Sea level rise. Part II – tide gauge analysis
Sea level rise Part I covered the stoush resulting from a paper on long-term tide gauge records for Australasia. The author was Phil Watson of the NSW Department of Environment, Climate Change and Water and the paper was published in the Journal of Coastal Research in March. Tamino has pointed out the limitations of the statistical methods used, showing that the conclusion of decelerating sea level cannot be sustained. Tamino removed the annual cycle then used 20-year and lowess smoothing to show that the opposite conclusion – recent sea level rise is accelerating – is probably true for the Australasian region. A conclusion I strongly support.
It’s generally accepted that long-term climate records are analysed using trend analysis; either as a linear or non-linear trend, usually quadratic. The use of a particular statistical method assumes a specific model of how a system behaves. That model can be made explicit but if not, there is still an assumed model being used. Sometimes the assumption won’t be declared because it’s a widely accepted paradigm.
So what is the model sitting behind trend analysis – measured as either a straight line or a curve – and what paradigm of change process does it support? By analysing single tide gauge records, I am asking “How does sea level respond to externally-driven warming at a given location?”
The use of trend analysis to measure climate change through variables such as air temperature assumes that the climate change signal is a smooth trend and deviations from this trend are climate variability (This depends on the ability to rule out other causes). An example, using artificially-generated data representing an air temperature anomaly is shown below. This type of change is also assumed for sea level rise, but longer-term processes in the ocean compared to the atmosphere recommend a minimum 50-60 years for trend analysis compared to 30 years for the atmosphere.
This is pretty much what Watson did with the 20-year smoothed records of tide gauge records, shown below for Fremantle and Auckland.
To be meaningful, a statistical method needs to adequately represent the underlying physical processes. Two lines of reasoning suggest that climate change may not be smooth: one is that climate is a complex system with non-linear behaviour, exhibiting abrupt changes (a theoretical argument that dates back to Lorenz) and the other is that palaeoclimatic reconstructions suggest abrupt changes also occur in the sea level record (reconstructed climate proxies). Although the latter are generally assumed to result from non-linear ice sheet dynamics, this may not be the whole story.
Here, three of the long-term time series used by Watson, Fremantle, Sydney and Auckland, are analysed for abrupt changes. Newcastle is omitted because it is several records stitched together and shows clear signs of artificial inhomogeneity. Tide gauge data was downloaded from psmsl and only annual data used, although gaps were filled by averaging incomplete years. That left some gaps where whole years were unrecorded. The method used to assess abrupt changes is the bivariate test of Maronna and Yohai, updated to test a series of step changes in a single record. The method is described in a paper submitted to Journal of Geophysical Research (draft supplied on request).
Pictured below is Fremantle with trends and shifts dating from 1920 (pre-1920 is gappy and may also be inhomogenous).
This chart shows two step changes. One in 1945 is about 75 mm and the other in 1996 is about 65 mm with little intervening trend. Both are statistically significant to the 1% level. They show little intervening trend. The Auckland record, which I couldn’t easily get data for after 2000 (Watson obtained it directly from the port authority), shows a signficant step change of about 75 mm in 1947. Figure 3 above shows that if I did have the last decade’s data, it would likely kick again in the late 1990s. The Sydney record is shown below.
Sydney shows a series of statistically signficant step changes (1% level) in 1909, 1923, 1950 and 1998. None of the intervening trends are signficant. Interestingly, 1923 and 1948 mark changes in the decadal variability of ENSO in the Pacific. Perhaps this is decadl variability associated with changes in the East Australian Current and the Pacific more generally. The shift in the late 1990s coincides with the “El Niño of the century” and a statistically significant increase in global mean air temperature of 0.3°C.
So, the reason why Phil Watson found a deceleration was because he started the analysis in 1920, found a large shift in all records in the late 1940s, static conditions until the late 1990s when another step change occurred. Put a curve through that and it will decelerate. It also misses the changes from the late 1990s which I interpret as step and trend and others interpret as trend change.
So how widespread is such behaviour in tide gauge records? I decided next to analyse one of the longest running continuous records in the world: San Francisco. This record is three sites combined and adjusted to create a homogenous, uninterrupted record. The results are shown below.
The San Francisco tide gauge record shows significant step changes in 1866, 1935, 1957 and 1982. The last two coincide with El Niño events, both of which were noted as significant high sea level events in a report analysing this record. I checked the shift dates using Rodionov’s STARS method for regime shifts set at p=0.1, white noise filtered (which is cruel to sea level data because of the high autocorrelation), and obtained the same dates to within a year.
These analyses show that step and trend analysis is a credible alternative to trend analysis. Are there compelling theoretical arguments to favour one method over the other? Trend analysis follows a signal-noise construct, where the signal is thought of as a monotonic curve as in the first chart in the post and the noise is variability. Step and trend analysis assumes the climate change signal is episodic in variables such as temperature and sea level rise, at least at the regional level. I will follow this up in another post. I believe the signal-noise construct does not adequately represent how climate actually changes and that the step and trend presented here is a more realistic model.