Sea level records artificially extended to 2100

We focus on 12 sea level records (see Methods and Table 1); 10 individual tide gauge records, a coastal mean time series and a global sea level reconstruction (Fig. 1). The coastal mean is an approximation based on a simple average of the 10 tide gauge records (hereafter ‘coastal mean sea level’ (CMSL)) and the other is the sophisticated reconstruction from Church and White2 (hereafter ‘global mean sea level’ (GMSL)). To cover the most commonly reported estimates1,3,4,5,6,7,15, we consider four sea level projections to the target year 2100. These correspond to 0.5 and 1 m (approximately mid and upper AR5 range1), and 1.5 and 2 m (upper end of range suggested by refs 3, 4, 5, 6, 7) of sea level rise by 2100 (hereafter P1, P2, P3, P4, respectively). Using each of the 12 records and each of the four sea level projections, we create time series that artificially extend the 12 records to 2100. These comprise the following: prior to 2010, the specific historic record; and from 2010–2100, one of the four sea level projections superimposed with realistic interannual variability, which we randomly generate using a noise model16 with autocorrelation and variance parameters obtained from the relevant historic records (Fig. 2). To account for uncertainty in the timing of future interannual variability, we create 10,000 randomly generated noise time series (see Methods), for each of the 12 sea level records in turn, and superimpose these on each of the four sea level projections from 2010–2100.

Table 1 Accelerations for the 12 records over their respective record lengths. Full size table

Figure 1: Mean sea level time series. (a) The 12 (10 tide gauge records, the CMSL and the GMSL) annual mean sea level records used in the present study, offset (by 200 mm) for clarity of presentation; (b) location of the 10 tide gauge sites. Full size image

Figure 2: Sea level time series artificially extended to 2100. (a) Fremantle; (b) Newlyn; and (c) the GMSL record. For the period from 2010–2100, the coloured lines (blue for 0.5 m of sea level rise by 2100; orange 1 m, red 1.5 m and green 2 m) show only 1 of the 10,000 randomly generated time series. The grey shaded areas (with the grey scale varied for each of four sea level projections) show the envelope for all 10,000 randomly generated time series. Full size image

Acceleration detection technique 1

The question whether the rate of sea level rise has increased has most often been addressed by adding a quadratic term to the linear regression model and estimating its value and uncertainty, using either individual tide gauge records17,18,19,20,21,22, or global reconstructions2,11,12,13,23,24. This is the first acceleration detection technique that we consider. Our main issues with this approach, as others (for example, refs 25, 26, 27) have highlighted before, is that: first, the actual year at which a significant acceleration is first identified depends strongly on the start date, time period and the length of the time period of the sea level record for which the quadratic coefficient is estimated; and, second, quadratic equations can be a poor fit to observed sea level change, because of the considerable natural internal and anthropogenic variability evident in sea level records over a range of timescales.

To illustrate this, we estimate quadratic coefficients (and hence accelerations) and their uncertainty (95% confidence) for the 12 sea level records considered here, for different historic periods (Tables 1, 2). Of the complete sea level records available, only the three longest records (New York, Brest and GMSL) have an acceleration significantly different from zero (Table 1), consistent with results from other studies (for example, refs 14, 17, 18, 21). However, when accelerations are estimated for just the periods 1880–2009 and 1900–2009, then the accelerations are no longer significantly different from zero at New York and Brest (Table 2). Only the GMSL retains an acceleration significantly different from zero for the period 1915–2009 when data are available for all sea level records, allowing direct comparison. For the period 1930–2009, none of the 12 records has an acceleration significantly different from zero (except Brest), in general agreement with results from the controversial study of Houston and Dean21. The acceleration at Brest is different from Newlyn, despite their close proximity, and may appear significantly different from zero because of a data gap in the 1940s. This highlights another problem with assessing sea level accelerations (that is, missing data). Missing data can also introduce spurious accelerations in averages of tide gauge records and also in sea level reconstructions that use a time-varying tide gauge distribution. Four of the records (Newlyn, Brest, Trieste and CMSL) have accelerations significantly different from zero for the period 1960–2009.

Table 2 Accelerations for the 12 records for five time periods. Full size table

The contrasts in both sign and magnitude of the estimated acceleration between the 12 records, and for different periods, highlight the challenges in comparing results among studies that focus on sea level records with varying start dates and which cover different periods. The contrasts also highlight the danger of choosing one particular start date (for example, 1930 used by ref. 21) to confirm an argument (for example, ‘the rate of sea level rise is not increasing’), while ignoring a significant portion of data that may contradict that position.

To avoid bias, we therefore recommend, and here use, the approach of Jevrejeva et al.12,24, (also applied in refs 25 and 26), which systematically estimates quadratic coefficients and their uncertainty (95% confidence) for all possible start dates and data lengths of our artificially extended records (see Methods). For just the historic records, our results (Fig. 3a,b), like ref. 26, show that accelerations (that is, two times the quadratic coefficient) are rarely diagnosed to be statistically different from zero in individual tide gauge records, particularly in records shorter than about 130 years. In tide gauge records, both the magnitude and sign of the acceleration are dominated by interannual to multidecadal variability: to a greater extent for sites with large variability such as Fremantle; and to a lesser but still significant extent for sites with smaller variability such as Newlyn. Note that large accelerations observed over shorter timescales are real. However, they are mainly due to natural internal variability and mask any externally forced accelerations (see Discussion).

Figure 3: Accelerations for historic sea level records. (a) Fremantle to illustrate a site with relatively large interannual variability; (b) Newlyn to illustrate a site with relatively small interannual variability; (c) the CMSL time series, created by averaging the 10 tide gauge records; and (d) the GMSL record. Hatched area identifies plot regions where accelerations are significantly different from zero (95% confidence interval). Full size image

For the records artificially extended to 2100, our results (Fig. 4a–h) suggest that accelerations statistically different from zero are only likely to consistently become evident in tide gauge records (irrespective of start dates) as late as the 2030s, for sea level rise pathways towards lower targets of 0.5–1 m (P1, P2) (if interannual and multidecadal variability is not accounted for, see Discussion). For sea level rise pathways towards upper targets of 1.5–2 m by 2100 (P3, P4), accelerations statistically different from zero are likely to consistently become evident in tide gauge records during the 2020s (again if variability is not taken into account).

Figure 4: Accelerations for sea level records artificially extended to 2100. (a–d) Fremantle to illustrate a site with relatively large interannual variability; (e–h) Newlyn to illustrate a site with relatively small interannual variability; (i–l) the CMSL time series, created by averaging the 10 tide gauge records; and (m–p) the GMSL record. Hatched area highlights plot regions where accelerations are significantly different from zero (95% confidence interval). Note, for each sea level record, the plots show results for just one of the 10,000 randomly generated noise time signals. Full size image

Research has often focused on global reconstructions (for example, refs 2, 11, 12, 13, 23), because global sea level has an order of magnitude smaller internal variability than sea level at individual sites2. For the CMSL (Fig. 3c) and GMSL (Fig. 3d) records, we find that the sign of the acceleration alternates between positive and negative for different start dates, when curves are fitted to periods shorter than about 90 years, indicative of a clear influence of multidecadal variability. However, over longer periods, positive accelerations statistically different from zero are consistently evident in the GMSL record and are likely to steadily increase in magnitude over the remainder of the 21st century (Fig. 4m–p). Positive accelerations are also evident, over longer periods, in the CMSL record, but these are not currently statistically different from zero (if interannual to multidecadal variability is not taken into account, see Discussion). For the CMSL records artificially extended to 2100, our results (Fig. 4i–l) suggest that accelerations statistically different from zero are likely to become evident later this decade for all four sea level projections. Note that all significant (95% confidence) accelerations observed in Figs 3, 4 are positive for window lengths greater than about 40 years, and that no significant deceleration is ever detected for any combination of window length and end year.

Houston and Dean21 argued that there is a lack of evidence for the accelerations that would be necessary to achieve the upper end of the IPCC projected range15 because the acceleration observed in the GMSL record2 and in long tide gauge records is an order of magnitude smaller than the required rates (~0.1 mm per year2). Our results (Fig. 4) clearly demonstrate that accelerations are not expected to exceed 0.1 mm per year2 until the second half of the 21st century for sea level rise pathways towards targets of 0.5–1 m (P1, P2), and will only exceed this threshold around 2030–2050 for pathways towards targets of 1.5–2 m (P3, P4). Thus, our analysis implies that the argument presented by Houston and Dean21 is invalid. In fact, by simply visually inspecting the projections from the earlier IPCC Third Assessment Report and Fourth Assessment Report (AR4), it is clear that only small rates of acceleration were predicted by the IPCC models for the period from 1990–2010. Hunter and Brown28 calculated an average acceleration in the central projection of the IPCCs AR4 A1FI emission scenario (including scaled-up ice sheet discharge) of 0.002 mm per year2 over the period 1990–2010 (see the value plotted at 2000 in their Fig. 1, ref. 28), which agrees closely with observations from altimetry and GMSL reconstructions, over this period. The recent projections, from the IPCCs AR5 representative concentration pathway (RCP) 8.5 (which we use here, see Methods), very closely resemble quadratic curves and have near constant accelerations of ~0.064, 0.096 and 0.136 mm per year2 over the period 1990–2100, for the lower, central and upper projection range, respectively. These accelerations are larger than the acceleration observed in the altimetry and GMSL reconstruction over the period 1990–2010, but are still within the (66% confidence) uncertainty range (see Table 1 in ref. 28). Therefore, it is intriguing that arguments persist that because only small accelerations are presently evident, the IPCC sea level projections must be wrong, when in fact the observations over the last 20 years agree closely with the Third Assessment Report and AR4 projections and are statistically consistently with AR5 RCP8.5 projections. Further, as we showed above, it will take time before accelerations that exceed 0.1 mm per year2 are detected for the upper RCP8.5 projection (that is, P2).

Acceleration detection technique 2

Next, we consider the implications of another commonly used approach. The question whether the observed high rates of sea level rise of the last two decades2,29,30,31 represent a significant and sustained acceleration has been regularly evaluated by estimation of linear rates for consecutive overlapping periods. This method has been applied widely, using both tide gauge records (for example, refs 32, 33, 34, 35, 36, 37) and global reconstructions (for example, refs 2, 11, 12, 13), with the paper by Holgate33 being one of the most cited examples. Studies that have applied this technique have (with the exception of ref. 37) inferred that the high rates of rise observed over the last two decades are not significantly larger than rates observed at other times within the past two centuries. That result has led some authors, notably Houston and Dean21,38, to argue that recent high rates might simply result from interannual to multidecadal variability, and hence to infer that there would be no evidence that sea level rise is following a high projection pathway.

The estimation of linear rates for consecutive overlapping periods is the second acceleration detection technique that we consider. The key weakness of this approach has already been demonstrated by Rahmstorf et al.39 Using essentially the approach we emulate and extend here (that is, a synthetic sea level time series, consisting of a smooth sea level rise plus artificially generated noise), they illustrated how the derivative of ‘noisy’ data is invariably more ‘noisy’ (see their Fig. 3 in ref. 39). Thus, even a small amount of noise in a sea level record obscures the acceleration signal when looking at decadal rates of rise. The pertinent question for our assessment with this method therefore is when we might (or more fundamentally should) expect to detect rates that are significantly higher than past rates for different sea level projections, given this key weakness of the method. (Note that because of these problems, like Rahmstorf et al.39, we advocate the use of low pass filtering techniques, such as those previously applied by Wahl et al.34,40 to detect changes in observed sea level records that deviate from a simple straight line or a quadratic curve).

In this assessment, we fit linear regressions over overlapping periods of different lengths to each of our artificial time series, and estimate the value and uncertainty (at 95% confidence) of the linear term for each period. For each artificially extended time series, we identify the end year of the period when the linear term for that particular period is (and remains) statistically higher than all the linear terms estimated for periods of the same length in the historic pre-2010 period. We also take into account the uncertainty due to future interannual variability (see Methods).

We detect linear rates that are significantly higher than past rates (that is, unprecedented rates) earliest when 30- to 40-year overlapping periods are used, and much later when shorter (10- to 20-year) periods are considered (Fig. 5). This is a particularly important finding, because previous authors (for example, refs 2, 11, 12, 13, 32, 33, 34, 35, 36, 37) tended to estimate linear rates for 10- to 20-year overlapping periods, to match the length of altimetry data available at the time of their analysis. Crucially, if sea level follows P1, an unprecedented rate of rise is unlikely to be detected using 10-year periods until after 2100 for each of the 12 records (Fig. 5a), because of the considerable interannual to multidecadal variability present in the records, and for P2 only after 2030 using the GMSL record (Fig. 5b). Holgate33 used 10-year overlapping periods, and our analysis reveals that that data length, on the sites considered, is not suited for the detection of unprecedented linear rates of sea level rise during the 21st century (for the range of sea level projections considered here), because of the considerable variability (see Discussion).

Figure 5: Years when unprecedented linear rates of sea level rise are first identified. Linear rates have been estimated for 10- (a–d), 20- (e–h), 30- (i–l), 40- (m–p) and 50-year (q–t) consecutive overlapping periods and for projections of 0.5 (P1), 1 (P2), 1.5 (P3) and 2 m (P4) of sea level rise by 2100. For each record and projection, box plots indicate the range of years identified for the 10,000 synthetic time series. On each box, the central mark is the median, the edges of the box are the 25th and 75th percentiles, the whiskers extend to the most extreme data points not considered outliers and outliers are plotted individually as circles. Values along the x axes indicate the decade within the 21st century (1 is 2010, 2 is 2020, and so on). Full size image

We find that unprecedented linear rates are detected earliest, in most records, when 40-year overlapping periods are used (Fig. 5m–p). Using 40-year overlapping periods on the GMSL record, we identify rates of sea level rise that are significantly higher than past rates in the mid to late 2010s for a rise towards 1.5–2 m (P3, P4), and late 2010s to early 2020s for a rise towards 0.5–1 m (P1, P2). Relative to this, the CMSL record reveals unprecedented rates up to 2 years later for P3 and P4 and up to 5 years later for P1 and P2. Individual tide gauge records only reveal an unprecedented rate up to 25 years later than GMSL for P3 and P4, and as much as 60 years later for P1 and P2.

Our analysis thus disproves arguments (for example, refs 21, 38) that unprecedented rates of sea level rise should have been detected by now if sea levels were currently following a high projection pathway. Instead, rates significantly higher than past rates are only likely to become detectable later this decade, or early next decade, in the CMSL and GMSL data sets, and up to 60 years later in individual tide gauge records (if interannual and multidecadal variability is not taken into account, see Discussion).