Guest essay by: Jan Kjetil Andersen

There is a well-established consensus concluding that the global sea level has risen over the last century, and that the level continues to rise. However, the question about whether the rate is accelerating or not, is more inconclusive.

To cast some light on this, I have analyzed the latest scientific papers on this topic. Thereafter I made my own time series analyzes based on tide gauges in the GLOSS network.

All data and software used in the analysis are available for download. See links in the end of the article.

I invite the readers to a discussion about the conclusions.

Firstly the findings from the academic papers:

I start by the IPPC AR5.

Chapter 3 is about Ocean observations, and here is exactly what I am looking for:

Figure 1 (IPCC AR 5 page 287 their figure 3.13)

(a) Shows the global mean sea level anomalies (in mm) from the different measuring systems as they have evolved in time, plotted relative to 5-year mean values that start at 1900. We see that the sea level has risen with 20-25 cm in the last 130 years, which gives an average rate of 1.5 to 1.9 mm/year.

(b) Shows the gauges observations from Church & White compared with satellite altimeter. In this close-up, we see a rise of 5 cm in 19 years, which gives an annual rate of 2.6 mm/year.

This shows that the rate has been higher in the last two decades than in the last century, but the next figure in AR 5 shows that this rate is not unprecedented in the record.

Figure 2: (IPCC AR5 page 289 their Figure 3.14)

Quote from IPCC text: “18-year trends of GMSL rise estimated at 1-year intervals. The time is the start date of the 18-year period, and the shading represents the 90% confidence.

The estimate from satellite altimetry is also given, with the 90% confidence given as

an error bar.”

The figure need some extra explanation to be understood outside the context of the AR5 report. According to the figure, there has been no accelerating since 1920. We see that both Church & White and Ray & Douglas observe approximately the same annual rise of around 2.5 mm/year between 1920 and 1940, and then there is a fall 1 mm/year before the rate rebounds to 2.5 mm in the late 1980-ies.

The Jevrejeva et. Al observes a maximum rate of 4 mm/year in the 1940-es but the series stop before the increase in recent decades. Satellite altimeters shows a steady rise with a relative small variation between 2.9 and 3.9 mm/year.

The satellite measurements has a very short series in the figure because the series only goes from 1992 to 2012. That means that only two years can be calculated with an 18-years trend.

I think a very important piece of information comes out of this figure. We see here that in reality IPCC find no evidence for accelerating sea level rise after 1920. The rise before 1920 was real, but can hardly have been caused by the small amounts of greenhouse gases emitted at that time. The CO2 level in 1920 was according to Nasa 303 ppm, or just 10% above the pre-industrial level and the warming that could have caused the sea level rise has to come before that. (http://data.giss.nasa.gov/modelforce/ghgases/Fig1A.ext.txt)

So why are we then hearing about the accelerating sea level rise in the media? Well, I think there are at least two reasons for that; firstly even though the figure does not show any acceleration, they does not draw that conclusion from it. What they say is this (AR5 Page 290): ”while there is more disagreement on the value of a 20th century acceleration in GMSL when accounting for multi-decadal fluc­tuations, two out of three records still indicate a significant positive value. The trend in GMSL observed since 1993, however, is not signif­icantly larger than the estimate of 18-year trends in previous decades”.

This is rather inconclusive.

Secondly, other academic papers show an acceleration, I examine one of those below.

First, I want to update the IPCC analysis with the latest data.

The results presented in this section of AR5 are quite old. The newest of the three papers presented in the figure is Church & White, which was published in 2011, and this paper use data up to December 2009 only.

However, the authors keep extending the raw data used in their paper and the data series now includes December 2013. The reason for not having newer data is that quite many stations around the globe report late and a large bias would be introduced if the last years were based on the early reporters only.

I have run the extended series through my own statistical analysis created in php, Javascript and Google Graph, which gives the results below.

Figure 3: Blue line show Church & White 2011, with data up to Decemebr 2009. Yellow line is the authors later added data. Red line is satellite altimeter data used in AR5. Green line is altimeter until February 2016.

Figure 4: My Results from running an18-year trends of GMSL rise estimated at 1-year intervals. The time is the start date of the 18-year period. This should be similar to IPCC figure for Church & White and Altimeter, except that I have not included any confidence interval, but I think the uncertainty is equally well visualized by plotting each monthly data point. I think the match is close, although not perfect, but it should be close enough to confirm that the same data sources are used.

Then I have extended with latest Church & White data, and latest altimeter data.

Figure 5. The data in this plot goes to December 2014 for Church & White and, February 2016 for Satellite altimeter.

We see that the last added gauge data (in orange color) lift the last part of the plot to unprecedented high rate, but the period is far too short to make any conclusions from that.

This is what we get out of the AR5 with updated data.

I then go to another recently published paper on the topic.

A resent paper is the Temperature driven global sea level variability in the Common Era by Kopp et al. of Rutgers University, published in PNAS January 4th 2016. This paper provides an estimate of the global sea level changes over the last 3000 years.

They claim:

Historic GSL rise began in the 19th century, and it is very likely (P≥0.93 P≥0.93) that GSL has risen over every 40-y interval since 1860 CE. The average rate of GSL rise was 0.4±0.5 0.4±0.5 mm/y from 1860 CE to 1900 CE and 1.4±0.2 1.4±0.2 mm/y over the 20th century. It is extremely likely (P≥0.95 P≥0.95) that 20th century GSL rise was faster than during any preceding century since at least −800 CE. “

That may be right, but it does not answer whether we experience an accelerating rate or not. The figure below is from this paper.

H

Figure 6 (From Kopp et al; PNAS2016 their figure 1d)

What I read from figure 6 is that the sea level started to rise in the 19th century, well before climate change could have any effect and has continued on a quite stable rate since then, but the authors project that an acceleration may occur soon.

Rather than to continue searching more academic papers, I decided it was time to make my own research, so I went to the sources.

Analysis of gauge data from the GLOSS network

Global Sea Level Observing System (Gloss) is a network of 281 globally distributed coastal tide gauge stations. The Core Network is designed to provide an approximately evenly-distributed sampling of global coastal sea level variations.

http://www.gloss-sealevel.org/

One of the challenges in making use of statistics from gauge stations is the importance of using a so-called common vertical datum i.e. a reference point. The stations in the GLOSS network has such reference called Revised Local Reference (RLR). Each station use a calibrated local datum for all the data series, but there are no common global vertical datum for all stations. This means that we get an error if we try to mend together different short series to make one large average.

However, if we limit the series and analysis to a timespan where all the selected series goes continuously from start to end, we do not need any common datum to make a correct average.

I have selected three set of series, which I call very long series, long series and medium long series.

Very long series are 1900 through 2013; long series 1925 through 2014 and medium long are 1950 through 2014.

In addition, all selected series have at least 80% complete monthly readings.

Of the 281 stations in the Gloss network only 6 fulfils the criteria for very long series, 9 for long series and 22 for medium long series. The list of these stations is given in the end of the article.

Two averages are made for each set of series; one simple average, and one global gridded average. The latter one was computed by dividing the globe in a 6×12 grid consisting of 72 cells measuring 30 degrees latitude times 30 degrees longitude. First, an average of all stations within each grid cell are computed. The global average is then an average of the all grid cells with a weighting of each grid cells according to its area. Because degrees longitude are shorter closer to the poles, the grid cells are also smaller. The relative length of one degree longitude, is cosinus of the degree latitude at the same spot. The weight of each grid cell is therefore the absolute value of cosinus of the degree latitude in the middle of the cell.

The benefit with this method is that we get less bias toward the areas with most stations. The gridded average is therefore the most important of the two.

The plots of absolute rise and 18-year trend are shown below.

a)Very long series(1900 through 2013):Simple average in blue, gridded in red. The plot shows 36 months floating average and linear trendline of mean sea level above local reference point. b)18-year trend for very long series. Both start and end years for the 18-year period are shown. No discernible acceleration is evident from the moving average plot, but the linear trend line reveals a very small acceleration. However, all of this small acceleration is due to the small spikes in each end of the series. c)Long series (1924 through 2014): The gridded average show smaller growths d)18-year trend for long series. We see that the largest rise occurred in the period starting around 1965. No discernible acceleration can be seen after the 1965 – 1973 period e)Medium long series(1950 through 2014), simple average in blue, gridded in red f)18-year trend for medium long series. We see an acceleration for the simple average, but any acceleration for the gridded set is more dubious. Except for a very short spike in the end, the rise in recent decades are no higher than 1960-ies. All the trend in the gridded series is due to the spike since 2011. To visualize this I have included a trend line of a series that stops in 2011 (green color).

Figure 7 a)-f). Absolute rise and 18-year trend for three different time intervals.

The plots in figure 7 suggest that there has been a small spike in the rise the last few years. This spike is also consistent with altimeter readings http://sealevel.colorado.edu/.

However, this spike may be contributed to natural variability. All the studies presented in AR5 above indicate 18-year trends that were significantly higher than the 20th century average at certain times and lower at other periods. This is likely related to multi-decadal variability like the Atlan­tic Multi-decadal Oscillation and/or Pacific Decadal Oscillation. The last spike may also have been caused by such a natural occurring variation.

So what to make of all this?

I have not made any regression analysis to show whether the small increase is statistically significant or not. I welcome anyone to do that. However, I think the graphs gives a quite clear message even without further analysis; if there is any acceleration, it is infinitesimal.

Regards

/Jan

References:

1. IPCC AR5 Chapter 3:

https://www.ipcc.ch/pdf/assessment-report/ar5/wg1/WG1AR5_Chapter03_FINAL.pdf

2. The Global Sea Level Observing System (GLOSS): http://www.gloss-sealevel.org/

3. Church, J. A., and N. J. White, 2011: Sea-level rise from the late 19th to the early 21st century. Surv. Geophys., 32, 585–602.

Both the paper and sources are freely accessible http://link.springer.com/article/10.1007%2Fs10712-011-9119-1

4. Kopp & al. Temperature-driven global sea-level variability in the Common Era. PNAS 2016

Full text: http://www.pnas.org/content/113/11/E1434.full

5. Nasa GHG gases: (http://data.giss.nasa.gov/modelforce/ghgases/Fig1A.ext.txt)

6. Satellite altimeter at Boulder university: http://sealevel.colorado.edu/

7. Data and software used to make this analysis: http://csens.org/mysource-txt/

List of GLOSS stations used:

Very long series (6 stations):

Station Country code Station ID Fremantle AUS 111 Stockholm SWE 78 Trieste ITA 154 Brest FRA 1 Marseille FRA 61 San Francisco USA 10

Long series (9 stations):

Tuapse RUS 215 Pensacol USA 246 Newlyn GBR 202 Atlantic City USA 180 Galveston II USA 161 Key West USA 188 Balboa PAN 163 La Jolla USA 256 Honolulu USA 155

Medium long series (22 stations):

Kushiro JPN 518 Mera JPN 359 Manila PHL 145 Legaspi Albay PHL 522 Ko Lak THA 174 Tregde NOR 302 Adak Sweeper Cove USA 487 Newport 351 USA Fort Pulaski USA 395 Hilo Hawaii USA 300 Ceuta ESP 498 La Couna ESP 484 Barentsburg SJM 541 Antofagasta 2 CHL 510 Tofino CAN 165 Prince Rupert CAN 167 Sitka USA 426 Apra Harbur Guam GUM 540 Pago Pago ASM 539 Kwajalein MHL 513 Midway Island UMI 523 Wellington Harbour NZL 221

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