1. Introduction
In the past, analyses of future sea surface height (SSH) projections have focused primarily on a globally averaged sea level rise (Bindoff et al. 2007). Over the last few years, however, the importance of regional patterns in these projections and their societal impacts has received increasing attention (Pardaens et al. 2011; Slangen et al. 2012; Yin 2012; Perrette et al. 2013). With the same model ensemble used in preparation for the fifth report of the Intergovernmental Panel on Climate Change (IPCC-AR5; Church et al. 2013), Slangen et al. (2014) provides an improved estimate of projected regional sea level changes, which incorporates most of the various known contributions to SSH changes. A multimodel ensemble highlights where regional SSH signals are robust and where they lack intermodel consistency. However, an ensemble spread contains an estimate of both internal variability and differences in model response to climate change. Such regional internal variability may have an impact on trends on multidecadal time scales, such as the 20 years for which altimeter SSH data is available, and the over 100 years for which climate projections are typically made. The relevance of natural long-term SSH variability for the interpretation of climate-related sea level change was recently discussed by Chambers et al. (2012), who found a 60-yr oscillation in tide gauge records at several locations around the globe.
Dynamic internal SSH variability can clearly be a source of uncertainty for regional SSH trends, as was shown recently by Hu and Deser (2013), since it responds to changes in climate modes due to winds and changes in buoyancy forcing (Köhl and Stammer 2008). This is less clear for other components contributing to SSH variability. For instance, the strength of internal SSH variability on multidecadal-to-centennial time scales due to changes in land ice is not well known. Proxy studies suggest that global sea level has not changed by much more than a few tens of centimeters per century over the last 2000 years (Lambeck et al. 2010; Kemp et al. 2011), but these studies may be regionally biased, and it is possible that proxy methods underestimate the long-term variability (von Storch et al. 2004). Such a weak global sea level variability would put a cap on land ice variability, but given a lack of direct, preindustrial, centennial-scale sea level observations, dynamic SSH is the only major source of regional internal variability that can be estimated by models with well-known processes. And this internal variability is reasonably assumed to play a role in the uncertainty of climate-related regional sea level rise (SLR) projections.
Here, an estimate of internal variability for regional SSH projections is presented based on the internal variability of dynamic SSH in coupled climate models’ preindustrial control runs. The approach is similar to that of Hu and Deser (2013), who used 40 realizations of a single model’s 60-yr SLR projections to show that internal variability in dynamic SSH can be a significant source of uncertainty on regional sea level trends (Hu and Deser 2013). However, in contrast to our approach of using preindustrial control runs, they compute the internal variability between forced runs of a single climate scenario separated by perturbed initial atmospheric conditions. Their method is likely to capture any internal modes of variability that are enhanced or different under additional forcing from the climate scenario, though there is some evidence that variability is not particularly different under additional climate forcing. Instead, we focus on the magnitude of this variability and its contribution to uncertainty. One advantage of our method is that it seeks a central value of the ensemble for an estimate of the internal variability at each location so as to find regional internal variability, which might be produced in various models. In addition to the 20- and 100-yr time scales, which were chosen as analogs of the satellite altimetry and standard projection periods for phase 5 of the Coupled Model Intercomparison Project (CMIP5), respectively, we also analyze the 50-yr time scale as an intermediate period and to compare with Hu and Deser (2013).
We intend to provide relevant information on the sources of uncertainty for the IPCC-AR5 SLR projections using the same ensemble that was used in that report. This analysis is performed only for regional dynamical sea level resulting from the CMIP5 models; that is, respective estimates resulting from glacial melt and land ice sheet changes within the context of internal variability were not included, as they are not part of the CMIP5 models.
2. Data and methods
Our study uses output from the same 21 CMIP5 (Taylor et al. 2012) models used by Slangen et al. (2014) to compute an ensemble mean of regional change for the 21st century. Only one realization per model was used in this study, as in the AR5 report and Slangen et al. (2014). Model submissions to CMIP5 do not all have the same number of ensemble members for the various forcing scenarios [representative concentration pathways (RCP); see Moss et al. (2010)], with, for example, a number of models only having one ensemble member for RCP8.5. While it also avoids the problem where different models in the multimodel ensemble are averaged with differing numbers of same-model ensemble members, using only one realization per model here allows for the multimodel ensemble spread to be compared to the estimates of internal variability, as the spread will be due to a combination of individual internal model variability, differences in the dynamic SSH response to RCP climate forcings, and model differences in ocean heat uptake. For a list of all models processed, see Slangen et al.’s (2014) online resource Table 1.
The model output used is the “zos” variable from the CMIP5 ensemble (sea surface height above geoid) computed in the preindustrial control runs, which are defined as model runs with annually repeating forcing conditions (Taylor et al. 2009). To compare these to future SSH projections, the same fields taken from the historical and RCP4.5-forced runs are used, with the data covering the period 2000–2100. Drift in both the control runs and in forced-scenario runs exists in the global mean, although these control drifts are lower in magnitude than the actual global steric SSH signal (i.e., the global mean sea level trend in the forced runs). At regional scales, model drift can be substantial and of the same magnitude as long-term changes. Linear control drifts are therefore removed from the forced RCP4.5 runs on both the global and regional level, though for a complete SSH signal in the forced runs, the global thermosteric SSH change is added back in.
The measure of internal variability is estimated here as the root-mean-square (RMS) spread in regional trends calculated for overlapping 20-, 50-, and 100-yr intervals from control runs for each model. Trend starting points are every 5 years, which are every 5 data points for annual SSH data. As an example, overlapping trend lines are shown in Fig. 1 estimated over 100-yr-long segments. It is clear that the internal variability at this location is significant, with the choice of time period important for the magnitude, and even the sign of, the resulting 100-yr trend. The resulting standard deviation from the set of trend magnitudes is calculated in each grid box, which will be referred to in the following as the “trend variability.” These individual model trend variabilities are combined together as a total ensemble RMS average, which we will refer to as the “ensemble RMS trend variability.” We found that one model produced large outlier values of trend variability in some high-latitude regions, relative to all the other models. To sytematically reduce the impact outliers have on the total multimodel RMS average, a truncated RMS mean was constructed by removing the largest and smallest RMS trend variability in each grid box before calculating the total RMS average so that this average is based on 19 models’ results. Though this process did not change the result very much, it was decided that this was a reasonable approach to obtain a better central estimate of trend variability for the ensemble. All model results are regridded to a common 1° × 1° grid.
Control run trends: Preindustrial control run time series (black) for a single model from one grid cell, with 100-yr fitted trend lines over various periods (colored lines).
Citation: Journal of Climate 28, 2; 10.1175/JCLI-D-14-00359.1
The internal variability in control runs is compared with the climate projections for the RCP4.5 scenario. The RMS trend variability can be used as a measure of the internal variability’s contribution to the dispersion around the trend magnitude in the RCP4.5-forced run over a given time scale, as long as the change in variability due to the additional climate forcing is small. For interannual variability (IAV), which may have some impact on the shorter, 20-yr time scale, a comparison of historical and RCP4.5 runs found similar magnitudes, with most changes in the standard deviation of IAV within ±5 mm [Fig. 13.15 of Church et al. (2013)]. On longer climate time scales, little is known about the impact of climate scenario forcing on internal low-frequency variability, although there have been indications of changes of probability density functions; for example, an increased or decreased likelihood of extreme events exists (see Rummukainen 2013). The assumption that changes in low-frequency variability are small is supported by findings from Menéndez and Woodworth (2010), who reported that changes on extreme sea level are explained mostly by changes in the mean. The methods used here seem to be a reasonable approach to estimate long-term variability, even in a warming climate. Note that, for example, for 20-yr trends, this method captures internal variability on scales ranging from about 20 years to longer time scales, not simply variability on a 20-yr time scale.
3. Results
a. The 20-yr trends
Regional 20-yr SSH trends are presented in Fig. 2, using the CMIP5 RCP4.5 projection for each model across the interval 2006–25 (the first 20 years of the RCP projections), which is represented by an ensemble mean of 21 model trends per grid box. The resulting ensemble mean trends differ geographically (Fig. 2a) and in many regions show trends peaking over 5 mm yr−1 to less than −2 mm yr−1.
The 20-yr trends: (a) RCP4.5 20-yr SSH trend (global thermosteric + dynamic) from the 21-member ensemble mean. (b) Ensemble spread (1σ) from the same ensemble. (c) Trend uncertainty from control runs: ensemble RMS of individual models’ standard deviations of 20-yr trends.
Citation: Journal of Climate 28, 2; 10.1175/JCLI-D-14-00359.1
The spread between ensemble members, calculated as the biased standard deviation of the 21-member ensemble of the same 20-yr trends, is generally smaller than the mean signal in tropical regions and a similar or larger magnitude in high-latitude and polar regions (Fig. 2b, compared to Fig. 2a). For about 40% of the ocean, the ensemble mean of the projected signal is smaller than the spread, and the individual models’ regional trends are of similar magnitude as the spread (not shown).
The estimate of internal multimodel 20-yr trend variability has a similar magnitude and spatial pattern to the ensemble spread (cf. Figs. 2b and 2c). Regional 20-yr control run trends strongly depend on the climate variability and specifically the initial climate state. Such variability can affect the estimation of a single regional trend by more than ±3 mm yr−1. The similarity to the spread shown in Fig. 2b demonstrates that the spread is in large part composed of internal variability (or different model-dependent structures of internal variability), as differing responses to climate forcing have not yet diverged to a large degree (relative to the internal variability) on this shorter time scale.
b. The 50-yr trends
An estimate of 50-yr trends was calculated, with the period chosen being the first 50 years of the RCP projections, nominally 2006–55, inclusive (Fig. 3). Although the ensemble mean trend is now larger than the ensemble spread, the spread is still greater than 40% of the mean trend for about 40% of the ocean, with the Arctic and part of the subpolar North Atlantic exhibiting much bigger differences between models (Figs. 3a,b). The estimated effect of internal variability on this time scale is smaller than the total ensemble spread but still greater than 50% of the spread for about 62% of the ocean area: most regions except for the equatorial band, much of the subpolar North Atlantic, and the Arctic (Figs. 3b,c). Thus, on this time scale, the results lie between the 20- and 100-yr (shown in the next section) time scales; the ensemble mean trend is now clearly bigger than the ensemble spread, which is still large relative to the mean and is dominated by internal variability in most extratropical locations.
The 50-yr trends: (a) RCP4.5 50-yr SSH trend (global thermosteric + dynamic) from the 21-member ensemble mean. (b) Ensemble spread (1σ) from the same ensemble. (c) Trend uncertainty from control runs: ensemble RMS of individual models’ standard deviations of 50-yr trends. The same color scale is used as in Fig. 2.
Citation: Journal of Climate 28, 2; 10.1175/JCLI-D-14-00359.1
Compared with Hu and Deser (2013), the regional internal variability estimates presented here (Fig. 3c) are in the same range as their spread in regional trend values (i.e., the range of trends in any given location) and are bigger in many regions, with many midlatitude and high-latitude regions having a 2σ spread of ensemble RMS trend variability of about 1.5 mm yr−1 (2 × values shown in Fig. 3c). The resultant range of trends for a single location (the mean ± 2σ from Fig. 3), can vary by a factor of 3 or more in extratropical regions, which is larger in many locations than the Hu and Deser (2013) estimates. We attribute this larger range of trends in part to including and combining the results of additional models. A single model, such as the one on which the Hu and Deser (2013) paper focuses, has its own specific regional pattern of internal variability. It is also likely that the internal variability impact on 50-yr trends is a bit larger than on 60-yr time scales.
c. The 100-yr trends
For 100-yr trends, the same procedure was followed as for the shorter trends, with the period chosen being the last 100 years ending in 2100 for each model (thus, for some models, the interval is 2000–99, inclusive). These data include the last few years from the historical CMIP5 runs, in addition to the RCP4.5 runs, which begin in 2006. The regional SSH trend in this 21-model ensemble average (Fig. 4a) is more evenly distributed than in the 20-yr trend average (Fig. 2a), though a distinct spatial pattern is still evident. However, the variability of the trend average, as estimated by the ensemble spread plotted on the same color scale (Fig. 2b), is much smaller relative to the trend magnitude. On this longer time scale, the regional signal-to-noise ratio is much higher, specifically because of the large, emergent global thermosteric SSH signal [a more complete treatment of the forced-run projections in CMIP5 can be found in Yin (2012), plus other SLR components and uncertainties in, e.g., Perrette et al. (2013) and Slangen et al. (2014)].
The 100-yr trends: (a) RCP4.5 100-yr SSH trend (global thermosteric + dynamic) from the 21-member ensemble mean. (b) Ensemble spread (1σ) from the same ensemble. (c) Trend uncertainty from control runs: ensemble RMS mean of individual models’ standard deviations of 100-yr trends. Note that the color scale is different in (c), which is one-third the scale of (a) and (b).
Citation: Journal of Climate 28, 2; 10.1175/JCLI-D-14-00359.1
Regional control run trends calculated on a 100-yr time scale (Fig. 4c) only weakly depend on climate variability for most of the ocean. On this time scale, internal variability is extant on regional scales but affects linear trends by not much more than ±0.5 mm yr−1. Centennial variability is largest in the higher latitudes and polar regions, and forced-run trend magnitudes are most comparable to control run trend variability in parts of the Southern Ocean. This is a region where the forced-run trend is smallest (Fig. 4a). The fact that the ensemble spread there (Fig. 2b) is also similar in magnitude demonstrates that, at least for this ensemble, a sizable portion of the ensemble spread (<50%) is due to model internal variability. Over most of the ocean, the spread is due more to different model climate sensitivities, largely in global ocean heat uptake, and model differences in dynamic sea level (e.g., Yin 2012).
d. Trend strength versus internal variability
A direct comparison of the trend magnitude to internal variability yields a clear picture of their relative intensities. Since estimates of internal variability shown in Figs. 2c and 4c are an RMS estimate of trend variability for the entire ensemble, and because the projected SSH results from a single model may be larger or smaller than the ensemble mean in any one location (Figs. 2a and 4a), a more consistent approach is to look at a single model. Results are shown for the Max Planck Institute Earth System Model with low resolution (MPI-ESM-LR; Jungclaus et al. 2013) in Fig. 5. The 20-yr trends do not exceed the size of the RMS trend variability over nearly 40% of the ocean (shown as the pale color between −1 and 1 in Fig. 5a), although the trends are substantially stronger in the tropical Atlantic and western tropical and northern Indian basins. Although the model may underestimate decadal variability regionally, these might be places to start looking for a clear trend in the observations. One place where this model shows a high trend-to-internal variability ratio is along the northeastern coast of the United States (Fig. 5a), which is also a location where the models mostly agree on a secular decadal trend, as shown in Yin et al. (2009) and Sallenger et al. (2012). This is an area of ongoing research, as one study found that this change could lie within natural variability (Kopp 2013), but a newer study on longer time scales estimated that the long-term sea level rise in many East Coast locations is larger than the local internal variability and also that substantial multidecadal variability is seen in local climate records (Ezer 2013).
Trend magnitude vs variability: (a) Ratio of the 20-yr RCP4.5-forced trend (2006–25) for the MPI-ESM-LR model to the same model’s 20-yr trend variability estimated from the control runs. (b) Ratio of the 50-yr RCP4.5-forced trend (2006–55) for the MPI-ESM-LR model to the same model’s 50-yr trend variability estimated from the control runs. (c) Ratio of the 100-yr RCP4.5-forced trend (2001–2100) for the MPI-ESM-LR model to the same model’s 100-yr trend variability estimated from the control runs.
Citation: Journal of Climate 28, 2; 10.1175/JCLI-D-14-00359.1
On the 50-yr time scale, the forced-run sea level trends are larger than the internal variability over about 91% of the ocean, so, by this time, the global sea level rise and the long-term regional response to the climate forcing has risen above the background variability (Fig. 5b). The internal variability can still be a significant portion of the regional trend magnitude, with the internal variability estimate being larger than a third of the trend magnitude for 30% of the regional trends and larger than 50% of the trend magnitude for much of those. These regions include solely extratropical regions: the Southern Ocean, the extratropical South Pacific, most of the Pacific north of 40°N, and large areas of the extratropical North Atlantic. The spatial pattern in Fig. 5b is very similar to the pattern of uncertainty from internal variability found by Hu and Deser (2013) (cf. their Fig. 2d).
For the 100-yr time scale, the forced-run SSH trends are larger than the internal variability over all of the ocean, except for a small region in the Pacific sector of the Southern Ocean (Fig. 5c). The signal of increasing SSH is much larger than the noise from model differences and internal variability and has a very similar spatial pattern to the 50-yr case (Fig. 5b). In spite of this, for some regions the trend is only a factor of 10, or less, of the estimated internal variability, which means that the uncertainty due to internal variability is still 10%, or more, of the trend (dark blue to black in Fig. 5c). This level of trend-to-variability ratio covers about 33% of the ocean, though much of this is in the Southern Ocean, where little projected change occurs. Some of these areas include the midlatitude North Pacific and Atlantic oceans, where the long-term trend is higher. Projected changes along coasts are less affected by internal variability, with the possible exceptions of northern Japan, New Zealand, and the southeast corner of Australia.
e. Satellite-era sea level rise
The internal variability impact on trends shown here is only applicable with certainty to the same models’ results. But under the assumption that the models would capture regional internal variability reasonably well, which likely won’t be true everywhere, a comparison to satellite altimetry data can provide insight where the satellite-era SSH trends (the longest observations we have globally) indicate changes outside of the climate variability. The strongest trends stand out from internal variability in all locations (Fig. 6), with the bulk of the signals that exceed the internal variability occurring in low- to midlatitude regions (Fig. 6b). The satellite trends shown here include more than the global thermosteric plus dynamic SSH signals; for instance, a large land ice melt signal. The gravitational pattern of SSH change from land ice loss (Slangen et al. 2014) is contained in satellite SSH data, since the altimetry is based on a static reference frame (e.g., Altamimi et al. 2011). But, as the long-term variability of land ice melt is poorly constrained, and the decadal variability of dynamic SSH appears to be a large part of total regional SSH variability (Milne et al. 2009), the comparison shown here is an early attempt in quantifying SSH trends versus internal variability. However, we attempted to remove the land ice melt signal from the altimetry records using the ice melt values in the AR5 report (Church et al. 2013) and scaling these values to ice melt gravity fingerprints used in that report and in Slangen et al. (2014) (see, e.g., their Figs. 1a and 1e); we show the comparison of this result to the modeled internal variability in Fig. 6c. Compared to the full altimetry data, satellite-era trends appear to exceed internal variability in the subtropical basins and in much of the tropical regions outside of the eastern tropical Pacific (Fig. 6b). For the altimetry data with the land ice signal removed, the subtropical and tropical Indian signal is weaker, and the tropical Pacific trends now reveal a “seesaw” in SSH between the western and eastern sides (Fig. 6c). This feature has been noticed in the altimetry records for many years (e.g., Cazenave and Nerem 2004), and Meyssignac et al. (2012) has linked SSH observations and reconstructed SSH in this region to a possible low-frequency modulation of ENSO, which might explain the seesaw pattern. Merrifield et al. (2012) explain the signal in the western tropical Pacific as a combination of global mean sea level rise and climatic wind variability linked to the Pacific decadal oscillation. Other reports find that the large changes seen in these regions are due to shifts in the long-term winds and ocean circulation (Roemmich et al. 2007; Qiu and Chen 2012) or changes in the mean hydrological cycle (Cravatte et al. 2009), any of which may be linked to multidecadal climate modes, although the degree to which secular trends are embedded in a multidecadal signal continues to be investigated (e.g., Zhang and Church 2012).
Satellite-era sea level rise: (a) Regional trends in SSH from satellite data, 1993–2012. (b) Ratio of the regional SSH trends in (a) to the 20-yr trend variability estimated from the control runs (Fig. 2c). (c) Ratio of the trends found from the altimetry data—minus an estimate of global land ice melt and its regional impact over the same period—to the 20-yr trend variability estimated from the control runs (Fig. 2c).
Citation: Journal of Climate 28, 2; 10.1175/JCLI-D-14-00359.1
4. Concluding remarks
We have shown here that, on shorter multidecadal time scales, regional SSH trend estimates to a large extent represent natural climate variability. On a centennial time scale, the internal trend variability is much smaller, making projections of regional SSH from dynamic and thermosteric components for the end of the twenty-first century more internally robust. However, since regional internal variability still has some impact on trend estimates, one way to reduce this effect in future estimates is to beat down the signal by averaging ensemble members for each model together. Unfortunately a number of models archived in the CMIP5 project have only a few ensemble members per scenario, sometimes only one. The multimodel ensemble average also reduces this signal, but different models have different patterns of variability, so intramodel ensemble averages are needed for intercomparisons, and care should be taken in future CMIP efforts to produce the required ensemble sizes.
While we have focused on the RCP4.5 scenario, which is a middle scenario in the AR5 report, the stronger RCP8.5 forcing exhibits a much larger change in global thermosteric SSH, which would overwhelm the internal variability signal even more by 2100. However, in these models, the difference between RCP4.5 and RCP8.5 is small for the first 20–30 years; thus, the results for the 20-yr trend uncertainty remains much the same. Also, for RCP8.5, the global increase continues well past 2100, though the estimates for longer-term variability become more difficult for some models that have shorter control runs; and when considering the entire SSH response including land ice and other components, the uncertainty in these estimates continue to grow and dominate on longer time scales.
These estimates of model internal variability of SSH are only certainly applicable to model projections of SSH change, and then only if the regional internal variability itself does not change much under additionally forced scenarios. In this context, one notable model feature is the Southern Ocean, for which little SSH change is projected over the next 100 years; or rather, a large negative change in SSH opposing the global signal exists there with decent model agreement, and internal variability being more noticeable there (Figs. 4a,c). It is unclear yet whether model SSH in this region, which isn’t always driven by the same processes in each model (Bouttes et al. 2012), is consistent with observations (e.g., Böning et al. 2008). Nevertheless, we have shown that internal variability can be a substantial portion of the model spread for short- and long-term projections. This is important even when acknowledging that the internal signal can be beaten down by averaging ensemble members and various model output together, as we have to contend with a single “realization” in real-world observations. We suggest that model internal variability on regional scales continue to be tested against existing and future observations.
Acknowledgments
This work was funded in part through CliSAP Excellence Cluster of the University of Hamburg, the DFG, the BMBF (Federal Ministry of Education and Science) Project RACE, and a Max Planck Society (MPG) Fellowship to D. Stammer. Satellite data courtesy of CSIRO (http://www.cmar.csiro.au/sealevel/). Data used to produce these results are available at icdc.zmaw.de. Special thanks to R.S.W. van de Wal and A.B.A. Slangen for helpful comments on the manuscript.
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