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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

The performance of altimetry missions is analysed in order to determine a precise budget of long-term errors. A study undertaken at CLS and published in 2009 [Ablain et al., 2009 (a)] describes this error budget and the statistical approach used. The following table, extracted from the study, shows the main sources of error which affect the global MSL and the related uncertainty in terms of slope. The biggest uncertainty is due to the correction for the wet troposphere (+/-0.3 mm/year) for the whole period encompassed by the altimetry.
In order to calculate the total error for the MSL slope, it is possible to sum the absolute value of the errors or to calculate the quadratic sum, which gives total errors respectively of 0.9 mm/year and 0.5 mm/year. But in both cases, this error is not realistic as it does not take into account the correlation of the errors. Consequently, when estimating the MSL slope it is preferable to use an inverse method [Bretherton, 1976] whose mathematical expression can describe the covariance of the errors and deduce a realistic formal adjustment error which can then be expressed as a confidence interval. In this way, the global MSL error deduced for the T/P and Jason-1 missions between 1993 and 2008 was estimated at +/-0.6 mm/year with a confidence interval of 90%.

Sources of error in the MSL calculationError in the slope of global MSL
Orbit determination+/-0.15 mm/year
Wet troposphere+/-0.30 mm/year
Corrections from weather data fields +/-0.10 mm/year
Altimetry parameters+/-0.10 mm/year
SSH bias+/-0.25 mm/year
Total error+/-0.6 mm/year
Confidence interval= 90%

Main sources of error affecting the global MSL deduced from the Jason-1 and Topex/Poseidon missions from 1993 to 2008, as well as an estimation of the total error [Ablain et al., 2009 (a)].

Comparison with in-situ measurements

Another approach for describing the MSL error consists in comparing the data with in situ data such as tide gauges or ARGO data (temperature and salinity profiles) [Ablain et al., 2009 (a), (b) and (c)]. The stability of the altimetry system can thus be verified by detecting drifts or leaps in the MSL (see Altimetry/Tide gauges and Altimetry/Argo  annual reports).

The measurement drifts obtained with the tide gauges (see figure below) reveal very small drifts for Jason-2 (0.0 mm/year), Jason-1 (0.3 mm/year), Envisat (0.8 mm/year) and T/P (0.6 mm/year). For Envisat, some millimetric variations (before the end of 2003 or in 2005 and 2006) still raise some questions and are under investigations. Similarly, for TOPEX-A (before February 1999), inter-annual instabilities are observed, probably linked to instrumental problems between 1996 and 1999.

Evolution of differences between altimetry sea surface heights and SSHs from tide gauges for the Jason-2, Jason-1, Envisat and Topex/Poseidon missions after having applied a low-pass filter (two months).

By taking into account the uncertainty of the estimation method which is close to 0.5 mm/year, caused in particular by the crustal drift of tide gauges and the fact that they only cover the coastline zone, the global error of MSL from Topex and Jason-1 then becomes 0.7 mm/year, in other words it has the same order of magnitude as that of the error budget estimated from all the individual corrections (0.6 mm per year).

This demonstrates in two independent ways the reliability of the global MSL evolution deduced from the Topex and Jason-1 altimetry missions. Nevertheless, this budget should be refined further in order to estimate the impact of error sources which have not yet been taken into account such as the contribution of the ocean covered by ice and eventually the impact of very long ocean tide periods (18.6 years).

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., 2009 (d)]. 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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