d0*(dnsun+dnmon)
xcorsta(1)=xcorsta(1)-de*sinla-dn*sinphi*cosla
xcorsta(2)=xcorsta(2)+de*cosla-dn*sinphi*sinla
xcorsta(3)=xcorsta(3) +dn*cosphi
return
end
*-----------------------------------------------------------------------
subroutine step2diu(xsta,fhr,t,xcorsta)
*** last change: vd 17 may 00 1:20 pm
*** these are the subroutines for the step2 of the tidal corrections.
*** they are called to account for the frequency dependence
*** of the love numbers.
implicit double precision (a-h,o-z)
double precision xsta(3),xcorsta(3),datdi(9,31)
double precision deg2rad
data deg2rad/0.017453292519943295769d0/
*** note, following table is derived from dehanttideinelMJD.f (2000oct30 16:10)
*** has minor differences from that of dehanttideinel.f (2000apr17 14:10)
*** D.M. edited to strictly follow published table 7.5a (2006aug08 13:46)
*** cf. table 7.5a of IERS conventions 2003 (TN.32, pg.82)
*** columns are s,h,p,N',ps, dR(ip),dR(op),dT(ip),dT(op)
*** units of mm
data ((datdi(i,j),i=1,9),j=1,31)/
* -3., 0., 2., 0., 0.,-0.01,-0.01, 0.0 , 0.0,
* -3., 2., 0., 0., 0.,-0.01,-0.01, 0.0 , 0.0,
* -2., 0., 1.,-1., 0.,-0.02,-0.01, 0.0 , 0.0,
*****-----------------------------------------------------------------------
****** -2., 0., 1., 0., 0.,-0.08,-0.05, 0.01,-0.02,
!*** original entry
!*** table 7.5a
* -2., 0., 1., 0., 0.,-0.08, 0.00, 0.01, 0.01,
*****-----------------------------------------------------------------------
* -2., 2.,-1., 0., 0.,-0.02,-0.01, 0.0 , 0.0,
*****-----------------------------------------------------------------------
****** -1., 0., 0.,-1., 0.,-0.10,-0.05, 0.0 ,-0.02,
!*** original entry
!*** table 7.5a
* -1., 0., 0.,-1., 0.,-0.10, 0.00, 0.00, 0.00,
*****-----------------------------------------------------------------------
****** -1., 0., 0., 0., 0.,-0.51,-0.26,-0.02,-0.12,
!*** original entry
!*** table 7.5a
* -1., 0., 0., 0., 0.,-0.51, 0.00,-0.02, 0.03,
*****-----------------------------------------------------------------------
* -1., 2., 0., 0., 0., 0.01, 0.0 , 0.0 , 0.0,
* 0.,-2., 1., 0., 0., 0.01, 0.0 , 0.0 , 0.0,
* 0., 0.,-1., 0., 0., 0.02, 0.01, 0.0 , 0.0,
*****-----------------------------------------------------------------------
****** 0., 0., 1., 0., 0., 0.06, 0.02, 0.0 , 0.01,
!*** original entry
!*** table 7.5a
* 0., 0., 1., 0., 0., 0.06, 0.00, 0.00, 0.00,
*****-----------------------------------------------------------------------
* 0., 0., 1., 1., 0., 0.01, 0.0 , 0.0 , 0.0,
* 0., 2.,-1., 0., 0., 0.01, 0.0 , 0.0 , 0.0,
!*** table 7.5a
* 1.,-3., 0., 0., 1.,-0.06, 0.00, 0.00, 0.00,
* 1.,-2., 0., 1., 0., 0.01, 0.0 , 0.0 , 0.0,
*****-----------------------------------------------------------------------
****** 1.,-2., 0., 0., 0.,-1.23,-0.05, 0.06,-0.06,
!*** original entry
!*** table 7.5a
* 1.,-2., 0., 0., 0.,-1.23,-0.07, 0.06, 0.01,
*****-----------------------------------------------------------------------
* 1.,-1., 0., 0.,-1., 0.02, 0.0 , 0.0 , 0.0,
* 1.,-1., 0., 0., 1., 0.04, 0.0 , 0.0 , 0.0,
!*** table 7.5a
* 1., 0., 0.,-1., 0.,-0.22, 0.01, 0.01, 0.00,
*****-----------------------------------------------------------------------
****** 1., 0., 0., 0., 0.,12.02,-0.45,-0.66, 0.17,
!*** original entry
!*** table 7.5a
* 1., 0., 0., 0., 0.,12.00,-0.78,-0.67,-0.03,
*****-----------------------------------------------------------------------
****** 1., 0., 0., 1., 0., 1.73,-0.07,-0.10, 0.02,
!*** original entry
!*** table 7.5a
* 1., 0., 0., 1., 0., 1.73,-0.12,-0.10, 0.00,
*****-----------------------------------------------------------------------
* 1., 0., 0., 2., 0.,-0.04, 0.0 , 0.0 , 0.0,
*****-----------------------------------------------------------------------
****** 1., 1., 0., 0.,-1.,-0.50, 0.0 , 0.03, 0.0,
!*** original entry
!*** table 7.5a
* 1., 1., 0., 0.,-1.,-0.50,-0.01, 0.03, 0.00,
*****-----------------------------------------------------------------------
* 1., 1., 0., 0., 1., 0.01, 0.0 , 0.0 , 0.0,
*****-----------------------------------------------------------------------
****** 0., 1., 0., 1.,-1.,-0.01, 0.0 , 0.0 , 0.0,
!*** original entry
!*** v.dehant 2007
* 1., 1., 0., 1.,-1.,-0.01, 0.0 , 0.0 , 0.0,
*****-----------------------------------------------------------------------
* 1., 2.,-2., 0., 0.,-0.01, 0.0 , 0.0 , 0.0,
*****-----------------------------------------------------------------------
****** 1., 2., 0., 0., 0.,-0.12, 0.01, 0.01, 0.0,
!*** original entry
!*** table 7.5a
* 1., 2., 0., 0., 0.,-0.11, 0.01, 0.01, 0.00,
*****-----------------------------------------------------------------------
* 2.,-2., 1., 0., 0.,-0.01, 0.0 , 0.0 , 0.0,
* 2., 0.,-1., 0., 0.,-0.02, 0.02, 0.0 , 0.01,
* 3., 0., 0., 0., 0., 0.0 , 0.01, 0.0 , 0.01,
* 3., 0., 0., 1., 0., 0.0 , 0.01, 0.0 , 0.0/
s=218.31664563d0+481267.88194d0*t-0.0014663889d0*t*t
* +0.00000185139d0*t**3
tau=fhr*15.d0+280.4606184d0+36000.7700536d0*t+0.00038793d0*t*t
* -0.0000000258d0*t**3-s
pr=1.396971278*t+0.000308889*t*t+0.000000021*t**3
* +0.000000007*t**4
s=s+pr
h=280.46645d0+36000.7697489d0*t+0.00030322222d0*t*t
* +0.000000020*t**3-0.00000000654*t**4
p=83.35324312d0+4069.01363525d0*t-0.01032172222d0*t*t
* -0.0000124991d0*t**3+0.00000005263d0*t**4
zns=234.95544499d0 +1934.13626197d0*t-0.00207561111d0*t*t
* -0.00000213944d0*t**3+0.00000001650d0*t**4
ps=282.93734098d0+1.71945766667d0*t+0.00045688889d0*t*t
* -0.00000001778d0*t**3-0.00000000334d0*t**4
*** reduce angles to between 0 and 360
s= dmod( s,360.d0)
tau=dmod(tau,360.d0)
h= dmod( h,360.d0)
p= dmod( p,360.d0)
zns=dmod(zns,360.d0)
ps= dmod( ps,360.d0)
rsta=dsqrt(xsta(1)**2+xsta(2)**2+xsta(3)**2)
sinphi=xsta(3)/rsta
cosphi=dsqrt(xsta(1)**2+xsta(2)**2)/rsta
cosla=xsta(1)/cosphi/rsta
sinla=xsta(2)/cosphi/rsta
zla = datan2(xsta(2),xsta(1))
do i=1,3
xcorsta(i)=0.d0
enddo
do j=1,31
thetaf=(tau+datdi(1,j)*s+datdi(2,j)*h+datdi(3,j)*p+
* datdi(4,j)*zns+datdi(5,j)*ps)*deg2rad
dr=datdi(6,j)*2.d0*sinphi*cosphi*sin(thetaf+zla)+
* datdi(7,j)*2.d0*sinphi*cosphi*cos(thetaf+zla)
dn=datdi(8,j)*(cosphi**2-sinphi**2)*sin(thetaf+zla)+
* datdi(9,j)*(cosphi**2-sinphi**2)*cos(thetaf+zla)
***** following correction by V.Dehant to match eq.16b, p.81, 2003 Conventions
***** de=datdi(8,j)*sinphi*cos(thetaf+zla)+
de=datdi(8,j)*sinphi*cos(thetaf+zla)-
* datdi(9,j)*sinphi*sin(thetaf+zla)
xcorsta(1)=xcorsta(1)+dr*cosla*cosphi-de*sinla
* -dn*sinphi*cosla
xcorsta(2)=xcorsta(2)+dr*sinla*cosphi+de*cosla
* -dn*sinphi*sinla
xcorsta(3)=xcorsta(3)+dr*sinphi+dn*cosphi
enddo
do i=1,3
xcorsta(i)=xcorsta(i)/1000.d0
enddo
return
end
*-----------------------------------------------------------------------
subroutine step2lon(xsta,fhr,t,xcorsta)
implicit double precision (a-h,o-z)
double precision deg2rad
double precision xsta(3),xcorsta(3),datdi(9,5)
data deg2rad/0.017453292519943295769d0/
*** cf. table 7.5b of IERS conventions 2003 (TN.32, pg.82)
*** columns are s,h,p,N',ps, dR(ip),dT(ip),dR(op),dT(op)
*** IERS cols.= s,h,p,N',ps, dR(ip),dR(op),dT(ip),dT(op)
*** units of mm
data ((datdi(i,j),i=1,9),j=1,5)/
* 0, 0, 0, 1, 0, 0.47, 0.23, 0.16, 0.07,
* 0, 2, 0, 0, 0, -0.20,-0.12,-0.11,-0.05,
* 1, 0,-1, 0, 0, -0.11,-0.08,-0.09,-0.04,
* 2, 0, 0, 0, 0, -0.13,-0.11,-0.15,-0.07,
* 2, 0, 0, 1, 0, -0.05,-0.05,-0.06,-0.03/
s=218.31664563d0+481267.88194d0*t-0.0014663889d0*t*t
* +0.00000185139d0*t**3
pr=1.396971278*t+0.000308889*t*t+0.000000021*t**3
* +0.000000007*t**4
s=s+pr
h=280.46645d0+36000.7697489d0*t+0.00030322222d0*t*t
* +0.000000020*t**3-0.00000000654*t**4
p=83.35324312d0+4069.01363525d0*t-0.01032172222d0*t*t
* -0.0000124991d0*t**3+0.00000005263d0*t**4
zns=234.95544499d0 +1934.13626197d0*t-0.00207561111d0*t*t
* -0.00000213944d0*t**3+0.00000001650d0*t**4
ps=282.93734098d0+1.71945766667d0*t+0.00045688889d0*t*t
* -0.00000001778d0*t**3-0.00000000334d0*t**4
rsta=dsqrt(xsta(1)**2+xsta(2)**2+xsta(3)**2)
sinphi=xsta(3)/rsta
cosphi=dsqrt(xsta(1)**2+xsta(2)**2)/rsta
cosla=xsta(1)/cosphi/rsta
sinla=xsta(2)/cosphi/rsta
*** reduce angles to between 0 and 360
s= dmod( s,360.d0)
***** tau=dmod(tau,360.d0) !*** tau not used here--09jul28
h= dmod( h,360.d0)
p= dmod( p,360.d0)
zns=dmod(zns,360.d0)
ps= dmod( ps,360.d0)
dr_tot=0.d0
dn_tot=0.d0
do i=1,3
xcorsta(i)=0.d0
enddo
*** 1 2 3 4 5 6 7 8 9
*** columns are s,h,p,N',ps, dR(ip),dT(ip),dR(op),dT(op)
do j=1,5
thetaf=(datdi(1,j)*s+datdi(2,j)*h+datdi(3,j)*p+
* datdi(4,j)*zns+datdi(5,j)*ps)*deg2rad
dr=datdi(6,j)*(3.d0*sinphi**2-1.d0)/2.*cos(thetaf)+
* datdi(8,j)*(3.d0*sinphi**2-1.d0)/2.*sin(thetaf)
dn=datdi(7,j)*(cosphi*sinphi*2.d0)*cos(thetaf)+
* datdi(9,j)*(cosphi*sinphi*2.d0)*sin(thetaf)
de=0.d0
dr_tot=dr_tot+dr
dn_tot=dn_tot+dn
xcorsta(1)=xcorsta(1)+dr*cosla*cosphi-de*sinla
* -dn*sinphi*cosla
xcorsta(2)=xcorsta(2)+dr*sinla*cosphi+de*cosla
* -dn*sinphi*sinla
xcorsta(3)=xcorsta(3)+dr*sinphi+dn*cosphi
enddo
do i=1,3
xcorsta(i)=xcorsta(i)/1000.d0
enddo
return
end
*-----------------------------------------------------------------------
subroutine st1idiu(xsta,xsun,xmon,fac2sun,fac2mon,xcorsta)
*** this subroutine gives the out-of-phase corrections induced by
*** mantle inelasticity in the diurnal band
*** input: xsta,xsun,xmon,fac2sun,fac2mon
*** output: xcorsta
implicit double precision (a-h,o-z)
dimension xsta(3),xsun(3),xmon(3),xcorsta(3)
data dhi/-0.0025d0/,dli/-0.0007d0/
rsta=enorm8(xsta)
sinphi=xsta(3)/rsta
cosphi=dsqrt(xsta(1)**2+xsta(2)**2)/rsta
cos2phi=cosphi**2-sinphi**2
sinla=xsta(2)/cosphi/rsta
cosla=xsta(1)/cosphi/rsta
rmon=enorm8(xmon)
rsun=enorm8(xsun)
drsun=-3.d0*dhi*sinphi*cosphi*fac2sun*xsun(3)*(xsun(1)*
* sinla-xsun(2)*cosla)/rsun**2
drmon=-3.d0*dhi*sinphi*cosphi*fac2mon*xmon(3)*(xmon(1)*
* sinla-xmon(2)*cosla)/rmon**2
dnsun=-3.d0*dli*cos2phi*fac2sun*xsun(3)*(xsun(1)*sinla-
* xsun(2)*cosla)/rsun**2
dnmon=-3.d0*dli*cos2phi*fac2mon*xmon(3)*(xmon(1)*sinla-
* xmon(2)*cosla)/rmon**2
desun=-3.d0*dli*sinphi*fac2sun*xsun(3)*
* (xsun(1)*cosla+xsun(2)*sinla)/rsun**2
demon=-3.d0*dli*sinphi*fac2mon*xmon(3)*
* (xmon(1)*cosla+xmon(2)*sinla)/rmon**2
dr=drsun+drmon
dn=dnsun+dnmon
de=desun+demon
xcorsta(1)=dr*cosla*cosphi-de*sinla-dn*sinphi*cosla
xcorsta(2)=dr*sinla*cosphi+de*cosla-dn*sinphi*sinla
xcorsta(3)=dr*sinphi +dn*cosphi
return
end
*-----------------------------------------------------------------------
subroutine st1isem(xsta,xsun,xmon,fac2sun,fac2mon,xcorsta)
*** this subroutine gives the out-of-phase corrections induced by
*** mantle inelasticity in the diurnal band
*** input: xsta,xsun,xmon,fac2sun,fac2mon
*** output: xcorsta
implicit double precision (a-h,o-z)
dimension xsta(3),xsun(3),xmon(3),xcorsta(3)
data dhi/-0.0022d0/,dli/-0.0007d0/
rsta=enorm8(xsta)
sinphi=xsta(3)/rsta
cosphi=dsqrt(xsta(1)**2+xsta(2)**2)/rsta
sinla=xsta(2)/cosphi/rsta
cosla=xsta(1)/cosphi/rsta
costwola=cosla**2-sinla**2
sintwola=2.d0*cosla*sinla
rmon=enorm8(xmon)
rsun=enorm8(xsun)
drsun=-3.d0/4.d0*dhi*cosphi**2*fac2sun*((xsun(1)**2-xsun(2)**2)*
* sintwola-2.*xsun(1)*xsun(2)*costwola)/rsun**2
drmon=-3.d0/4.d0*dhi*cosphi**2*fac2mon*((xmon(1)**2-xmon(2)**2)*
* sintwola-2.*xmon(1)*xmon(2)*costwola)/rmon**2
dnsun=1.5d0*dli*sinphi*cosphi*fac2sun*((xsun(1)**2-xsun(2)**2)*
* sintwola-2.d0*xsun(1)*xsun(2)*costwola)/rsun**2
dnmon=1.5d0*dli*sinphi*cosphi*fac2mon*((xmon(1)**2-xmon(2)**2)*
* sintwola-2.d0*xmon(1)*xmon(2)*costwola)/rmon**2
desun=-3.d0/2.d0*dli*cosphi*fac2sun*((xsun(1)**2-xsun(2)**2)*
* costwola+2.*xsun(1)*xsun(2)*sintwola)/rsun**2
demon=-3.d0/2.d0*dli*cosphi*fac2mon*((xmon(1)**2-xmon(2)**2)*
* costwola+2.d0*xmon(1)*xmon(2)*sintwola)/rmon**2
dr=drsun+drmon
dn=dnsun+dnmon
de=desun+demon
xcorsta(1)=dr*cosla*cosphi-de*sinla-dn*sinphi*cosla
xcorsta(2)=dr*sinla*cosphi+de*cosla-dn*sinphi*sinla
xcorsta(3)=dr*sinphi+dn*cosphi
return
end
*-----------------------------------------------------------------------
subroutine sprod(x,y,scal,r1,r2)
*** computation of the scalar-product of two vectors and their norms
*** input: x(i),i=1,2,3 -- components of vector x
*** y(i),i=1,2,3 -- components of vector y
*** output: scal -- scalar product of x and y
*** r1,r2 -- lengths of the two vectors x and y
implicit double precision (a-h,o-z)
double precision x(3),y(3)
r1=dsqrt(x(1)*x(1) + x(2)*x(2) + x(3)*x(3))
r2=dsqrt(y(1)*y(1) + y(2)*y(2) + y(3)*y(3))
scal= x(1)*y(1) + x(2)*y(2) + x(3)*y(3)
return
end
*-----------------------------------------------------------------------
double precision function enorm8(a)
*** compute euclidian norm of a vector (of length 3)
double precision a(3)
enorm8=dsqrt(a(1)*a(1) + a(2)*a(2) + a(3)*a(3))
return
end
*-----------------------------------------------------------------------
subroutine zero_vec8(v)
*** initialize a vector (of length 3) to zero
double precision v(3)
v(1)=0.d0
v(2)=0.d0
v(3)=0.d0
return
end
*@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@@
subroutine moonxyz(mjd,fmjd,rm,lflag)
*** get low-precision, geocentric coordinates for moon (ECEF)
*** UTC version
*** input: mjd/fmjd, is Modified Julian Date (and fractional) in UTC time
*** output: rm, is geocentric lunar position vector [m] in ECEF
*** lflag -- leap second table limit flag, false:flag not raised
*** 1."satellite orbits: models, methods, applications" montenbruck & gill(2000)
*** section 3.3.2, pg. 72-73
*** 2."astronomy on the personal computer, 4th ed." montenbruck & pfleger (2005)
*** section 3.2, pg. 38-39 routine MiniMoon
implicit double precision(a-h,o-z)
dimension rm(3)
logical lflag,leapflag
!*** leap second table limit flag
!*** leap second table limit flag
save /limitflag/
common/limitflag/leapflag
common/stuff/rad,pi,pi2
*** use TT for lunar ephemerides
leapflag=lflag
!*** UTC time (sec of day)
!*** TT time (sec of day)
!*** TT time (fract. day)
tsecutc=fmjd*86400.d0
tsectt =utc2ttt(tsecutc)
fmjdtt =tsectt/86400.d0
lflag = leapflag
*** julian centuries since 1.5 january 2000 (J2000)
*** (note: also low precision use of mjd --> tjd)
!*** Julian Date, TT
!*** julian centuries, TT
tjdtt = mjd+fmjdtt+2400000.5d0
t = (tjdtt - 2451545.d0)/36525.d0
*** el0 -- mean longitude of Moon (deg)
*** el -- mean anomaly of Moon (deg)