The Earth orientation can be described either as a 3×3 rotation matrix that transforms a Cartesian vector from the rotating terrestrial coordinate system to the inertial non-rotating celestial coordinate system or as parameters on which this matrix depends. For practical needs the rotation matrix and its time derivatives are sufficient to perform astronomical reduction for Earth's rotation. However, NERS also provides the parameters that describes the Earth's rotation on which the rotation matrix depends as well. These parameters are empirical corrections to a deterministic model. Since the Earth's rotation depends on motion of the hydrosphere and atmosphere, it cannot be described with a deterministic model with the accuracy comparable with accuracy of observations and should be continuously monitored using space geodesy observations. For historical reasons several alternative Earth orientation parameters were used. For instance. For instance the rate of change of the angular variable along the axis 3, i.e. the axial motion can be described as Euler angle 3, UT1 rate, or the length of day. NERS provides many alternative Earth orientation parameters. These parameters are not independent.
See example/ners_fortran_example_01.f and example/ners_c_example_01.c.
See example/ners_fortran_example_02.f and example/ners_c_example_02.c.
See example/ners_fortran_example_04.f and example/ners_c_example_04.c.
FORTRAN: NERS_INIT ( CONFIG_FILE, NERS, TIME_TAI_START, TIME_TAI_STOP, IUER ) C: cners_init ( char * config_file, struct ners_struct * ners, double time_tai_beg, double time_tai_end, int * iuer ) Input parameters: config_file ( CHARACTER*(*) ) -- name of the NERS configuration file NERS__CONFIG defined in ners_local.i specifies the default configuration file ners ( NERS__TYPE ) -- NERS internal data structure time_tai_start ( REAL*8 ) -- Start time of the time range Units: seconds since 2000.01.01_00:00:00.0 TAI time_tai_stop ( REAL*8 ) -- Stop time of the time range. Units: seconds since 2000.01.01_00:00:00.0 TAI Input/Output parameter: iuer ( INTEGER*4 ) -- Error parameter. On input: -1 -- to print the error message if an error is detected; otherwise, not to print the message: On output: 0 -- normal completion >0 -- error code during NERS initialization
FORTRAN: NERS_GET_EOP ( NERS, TIME_TAI, CPAR, M_PAR, L_PAR, PARS, IUER ) C: cners_get_eop ( struct ners_struct * ners, double time_tai_obs, char * cpar, int mpar, int * lpar, double eops[], int * iuer ) Input parameters: ners ( NERS__TYPE ) -- NERS internal data structure time_tai ( REAL*8 ) -- Time. Units: seconds since 2000.01.01_00:00:00.0 TAI cpar ( CHARACTER*(*) ) -- Earth orientation parameter name: mat -- 3x3 matrix of the transformation from the terrestrial coordinate system to the celestial coordinate system matr -- First time derivative of the 3x3 matrix of the transformation from the terrestrial coordinate system to the celestial coordinate system matrr -- Second time derivative of the 3x3 matrix of the transformation from the terrestrial coordinate system to the celestial coordinate system matall -- 3x3x3 array of the matrix of the transformation from the terrestrial coordinate system to the celestial coordinate system, its first and second time derivative. [1:3,1:3,1] -- transformation matrix from the terrestrial coordinate system to the celestial coordinate system, [1:3,1:3,2] -- first time derivative of the transformation matrix above. [1:3,1:3,3] -- second time derivative of the transformation matrix above. utcmtai -- Value of function UTC minus TAI. Units: s. e1 -- Euler angle around axis one. Units: rad. e2 -- Euler angle around axis two. Units: rad. e3 -- Euler angle around axis three. Units: rad. e1r -- First time derivative of Euler angle around axis one. Units: rad/s. e2r -- First time derivative of Euler angle around axis two. Units: rad/s. e3r -- First time derivative of Euler angle around axis three. Units: rad/s. e1rr -- Second time derivative of Euler angle around axis one. Units: rad/s. e2rr -- Second time derivative of Euler angle around axis two. Units: rad/s. e3rr -- Second time derivative of Euler angle around axis three. Units: rad/s. ut1mtai -- Angle UT1 minus TAI. Units: s. ut1rat -- First time derivative of angle UT1 minus TAI. Units s/s. ut1rr -- Second time derivative of angle UT1 minus TAI. Units s/s^2. lod -- Length of day. Units: s. xpol -- X pole coordinate. Unit: arcsec. ypol -- Y pole coordinate. Unit: arcsec. xpolr -- First time derivative of X pole coordinate. Unit: arcsec/day. ypolr -- First time derivative of Y pole coordinate. Unit: arcsec/day. xpolrr -- Second time derivative of X pole coordinate. Unit: arcsec/day**2. ypolrr -- Second time derivative of Y pole coordinate. Unit: arcsec/day**2. eop3 -- Array of three EOP parameters: 1: X pole coordinate. Unit: arcsec. 2: Y pole coordinate. Unit: arcsec. 3: UT1 minus TAI. Unit: s. eop3r -- Array of six EOP parameters: 1: X pole coordinate. Unit: arcsec. 2: Y pole coordinate. Unit: arcsec. 3: UT1 minus TAI. Unit: s. 4: First time derivative of X pole coordinate. Unit: arcsec/day. 5: Second time derivative of Y pole coordinate. Unit: arcsec/day. 6: First time derivative of UT1 minus TAI coordinate. Unit: s/day. dpsi -- Nutation angle in longitude. Units: rad deps -- Nutation angle in obliquity. Units: rad dpsir -- First time derivative of nutation angle in longitude. Units: rad/s. depsr -- First time derivative of nutation angle in obliquity. Units: rad/s. nut -- Array of two EOP parameters: 1: Nutation angle in longitude. Units: rad 2: Nutation angle in obliquity. Units: rad nutr -- Array of four EOP parameters: 1: Nutation angle in longitude. Units: rad 2: Nutation angle in obliquity. Units: rad 3: First time derivative of nutation angle in longitude. Units: rad/s. 4: First time derivative of nutation angle in obliquity. Units: rad/s. eops -- Array of eight EOP parameters: 1: X pole coordinate. Unit: arcsec. 2: Y pole coordinate. Unit: arcsec. 3: UT1 minus TAI. Unit: s. 4: First time derivative of X pole coordinate. Unit: arcsec/day. 5: Second time derivative of Y pole coordinate. Unit: arcsec/day. 6: First time derivative of UT1 minus TAI coordinate. Unit: s/day. 7: Nutation angle in longitude. Units: arcsec 8: Nutation angle in obliquity. Units: arcsec h1 -- Contribution of empirical harmonic variations in the EOPs with respect to axis 1. Units: rad. h2 -- Contribution of empirical harmonic variations in the EOPs with respect to axis 2. Units: rad. h3 -- Contribution of empirical harmonic variations in the EOPs with respect to axis 3. Units: rad. h1r -- First time derivative of the contribution of empirical harmonic variations in the EOPs with respect to axis 1. Units: rad/s. h2r -- First time derivative of the contribution of empirical harmonic variations in the EOPs with respect to axis 2. Units: rad/s. h3r -- First time derivative of the contribution of empirical harmonic variations in the EOPs with respect to axis 3. Units: rad/s. h1rr -- Second time derivative of the contribution of empirical harmonic variations in the EOPs with respect to axis 1. Units: rad/s^2. h2rr -- Second time derivative of the contribution of empirical harmonic variations in the EOPs with respect to axis 2. Units: rad/s^2. h3rr -- Second time derivative of the contribution of empirical harmonic variations in the EOPs with respect to axis 3. Units: rad/s^2. heo -- Array of three components of the contribution of empirical harmonic variations in the EOPs: 1: Contribution of empirical harmonic variations in the EOPs with respect to axis 1. Units: rad. 2: Contribution of empirical harmonic variations in the EOPs with respect to axis 2. Units: rad. 3: Contribution of empirical harmonic variations in the EOPs with respect to axis 3. Units: rad. heor -- Array of three components of the first time derivative of the contribution of empirical harmonic variations in the EOPs: 1: First time derivative of the contribution of empirical harmonic variations in the EOPs with respect to axis 1. Units: rad/s. 2: First time derivative of the contribution of empirical harmonic variations in the EOPs with respect to axis 2. Units: rad/s. 3: First time derivative of the contribution of empirical harmonic variations in the EOPs with respect to axis 3. Units: rad/s. heorr -- Array of three components of the first time derivative of the contribution of empirical harmonic variations in the EOPs: 1: Second time derivative of the contribution of empirical harmonic variations in the EOPs with respect to axis 1. Units: rad/s^2. 2: Second time derivative of the contribution of empirical harmonic variations in the EOPs with respect to axis 2. Units: rad/s^2. 3: Second time derivative of the contribution of empirical harmonic variations in the EOPs with respect to axis 3. Units: rad/s^2. m_par ( INTEGER*4 ) -- Maximum number of the elements in the output array. Output parameters: l_par ( INTEGER*4 ) -- Actual number of the EOPs pars ( REAL*8 ) -- Array of EOPs. Dimension: m_par. Input/Output parameter: iuer ( INTEGER*4 ) -- Error parameter. On input: -1 -- to print the error message if an error is detected; otherwise, not to print the message: On output: 0 -- normal completion >0 -- error code during NERS initialization
FORTRAN: NERS_QUIT ( CODE, NERS ) C: cners_quit ( int * quit_code, struct ners_struct * ners ) Input parameter: code ( INTEGER*4 ) -- Level of re-initialization: NERS__EXP -- release memory with coefficients of EOP expansion for the interval of time specified in previous call of routine ners_init. NERS__FCS -- release memory with the NERS forecast message NERS__ALL -- release memory for all internal data structures Input/Output parameter: ners ( NERS__TYPE ) -- NERS internal data structure
FORTRAN: NERS_INQ ( NERS, REQ, M_PAR, L_PAR, PARS, IUER ) C: cners_quit ( int * quit_code, struct ners_struct * ners ) Input parameter: ners ( NERS__TYPE ) -- NERS internal data structure req ( CHARACTER*(*) ) -- request type. Supported requests: range -- request of the EOP range. Returns three values: 1: start time of EOP availability. Units: seconds since 2000.01.01_00:00:00.0 TAI. 2: stop time of the EOP or the EOP forecast availability. Units: seconds since 2000.01.01_00:00:00.0 TAI. 3: stop time of the long-term EOP prediction fcs_gen_time -- request of the EOP forecast message generation time. Return one value: 1: time of the EOP forecast generation. Units: seconds since 2000.01.01_00:00:00.0 TAI. m_par ( INTEGER*4 ) -- Maximum number of the elements in the output array. Output parameters: l_par ( INTEGER*4 ) -- Actual number of the EOPs pars ( REAL*8 ) -- Array of EOPs. Dimension: m_par. Input/Output parameter: iuer ( INTEGER*4 ) -- Error parameter. On input: -1 -- to print the error message if an error is detected; otherwise, not to print the message: On output: 0 -- normal completion >0 -- error code during NERS
FORTRAN: NERS_GET_SERIES ( NERS, TIME_TAI_START, TIME_TAI_STOP, TIME_STEP, CPAR, DIM1, DIM2, NS, TIM, SER, IUER ) C: cners_get_series ( struct ners_struct * ners, double time_tai_beg, double time_tai_end, double tim_step, char * cpar, int m_par, int m_ser, int * ns, double tim[], double ser[], int * iuer ) Input parameters: ners ( NERS__TYPE ) -- NERS internal data structure time_tai_start ( REAL*8 ) -- Start time of EOP series. Units: seconds since 2000.01.01_00:00:00.0 TAI time_tai_stop ( REAL*8 ) -- Stop time of EOP series. Units: seconds since 2000.01.01_00:00:00.0 TAI time_step ( REAL*8 ) -- Time step of the EOP series. Units: seconds since 2000.01.01_00:00:00.0 TAI cpar ( CHARACTER*(*) ) -- Earth orientation parameter name. euler -- Euler angles of the Earth rotation 1: Euler angle around axis one. Units: rad. 2: Euler angle around axis two. Units: rad. 3: Euler angle around axis three. Units: rad. euler_r -- First time derivative of Euler angles of the Earth rotation 1: First time derivative of Euler angle around axis one. Units: rad/s. 2: First time derivative of Euler angle around axis two. Units: rad/s. 3: First time derivative of Euler angle around axis three. Units: rad/s. polu -- Array of three EOP parameters: 1: X pole coordinate. Unit: arcsec. 2: Y pole coordinate. Unit: arcsec. 3: UT1 minus TAI. Unit: s. polur -- Array of six EOP parameters: 1: X pole coordinate. Unit: arcsec. 2: Y pole coordinate. Unit: arcsec. 3: UT1 minus TAI. Unit: s. 4: First time derivative of X pole coordinate. Unit: arcsec/day. 5: Second time derivative of Y pole coordinate. Unit: arcsec/day. 6: First time derivative of UT1 minus TAI coordinate. Unit: s/day. eops -- Array of eight EOP parameters: 1: X pole coordinate. Unit: arcsec. 2: Y pole coordinate. Unit: arcsec. 3: UT1 minus TAI. Unit: s. 4: First time derivative of X pole coordinate. Unit: arcsec/day. 5: Second time derivative of Y pole coordinate. Unit: arcsec/day. 6: First time derivative of UT1 minus TAI coordinate. Unit: s/day. 7: Nutation angle in longitude. Units: arcsec 8: Nutation angle in obliquity. Units: arcsec heo -- Array of three components of the contribution of empirical harmonic variations in the EOPs: 1: Contribution of empirical harmonic variations in the EOPs with respect to axis 1. Units: rad. 2: Contribution of empirical harmonic variations in the EOPs with respect to axis 2. Units: rad. 3: Contribution of empirical harmonic variations in the EOPs with respect to axis 3. Units: rad. heor -- Array of three components of the first time derivative of the contribution of empirical harmonic variations in the EOPs: 1: First time derivative of the contribution of empirical harmonic variations in the EOPs with respect to axis 1. Units: rad/s. 2: First time derivative of the contribution of empirical harmonic variations in the EOPs with respect to axis 2. Units: rad/s. 3: First time derivative of the contribution of empirical harmonic variations in the EOPs with respect to axis 3. Units: rad/s. dim1 ( INTEGER*4 ) -- First dimension of the EOP series array. The dimension runs over time. dim2 ( INTEGER*4 ) -- Second dimension of the EOP series array. The dimension runs over parameters. Output parameters: ns ( INTEGER*4 ) -- the number of returned EOP values tim ( REAL*8 ) -- Array of EOP time epochs. Dimension: ns. Units: seconds since 2000.01.01_00:00:00.0 TAI ser ( REAL*8 ) -- Two dimensional Array of EOPs. Dimensions: dim1,dim2. The number of filled elements along the first dimension is ns. The number of filled elements along the second dimension depends on value of parameter cpar. Input/Output parameter: iuer ( INTEGER*4 ) -- Error parameter. On input: -1 -- to print the error message if an error is detected; otherwise, not to print the message: On output: 0 -- normal completion >0 -- error code during NERS
FORTRAN: NERS_GET_UTCMTAI ( NERS, UTC, UTC_M_TAI, IUER ) C: cners_get_utcmtai ( struct ners_struct * ners, double * utc_obs, double * utc, int * iuer ) Input parameters: ners ( NERS__TYPE ) -- NERS internal data structure utc ( REAL*8 ) -- UTC time tag. Units: seconds elapsed since 2000.01.01_00:00:00.0 UTC. Output: utc_m_tai ( REAL*8 ) -- UTC minus TAI function. Units: seconds. Input/Output parameter: iuer ( INTEGER*4 ) -- Error parameter. On input: -1 -- to print the error message if an error is detected; otherwise, not to print the message: On output: 0 -- normal completion >0 -- error code during NERS