Reference Frame Representations: The ITRF from the user perspective Zuheir Altamimi Paul Rebischung Laurent Métivier Xavier Collilieux Kristel Chanard IGN, France Email: zuheir.altamimi@ign.fr

Key Points Possible reference frame representations and: the reality of a deformable Earth Linear motion Nonlinear variations technique systematic errors User needs The ITRF from the user perspective Science applications Operational geodesy The ITRF should satisfy both types of applications

What is a Reference Frame in practice? Earth fixed/ centered RF: allows determination of station locations/positions as a function of time It appears simple, but … we have to deal with: Relativity theory Forces acting on the satellite The atmosphere Earth rotation Solid Earth and ocean tides … Whatever the mathematical formulation you choose, you need to precisely specify the frame definition: Origin, Scale, Orientation & their time evolution

Why a Reference System/Frame is needed? Precise Orbit Determination for: GNSS: Global Navigation Satellite Systems Other satellite missions: Altimetry, Oceanography, Gravity Earth Sciences Applications Tectonic motion and crustal deformation Mean sea level variations Earth rotation … Operational geodesy applications (today: via GNSS only!) National geodetic systems/frames (see next) Positioning : Real Time or a posteriori Navigation: Aviation, Terrestrial, Maritime Require the availability of the orbits and the RF (ITRF) Many, many users…

National/Regional Reference Frames Use of GNSS technology only (no SLR, VLBI or DORIS) Use of and rely on the IGS products (orbits, clocks,..) Rely on the ITRF More than 80% of National RFs are aligned to the ITRF (source: UN-GGIM GGRF questionnaire) Materialized by station coordinates at a given epoch + possibly a deformation model or minimized velocities May need to apply PSD corrections (if ITRF2014 is used) Some countries will move soon to a “dynamic” RF, ITRF-compatible, e.g. Australia

How to define the frame parameters ? Origin: CoM (Satellite Techniques, mainly SLR, and potentially DORIS but subject to uncertainties) Scale: Depends on physical parameters (SLR, VLBI and potentially DORIS, but subject to biases anyway) Orientation: Conventional Time evolution: Geophysical meaning (e.g. NNR condition) ==> Lack of information for some parameters: Orientation & time evolution (all techniques) Origin & time evolution in case of VLBI ==> Rank Deficiency in terms of Normal Equation System

“Motions” of the deformable Earth & technique systematic errors Nearly linear motion: Tectonic motion: mainly horizontal (Plate Motion Model) Post-Glacial Rebound: Vertical & Horizontal Nonlinear motion: Loading deformation, including Annual, Semi & Inter-Annual, etc. Co- & Post-seismic deformations, Transient deformations, Volcano Eruptions, local events… Systematic errors, e.g. draconitics, fortnightly,…

Crust-based TRF The instantaneous position of a point on the Earth surface at epoch t could be written as : 𝑋 𝑡 =𝑋 𝑡0 + 𝑋 . 𝑡− 𝑡 0 + ∆𝑋 𝑐 𝑡 + 𝑋 𝑛𝑐 (𝑡) 𝑿 𝒕𝟎 : position at a reference epoch t0 𝑿 : linear velocity ∆𝑿 𝒄 (𝒕) : Class 1 Conventional models, e.g. : - Solid Earth, Ocean & Pole tides (models, IERS Conv.) ∆𝑿 𝒏𝒄 (𝒕) : : Class 2 models or estimated quantities: - Loading deformation (seasonal and non-seasonal) - Post-Seismic Deformation - …

Reference Frame Representations Long-Term linear Frame: mean station positions at a reference epoch (t0) and station velocities: The indispensable basis for science and operational geodesy applications Secular Frame + corrections (PSDs, Seasonals, Geocenter motion) ==> modeled “Quasi-Instantaneous” station positions "Quasi-Instantaneous" RF: mean station positions at a "short” & “regular” interval: Daily or weekly representations Nonlinear motion embedded in their time series Still rely on the ITRF for at least the orientation definition <= Regularized Position With piece-wise linear function 𝑋 𝑡 =𝑋 𝑡0 + 𝑋 . 𝑡− 𝑡 0 +𝑋(𝑡)𝑃𝑆𝐷+𝑋 𝑡 𝑆+𝑋(𝑡)𝐺

“Instantaneous” position: linear & nonlinear parts Regularized position 𝑋 𝑡 =𝑋 𝑡0 + 𝑋 . 𝑡− 𝑡 0 +𝑋(𝑡)𝑃𝑆𝐷+𝑋 𝑡 𝑆+𝑋(𝑡)𝐺 Post-Seismic Deformations Seasonal Signals of all frequencies Caution: significant discrepancies between techniques Or a Loading model with ALL contributions (ATM, …) in CF Geocenter Motion Caution: different models exist, with significant differences All the 𝑿 corrections could be part of future ITRF products

Up annual signals : VLBI January A f April Dh = A.cos( 2p f (t – t0 ) + f )

Up annual signals : VLBI + GNSS January A f April Dh = A.cos( 2p f (t – t0 ) + f )

“Instantaneous” position: linear & nonlinear parts Science Applications in general 𝑋 𝑡 =𝑋 𝑡0 + 𝑋 . 𝑡− 𝑡 0 +𝑋(𝑡)𝑃𝑆𝐷+𝑋 𝑡 𝑆+𝑋(𝑡)𝐺 Operational Geodesy & certain science applications

ITRF2014 error propagation: GNSS coordinates Spherical error = sqrt(sigx^2 + sigy^2 + sigz^2 + 2sigxy + 2sigxz + 2sigyz)

ITRF2014 error propagation: VLBI coordinates

ITRF2014 error propagation: SLR coordinates

ITRF2014 error propagation: DORIS coordinates

Conclusion The ITRF as a secular frame is the basis for Science and operational geodesy applications ITRF “Instantaneous” station position, if needed, can easily be derived. Cautions: Seasonal signals: discrepancies among techniques at colocation sites, due to technique systematic errors Different & discrepant Geocenter motion models exist Time series of “Quasi-instantaneous” frames: scientifically sound approach. Cautions: Predictability ? Less practical for Operational Geodesy & some geophysical applications Co-motion constraints at co-location sites ?? If needed: Identify users and how to do it ?

Backup

Up annual signals : GNSS January A f April Dh = A.cos( 2p f (t – t0 ) + f )