Interannual to decadal sea level trends are indicators of climate variability
and change. A major source of global and regional sea level data is satellite
radar altimetry, which relies on precise knowledge of the satellite's orbit.
Here, we assess the error budget of the radial orbit component for the
TOPEX/Poseidon mission for the period 1993 to 2004 from a set of different
orbit solutions. The errors for seasonal, interannual (5-year), and decadal
periods are estimated on global and regional scales based on radial orbit
differences from three state-of-the-art orbit solutions provided by different
research teams: the German Research Centre for Geosciences (GFZ), the Groupe de
Recherche de Géodésie Spatiale (GRGS), and the Goddard Space Flight Center
(GSFC). The global mean sea level error related
to orbit uncertainties is of the order of 1 mm (8 % of the global mean sea
level variability) with negligible contributions on the annual and decadal
timescales. In contrast, the orbit-related error of the interannual trend is
0.1 mm yr

Sea level is an important indicator of climate variability and change. Based
on tide gauge data using different techniques, the global mean sea level
rise for the last century is estimated to be 1.2–1.9 mm yr

Couhert et al. (2015) investigated the main contributions to the radial
orbit error budget for the Jason-1 and Jason-2 series based on Geophysical
Data Records (GDR)-D at seasonal to decadal timescales for the second
altimetry decade (2002–2013). According to their analysis, the orbit-related
uncertainty of the global mean interannual and decadal trends is less than
0.1 mm yr

We assess the error budget of the radial orbit component for the TOPEX/Poseidon mission for the period 1993 to 2004 from a set of different orbit models. We have chosen TOPEX/Poseidon, since it is the reference altimetry mission used in the European Space Agency's (ESA) Climate Change Initiative (CCI) Sea Level project over this time span (Ablain et al., 2016). We assess the radial orbit error budget at regional and global scales at seasonal, interannual, and decadal timescales by the analysis of three state-of-the-art orbit solutions derived and provided by different research teams from the German Research Centre for Geosciences (GFZ), the Groupe de Recherche de Géodésie Spatiale (GRGS), and the Goddard Space Flight Center (GSFC). Note that our assessment necessarily excludes contributions from errors common to these three orbits. However, since the three orbits were derived using various up-to-date models, the errors common to the three orbits should be rather low, which makes us confident that our error estimates represent most of the error. In our further analyses, we use test orbits calculated at GFZ to investigate the impact of uncertainties of the tracking station subnetworks, of the reference frame, and of the Earth's time-variable gravity field models on the radial orbit component and hence the derived sea level.

A detailed description and assessment of the analysed orbits as well as specifications of the altimeter data processing are given in Sect. 2. Section 3.1 describes the methods implemented to assess the orbit errors for the different timescales and the corresponding results for global and regional scales. The estimates of the orbit-related error for global mean and regional sea level are given in Sect. 3.2 and 3.3, respectively. The specific orbit-related errors for ascending and descending passes are investigated in Sect. 3.4. In Sect. 3.5, we examine for which areas the orbit error reaches more than 10 % of the corresponding sea level variability. The main findings are summarized and discussed in Sect. 4.

The main models used for calculation of GFZ VER11, GSFC std1504, and GRGS orbits.

Note:

Our aim is to assess the range and the characteristics of radial orbit errors on regional and global scales. Therefore, the differences between three independent state-of-the-art orbit solutions available for the TOPEX/Poseidon mission are analysed. All orbit solutions are derived in the International Terrestrial Reference Frame (ITRF) 2008 (Altamimi et al., 2011) and use satellite laser ranging (SLR) and Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) tracking data but are based on different software and on distinct models. The actual multi-mission GFZ orbit solution VER11 (Rudenko et al., 2017) is used as a reference in this paper and is called REF hereafter. The GSFC std1504 orbit (Lemoine et al., 2010; Beckley et al., 2015) has been chosen by the ESA CCI Sea Level Phase 2 project and differs in many aspects from the GFZ orbit, regarding software as well as the suite of implemented models including another Earth's gravity field model. As the third model, we have chosen the GRGS orbit solution (Soudarin et al., 2016), which is derived using models similar to those of the GFZ solution but employs another software package. The main models used for GFZ REF, GRGS, and GSFC std1504 orbits are described in Table 1. The main differences in these three orbit solutions are related to the choice of the Earth's time-variable gravity (TVG) field models, ocean tide model, modelling of non-tidal atmospheric and oceanic gravity, and the treatment of geocentre variations in station displacements, as well as the constraints of the observation data (SLR/DORIS). While for the GRGS solution comparatively high weight is on the SLR data, for the GFZ solution there is higher weight on the DORIS data. Proper modelling of the Earth's gravity field, in particular of its time-variable part, is crucial for the computation of precise orbits of altimetry satellites and has been shown to contribute to errors in regional sea level trends and seasonal signals (Rudenko et al., 2014; Esselborn et al., 2015). For the pre-GRACE (Gravity Recovery and Climate Experiment) period, the TVG field is poorly constrained. The weekly TVG solutions used for the GSFC orbit were derived up to degree and order 5 from the analysis of SLR and DORIS observations to 20 geodetic satellites starting from 1993 (Lemoine et al., 2016). The TVG part used for the GFZ REF (GRGS) orbits consists of the combination of yearly coefficients, drift terms, and annual and semi-annual variations for degrees and orders 1 to 80 (2 to 50) derived from GRACE data and SLR measurements to the Laser Geodynamic Satellite (LAGEOS)-1/2. The annual and semi-annual coefficients used for the GFZ REF orbit are fitted yearly starting from August 2002. For the pre-GRACE period before August 2002 (January 2003), only the degree-2 terms exhibit yearly values and drift terms; however, the annual and semi-annual variations, which were derived for the GRACE period, are applied for degrees and orders 1–80 (2–50) (Rudenko et al., 2014, Förste et al., 2016).

The approach adopted for the estimation of the radial orbit errors
implies that errors common to all three orbits cannot be detected. In
particular, all three orbits rely on the ITRF2008 reference frame and
basically the same set of tracking stations. To further estimate the
orbit-related radial orbit error budget due to the most significant factors, we
have derived five test orbits based on the GFZ REF orbit. The errors related
to inconsistencies of the tracking data networks are tested by using only
one tracking network instead of two. Since the GRGS orbit was derived
without estimation of the DORIS system time bias, we have studied the impact
of this bias on the radial orbit differences with special focus on
systematic differences between ascending and descending passes. The effect
of errors in the realization of the terrestrial reference frame is tested by
the implementation of the most recent ITRF2014 version. The effects of
uncertainties in Earth's TVG field models are tested by the implementation
of the EIGEN-6S2 model which is the predecessor of the EIGEN-6S4 model. For
each case, the same background models and estimated parameters were used as
for the REF orbit, except for those that represent the changes for the
specific test case. The five test orbits and the differences with respect to
the GFZ REF orbit are

SLR orbit: derived by using SLR tracking observations only;

DORIS orbit: computed by using DORIS tracking observations only;

TBias orbit: calculated without estimation of the DORIS system time bias;

ITRF14 orbit: calculated by using the information on station positions and velocities from ITRF2014 (Altamimi et al., 2016) instead of ITRF2008; and

Geoid orbit: obtained by using the EIGEN-6S2 (Rudenko et al., 2014), Earth's gravity field model, instead of the EIGEN-6S4 model (Förste et al., 2016). Note that the Geoid orbit is based on the same gravity field model as the GRGS orbit.

In order to assess the orbit accuracy at crossover points and to relate the
estimated errors to the total variability of the sea level data, along-track
TOPEX Sea Level v1.1 Essential Climate Variable (ECV) data (Ablain et al., 2015) released from the ESA
CCI Sea Level project have been included in the analyses. The along-track
data have been corrected for all instrumental and geophysical effects by the
state-of-the-art models provided with the data. However, for some
corrections, updated models were applied. These include EOT11a ocean tides
and loading tides (Savcenko and Bosch, 2012), solid Earth tides following
the International Earth Rotation and Reference Systems Service (IERS) 2003 Conventions, and updated GPD

Average values of SLR and DORIS root mean square (rms) fits; radial, cross-track, and along-track 2-day arc overlaps; and the number of the arcs used to compute these values for the reference and five test orbits.

In the following, the performance of the analysed orbits is evaluated. For the GFZ orbit solutions, the consistency with tracking data and at arc overlaps is assessed. Table 2 provides the main results of precise orbit determination of the GFZ reference and test orbits, namely, the average values of SLR and DORIS root mean square (rms) fits; radial, cross-track, and along-track 2-day arc overlaps, illustrating the internal orbit consistency in these directions; and the number of the arcs used to compute these values for the reference and five test orbits. When using the same observation types and weighting, smaller values of arc overlaps and observation fits indicate improved orbit quality. Reduced radial arc overlaps characterize reduced radial orbit error. SLR observations were used at all 494 orbital arcs of five GFZ orbits, except for the DORIS orbit for which no SLR observations were used at all. Since DORIS data are available for TOPEX/Poseidon only until 31 October 2004, these data were used at 459 orbital arcs preceding this date, except for the SLR orbit for which no DORIS observations were used at all. All orbital arcs for GFZ orbits are manoeuvre free. Thus, 2-day arc overlaps were computed for 433 overlaps for the REF, TBias, ITRF14, and Geoid orbits. In the case of the SLR and DORIS orbits, a few gaps in the observations caused radial arc overlap larger than 0.5 m. Those arc overlaps have been excluded from the statistics resulting in fewer arc overlaps shown for these orbits in Table 2.

Figure 1 provides information on the SLR rms fit of the reference and tests
orbits, while Fig. 2 displays the radial arc overlap of two consecutive
2-day orbit arcs. The four orbits derived using SLR and DORIS observations
provide comparable levels of average SLR rms fits (1.96–1.99 cm; Fig. 1).
The smallest SLR rms fit (1.59 cm) but largest radial arc overlap (1.72 cm)
are obtained for the SLR-only orbit, indicating a weak orbit quality over
large geographical areas. The largest SLR rms fit is obtained for the TBias
orbit. When no DORIS system time bias is estimated, inconsistencies between
the timing of the observation system result in higher misfits. Among the
five orbits derived using DORIS observations, a slightly increased average
value of the DORIS rms fits (0.04795 cm s

SLR rms fits of TOPEX/Poseidon REF, SLR, TBias, ITRF14, and Geoid orbits.

The DORIS system time bias is regularly estimated and applied during GFZ's
POD process to adjust the DORIS time system to the SLR time system. Zelensky
et al. (2006) showed that there is a strong linear relationship between
along-track orbit position and the DORIS time bias. The comparison of the
fits and overlap values of the REF and the TBias orbits (Table 2) shows that
the estimation of the DORIS time bias improves the orbit quality. The
temporal behaviour of the DORIS system time bias derived for the TOPEX/Poseidon
REF, ITRF14, and Geoid test orbits is in close agreement (Fig. A1) and
resembles the estimation given by Lemoine et al. (2016). For the GFZ VER11
(REF) orbit, it indicates variations between

Crossover point analysis: median and rms values of global mean height differences for maximum time lapses of 5 days for all orbit solutions during the period April 1993–September 2004. The highest and lowest values of each quantity are marked in bold.

Radial arc overlaps of TOPEX/Poseidon REF, SLR, DORIS, TBias, ITRF14, and Geoid orbits.

For all orbit solutions, a crossover point analysis for the period April
1993 to September 2004 has been performed based on the altimeter data
described in Sect. 2.2. Differences between the values of ascending and
descending passes at crossover points are caused by oceanic variability and
errors related to the measurements, the orbit, and the applied corrections.
Since in our study errors related to the measurements and the applied
corrections and oceanic variability are always identical, here, smaller
absolute median differences and decreased rms values at crossover points are
indicative of increased orbit quality. The median of the time series of
global mean height differences and rms values at the crossover points are
provided in Table 3. The smallest ascending/descending differences (

Sea level varies on typical temporal and spatial scales that are often connected to the driving processes. At the same time, orbit errors are not randomly distributed but exhibit also typical temporal and spatial patterns. Here, we apply statistical methods in order to assess the errors related to the orbit solutions for global and regional sea level at seasonal to decadal timescales.

In order to estimate the orbit-related errors in sea level height, the differences between the radial components of the GFZ REF orbit and the two independent orbit solutions (GSFC and GRGS) have been analysed. To assess the effect of uncertainties in the reference system, in the realization of the tracking station networks and in Earth's time-variable gravity on the radial error budget, we have evaluated the differences of the radial orbit components between the GFZ's REF and ITRF14, SLR, DORIS, and Geoid test orbits. Since the radial orbit components map directly to the derived sea level heights, we consider the differences presented here to represent estimates of the orbit-related sea level error. However, since the orbit error analysis is based on orbit differences, any error common to all three orbits will be lacking in our assessment.

The differences of the radial orbit components at the time of the altimetry
measurement (1 Hz,

Since we are not interested in the orbit error itself, but rather in the
effect of radial orbit errors on global and regional sea level, we treat the
radial orbit differences the same way as the sea level values from
altimetry. For the estimation of global mean errors, the gridded radial
orbit differences are averaged (with area weighting) over the ocean (

In order to relate the estimated errors to the total variability of the sea level data, TOPEX altimeter data have been included as well. The data and the processing are described in Sect. 2.2. From the gridded sea level anomalies, seasonal, interannual, and decadal trends were derived using the methods described above.

In the following, we investigate the orbit-related global sea level error, differentiating between the total error and its annual, interannual, and decadal components. The TBias orbit differences are not included in these analyses but will be further investigated for the study of changes between ascending and descending passes (Sect. 3.4). The time series of the global mean rms of gridded radial orbit differences per cycle are shown in Fig. 3 for all orbit solutions relative to GFZ's REF orbit. The largest differences occur between the REF and the GRGS orbits; the smallest changes occur for the ITRF14 test orbit. Most orbit differences are dominated by subseasonal variability; only for the Geoid and ITRF14 orbits the rms per cycle series are governed by seasonal and decadal periods. For the Geoid, GSFC, and GRGS orbit differences relative to the REF orbit, the rms series exhibit a seasonal cycle, which is an indication for seasonal orbit differences on regional scales. The rms of the REF minus Geoid orbit difference is decreased after August 2002, indicating that the main differences between the two orbits originate from the pre-GRACE period. In contrast, the differences between the REF and the ITRF14 orbits slightly increase from 2000 onwards.

Estimates of global mean orbit-related errors for the total signal, interannual, and decadal trends. Values are derived from the mean radial orbit differences over the oceans for REF minus SLR, REF minus DORIS, REF minus ITRF14, REF minus Geoid, REF minus GSFC, and REF minus GRGS for the period April 1993–June 2004. The corresponding values derived from the altimetric sea level anomalies (SLAs) are added for comparison. Details on the estimation method are given in Sect. 3.1.

Time series of the global mean rms per cycle of gridded radial orbit
differences for REF minus GSFC (dark blue) and REF minus GRGS (red,

From the time series of global mean orbit differences over the oceans, the rms,
annual cycle, 5-year trend variability, and decadal trend differences are
calculated and used as an estimate of the orbit-related error on different
timescales. These orbit errors are summarized in Table 4 for all orbit
models together with the corresponding values derived from altimetric sea
level anomalies. The global mean rms of the radial orbit differences between
the REF and GRGS (GSFC) orbits amounts to 1.2 (1.1) mm, which corresponds to
8 % of the global mean sea level variability of 13.0 mm. The restriction
to one tracking station subnetwork leads to large changes of the orbit; for
the DORIS (SLR) orbit solution, the rms values of the radial differences with
respect to the REF orbit amount to 1.8 mm (0.7 mm), which exceeds the size of
the estimated total orbit errors. This highlights the importance of
manifold, precise, and consistent tracking data for accurate global mean sea
level estimates. The substitution of the Earth's gravity field model
(EIGEN-6S4 by EIGEN-6S2) and the ITRF realization (ITRF2008 by ITRF2014)
accounts for 0.2 and 0.3 mm, respectively, of the mean rms orbit errors.
A spectral analysis of the global mean radial differences (Fig. A2) exhibits
peaks at

Estimates of regional maximum orbit-related errors for the total and seasonal signals, and interannual and decadal trends. Values are derived from the radial orbit differences for REF minus SLR, REF minus DORIS, REF minus ITRF14, REF minus Geoid, REF minus GSFC, and REF minus GRGS for the period April 1993–June 2004. Details on the estimation method are given in Sect. 3.1.

The 5-year running trends for the global mean radial orbit differences
over the oceans for REF minus GSFC (dark blue), REF minus GRGS (light blue), and GRGS minus GSFC (green,

The maximum regional errors derived from the analysis of the gridded orbit
difference series over the oceans are summarized in Table 5. The TBias orbit
differences are not included in these analyses but will be further
investigated for the study of changes between ascending and descending
passes (Sect. 3.4). Regionally, the maximum radial orbit differences on the
1

Annual amplitude of the radial orbit differences for REF minus GSFC, REF minus GRGS, GRGS minus GSFC, and REF minus Geoid. The regions with formal errors larger than the fitted value are masked out (white). The maximum amplitude difference is given in Table 5.

Annual difference signals with respect to the REF orbit are most prominent for the GSFC and GRGS solutions, while they are negligible for the SLR, DORIS, and ITRF14 orbits. The corresponding patterns of the annual amplitudes for the differences of REF versus GSFC, GRGS, and Geoid orbits and of GRGS versus GSFC orbits are shown in Fig. 5. The observed patterns for the GSFC and GRGS orbit differences consist of a dipole with centres in the south-eastern Indian Ocean and the Caribbean. Since the two centres are phase shifted by half a year, the effect on the global mean differences is marginal. The pattern coincides with the patterns already shown to be related to the use of AOD1B products (Rudenko et al., 2016a) and different time-variable gravity fields for TOPEX/Poseidon POD (Esselborn et al., 2015). However, the annual differences between the REF and Geoid orbits can only explain part of the observed differences between the REF and GRGS orbits. In addition, the annual differences between GRGS and GSFC orbits are quite small and show no distinct pattern. Another plausible source of the relatively strong signal for the GSFC and GRGS orbit cases is the differences in the annual corrections for station coordinates by geocentre motion corrections and non-tidal atmospheric loading. A careful consideration of the relevant models used for the POD of these three orbits suggests that the observed differences originate in part from the non-tidal atmospheric loading effect on the stations which was applied for the GFZ but not the GRGS and GSFC orbits. There is evidence that the annual signal from the EIGEN-6S2 gravity field model is closer to the gravity field solution applied for the GSFC orbits than to the one from EIGEN-6S4 – at least in the pre-GRACE period (Fig. 5).

The rms of 5-year running trend differences of the radial orbit components for REF minus GSFC, REF minus GRGS, REF minus SLR, REF minus DORIS, REF minus ITRF14, and REF minus Geoid for the period April 1993–June 2004. The global mean rms of the differences over the ocean is given in Table 4.

The patterns of the interannual variability of the regional trends are shown
in Fig. 6 for all orbit differences. The trend errors reach up to 1.2 (0.9) mm yr

Decadal trend differences of radial orbit components for REF minus GSFC, REF minus GRGS, REF minus SLR, REF minus DORIS, REF minus ITRF14, and REF minus Geoid for the period April 1993–June 2004. Regions with formal errors larger than the fitted value are masked out (white). The global mean trend difference over the ocean is given in Table 4.

The strongest regional changes in the decadal trend (Fig. 7 and Table 5) are
observed for the differences between the REF and GSFC orbits (up to
1.0 mm yr

The crossover point analysis (Table 3) reveals considerable global mean differences between ascending and descending passes for most orbits. Fu and Haines (2013) showed that orbit errors might induce diverging drifts for sea level derived from ascending and descending passes. In the following, we study whether there are systematic changes to the results obtained so far when ascending and descending passes are investigated separately. Therefore, for a subset of orbit solutions, the same analyses were performed as before but for data sets derived from ascending and descending passes only. Since the DORIS orbit reveals the most pronounced median ascending/descending differences, we have chosen to study the REF minus DORIS and the REF minus TBias orbit differences further. During the POD of the GRGS orbit, the DORIS system time bias has not been estimated; therefore, we include the GRGS orbit in the analysis as well. However, in contrast to the previous analysis, we study the difference of Geoid minus GRGS instead of REF minus GRGS in order to exclude the effects of different time-variable gravity fields from the analysis.

Differences of interannual trend variability and decadal trend for merged, ascending, and descending passes related to the orbit solution. Values are derived from the mean radial orbit differences over the oceans for Geoid minus GRGS, REF minus DORIS, and REF minus TBias for the period April 1993–June 2004. Values for ascending and descending passes are given in brackets.

The global mean radial orbit differences for ascending and descending passes
are for all three cases in the range of

Decadal trend differences of radial orbit components for
ascending

The regional patterns of the decadal trend differences for ascending and
descending passes are shown in Fig. 8. The DORIS orbit differences reveal a
striking spread between the decadal trends of the ascending and descending
passes. The trends are opposite for ascending and descending passes for most
areas of the global ocean and reach regionally absolute values of up to
0.8 mm yr

The rms of sea level, annual amplitude, rms of interannual (5-year) running trend, and decadal trends from TOPEX altimeter data for the period February 1993–October 2005. Colour coded are sea level values for which the local orbit errors (estimated from GFZ minus GRGS) reach more than 10 % of the local sea level values. All other regions are masked out (white).

Our analysis exhibits large-scale patterns of the orbit-related error.
Errors for interannual to decadal sea level trends of more than 1 mm yr

We have investigated the radial orbit error budget associated with three state-of-the-art orbit solutions from GFZ, GSFC, and GRGS over the first altimetry decade (1993–2004). It is crucial to know the accuracy of these early altimeter data in order to judge the reliability of long-term sea level trends and of estimates of the acceleration of global mean sea level rise. For this purpose, we have chosen the TOPEX/Poseidon mission, since it is the reference altimetry mission used in the ESA CCI Sea Level project over this time span. We estimate the orbit errors from the radial orbit differences which implies that errors common to all orbits cannot be detected. However, since the three orbits were derived using various up-to-date models, the errors common to the three orbits should be rather low, which makes us confident that our error estimates represent most of the error. A set of five test orbit solutions derived at GFZ is used to estimate the contributions of the most significant factors to the error budget. We have focused on the impact of uncertainties of the tracking station subnetworks (SLR and DORIS), of the DORIS system time bias, of the reference frame, and of the Earth's time-variable gravity field models on the radial orbit component and hence the derived sea level. The estimates of the radial orbit errors at seasonal, interannual (5-year), and decadal timescales are given in Table 4 for the global mean sea level and in Table 5 for the regional sea level.

According to our study, the contribution of orbit uncertainties to the error
of the global mean sea level during the TOPEX period are of the order of 1.2 mm, which corresponds to 8 % of the variability of the global mean sea
level (13 mm). The global mean annual (seasonal) component of the radial
error is well below 1 mm and can be neglected. The orbit-related errors of
the decadal trends are up to 0.08 mm yr

For regional scales, the maximum rms of the gridded radial orbit error is
11 mm. This error is indicative of the orbit-related sea level error on the
1

When using ascending and descending passes separately, the interannual and decadal trend errors can reach multiples of the values derived from the merged data. This is the case for global mean values as well as for regional values. The corresponding large-scale pattern is coherent for low and medium latitudes and is strongly anti-correlated for ascending and descending passes. Even though such effects tend to cancel, whenever both components are merged, they might still introduce considerable errors in regional studies, that are based on along-track data, e.g. at calibration sites.

Orbit errors related to discrepancies between the tracking station
subnetworks (distribution of tracking stations, observation sampling, etc.)
are studied based on GFZ's SLR, DORIS, and TBias orbit solutions. Using SLR
and DORIS observations for TOPEX POD together reduces (improves) the rms of
the altimetry single-satellite crossover differences considerably (2–3 %),
though the DORIS observations seem to aggravate the median differences
between ascending and descending passes. The proper estimation of the DORIS
system time bias has proven to be a critical factor for the minimization of
this effect. The most significant changes are observed for the DORIS orbit
solution, suggesting that uncertainties of the SLR station subnetwork should
have the most prominent effects on the orbit accuracy – at least for GFZ's
orbit solutions. This fact is, most probably, related to the weighting
factors applied to the observations within the GFZ orbit determination
process. Using the latest reference frame (ITRF2014) instead of the
predecessor (ITRF2008) slightly improves the accuracy of the TOPEX/Poseidon
orbit solution. The contribution of the uncertainties in the ITRF
realization to the regional upper bound error is only marginal. Errors
induced by uncertainties of the Earth's time-variable gravity field model
are studied on the base of GFZ's Geoid orbit solution. The orbit evaluations
show that the Geoid orbit performs slightly better than the REF orbit in the
pre-GRACE period due to differences in the periodic annual and semi-annual
variations applied to the TVG field models. Uncertainties of the gravity
field model give rise to orbit errors at all analysed periods. We estimate
regional upper bound errors of

The regional upper bound radial orbit errors obtained from our study are by factors of 2 to 5 smaller than the ones reported by Couhert et al. (2015) for the period 2002 to 2012. This might partly reflect recent improvements of the stability of reference frames which results in smaller changes from ITRF2008 to ITRF2014 than previously from ITRF2005 to ITRF2008. However, the accuracy of the Earth's time-variable gravity model and the tracking observations for the 1990s should be inferior to more recent periods. The error related to the uncertainties of the tracking station subnetworks might be underrated in our study since all analysed orbits rely on basically the same set of tracking observations. The effect of uncertainties of the TVG field might be underestimated as well, since both EIGEN-6S4 and EIGEN-6S2 model the TVG field in the pre-GRACE period by periodic annual and semi-annual variations derived from GRACE plus annual values and drift terms for degree-2 terms derived from SLR measurements. In contrast, the TVG field used for the GSFC orbit determination is changing weekly. Using SLR measurements of geodetic cannon-ball satellites (Sośnica et al., 2015; Bloßfeld et al., 2016) and in combination with DORIS measurements of altimetry and remote sensing satellites (Lemoine et al., 2016) allows to determine Earth's time-variable gravity for the period 1993–2003, i.e. before GRACE, more precisely than just using SLR measurements of LAGEOS-1/2. Combined use of GRACE measurements with SLR and DORIS measurements of numerous geodetic satellites should further improve Earth's time-variable gravity field models, especially for the period 1990–2003. This will further enhance orbit solutions for the European Remote Sensing (ERS) and the TOPEX/Poseidon altimetry missions.

The GFZ VER11 orbits (Rudenko et al., 2016b) can be accessed at GFZ Data Services via

We are grateful for the insightful comments of the reviewers Nikita Zelensky
and John Huthnance which helped to improve the manuscript substantially. We thank
Goddard Space Flight Center and Groupe de Recherche de Géodésie Spatiale for
providing GSFC std1504 and GRGS orbit solutions, ESA CCI for along-track
TOPEX Sea Level v1.1 ECV data, and Joana Fernandes for providing updated wet
troposphere corrections (GPD