Validation and estimation of MSL altimetry errors

When calculating and analysing the evolution of mean Sea level, (MSL) the question legitimately arises as to whether altimeters are reliable enough to measure a rise in MSL of a few millimetres per year over a period of almost 20 years. The question is even more crucial in that there are potentially a lot of possible sources of errors for long-term stability. These are mainly related to the ageing of instruments and uncertainty as to their calibration, to the impact of events which affect the satellite's lifetime (satellite manoeuvres, incidents on the platform or affecting instruments, etc), to orbit determination calculations and to all the corrections computed by models for calculating the SSH (tides, weather, ionosphere, etc).

Error budget estimated from all the individual corrections

GMSL trend uncertainties 

Based on an assessment of all sources of errors affecting the altimetric system (Ablain et al. 2017), the GMSL trend uncertainty (90% confidence level) is estimated at ~0.4 mm/yr over the whole altimetry era (1993-2017). The main source of error is the wet tropospheric correction with a drift uncertainty in the order of 0.2 mm/yr (Legeais et al. 2018) over a 10-year period. To a lesser extent, the orbit error (Couhert et al. 2015; Escudier et al., 2017) and the instability of the altimeter parameters (range, sigma-0, significant wave height/SWH) (Ablain et al., 2012) also contribute to the GMSL trend uncertainty, at the order of 0.1 mm/yr. Furthermore, imperfect links between successive altimetry missions lead to an additional trend uncertainty of about 0.15 mm/yr over the 1993-2017 period (Zawadzki and Ablain, 2016).

Taking into account the temporal correlation of each source of error and their evolution in time (e.g. see next section describing larger errors on the first decade 1993-2002 of the altimetry record), (Ablain et al., 2018) allows estimating the GMSL trend uncertainty (within a 90% confidence interval) for any altimeter periods between 1993 and 2017 (see figure below).

GMSL trend uncertainties (mm/yr) estimated for any altimeter periods between 1993 and 2017. The confidence level is 90 % (1.65-sigma). On the Y-axis is represented the length of the window (in years) and on the X-axis the central date of the window used (in years).

Focus on TOPEX-A instrumental drift and its impact on the GMSL curve

The GMSL uncertainty is significantly larger during the first decade (1993-2002) of the record, due to larger errors affecting the T/P sea level measurements on climatic time scales, compared to subsequent missions. For instance, the T/P orbit solutions are more uncertain due to lower precision of the gravity field solutions estimated without GRACE data. Furthermore, the switch from TOPEX-A to TOPEX-B in February 1999 leads to a 3 mm bias uncertainty in the GMSL time series (Escudier et al., 2017). 

However, the most significant error affecting the first 6 years (January-1993 to February 1999) of the T/P GMSL measurements comes from an instrumental drift of TOPEX-A altimeter. This effect on the GMSL time series was recently highlighted via comparisons with tide gauges (Valladeau et al. 2012; Watson et al. 2015; Chen et al. 2017; Ablain et al. 2017), via a sea level budget approach (i.e., comparison with the sum of mass and steric components; Dieng et al., 2017) and via comparisons to Poseidon-1 measurements (Zawadzki, personal communication). In a recent study, Beckley et al. (2017) suggested that the corresponding error on the GMSL during the 1993-1998 time-span, results from incorrect onboard calibration parameters. 

All three approaches conclude that during the period January 1993 to February 1999, the altimetry-based GMSL slope was overestimated by ~1.5 mm/yr, with an uncertainty in the range of 0.5 to 1.0 mm/yr (Watson et al. 2015; Chen et al. 2017; Dieng et al. 2017). Beckley et al. (2017) proposed to not apply the suspicious onboard calibration correction on TOPEX-A measurements. The latter approach is similar to apply the TOPEX-A drift correction estimated by Dieng et al. (2017) and Ablain et al. (2017b). In the latter study, accurate comparisons between TOPEX A-based GMSL and tide gauge measurements lead to a drift correction of about -1.0 mm/yr between January 1993 and July 1995, and +3.0 mm/yr between August 1995 and February 1999, with an uncertainty of 1.0 mm/yr (68% confidence level). 

Evolution of the ensemble mean GMSL time series (average of the 6 GMSL products from AVISO/CNES, SL_cci/ESA, University of Colorado, CSIRO, NASA/GSFC, and NOAA). On the black, red and green curves, the TOPEX-A drift correction is applied, using the correction proposed respectively by Ablain et al.(2017b), Watson et al. (2015), Dieng et al. (2017) and Beckley at al. (2017). On the figure, the annual signal is removed, and a 6-month smoothing is applied; The GIA correction is also applied. Uncertainties (90% confidence interval) of correlated errors over a 1-year period are superimposed for each individual measurement (shaded area).

Comparison with in-situ measurements

Another approach for describing the GMSL error consists in comparing the sea level data with in situ data such as tide gauges or ARGO data (temperature and salinity profiles) (Ablain et al., 2009 (a), (b)). The stability of the altimetry system can thus be assessed by detecting drifts or leaps in the GMSL (SALP annual GMSL report 2017).

Comparison to tide gauges

The method to compare altimeter and tide gauges data (noted Alti-TG hereafter) is based on the main following steps: 

- The along-track altimeter data are averaged on 360x180 global grids (1°x1° cells). One grid is computed per mission cycle, except for comparisons to the PSMSL tide gauge network, where monthly grids are used.

- In a 300 km radius around each tide gauge, the best correlated grid element is chosen and a GMSL difference time series (Altimeter GMSL - Tide gauge GMSL) is computed.

- A mean global Alti-TG time series is computed from Alti-TG time series. The trend difference is computed from this global time series, which represents the estimated altimeter GMSL drift.

- Vertical Land Motion (VLM) correction: each trend difference is corrected for Glaciar Isostatic Ajustment (GIA) induced VLM, using Pr. Peltier’s ICE-5G(VM2) model (see Peltier 2004). Due to insufficient GPS data at the tide gauge locations over the whole GLOSS-CLIVAR or PSMSL networks, no correction is applied for the other VLM contributions.

The altimeter GMSL drift is estimated within a confidence level depending on different source of errors: vertical land motion at the tide gauges, high-frequency noise from altimeter and tide gauge data, collocation errors from both datasets, and the global alti-TG averaging scheme. Describing the temporal correlation of these errors and their evolution with time allows to provide the uncertainty of the GMSL altimeter drift over the entire altimetry period. It is estimated to 0.4 mm/yr between 1993 and 2017 at 90% confidence level (Ablain et al., 2018). Furthermore, the uncertainties have been also provided for any altimeter periods between 1993 and 2017 (see figure below).

Altimeter GMSL drift uncertainties (mm/yr) estimated from alti-TG comparison using the GLOSS/CLIVAR tide gauge network for any altimeter periods between 1993 and 2017. The confidence level is 90 % (1.65-sigma). On the Y-axis is represented the length of the window (in years) and on the X-axis the central date of the window used (in years).

The GMSL drifts and associated uncertainties (at the 90% confidence level), based on comparisons with GLOSS-CLIVAR and PSMSL data, are shown for each altimeter on the figure below. For most missions, no significant drift can be detected. Most notably, the drift for the reference GMSL time series provided on the AVISO website is estimated between -0.35 mm/yr and +0.45 mm/yr at the 90% confidence level, thus is not considered as significant.

It is worth noting that a significant drift is detected on the TOPEX-A –based GMSL. This drift is evaluated at 1.6 +/- 1.2 mm/yr (90% confidence level) when compared to data from the GLOSS-CLIVAR tide gauge network. Such a drift is well-known by the scientific community, and several corrections have been proposed. A significant drift, of -1.3 +/- 0.8 mm/yr, is also detected in the ERS-2 GMSL time series. Data from this altimeter are not used to compute the AVISO reference GMSL (based on only TOPEX and Jason missions). The ERS-1 altimeter may have been affected by a significant drift but the uncertainty from the comparison to tide gauges for this specific mission is too high to accurately estimate a drift. This high uncertainty is due to the short duration of the mission (only 3.5 years, with many data gaps) and very high altimeter noise levels.

At the moment, the Jason-3 and Sentinel-3A records are too short for a comparison with tide gauges and the detection of a drift.

GMSL drift on each altimeter estimated by comparison to tide gauges from the GLOSS-CLIVAR and PSMSL networks
Global MSL difference between the AVISO reference missions (Topex + Jason missions) and tide gauges from the GLOSS-CLIVAR network. This is obtained by the Alti-TG comparison process described previously

Local errors in MSL slopes

With respect to local errors of MSL slopes, the same statistical approach was applied in order to describe locally the different sources of uncertainty in altimetry data [Ablain et al., 2010]. This work revealed the strong local impact of inter-annual variability since it accounts for 80% of the formal adjustment error, which demonstrates that the periods of altimetry data are still too short to estimate slopes locally. The residual errors (20%) due to errors in the altimetry system vary essentially according to latitude between 1 and 2 mm/year due to uncertainties in orbit determination and correction for the wet troposphere respectively at high latitudes and in the tropical band. In this case as well, the description of local errors should be refined to take into account in particular the impact of variable gravity fields for the orbit calculation [Cerri et al., 2010] or again uncertainty in zones close to coasts or to ice due to the degradation of the altimetry measurement.


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