SUBROUTINE RG_ZONT2 ( T, DUT, DLOD, DOMEGA )
*+
* - - - - - - - - - - -
* R G _ Z O N T 2
* - - - - - - - - - - -
*
* This routine is part of the International Earth Rotation and
* Reference Systems Service (IERS) Conventions software collection.
*
* This subroutine evaluates the effects of zonal Earth tides on the
* rotation of the Earth. The model used is a combination of Yoder
* et al. (1981) elastic body tide, Wahr and Bergen (1986) inelastic
* body tide, and Kantha et al. (1998) ocean tide models
* as recommended by the IERS Conventions (2010). Refer to
* Chapter 8 pp. 105 - 106. The latest version of the model is located
* at http://tai.bipm.org/iers/convupdt/convupdt_c8.html.
*
* In general, Class 1, 2, and 3 models represent physical effects that
* act on geodetic parameters while canonical models provide lower-level
* representations or basic computations that are used by Class 1, 2, or
* 3 models.
*
* Status: Class 3 model
*
* Class 1 models are those recommended to be used a priori in the
* reduction of raw space geodetic data in order to determine
* geodetic parameter estimates.
* Class 2 models are those that eliminate an observational
* singularity and are purely conventional in nature.
* Class 3 models are those that are not required as either Class
* 1 or 2.
* Canonical models are accepted as is and cannot be classified as
* a Class 1, 2, or 3 model.
*
* Given:
* T d TT, Julian centuries since J2000 (Note 1)
*
* Returned:
* DUT d Effect on UT1 (Note 2)
* DLOD d Effect on excess length of day (LOD) (Note 3)
* DOMEGA d Effect on rotational speed (Note 4)
*
* Notes:
*
* 1) Though T is strictly TDB, it is usually more convenient to use
* TT, which makes no significant difference. Julian centuries since
* J2000 is (JD - 2451545.0)/36525.
*
* 2) The expression used is as adopted in IERS Conventions (2010).
* DUT is expressed in seconds and is double precision.
*
* 3) The expression used is as adopted in IERS Conventions (2010).
* DLOD is the excess in LOD and is expressed in seconds per day
* and is double precision. The phrase 'per day' is generally
* understood, so it has been omitted commonly in speech and
* literature.
* See: Stephenson, F. R., Morrison, L. V., Whitrow, G. J., 1984,
* "Long-Term Changes in the Rotation of the Earth: 700 B. C. to
* A. D. 1980 [and Discussion]", Phil. Trans. Roy. Soc. of London.
* Series A, 313, pp. 47 - 70.
*
* 4) The expression used is as adopted in IERS Conventions (2010).
* Rotational speed is expressed in radians per second and is
* double precision.
*
* Called:
* FUNDARG Computation of the fundamental lunisolar arguments
*
* Test case:
* given input: T = .07995893223819302 Julian centuries since J2000
* (MJD = 54465)
* expected output: DUT = 7.983287678576557467E-002 seconds
* DLOD = 5.035331113978199288E-005 seconds / day
* DOMEGA = -4.249711616463017E-014 radians / second
*
* References:
*
* Yoder, C. F., Williams, J. G., and Parke, M. E., (1981),
* "Tidal Variations of Earth Rotation," J. Geophys. Res., 86,
* pp. 881 - 891.
*
* Wahr, J. and Bergen, Z., (1986), "The effects of mantle
* anelasticity on nutations, Earth tides, and tidal variations
* in rotation rate," Geophys. J. Roy. astr. Soc., 87, pp. 633 - 668.
*
* Kantha, L. H., Stewart, J. S., and Desai, S. D., (1998), "Long-
* period lunar fortnightly and monthly ocean tides," J. Geophys.
* Res., 103, pp. 12639 - 12647.
*
* Gross, R. S., (2009), "Ocean tidal effects on Earth rotation,"
* J. Geodyn., 48(3-5), pp. 219 - 225.
*
* Petit, G. and Luzum, B. (eds.), IERS Conventions (2010),
* IERS Technical Note No. 36, BKG (2010)
*
* Revisions:
* 2008 January 18 B.E. Stetzler Initial changes to header
* and used 2PI instead of PI as parameter
* 2008 January 25 B.E. Stetzler Additional changes to header
* 2008 February 21 B.E. Stetzler Definition of (excess) LOD clarified
* 2008 March 12 B.E. Stetzler Applied changes to wording of notes.
* 2008 March 14 B.E. Stetzler Further changes applied to code.
* 2008 April 03 B.E. Stetzler Provided example test case
* 2009 February 11 B.E. Stetzler Updated test case due to changes made
* to FUNDARG.F subroutine
* 2009 April 10 B.E. Stetzler DLOD corrected to say it is expressed
* in seconds per day
* 2009 May 04 B.E. Stetzler Code formatting changes based on
* client recommendations
* 2009 May 07 B.E. Stetzler Updated test case due to above changes
* 2010 February 19 B.E. Stetzler Replaced Conventions 2003 recommended
* model with Conventions 2010 model
* 2010 February 22 B.E. Stetzler Provided example test case
* 2010 February 23 B.E. Stetzler Updated values to two decimal places
* 2010 February 23 B.E. Stetzler Split fundamental arguments and
* coefficients for four decimal place
* precision
* 2010 February 25 B.E. Stetzler Recalculation of fundamental arguments
* 2010 March 01 B.E. Stetzler Updated table values to four decimal
* places and double precision
* 2010 March 12 B.E. Stetzler Applied changes to wording of notes.
* 2010 March 22 B.E. Stetzler Corrected DOMEGA output for test case
* 2011 December 20 B.E. Stetzler Corrected typo in the sine coefficient
* of the 365.26 period for delta LOD.
* Noted by J. Lundberg. Test case output
* for DLOD updated.
*-----------------------------------------------------------------------
IMPLICIT NONE
INTEGER I, J
DOUBLE PRECISION T, DUT, DLOD, DOMEGA, L, LP, F, D, OM, ARG, D2PI
* Arcseconds to radians
DOUBLE PRECISION DAS2R
PARAMETER ( DAS2R = 4.848136811095359935899141D-6 )
* Arcseconds in a full circle
DOUBLE PRECISION TURNAS
PARAMETER ( TURNAS = 1296000D0 )
* 2Pi
PARAMETER (D2PI= 6.283185307179586476925287D0)
* ----------------------
* Zonal Earth tide model
* ----------------------
* Number of terms in the zonal Earth tide model
INTEGER NZONT
PARAMETER ( NZONT = 62 )
* Coefficients for the fundamental arguments
INTEGER NFUND(5,NZONT)
* Zonal tide term coefficients
DOUBLE PRECISION TIDE(6,NZONT)
* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
* --------------------------------------------------
* Tables of multiples of arguments and coefficients
* --------------------------------------------------
* Luni-Solar argument multipliers
* l l' F D OMEGA
DATA ( ( NFUND(I,J), I=1,5 ), J= 1, 20 ) /
: 1, 0, 2, 2, 2,
: 2, 0, 2, 0, 1,
: 2, 0, 2, 0, 2,
: 0, 0, 2, 2, 1,
: 0, 0, 2, 2, 2,
: 1, 0, 2, 0, 0,
: 1, 0, 2, 0, 1,
: 1, 0, 2, 0, 2,
: 3, 0, 0, 0, 0,
:-1, 0, 2, 2, 1,
:-1, 0, 2, 2, 2,
: 1, 0, 0, 2, 0,
: 2, 0, 2, -2, 2,
: 0, 1, 2, 0, 2,
: 0, 0, 2, 0, 0,
: 0, 0, 2, 0, 1,
: 0, 0, 2, 0, 2,
: 2, 0, 0, 0, -1,
: 2, 0, 0, 0, 0,
: 2, 0, 0, 0, 1 /
DATA ( ( NFUND(I,J), I=1,5 ), J= 21, 40 ) /
: 0, -1, 2, 0, 2,
: 0, 0, 0, 2, -1,
: 0, 0, 0, 2, 0,
: 0, 0, 0, 2, 1,
: 0, -1, 0, 2, 0,
: 1, 0, 2, -2, 1,
: 1, 0, 2, -2, 2,
: 1, 1, 0, 0, 0,
:-1, 0, 2, 0, 0,
:-1, 0, 2, 0, 1,
:-1, 0, 2, 0, 2,
: 1, 0, 0, 0, -1,
: 1, 0, 0, 0, 0,
: 1, 0, 0, 0, 1,
: 0, 0, 0, 1, 0,
: 1, -1, 0, 0, 0,
:-1, 0, 0, 2, -1,
:-1, 0, 0, 2, 0,
:-1, 0, 0, 2, 1,
: 1, 0, -2, 2, -1 /
DATA ( ( NFUND(I,J), I=1,5 ), J= 41, 60 ) /
:-1, -1, 0, 2, 0,
: 0, 2, 2, -2, 2,
: 0, 1, 2, -2, 1,
: 0, 1, 2, -2, 2,
: 0, 0, 2, -2, 0,
: 0, 0, 2, -2, 1,
: 0, 0, 2, -2, 2,
: 0, 2, 0, 0, 0,
: 2, 0, 0, -2, -1,
: 2, 0, 0, -2, 0,
: 2, 0, 0, -2, 1,
: 0, -1, 2, -2, 1,
: 0, 1, 0, 0, -1,
: 0, -1, 2, -2, 2,
: 0, 1, 0, 0, 0,
: 0, 1, 0, 0, 1,
: 1, 0, 0, -1, 0,
: 2, 0, -2, 0, 0,
:-2, 0, 2, 0, 1,
:-1, 1, 0, 1, 0 /
DATA ( ( NFUND(I,J), I=1,5 ), J= 61, 62 ) /
: 0, 0, 0, 0, 2,
: 0, 0, 0, 0, 1 /
* Multiple of DUT DLOD DOMEGA
* sin cos cos sin cos sin
DATA ( ( TIDE(I,J), I=1,6 ), J = 1,20 ) /
: -0.0235D0,0.0000D0, 0.2617D0, 0.0000D0, -0.2209D0, 0.0000D0,
: -0.0404D0,0.0000D0, 0.3706D0, 0.0000D0, -0.3128D0, 0.0000D0,
: -0.0987D0,0.0000D0, 0.9041D0, 0.0000D0, -0.7630D0, 0.0000D0,
: -0.0508D0,0.0000D0, 0.4499D0, 0.0000D0, -0.3797D0, 0.0000D0,
: -0.1231D0,0.0000D0, 1.0904D0, 0.0000D0, -0.9203D0, 0.0000D0,
: -0.0385D0,0.0000D0, 0.2659D0, 0.0000D0, -0.2244D0, 0.0000D0,
: -0.4108D0,0.0000D0, 2.8298D0, 0.0000D0, -2.3884D0, 0.0000D0,
: -0.9926D0,0.0000D0, 6.8291D0, 0.0000D0, -5.7637D0, 0.0000D0,
: -0.0179D0,0.0000D0, 0.1222D0, 0.0000D0, -0.1031D0, 0.0000D0,
: -0.0818D0,0.0000D0, 0.5384D0, 0.0000D0, -0.4544D0, 0.0000D0,
: -0.1974D0,0.0000D0, 1.2978D0, 0.0000D0, -1.0953D0, 0.0000D0,
: -0.0761D0,0.0000D0, 0.4976D0, 0.0000D0, -0.4200D0, 0.0000D0,
: 0.0216D0,0.0000D0,-0.1060D0, 0.0000D0, 0.0895D0, 0.0000D0,
: 0.0254D0,0.0000D0,-0.1211D0, 0.0000D0, 0.1022D0, 0.0000D0,
: -0.2989D0,0.0000D0, 1.3804D0, 0.0000D0, -1.1650D0, 0.0000D0,
: -3.1873D0,0.2010D0,14.6890D0, 0.9266D0,-12.3974D0,-0.7820D0,
: -7.8468D0,0.5320D0,36.0910D0, 2.4469D0,-30.4606D0,-2.0652D0,
: 0.0216D0,0.0000D0,-0.0988D0, 0.0000D0, 0.0834D0, 0.0000D0,
: -0.3384D0,0.0000D0, 1.5433D0, 0.0000D0, -1.3025D0, 0.0000D0,
: 0.0179D0,0.0000D0,-0.0813D0, 0.0000D0, 0.0686D0, 0.0000D0 /
DATA ( ( TIDE(I,J), I=1,6 ), J = 21,40 ) /
: -0.0244D0,0.0000D0, 0.1082D0, 0.0000D0, -0.0913D0, 0.0000D0,
: 0.0470D0,0.0000D0,-0.2004D0, 0.0000D0, 0.1692D0, 0.0000D0,
: -0.7341D0,0.0000D0, 3.1240D0, 0.0000D0, -2.6367D0, 0.0000D0,
: -0.0526D0,0.0000D0, 0.2235D0, 0.0000D0, -0.1886D0, 0.0000D0,
: -0.0508D0,0.0000D0, 0.2073D0, 0.0000D0, -0.1749D0, 0.0000D0,
: 0.0498D0,0.0000D0,-0.1312D0, 0.0000D0, 0.1107D0, 0.0000D0,
: 0.1006D0,0.0000D0,-0.2640D0, 0.0000D0, 0.2228D0, 0.0000D0,
: 0.0395D0,0.0000D0,-0.0968D0, 0.0000D0, 0.0817D0, 0.0000D0,
: 0.0470D0,0.0000D0,-0.1099D0, 0.0000D0, 0.0927D0, 0.0000D0,
: 0.1767D0,0.0000D0,-0.4115D0, 0.0000D0, 0.3473D0, 0.0000D0,
: 0.4352D0,0.0000D0,-1.0093D0, 0.0000D0, 0.8519D0, 0.0000D0,
: 0.5339D0,0.0000D0,-1.2224D0, 0.0000D0, 1.0317D0, 0.0000D0,
: -8.4046D0,0.2500D0,19.1647D0, 0.5701D0,-16.1749D0,-0.4811D0,
: 0.5443D0,0.0000D0,-1.2360D0, 0.0000D0, 1.0432D0, 0.0000D0,
: 0.0470D0,0.0000D0,-0.1000D0, 0.0000D0, 0.0844D0, 0.0000D0,
: -0.0555D0,0.0000D0, 0.1169D0, 0.0000D0, -0.0987D0, 0.0000D0,
: 0.1175D0,0.0000D0,-0.2332D0, 0.0000D0, 0.1968D0, 0.0000D0,
: -1.8236D0,0.0000D0, 3.6018D0, 0.0000D0, -3.0399D0, 0.0000D0,
: 0.1316D0,0.0000D0,-0.2587D0, 0.0000D0, 0.2183D0, 0.0000D0,
: 0.0179D0,0.0000D0,-0.0344D0, 0.0000D0, 0.0290D0, 0.0000D0 /
DATA ( ( TIDE(I,J), I=1,6 ), J = 41,60 ) /
: -0.0855D0,0.0000D0, 0.1542D0, 0.0000D0, -0.1302D0, 0.0000D0,
: -0.0573D0,0.0000D0, 0.0395D0, 0.0000D0, -0.0333D0, 0.0000D0,
: 0.0329D0,0.0000D0,-0.0173D0, 0.0000D0, 0.0146D0, 0.0000D0,
: -1.8847D0,0.0000D0, 0.9726D0, 0.0000D0, -0.8209D0, 0.0000D0,
: 0.2510D0,0.0000D0,-0.0910D0, 0.0000D0, 0.0768D0, 0.0000D0,
: 1.1703D0,0.0000D0,-0.4135D0, 0.0000D0, 0.3490D0, 0.0000D0,
: -49.7174D0,0.4330D0,17.1056D0, 0.1490D0,-14.4370D0,-0.1257D0,
: -0.1936D0,0.0000D0, 0.0666D0, 0.0000D0, -0.0562D0, 0.0000D0,
: 0.0489D0,0.0000D0,-0.0154D0, 0.0000D0, 0.0130D0, 0.0000D0,
: -0.5471D0,0.0000D0, 0.1670D0, 0.0000D0, -0.1409D0, 0.0000D0,
: 0.0367D0,0.0000D0,-0.0108D0, 0.0000D0, 0.0092D0, 0.0000D0,
: -0.0451D0,0.0000D0, 0.0082D0, 0.0000D0, -0.0069D0, 0.0000D0,
: 0.0921D0,0.0000D0,-0.0167D0, 0.0000D0, 0.0141D0, 0.0000D0,
: 0.8281D0,0.0000D0,-0.1425D0, 0.0000D0, 0.1202D0, 0.0000D0,
: -15.8887D0,0.1530D0, 2.7332D0, 0.0263D0, -2.3068D0,-0.0222D0,
: -0.1382D0,0.0000D0, 0.0225D0, 0.0000D0, -0.0190D0, 0.0000D0,
: 0.0348D0,0.0000D0,-0.0053D0, 0.0000D0, 0.0045D0, 0.0000D0,
: -0.1372D0,0.0000D0,-0.0079D0, 0.0000D0, 0.0066D0, 0.0000D0,
: 0.4211D0,0.0000D0,-0.0203D0, 0.0000D0, 0.0171D0, 0.0000D0,
: -0.0404D0,0.0000D0, 0.0008D0, 0.0000D0, -0.0007D0, 0.0000D0 /
DATA ( ( TIDE(I,J), I=1,6 ), J = 61,62 ) /
: 7.8998D0,0.0000D0, 0.1460D0, 0.0000D0, -0.1232D0, 0.0000D0,
: -1617.2681D0,0.0000D0,-14.9471D0,0.0000D0, 12.6153D0, 0.0000D0 /
* -------------------------------------
* Computation of fundamental arguments
* -------------------------------------
CALL FUNDARG(T,L,LP,F,D,OM)
* - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
* Set initial values to zero.
DUT = 0.0D0
DLOD = 0.0D0
DOMEGA = 0.0D0
* Sum zonal tide terms.
DO 10 I = 1, NZONT
* Formation of multiples of arguments.
ARG = MOD ( DBLE ( NFUND(1,I) ) * L
. + DBLE ( NFUND(2,I) ) * LP
. + DBLE ( NFUND(3,I) ) * F
. + DBLE ( NFUND(4,I) ) * D
. + DBLE ( NFUND(5,I) ) * OM, D2PI )
IF (ARG.LT.0D0) ARG = ARG + D2PI
* Evaluate zonal tidal terms.
DUT = DUT + TIDE(1,I) *DSIN(ARG) + TIDE(2,I) *DCOS(ARG)
DLOD = DLOD + TIDE(3,I) *DCOS(ARG) + TIDE(4,I) *DSIN(ARG)
DOMEGA = DOMEGA + TIDE(5,I) *DCOS(ARG) + TIDE(6,I) *DSIN(ARG)
10 CONTINUE
* Rescale corrections so that they are in units involving seconds.
DUT = DUT * 1.0D-4
DLOD = DLOD * 1.0D-5
DOMEGA = DOMEGA * 1.0D-14
* Finished.
*+----------------------------------------------------------------------
*
* Copyright (C) 2008
* IERS Conventions Center
*
* ==================================
* IERS Conventions Software License
* ==================================
*
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*
* BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS
* WHICH APPLY TO ITS USE.
*
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*
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*
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* Correspondence concerning IERS Conventions software should be
* addressed as follows:
*
* Gerard Petit
* Internet email: gpetit[at]bipm.org
* Postal address: IERS Conventions Center
* Time, frequency and gravimetry section, BIPM
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* Brian Luzum
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*-----------------------------------------------------------------------
END