SUBROUTINE PMSDNUT2 (RMJD, PM)
*+
* - - - - - - - - - - -
* P M S D N U T 2
* - - - - - - - - - - -
*
* This routine is part of the International Earth Rotation and
* Reference Systems Service (IERS) Conventions software collection.
*
* This subroutine evaluates the model of polar motion for
* a nonrigid Earth due to tidal gravitation. This polar motion
* is equivalent to the so-called "subdiurnal nutation." The model
* is a sum of a first order polynomial and 25 trigonometric terms
* (15 long periodic and 10 quasi diurnal) with coefficients given
* in Table 5.1a of the IERS Conventions (2010).
*
* :------------------------------------------:
* : :
* : IMPORTANT :
* : :
* : In the present version this subroutine :
* : neglects the linear trend and the long :
* : periodic terms of the expansion, for the :
* : reasons explained in Section 5.x.x of :
* : the IERS Conventions (2010), last para- :
* : graph before Table 5.1. If the full :
* : expansion is needed, set the parameter :
* : iband to 0 instead of 1, that is replace :
* : the statement :
* : PARAMETER ( iband = 1 ) :
* : to PARAMETER ( iband = 0 ) :
* : :
* :__________________________________________:
*
* 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:
* rmjd d Time expressed as modified Julian date
*
* Returned:
* pm d(2) Vector of length 2 (Note 1)
*
* Notes:
*
* 1) The polar motion coordinates (dx, dy) are expressed in
* microarcseconds.
*
* Called:
* FUNDARG Compute the angular fundamental arguments
*
* Test case:
* given input: rmjd = 54335D0 ( August 23, 2007 )
*
* expected output: (dx) pm(1) = 24.65518398386097942D0 microarcseconds
* (dy) pm(2) = -14.11070254891893327D0 microarcseconds
*
* References:
*
* Petit, G. and Luzum, B. (eds.), IERS Conventions (2010),
* IERS Technical Note No. 36, BKG (2010)
*
* Revisions:
* 2005 March A.Brzezinski Original code
* 2008 November 26 B.E.Stetzler Initial changes to code
* 2008 December 01 B.E.Stetzler Provided test case
* 2009 August 18 B.E.Stetzler Capitalized all variables for FORTRAN
* 77 compatibility
* 2010 May 14 B.E.Stetzler Replaced call to PMARGS to FUNDARG
* for universal fundamental argument
* subroutine
* 2010 May 17 B.E.Stetzler Validated test case using internally
* computed GMST and call to FUNDARG
* matched previous external call to
* PMARGS for all six parameters
* 2010 June 23 B.E.Stetzler Modified coefficients of the long
* and short period terms in polar
* motion and secular polar motion
* rate to coincide with Table 5.1a
*-----------------------------------------------------------------------
IMPLICIT NONE
DOUBLE PRECISION RMJD, PM(2)
* ----------------------------
* D E F I N I T I O N S
* ----------------------------
* iband - parameter defining the range of periods for the terms which
* are included in computations; if equal to 1 only the quasi
* diurnal terms are computed, otherwise the full model
* iarg - array defining for each of the 25 trigonometric terms a set
* of 6 integer multipliers of the fundamental angular arguments
* arg - vector of the following 6 fundamental arguments used to
* compute the angular argument of the trigonometric functions
* arg(1:6) = [ GMST+pi, el, elp, f, d, om ]; this vector is
* evaluated by the subroutine FUNDARG which is called as an
* external subroutine. Originally evaluated by the subroutine
* PMARGS.
* period - array of periods of the trigonometric terms of expansion, in
* mean solar days; only for a check - not used in computations
* xs, xc - sine and cosine coefficients of the x coordinate of the pole,
* in microarcseconds
* ys, yc - sine and cosine coefficients of the y coordinate of the pole,
* in microarcseconds
* angle - angular argument of the trigonometric functions
* angle = Sum(i=1:6) iarg(i,j)*arg(i), for j=1,25
INTEGER IBAND, I, J, JSTART
PARAMETER ( IBAND = 1 )
INTEGER IARG(6,25)
DOUBLE PRECISION T, GMST, L, LP, F, D, OM
DOUBLE PRECISION ARG(6)
DOUBLE PRECISION PER(25), XS(25), XC(25), YS(25), YC(25)
DOUBLE PRECISION ANGLE, XRATE, YRATE
* Set constants
* Arcseconds to radians
DOUBLE PRECISION DAS2R
PARAMETER ( DAS2R = 4.848136811095359935899141D-6 )
* Arcseconds in a full circle
DOUBLE PRECISION TURNAS
PARAMETER ( TURNAS = 1296000D0 )
* rmjd0 - modified Julian date of J2000
* twopi - 2*pi
DOUBLE PRECISION RMJD0, PI, TWOPI
PARAMETER ( RMJD0 = 51544.5D0 )
PARAMETER ( PI = 3.141592653589793238462643D0 )
PARAMETER ( TWOPI = 6.283185307179586476925287D0 )
* Radians to seconds
DOUBLE PRECISION RAD2SEC
PARAMETER ( RAD2SEC = 86400D0/TWOPI )
* Coefficients of the long periodic terms in polar motion
* Source: IERS Conventions (2010), Table 5.1a
DATA
. ( (IARG(I,J),I=1,6), PER(J), XS(J), XC(J), YS(J), YC(J),
. J=1,15)
./ 0, 0, 0, 0, 0, -1, 6798.3837, 0.0, 0.6, -0.1, -0.1,
. 0, -1, 0, 1, 0, 2, 6159.1355, 1.5, 0.0, -0.2, 0.1,
. 0, -1, 0, 1, 0, 1, 3231.4956, -28.5, -0.2, 3.4, -3.9,
. 0, -1, 0, 1, 0, 0, 2190.3501, -4.7, -0.1, 0.6, -0.9,
. 0, 1, 1, -1, 0, 0, 438.35990, -0.7, 0.2, -0.2, -0.7,
. 0, 1, 1, -1, 0, -1, 411.80661, 1.0, 0.3, -0.3, 1.0,
. 0, 0, 0, 1, -1, 1, 365.24219, 1.2, 0.2, -0.2, 1.4,
. 0, 1, 0, 1, -2, 1, 193.55971, 1.3, 0.4, -0.2, 2.9,
. 0, 0, 0, 1, 0, 2, 27.431826, -0.1, -0.2, 0.0, -1.7,
. 0, 0, 0, 1, 0, 1, 27.321582, 0.9, 4.0, -0.1, 32.4,
. 0, 0, 0, 1, 0, 0, 27.212221, 0.1, 0.6, 0.0, 5.1,
. 0, -1, 0, 1, 2, 1, 14.698136, 0.0, 0.1, 0.0, 0.6,
. 0, 1, 0, 1, 0, 1, 13.718786, -0.1, 0.3, 0.0, 2.7,
. 0, 0, 0, 3, 0, 3, 9.1071941, -0.1, 0.1, 0.0, 0.9,
. 0, 0, 0, 3, 0, 2, 9.0950103, -0.1, 0.1, 0.0, 0.6/
* Coefficients of the quasi diurnal terms in polar motion
* Source: IERS Conventions (2010), Table 5.1a
DATA
.( (IARG(I,J),i=1,6), PER(J), XS(J), XC(J), YS(J), YC(J),
. J=16,25)
./ 1, -1, 0, -2, 0, -1, 1.1196992, -0.4, 0.3, -0.3, -0.4,
. 1, -1, 0, -2, 0, -2, 1.1195149, -2.3, 1.3, -1.3, -2.3,
. 1, 1, 0, -2, -2, -2, 1.1134606, -0.4, 0.3, -0.3, -0.4,
. 1, 0, 0, -2, 0, -1, 1.0759762, -2.1, 1.2, -1.2, -2.1,
. 1, 0, 0, -2, 0, -2, 1.0758059, -11.4, 6.5, -6.5, -11.4,
. 1, -1, 0, 0, 0, 0, 1.0347187, 0.8, -0.5, 0.5, 0.8,
. 1, 0, 0, -2, 2, -2, 1.0027454, -4.8, 2.7, -2.7, -4.8,
. 1, 0, 0, 0, 0, 0, 0.9972696, 14.3, -8.2, 8.2, 14.3,
. 1, 0, 0, 0, 0, -1, 0.9971233, 1.9, -1.1, 1.1, 1.9,
. 1, 1, 0, 0, 0, 0, 0.9624365, 0.8, -0.4, 0.4, 0.8/
* Rate of secular polar motion, in microarcseconds per year
* Source: IERS Conventions (2010), Table 5.1a
DATA XRATE, YRATE / -3.8, -4.3/
* Compute the periodical part of the model
* Coordinates of the pole are set to zero first
PM(1) = 0D0
PM(2) = 0D0
* Evaluate the vector of the fundamental arguments
* arg(1:6) = [ GMST+pi, el, elp, f, d, om ] at t = rmjd
* Convert the input epoch to Julian centuries of TDB since J2000
T = (RMJD-RMJD0)/36525D0
* Compute GMST + pi
GMST = MOD ( 67310.54841D0 +
. T*( (8640184.812866D0 + 3155760000D0) +
. T*( 0.093104D0 +
. T*( -0.0000062 ))), 86400D0 )
CALL FUNDARG ( T, L, LP, F, D, OM )
ARG(1) = GMST / RAD2SEC + PI
ARG(1) = DMOD( ARG(1), TWOPI )
ARG(2) = L
ARG(3) = LP
ARG(4) = F
ARG(5) = D
ARG(6) = OM
IF (IBAND.EQ.1) THEN
JSTART = 16
ELSE
JSTART = 1
ENDIF
DO 20 J=JSTART,25
* For the j-th term of the trigonometric expansion, compute the angular
* argument angle of sine and cosine functions as a linear integer
* combination of the 6 fundamental arguments
ANGLE = 0D0
DO 10 I=1,6
ANGLE = ANGLE + IARG(I,J) * ARG(I)
10 CONTINUE
ANGLE = DMOD( ANGLE, TWOPI )
* Compute contribution from the j-th term to the polar motion coordinates
PM(1) = PM(1) + XS(J)*DSIN(ANGLE) + XC(J)*DCOS(ANGLE)
PM(2) = PM(2) + YS(J)*DSIN(ANGLE) + YC(J)*DCOS(ANGLE)
20 CONTINUE
IF (IBAND.EQ.1) RETURN
* Add the secular term of the model
PM(1) = PM(1) + XRATE * (RMJD-RMJD0) / 365.25D0
PM(2) = PM(2) + YRATE * (RMJD-RMJD0) / 365.25D0
RETURN
* Finished.
*+----------------------------------------------------------------------
*
* Copyright (C) 2008
* IERS Conventions Center
*
* ==================================
* IERS Conventions Software License
* ==================================
*
* NOTICE TO USER:
*
* BY USING THIS SOFTWARE YOU ACCEPT THE FOLLOWING TERMS AND CONDITIONS
* WHICH APPLY TO ITS USE.
*
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*
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* c) The name(s) of all modified routine(s) that you distribute
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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
* Pavillon de Breteuil
* 92312 Sevres FRANCE
*
* or
*
* Brian Luzum
* Internet email: brian.luzum[at]usno.navy.mil
* Postal address: IERS Conventions Center
* Earth Orientation Department
* 3450 Massachusetts Ave, NW
* Washington, DC 20392
*
*
*-----------------------------------------------------------------------
END