Two recent papers refocus attention on how much we really know about the causes of sea level rise and how accurately we can measure it. The most recent, Twentieth century increase in snowfall in coastal West Antarctica by Thomas et al. reports large increases in the rate of snow accumulation over the last 100 years on the West Antarctic Ice Sheet – which is said to be on the point of collapse – but provides no specifics on ice sheet volumes. But the earlier paper, Mass gains of the Antarctic ice sheet exceed losses by Zwally et al., does. The press release that accompanies it contains the following statement:

The good news is that Antarctica is not currently contributing to sea level rise, but is taking 0.23 millimeters per year away,” Zwally said. “But this is also bad news. If the 0.27 millimeters per year of sea level rise attributed to Antarctica in the IPCC report is not really coming from Antarctica, there must be some other contribution to sea level rise that is not accounted for.”

“There must be some other contribution to sea level rise that is not accounted for”. No there doesn’t. It could simply mean that sea level rise has been overestimated.



Estimates of global sea level rise have historically been bedeviled by the “attribution problem”, which Miller & Douglas (2004) summed up thus:

The rate of twentieth-century global sea level rise and its causes are the subjects of intense controversy. Most direct estimates from tide gauges give 1.5–2.0 mm yr-1, whereas indirect estimates based on the two processes responsible for global sea level rise, namely mass and volume change, fall far below this range. Estimates of the volume increase due to ocean warming give a rate of about 0.5 mm yr-1 and the rate due to mass increase, primarily from the melting of continental ice, is thought to be even smaller. Therefore, either the tide gauge estimates are too high, as has been suggested recently, or one (or both) of the mass and volume estimates is too low.

Either the tide gauge estimates are too high … or … the mass and volume estimates (are) too low. Over the last ten years efforts have concentrated almost exclusively on proving that the mass and volume estimates are too low, and until Zwally et al. came along the IPCC had made progress towards closing the gap, as shown in Table 13.1 of the AR5 . The tide gauge estimates, however, have not been seriously questioned.

So here we will question them.

There are two ways of measuring sea level rise. The accepted approach is to measure absolute (or geocentric, or eustatic) sea level rise – essentially how much global sea level has risen relative to the center of the Earth. This approach is adopted because only absolute sea level rise provides the estimates of ocean volume change that are needed for mass balance calculations. The Church & White global sea level series shown in Figure 1 – one of the series featured in the IPCC AR5 – is typical of the results obtained. It shows a continuous rising trend since 1880 and about 240mm of absolute sea level rise since then:

Figure 1: The Church & White absolute sea level rise time series



Church & White constructed their series from raw tide gauge records selected from the Permanent Service for Mean Sea Level (PSMSL) data base . The records were adjusted for vertical land movements at the tide gauge sites, a requirement if one wishes to measure absolute sea levels, and the results were then combined with recent satellite sea level observations and analyzed using a complicated statistical approach that Church & White summarize as follows:

The other way to estimate sea level rise is the way I did it. I selected 382 raw PSMSL tide gauge records – substantially the same records that Church & White used, incidentally – reduced them to a common baseline, weighted them relative to the length of coastline they covered and averaged them. This approach yields estimates of “relative” global sea level rise, or how much sea level has risen relative to the global coastline. Relative sea level rise estimates can’t reliably be used for mass balance calculations, but they don’t require vertical land movement adjustments or complex statistical manipulation and they also tell us a lot more more about the physical impacts of sea level rise. (Absolute sea level rise is of academic interest in cities like Bangkok and Jakarta, large chunks of which are on the point of disappearing beneath the waves because of subsidence caused by groundwater pumping.)

Figure 2 shows the location of the 382 tide gauge stations. I estimate that they provide coverage over at least half of the global coastline after 1950. However, coverage decreases before 1950 to the point where in 1900 only 30 stations, almost all of them in the North Hemisphere, were operating.

Figure 2: The 382 PSMSL tide gauge stations used in the analysis



I segregated the 382 records into 34 areas with similar trends and Figure 3 shows the raw tide gauge records from ten of them – the good, the bad and the ugly (note the variable scales). Note also the differences in trend and the rapidly dwindling number of records before mid-century, which raises the question of whether we have enough to make good estimates of global sea level much before 1950:

Figure 3: Illustrative plots of tide gauge records

Figure 4 shows my relative global sea level series superimposed on the Church & White absolute global sea level series. The two track each other quite closely between 1910 and 1950 (the mismatch before 1910 is probably caused by a lack of data) but after 1950 the Church & White series continues to climb while mine flattens out. My series in fact shows no sea level rise at all between 1948 and 1970, although it does broadly replicate the sea level rise shown by the Topex-Jason satellite data after 1993:

Figure 4: Church & White’s absolute sea level rise series versus my length-weighted relative sea level rise series

Why does the Church & White series show ~120mm of global sea level rise between 1950 and 2010 while mine shows only about half as much? I filled a spreadsheet with 67 megabytes of data trying to find out, but because Church & White don’t publish their adjusted tide gauge records not a great deal of diagnostic information emerged. I did, however, run two checks that I present here.

Church & White measure absolute sea level rise over all the world’s oceans while I measure relative sea level rise along the world’s coastlines, so to make the comparison more apples-to-apples I first constructed an area-weighted series using a 500km radius of influence around individual tide gauge stations, which heavily de-weighted records in confined seas like the Baltic while greatly increasing the weighting of Pacific Island records. This series showed about 20mm more sea level rise since 1950 than the length-weighted series but still 40mm less than Church & White:

Figure 5: Church & White’s absolute sea level rise series versus my length-weighted and area-weighted relative sea level rise series. All three series are zeroed over 1950-55.



Second I checked Church & White’s vertical land movement corrections, which are potentially suspect because they are mostly derived from crustal deformation models that simulate the impacts of glacial isostatic adjustment (GIA) and don’t allow for any other sources of vertical movement, such as sediment compaction or tectonic uplift. Figure 6 shows what a typical GIA model – in this case the Paulson 2007 model – looks like. The red-shaded areas show where the surface is still rebounding from ice unloaded since the end of the last Ice Age. The blue-shaded areas over the oceans show where the increased mass of meltwater in the oceans is depressing the ocean floor and the pink areas in Australia, Southern Africa and Southern South America show where this is generating mild isostatic uplift in the surrounding landmasses:

Figure 6: The Paulson 2007 glacial isostatic rebound model (image credit Basement Geographer)

I had no data for the Matrovica GIA model that Church & White based their corrections on but I did have data for the comparable Peltier GIA model. I therefore used the Peltier data to “correct” the tide gauge records and reconstructed the area-weighted series with the results shown in Figure 7. Peltier’s GIA adjustments add another ~10mm of sea level rise but I still fall about 20mm short of Church & White:

Figure 7: Church & White’s absolute sea level rise series versus my length-weighted, area-weighted and GIA-corrected area weighted relative sea level rise series

These plots don’t of course prove that Church & White’s ~210mm of sea level rise since 1900 is an overestimate, but neither do they eliminate the possibility that a significant fraction of it could be the product of statistical adjustments similar to those applied to some of the land temperature records. And as noted at the beginning of the post Church & White still have an attribution problem. The IPCC’s AR5 estimates of the combined ice melt, thermal expansion and “land water” contributions to sea level rise since 1900 range from 120 to 140mm depending on how one sums them, less if the Antarctic ice sheet is gaining ice and not losing it as Zwally et al. now claim. My ~100mm of relative sea level rise since 1900 is a good deal closer.

Finally, Figure 8 compares the Church & White series with GISS’s man-made radiative forcing estimates . If GISS and Church & White are correct then global sea levels were rising steadily long before AGW became significant, although I’m not the first to recognize this. (The flattening in the forcing plot after 1990 is GISS’s attempt to explain the “warming pause”, incidentally):

Figure 8: Church & White sea level rise series versus GISS man-made radiative forcings