Amazingly enough, when you look at their methods they all have one thing in common. They are all eventually modified by computer models. Huh. Imagine that. Take real data, massage it through the magic of computer modelling, and voila, you have the result you desire. But....it ain't data. It's computer derived fiction.
Methods
Altimeter Data Processing.
The altimeter data were processed following the recommendations set forth in ref. 15, including the latest orbits, tide models, sea-state bias models, water vapor corrections, etc. Following ref.
15, the “cal mode” correction to the TOPEX data was not applied, because the correction degraded comparisons to tide-gauge sea-level measurements, and because later investigation showed it should not have been applied in the first place. Not applying the cal-mode correction slightly increases the estimated sea-level acceleration. Measured GMSL was corrected for the effects of Glacial Isostatic Adjustment with a global model, which increased the GMSL rate by 0.25 mm/y (
25).
Pinatubo GMSL Contribution.
The computation of the effects of the eruption of Mount Pinatubo on GMSL using the NCAR LE of models (21) is described in ref. 12. Because this model ends in 2010, we assumed an exponential decay from 2010 to the present. This correction increases the quadratic acceleration estimate by 0.02 mm/y2. The error in this correction was estimated from the variance of the NCAR LE at 0.01 mm/y2.
Computation of the ENSO GMSL Contribution.
We removed the effects of ENSO and Pacific Decadal Oscillation (PDO)-related variations on GMSL by
computing a correction. This correction was computed via a joint cyclostationary empirical orthogonal function (CSEOF) analysis of altimeter GMSL, GRACE land water storage, and Argo-based thermosteric sea level from 2005 to present. The physical interpretation of these two modes is discussed in ref.
26, although here the understanding of the modal decomposition is extended through the inclusion of additional variables. The two leading CSEOF modes were subsequently projected onto the altimeter data from 1993 to present and averaged over the global ocean to arrive at what we refer to as a GMSL ENSO correction. Applying this correction reduced the quadratic acceleration value by 0.033 mm/y2. Based on the ENSO and PDO variability during the altimeter record, a positive acceleration is expected due both to the presences of two large El Niños at either end of the record and the recent shift from the positive to negative phase of the PDO. To allow for the possibility that this correction might have not removed all of the ENSO signal and also based on sensitivity tests of the decomposition, we carry an error estimate of 0.01 mm/y2 for this correction.
Calculation of Acceleration.
We perform a least-squares fit of a quadratic using a time epoch of 2005.0 (the midpoint of the altimeter time series), where acceleration is twice the quadratic coefficient.
All of the data were weighted equally––weighting the data based on error estimates from tide-gauge differences did not appreciably change the results.
Tide-Gauge–Based Altimeter Acceleration Error Estimate.
The altimeter sea-level measurements were differenced with individual tide-gauge sea-level measurements,
and then stacked and globally averaged to detect changes in the altimeter instrument behavior, assuming the tide-gauge measurements are perfect, following ref. 13. While there are overlaps between each of the four satellites in the time series, allowing instrumental biases to be determined and removed, there was no overlap in early 1999 when the TOPEX altimeter was switched from Side A to Side B of its electronics. As a consequence we estimated a bias here of 5.7 mm by leveling the TOPEX Side A tide-gauge differences to an average of the Jason-1–3 differences. This is a slightly different value than was found in ref.
15 (5 mm) because our analysis technique was different. Once this adjustment was made, an AR1 noise model was used to estimate the 1σ error in the quadratic acceleration coefficient of 0.011 mm/y2. This is almost certainly a conservative error estimate because it assumes the tide-gauge sea-level measurements are perfect.
Acceleration Validation.
We computed a rough validation (Table 2) of the altimeter-based acceleration estimate by comparing to other datasets, although they cover different time periods. We used the GRACE mascon data from ref.
27 and computed time series by averaging the mascons over (
i) Greenland, (
ii) Antarctica, and (
iii) mountain glaciers and small ice caps (areas updated from ref.
28).
Constraining the thermosteric contribution to sea-level acceleration is hampered by the large discrepancies and related uncertainties that exist in ocean heat content datasets (
20,
29). The root cause of these discrepancies has been attributed to errors in the raw data and mapping methods used to infill data gaps, which are particularly large in the southern oceans, but substantial progress has been made recently in dealing with these issues (
30,
31). Given the systematic biases imparted by both data errors and infilling methods, a simple averaging across available datasets is not an effective means of minimizing bias (
32). Rather, the optimization of mapping methods is likely to offer a suitable best estimate for quantifying both thermosteric contributions to acceleration and their uncertainty. Here we use the estimate provided from ref.
23. Comparison with independent data, such as the top of atmosphere (TOA) radiative balance also provides insight (
32). We find the TOA reconstruction of ref.
33 to be broadly consistent with the value of acceleration derived from ref.
23.