(Note: The following text is mainly taken from Plag, 2006). The \index{reference systems!ITRS}ITRS is also defined and maintained by the IERS. It is adopted by IAG and IUGG as the primary terrestrial reference system, in particular, for Earth science applications. Unlike the ICRS, the realization of the ITRS through the ITRF is based on a combination of results from several space geodetic techniques, and local survey measurements between reference points of geodetic instruments (so-called local ties)\index{local ties} co-located at the same sites. The combination is coordinated by the IERS, while the observational aspects for each individual technique involved are coordinated by technique-specific Services. Co-location sites (where two or more instruments are operating in close vicinity), are key elements in the ITRF combinations. While any individual space geodesy technique (VLBI, SLR, DORIS, GNSS) is able to provide necessary information for the ITRF, only the combination of the independent techniques allows for the complete determination of ITRF (origin, scale and orientation). In principle, the particular strengths of one observing method can compensate for weaknesses in others if the combination is properly constructed, suitable weights are found, and accurate local ties in co-location sites are available. The conventions for both the ITRS and ICRS and their realizations are detailed in the \index{IERS!Conventions}IERS Conventions \cite[e.g.,][]{mccarthy+pet2004}. As accuracy requirements evolve and technical and modeling capabilities increase, these conventions are modified and developed under the auspice of IERS in a continuous process with support from the broad geodetic science community. In the conventions, the motion of the reference points in ITRF currently is described by a linear model, thus reducing the information necessary to determine the motion of the reference points relative to their coordinates at a reference epoch and a constant velocity. This representation is no longer appropriate to accommodate possible future user requirements to have access to the actual instantaneous point position over the Earth surface and new representation and models are being discussed (see Chapter~\ref{s-futureref}). The coordinates and constant velocities of the points that define a particular reference frame depend on the points, techniques, models, and analysis tools used in the determination of these quantities. Therefore, for any given reference system, there can be a multitude of reference frames realizing the system at various degrees of accuracy. For global terrestrial reference frames, the ITRS is increasingly used as the underlying system, thus gaining importance for practical applications. For example, the U.S. Government and the European Commission agreed to align the reference frames of the \ac{GPS} and GALILEO as close as possible to ITRS \cite[]{europeancom2004}. In practice, this goal is achieved by aligning the GNSS reference frames to the ITRF, which is the most accurate realization of ITRS. The reference frame of the positioning services provided by GPS, is the most recent realization of the \index{reference systems!WGS84}\index{WGS84!see{reference systems}}\ac{WGS84} \cite[e.g.,][]{ASD2001}. As a consequence, this realization of WGS84 is today closely aligned to ITRF and in fact supported by ITRF. ITRF is currently the most accurate realization of ITRS \cite[]{altamimi++2002,altamimi++2007}. The ITRF is updated regularly with the most recent versions being ITRF97, \index{reference frames!ITRF2000}ITRF2000, and \index{reference frames!ITRF2005}ITRF2005. In geodetic analyses of observations of different groups using different techniques and different software packages, coordinates agree to the centimeter level. Secular trends determined from long GPS records using different analysis approaches may disagree on the order of 1 to 2 mm/yr, but most of these discrepancies are due to the approach used to align the solution to ITRF. A significant bias may result from a potential secular translation of the \index{reference frames!origin}\ac{RFO} with respect to the \index{Earth system!center of mass of}\ac{CM}. Recent studies estimate the bias to be of order $\pm2$ mm/yr \cite[e.g.,][]{ray++2004,morel+wil2005,plag2006f,plag++2007a}, depending on the geographical location. \index{CM|see{Earth system, center of mass}} The translation of the RFO with respect to the CM introduces particularly large uncertainties in \index{sea level}sea level studies. Taking the effect on vertical velocities of the secular translation between ITRF2000 and ITRF2005 (Figure~\ref{f-ITRF2005-height}) as an indication of the uncertainty in the tie of the RFO to the CM, the effect on global sea level trend estimates is of the order 0.2 to 0.3 mm/yr. Consequently, not only maintenance but also improvement of the ITRF as the essential architecture for almost all geodetic measurements is a crucial requirement for sea level studies. \begin{figure} \bc \vspace*{-0.5cm} \includegraphics[width=11cm]{figures/figure2.2.eps} \ec \vspace{-0.5cm} \caption[Effect of secular translation between ITRF2000 and ITRF2005 on vertical rates]{\label{f-ITRF2005-height}Effect of secular translation between ITRF2000 and ITRF2005 on vertical rates. The vertical rates are for a secular translation velocity of $\vec{d} = (-0.2,0.1,-1.8)$ mm/yr as given on http://itrf.ensg.ign.fr/ITRF\_solutions/2005/.} \end{figure} --------------------------------------------------- Attempts to define and realize reference systems or at least global reference surfaces and parameters of the Earth were made in the beginning of the \cent{19}{th} century, though mainly on national or regional level. An example is the sequence of reference ellipsoids starting with the one defined by Bessel in 1841, which was used for the German national reference frame (DHDN) determined by triangulation. Other such national reference frames were the OSGB36 in the U.K. and NTF in France. After world war II, the ED50 was introduced as a European unification. It should also be mentioned that separate attempts were made for systems for geographical coordinates and height datums. Geoidal reference surfaces provide another example for a reference, which, in principle, could have been used as a global reference for height. \begin{table*} \caption[List of reference ellipsoids introduced in the past.]{\label{t-refellips} List of reference ellipsoids introduced in the past.} \bc {\small \begin{tabular}{lrll} \hline {\bf Name of ellipsoid} & {\bf semimajor} & {\bf flattening} & {\bf applied for} \\ & {\bf axis} $a$ [m] & $f = (a-b)/a$ & \\ \hline \hline Geodetic Reference System 1980 (GRS80) & 6 378 137. & 1 : 298.25722 & World Geodetic \\ &&& System 1984 \\ World Geodetic System 1972 (WGS72) & 6 378 135. & 1 : 298.26 & World Geodetic \\ &&& System 1972 \\ Geodetic Reference System 1967 & 6 378 160. & 1 : 298.25 & Australian Datum \\ &&& 1966 \\ & & & South American \\ &&& Datum 1969 \\ Krassovski (1942) & 6 378 245. & 1 : 298.3 & Pulkovo Datum \\ &&& 1942 \\ International (Hayford 1924) & 6 378 388. & 1 : 297.0 & European Datum \\ &&& 1950 \\ Clark (1866) & 6 378 206. & 1 : 294.98 & North American \\ &&& Datum 1927 \\ Bessel (1841) & 6 377 397. & 1 : 299.15 & German DHDN \\ \hline \end{tabular} } \ec \end{table*} One of the first geodetic application requiring a precise global terrestrial reference system in three dimensions was the observation of Earth rotation starting around the middle of the \cent{19}{th} century \cite[see][for a historical overview]{mulholland+car82}. Subsequently, a number of global reference systems were introduced on national or international level and realized in various ways. A prominent role was attached to the international scientific bodies responsible for Earth rotation monitoring, such as the International Latitude Service (ILS), the International Polar Motion Service (IPMS), the Bureau International de l'Heure (BIH), and, currently, the IERS. The IAG has a historical role in the development of conventional reference frame responding to or even prompting the development of observational techniques. Thus, the IAG Commission RETRIG continued to update ED50 until 1987 through ED79 and ED87. In 1967, the IAG and also the IAU adopted the Conventional International Origin (CIO) frame, with a pole defined for the epoch 1903.0 as the mean of the ILS observations of the pole during the period 1900.0 to 1906.0. These two scientific bodies also introduced the systems presently used for most accurate applications (see below). Until 1984, the international accepted TRS was the CIO-BIH system, which was realized by use of Earth Rotation Parameters (EOP). The frame was a network of astronomical instruments with coordinates determined by astronomical observations. In 1984, the BIH started to produce the BTS, which was realized through a new type of TRF based on space geodesy. In 1987, the IERS was established by IUGG and IAU as a FAGS services with the mission to materialize the a CRS and a TRS as well as determine EOP. The IERS replaced the BIH. As milestones in the development of the scientifically promoted (i.e.~through IUGG and IAG) system, it should be mentioned that in 1979, the IUGG accepted the Geodetic Reference System 1980 (GSR80), which, among others, specifies relevant constants and the geometrical and physical parameters of the figure of the Earth (table \ref{t-grs80}). The need for global terrestrial reference systems allowing, in principle, for materializations on the sub-centimeter level did not arise before the invention of the space- and satellite-geodetic techniques allowing for ground-based geodesy on global scale. At the same time, these techniques for the first time provided the means for high-accuracy materializations of such systems. These techniques are the satellite- and space-geodetic methods (such as Transit, SLR, GPS, LLR, VLBI) developed over the last four decades. \begin{table*} \caption[Geodetic Reference System 1980 (GRS80).]{\label{t-grs80} Geodetic Reference System 1980 (GRS80). The GRS80 was adopted by IAG during the General Assembly 1979. Here, the principal parameters are given.} \bc {\small \begin{tabular}{lll} \hline {\bf parameter} & {\bf symbol} & {\bf value} \\ \hline \hline \multicolumn{3}{c}{\bf def\-ining constants} \\ equatorial radius of the Earth & $a$ & 6378137 m \\ geocentric gravitational constant & $ GM $ & $3986005 \cdot 10^8$ m$^3$s$^{-2}$ \\ (including the atmosphere) & & \\ dynamical form factor & $J_2$ & $108263 \cdot 10^{-8}$ \\ (excluding permanent tides) & & \\ angular velocity of the Earth & $\omega$ & $7292115 \cdot 10^{-11}$ rad s$^{-1}$ \\ \hline \multicolumn{3}{c}{\bf derived geometrical parameters} \\ semiminor axis (polar radius) & $b$ & 6356752.3141 m \\ f\-irst excentricity & $e^2$ & 0.00669438002290 \\ flattening & $f$ 1 : 298.257222101 \\ mean radius & $R_1$ & 6371008.7714 m \\ radius of sphere with same surface & $R_2$ & 6371007.1810 m \\ radius of sphere with same volume & $R_3$ & 6371000.7900 m \\ \hline \multicolumn{3}{c}{\bf derived physical parameters} \\ normal potential at ellipsoid & $U_0$ & 62636860.850 m$^2$s$^{-2}$ \\ Normal gravity at equator & $g_{\rm e}$ & 9.7803267715 m s$^{-2}$ \\ Normal gravity at pole & $g_{\rm p}$ & 9.8321863685 m s$^{-2}$ \\ \hline \end{tabular} } \ec \end{table*} The development of particularly VLBI and SLR led to a number of single or two-technique defined reference frames used mainly for scientific geodetic purposes. The successor of the BIH, the IERS started to produce a sequence of annual realizations of the IERS Terrestrial Reference System (again the successor of the BTS) with the IERS Terrestrial Reference Frame 1988 (ITRF88). The ground for a formal acceptance of this TRF through the relevant international scientific organizations as the CTRS was laid at the 1991 IUGG Assembly in Vienna, when the IUGG in its Resolution 2 specified the Conventional Terrestrial Reference System to be used (see Appendix \ref{a-IUGG91}). The system specified by this Resolution was at that time already under implementation by the IERS and several realizations through IERS Terrestrial Reference Frames had already been determined (ITRF88, ITRF89, ITRF90) and published. Following this Resolution, the IAG in 1991 adopted the Resolution 1, which specifies the currently accepted CTRS (Appendix \ref{a-IAG91}). Today, the most accurate global terrestrial reference system is maintained by the IERS through international cooperation. The ITRS is specified in detailed in the IERS Conventions \cite[]{mccarthy+pet2003}. In Newtonian theory, the underlying ideal Terrestrial Reference System can be considered to be a three-dimensional coordinate system with origin close to the Earth and co-rotating with it. The geometry of an Euclidian affine space of dimension 3 provides a standard model of such a system. Using the affine frame $(O,E)$, where $O$ is a point in space called origin and $E$ a vector base of the associated vector space. Currently, $E$ is restricted to be orthogonal with all base vectors having the same length. The common length of the base vectors is named the scale of the TRS. However, it should be kept in mind that this this Newtonian model is valid to visualize the concept for practical users, but the actual definition of the CTRS today has to be based on the General Theory of Relativity, where the CTRS is a local Earth system as specified in the IAU 1991 resolutions. The ITRS follows the criteria given in \cite{boucher90}: \bi \item[a)] It is geocentric, the center of mass being defined for the whole Earth, including oceans and atmosphere. \item[b)] Its scale is that of a local Earth frame, in the meaning of a relativistic theory of gravitation. \item[c)] Its orientation was initially given by the BIH orientation at 1984.0. \item[d)] Its time evolution in orientation will create no residual global rotation with respect to the crust. \ei In agreement with the relevant IAU 1991 resolutions, the unit of length is the SI meter. The scale is obtained by appropriate relativistic modeling. The orientation is defined by adopting IERS Earth orientation parameters at a reference epoch. In case of dynamical observation techniques, an additional constraint in longitude is necessary to remove ill-conditioning. The IERS Reference Pole (IRP) and Reference Meridian (IRM) are consistent with the corresponding directions of the BTS within $\pm 5$ mas. The BIH reference pole was adjusted to the CIO in 1967 and was kept stable until 1987. The uncertainty in the tie of the IRP with the CIO is $\pm 30$ mas. The time evolution of the orientation is to be ensure by using a No-Net-Rotation (NNR) condition with respect to horizontal tectonic motion averaged over the whole Earth. It should be mentioned here that there are several controversial conventions, including the implementation of the NNR condition, but also the treatment of the permanent tide, which is in disagreement with the conventions in gravity and IUGG resolutions.