Impact of ITRS 2014 realizations on altimeter satellite precise orbit determination

Accepted Manuscript Impact of ITRS 2014 Realizations on Altimeter Satellite Precise Orbit Determination Nikita P. Zelensky, Frank G. Lemoine, Brian D. Beckley, Douglas S. Chinn, Despina Pavlis PII: DOI: Reference:

S0273-1177(17)30554-9 http://dx.doi.org/10.1016/j.asr.2017.07.044 JASR 13354

To appear in:

Advances in Space Research

Received Date: Revised Date: Accepted Date:

8 May 2017 26 July 2017 30 July 2017

Please cite this article as: Zelensky, N.P., Lemoine, F.G., Beckley, B.D., Chinn, D.S., Pavlis, D., Impact of ITRS 2014 Realizations on Altimeter Satellite Precise Orbit Determination, Advances in Space Research (2017), doi: http://dx.doi.org/10.1016/j.asr.2017.07.044

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Impact of ITRS 2014 Realizations on Altimeter Satellite Precise Orbit Determination Nikita P. Zelensky b,a, *, Frank G. Lemoine a, Brian D. Beckley b,a, Douglas S. Chinn b,a, Despina Pavlis b,a a) NASA Goddard Space Flight Center, Planetary Geodynamics Laboratory, Code 698, Greenbelt, MD 20771, USA b) SGT Inc., 7701 Greenbelt Road, Greenbelt, MD 20770, USA ABSTRACT This paper evaluates orbit accuracy and systematic error for altimeter satellite precise orbit determination on TOPEX, Jason-1, Jason-2 and Jason-3 by comparing the use of four SLR/DORIS station complements from the International Terrestrial Reference System (ITRS) 2014 realizations with those based on ITRF2008. The new Terrestrial Reference Frame 2014 (TRF2014) station complements include ITRS realizations from the Institut national de l'information géographique et forestière (IGN) ITRF2014, the Jet Propulsion Laboratory (JPL) JTRF2014, the Deutsche Geodätische Forschungsinstitut (DGFI) DTRF2014, and the DORIS extension to ITRF2014 for Precise Orbit Determination, DPOD2014. The largest source of error stems from ITRF2008 station position extrapolation past the 2009 solution end time. The TRF2014 SLR/DORIS complement impact on the ITRF2008 orbit is only 1-2 mm RMS radial difference between 1992-2009, and increases after 2009, up to 5 mm RMS radial difference in 2016. Residual analysis shows that station position extrapolation error past the solution span becomes evident even after two years, and will contribute to about 3-4 mm radial orbit error after seven years. Crossover data show the DTRF2014 orbits are the most accurate for the TOPEX and Jason-2 test periods, and the JTRF2014 orbits for the Jason-1 period. However for the 2016 Jason-3 test period only the DPOD2014-based orbits show a strong and statistically significant margin of improvement. The positive results with DTRF2014 suggest the new approach to correct station positions or normal equations for non-tidal loading before combination is beneficial. We did not find any compelling POD advantage in using nonlinear over linear station velocity models in our SLR & DORIS orbit tests on the Jason satellites. The JTRF2014 proof-of-concept ITRS realization demonstrates the need for improved SLR+DORIS orbit centering when compared to the Ries (2013) CM annual model. Orbit centering error is seen as an annual radial signal of 0.4 mm amplitude with the CM model. The unmodeled CM signals show roughly a 1.8 mm peak-to-peak annual variation in the orbit radial component. We find the TRF network stability pertinent to POD can be defined only by examination of the orbit-specific tracking network time series. Drift stability between the ITRF2008 and the other TRF2014-based orbits is very high, the relative mean radial drift error over water is no larger than 0.04 mm/year over 1993-2015. Analyses also show TRF induced orbit error meets current altimeter rate accuracy goals for global and regional sea level estimation. *

Corresponding author: Nikita Zelensky, [email protected], 703.660.2304

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Key Words ITRF2014, POD, DORIS, SLR, altimetry, satellite orbit 1. Introduction A precise geodetic reference frame and precise orbits are a fundamental science requirement for satellite altimetry. The terrestrial reference frame is the means by which the orbit reference is computed for analysis of satellite altimeter data, and the accuracy with which altimeter data can be tied to tide gauges for validation. Error in the terrestrial coordinates and frame will transfer to the orbit, and through the orbit directly to the altimeter measurement. This paper evaluates both, the impact of the new TRF2014 SLR/DORIS complements on the TOPEX/Poseidon, Jason-1, Jason-2, Jason-3 altimeter satellite orbits, and the accuracy of the TRF2014 station coordinates relative to ITRF2008 (Altamimi et al. 2011). These four altimeter missions have provided continuous observation of the ocean surface from a consistent measurement frame over a span of more than 24 years, and have significantly advanced the science of satellite altimeter oceanography. The 1992 launch of TOPEX/Poseidon ushered in a new age of highly accurate radar altimeter observations of the ocean surfaces. In time and over subsequent missions, the altimeter data record proved essential not only for high precision and accuracy in revealing aspects of sea surface variability such as ocean tides, currents, ocean-climate cycles like El Niño, the North Atlantic Oscillation, and the Pacific Decadal Oscillation, but also for secular changes in global and regional sea levels (e.g. Knudsen et al., 2011; Becker et al., 2012; Hamlington et al., 2013, Stammer et al., 2014, Ablain et al., 2017). An example of the global mean sea level change computed over the altimeter record span from 1993 to the present using TOPEX/Poseidon, Jason-1, Jason-2 and Jason-3 data can be viewed on the NASA Physical Oceanography Data Active Archive Center (PODAAC) website (https://podaac.jpl.nasa.gov/Integrated_Multi-Mission_Ocean_AltimeterData). Altimeter data accuracy must be improved however, in order to answer today’s important questions such as: “is the global mean sea level rise accelerating? (Fasullo et al. 2016)” , “can regional sea level rates be forecast for better flood planning?”, “can an anthropogenic footprint be seen in the sea level changes? (Palanisamy et al. 2015)”. Considering the GCOS (GCOS 2011) analysis, Ablain et al (2015) have estimated altimeter data accuracy requirements for responding to these and other such questions. The requirements call for accuracies of 0.3 mm/year on a global scale, and to better than 1 mm/year on a regional scale (Table 1.1). Needless to say, the orbit is only one of many components of a sea surface height measurement. In fact current levels of orbit error may exceed some of these altimeter data accuracy requirements (Couhert et al. 2015), however the focus of this paper concerns the impact of error of the terrestrial frame and tracking station positions on the orbit, and specifically the impact of the transition from ITRF2008-based SLR/DORIS complements to the TRF2014-based complements on the orbits of the TOPEX/Poseidon, Jason-1, Jason-2, and Jason-3 altimeter satellite missions. Previous studies have shown that 2017-08-04

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the transition from the CSR95 frame (Eanes 1995) to ITRF2005 (Altamimi et al. 2007) contributed artifact regional drifts of up to  1.5 mm/year to altimeter mean sea level (MSL) analysis (Beckley et al. 2007). The transition from ITRF2005 to ITRF2008 contributed smaller artifact regional drifts of up to  0.3 mm/year (Couhert et al. 2015). Such measures of orbit drift reflect stability however, and not the accuracy for meeting the altimeter budget requirements (Table 1.1). In fact it has been reported shortcomings in the realization of the terrestrial frame pose the major limitation to progress in the study of long-term evolution of sea level records, including the altimeter record (Wöppelmann and Marcos, 2016). In order to meet the scientific needs of Geodesy, the Global Geodetic Observing System (GGOS) of the International Association of Geodesy (http://www.ggos.org) has expressed the terrestrial reference frame should be accurate at a level of 1 mm with respect to the geodetic station positions on the Earth's surface and stable with time at a level of 0.1 mm/year (Plag and Pearlman, 2009). Table 1.1

Over the last two years three Terrestrial Reference Frame (TRF) realizations of the theoretically defined International Terrestrial Reference System (ITRS) (IERS Technical Note 36 (Petite and Luzum 2010)) have been released: ITRF2014 (Altamimi et al. 2016), DTRF2014 (Seitz et al. 2016), and JTRF2014 (Abbondanza et al. 2017), as well as a DORIS update to ITRF2014, DPOD2014 (Moreaux et al. 2016a). This paper evaluates both the impact of these new SLR/DORIS complements on the orbit, and the accuracy of the new station coordinates relative to ITRF2008. The paper is divided into six sections: 1) Introduction, 2) Altimeter satellite orbit modeling pertinent to the TRF tests, 3) ITRS 2014 realizations and POD tests, 4) TRF2014 Orbit accuracy and station accuracy, 5) Orbit sensitivity to SLR/DORIS network frames, 6) Conclusion. 2. Altimeter satellite orbit modeling pertinent to the TRF tests 2.1. POD standards 2.2. SLR+DORIS orbit centering and gravity modeling 2.1 POD standards. The same ~9.91 day repeat orbit is used by the four successive altimeter satellite missions: TOPEX/Poseidon (TP), Jason-1 (J1), Jason-2 (J2), Jason-3 (J3), and ensures the measurement frame consistency of the altimetry data record (Table 2.0). Based on SLR/DORIS POD testing of TP, J1, and J2 satellites we have Table 2.0 defined the latest set of pre-ITRF2014 standards, std1504, which guarantee the orbit quality and consistency across all missions (Lemoine et al. (2010) and Lemoine et al. (2015)), and serve as the common set of POD models for the TRF2014 SLR/DORIS complement tests (Table 2.1). The std1504 standards account for three corrections to the station position: Earth tides, ocean tidal loading, and geocenter motion. In several special comparison tests of JTRF2014 we also model atmospheric loading since the JTRF2014 weekly series by design includes Earth

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deformation effects due to loading for all geophysical fluids (non-tidal ocean, atmosphere, hydrology) and geocenter motion (Table 2.1, Special Testing). Naturally, neither geocenter motion nor non-tidal loading models are included in the POD using JTRF2014, but only in the special tests for comparison with JTRF2014. Table 2.1

2.2 SLR+DORIS orbit centering and gravity modeling Orbit centering is a measure of the computed orbit’s ability to assume the Earth’s center of mass (CM) as the center of the orbit frame. Ideally the altimeter measurement frame origin should be aligned with the instantaneous CM (Fu and Haines 2013). Our objective is to best center the SLR+DORIS orbit. Orbit centering can be evaluated by studying orbit differences expressed in Earth-Center-Fixed (ECF) Cartesian coordinates X,Y, and Z. In addition, CM estimates can be evaluated by using satellite tracking data processed with and without CM modeling. The application of an annual geocenter motion model, which corrects the SLR/DORIS station positions with annual signature in XYZ helps to align the SLR+DORIS orbit with the instantaneous CM, mostly in Z (Zelensky et al. 2014, Couhert et al. 2015). The SLR-based CM model (Ries 2013) is included in the POD std1504 standards. In addition to the Ries (2013) CM model, three other SLR-based annual CM models are tested for orbit centering and compared with the JTRF2014-based orbits: ITRF2014 CM (Altamimi et al., 2016), GSFC test1 CM and GSFC test2 CM+APL (Zelensky et al, 2016) (Table 2.1). The GSFC test CM models are based on LAGEOS-1/2 weekly solutions spanning 4-years, 2008-2011. The GSFC weekly CM solution is a geometric estimate of the center-of-network shift to the center-of-mass. Since non-tidal loading was not explicitly modeled in the Ries (2013), ITRF2014, or GSFC test1 SLR CM model estimation, such models should implicitly include the annual contribution due to non-tidal loading effects. The JTRF2014 SLR-defined origin station series should include all station motion due to CM and non-tidal loading. The special GSFC test2 CM+APL model explicitly considers atmospheric pressure loading (APL) at the observation level in its derivation, and so atmospheric loading is then explicitly applied at the observation level when the GSFC test2 CM+APL model is used. The amplitudes and phases of the four annual CM models are shown in Table 2.2. Note that more than 15-years of SLR data are used in the ITRF2014 and Ries 2013 CM model derivations, whereas only 4years are used for the GSFC test models. The differences in phase Table 2.2 and amplitude between the GSFC test1 CM and the Ries (2013) or ITRF CM models (Table 2.2) may suggest the annual signal changes in both phase and amplitude over time. The 4-year GSFC solution span coincides with the test period. The differences in phase and amplitude between GSFC test1/test2 models illustrate the impact of applying atmosphere loading at the observation level in the CM model derivation (Table 2.2). The std1504 standards describe a dynamic POD approach, an approach where orbit accuracy largely depends on the fidelity of the force models. In a reduced-dynamic approach the tracking data capabilities are exploited though the estimation of empirical parameter time series tied with correlated constraints in order to compensate for deficiencies in the POD force models (e.g. Bertiger et al. 1994; Luthcke et al. 2003). Our 2017-08-04

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standards include a consistent way to model time-variable gravity for altimeter missions from 1993 to the present. It allows the use of a GRACE-derived gravity model and its annual variations, while still accommodating variations in the low degree field back to 1993. Using our weekly time series of low-degree harmonics based on processing data to 20 different LEO satellites tracked by SLR and DORIS, we estimated linear and harmonic fits to this time series over two spans: 1993-2002, 2002-2015. These 5x5 low-degree terms are overlain on the static model derived from GRACE and GOCE (GOCO02s, Goiginger et al. 2011) and supplemented by using GRACE-derived annual harmonics for degrees six to 20. The NASA GSFC precise orbit determination and geodetic parameter estimation program GEODYN is used for the tests (Pavlis et al. 2017). In short, the std1504 POD standards define our most accurate force and measurement models for precise orbit determination in order to ensure a precise evaluation of the TRF2014 SLR/DORIS complements and their impact on the orbit compared to ITRF2008.

3. ITRS 2014 realizations and POD tests 3.1. ITRF2008, ITRF2014, DTRF2014, JTRF2014, DPOD2014, and augmented datasets 3.2. POD tests 3.1 ITRF2008, ITRF2014, DTRF2014, JTRF2014, DPOD2014, and augmented datasets The orbit, which defines the altimeter measurement frame, is determined through dynamical modeling of the equations of motion, and performing a least squares fit to the satellite tracking data using least squares batch estimation (c.f. Tapley et al., 2004). The International Terrestrial Reference Frame (ITRF) is a set of estimated station positions and velocities observed by SLR, DORIS, GPS, and VLBI, which realize the definition of the International Terrestrial Reference System (ITRS) (IERS Technical Note 36 (Petit and Luzum 2010)). Due to geophysical causes (e.g. plate tectonics, and glacial isostatic adjustment) or other phenomena (e.g. locally induced subsidence or uplift) the station positions change over time. A new ITRF is realized every few years to update station position/velocity estimates with additional tracking data and improvements in modeling, and to incorporate new stations. In 2015 three TRF realizations of the ITRS were released for testing: ITRF2014 IERS/IGN (Altamimi et al. 2016, IERS Technical Note 38 (Altamimi et al., 2017)), DTRF2014 (Seitz et al. 2016, IERS Technical Note 38 (Altamimi et al., 2017)), and JTRF2014 (Abbondanza et al. 2017, IERS Technical Note 38 (Altamimi et al., 2017)). Soon afterwards a 2014 update to the DORIS Precise Orbit Determination 2008 (DPOD2008) station complement, DPOD2014, was also released for testing (Moreaux et al. 2016a). All three TRF2014 realizations of the ITRS are based on the same SLR, DORIS, GPS, and VLBI input data as provided by the corresponding technique services (Bachmann et al., 2016; Moreaux et al., 2016b; Rebischung et al., 2016). SLR data are used to define the TRF origin as the long-term position of the Earth’s CM, and SLR/VLBI data to define the scale. The orientation is constrained with application of a no-net-rotation condition w.r.t. ITRF2008 (Altamimi et al. 2011). However the realizations greatly differ in their approaches to modeling station motion. 2017-08-04

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The IGN ITRF2014 station position model departs from the strictly linear model used in its previous realizations by including non-linear post seismic deformation motion (PSD) for selected stations. This very interesting new approach more closely matches the actual measured post-seismic station motion for the four geodetic techniques (Altamimi et al. 2016, see GPS and VLBI plots). A geocenter motion model consistent with ITRF2014 data is also provided (Altamimi et al. 2016, see Table 3). The JPL ITRS 2014 realization (JTRF2014) consisting of a smoothed weekly time series of station positions, uses a Kalman filter to combine input data from the four geodetic techniques (Wu et al., 2015). The JTRF2014 origin is at the quasi-instantaneous Center of Mass as measured by SLR. By filter design, both seasonal and non-seasonal motions are allowed in the temporal evolution of the station positions. The station position series also closely match the actual measured post seismic deformation station motion ((Gross et al. 2015), see GPS and VLBI plots). Since the JTRF2014 station series extend only to February 12, 2015, and no periodic updates have been announced, the JTRF2014 station series cannot be considered for operational use. The JTRF2014 is included as a proof-of-concept test. The DFGI ITRS 2014 realization (DTRF2014) is the first realization of ITRS to consider nontidal signals in station positions. Station positions or normal equations obtained from the input SINEX data are corrected for atmospheric and hydrological loading before combination. Although the station positions/velocities are expressed with the traditional linear model, DGFI also provides SLR-based CM series and non-tidal loading correction data to allow user computation of the quasi-instantaneous CM station positions. In our tests however, only the linear station motion model is applied; the supporting CM and nontidal loading data are not applied. DPOD2014, like its DPOD predecessors, is the DORIS extension of the latest IERS ITRS realization, ITRF2014, developed and maintained to serve the operational POD requirements of DORIS-tracked satellites (Moreaux et al. 2016a). As with its predecessor, DPOD2008 (Willis and Ries (2005) and Willis et al., (2015)) a linear model is also used for station motion. A distinguishing DPOD objective is to maintain a complete set of DORIS stations, building on the most recent IERS realization of the ITRS. The station network defined by the ITRS realization defines the SLR+DORIS orbit reference through precise orbit determination. These analyses test the impact of the new TRF2014 station solutions on the SLR+DORIS orbit in comparison to using the SLR/DORIS updates to ITRF2008, the ILRS-maintained SLRF2008 (ILRS Analysis Work Group, 2012, http://ilrs.gsfc.nasa.gov/science/awg/SLRF2008.html) and DPOD2008. The POD tests also reflect the accuracy of the station coordinates and efficacy of the different station motion models. 3.2 POD Tests The DORIS+SLR tests of the ITRS 2014 realizations are listed in Table 3.1. The TRF2014 complement tests include, itrf2014_test, itrf2014_aug_test, jtrf2014_test, dtrf2014_test, 2017-08-04

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dtrf2014_aug_test, and dpod2014_test. All share the same std1504 POD models (Table 2.1). The tests are compared to the baseline itrf2008_test. In this Table 3.1 paper the TRF tests are expressed in lower-case, whereas the ITRS realizations in upper case.

The SLR and DORIS TRF test complements are of unequal size (Table 3.1). We show that their size or completeness is an important attribute in the POD tests. In order to include DPOD2014 in the DORIS+SLR POD tests, the ITRF2014 SLR complement was augmented by 36 stations from SLRF2008 and used together with the DPOD2014 DORIS complement (dpod2014_test). The missing stations are first moved to the ITRF2014 frame with application of the ITRF2008 to ITRF2014 14-parameter transformation (c.f. http://itrf.ign.fr/ITRF_solutions/2014/tp_14-08.php). The dpod2014_test has the most complete set of SLR+DORIS stations. To better evaluate the significance to POD for having a complete set of stations, two more hybrid test cases are constructed, itrf2014_aug, and dtrf2014_aug. For itrf2014_aug both SLR and DORIS ITRF2014 complements are augmented for missing stations from SLRF2008/DPOD2008 following the 14-parameter transform. Although ITRF2014 contains all DORIS stations submitted by IDS, a number of stations found in DPOD2008 did not meet the submission criteria. For dtrf2014_aug_test only the missing DORIS stations tracking Jason-3 are added to the DTRF2014 complement from DPOD2014. The dtrf2014_aug_test is then only run for Jason-3.

4. TRF2014 Orbit accuracy and station accuracy 4.1. TRF2014 orbit accuracy 4.2. TRF2014 station accuracy 4.3. JTRF2014, Earth center of mass, and non-tidal loading 4.1 TRF2014 orbit accuracy Improved accuracy of the tracking station position at each observation epoch will reduce the error component in the computed observation which otherwise might contribute to orbit error in the process of orbit determination. The sensitivity of the orbit to perturbations in station position is illustrated with Fig 4.0 which compares the RSS (residual sum of squares) DORIS station position differences to the RMS (root mean square) radial orbit differences by arc between the itrf2008_test and dpod2014_test solutions. Only DORIS stations used in POD are included in the comparison. The figure indicates that DORIS data drives the GSFC SLR+DORIS orbits for such satellites, as shown previously in other studies (Zelensky et al. 2010, Zelensky et al. 2016), and that the magnitude of the RSS DORIS station position error will directly impact the magnitude of the SLR+DORIS RMS radial orbit error. Fig 4.0 suggests a linear correspondence between a change in the RSS DORIS station position error and the SLR+DORIS radial RMS orbit error Figure 4.0

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Another factor determining accuracy in POD is the geometric strength of the tracking network. Thus, the number of stations included in the TRF complement can influence POD accuracy as well. Sensitivity to station completeness is illustrated with Fig 4.1 comparing a time series of Jason-2 orbits computed using the ITRF2014 (itrf2014_test) complements to using the ITRF2014 augmented with missing stations (itrf2014_aug_test). A closer look at the missing stations by year (Table 4.1) shows that the orbits begin to significantly diverge when the total number of DORIS ITRF2014 stations tracking Jason-2 falls well below the optimized homogenous network coverage of about 56 stations (Fagard, 2006). These results may also suggest that further densification of the DORIS network would help to further improve POD accuracy. Table 4.1

Orbit accuracy can be measured with independent altimeter crossover data for the radial component, and with independent SLR data for the radial and horizontal components. SLR and to some extent DORIS residuals reflect both the computed orbit accuracy and the station position accuracy. Since SLR/DORIS data are included in our POD processing, orbit error will be minimized over regions of SLR/DORIS tracking according to the merits of the specific TRF compliment used for POD. Altimeter crossovers serve as our independent measure of the SLR+DORIS radial orbit accuracy. Exactly the same crossover data are used for each orbit test. Regardless of the number of stations available in each of the TRF2014 test complements, the POD tests show an improvement in the SLR residuals relative to the itrf2008_test baseline, beginning about 2010 for all test complements (Fig 4.2 – 4.5). No doubt this is largely due to ITRF2008 station position extrapolation error past the station solution span ending 2009 (Table 4.2). This can also be seen for the DORIS stations but with the ITRF2008 degradation starting a bit earlier, around 2009 (Fig 4.6). The relative improvement of the ITRF2014 DORIS residuals beginning with Table 4.2 Jason-2 (mid 2008) probably also reflects the inclusion of this satellite's DORIS data in the IDS solution (Moreaux et al., 2016b) Figures 4.2 -4.6

Tables 4.3-4.6 provide a summary of POD statistics for each of the TRF tests across the four missions. Since the number of stations vary between the TRF test complements it is difficult to finely discriminate the relative orbit accuracy or station performance using the SLR/DORIS residual statistics by test period as shown in Tables 4.3-4.6. The independent crossover residuals however suggest all TRF2014 orbits, if not comparable, show a marginal improvement in orbit accuracy relative to itrf2008_test. The margin of improvement for the TRF2014 orbits progressively increases over time considering the Jason-1, Jason-2, and finally Jason-3 periods (Tables 4.3 -4.6). Beginning with Jason-3 2017-08-04

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(early 2016) dtrf2014_test no longer shows improvement over itrf2008_test. Since dtrf2014_test also contains the smallest number of stations (Table 4.6), this largely contributes to the relative degradation. Indeed, using the DTRF2014 DORIS complement augmented with the missing stations (Table 4.7), significantly improves the orbit (see dtrf2014_aug_test Table 4.6). Comparison of DORIS/SLR residuals over 1992-2008 (Tables 4.3-4.4) suggest it is the small improvement in the TRF2014 DORIS station position modeling which drives the small improvement seen for the TRF2014-based orbits over this period. Tables 4.3 -4.7

To better address the statistical significance of any improvement or degradation seen in the crossover residual comparisons, we investigate the differences in the residual variances. The Z-score is used with a one-tailed hypothesis distribution to compute the confidence level, testing that the true mean is not zero. The confidence level will show the statistical significance for any improvement when the computed mean is greater than zero, and for any degradation when the computed mean is less than zero. To illustrate consider Fig 4.7 showing the itrf2008_test-itrf2014_test crossover residual variance differences across TOPEX, J1, and J2 missions. Thus one can say the slight degradation of the itrf2014_test TOPEX crossover residuals by 0.79 mm 2 is statistically significant at the 90% confidence level. The small improvement in the itrf2014_test Jason-1 crossovers (2.53 mm2) and Jason-2 crossovers (4.36 mm2) have high statistical significance at the 99.9% confidence level. Only the itrf2014_test and itrf2014_aug_test TOPEX crossovers indicate some lose of accuracy in the orbits compared to itrf2008_test. The slight degradation seen with itrf2014_aug_test is not significant. All other TRF2014 complements over all test periods indicate some margin of orbit improvement (Table 4.8). Through time over the succession of satellite tests, the margin of TRF2014-based orbit improvement and statistical significance progressively increases. An important exception to this is for Jason-3, where only the dpod2014_test crossover improvement over itrf2008_test is seen to increase with any statistical significance. Tables 4.6-4.8 illustrate POD accuracy depends on both station position accuracy and network geometry strength. Dpod2014_test represents the most complete set of SLR/DORIS stations, and dtrf2014_test the least complete. DTRF2014 contains about 70% of the DORIS stations tracking Jason-3. Itrf2014_aug_test, while complete, does not show superior performance to itrf2014_test, probably due to extrapolation error of its ITRF2008-based augmented stations. The tests with Jason-3 clearly show that for current and future SLR/DORIS POD the most complete ITRF2014 complements should be used. The next ITRF realization may become available only in several more years. Although anticipated, the test results underscore the importance for having readily available DORIS and SLR complement updates to ITRF2014.

Figure 4.7

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4.2 TRF2014 station accuracy In addition to orbit error SLR/DORIS residuals also indicate the TRF2014 station position accuracy relative to ITRF2008. The POD residuals suggest improvement in TRF2014 DORIS station accuracy over all periods. Up to 2009 the TRF2014 DORIS improvement is very small and degradation seen in the TRF2014 SLR positions is marginal. Following 2009 the increasing ITRF2008 station position extrapolation error contributes to the main differences in station accuracy (Tables 4.3-4.6, Fig 4.2 – 4.5). To better evaluate the station position accuracies we use an orbit independent of SLR/DORIS tracking. The choice of an independent orbit is important. Orbit error is expected to be minimized over regions where tracking stations supply data for the POD processing, as suggested with Table 4.9. For example, even though independent crossover residuals indicate the jpl16a GPS orbit is the most accurate, the std1504 orbit SLR residuals are smaller (Table 4.9). Since SLR data are used for the std1504 orbit determination, the orbit error is minimized over regions of SLR tracking. An Table 4.9 accurate orbit computed independently of SLR/DORIS tracking should not show preference to any one specific SLR/DORIS TRF complement. The JPL GPS reduced-dynamic orbit altimeter crossover analysis has shown superior accuracy to SLR+DORIS Jason-1, Jason-2, and Jason-3 orbits (Bertiger et al. 2010). Three JPL GPS orbits are used to evaluate the relative accuracies of the SLR/DORIS TRF station positions from analysis of SLR/DORIS residuals: jpl11a for Jason-1, jpl14a for Jason2, and jpl16a for Jason-3 (see Bertiger et al. 2010). Tables 4.10 – 4.12 show by Jason mission SLR/DORIS residuals computed using independent GPS orbits and only for stations common across the TRF test complements. Although the Jason-3 2016 test period lies outside the solution spans of all TRF complements, extrapolation error is expected to be much greater for ITRF2008 than TRF2014 over this period (Table 4.2). Indeed the Jason-3 test results confirm this expectation (Table 4.10), with improvement over ITRF2008 for almost all of the matched TRF2014 DORIS stations (Fig 4.8a) and for the majority of the matched SLR stations (Fig 4.8b). The DORIS stations showing the largest improvement are located under the region of the South Atlantic Anomaly (SAA) (Fig 4.8a). The SSA is an area over most of South America and a large portion of the Atlantic where the Earth's inner Van Allen radiation belt comes closest to the Earth's surface, dipping down to an altitude of 200 kilometers. The increased radiation has a progressive destabilizing effect on the Ultra Stable Oscillator of a DORIS satellite passing through this region. Special shielding and pre-launch radiation of the Ultra Stable Oscillator reduce the DORIS sensitivity to this effect (see Willis et al., 2004). For SLR, the larger improvement is seen for non-core stations and for stations identified by IGN for modeling post-seismic drift (Fig 4.8b). The Jason-2 2008-2015 test period includes the tail end of the ITRF2008 solution span and lies within the TRF2014 solutions span. As could be 2017-08-04

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expected, both the DORIS and SLR TRF2014 station positions are more accurately modeled over this period than with ITRF2008 (Table 4.11). However for the Jason-1 test period which lies within both ITRF2008 and TRF2014 solution spans, there is only marginal improvement for the DORIS TRF2014 complements, and no improvement for the SLR (Table 4.12). A comparison by individual SLR stations shows any improvement seen with TRF2014 are for the non-core stations, and accuracy is actually slightly worse for the core stations (Fig 4.9a). The core stations shown include Potsdam (7841, 7846), Arequipa (7403), Yarragadee (7090), Monument Peak (7110), Mount Stromlo (7849), and Tahiti (7124). These results are consistent with the POD tests (Tables 4.3-4.6) and lend support to the general observation that the TRF station position accuracies only marginally differ over the common TRF solution span, with improvement only for the DORIS TRF2014 positions. Tables 4.10 – 4.12

Figures 4.8 – 4.10

For evaluation of station velocity models only the matching “PSD” station residuals are compared using JPL GPS orbits over Jason-1, Jason-2, and Jason-3. PSD stations are identified in ITRF2014 for additional non-linear station motion modeling. The same “PSD” stations are found across each ITRS realization for each test, although PSD modeling is applied only to the ITRF2014 stations. The SLR/DORIS residual tests suggest ITRF2014 PSD modeling has little impact on station position accuracy as measured with the GPS orbits (Tables 4.13a – 4.13c). These results suggest that for altimeter satellite POD purposes, the conventional linear station velocity model serves as well as the non-linear post-seismic relaxation ITRF2014 PDF model. The JTRF2014 station position series also do not show any advantage for the selected “PDF” stations over TRF complements with linear velocity models. Tables 4.13a -4.13c

The orbit evaluation of station position accuracy appears consistent with other indices of station solution fidelity. For example the DPOD2014 CADB station (Fig 4.8a) also shows the largest DORIS-GNSS vector tie residuals (Moreaux et al. 2016a). In another study AREB (Fig 4.10b) had also shown large DORIS-GNSS tie vector residuals (Moreaux et al. 2016c). For the reader’s interest Figures 4.9a, 4.9b, 4.10a, 4,10b show selected TRF2014 SLR/DORIS tracking stations with the best and worst performance compared to ITRF2008 for J1 and TP. For TP there are no SLR/DORIS independent orbits spanning the test period, and so SLR+DORIS POD generates the residuals used in the station comparisons. Fig 4.10a indicates it is largely the POD performance of SLR core stations that determines the overall improvement or degradation of the TRF2014 SLR stations compared to itrf2008_test as shown in Table 4.3.

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Three DORIS stations experienced strong non-linear motion close to the TP test interval. The Arequipa and Santiago sites both experienced earthquakes: Arequipa (Arequipa M8.4, June 23, 2001), Santiago (San Juan M5.7, May 27, 2003). The DORIS Arequipa (AREB) tracking data extend for just a short time following the earthquake from December 26 2001. For this station, only the DPOD2014 position shows slightly degraded POD performance (Fig 4.10b). The DORIS Santiago (SANA) tracking window used (December 1994 – December 1994) is distant from the seismic event and shows nothing peculiar (Fig 4.10b). Socorro (SODA) has nonlinear motions due to volcano inflation and deflation (Briole et al., 2009). One could expect a station solution time series could best represent such nonlinear motions. Surprisingly, the performance the JTRF2014 SANA solution does not show improvement, but instead illustrates the occasional weakness seen in the JTRF2014 station position series (Fig 4.10b). Station position error is directly shown with TRF2014/ITRF2008 station position differences. Naturally common error is removed in the difference. Assuming the common error equals the independent error, station position differences can offer an estimate of the total station position error. Selecting only stations used in the orbit determination to form differences will allow an evaluation of orbit sensitivity to station position error. The RSS DORIS station position differences between DPOD2008 and DPOD2014 range from 1.3 cm to over 3 cm depending on the tracking period (Fig 4.0). The decrease in station error from 1992 to 2008 probably reflects improvement in the DORIS constellation, growing from two to six satellites: 1992-1994 (2 satellites: SPOT-2, TP), 1994-1997 (3 satellites: SPOT-2/3, TP), 1997-1998 (2 satellites: SPOT-2, TP), 1998-2002 (3 satellites: SPOT-2/4, TP), 2002 2008 (6 satellites: + J1, Envisat, SPOT-5). The decrease in station error over the 1992-2008 period is consistent with the increased improvement in comparison between the weekly IDS solutions and the DORIS ITRF2014 (IGN) station positions over time (Moreaux et al., 2016b). Although the RSS difference of the IDS weekly solutions and the ITRF2014 DORIS station positions over the same period is about twice as large as the ITRF2008 / ITRF2014 differences, most of the error is very likely due to noise in the weekly solutions (see Table 9, Moreaux et al., 2006b). The increase in DORIS station error following 2009 reflects the increase in ITRF2008 extrapolation error. Considering the apparently very small differences in relative DPOD2008/DPOD2014 station accuracies over 1992-2008, the overall RSS difference of 15.3 mm can serve as an accuracy estimate for both DORIS complements over this period. For the same reasons the SLR core station overall RSS difference of 12.6 mm can serve as the accuracy estimate for both SLRF2008/ITRF2014 complements over the same period (1992-2008). Looking forward 7-years the station differences seen for Jason-3 are 34 mm for DORIS, and 27 mm for SLR. This suggests that after 7-years of ITRF2008 extrapolation, the station position error has doubled for both DORIS and SLR. Consideration that no common error is removed in the station differences provides a lower bound to the error estimate, and allows a station position error range of 11–15 mm accuracy for the DORIS and 8–13 mm accuracy for the SLR stations. These results suggest DORIS/SLR station coordinates are at least an order of magnitude away from reaching the 1-mm GGOS goal. 4.3 JTRF2014, Earth center of mass, and non-tidal loading 2017-08-04

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JTRF2014 consists of a weekly time-series of station positions, which by Kalman filter design can include Earth CM displacement and surface deformation caused by surface fluids loading. Independent altimeter crossover results show it produces the most accurate Jason-1 orbits (Tables 4.4, 4.8). To evaluate the presence of station motion due to the geocenter and non-tidal loading motion implicit in the JTRF2014 position series, we conduct several special POD comparison tests with Jason-2: 1) the CM model is not applied, 2) the Ries 2013, ITRF2014, and GSFC test1 CM models are applied, 3) the special GSFC test2 CM+APL model consistent with APL is applied together with atmospheric pressure loading (APL) (Table 2.1 Special Testing, Table 2.2). Fig 4.11 illustrates orbit error signal when the true CM is left unmodeled. From the amplitudes and phases of the dominant annual orbit signals (shown in Table 4.14) one can see the orbit is most affected by the CM models in Z having about 80% of the model amplitude (Table 2.2). The jtrf2014_test shows the smallest annual orbit signal in Z (1.7 mm amplitude), but also shows a strong semi-annual signal which may be destructively combining with the annual (Table 4.14). No other orbit differences show power at the semi-annual period. Fig 4.11 and Table 4.14 show the jtrf2014_test orbit centering is most similar in structure and phase to the GSFC CM+APL test2 suggesting the effect of APL on both orbits. The systematic orbit Table 4.14 impact of APL alone shows a dominant annual signal with 1.3 mm amplitude in Z (Table 4.14). To address the question of which model best centers the orbit, Jason-2 tracking data are used to estimate a geocenter series for six test cases: no CM, CM (Ries 2013), CM (ITRF2014), CM GSFC test1, CM+APL GSFC test2, and jtrf2014_test. GEODYN (Pavlis et al., 2017) is used to explicitly estimate the Center of Network (CN)-CM vector per Cartesian component over 137 10-day arcs from July 2008 through 2011. As with all SLR/DORIS CNCM estimates CN approximates the theoretical Center of Figure (CF). The Jason-2 CM estimates where CM is modeled should show a residual geocenter series of diminished magnitude depending on the accuracy of the test CM representation. Spectral analysis of the estimated geocenter series shows all annual amplitudes of the residual series are smaller when CM is modeled than when it is not (Fig 4.12). Furthermore, given the Jason-2 SLR/DORIS sensitivity to orbit centering, some models perform better than others. The GSFC test CM models perform best, however the GSFC CM solution spans are almost the same as the test span and suggest that all the models are a best fit to an annual signal which varies in amplitude and phase. It is important to note the GSFC test2 CM+APL model performs better than any other and indicates there is benefit for using a CM model which considers APL through explicit modeling of APL at the observation level. The jtrf2014_test performs better than the standard annual Ries (2013) and ITRF2014 CM models for orbit centering, and alone shows improvement in the semi-annual term (Fig 4.12). The Jason-2 CM estimate time-series show power at the semi-annual period with amplitudes of around 3-mm . The Jason-2 SLR/DORIS tracking data indicate geocenter motion and non-tidal surface loading are more accurately represented with the CM+APL model and JTRF2014, which un2017-08-04

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modeled reach 15 mm peak-to-peak annual variation in the orbit Z component. The tests show that explicit modeling of APL is important to orbit centering. The Jason-2 SLR/DORIS data indicate the JTRF2014 realization has captured much of the annual and semi-annual variations of surface deformation due to non-tidal loading and geocenter motion. Evaluation of JTRF2014 also underscores the value to POD in accounting for non-tidal loading and the geocenter at the observation level. Figure 4.11

Figure 4.11

5. Orbit sensitivity to SLR/DORIS network frames 5.1. Sensitivity of the orbit to drift in TRF origin 5.2. Orbit drift and stability 5.1 Sensitivity of the orbit to drift in the TRF origin Orbit drift in Z maps to a mean radial orbit drift over water, impacting estimates of regional and also global sea level change due to the unequal north-south distribution of ocean surface area. Drift in the tracking station network origin directly impacts the computed orbit. Linear transfer functions relating the station network drift and drift in the orbit have been derived from TOPEX DORIS POD simulations (Morel and Willis 2005), and have been confirmed in analysis of TOPEX/Jason-1 altimeter data (Beckley et al. 2007). The derived relationships in mm/year are Z (orbit) = +0.74 * Z (network), and approximately Radial orbit (over water) = -0.12 * Z (network). Drift in the network X and Y also contribute to the radial drift over water but by an order of magnitude less, and drift in scale by two orders of magnitude less (Morel and Willis 2005). It is easy to picture that the regional Zto-radial projected error varies by latitude, being zero at the equator and having the largest error at the high latitudes. The ITRF provides the definitive realization of the terrestrial origin, scale, orientation, and their time derivatives. Linear geocenter motion (CF–CM) of 1 mm/year is possible due to GIA and present day ice melt (Métivier et al, 2010). An acceleration in geocenter motion is also possible due to acceleration in the ice melt (Métivier et al, 2010), and thus the implied TRF origin secular motion may also depend on the sampling period. Drift error in the network is caused by misalignment of the realized station network origin with the Earth’s center of mass, and thus the linear motion of the network origin will not exactly correspond to the long-term motion of the geocenter. Different realizations of ITRS vary in part due to their imperfection of their alignment with the geocenter. Thus orbits determined using the different ITRS realizations will show some drift in Z. This measure, however, cannot show the true orbit drift, much as comparison between different TRF complements cannot show network origin misalignment with the true geocenter. Ours is a measure of radial drift stability. At best, orbit stability can serve as a lower bound estimate of the drift error.

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To meet the present goals of geodetic research, the Global Geodetic Observing System (GGOS) has determined that the terrestrial reference frame should be accurate at a level of 1 mm in station position, and stable with time at a level of 0.1 mm/year (Plag and Pearlman, 2009). Since ITRF2000, differences in the network origin drift have progressively decreased between the later ITRF realizations. The present ITRF2008/ITRF2014 IGN computed origin drift may seem to accommodate the GGOS stability requirement of 0.1 mm/year (Table 5.1), however the IGN definition may not be pertinent to the ITRF network which defines the orbit frame. The Table 5.1 IGN Helmert translation rate parameters between ITRF frames shown in Table 5.1 are computed using a fixed set of stations selected from the four defining technologies: SLR, DORIS, GPS, and VLBI. The IGN computed Helmert values will not necessarily correspond to what is observed between the ITRF networks used in altimeter satellite POD for two reasons: 1) POD stations are selected from at most three technologies but not four, 2) the number of POD stations are only fixed over an arc, with selected stations varying from arc to arc. We have computed Helmert parameters between the DORIS ITRF2008 and ITRF2014 complements for stations used in POD for each arc. Figure 5.1 illustrates that the Z-drift observed from the time series of DORIS ITRF2008/ITRF2014 complements used in POD is more than twice as steep as the IGN estimate. More importantly the Z-drift observed from the time series of DORIS POD complements directly impacts the orbit, and thus the altimeter measurement frame. Fig 5.1 shows the Mean-Z SLR+DORIS orbit differences are largely explained by the estimated Helmert Z- translation (TZ ) parameter series describing DORIS network changes. One can also see the stochastic component of DORIS station arc availability influencing patterns of orbit change. The majority of DORIS stations are uniformly weighted in POD. Although it is the network shift in Z which most directly impacts the radial orbit, one can see the radial orbit will also be influenced by drift in TX, TY, and Scale (Table 5.2). Also notice that the network changes which impact the orbit are not represented by the IGN estimates (Table 5.2). Thus the TRF network stability pertinent to POD can be defined only by examination of the orbit-specific tracking network time series. Over the three missions the Table 5.2 observed orbit rates in “Z” (Fig 5.1) and in the radial directions (Fig 5.2a) confirm the station network-orbit Morel and Willis (2005) transfer functions. Although drift in the SLR network origin may differ from that of DORIS and even have a different orbit transfer function (Cerri et al. 2010, table 7), our SLR+DORIS orbits are driven by DORIS data given the specified relative data weighting (Table 2.1). Figure 5.1

5.2 Orbit drift and stability The radial orbit drifts (over water) relative to ITRF2008 show variation depending on the ITRS 2014 realization and by mission (Fig 5.2a – 5.2d). Radial drift is an important measure of stability for altimeter satellite orbits. Variation in the mean radial differences can be 2017-08-04

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viewed as a more general measure of orbit stability, driven by differences between the two tracking reference frame origins. In this respect Fig 5.2b and 5.2d suggest a greater instability in the DTRF2014 and JTRF2014 DORIS network origins compared to ITRF2014 or DPOD2014. However, by any measure, stability between the ITRF2008/TRF2014 orbits is very high (Figs 5.2a–5.2d, Table 5.3), and indicates no appreciable systematic orbit inconsistency should accompany the POD transition from ITRF2008 to any of the ITRS 2014 realizations for altimeter data analysis. Table 5.3 – 5.4

Fig 5.2d shows differences between an orbit centered using the Ries (2013) annual CM model and one using the JTRF2014 DORIS/SLR station position series. Considering the superior orbit centering offered by JTRF2014 (Section 4.3), Fig 5.2d suggests an annual term deficiency in the Ries (2013) model which shows as a 0.4 mm amplitude signal in the radial orbit. Although the goal for altimetry annual signal accuracy has not yet been defined (Table 1.1), omission of POD modeling of geocenter motion and non-tidal station loading contributes to an annual error of 0.6 – 0.9 mm amplitude in the mean sea level (Fig 4.11). Figures 5.2a – 5.2d

Figure 5.3 illustrates orbit drift by geographical region for the itrf2014_aug_testitrf2008_test comparison, and indicates systematic ITRF2008 / ITRF2014 orbit differences will have a negligible impact on altimeter MSL rates and altimeter tide gauge analysis. For example, an equal weighting of the 64 tide gauges typically used in our altimeter calibration (Mitchum, 2000; Beckley et al., 2010) will average to an orbit drift error of only +0.012 mm/year in the worst case (Fig 5.3). The eight Atlantic tide gauge subset average to an orbit drift error of +0.139 mm/year. Note drift in the network “X”, “Y” and Scale also influence the radial orbit drift, but by 1-2 orders of magnitude less than for drift in “Z” (see Table 5.2). Figure 5.3

We have also compared radial drift stability between the TRF2014 test cases. Although the JTRF2014 solution may include geocenter linear motion by filter design, it is beyond the scope of this paper to assess the accuracy of such CM motion estimates, and so our assessment is one of TRF2014 orbit drift stability. The comparison between the TRF2014 SLR+DORIS orbits shows there is no appreciable radial drift between the orbits over water (Table 5.4). The largest drift magnitudes seen between the DTRF2014 and JTRF2014 solutions of 0.02 mm/year are of the same order of magnitude, and thus comparable to the ITRF2008/TRF2014 orbit drifts (Tables 5.2 - 5.4).

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Another measure of stability pertinent to this study can be expressed as the RMS radial orbit sensitivity to observed RSS ITRF2008 - ITRF2014 station position differences over an arc, or the relation of radial orbit error to total station position error. Figure 4.0 suggests a linear orbit sensitivity to the RSS differences in the DORIS station positions. Indeed, a closer look at the Jason-2 orbits indicates for all practical purposes the orbit sensitivity can be expressed as a simple ratio of the RSS perturbation in DORIS station positions (Fig 5.4). Figure 5.4 also indicates it is the DORIS data which drives the SLR+DORIS orbits, and that inclusion of SLR improves stability of the DORIS-only orbits. This is shown through comparison of the (SLR+DORIS RMS orbit Table 5.5 differences/ DORIS RSS station differences) and (DORIS RMS orbit differences / DORIS RSS station differences) ratios (Fig 5.4). The ratio defines the orbit stability. Thus for the Jason-2 orbits we have 1 cm DORIS station error will cause 0.5 mm SLR+DORIS orbit error, and 0.7 mm DORIS-only radial orbit error. It is expected the SLR+DORIS orbits should be less sensitive to perturbation in the DORIS station positions than the DORIS-only orbits. Across each of the three missions the average ratios indicate 1 cm DORIS station error produces 0.9 mm of TP SLR+DORIS orbit error, 0.8 mm of orbit error for Jason-1, and 0.5 mm of orbit error for Jason-2 (Fig 5.5). The difference in ratios between missions probably reflects progressive improvement in the DORIS tracking system and the increasing quanity of DORIS data available for POD. For example, the DGXX 3rd generation receiver onboard Jason-2 capable of simultaneously tracking 7 DORIS beacons, allows the most stable orbit solution (Auriol and Tourain, 2010). The Jason-1 DORIS 2nd generation receiver capable of simultaneously tracking 2 DORIS beacons offers an improvement over the TOPEX/Poseidon 1st generation receiver, and recorded 50% more data (Willis et al., 2003). Furthermore changes in the ratio time series correspond to additional changes in the DORIS tracking system: the TOPEX DORIS receiver was switched in December 1998 (DORISMail 356), and the Jason-1 DORIS receiver Ultra Stable Oscillator (USO) was switched at end of June 2004 (DORISMail 326). The DORIS beacon performance and stability were also improved over a 6-year transition period to 2nd generation Starec antenna beacons beginning 2000 (Fagard 2006). The time evolution of the orbit/station differences ratios does seem to suggest a possible new diagnostic index of DORIS POD system performance and health (Fig 5.4) In conclusion two kinds of orbit stability have been evaluated: stability in radial drift over water, and radial sensitivity to station error. These estimates are summarized in Table 5.5 Figure 5.4

Figure 5.5

6. Conclusion We have compared ITRF2008-based SLR+DORIS orbits and stations across the TOPEX/Poseidon, Jason-1, Jason-2, and Jason-3 24+ year altimeter mission span with the TRF2014-based orbits and stations. The TRF2014 test complements consist of ITRF2014, DTRF2014, JTRF2014, and DPOD2014 station positions.

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The largest source of TRF error stems from ITRF2008 station position extrapolation past the 2009 solution end time. Following 2009/2010, ITRF2008 DORIS/SLR station position extrapolation error dominates the comparison with TRF2014 stations and orbits. The TRF2014 SLR/DORIS complement impact on the orbit is small compared to ITRF2008, typically 1-2 mm radial RMS difference across 1992-2009, and increases following 2009 up to 5 mm. SLR/DORIS residuals show that station position extrapolation error past the solution span becomes evident after 1-2 years, and will contribute to about 3-4 mm radial orbit error after seven years. Analysis of the station position differences suggests an overall station position RSS error of 11 – 15 mm for the DORIS, and 8 – 13 mm for the SLR over the TRF solution period. Seven years of station position extrapolation doubles the ITRF2008 station position error. Independent crossover residuals indicate that the orbit radial accuracies marginally differ over the 1992-2002 TOPEX/Poseidon period. Only the DTRF2014 orbits show statistical improvement over the ITRF2008 orbits. However beginning with Jason-1 (2002) all TRF2014 orbits show, albeit small, a statistically significant improvement in accuracy, with JTRF2014 showing the largest improvement. The margin of improvement and statistical confidence further increase over the Jason-2 period (2008-2016) for all TRF2014 orbits, with DTRF2014 showing the largest margin. However, for Jason-3 (2016) only the DPOD2014-based orbits show a statistically significant increase in accuracy. The DPOD2014-based station complement is the most complete in our series of tests. The Jason-3 test results underscore the importance to POD of station complements that are routinely updated w.r.t. ITRF2014. Prior to 2009, SLR/DORIS residuals suggest, the small improvement seen for the TRF2014 orbits stems from improvement to the respective TRF2014 DORIS station position accuracies. Over this period the TRF2014 SLR comparison results are mixed, and some even show a marginal degradation w.r.t. ITRF2008. DTRF2014 is the first ITRS realization to correct station positions or normal equations for atmospheric and hydrological loading before combination. Our positive results suggest such an approach is beneficial. The ITRS 2014 realizations are distinguished by their treatment of station motion. Looking at GPS-orbit independently determined SLR/DORIS residuals for just the ITRF2014 PSD identified stations across the Jason 1 to 3 missions we find that use of the IGN post-seismic deformation modeling offers no advantage to SLR+DORIS POD over the linear motion model. We also find the JTRF2014 position series offer no advantage for these same stations. Our analysis indicates the JTRF2014 proof-of-concept series reliably represent non-tidal station loading and geocenter motion. JTRF2014 – based orbit comparisons suggest a deficiency in our current POD standard Ries (2013) CM model, which shows as an annual radial orbit signal of 0.4 mm amplitude. When left unmodeled, the annual radial orbit centering error will show 1.8 mm peak-to-peak variations. Although altimeter goals for annual signal accuracy have not yet been defined (Ablain et al., 2015), our POD objective is to best center the SLR+DORIS computed orbit. In a preliminary series of SLR-derived CM tests which include JTRF2014, Ries (2013) CM, ITRF2014 CM (Altamimi et al., 2016), and two special GSFC CM models, Jason-2 orbit-centering sensitivity suggests the most 2017-08-04

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promising approach is to model atmosphere pressure loading at the observation level together with the appropriate CM model. We plan to continue this investigation. Analysis shows the SLR+DORIS radial orbit is sensitive to changes in the DORIS network origin. Although the SLR network origin drift and orbit transfer function will differ from that of the DORIS (Cerri et al., 2010), our POD relative weighting allows DORIS data to dominate the SLR+DORIS orbits. The ITRF2008-ITRF2014 orbit changes in Z directly correspond to the Helmert Z translation parameter T Z series, estimated for the DORIS stations used in each arc. The slope of the linear fit to the ITRF2008-ITRF2014 TZ time series represents the actual measure of TRF stability pertinent to SLR+DORIS altimeter satellite POD and the altimeter measurement frame. The corresponding orbit rates in Z and in the radial direction are consistent with the Morel and Willis (2005) transfer functions. The ITRF2008-ITRF2014 DORIS network time series rates for changes in X, Y, Z, and the Scale differ from the IGN ITRF2014->ITRF2008 rate estimates computed with a fixed network consisting of all four geodetic station types. The mean global radial drift stabilities over water range between +0.01 to +0.04 mm/yr depending on the ITRF2014 realization. On a regional scale the radial orbit drifts reach  0.2 mm/yr over water. Radial orbit drift stability between only TRF2014 solutions is comparable overall, ranging -0.01 to +0.02 mm/yr, but larger over individual missions, up to 0.22 mm/yr for TP. These estimates indicate that the transfer error between ITRF2008 to any of the TRF2014 based orbits will have a small impact on altimeter data estimates of global MSL and corresponding tide gauge validation analysis. For example, an equal weighting of the 64 tide gauges typically used in our altimeter calibration (c.f. Beckley et al., 2010) will average to an orbit drift error of only +0.012 mm/year for the worst case. However, these estimates of orbit stability do not necessarily confirm that the Ablain et al (2015) altimetry accuracy requirements have been reached. By definition of terms, the GGOS TRF stability goal may be reached without satisfying the altimeter drift accuracy requirement. Drift error of the ITRF origin has been a subject of study over several years. Most recently Wu et al. (2011) inverted ITRF2008 station velocities, GRACE gravity trend data, and ocean bottom pressure linear trend data and found that the ITRF2008 origin accuracy was likely to be 0.5 mm/year in each component. A special IAG task force commissioned to evaluate TRF accuracy has summarized all these analyses (Collilieux et al. 2014). The Morel and Willis (2005) transfer function indicates the TRF origin Z component must be accurate at a level of 2.5 mm/year in order to satisfy the radial 0.3 mm/year altimeter accuracy goal (Table 1, Ablain et al., 2015). Thus origin drift error in either ITRF2008 or the TRF2014 complements is not likely to be an obstacle for meeting both the 0.3 mm/year global MSL altimeter accuracy goal, and the regional 1 mm/year goal. SLR+DORIS radial orbit sensitivity to DORIS station position error was evaluated as another measure of orbit stability. The ratio of the RMS radial orbit differences to RSS station position differences was nearly constant over each altimeter mission. Changes in the ratio time series corresponds to changes in the DORIS tracking system, which prompts one to ask whether such ratios could also serve as an index to DORIS tracking health and accuracy? Considering 15-mm DORIS station position error the ratios suggest corresponding radial errors of 1.4 mm for TOPEX/Poseidon, 1.2 mm for Jason-1, and 0.75 2017-08-04

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mm for Jason-2. Such an ITRF limitation to orbit accuracy is not far from meeting the 0.5 mm inter-annual radial position altimetry accuracy goal (Ablain et al 2015), and offers the prospect that future ITRS realizations will bring us closer to meeting this objective. On consideration of the following: a) the small differences between the TRF2014 complement test results over 1992 to 2009, b) when looking forward to 2016 that only DPOD2014 is able to provide superior orbits, c) the very high stability in transition from ITRF2008 to any of the 2014 ITRS realizations, and d) the altimeter need for a CM centered measurement frame, we have two recommendations for current and continued SLR+DORIS altimeter satellite POD: 1) use of maintained full complement updates to ITRF2014, 2) continued investigation towards improving orbit centering. Acknowledgments We acknowledge the International DORIS Service (IDS) and International Laser Ranging Service (ILRS) for their support and leadership in providing DORIS and Satellite Laser Ranging data (Pearlman et al., 2002; Willis et al., 2010), as well as the providers of the ITRF2014 DORIS/SLR station complements used in this paper: IGN (Altamimi et al, 2016), DGFI (Seitz et al, 2016), JPL (Abbondanza et al., 2017), IDS (Moreaux et al 2016a). The U.S. National Aeronautics and Space Administration (NASA) supported this research under the auspices of the OSTST (Ocean Surface Topography Science Team) and the Making Earth System Data Records for Use in Research Environments (MEaSUREs) program.

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ST (2010), Assessment of the Jason-2 extension to the TOPEX/ Poseidon, Jason-1 sea-surface height time series for global mean sea level monitoring, Marine Geodesy, 33(S1), 447-471, doi:10.1080/01490419.2010.491029. Bertiger WI, Bar-sever YE, Christensen EJ, et al., 1994. GPS precise tracking of TOPEX/Poseidon, results and implications. J. Geophys. Res. 99 (C12), 24449–24464. Bertiger WI, Desai S, Dorsey A, et al., (2010). Sub-centimeter precision orbit determination with GPS for ocean altimetry. Mar. Geodesy 33 (Suppl. 1), 363–378. doi:10.1080/01490419.2010.487800. Blewitt, G., et al. (2010), Geodetic observations and global reference frame contributions to understanding sea-level rise and variability, in Understanding Sea Level Rise and Variability, edited by J. A. Church et al., pp. 256–284, Wiley, Chichester. Briole P, Willis P, Dubois J, Charade O, (2009), Potential volcanological applications of the DORIS system. A geodetic study of the Socorro Island (Mexico) coordinate timeseries, Geophysical Journal International, 178(1), 581-590, doi:10.1111/j.1365246X.2009.04087.x Cerri L, Berthias JP, Bertiger W, Haines BJ, Lemoine FG, Mercier F, Ries JC, Willis P, Zelensky NP and Ziebart M ﴾2010) Precision Orbit Determination Standards for the Jason Series of altimeter missions, Marine Geodesy, 33 (Suppl. 1), 379-418, doi:10.1080/01490419.2010.488966 Couhert A, Cerri L, Legeais J, Ablain M, Zelensky N, Haines B, Lemoine F, Bertiger W, Desai S, and M. Otten (2015) Towards the 1 mm/y stability of the radial orbit error at regional scales. Adv. Space Res., 55 (1), 2-23; doi:10.1016/j.asr.2014.06.041 Eanes RJ (1995), Earth orientation and site coordinates from the Center for Space Research Solution CSR 95L01, in IERS Tech. Note No. 19 (Sec. L-7), Ed.: P. Charlot, Observatoire de Paris, Paris, France. Fagard H, (2006), Twenty years of evolution for the DORIS permanent network: from its initial deployment to its renovation. J. Geodesy, 80 (8–11), 429–456. doi:10.1007/s00190-006-0084-2. Fasullo JT, Nerem RS, Hamlington B (2016), Is the detection of accelerated sea level rise imminent? Scientific Reports. 2016;6:31245. doi:10.1038/srep31245. Fu L-L and Haines BJ (2013), The challenges in long-term altimetry calibration for addressing the problem of global sea level change, Adv. Space Res, 51(8), 12841300, doi:10.1016/j.asr.2012.06.005

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oiginger , ieser D, Mayer- urr T, et al (2011). The combined satellite-only global gravity field model GOCO02S, Geophysical Research Abstracts, 13, EGU2011–10,571. http://www.goco.eu/data/egu2011-10571-goco02s.pdf Gross R, Abbondanza C, Chin M, Heflin M, Parker J, and Wu X (2015), IERS Annual Report 2015, International Earth Rotation and Reference Systems Service, pp. 137-142, ISBN: 978-3-86482-087-8, Ed.: Dick WR and Thaller D, http://www.iers.org/AR2015 Hamlington, BD, Leben RR, Strassburg MW, Nerem RS, Kim KY (2013), Contribution of the Pacific Decadal Oscillation to global mean sea level trends, Geophys. Res. Lett., 40(19), 5171-5175, doi: 10.1002/grl.50950. Knudsen P, Bingham R and Andersen O (2011), A global mean dynamic topography and ocean circulation estimation using a preliminary GOCE gravity model, J. Geodesy, 85(11), 861-879, doi: 10.1007/s00190-011-0485-8 Lemoine FG, Zelensky NP, Chinn DS, et al., (2010). Towards development of a consistent orbit series for TOPEX, Jason-1, and Jason-2. Adv. Space Res., 46 (12), 1513–1540. doi:10.1016/j.asr.2010.05.007. Lemoine FG, Zelensky NP, Chinn DS, et al. (2015), A new time series of orbits (std1504) for TOPEX/Poseidon, Jason-1, Jason-2 (OSTM), OSTST POD oral presentation, Reston Virginia, October 2015, http://meetings.aviso.altimetry.fr/programs/completeprogram.html Luthcke SB, Zelensky NP, Rowlands DD, et al., (2003). The 1-cm orbit: Jason-1 precision orbit determination using GPS, SLR, DORIS, and altimeter data. Marine Geod., 26 (3– 4), 261–284, doi: 10.1080/01490410390256727, Métivier L, Greff-Lefftz M, Altamimi Z (2010), On secular geocenter motion: the impact of climate changes. Earth Planetary Sci. Lett., 296, 360–366, doi:10.1016/j.epsl.2010.05.021 Mitchum GT (2000), An improved calibration of satellite altimetric heights using tide gauge sea levels with adjustment for land motion, Marine Geodesy, 23(3), 145-166, doi: 10.1080/01490410050128591 Morel L and Willis P (2005), Terrestrial reference frame effects on sea level rise determined by TOPEX/Poseidon. Adv. Space Res. 36(3), 358–368, doi: 10.1016/j.asr.2005.05.113. Moreaux G, Willis P, Lemoine FG, et al. (2016a), DPOD2014: a new DORIS extension of ITRF2014 for Precise Orbit Determination, Poster G41A-1006, 2016 Fall AGU, San Francisco, http://ids-doris.org/documents/report/meetings/AGU2016_IDS_CCDPOD2014-Moreaux.pdf 2017-08-04

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Moreaux G, Lemoine FG, Capdeville H, et al. (2016b). The International DORIS Service contribution to the 2014 realization of the International Terrestrial Reference Frame, Adv. Space Res., 58(12), 2479-2504, doi:10.1016/j.asr.2015.12.021. Moreaux G, Lemoine FG, Argus DF, et al. (2016c). Horizontal and vertical velocities derived from the IDS contribution to ITRF2014, and comparisons with geophysical models, Geophys. J. Intl. 207, 209–227, doi: 10.1093/gji/ggw265 Palanisamy H., Meyssignac B, Cazenave A, Delcroix T (2015), Is antropogenic fingerprint of sea level already detectable in the Pacific Ocean? Env. Res. Letters, 10(8), doi:10.1088/1748-9326/10/8/084024. Pavlis DE, Wimert J, McCarthy JJ, (2017), GEODYN II system description, Vol. 1–5, contractor report, SGT Inc., Greenbelt, Maryland, U.S.A. Pearlman MR, Degnan JJ, Bosworth JM, (2002), The international laser ranging service. Adv. Space Res. 30 (2), 135–143. doi:10.1016/S0273-1177(02)00277-6. Petit , and u um , S Conventions , S Technical ote erlag des undesamts fur Kartographie und Geodäsie, Frankfurt am Main, 179 pp. Plag H-P, Pearlman M (eds) (2009) The global geodetic observing system: meeting the requirements of a global society on a changing planet in 2020, vol 332. Springer, Berlin/Heidelberg. ISBN:978-3-642-02686-7 Rebischung, P, Altamimi Z, Ray J, Garayt B (2016), The IGS contribution to ITRF2014, J. Geodesy, 90(7), 611-630, doi: 10.1007/s00190-016-0897-6. Ries JC, (2013), Annual Geocenter Motion from Space Geodesy and Models, G12A-08, presented at 2013 Fall AGU Meeting, San Francisco, CA, 9–13 December 2013. (http://ids-doris.org/report/publications/on-line-publications.html) Seitz M, Bloßfeld M, Angermann D, Schmid R, Gerstl M, Seitz F (2016), The new DGFI-TUM realization of the ITRS: DTRF2014 (data). Deutsches Geodätisches Forschungsinstitut, München, 10.1594/PANGAEA.864046, 2016. Stammer, D., R.D. Ray, O.B. Andersen, et al., Accuracy assessment of global baratropic ocean tide models, Rev. Geophys., 52, 243-282, doi:10.1002/2014RG000450. Tapley BD, Schutz BE, and Born, GH (2004), Statistical Orbit Determination, Elsevier Academic Press, New York, N.Y., ISBN: 0-12-683630-2. Willis P, Haines B, Bar-Sever Y, et al. (2003), TOPEX/Jason combined GPS/DORIS orbit determination in the tandem phase. Adv. Space Res. 31 (8), 1941–1946, doi:10.1016/S0273-1177(03)00156-X. 2017-08-04

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Willis P, Haines B, Berthias JP, Sengenes P, Le Mouel JL (2004), Behavior of the DORIS/Jason oscillator over the South Atlantic Anomaly. CR Geosci., 336(9),839– 846, doi: 10.1016/.crte.2004.01.004. Willis P, Ries JC (2005) Defining a DORIS core network for Jason-1 Precise Orbit Determination based on ITRF2000, methods and realization. J Geod 79(6–7):370– 378, doi: 10.1007/s00190-005-0475-9. Willis P, Fagard H, Ferrage P, Lemoine FG, Noll CE, Noomen R, Otten M, Ries JC, Rothacher M, Soudarin L, Tavernier G, Valette JJ (2010) The international DORIS service, toward maturity. In: Willis P (ed) DORIS: scientific applications in geodesy and geodynamics. Adv. Space Res., 45(12), 1408–1420, doi:10.1016/j.asr.2009.11.018 Willis P, Zelensky NP, Ries J, et al., (2015). “DPOD2008, a DORIS-oriented terrestrial reference frame for precise orbit determination”, in IAG Symposium Series 143. IAG 150 Years: Proceedings of the IAG Scientific Assembly in Potsdam, Germany, 2013, pp. 175-183, doi:10.1007/13452015125. Wöppelmann G and Marcos M (2016), Vertical land motion as a key to understanding sea level change and variability, Rev. Geophys., 54, 64–92, doi:10.1002/2015RG000502. Wu X, Abbondanza C, Altamimi Z, Chin TM, Collilieux X, Gross RS Heflin MB, Jiang Y, and Parker JW (2015), KALREF—A Kalman filter and time series approach to the International Terrestrial Reference Frame realization. J. Geophys. Res. Solid Earth, 120, 3775–3802. doi: 10.1002/2014JB011622. Zelensky NP, Lemoine FG, Ziebart M, et al., (2010). DORIS/SLR POD modeling improvements for Jason-1 and Jason-2. Adv. Space Res. 46 (12), 1541–1558. doi:10.1016/j.asr.2010.05.008. Zelensky NP, Lemoine FG, Melachroinos S, et al. (2014) Impact of atmosphere loading and geocenter motion station corrections on the Jason-2 and Envisat SLR+DORIS orbits , OSTST POD oral presentation, Konstanz Germany, October 2014. http://meetings.aviso.altimetry.fr/programs/complete-program.html Zelensky NP, Lemoine FG, Chinn DS, (2016). Towards the 1-cm Saral orbit. Adv. Space Res. 58 (12), 2651–2676. doi:10.1016/j.asr.2015.12.011.

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Figure Captions Figure 4.0 itrf2008_test-minus-dpod2014_test SLR+DORIS radial orbit RMS differences and DORIS station position RSS differences. Note, SLR+DORIS radial orbit differences are largely explained by the differences in DORIS station positions. Figure 4.1 Jason-2 (itrf2014_aug_test – itrf2014_test) SLR+DORIS radial orbit and number tracking station differences. Note, increase in radial orbit differences (green dots) corresponds to increase in discrepancy in number of DORIS stations (blue dots). Figure 4.2 itrf2008_test – itrf2014_test change in SLR RMS fit per arc; Positive implies an improvement for itrf2014_test Figure 4.3 itrf2008_test – dtrf2014_test change in SLR RMS fit per arc; Positive implies an improvement for dtrf2014_test Figure 4.4 itrf2008_test – jtrf2014_test change in SLR RMS fit per arc; Positive implies an improvement for jtrf2014_test Figure 4.5 itrf2008_test – dpod2014_test change in SLR RMS fit per arc; Positive implies an improvement for dpod2014_test Figure 4.6 itrf2008_test – itrf2014_test change in DORIS RMS fit per arc; Positive implies an improvement for itrf2014_test Figure 4.7 SLR+DORIS orbit (itrf2008_test – itrf2014_test) Crossover Residual Variance differences; Positive implies an improvement for itrf2014_test Figure 4.8a Jason-3 DORIS itrf2008_test-minus-tested solution residual differences computed using jpl16a orbit over 53 common stations (February 2016 – August 2016). ote: “*” identifies an T F 4 PSD station, “+” identifies a SAA station. Figure 4.8b Jason-3 SLR itrf2008_test-minus-tested solution residual differences computed using jpl16a orbit over 29 common stations (February 2016 – August 2016). ote: “*” identifies an ITRF2014 (IGN) PSD station. Figure 4.9a Jason-1 SLR itrf2008_test -minus-tested solution residual differences using jpl11a orbit for best & worst performing stations; April 2002 – May 2006 (cycles 9-161). ote: “*” identifies an ITRF2014 (IGN) PSD station. Figure 4.9b Jason-1 DORIS itrf2008_test-minus-tested solution residual differences using jpl11a orbit for best & worst performing stations; April 2002 – May 2006 (cycles 9-161). ote: “*” identifies an T F 4 PSD station, “+” identifies a SAA station.

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Figure 4.10a TOPEX SLR itrf2008_test-minus-tested solution residual differences for largest contributing stations; September 1992 – January 2002 (cycles 1-343). ote: “*” identifies an ITRF2014 (IGN) PSD station. SLR residuals from SLR+DORIS POD. Figure 4.10b TOPEX DORIS itrf2008_test-minus-tested solution residual differences for best & worst performing stations; September 1992 – January 2002 (cycles 1-343). ote: “*” identifies an ITRF2014 PSD station, “+” identifies a SAA station. DORIS residuals from SLR+DORIS POD. Figure 4.11 Orbit centering model impact on Jason-2 mean Z orbit component. Note, JTRF2014 orbit centering in Z is most similar in structure and phase when geocenter motion and atmospheric loading are both modeled (CM+APL). Figure 4.12 Spectral analysis Jason-2 SLR+DORIS CM estimate Z component time series. Note, diminished amplitudes for annual and semi-annual terms suggest the effects of geocenter motion and non-tidal surface loading are well represented with JTRF2014. Figure 5.1 itrf2008_test-minus-itrf2014_test mean Z orbit differences and Helmert T Z translation estimates between DORIS networks used for POD in each arc. Illustrates ITRF2008/ITRF2014 station network and orbit frame stability in Z. Note IGN TZ rate estimate twice as small as estimated from time series. TZ time series slope supports the Morel and Willis (2005) orbit transfer function in Z. Figure 5.2a itrf2008_test-minus-itrf2014_test mean radial orbit differences over water. Illustrates ITRF2008 vs. ITRF2014 radial orbit drift stability impact on Global Mean Sea Level (GMSL). Note TZ time series rate (Fig 5.1) supports the Morel and Willis (2005) radial orbit transfer function. Figure 5.2b itrf2008_test-minus-dtrf2014_test mean radial orbit differences over water. Illustrates ITRF2008 vs. DTRF2014 radial orbit drift stability impact on Global Mean Sea Level (GMSL ). Figure 5.2c itrf2008_test-minus-dpod2014_test mean radial orbit differences over water. Illustrates ITRF2008 vs. DORIS DPOD2014/SLR ITRF2014 radial orbit drift stability impact on Global Mean Sea Level (GMSL). Figure 5.2d itrf2008_test-minus-jtrf2014_test mean radial orbit differences over water. Illustrates ITRF2008 .vs. JTRF2014 radial orbit drift stability impact on Global Mean Sea Level (GMSL). Residual annual signal (black line) suggests a deficiency in the Ries (2013) CM model. Figure 5.3 itrf2014_aug_test – itrf2008_test geographic radial orbit drift computed over 1992-2016. Illustrates ITRF2008 .vs. ITRF2014 radial orbit drift stability impact on Regional Mean Sea Level.

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Figure 5.4 Jason-2 itrf2008_test-minus-dpod2014_test radial orbit RMS differences and DORIS station position RSS differences, and their ratios. Figure 5.5 Ratio of the itrf2008_test-minus-dpod2014_test radial orbit RMS differences / DORIS station position RSS differences

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Figure

Figure 4.0 itrf2008_test-minus-dpod2014_test SLR+DORIS radial orbit RMS differences and DORIS station position RSS differences. Note, SLR+DORIS radial orbit differences are largely explained by the differences in DORIS station positions.

Figure 4.1 Jason-2 (itrf2014_aug_test – itrf2014_test) SLR+DORIS radial orbit and number tracking station differences. Note, increase in radial orbit differences (green dots) 2 corresponds to increase in discrepancy in number of DORIS stations (blue dots).

Figure 4.2 itrf2008_test – itrf2014_test change in SLR RMS fit per arc; Positive implies an improvement for itrf2014_test.

Figure 4.3 itrf2008_test – dtrf2014_test change in SLR RMS fit per arc; Positive implies an improvement for dtrf2014_test .

Figure 4.4 itrf2008_test – jtrf2014_test change in SLR RMS fit per arc; Positive implies an improvement for jtrf2014_test .

Figure 4.5 itrf2008_test – dpod2014_test change in SLR RMS fit per arc; Positive implies an improvement for dpod2014_test .

Figure 4.6 itrf2008_test – itrf2014_test change in DORIS RMS fit per arc; Positive implies an improvement for itrf2014_test .

Satellite

Mean

Median

Std. Dev.

Confidence

TP

-0.79

-1.09

9.26

93 %

J1

2.53

2.24

9.47

99.9%

J2

4.36

2.14

13.92

99.9%

Figure 4.7 SLR+DORIS orbit (itrf2008_test – itrf2014_test) Crossover Residual Variance differences; Positive implies an improvement for itrf2014_test .

8

RMS residuals (mm/s) for 39 matched stations ITRF2008

ITRF2014

DTRF2014

DPOD2014

0.4137

0.4113

0.4116

0.4116

Figure 4.8a Jason-3 DORIS itrf2008_test-minus-tested solution residual differences computed using jpl16a orbit over 53 common stations (February 2016 – August 2016). Note: “*” identifies an ITRF2014 (IGN) PSD station, “+” identifies a SAA station.

RMS residuals (cm) for 28 matched stations ITRF2008

ITRF2014

DTRF2014

1.499

1.318

1.335

Figure 4.8b Jason-3 SLR itrf2008_test-minus-tested solution residual differences computed using jpl16a orbit over 29 common stations (February 2016 – August 2016). Note: “*” identifies an ITRF2014 (IGN) PSD station.

Figure 4.9a Jason-1 SLR itrf2008_test -minus-tested solution residual differences using jpl11a orbit for best & worst performing stations; April 2002 – May 2006 (cycles 9-161). Note: “*” identifies an ITRF2014 (IGN) PSD station.

Figure 4.9b Jason-1 DORIS itrf2008_test-minus-tested solution residual differences using jpl11a orbit for best & worst performing stations; April 2002 – May 2006 (cycles 9-161). Note: “*” identifies an ITRF2014 (IGN) PSD station, “+” identifies a SAA station.

Figure 4.10a TOPEX SLR itrf2008_test-minus-tested solution residual differences for largest contributing stations; September 1992 – January 2002 (cycles 1-343). Note: “*” identifies an ITRF2014 (IGN) PSD station. SLR residuals from SLR+DORIS POD.

Figure 4.10b TOPEX DORIS itrf2008_test-minus-tested solution residual differences for best & worst performing stations; September 1992 – January 2002 (cycles 1-343). Note: “*” identifies an ITRF2014 (IGN) PSD station, “+” identifies a SAA station. DORIS residuals from SLR+DORIS POD.

Figure 4.11 Orbit centering model impact on Jason-2 mean Z orbit component. Note, JTRF2014 orbit centering in Z is most similar in structure and phase when geocenter motion and atmospheric loading are both modeled (CM+APL)

15

Figure 4.12 Spectral analysis Jason-2 SLR+DORIS CM estimate Z component time series. Note, diminished amplitudes for annual and semi-annual terms suggest the effects of 16 geocenter motion and non-tidal surface loading are well represented with JTRF2014 .

-0.1 mm/yr

-0.23 mm/yr -0.16 mm/yr

Figure 5.1 itrf2008_test-minus-itrf2014_test mean Z orbit differences and Helmert TZ translation estimates between DORIS networks used for POD in each arc.

Combined rate: 0.028 mm/y

Figure 5.2a itrf2008_test-minus-itrf2014_test mean radial orbit differences over water. Illustrates ITRF2008 vs. ITRF2014 radial orbit drift stability impact on Global Mean Sea Level (GMSL).

Figure 5.2b itrf2008_test-minus-dtrf2014_test mean radial orbit differences over water. Illustrates ITRF2008 vs. DTRF2014 radial orbit drift stability impact on Global Mean Sea Level (GMSL ). .

Figure 5.2c itrf2008_test-minus-dpod2014_test mean radial orbit differences over water. Illustrates ITRF2008 vs. DORIS DPOD2014/SLR ITRF2014 radial orbit drift stability impact on Global Mean Sea Level (GMSL).

Figure 5.2d itrf2008_test-minus-jtrf2014_test radial orbit drift stability impact on Global Mean Sea Level (GMSL ) . Residual annual signal (black line) suggests a deficiency in the Ries (2013) annual CM model.

Figure 5.3 itrf2014_aug_test – itrf2008_test geographic radial orbit drift impacting regional MSL, 1992-2016 .

Figure 5.4 Jason-2 itrf2008_test-minus-dpod2014_test radial orbit RMS differences and DORIS station position RSS differences, and their ratios .

Figure 5.5 Ratio of the itrf2008_test-minus-dpod2014_test radial orbit RMS differences / DORIS station position RSS differences .

Table 1.1 Altimeter error budget1 Spatial scale Temporal scale State-of-the-art Long term evolution (> 10 years) 0.5 mm/year Global Inter-annual signals (< 5 years) < 2mm over 1 year MSL Annual signals < 1mm Long term evolution (> 10 years) < 3 mm/year Regional MSL Annual signals < 1cm 1) Courtesy of M. Ablain et al, 2015 (see Table 2).

Required 0.3 mm/year 0.5mm over 1 year Not defined < 1 mm/year Not defined

Table 2.0 TOPEX/Poseidon and Jason Orbit altitude 1336 km eccentricity 0.0001 inclination 66  repeat period 9.92 days Table 2.1. GSFC POD Model 2015 Standards: std1504 Reference frame and displacement of reference points SLR SLRF2008 (150928 version); ILRS April 2014 data handling DORIS DPOD2008 (DPOD2008.v15 with updates from CLS) Earth tide IERS2003 Ocean loading Got4.10 all stations Atmospheric none loading Got4.7 tidal variations, annual SLR-derived (Ries 2013) (except for CoM JTRF2014) IERS Bulletin A daily (consistent with ITRF2008); Diurnal and semiEOP diurnal variations in polar motion and UT1 due to ocean tides. Precession / IAU2000 Nutation Gravity stack5x5_nom9k8 5x5 weekly normal equations from 21 SLR/DORIS Static satellites estimated over two spans: 1993-2002, 2003-2014; GOCO2S (from 6x6) stack5x5_nom9k8 linear, annual, semi-annual estimates from stacked 5x5 SLR+DORIS 21-years of weekly normal equations for two spans as Time varying above + 6x20 annual terms from GRACE, IERS2010 C21/S21, estimate C31/S21 per arc Atmospheric ECMWF, 50x50@6hrs Tides Got4.10 50x50 (ocean); IERS2003 (Earth) Satellite Surface Forces and attitude Albedo /IR Knocke et al. (1988) Atmospheric MSIS86 drag

Radiation pressure Radiation scale coeff.

TOPEX tuned 8-panel

Jason-1 10-panel

Jason-2 Jason-1 10-panel

CR = 1.0

CR = 0.916 (tuned)

CR = 0.945 (tuned)

nominal: yaw model Quaternions Quaternions off-nominal: quaternions measured sapa measured sapa Tracking data and parameterization Tracking data SLR/DORIS (Jason1 DORIS corrected for SAA) Troposphere SLR: Mendez-Pavlis; DORIS: VMF1 model Drag/8 hrs + opr along & cross-track /12 hrs (TP 24 hrs)+ DORIS time Parameterization bias /arc; 10-day arc dynamic solution DORIS modeling DORIS beacon frequency bias modeling; beacon phase center Antenna TOPEX Jason-1 Jason-2 reference Satellite CoM table corrected table table SLR LRA model re-tuned tuned DORIS pre-launch pre-launch tuned SLR, DORIS 10-cm , 3-mm/s; down10-cm, 2-mm/s 10-cm , 2-mm/s weight weight 14 SAA stations Special testing Atmospheric Non-tidal atmospheric station surface displacements from ECMWF 6loading hour pressure data (courtesy Tonie Van Dam, 2012) 1) CM (Ries 2013): Annual SLR-derived, implicitly includes non-tidal loading; mentioned above in this table as part of std1504 standards. 2) CM (ITRF2014): Annual SLR-derived, implicitly includes non-tidal loading (Altamimi et al 2016). CoM 3) CM (GSFC test1): Annual SLR-derived, implicitly includes non-tidal loading. (Zelensky et al., 2016) 4) CM+APL (GSFC test2): Annual SLR-derived, explicitly considers atmospheric loading. (Zelensky et al., 2016) Note. GSFC test CM weekly estimates use 2008-2011 LAGEOS-1/2 data. Attitude

Table 2.2 Annual Earth CM SLR-based models used in testing (CM-CN(center of network); Amplitude*Cosine(θ-phase)) Amplitude (mm) Center-of-Mass Model X Y Z 1) CM (Ries 2013) -nominal std1504 2.7 2.8 5.5 (implicitly includes non-tidal loading) 2) CM (ITRF2014) 2.6 2.9 5.7 (implicitly includes non-tidal loading) 3) CM (GSFC test1; 2008-2011) 4.0 2.4 6.6 (implicitly includes non-tidal loading) 4) CM+APL (GSFC test2; 2008-2011) 3.5 2.0 5.1 (explicitly considers atmospheric loading)

Phase (deg) X Y Z 41 321 27 36 320 28 51 305 40 60 289 61

Table 3.1 DORIS + SLR complement tests Complement Description / Number stations (4-character ID) DORIS+SLR Test DORIS SLR itrf2008_test DPOD2008_v15 / 189 SLRF2008 (version 150928) / 168 itrf2014_test ITRF2014 (IGN) / 160 ITRF2014 (IGN) / 137 dtrf2014_test DTRF2014 (DGFI) / 153 DTRF2014 (DGFI) / 97 jtrf2014_test JTRF2014 (JPL) / 159 JTRF2014 (JPL) / 71 dpod2014_test DPOD2014_v04 / 195 ITRF2014 (IGN)+SLRF2008 / 173 ITRF2014 (IGN)+DPOD2008 / itrf2014_aug_test ITRF2014 (IGN)+SLRF2008 / 173 192 DTRF2014 (DGFI)+ dtrf2014_aug_test DTRF2014 (DGFI) / 97 DPOD2014_v04 (Jason-3) / 172 Table 4.1 DORIS Jason-2 stations missing in ITRF2014 and contained in DPOD2008 Year ITRF2014 Augmented missing stations 2013 54 56 LAOB PAUB 2014 55 59 LAOB OWEC PAUB PDNC ADHC GONC KEUC LAOB 2015 49 57 OWEC PAUB PDNC ROWC ADHC GONC JIWC KEUC 2016 44 56 KEVC LAOB MNAC OWEC PAUB PDOC ROWC SAPC Note. missing stations are well distributed in latitude and longitude Table 4.2 SLR/DORIS data in IGN ITRF realizations Realization SLR DORIS ITRF2008 1983-2009 1993-2009 ITRF2014 1983-2015 1993-2015 Table 4.3 Summary TOPEX/Poseidon SLR+DORIS POD (1992/09/25 – 2002/01/15; cycles 1-343) Total stations Average RMS residuals Radial orbit Test DORIS SLR Xover RMS diff. DORIS SLR (mm/s) (cm) (cm) (mm) itrf2008_test 96 76 0.5113 1.587 5.644 --itrf2014_test 89 75 0.5100 1.611 5.644 1.5 jtrf2014_test 89 49 0.5103 1.602 5.643 2.4 dtrf2014_test 89 67 0.5093 1.580 5.641 2.1 itrf2014_aug_test 96 76 0.5116 1.616 5.644 1.4 dpod2014_test 94 76 0.5110 1.615 5.643 1.3

Table 4.4 Summary Jason-1 SLR+DORIS POD (2002/01/15 – 2008/07/12; cycles 1-239) Total stations Average RMS residuals Radial orbit Test DORIS SLR Xover RMS diff. DORIS SLR (mm/s) (cm) (cm) (mm) itrf2008_test 97 52 0.3691 0.744 5.515 --itrf2014_test 96 50 0.3689 0.744 5.512 1.4 jtrf2014_test 94 41 0.3665 0.737 5.510 2.0 dtrf2014_test 94 45 0.3684 0.750 5.514 2.3 itrf2014_aug_test 97 52 0.3689 0.744 5.514 1.4 dpod2014_test 97 52 0.3688 0.744 5.514 1.5 Table 4.5 Summary Jason-2 SLR+DORIS POD (2008/07/12 – 2015/02/15; cycles 1-243) Total stations Average RMS residuals Radial orbit Test RMS diff. DORIS SLR Xover DORIS SLR (mm/s) (cm) (cm) (mm) itrf2008_test 87 38 0.3787 0.863 5.318 --itrf2014_test 83 43 0.3762 0.808 5.314 1.6 jtrf2014_test 83 40 0.3762 0.823 5.314 1.9 dtrf2014_test 78 42 0.3764 0.813 5.315 1.9 itrf2014_aug_test 87 43 0.3776 0.813 5.314 1.4 dpod2014_test 87 43 0.3776 0.815 5.315 1.4 Table 4.6 Summary Jason-3 SLR+DORIS POD (2016/02/17 – 2016/11/21; cycles 1-28) Total stations Average RMS residuals Radial orbit Test DORIS * SLR Xover** RMS diff. DORIS SLR (mm/s) (cm) (cm) (mm) itrf2008_test 53 34 0.3868 0.938 5.324 --43 33 0.3783 0.831 5.318 itrf2014_test 3.6 dtrf2014_test 39 31 0.3764 0.828 5.324 4.9 itrf2014_aug_test 55 34 0.3870 0.873 5.320 2.8 dtrf2014_aug_test 58 31 0.3852 0.883 5.319 3.1 dpod2014_test 58 34 0.3852 0.863 5.317 2.6 * SAA DORIS stations down-weighted ** independent altimeter GDRT data cycles 1-19 Table 4.7 DORIS Jason-3 stations missing in DTRF2014 and contained in DPOD2014 Year DTRF2014 Augmented 19 missing stations GR4B SOEB SYQB MAUB 2016 39 58 OWEC ROWC ADHC KEUC

GONC WEUC JIWC PDOC SAPC KEVC MNAC OWFC KIVC PAUB LAOB Table 4.8 Summary itrf2008_test-Tested solution crossover variance differences (mm2) Test TRF Mean Median Stnd. Dev. Confidence TOPEX/Poseidon (1992/09/25 – 2002/01/15) itrf2014_test -0.79 -1.09 9.26 93 % dtrf2014_test 2.58 2.10 21.66 98 % dpod2014_test 0.47 -1.15 20.47 66 % itrf2014_aug_test -0.19 -1.06 7.77 66 % jtrf2014_test 0.72 0.54 13.4 83 % Jason-1 (2002/01/15 – 2008/07/12) itrf2014_test 2.53 2.23 9.37 99.9% dtrf2014_test 0.91 0.00 12.85 96 % dpod2014_test 0.68 0.00 10.51 91 % itrf2014_aug_test 2.54 2.23 9.37 99.9% jtrf2014_test 4.68 4.05 14.09 99.9% Jason-2 (2008/07/12 – 2015/02/15) itrf2014_test 4.36 2.14 13.92 99.9% dtrf2014_test 5.22 2.21 17.30 99.9% dpod2014_test 4.20 2.63 16.18 99.9% itrf2014_aug_test 4.04 2.11 14.99 99.9% jtrf2014_test 4.27 2.15 16.63 99.9% Jason-3 (2016/02/17 – 2016/11/21) itrf2014_test 6.87 8.29 34.22 83 % dtrf2014_test 0.35 -2.73 37.19 52 % dpod2014_test 8.17 2.71 20.70 97 % itrf2014_aug_test 4.40 -1.52 21.12 84 % dtrf2014_aug_test 6.36 -1.65 26.13 87 % Table 4.9 Jason-2 DORIS/SLR/Crossover residuals using external orbits and the itrf2008_test complement; July 2008 – September 2016 (cycles 1-297) DORIS SLR Crossovers Orbit (mm/s) (cm) (cm) GSFC std1504 (SLR+DORIS) 0.3822 0.995 5.325 CNES gdre (GPS+DORIS) 0.3819 1.193 5.243 JPL jpl16a (GPS) 0.3630 1.167 5.235 Table 4.10 Summary Jason-3 DORIS / SLR residuals using jpl16a orbit for 39 DORIS / 28 SLR matching stations;

February 2016 – August 2016 (cycles 1-20) Test DORIS Complements (mm/s) itrf2008_test 0.4137 itrf2014_test 0.4113 dtrf2014_test 0.4116 dpod2014_test 0.4116 Note. All stations have uniform weighting

SLR (cm) 1.499 1.318 1.335 ----

Table 4.11 Summary Jason-2 DORIS / SLR residuals using jpl14a orbit for 77 DORIS / 37 SLR matching stations; July 2008 – August 2015 (cycles 1-243) Test DORIS SLR Complements (mm/s) (cm) itrf2008_test 0.3647 1.403 itrf2014_test 0.3630 1.312 dtrf2014_test 0.3632 1.323 jtrf2014_test 0.3632 1.332 dpod2014_test 0.3627 ----Note. All stations have uniform weighting Table 4.12 Summary Jason-1 SLR, DORIS residuals using jpl11a orbit for 76 DORIS / 40 SLR matching stations; April 2002 – May 2006 (cycles 9-161) Test DORIS SLR Complements (mm/s) (cm) itrf2008_test 0.4067 1.457 itrf2014_test 0.4064 1.485 dtrf2014_test 0.4061 1.497 jtrf2014_test 0.4065 1.470 dpod2014_test 0.4067 ----Note. All stations have uniform weighting Table 4.13a Summary Jason-1 SLR, DORIS residuals using jpl11a orbit for 8 DORIS / 8 SLR stations with active PSD modeling; April 2002 – May 2006 (cycles 9-161) Test DORIS SLR DORIS PSD stations Complements (mm/s) (cm) ADEB AREB FAIB GOMB itrf2008_test 0.4067 1.457 REYB REZB SAKA SAKB itrf2014_test (PSD) 0.4064 1.485 SLR PSD stations dtrf2014_test 0.4061 1.497 MNPE7110 BEIJ7249 jtrf2014_test (non-linear) 0.4065 1.470 CRL_7308 GMSL7358 dpod2014_test 0.4067 ----- AREL7403 CONC7405 SHAN7821 SHO_7838 Note. All stations have uniform weighting

Table 4.13b Summary Jason-2 SLR, DORIS residuals using jpl14a orbit for 7 DORIS / 10 SLR stations with active PSD modeling; July 2008 – August 2015 (cycles 1-243) Test DORIS SLR DORIS PSD stations Complements (mm/s) (cm) ADFB ADGB ARFB FAIB itrf2008_test 0.3819 1.915 REZB SAKB SANB itrf2014_test (PSD) 0.3779 1.703 SLR PSD stations dtrf2014_test 0.3781 1.702 MNPE7110 CHAC7237 jtrf2014_test (non-linear) 0.3780 1.738 BEIJ7249 CRL_7308 dpod2014_test 0.3773 ----- KOGA7328 GMSL7358 AREQ7403 CONC7405 Note. All stations have uniform weighting SHAN7821 SHO_7838 Table 4.13c Summary Jason-3 SLR, DORIS residuals using jpl16a orbit for 2 DORIS / 6 SLR stations with active PSD modeling; February 2016 – August 2016 (cycles 1-20) Test DORIS SLR DORIS PSD stations Complements (mm/s) (cm) ARFB REZB itrf2008_test 0.4649 1.525 itrf2014_test (PSD) 0.4624 0.921 SLR PSD stations dtrf2014_test 0.4610 0.886 MNPE7110 CHAC7237 dpod2014_test 0.4631 ----- BEIJ7249 AREQ7403 Note. All stations have uniform weighting SHAN7821 SHO_7838 Table 4.14 Impact CM modeling on Jason-2 orbit centering Dominant annual orbit signal Amplitude (mm) Phase (deg) Center-of-Mass Model X Y Z X Y Z 0) jtrf2014_test * 0.5 0.9 1.7 22 151 47 1) CM (Ries 2013) 0.6 0.8 4.2 28 168 67 2) CM (ITRF2014) 0.7 0.8 4.5 23 164 66 3) CM (GSFC test1; 2008-2011) 1.0 1.1 5.1 32 189 55 4) CM+APL (GSFC test2; 2008-2011) w APL 0.9 1.0 4.7 26 180 48 --0.2 1.3 --- 92 98 5) APL only * Note. JTRF2014 also impacts orbit with a strong semi-annual signal of amplitudes 0.3, 0.2, 1.0 mm in XYZ, which are about 160° out of phase with the annual signal. Table 5.1 IGN ITRF Helmert translation rates (mm/year) ITRF transform * TX TY TZ ITRF2005 -> ITRF2000 -0.2 0.1 -1.8 ITRF2008 -> ITRF2005 0.3 0.0 0.0

ITRF2014 -> ITRF2008 0.0 0.0 -0.1 * http://itrf.ign.fr/trans_para.php Table 5.2 ITRF Helmert transform rates (mm/year) ITRF2014 -> ITRF2008 TX TY TZ Scale IGN (fixed network, 0.0 ± 0.2 0.0 ± 0.1 -0.1 ± 0.1 0.2 ± 0.1 4 technologies) DORIS Jason-2 arc -0.17 ± 0.007 0.29 ± 0.004 -0.23 ± 0.003 -0.26 ± 0.007 network time series Table 5.3 Radial orbit difference rates over water : itrf2008_test – Test Orbit drift Stability Test TOPEX Jason-1 Jason-2 Combined Scatter Orbit (cycles 1-343) (cycles 1-239) (cycles 1-303) (TP-J2) residuals (mm/yr) (mm/yr) (mm/yr) (mm/yr) (mm) itrf2014 0.02 0.04 -0.02 0.03 0.17 itrf2014_aug 0.02 0.04 0.02 0.04 0.15 dpod2014 0.01 0.03 -0.07 0.01 0.18 drtf2014 0.10 0.00 -0.15 0.03 0.37 jtrf2014 -0.11 0.07 0.01* 0.02 0.55 * jtrf2014 Jason-2 test orbit cycles 1-243 Table 5.4 Radial orbit difference rates over water : TRF2014 drift Stability TRF2014 test TOPEX Jason-1 Jason-2 Combined orbit differences (cycles 1-343) (cycles 1-239) (cycles 1-303) (TP-J2) (mm/yr) (mm/yr) (mm/yr) (mm/yr) jtrf2014 - itrf2014 0.14 -0.03 -0.04 0.01 jtrf2014 - dpod2014 0.12 -0.04 -0.10 -0.01 jtrf2014 - drtf2014 0.22 -0.07 -0.17 0.02 dtrf2014 - itrf2014 -0.08 0.04 0.13 0.00 dtrf2014 - dpod2014 -0.09 0.03 0.09 -0.02 itrf2014 - dpod2014 -0.01 -0.01 -0.05 -0.02 * jtrf2014 Jason-2 test orbit cycles 1-243 Table 5.5 SLR+DORIS radial orbit stability over water Stability type stability ITRF2008-TRF2014 radial drift 0.04 mm/yr (worst case across TP-J1-J2) TRF2014 realizations radial drift 0.02 mm/yr (worst case across TP-J1-J2) radial sensitivity to TP 0.9 mm

1-cm DORIS station error

J1 J2

0.8 mm 0.5 mm