Terrestrial Reference Systems and Frames

Home , Spatial reference system, Terrestrial Time

.. ai concepts Basic terminology 4.1.1 and frames Concepts and systems reference 4.1 Terrestrial 4 hsclsaei osdrda ulda ffiesaeo ieso .I this In ( frame 3. affine dimension Euclidean of a space is the affine trihedron framework, Euclidean trihe- reference Newtonian a the a reference In as such a case, it. considered as with is modeled co-rotating space and is to the physical Earth TRS varia- In attached the a small to deformations). points astrogeodesy, close only tidal of dron in or undergo (tectonic adopted positions which effects model geophysical system, coordinates physical to have a due in Earth such time, Earth the with In the tions of with surface space. co-rotating solid system in the reference motion spatial diurnal a its is realizations (TRS) their System and erence Systems Reference Terrestrial ftesaenamed space the of aelnt o h ai etr.Tetilto ntvcoscliert h basis the to collinear vectors unit its of vectors triplet the The expresses vectors. vectors basis the for length same on restrictions adopted currently oainmatrix) rotation faypitcoet h at rmTS()t R 2 sgvnb three- a by given is (2) TRS to (1) TRS from Earth the coordinates ( to Cartesian similarity close the dimensional of point coordinate co- transformation any on Cartesian general of reference the to hypotheses, general addition these a In Under For (2001). meter. systems, Boucher used. SI coordinate see be an other systems, TRS), could to a close coordinates, such is geographical with scale associated (the the (naturally cen- equatorial Earth’s and ordinates is the pole) to orientation close the the is of (geocenter), origin the mass which of for ter TRSs geocentric consider we Here, X scale one components, Eu- respectively, designated translation a angles, R and is three rotation formulas systems three parameters: linearized and reference seven factor, the two of uses between similarity IERS transformation clidean the standard (4.2), The Equation notation. of local application 11. a the and of 10 In general part Chapters concerning model spatial see details background more the models, For relativistic using relativistic 1986). a Relativity, (Boucher, of of system coordinate frame Theory Cartesian General the Einstein’s in as generalized such be can concept This es n ieecsi cl n retto r ttelvlo 10 me- of hundred level gives few the time at a to are respect about orientation are and provided scale differences coordinates in Origin station differences of and sets techniques. for ters, linear geodesy is space (4.3) Equation by that assumed is It vector vector coordinate a of tion where ~ ,adterfis iederivatives: time first their and 3, 1 , X ~ 2 λ X X X T ~ ~ ~ ~ , X ˙ ~ T 2 2 = (2) 2 = D , = = xrse nrfrnesse 2,i ie by given is (2), system reference in expressed , k scale = T ~ E ~ X X ~ ~ 1 ˙ i , and T ~ 1 1 k 2 1 , i + + T , , D 2 T T + ~ ~ R = ˙ = + + origin λ i      r ucin ftm.Dffrnitn qain(.)with (4.3) Equation Differentiating time. of functions are λ 1 orientation 1 = D D , 1 2 ˙ T , ~ T T T 2 X X · ~ ~ 1 3 2 1 , − R , 1 1 X 2 2 ~ 1 1, , and + +      satasainvector, translation a is 1 , 3 2 xrse nrfrnesse 1,it coordinate a into (1), system reference in expressed , . D R R , · X X X ~ E ~ ~ ( = ˙ R (1) E 1 1 , sabsso h soitdvco pc.The space. vector associated the of basis a is + fteTSadtecmo egho these of length common the and TRS the of T R = . r ob ih-add rhgnlwt the with orthogonal right-handed, be to are ˙ 1, R 1      ˙ , 2 X T ~ − ˙ 1 2, − R I + 0 R ,and ), T 0 3 ˙ 2 R 3, X ~ ˙ D − ˙ 1 R , . I R 0 1 R λ steiett arxs that so matrix identity the is ˙ 3 1 1, , 2 R − cl atrand factor scale a ˙ R T 2, R Z 2 1, 1 R ersra Ref- Terrestrial A . ˙ O xsi h direction the is axis T .Tetransforma- The 3.      , 2, E . T ). − 3, 5 O Generally, . D Technical sapoint a is , R R 1, IERS Note (4.1) (4.2) (4.4) (4.3) 1 R , e.g. 2 2, a 31 No. 36 32 No. 36 Note Technical .. R nsaegeodesy space in TRF 4.1.2 IERS qain(.)cudb rte as written be could (4.4) Equation and D ncs frmvbeo os osrit,ti mut oadn h following the adding to amounts this constraints, alter loose may or equation and removable observation suitable of longer parameters. case no estimated In is the remove), of quality to real easy ( the not constraints tight numerically very are where (which method, old the that Note stations: one of add sub-set currently a centers or analysis all the upon deficiency, constraints rank following this the observations. with of the cope by to reduced order not In normal are upon the which that constructed parameters fact datum usually the of equations, by reflected normal is complete of situation matrix, to this terms needed observations, In is geodesy to space information information definition. additional necessary datum some the the TRF, all contain a not establish do completely observations geodesy a space sur- using Since Earth’s evolution the over time motions orientation’s horizontal to face. the respect define with to condition no-net-rotation recommended defined. conventionally is ( or it arbitrary parameters is Meanwhile physical technique, any some by unobservable on orientation, TRF which depends around the scale (point constant The of mass tech- gravitational of parameters dynamical center orbits). the through satellite the being accessible the DORIS), all theoretically GNSS, to SLR, is (LLR, origin sensitive niques The not definition. are datum techniques 14 the geodesy orienta- of added Space scale, evolution. selection are origin, time which The TRF their to evolution. the and epoch, establishes time tion given definition,” TRF a “datum the at called define TRF parameters, to a derivatives fix time to their needed are parameters Seven sas eintda rs-ae R n ecie nmr eali Section in detail more in It described System. is and a Reference TRF in realization Terrestrial crust-based coordinates the a a determined 4.1.3. of that as precisely realization designated here with a also consider as points is We system physical axes coordinate of orientation evolution. origin, specific set its time a of by their realization achieved the and through scale, TRS, a and have of realization users the which as to (TRF) Frame (TRF), definition, Reference Frame Terrestrial theoretical Reference a Terrestrial having a TRS, access. a realization, between its distinguish and to fundamental is It Mnmmcntansue oeyt en h R sn iiu amount minimum a using TRF the define to solely used constraints Minimum constraints 3. the to applied uncertainty the where solutions constraints: Loose 2. positions station estimated the which for solutions constraints: Removable 1. and R frqie nomto.Frmr eal ntecnet n practical or and (2001) Boucher concepts and the Sillard instance on for details see Altamimi more constraints, minimum For of use information. required of is Altamimi uncertainty instance an for see within removable, values easily external to constrained σ are velocities and/or X X X ~ ~ ~ ˙ R ˙ ≈ σ N 2 1 − = r tte10 the at are ≥ 10 hc ersn bu . moe 0 er r elgbe Therefore, negligible. are years 100 over mm 0.1 about represent which ssnua,snei a akdfiinycrepnigt h number the to corresponding deficiency rank a has it since singular, is , X ~ X o oiin and positions for m 1 − ~ 0 ˙ 5 1 0 = o oiin n / o eoiis hstp fcntan is constraint of type This velocities. for m/y and positions for m + tal. et T ~ , ˙ + (2002a). D − GM ˙ 5 X ~ ee and level 1 + n pe flight of speed and R ˙ X ~ 1 ≥ . X ~ ˙ 0c/ o velocities. for cm/y 10 saot1 mprya,s h terms the so year, per cm 10 about is ersra eeec rm sdefined is Frame Reference Terrestrial A . ersra eeec ytm n frames and systems reference Terrestrial 4 c n eaiitcmdln.The modeling. relativistic and ) tal. et 20a 2002b). (2002a; σ ≤ 10 − 10 )aeapplied are m) e.g. D (4.5) (4.6) geo- X ~ ˙ 1 4.1 Concepts and terminology IERS Technical

Note No. 36

where X~ is the vector of estimated parameters (positions and/or velocities) and X~ 0 is that of the a priori parameters. Meanwhile, in the case of minimum constraints, the added equation is of the form

B(X~ − X~ 0) = 0, (4.7)

where B = (AT A)−1AT and A is the design matrix of partial derivatives, constructed upon a priori values (X~ 0) given by either   ......    i i i   1 0 0 x0 0 z0 −y0          A =  i i i  (4.8)  0 1 0 y0 −z0 0 x0           i i i   0 0 1 z0 y0 −x0 0    ......

when solving for only station positions, or

  ......    i i i   1 0 0 x0 0 z0 −y0     i i i   0 1 0 y0 −z0 0 x0 0     i i i   0 0 1 z0 y0 −x0 0  A =   (4.9)  i i i   1 0 0 x0 0 z0 −y0     i i i   ≈ 0 0 1 0 y0 −z0 0 x0     i i i   0 0 1 z0 y0 −x0 0    ......

when solving for station positions and velocities. The fundamental distinction between the two approaches is that in Equation (4.6), we force X~ to be equal to X~ 0 (to a given σ), while in Equation (4.7) we express X~ in the same TRF as X~ 0 using the projector B containing all the necessary information deﬁning the underlying TRF. Note that the two approaches are sensitive to the conﬁguration and quality of the subset of stations (X~ 0) used in these constraints. In terms of normal equations, Equation (4.7) could be written as T −1 ~ ~ B Σθ B(X − X0) = 0, (4.10)

where Σθ is a diagonal matrix containing small variances for each of the transformation parameters. The general form of the singular normal equation constructed upon space geodesy observations could be written as

N(∆X~ ) = K, (4.11)

where ∆X~ = X~ − X~ 0 designates the linearized unknowns and K is the right-hand side of the normal equation. Adding Equation (4.10) to the normal equation (4.11) allows it to be inverted and simultaneously to express the estimated solution X~ in the same TRF as the a priori solution X~ 0. Note that the 7 columns of the design matrix A correspond to the 7 datum parameters (3 translations, 1 scale factor and 3 rotations). Therefore, this matrix should be reduced to those parameters which need to be deﬁned (e.g. 3 rotations in almost all techniques and 3 translations in case of VLBI). For more practical details, see, for instance, Altamimi et al. (2002a).

33 34 No. 36 .. h nentoa ersra eeec System Reference Terrestrial International The 4.1.4 TRF Crust-based 4.1.3 Note Technical IERS h TSdfiiinfllstefloigconditions: following the 1984.0. fulfills coincides epoch orientation definition the ITRS ITRS at the the The system that at BIH consideration IERS previous the the the to by with led adopted work statement its procedure de of practical the International the beginning Following The (Bureau to considering agreements orientation). assimilated system). fixed, international (BIH) is coordinate the fully l’Heure ITRS 4d fulfills therefore orientation the the is its that to ITRS that way not the a (and summary, such GTRS previous in of read part spatial be the should naviga- text system. (mapping, Perugia three-dimensional applications The a within practical as practical developed all ITRS and presently that consider ex- are scientific tion) and For models various framework geophysical three-dimensional. as Newtonian accurate as well the that ITRS as note the we 1991, defining ample, to of explicitly Resolution led IAG considerations, the fact, In Resolutions) 1991 IAU of latest resolutions IUGG with and consistent Resolution (IAG 2007, texts its legal and through these synthesize (2007), and Perugia summarize To in C). adopted Assembly Appendix formally General recently (see its Ter- 2 been International at has the IUGG ITRS promoting the The and by realizing (ITRS). defining, System of Reference charge restrial in is IERS The all by used models and adopted adopted currently The be 7. Chapter data. models in geodesy conventional described space high- are same with remove the dealing centers to that analysis is essential is position It regularized a corrections conventional of using ∆ ones) introduction geophysical (mainly variations the time frequency of purpose The on anchored point a epoch of at position crust instantaneous Earth’s the the connecting (see model products by general IERS either The as activities, ultimately and IERS 4.1.5). centers, in combination Section by determined or currently centers those analysis are TRFs Crust-based X ~ Tetm vlto fteoinaini nue yuigano-net-rotation a using by ensured is orientation 1984.0; the at of orientation evolution BIH time the by The given 4. initially was orientation Its TCG the 3. with consistent is Earth, scale whole The (SI). the meter for the mass is length of of center unit the The being 2. origin its geocentric, is It 1. • • • • i ( odto ihrgrst oiotltcoi oin vrtewoeEarth. whole the over motions tectonic horizontal to regards with condition and IAU mod- with relativistic appropriate agreement by in obtained frame, is eling; This local resolutions. geocentric (1991) a IUGG for coordinate time atmosphere; and oceans including no-net-rotation a surface. follows Earth GTRS horizontal the of to orientation regards fact. the with this condition with of (NNR) consistent evolution is There- time coordinates spatial Time). The the Coordinate of (Geocentric scale TCG system the is Earth fore, coordinate whole time the GTRS for The atmosphere. considered and orientation. geocenter, oceans and the TRS including scale body, is specific origin, a origin the of GTRS fixing identification rules The the conventional designate is of of to list CTRS term a designation term generic through the new a while as the used system), is now reference system) terrestrial (conventional reference CTRS terrestrial (geocentric GTRS t X ,i re ooti oiinwt oerglrtm variation. time regular more with position a obtain to order in ), ~ ( t = ) X ~ R ( t + ) X i ∆ t , X ~ X ~ i ( ( t t ) ,adarglrzdposition regularized a and ), . ersra eeec ytm n frames and systems reference Terrestrial 4 X ~ R ( t is ) (4.12) 4.2 ITRF products IERS Technical

Note No. 36

4.1.5 Realizations of the ITRS Primary realizations of the ITRS are produced by the IERS ITRS Center (ITRS-PC) under the name International Terrestrial Reference Frame (ITRF). Twelve ITRF versions were produced, starting with ITRF88 and ending with the ITRF2008. Up to the ITRF2000 solution, long-term global solutions (comprising station positions and velocities) from four techniques (VLBI, SLR, GPS and DORIS) were used as input for the ITRF generation. As described in more detail later, starting with the ITRF2005, time series of station positions and Earth Ori- entation Parameters (EOPs) are used as input data for the ITRF construction. The current procedure is to combine the technique TRF solutions using a combination model which is essentially based on the transformation formulas (4.3) and (4.5). The combination method makes use of local ties in co-location sites where two or more geodetic techniques are operated. The local ties are used as additional observations with proper variances. They are usually derived from local surveys using either classical geodesy or the global navigation satellite systems (GNSS). As they represent a key element of the ITRF combination, they should be more, or at least as accurate as the individual space geodesy solutions incorporated in the ITRF combination. Up to ITRF2000 ITRF solutions were published by the ITRS-PC in Technical Notes (cf. Boucher et al., 1996, 1998, 1999, 2004). The number following the designation “ITRF” speciﬁes the last year whose data were used for the formation of the frame. Hence, ITRF2008 designates the frame of station positions and velocities constructed in 2010 using data available until the end of 2008 (2009.5 for GPS).

The current ITRF model is linear (position at a reference epoch t0 and velocity). Therefore, the station position at an epoch t is expressed as: ˙ X~ (t) = X~ 0 + X~ · (t − t0). (4.13)

˙ The numerical values are (X~ 0, X~ ). In the past (ITRF88 and ITRF89), constant positions were used as models (X~ 0), the linear motion being incorporated as conventional corrections derived from a tectonic plate motion model (see Sec- tion 4.2.2). The reader may also refer to an earlier report of the ITRF Working Group on the ITRF Datum (Ray et al., 1999), which contains useful information related to the history of the ITRF datum definition. It also details technique-specific effects on some parameters of the datum definition, in particular the origin and the scale. More details on the formation of ITRF2000 and ITRF2005 are available in Altamimi et al. (2002b, 2007).

4.2 ITRF products 4.2.1 The IERS network The initial definition of the IERS network The IERS network was initially defined through all tracking instruments used by the various individual analysis centers contributing to the IERS. All SLR, LLR and VLBI systems were included. Eventually, GPS stations from the IGS were added as well as the DORIS tracking network. The network also included, from its beginning, a selection of ground markers, specifically those used for mobile equipment and those currently included in local surveys performed to monitor local eccentricities between instruments for co-location sites or for site stability checks. Each point is currently identified by the assignment of a DOMES (Directory of MERIT Sites) number. The explanation of the DOMES numbering system is given below. Close points are clustered into one site. The current rule is that all points which could be linked by a co-location survey (up to 30 km) should be included into the IERS network as a unique site having a unique DOMES site number. In reality, for a local tie to be precise at the 1 mm level, the extension of a co-location site should not exceed 1 km.

35 36 No. 36 .. itr fIR products ITRF of History 4.2.2 Note Technical IERS rmIR8 ilIR9,teIR au ento a esmaie as summarized be can definition datum ITRF predecessor. the its ITRF93, superseded follows: which till of ITRF88 each with starting From ITRF2008, published, with were ITRF ending the and of versions IUGG ITRF88 twelve the writing, by of time created the was Until IERS the IAU. then 1988, were the in realizations in- and before BTS the BTS87, successive Intercomparison for with other and ending center Three achieved, Rotation coordinating 2000). Earth a Wilkins, of being Techniques; BIH, of (Monitoring realized of was project activities BTS84 MERIT the prede- ternational 1985). of combined Altamimi, (the framework a and Doppler/TRANSIT the time (Boucher station and in observations first using SLR GPS) the established LLR, of for was VLBI, cessor when BTS84) from 1984, 1984 derived to System coordinates Terrestrial back BIH goes (called ITRF TRF the of history The emnn NSntok ra es ogtDMSnmes(o ntnethe instance USA). (for the numbers in network DOMES (EUREF) (CORS) get either Frame Stations to Reference network, Reference least European IERS Operating at the orga- Continuously the or instance national network) into (for GNSS or included IERS permanent continental by networks computed some fiducial be of their to wish see the to is nizations time for extension systems important instance (for Another gravimeters, useful absolute as regarded or was super-conducting it transfer, if considered, be processing also the could during estimated measurements, be radio parameters can of tropospheric that raw delays measurements, derive Observing propagation surface to tropospheric Level order meteorological from in Sea accurate pressure, atmospheric Global collect particular to in the UNESCO. is for of application auspices interest in Another the of instruments, under IERS is program with (GLOSS) DORIS, co-located System or gauges tide GNSS of particular cataloging the instance, For each for code character a one which a for interest. uses and potential (IERS IERS are of the assigned are in type): be allowed which can points systems number of of DOMES types types current new network the IERS include Consequently, initial to the communities, expanded user was various of requirements the network Following IERS the of Extensions IERS unique a to belong same should the points site. co-located of Usually, instruments techniques. and such different situations measurements or include non-simultaneous These or that dimensions. fact simultaneous three the as in as surveyed locations defined precisely close very be very are can subsequently that or co-location simultaneously of occupying concept are the instruments IERS, two the of frame the In Co-locations • • • • • • • • • • rgnadsae endb naeaeo eetdSRsolutions; SLR selected of average an by defined scale: and Origin o eerlgclsensor. meteorological for W (PRARE), gauge, equipment tide rate for range T and BIH), range the precise by for used past), X (formerly the astrometry in optical (NNSS) for System A Satellite Navigation Navy Doppler also RIS; intégrés (DO- radiopositionnement satellite et détermination par (GNSS), d’orbite for systems D satellite navigation global for (VLBI), interferometry P baseline long very for (LLR), R ranging laser lunar for (SLR), M ranging laser satellite for L e.g. aeb h NS LI rDRS te systems Other DORIS. or VLBI, GNSS, the by made ersra eeec ytm n frames and systems reference Terrestrial 4 etc. ). 4.2 ITRF products IERS Technical

Note No. 36

• Orientation: defined by successive alignment since BTS87 whose orientation was aligned to the BIH EOP series. Note that the ITRF93 orientation and its rate were again realigned to the IERS EOP series; • Orientation time evolution: No global velocity field was estimated for ITRF88, ITRF89 and ITRF90, so the AM0-2 model of Minster and Jordan (1978) was recommended. Starting with ITRF91 and till ITRF93, combined velocity fields were estimated. The ITRF91 orientation rate was aligned to that of the NNR- NUVEL-1 model (Argus and Gordon, 1991), and ITRF92 to NNR-NUVEL-1A, adapted from NNR-NUVEL-1 according to DeMets et al. (1994), while ITRF93 was aligned to the IERS EOP series.

Since the ITRF94, full variance matrices of the individual solutions incorporated in the ITRF combination have been used. At that time, the ITRF94 datum was achieved as follows (Boucher et al., 1996): • Origin: defined by a weighted mean of selected SLR and GPS solutions; • Scale: defined by a weighted mean of VLBI, SLR and GPS solutions, corrected by 0.7 ppb to meet the IUGG and IAU requirement to be compatible with TCG, while analysis centers provide solutions that are compatible with TT (Terrestrial Time); • Orientation: aligned to the ITRF92; • Orientation time evolution: velocity field aligned to the model NNR-NUVEL- 1A, using the 7 rates of the transformation parameters. The ITRF96 was then aligned to the ITRF94, and the ITRF97 to the ITRF96 using the 14 transformation parameters (Boucher et al., 1998; 1999). The ITRF2000 was intended to be a standard solution for geo-referencing and all Earth science applications. Therefore, in addition to primary core stations observed by VLBI, LLR, SLR, GPS and DORIS, the ITRF2000 was densified by regional GPS networks in Alaska, Antarctica, Asia, Europe, North and South America and the Pacific. The individual solutions used for the ITRF2000 combination were generated by the IERS analysis centers using removable, loose or minimum constraints. In terms of datum definition, the ITRF2000 is characterized by the following properties:

• Origin: realized by setting to zero the translation components and their rates between ITRF2000 and a weighted average of the most consistent SLR solutions; • Scale: realized by setting to zero the scale and scale rate parameters between ITRF2000 and a weighted average of VLBI and the most consistent SLR solutions. Unlike the ITRF97 scale which is compatible with TCG, that of the ITRF2000 is compatible with TT; • Orientation: aligned to that of the ITRF97 at 1997.0; • Orientation time evolution: aligned, conventionally, to that of the geological model NNR-NUVEL-1A (Argus and Gordon, 1991; DeMets et al., 1990; 1994).

The ITRF network has improved with time in terms of the number of sites and co- locations as well as their distribution over the globe. Figure 4.1 shows the ITRF88 network including about 100 sites and 22 co-locations (VLBI/SLR/LLR), and the ITRF2008 network containing 580 sites and 105 co-locations (VLBI/SLR/GPS/- DORIS).

4.2.3 ITRF2005 For the ﬁrst time in ITRF history, the ITRF2005 used as input data time series of station positions (weekly from satellite techniques and 24-hour session-wise from VLBI) and daily EOPs. One set of time series per space geodesy technique was considered as input to the ITRF2005 combination. These solutions are the oﬃcial

37 38 No. 36 Note Technical IERS Co-located techniques--> 1 2 3 2 1 h eoe ecne oin r eandi h ekySNXfie ne h aaeesXC G,adZGC. and YGC, XGC, parameters the under files SINEX weekly the in retained are motions geocenter removed The iue41 TF8(et n TF08(ih)stsadc-oae techniques. co-located and sites (right) ITRF2008 and (left) ITRF88 4.1: Figure 02 20 08.TeIR20 retto a pc 000 n t aeaeaindto aligned are rate quality. its Collilieux, geodetic and high and 2000.0) of (Altamimi epoch stations ITRF2005 70 ppb (at for using -0.5 orientation used ITRF2000 of ITRF2005 offset solutions The scale IVS constant the 2008). a the to revealed where applied respect solutions was with IVS correction of was tide analyses it by pole did Post-ITRF2005 recommended mean ITRF2005 construction path 2003. pole of ITRF2005 the Conventions mean years the the of IERS to 26 for the referenced release corrections spanning used the tide solutions series nullifying pole after include VLBI time by not that IVS VLBI defined noted the the is that be to scale discovered respect should SLR Its the with and It by rate translations observations. averaged observations. its zero of mass, and has years of scale it center 13 the that Earth spanning way the series a to time such respect in with defined rates translation is origin ITRF2005 The oiin n eoiis,ohripratIR20 eut r loaalbeto (station available products also are ITRF results ties usual namely: ITRF2005 the local users, important to the the the other addition combining with velocities), in (2) together and and Therefore, techniques positions EOPs; four sites. daily the co-location as well of in as solutions positions velocities long-term station and comprising resulting epoch technique time reference per individual solution a the long-term stacking at a (1) estimate steps: to to two refer series of may consisted reader generation sub- the ITRF2005 The details were more solutions For individual centers. that analysis Altamimi so DORIS available, two not time by International the were the mitted from At (IDS) solutions (IGS). combined Service weekly Service Laser DORIS official International GNSS release, Interna- International the ITRF2005 the the the (IVS), by of and Astrometry ITRF2005 activities (ILRS) and the Service to the Geodesy Ranging submitted for in indi- were Service participating corresponding series VLBI centers time the tional Official analysis of solutions TC. basis the each TC (daily) by of official weekly as provided these the known solutions at that techniques, vidual combination Note 4 a IERS. the from of the result services within international (TC) the Centers Technique by provided series time fl iesre fEP ossetwt h ITRF2005. the with consistent EOPs of series time full 4. goetrtm eisfo L n OI.Teei oueu geocenter useful no is There DORIS. and SLR the from of series stacking time the geocenter from 3. resulting residuals position station of series positions, time station containing 2. files SINEX technique per and ITRF2005 full 1. 3 umte ekysltosbigaindt ITRF2000; to aligned being solutions weekly submitted oinifrainfo P/G eas thsbe removed been has it because GPS/IGS from information motion techniques; 4 the of series time individual matrices; variance-covariance complete with EOPs and velocities tal. et (2007). Co-located techniques--> 1 ersra eeec ytm n frames and systems reference Terrestrial 4 71 2 28 3 < 1 > 6 the , 4 4.2 ITRF products IERS Technical

Note No. 36

4.2.4 ITRF2008, the current reference realization of the ITRS Following the same strategy initiated with the ITRF2005 release, the ITRF2008 is a reﬁned solution based on reprocessed solutions of four space geodesy techniques: VLBI, SLR, GPS and DORIS, spanning 29, 26, 12.5 and 16 years of observations, respectively. The ITRF2008 is composed of 934 stations located at 580 sites as illustrated in Fig. 4.1, with an imbalanced distribution between the northern (463 sites) and the southern hemisphere (117 sites). As illustrated by Fig. 4.1, there are in total 105 co-location sites; 91 of these have local ties available for the ITRF2008 combination. Note that, unfortunately, not all these co-located instruments are currently operating. For instance, among the 6 sites having 4 techniques, only two are currently fully operational: Harte- beesthoek, South Africa and Greenbelt, MD, USA. The ITRF2008 is speciﬁed by the following frame parameters:

• Origin: The ITRF2008 origin is defined in such a way that there are zero translation parameters at epoch 2005.0 and zero translation rates with respect to the ILRS SLR time series. • Scale: The scale of the ITRF2008 is defined in such a way that there is a zero scale factor at epoch 2005.0 and a zero scale rate with respect to the mean scale and scale rate of VLBI and SLR time series. • Orientation: The ITRF2008 orientation is defined in such a way that there are zero rotation parameters at epoch 2005.0 and zero rotation rates between ITRF2008 and ITRF2005. These two conditions are applied over a set of 179 reference stations located at 131 sites, including 107 GPS, 27 VLBI, 15 SLR and 12 DORIS sites.

4.2.5 ITRF as a realization of the ITRS The procedure used by the IERS to determine ITRF products includes the following steps:

1. definition of individual TRF used by contributing analysis centers. This implies knowing the particular conventional corrections adopted by each analysis center; 2. determination of the ITRF by the combination of individual TRF and datum fixing. This implies the adoption of a set of conventional corrections for the ITRF and ensures the consistency of the combination by removing possible differences between corrections adopted by each contributing analysis center.

Meanwhile, for various reasons, there are particular cases where users would need to add speciﬁc corrections to ITRF coordinates in order to meet their particular applications. The currently identiﬁed cases are the following:

A) Solid Earth tides To account for the displacement due to solid Earth tides, all analysis centers use a model ∆X~ tidM that contains a time-independent part, so that the regularized positions obtained are termed “conventional tide-free”, according to the nomen- clature in the Introduction of the Conventions. Such a hypothesis has been taken since the ﬁrst solid Earth tides model of the MERIT Standards. Consequently, the ITRF has adopted the same option and is therefore a “conventional tide- free” frame. To adopt a diﬀerent model, ∆X~ tid, a user would need to apply the following formula to obtain coordinates X~ consistent with this model:

X~ = X~ IT RF + (∆X~ tid − ∆X~ tidM ). (4.14)

For more details concerning tidal corrections, see Chapter 7.

B) Relativistic scale All individual centers use a scale consistent with TT. In the same manner the ITRF has also adopted this option (except ITRF94, 96 and 97, see Section 4.2.2).

39 40 No. 36 ngohsc rohrcommunities. other or geophysics in ITRS the to Access 4.3 Note Technical .. rnfrainprmtr ewe TFsolutions ITRF between parameters Transformation 4.2.6 IERS 5 4 3 2 oeta hscneto steoems fe sdwti pc eds u tmgtntb nvral used universally be not might http://itrf.ensg.ign.fr/ITRF it but geodesy http://www.iausofa.org/ space within used often http://tai.bipm.org/iers/conv2010/conv2010 most one the is convention this that Note aino TFsltossneIR9 a efudat found infor- be All may (1996). ITRF94 Altamimi since and solutions Boucher ITRF in on available also mation are details useful Other ITRS, the in positions point express to used be could ways Several transformation. TCG. with consistent be to specified is scale ITRS the coordinates that if noted Consequently, be should It rvdsaruieiau routine a provides (linear) position secular geocentric a as instantaneous as computed an modeled and be If averaged used mass, observations time. of SLR of center the Earth function of mean span the time as the considered over be should origin ITRF The 1. Chapter in C) described as ensured be should constants numerical where formula: following the apply hpe ) e h ESCnetos e aefrtesbotn,GCONV2.F, (semi-major subroutine, the recommended for is page web ellipsoid Conventions’ IERS at GRS80 the See the 1). case Chapter this ( coordinates In geographical axis to ellipsoid. coordinates transformed an be equatorial to can Cartesian they by needed, specified If are solutions 4.1. ITRF Table values of these ITRF yield those between two necessarily with not between sites would consistent stations common parameters common transformation implied estimate of the to subsets as solutions different of weighting using the distribution Therefore, on and frames. dependent number these heavily the that are as noted which well values be adjusted should are it ITRF2000/ITRF2005 Moreover, parameters ITRF97/ITRF2000, from comparisons. previous as ITRF2005/ITRF2008 in val- published well and already The as those (4.5). from Notes compiled and Technical been (4.3) IERS have Equations table with this in previ- used listed to be ues ITRF2008 should from which rates versions, their ITRF and ous parameters transformation lists 4.1 Table mass) of center instantaneous the to where • • • • solutions/index.php s ftasomto omlswihwudb siae ewe particular a solution. between ITRF estimated an be and would which TRF GNSS formulas of transformation of analysis use stations; the permanent in the or coordinates for campaign station of used ITRF measurements version some constraining ITRF or the fixing of products. aware IGS be the should of generation users However, ITRF. ( the products velocities; IGS and of positions use station ITRF of use direct < ecnrcpositions Geocentric 3 a > X X O L ~ ~ ~ 6378137 = h OA(tnad fFnaetlAtooy service Astronomy) Fundamental of (Standards SOFA The . G G = + (1 = sacrigt al . nCatr1 oeta ossec between consistency that Note 1. Chapter in 1.1 Table to according is ersnstegoetrmto nIR vco rmteIR origin ITRF the from (vector ITRF in motion geocenter the represents X ~ TRF IT L c4.html . G ,ivreflteig1 flattening inverse m, 0 − ) X ~ O ~ TRF IT CGEi ohFrrn7 n NICt efr the perform to C ANSI and 77 Fortran both in GC2GDE G e.g. , risadcok)wihaenmnlyalrfre to referred all nominally are which clocks) and orbits X ~ ossetwt C r edd sr edto need users needed, are TCG with consistent < 2 > ersra eeec ytm n frames and systems reference Terrestrial 4 . /f 298 = . 5220,seTbe12in 1.2 Table see 257222101, X ~ < srqie,i should it required, is 5 > . ,φ h φ, λ, X e.g. , Y < referred ) 4 and > (4.15) (4.16) also e.g. Z . 4.3 Access to the ITRS IERS Technical

Note No. 36

Table 4.1: Transformation parameters from ITRF2008 to past ITRFs. “ppb” refers to parts per billion (or 10−9). The units for rates are understood to be “per year.” ITRF Solution T 1 T 2 T 3 DR1 R2 R3 (mm) (mm) (mm) (ppb) (mas) (mas) (mas) Epoch ITRF2005 -2.0 -0.9 -4.7 0.94 0.00 0.00 0.00 2000.0 rates 0.3 0.0 0.0 0.00 0.00 0.00 0.00 ITRF2000 -1.9 -1.7 -10.5 1.34 0.00 0.00 0.00 2000.0 rates 0.1 0.1 -1.8 0.08 0.00 0.00 0.00 ITRF97 4.8 2.6 -33.2 2.92 0.00 0.00 0.06 2000.0 rates 0.1 -0.5 -3.2 0.09 0.00 0.00 0.02 ITRF96 4.8 2.6 -33.2 2.92 0.00 0.00 0.06 2000.0 rates 0.1 -0.5 -3.2 0.09 0.00 0.00 0.02 ITRF94 4.8 2.6 -33.2 2.92 0.00 0.00 0.06 2000.0 rates 0.1 -0.5 -3.2 0.09 0.00 0.00 0.02 ITRF93 -24.0 2.4 -38.6 3.41 -1.71 -1.48 -0.30 2000.0 rates -2.8 -0.1 -2.4 0.09 -0.11 -0.19 0.07 ITRF92 12.8 4.6 -41.2 2.21 0.00 0.00 0.06 2000.0 rates 0.1 -0.5 -3.2 0.09 0.00 0.00 0.02 ITRF91 24.8 18.6 -47.2 3.61 0.00 0.00 0.06 2000.0 rates 0.1 -0.5 -3.2 0.09 0.00 0.00 0.02 ITRF90 22.8 14.6 -63.2 3.91 0.00 0.00 0.06 2000.0 rates 0.1 -0.5 -3.2 0.09 0.00 0.00 0.02 ITRF89 27.8 38.6 -101.2 7.31 0.00 0.00 0.06 2000.0 rates 0.1 -0.5 -3.2 0.09 0.00 0.00 0.02 ITRF88 22.8 2.6 -125.2 10.41 0.10 0.00 0.06 2000.0 rates 0.1 -0.5 -3.2 0.09 0.00 0.00 0.02

References

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