C++ library implementing the IERS 2010 standards.

This project contains a number of functions implementing models defined in IERS Conventions (2010) as described in ¹. The International Earth Rotation and Reference Systems Service (IERS) publishes the Conventions along with relevant documents, model implementations and respective test cases; the latter two are available in the FORTRAN programming language at the IERS website.

This repository is an effort to translate the algorithms in the C++ programming language with (as much as possible) minor modifications. Note that the software found at this website is routinely updated.

The C++ library ggdatetime is used in the library to handle datetime instances when needed. Hence, you should have ggdatetime on your system.

The C++ library ggeodesy is used to handle basic geodesy when needed. Again, you should have the library installed (on your system) to successefuly compile this library.

Vector/Matrix operations are implemented using the eigen3 library. Availability of this library is also mandatory.

Interaction with planetary ephemeris files (i.e. JPL's published DE), is done via the SPICE Toolkit. The toolkit is a C library with a corresponding API.

• Download the C library from the correponding site and uncompress.

• Use the script c2cpp_header.py to tranform C header file. Run the script using the cspice include folder path as command line argument. I.e. if the uncompressed cspice folder is at /home/work/var/cspice, use $> c2cpp_header.py /home/work/var/cspice.

• Run the makeall.csh script provided by the distribution (under cspice folder). Note that the script is in the C-sheel, hence you might need to $>csh makeall.csh.

• Copy the install.sh script under the cspicer folder; run it as root, to install the library. Header files will be available at /usr/local/include and the library at /usr/local/lib.

January 2022: From now on, only the scons build will be supported; support for autotools is dropped.

The project is built via the scons built system:

$> git clone https://github.com/xanthospap/iers2010.git && cd iers2010
$> scons
$> sudo scons install

To compile the test utilities, use the make-test switch (i.e. scons make-test=1). Note that the SOFA ² library is needed to compile and run the tests.

The library can parse EOP information from IERS files using the IERS C04/14 (see updateC04.txt) and IERS C04/20 (see eopc04.txt) file formats/series. The files can be downloaded from IERS, e.g. eopc04_IAU2000.62-now and eopc04.1962-now.

Normally, EOP information is stored in an EopSeries instance, which can hold records for multiple epochs (ordered chronologically) and perform basic utilities such as interpolation.

Users can choose to "regularize" ΔUT1 and LOD values, i.e. remove zonal tidal variations with frequencies ranging from 5 days to 8.6 years from UT1 values (result typically denoted UT1R) and LOD (see Chapter 8.1 of ¹ and [^3]).

The most important and usual operation an EopSeries instance performs, is the interpolation of EOP values for an epoch of interest. This can be done with a simple call to EopSeries::interpolate method. Note that for utmost accuracy certain corrections will have to be applied to the resulting interpolated values, such as removal of libration and ocean tidal effects (see the example source code).

For a complete example of EopSeries usage, see eop_interpolation.cpp.

This library makes use of ggdatetime for handling dates and datetime instances. By default, this means that we are (mostly) handling datetimes in the so-called Modified Julian Date format, instead of the Julian Date format used throughout most of the SOFA ² functions.

The library contains a list of functions for basic astronomical computations, especially related to computations involved in transforming from/to the Geocentric Celestial Reference Frame (GCRF). Declerations can be found in the header files iau.hpp and fundarg.hpp.

There are a number of ways to transform between (geocentric) inertial and earth-fixed frames; in this library, we target the so called "CIO-based" transformation, based on the IAU 200/2006 model (see ² and ¹), as this is the recommended approach as described in the IERS2010 standards.

Once you have compiled the test-suite, you can use the script run_sofa_checks.py to check the compliance with respect to the IAU SOFA library (e.g. run_sofa_checks.py --progs-dir test/sofa_unit_tests/). This will run a number of checks and provide discrepancies (w.r.t. SOFA) for all functions/parameters common to both libraries. Explicit results can be found in this table.

Descripancies for angular parameters are usually checked in units of arcseconds. Descripancies for rotation matrices (.e.g. $R_A$ and $R_B$) are obtained by the axis-angle of the combined matrix as: $\theta = arccos(\frac{(R_A^T R_B) -1}{2})$ again transformed in arcseconds.

• Discrepancies between the SOFA implementation and libiers2010 for one day of GRACE orbit are presented in ??. They ammount up to $\approx 1\times10^{-4} mm$ for the $X$ and $Y$ components and $\approx 2\times10^{-6} mm$ for $Z$. See results here

• The accuracy of the transformation is presented in presented in ??. It is $\approx 5\times10^{-6} mm$ for each of the $X$, $Y$ and $Z$ components.(Note that this is checked again using one day of GRACE orbit, and performing the circular transformation ICRF->ITRF->ICRF). See results here

Once you have compiled the test-suite, you can use the script run_fortran_checks.py to check the compliance of the current library against the FORTRAN subroutines distributed by the IERS. Example run:

$>./run_fortran_checks.py --for-dir fortran_impl/ \
    --cpp-dir test/fortran_unit_tests/ \
    --verbose

To run these unit tests however, you will need to have downloaded the IERS-distributed source code accompanying the standards. Explicit results can be found in this table.

In this implementation computation of GMST is performed using the IAU2006 model, i.e. using both UT1 and TT (see Sec. 5.5.7, ERA based expressions for Greenwich Sidereal Time). Contrary to this, some IERS-distributed FORTRAN subroutines use an older model for GMST (i.e. FCNNUT, PMSDNUT2).

[^3] Bradley, B. K., A. Sibois, and P. Axelrad (2016). “Influence of ITRS/GCRS im- plementation for astrodynamics: Coordinate transformations”. In: Advances in Space Research 57.3, pp. 850–866. issn: 0273-1177. doi: https://doi.org/ 10.1016/j.asr.2015.11.006. url: https://www.sciencedirect.com/ science/article/pii/S0273117715007929.

Software Routines from the IAU SOFA Collection were used. Copyright © International Astronomical Union Standards of Fundamental Astronomy (http://www.iausofa.org)