AR6 and Sea Level, Part 2: The complexity of measuring GMSL

By Andy May

Thomas Frederikse and colleagues published a study of sea level data, considering both tide gauges and satellite data in 2020 (Frederikse, et al., 2020). This paper is frequently cited in the Chapter 9 AR6 sea level discussion. They found that there are many causes of global and regional sea level change that need to be considered. Land over much of the Northern Hemisphere is still rebounding from the melting of the massive glaciers they supported during the Last Glacial Maximum. This causes many northern tide gauges to record sea level falling as the land rises. Further, dam construction during the twentieth century caused water to be withheld from the oceans and stored in reservoirs on land, especially between 1960 and 1980. They also tell us that previous assessments of sea level were unable to reconcile observations with the calculated contributions of ice-mass loss, dam construction, and thermal expansion of water. As mentioned in Part 1 of this series, observed sea level change is very small, so this is not surprising. Yearly changes are below the measurement accuracy of the instruments.

The observations of sea level, ocean temperature, ice-mass loss, water held in man-made reservoirs, and total river discharge to the oceans all have considerable uncertainty, which is why studies have not been able to close the gap between observations. Frederikse and colleagues make another attempt to close the gap. They note that over the past few years much more accurate estimates of all the critical observations have been made available and they collected these in a new estimate.

Their best estimate of the observed sea-level rise trend from 1900 to 2018 is 1.56 ±0.33 mm/year, an error of ±20%. In Part 1 using the NOAA sea level record we derived a slope of 1.74 mm/year, with an R2 of 0.97, this value falls within the 90% confidence limits given by Frederikse and colleagues. The observed sea level change estimate is shown in dark blue in Figure 1. The sum of sea level change components is shown in black. The two major components of sea level change are also shown for comparison. Barystatic (ocean volume, excluding thermal expansion) changes are shown in red and thermosteric (ocean volume changes due to thermal expansion) are shown in orange. All curves are centered on their 2002 to 2018 means. Due mostly to the centering period, the match in the component sum and the sea level observations looks good in the 21st century. Prior to 1990 it is not very good, but both the sum and the observations match within their respective margins of error. The observed sea level uncertainty, prior to 1990, generally exceeds ±10 mm; prior to 1960, it exceeds ±15 mm. Prior to 1940, it exceeds ±20 mm.

Figure 1. Frederikse, et al.’s estimate of sea level from 1900 to 2018 is shown in blue and compared to the sum of his estimate of barystatic and thermosteric change in black. Barystatic change is shown in red and thermosteric in orange.

The sub-components of barystatic changes examined in the paper are: glacier melting, melting of the Greenland and Antarctic Ice Sheets, and terrestrial water storage (including new dam construction and groundwater depletion). Thermosteric changes are estimated using ocean subsurface temperature measurements. Frederikse, et al. try to reconcile the component total with observed sea level changes as measured by satellite and tide gauges using a model and find modest agreement, within the respective margins of error.

The results of his study increase the previous estimates of GMSL (global mean sea level) rise in the 1960s and 1970s, after excluding the effect of dam construction. His model also increases the uncertainty prior to 1940. The match is quite poor in the 1920s and 1930s, and the steep rise in sea level from 1930 to 1950, nearly as rapid as in the 21st century, is also not matched well.

While the GMSL rate uncertainty narrows for the period 1993 to 2018, it still exceeds ±0.4 mm/year as shown in Figure 2. Both figures are a portion of Frederikse et al.’s Figure 1. Figure 2 shows the 30-year rate of change from his models of barystatic and thermosteric change in red and orange respectively, along with their sum in black. These are compared to the observed 30-year rate of change rate, in blue. Clearly the rate of sea level rise oscillates on a multidecadal scale and probably rose as fast as today in the 1940s, within the margin of error.

In Figure 2, the shaded regions are the 90% confidence intervals. The graph plots the rate of sea level rise in mm/year. The periods where the match between the observations, in blue, and the model, in black do not match are clearer in Figure 2. The match is particularly poor from 1915 to 1950. The rapid slowing of the rate of rise between 1950 and 1965 is not matched well at all. The rapid rise from 1990 to 2005 is only marginally better than the other periods.

Figure 2. The curves are colored as in Figure 1, but this is a chart of the 30-year rate of change in sea level, due to thermosteric and barystatic changes in orange and red respectively. The black curve is the sum of the two, and the blue curve is the observed change in sea level, the shaded regions are the 90% confidence intervals.

Frederikse et al.’s model has a total rate uncertainty of at least one-half mm/year (see black shading in Figure 2) and the uncertainty in the data (blue shading) is even larger. Figure 2 is uncertain, but the roughly 60-year oscillation is significant and matches normal long-term ocean oscillations as described by Wyatt and Curry.[1] Wyatt and Curry’s stadium wave can be seen in Figures 8 and 9 here. Their roughly 60-year cycle can be divided into a 30-year warming cycle and a 30-year cooling cycle. 1918 to 1942 was a warming period and 1942 to 1976 was a cooling period in their analysis, this fits the data shown in Figure 2 fairly well.

Combining the analysis in Wyatt and Curry with Frederikse et al.’s analysis we can see that variations in sea level rise rates in the 20th century are probably, in part, a result of natural ocean oscillations. The Earth went into a natural warming regime in 1976, that probably ended early in the 21st century, perhaps around 2005, and then entered a cooling regime. Judging from Figure 2, it seems possible that the apparent acceleration in sea level rise from the late-1980s to about 2005 was merely a repeat of the acceleration from about 1925 to the early 1940s. Even if this is not true, it is clear that the data shown in Figures 1 and 2 are not accurate enough to conclude that the overall rate of sea level rise is accelerating, in fact it is possible that we will see a deceleration of sea level rise in the near future.

The statistical methods used in AR6 to show sea level rise acceleration were quite crude, as discussed in Part 1. They simply cherry-picked data and used least squares fits of them to estimate acceleration. In this part we show that the error in estimating sea level rise and its components is so large that showing acceleration definitively is probably not possible. In the next post we will discuss the problems with that approach and provide a more statistically sound projection of the rate of sea level rise.

The bibliography can be downloaded here.

  1. (Wyatt & Curry, Role for Eurasian Arctic shelf sea ice in a secularly varying hemispheric climate signal during the 20th century, 2014) and (Wyatt, The “Stadium Wave”, 2014)

Published by Andy May

Petrophysicist, details available on

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