Long-term climate change impacts on regional Sea Level Statistics analyzed from the MPI-ESM Large Ensemble Simulation

doi:10.21203/rs.3.rs-2827687/v1

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Long-term climate change impacts on regional Sea Level Statistics analyzed from the MPI-ESM Large Ensemble Simulation

https://doi.org/10.21203/rs.3.rs-2827687/v1

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published 07 Oct, 2023

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Statistics of regional sea level variability are analyzed in terms of probability density functions of a 100-member ensemble of monthly mean sea surface height (SSH) timeseries simulated during the low-resolution Max Planck Institute Grand Ensemble (MPI-GE) experiment for historical and climate change conditions. To analyze the impact of climate change on sea level statistics, fields of SSH variability, skewness and excess kurtosis representing the historical period 1986–2005 are compared with similar fields from projections for the period 2081–2100 obtained under moderate (RCP4.5) and strong (RCP8.5) climate forcing conditions. Overall, larger deviations from Gaussian SSH statistics are limited to the western and eastern tropical Pacific. Under future climate warming conditions, SSH variability of the western tropical Pacific tends to become more Gaussian in agreement with weaker zonal easterly wind stress pulses, suggesting a reduced El Niño Southern Oscillation activity in the western warm pool region. Otherwise SSH variability changes show a complex amplitude pattern with some regions becoming less variable, e.g., off the eastern coast of the north American continent, while other regions become more variable, notably the Southern Ocean. A west (decrease)-east (increase) gradient in variability changes across the subtropical Atlantic under RCP8.5 forcing is related to changes in the gyre circulation and a declining Atlantic Meridional Overturning Circulation in response to external forcing changes. We diagnosed regional changes of the 99th percentiles as well as global mean that increase by 16cm for RCP4.5 and by 24cm for RCP8.5, respectively, suggesting increased high-end sea level extremes for warmer climate conditions.

Knowledge about sea surface height variability in the form of probability density functions (PDFs) is an important ingredient for understanding and projecting sea level change under global warming conditions (Church et al. 2013; Stammer et al. 2019). Information about complete sea level PDFs is especially useful to stakeholders and decision makers as it contains information about potential future high-end sea level changes, information that is embedded in the upper tails of distribution functions and resides outside the likely range usually provided by the Intergovernmental Panel on Climate Change (IPCC) (Stammer et al. 2019). High-end sea level changes pose the greatest risk for flooding and highest costs in adaptation efforts (Le Cozannet et al. 2017; Hinkel et al. 2019); yet, respective information is incomplete, due to a hitherto missing data basis required to infer full sea level PDFs that account for all processes involved. Consequently, there exist little consensus on changes in regional probabilistic sea level, and on potential consequences for coastal risk management (Rasmussen et al. 2018; Oppenheimer et al. 2019). In fact, not much is known about the impact of climate change on sea level statistics as only limited statistical sea level information exists even for today, although regionally, observational and modeling studies have attempted to address these questions (Johansson et al. 2001; Dangendorf et al. 2017; Lang and Mikolajewicz 2019, 2020).

In the absence of any detailed PDF tail-information, high-end sea level estimates are so far based on probabilistic approaches (Kopp et al. 2014; Jevrejeva et al. 2019) or on expert solicitations (Bamber et al. 2019). Faced with shortcomings intrinsic to both, Stammer et al. (2019) introduced a new approach for estimating future high-end sea level rise as function of time scale using a new methodology. Building on this approach, van de Wal et al. (2022) recently provided first estimates of high-end numbers as function of time scale. Despite of this progress, strong demands remain for an actual estimate of PDFs of sea level variability and for information about their changes in a warming world. In particular, understanding the extent to which future high-end sea level rise will occur still requires an improved knowledge of regional probabilistic sea level projections that provide the full information on possible sea level variability.

Estimating probablistic sea level information typically involves computing PDFs of sea surface height (SSH) and its changes (changes in distribution of likely range and high-end tails called percentiles) from either observations (Sura and Gille 2010) or CMIP-type climate models. Contemporary probabilistic sea level information, estimated previously from satellite altimetry (Sura and Gille 2010), shows substantial geographic variations in sea level variability statistics in particular in eddy-rich regions. Concerning future regional sea level change patterns, Slangen et al. (2014) analyzed sea-level changes based on CMIP5 scenarios amended by off-line information on contributions from the cryosphere and the solid Earth. Respective analyses are also available along coastlines providing estimates of sea level distribution functions and coastal relative sea-level (RSL) change statistics (Carson et al. 2016) that could support of coastal adaptation considerations (Haasnoot et al. 2019).

Recently improved approaches toward more reliable regional sea level statistics were made possible through the initiation of large ensemble simulations (Deser et al. 2012) allowing to estimate full sea level distribution functions in the model world as well as to detect significant changes in SSH statistics in space and time (Widlansky et al. 2015; Frankcombe et al. 2018). At the time of writing, several large ensemble simulations exist generated using single coupled models by applying small changes to the initial conditions of each member to establish the full ensemble spread (Maher et al. 2019; Deser et al. 2020). These ensembles were run for historical conditions and under various climate change radiative forcing scenarios.

Building on previous research involving large ensemble climate model simulations, here we aim to use the results to further improve our knowledge about sea level statistics as a function of geographic location, thereby also linking changes in statistics to adjustments of underlying dynamical processes. In detail, we use the Max Planck Institute Grand Ensemble (MPI-GE) simulations (Maher et al. 2019) to estimate sea level probability density functions (PDFs) and their regional variations from the 100 ensemble members, as well as related statistical properties, such as variance, skewness and kurtosis, the latter two being indicative of the Gaussian nature or deviations thereof. In addition, we investigate changes in projected regional sea level statistics by the end of the 21st century simulated under the two emission scenarios RCP4.5 and RCP8.5, such as shifts in in skewness and kurtosis, as well as the probability distribution statistics at selected locations.

We note that sea level variability originating from any process not included in the model will not be accounted for, such as ocean eddies, storm surges, changes in ocean tides, or sea level contributions originating from the solid earth in terms of sea floor uplift or gravity changes, nor contributions arising from terrestrial ice mass loss or terrestrial water storage changes.

The remaining paper is structured as follows: in Section 2 we describe the methodology, including the MPI-GE model and the statistical analysis method of the model output. Changes of sea level statistics under climate change conditions are discussed in Section 3. Mechanisms behind changes of sea level variability in the North Atlantic and the Southern Ocean are described in Section 4. Concluding remarks follow in Section 5.

2.1 The MPI Grand Ensemble

The Max Planck Institute Grand Ensemble (MPI-GE; Maher et al. (2019)) is based on a variant of the MPI Earth System Model (MPI-ESM), Version 1.1, used during WCRP’s fifth Coupled Model Intercomparison project (CMIP5) (Giorgetta et al. 2013) but in detail is closer to the MPI-ESM Version 1.2 used during CMIP6 (Mauritsen et al. 2019). The MPI-GE ocean component is implemented at a horizontal resolution of 1.5° and 40 vertical layers with grid poles located over Greenland and Antarctica. We note that, given this resolution, the model is not capable of representing ocean eddies. The atmosphere model ECHAM6 has a spectral horizontal resolution of T63 (equivalent to ~ 1.8° spatial resolution) and 47 vertical layers. The MPI-ESM 1.1 has been evaluated previously against observational records for the atmosphere (Giorgetta et al. 2013), the ocean (Jungclaus et al. 2013) and sea ice (Notz et al. 2013).

As part of the MPI-GE effort, experiments were carried out using historical forcing conditions as well as RCP4.5 and RCP8.5 climate-change forcing, each experiment encompassing 100 ensemble members. Historical and RCP simulations follow the experimental design guidelines of CMIP5 (Taylor et al. 2012). This MPI-GE model output has been analyzed previously to assess responses in Northern Hemisphere stratosphere after tropical volcanic eruptions (Bittner et al. 2016), the influence of internal variability on global radiation budget (Hedemann et al. 2017) and changes in Artic sea-ice in a 1.5°C warmer world (Niederdrenk and Notz 2018). Here we use the output to study sea level statistics in its largest extent possible hitherto.

To compute sea level statistics from the GE output, we use the model’s sea surface height (SSH) field in its sterodynamic form defined as the sum of the global mean steric and the dynamical sea surface height on the native model grid (Gregory et al. 2019). Changes in statistical properties of sterodynamic sea level were assessed as a function of climate forcing by examining differences in statistical parameters as they emerge between the historical period (1986–2005) and the end of the two RCP 4.5 and 8.5 projections (2081–2100). To account for model drift, the influence of pre-industrial control simulation was removed from each ensemble member (of historical, RCP4.5 and RCP8.5 simulations) prior to computing statistical parameters.

2.2 Statistical Analysis

All statistical analyses are based on monthly SSH (as well as SST and wind fields), from which the ensemble mean was removed.

Taking advantage of the large ensemble, throughout this paper, statistics are computed in the ensemble domain, i.e., at each month over all ensemble members. Computations include changes in ensemble mean, as well as in 99th percentiles relative to the ensemble mean, timeseries analysis, ensemble spread as well as global spatial maps for SSH statistics over 20- years of between the historic period (1986–2005) and the RCP projections (2081–2100).

To infer percentiles and higher statistical moments (skewness and kurtosis), probability distribution functions (PDFs) are computed in the form of histograms on the combined time and ensemble dimension to capture the total variability. For this purpose, occurrence frequencies were computed based on counts of regional SSH anomalies. The bin-size is calculated based on the maximum and minimum in the dataset of all three distributions (historical, RCP4.5 and RCP8.5) to create an array of equally spaced bins. This results in the same number of bins with their bin width changing according to how the whole PDF width changes and hence consistently representing the same percentage of PDF per bin for all selected regions and periods.

For each PDF, the three central statistics were evaluated: (i) standard deviation (SD), (ii) skewness (S) and (iii) excess kurtosis (K’). Positive values of S imply that the PDF is skewed to the right, i.e., toward high extremes, the opposite holds for negative skewed values. Here, we define the amount of S as defined in Bulmer (1979), as distributions with S between ±0.5 as “approximately symmetric”, between ±0.5 and ±1.0 as “moderately skewed” and between > + 1.0 or <-1.0 as “highly skewed”. The excess kurtosis (K’) is defined as K-3, with 3 corresponding to the kurtosis for a Gaussian distribution. A Gaussian (symmetrical) distribution would have zero S and K’ of 0. For K > 3, the PDF is more peaked than a Gaussian distribution, whereas for K < 3, it is flattened.

To evaluate if the distributions for the two periods are significantly different from each other, we used Student’s t-test (to test if the sample means are different) and an f-test (to test whether the sample variances are from different populations/distributions) thereby following Zwiers and von Storch (1995) for the calculation of the equivalent sample sizes. From the PDFs, we also show the shifts in the high-end tails in the 95th percentiles.

To illustrate the statistical parameters evaluated during the course of this paper, thereby also providing a small tutorial for using a large ensemble to evaluate statistics, Fig. 1 together with Table 1 summarize the MPI-GE results, taking a single location nearby New York as an example because here sea level rise projections are particularly high (Carson et al. 2016).

In its top left panel, the figure shows SSH time series covering all 100 ensemble members in blue over the period 1850–2005 from the historical run and in purple and red over the subsequent period until 2100 from the two RCP simulations, respectively. In each case, bold lines denote ensemble mean time series (i.e., averages over all ensemble members at each time step), while black thin lines denote one single member from each ensemble to illustrate the full temporal model SSH variability at this location and its change under climate forcing conditions. Relative to the historical run, the ensemble mean SSH increases at this location by about 25cm until the year 2100 in RCP4.5 and by 40cm in RCP8.5. A comparison to the 15cm and 25cm respective global mean increases confirms Carson et al. (2016) in that the long-term sea level increase near New York is > 50% higher than the global mean.

Table 1

**Statistical parameters associated with the PDFs shown in** Figs. 1c **(i, ii, iii), respectively**
	Experiment	Variance (cm)	Significance	S	K’
i) original	HIST	16.8		0.1	0.6
	RCP4.5	15.8	F-test1: 0.0012	0.2	0.9
	RCP8.5	23.6	F-test2: 0.0020	0.1	0.0
ii) detrended	HIST	13.2		0.2	1.0
	RCP4.5	13.4	F-test1: 0.0000	0.2	1.2
	RCP8.5	12	F-test2: 0.0010	0.1	0.9
iii) ensemble mean removed	HIST	16.2		0.2	0.6
	RCP4.5	15.3	F-test1: 0.0000	0.2	1.0
	RCP8.5	13.3	F-test2: 0.0001	0.2	0.9

The statistical significance of change in variance between periods was assessed using an f-test at the 95% level where f-test1 is between the RCP4.5 and historical runs, and f-test2 is between RCP8.5 and historical runs.

The ensemble spread, depicted by the shaded region in Fig. 1a, and its change over time is quantified in Fig. 1b, showing the ensemble standard deviation evaluated for every monthly time step across all ensemble members. Under ergodic and homogeneous statistical conditions, this spread would be essentially constant and would also represent the variability in the time domain. Visually, however, there is a tendency from about 3cm (root mean square, RMS) ensemble spread during the historical period to 2.3cm and 2.2cm (RMS), for RCP4.5 and RCP8.5, respectively. In agreement with the amplitude of the individual members (see Fig. 1a), Fig. 1b suggests that at this location near New York, sea level variance declines in the MPI-GE runs under global warming conditions by up to ~ 40%. The figure shows that sea level statistics over longer periods are not stationary; however, over the chosen 20-year time windows after removing the ensemble mean the assumption of ergodicity appears plausible.

Shown in the right column of the figure are histograms of monthly SSH for each of the above 20-yr periods, respectively. The illustrated three different sets of histograms demonstrate the impact of different data processing steps on the results, such as the removal of the seasonal cycle, or the removal of both the seasonal cycle and trend or the removal of the ensemble mean (compare Fig. 1ci, ii, iii, respectively). Including the trend in RCP8.5 would artificially increase the variance and reduce the K’ as compared to the historical run (Fig. 1ci). Removing the trend prior to computing statistics accordingly leads to a reduced variance and a closer statistical agreement between all three runs (Fig. 1cii). In the presence of nonlinear changes and low frequency variability, the best way to infer statistics of sea level variability on time scale below the 20-year averaging period is to remove the ensemble mean prior to the PDF analysis (Fig. 1ciii).

We stress that throughout the remainder of the paper this latter approach is used to establish SSH statistics from the MPI-GE output, which also removes the ensemble mean trend and the climatological seasonal cycle of individual ensemble members.

The resulting PDFs and their parameters (see also Table 1) suggest that for our example the SSH variance declines from 16.2cm² for the historical run, to 15.3, and 13.3cm² (i.e., by up to 12%) for RCP 4.5 and 8.5, respectively. The S remains at a level of 0.2 throughout, i.e., the PDF is approximately symmetric. The K’ changes from 0.6, to 1, and to 0.9 indicating the PDFs become peakier and thus increasingly non-Gaussian. Tails of this PDF become narrower as indicated by the 5% and 95% percentiles also shown in the figure, which is consistent with the declining variance and the peakier shape of the PDF under RCP8.5. In all cases, the differences between the distribution functions from the two periods (RCP4.5 minus historical; RCP8.5 minus historical) are statistically significant at the 95% level using a f-test.

To set the stage for the later analysis of statistical SSH parameters and their changes under global warming conditions, shown in Fig. 2 are the ensemble mean fields of the sterodynamic SSH averaged over the 20-year period (2081 to 2100) for the RCP 4.5 and 8.5 runs, respectively, minus the 20-year mean from the historical run (1986 to 2005). In comparison to the CMIP5 multi-model ensemble mean SSH change for RCP4.5 (see Church et al. (2013); their Fig. 13.13a), MPI-GE shows a comparable regional pattern suggesting a decreased subtropical gyre circulation in the North Atlantic (Gulf Stream region) and an increase in the North Pacific (Kuroshio region) with similar patterns seen in eddy evolution for both regions (Beech et al. 2022). However, sea level anomalies are more pronounced in our single-model (MPI-GE) ensemble mean which agrees to what can be observed for sterodynamic change resulting from individual CMIP5 models (see Church et al. (2013); their Fig. 13.18). Between the two RCP runs, amplitudes appear larger by approximately a factor of 1.5 for RCP8.5.

Shown in the upper row of Fig. 3 are maps of SSH standard deviation (SD), as they emerge under historical, RCP4.5 and RCP8.5 conditions. High SSH variability regions include the North Pacific, eastern Atlantic, Southern and the Indian Ocean and low variability is seen for the western Atlantic, most of the western Pacific Ocean, as well as in the Ross and Weddell Sea. This figure suggests that overall, the model is capable of simulating the observed (by satellite altimetry (e.g., Sura and Gille 2010) pattern of SSH variability. However, variance amplitudes remain at a 25% level of what is being observed as the model is not capable of simulating eddies. All statistical considerations presented in this paper are thus confined to large-scale variability patterns.

Much of the regional sea level variability has been attributed to internal variability in the climate system associated, e.g., with large scale climate modes, such as the El Niño Southern Oscillation (ENSO) (Stammer et al. 2013; Han et al. 2017). This SSH variability link to ENSO was also identified previously (Sura and Gille 2010; Widlansky et al. 2015, 2020). However, the extent to which these climate modes and their associated mechanisms impact local and remote sea level variability is not always clear (Han et al. 2019).

Shown in the middle and bottom rows of Fig. 3 are fields of S, and K’, for each of the above three 20-year periods. In stochastically forced systems, non-Gaussian statistics are characteristic for the non-linearity of the system (e.g., Sura and Gille 2010). For Gaussian statistics to hold, fields of S and K’ should be zero. Clearly this is approximately the case for most of the global ocean. However, it does not hold in the tropics, especially in the Pacific, where S < -1 in western tropical area and S > 1 in the east. With respect to K’, a clear deviation from its Gaussian value of zero can be found in the western tropical Pacific, exceeding 3.5 there as it is the case for PDFs broader than bell-shaped normal distributions.

In comparison to contemporary SSH variability inferred from altimetry (Sura and Gille 2010) we note substantial agreement in the tropics with respect to S. In this respect, the asymmetric pattern across the tropical Pacific can be associated with ENSO oscillations, leading to negative tails in the west and positive tails in the east due to strong El Niño - La Niña asymmetry in amplitude. With respect to K’, however, patterns are quite different as compared to altimetric results from Sura and Gille (2010). However, model simulations by Beech et al. (2022) show high eddy kinetic energy at western tropical Pacific, where we have the highest K’. This holds not just in low latitudes but around the world in all eddy-rich regions (e.g., western boundary current regions) where the eddy variability is not simulated by the MPI-GE climate model to reproduce observed sea level statistics.

The changes of the statistical parameters under RCP4.5 and RCP8.5 conditions relative to the historical run are shown in Fig. 4. In both projections, the variability increases relative to the historical run over large parts of the Atlantic, the Arctic, the Pacific and the Indian Ocean (Figs. 4a-c). However, it decreases in the western North Atlantic and the Pacific and Atlantic sectors of the Southern Ocean (top row of Fig. 4). In the difference between RCP8.5 and the historical run the variability also decreases over the western tropical Pacific Ocean. In contrast, variability increased markedly in the RCP8.5 run southwest of Australia; a fact that also shows up between the two RCP runs, albeit smaller in amplitude.

Compared with the historical period, RCP8.5 shows the largest reduction in both S and K' for the western tropical Pacific region, which can be linked with changes in future ENSO activities. ENSO is known to dominate this region by altering surface winds, ocean currents, increased sea surface temperature (SST) variability, salinity and wind-driven shifts of the thermocline, which in turn can affect SSH (Widlansky et al. 2015, 2020). Given that SSH variability is linked to ENSO, it can be hypothesized that any change in ENSO activity can drive key changes in SSH statistics.

As pulses of the easterly wind stress are among the important mechanisms for initiating ENSO events, we investigate changes in the statistics of the easterly wind stress to occur in Fig. 5. We find a consistent change in zonal winds stress statistics, which suggests that the S originating from easterly wind stress pulses reduce under RCP8.5 warming conditions. Similarly, the reduction in the historical positive K' for both SSH and wind stress also points to a reduction of extremes for both quantities.

Our MPI-GE analysis suggests that a reduction of ENSO activity is reflected by changes in SSH S and K' in the western tropical Pacific, especially under RCP8.5 forcing. However, it is plausible that future ENSO intensity does not weaken as influences from other mechanisms may not only become stronger, but also influence parts of the Pacific region, e.g., for increasing Central Pacific (CP) El Niño and not the Eastern Pacific (EP)- El Niño. Some modeling studies suggest a strong occurrence of the CP type El Niño in the future; compared with the EP type (Trenberth and Stepaniak 2001; Ashok et al. 2007; Kug et al. 2009) in response to future warming. Other studies, like Cai et al. (2018) diagnose a robust increase in the RCP8.5 EP-Niño SST variability and suggested this increase is largely due to greenhouse gas-warming-induced intensification in the equatorial Pacific. However, large single model ensembles like the MPI-GE and the CESM-LE/CESM-ME (Maher et al. 2019; Ng et al. 2021) and multi-model ensembles like the CMIP5 projections under different IPCC scenarios (Cai et al. 2014, 2018, 2022) suggests that the range in ENSO variability is large and differs widely between model simulations.

Fields of S and K’ shown in Fig. 3 led us to conclude that generally the model sea level variability for this 20 years time scale appears to be close to Gaussian. This holds for the historical period (1986–2005) as well as the RCP4.5 and RCP8.5 (2081–2100) projections. However, a few regions stick out as non-Gaussian as discussed in the previous section. To analyze these regions in more detail, we show in Fig. 6 estimates of the underlying probability density function (PDF) computed as histograms of the SSH anomalies in several dynamically distinct regions. Statistics related to the respective PDF shapes are provided in Table 2.

Table 2

Statistics associated with the PDFs shown in Fig. 6
	Experiment	Variance (cm)	Significance	S	K’
a) Northwest Atlantic	HIST	12.6		0	0.2
	RCP4.5	12.9	F-test1: 0.094	0	-0.1
	RCP8.5	11	F-test2: 0.000	-0.1	-0.1
b) Northeast Atlantic	HIST	11.1		0.1	-0.1
	RCP4.5	11.4	F-test1: 0.024	0	-0.1
	RCP8.5	14	F-test2: 0.000	-0.1	0
c) Western Pacific	HIST	22.1		-2	6.5
	RCP4.5	23.2	F-test1: 0.000	-1.7	4.8
	RCP8.5	14.5	F-test2: 0.000	-1.8	7.3
d) Eastern Pacific	HIST	7.6		0.9	2.2
	RCP4.5	8	F-test1: 0.000	1	2.4
	RCP8.5	7.7	F-test2: 0.122	0.9	2.6
e) North Pacific	HIST	24.4		0	0.2
	RCP4.5	25.3	F-test1: 0.005	0.1	0.1
	RCP8.5	23.7	F-test2: 0.026	0.1	0.2
f) South Pacific	HIST	31.4		0	0
	RCP4.5	28.4	F-test1: 0.000	0	0
	RCP8.5	27.8	F-test2: 0.000	0	0

The statistical significance of change in variance between periods was assessed using an f-test at the 95% level where f-test1 is between the RCP 4.5 and historical, and f-test2 is between RCP 8.5 and historical.

Figures 6a, b confirm earlier findings of variance changes resulting in different shapes of the PDFs in the western and eastern subtropical Atlantic. To test that the PDFs for the variance from the three time periods are significantly different from each other, we used an f-test (Table 2) following Zwiers and von Storch (1995). The impact of global warming is thus limited to a narrower PDF in the west resulting in contracted tails, the opposite holds for the eastern side. Similar findings hold for the subtropical North and South Pacific (Figs. 6e, f). In contrast, in the tropical Pacific (Figs. 6c, d), where over the historical period ENSO related SSH variability leads to PDFs highly skewed to the left in the west and moderately skewed right in the east (see above), this behavior reverses in the western Pacific in the RCP8.5 scenario, making the PDF more Gaussian as discussed above.

Changes in SSH statistics under global warming conditions are typically assumed to be small and changes in extremes SSH are proposed to go hand in hand with changes in SSH mean (Menéndez and Woodworth 2010). Under these assumptions, future changes in regional mean SSH have been used to predict the frequency of the occurrence of extreme events simply by shifting the relation between extreme sea level and return period derived from extreme value distributions upward by the expected mean sea level rise (Hunter 2010, 2012; Lowe and Gregory 2010; Lin et al. 2016; Garner et al. 2017). Using the MPI-GE results, we are now able to explicitly calculate the change of the 99th percentiles relative to the ensemble mean for both RCP runs. Comparing future changes of the 99th percentiles to the historical period provides a measure of change in natural variability that can contribute to high-end changes in RCP4.5 and RCP8.5 beyond a simple shift in mean sea level.

Shown in Fig. 7a are the differences of the 99th percentiles relative to the mean for SSH PDFs of the historical run. Overall, the figure reproduces the variability pattern over the ocean indicating that the regional differences in 99th percentiles is governed primarily by differences in SSH variability rather than other changes of the PDF characteristics. The figure thus suggests that, under present-day conditions, natural variability enhances the likelihood of high-end sea level to occur in high-variability regions, especially along western boundary currents of the ocean.

To quantify future shifts in the high-end tails under climate warming conditions, Figs. 7b, c show the same diagnostics from the last 20-year period of the RCP4.5 and RCP8.5 runs relative to the historical SSH 99th percentile. Both panels reveal that high-end tails contract in a warmer climate over the Gulf Stream along the east coast of the U.S. and Canada, confirming findings from Fig. 2b of a reduced variability there. Tails also contract over parts of the Southern Ocean, e.g., the Ross Sea. In contrast, RCP8.5 changes suggest that most of the global ocean will see increased 99th percentile values in the future due to an increase of SSH variability under global warming conditions. This is most obvious for the Southern Ocean southwest of Australia, the eastern North Atlantic as well as the Kuroshio/ Oyashio region. Most importantly, this figure suggests that sea level extremes (computed as 99th percentiles) shift toward higher values than those expected from the pure change of the mean, which is linked primarily to changes in sea level variability. We diagnosed regional changes of the 99th percentiles as well as global mean that increase by 16cm for RCP4.5 and by 24cm for RCP8.5, respectively, suggesting increased high-end sea level extremes for warmer climate conditions. This serves as vital information for coastal adaptions under climate change.

In this context, we recall that the underlying model is only coarse resolution and does not produce ocean eddies. Its variability therefore is substantially underestimated as compared to altimetric SSH observations (see also below). However, when using eddy-resolving model simulations in the CMIP6 framework, a recent study by Beech et al. (2022) provides a mixed evaluation of long-term evolution of ocean eddies in a warming world; with eddies increasing in some regions and decreasing in other regions (see Beech et al. (2022); their Fig. 2). Moreover, important processes such as storm-surges or tide are not included in the model. Hence, future changes in the SSH tails might therefore be very different in the real world than suggested here by the low-resolution climate model.

4.1 North Atlantic

Figure 4 suggests that several geographic regions show pronounced changes in SSH variances under climate change conditions, and in its Gaussian characteristics. In the following we will analyze in more detail the variability changes in selected regions.

While searching for dynamical causes for the large-scale changes in variance in the North Atlantic and the Southern Ocean, we compare in Fig. 8 the standard deviations of SSH with that of SST. Visually, both rows reveal a similar resemblance of changes in variance, with decreases in western North Atlantic, and increases in eastern North Atlantic, suggesting that both changes are related and linked to changes in circulation pattern, specifically variability associated with climate modes. The resemblance holds especially for the North Atlantic, where the decrease in variability visible in its western part may be related to a shift in the western boundary current system and its variability eastward. The increase in SSH variability in eastern North Atlantic, seen from Fig. 9, can be linked with future increases in surface ocean warming.

For the North Atlantic, basin-scale SSH variability was argued previously by Han et al. (2012) to be driven by seasonal and interannual processes that dominate the North Atlantic Gyre circulation. Notably this would entail coupled atmospheric-ocean patterns, such as the North Atlantic Oscillation (NAO) (Hurrell and Deser 2009; Deser et al. 2017), evolution of ocean eddies (Beech et al. 2022) and changes between wind and heat fluxes driven variations in the Atlantic Meridional Overturning Circulation (AMOC) (Häkkinen 2001; Han et al. 2017, 2019). We also note that under global warming conditions, the MPI-GE projects a decrease in both the ensemble mean AMOC strength at 26ºN (compared to 19Sv for the historical run in 2000, the RCP8.5 declines to 14Sv, while the RCP4.5 declines to 16Sv by the end of 2100) and, similarly, its variability (ensemble spread) over time (see Maher et al. (2019), their Fig. 10). Since AMOC and the gyre circulation are dynamically coupled in the subpolar North Atlantic (Yeager et al. 2015), changes in both strength and variability characteristics of AMOC will translate to the strength and variability of the subpolar gyre. Several studies have highlighted that increased heat and freshwater fluxes in the subpolar North Atlantic weaken the AMOC and cause a reduction of AMOC strength and northward ocean heat transport (Jungclaus et al. 2014; Lobelle et al. 2020). The decreased sea levels seen in the western North Atlantic can be associated with a reduced transport of the Gulf Stream and the North Atlantic Current that leads to declining sea level gradients across these currents with a large scale impact on sea level (Häkkinen 2001; Brunnabend et al. 2014; Landerer et al. 2014; Hu and Bates 2018; Hand et al. 2020). A future declining AMOC and weakened westerly winds (Figs. 9a-c) can potentially be responsible for weak/slow circulation and poleward shift of the Gulf Stream.

Using the ensemble members from the CESM1 climate model outputs, for the RCP4.5 and RCP8.5, Hu and Bates (2018), show no change in the pattern, magnitude, or position of the North Atlantic Oscillation (NAO), but relate the reduced intra-ensemble sea level variability to the decrease in AMOC variability. Moreover, future changes in sea level pressure and the North Atlantic jet Stream (westerly wind stress) patterns related with the NAO are predicted to change by shifting poleward and weakening (Deser et al. 2012, 2017; Woollings and Blackburn 2012; Hu and Bates 2018). This, in turn, can influence the gyre circulation and the structure of the AMOC and can influence the North Atlantic (increase-decrease) SSH variations. Also, Beech et al. (2022) predict that future eddy activities intensify poleward for the North Atlantic (shown in their Fig. 2c) and along most eddy rich areas like the Western Boundary Currents. However, this includes a mixed outlook, with both increases and decreases shown regionally.

4.2 Southern Ocean

According to the findings presented above, the most pronounced changes in future SSH variability in the RCP 8.5 scenario occurs in the Southern Ocean south-west (SW) of Australia [48–56°S, 78–123°E]. In this region, the SSH variability increases more rapidly since mid the 1960s and undiminished until 2100 for RCP8.5 while the increase saturates in the mid-century for the RCP4.5 runs (Fig. 9). This variance increase is primarily related to changes of interannual variability and tapers off towards shorter and longer time scales, suggesting that interannual changes in the flow field become very prominent in this region characterized by strong topographic interaction with the Antarctic Circumpolar Current (ACC) flow field. Previously, several studies using CMIP5 models and satellite altimeter have linked changes in the large meandering mesoscale band south of Australia [100°E − 140°E] to shifts in the southern frontal position of the ACC transport (Gille, 1994, 2014; Landerer et al., 2014).

The large scale changes based on CMIP5 models suggest that changes of the Southern Ocean circulation are driven by a combination of factors such as wind stress variability, changes in horizontal circulation in form of the mean path and strength of the ACC, and associated interactions between topography and poleward eddy transports in the subpolar gyre area (Meijers 2014). This is shown by recent quantification of historical and projected Southern Hemisphere westerly wind changes based on analysis of CMIP5, CMIP6 and reanalysis data (ERA 5) by Goyal et al. (2021), suggests CMIP6 models have less equatorward bias in the westerlies as compared to CMIP5, and an associated reduction in projected poleward shift when compared to CMIP5 models (their Fig. 1a and 1b). Also, under the higher emission scenarios (e.g., SSPS-8.5) the CMIP6 ensemble mean shows a stronger jet strength compared with the CMIP5 ensemble mean (see Goyal et al. (2021); their Fig. 1b) and this poleward intensification projects onto a positive trend in the SAM (their Fig. S3). Other studies such as Beech et al. (2022) also show an increase in future simulated eddy activity that moves poleward in the ACC region; suggesting it to be driven by the intensification shifting westerly winds.

Regarding specifically the region SW of Australia [100–140°E], several studies have linked changes in the large meandering mesoscale band to shifts in the southern ACC front(Gille 1994, 2014; Landerer et al. 2014) as well as the strengthening and southward shift in westerly wind stress on sea level change (Bouttes et al. 2012). The SSH variance increase in the MPI-GE under RCP8.5 forcing SW of Australia may be linked to increases in projected zonal eastward wind stress (see Figs. 5a-c, Figs. 9a-c and Fig. 10). Moreover, altimetry and reanalysis data also shows that SSH variability is linked to both the Southern Oscillation and the SAM (Armitage et al. 2018) and seem to be reflected in the southward shifts in southern ACC front and associated topography interactions (Sokolov and Rintoul 2009).

To further investigate the mentioned variability changes and underlying mechanisms, we high pass filter the SSH variability with a 36- month window, focusing on the central location 106˚E, 53.35˚S. Results reveal that the intra-annual to interannual variability increases consistently from 12.5cm for the historical to 15.0cm and 19.5cm for the RCP4.5 and RCP8.5 run, respectively (Fig. 9c).

As it will be difficult to entail in detail the causes for the reduction and recovery of the low frequency variability here, we focus instead on the high frequency component as it can be linked directly to wind stress changes. Since the pattern of enhanced SSH variability SW of Australia shown in Fig. 4b has a similarity to the first mode of SSH variance shown by Webb and Cuevas (2002, their Fig. 1), their proposed relation to a trapped geostrophic mode serves as a starting point to also explain the change in variability seen here. According to Webb and Cuevas (2002) wind driven Ekman pumping excites the first empirical mode, which they demonstrated through a correlation of up to 0.5 between area averaged wind stress curl and the first mode time series. As the mode appears to have a short decay time scale, high frequency barotropic variability can be explained by it.

Following the close connection between wind stress curl and SSH, we perform a correlation analysis across the ensemble members between the standard deviations of SSH and wind stress curl for RCP4.5 and RCP8.5 (Fig. 11). The data period is the last 20 years, and the time series were high pass (< 36 months) filtered to focus on the higher frequency part of the signal. Note that the relevant signal on time scales shorter than 1 month is not resolved since only monthly mean data is available. For both scenarios, an enhanced correlation (> 0.2) is visible near and west of the location of the SSH variability marked by a green dot, confirming local Ekman pumping variability (shown as contours) as the relevant agent for modulating the SSH variability.

Also shown in Fig. 11 are the changes in the standard deviation of the Ekman pumping as difference between the RCPs minus the historical period. Both RCP runs show a southward shift of pumping variability SW of Australia signified by a zonally elongated dipole with the axis located roughly along 48°S. The shift leads to an enhanced pumping variability in a region that matches the enhanced SSH variability seen in Fig. 3b and provides therefore a simple mechanism for the enhanced variability. Furthermore, the change in Ekman pumping variability is about 2–3 times larger for RCP8.5 in comparison to RCP4.5 which agrees well with the change of high frequency SSH variability in this region.

Focusing on the Southern Hemisphere (SH), we suggest the above SSH correlation (Fig. 11) to be linked with changes in the Southern Ocean circulation and especially to the SAM variability and its influence on surface wind stress (and curl) that affects the Southern Ocean variability, through its southward movement of the westerly wind belt that circles Antarctica (also examined from CMIP5 models, see Zheng et al. (2013)). Most CMIP5 RCP scenarios suggest a trend in westerly winds towards stronger and more southward jets, correlated to a positive trend in the SAM (driven by opposing changes in stratospheric ozone concentrations and increasing concretions of GHGs) (Meijers, 2014; Meijers et al., 2012).

The MPI-GE wind stress changes for the high emission scenario of RCP8.5, agrees with the above findings in suggesting a projected pattern that resembles the positive phase of the SAM (Fig. 12). These wind-stress changes occurring in the middle of the 21st century can be linked to changes in radiative forcing and the cumulative CO₂ emissions in the RCP8.5 that continues to rise throughout the 21st century for RCP8.5 (CO₂ emissions more than double by 2050) but stabilizes in 2050 for RCP4.5.

The threshold near the maximum RCP8.5 changes (see Figs. 9 and 10) for SSH variability and zonal wind stress is further substantiated by increased RCP8.5 mean zonal wind stress. It is 2.5 times larger compared to the RCP4.5 and shows characteristics of the positive phase of the SAM southwest of Australia (Fig. 12), suggesting that the wind variability shifts as the mean does. In summary, we suggest that this shift in the location of the wind is relevant, by the associated shift in wind stress curl variability. Here, we also suggest that future large scale atmospheric changes in the Southern Hemisphere (e.g., nonlinear response of the stratospheric vortex via loss of stratospheric ozone, warming in lower stratosphere and strengthening the stratospheric westerly winds) and wind stress curl changes and respective ocean responses, induce this large RCP8.5 SSH threshold behavior. Several studies also showed increases in SSH variability linked to non-linear changes of threshold crossings seen from surface ocean warming (Widlansky et al. 2020). Identifying the exact mechanisms behind this is beyond the scope of this paper and requires an analysis of several single model large ensembles to detangle the mechanisms in the Southern Ocean responsible for such RCP8.5 SSH and zonal wind stress changes from mid-century onwards.

In this paper we used the MPI-GE to investigate historical SSH statistics and its changes under RCP4.5 and RCP8.5 climate change conditions. The large ensemble allows us to infer SSH statistics to an extent not previously conducted, thereby obtaining a more complete picture of SSH statistics than hitherto available from climate models. Using the model output, we were able to investigate the nature of large-scale sea level variability represented by the model and its relation to Gaussian statistics.

The most pronounced deviation from Gaussian SSH statistics we find in the model’s western and eastern tropical Pacific (see section 3). With respect to changes in the shape of underlying PDFs, our model’s tropical SSH variability shows a most pronounced deviation from Gaussian statistics, notably in the western and eastern tropical Pacific. By the end of 2100, SSH variability of the western tropical Pacific shows the tendency toward a more Gaussian variability linked with weaker zonal easterly wind stress pulses (see section 3), suggesting a reduced El Niño Southern Oscillation activity in the western warm pool region in the future.

During the 21st century, regional changes in SSH variability are most pronounced for the RCP 8.5 scenario, where SSH variability is projected to increase in amplitude over much of the globe, with the largest increase in the ACC region visible southwest of Australia in the Southern Ocean (see section 3). This is highly correlated with changes in the wind stress curl (see section 4), which can lead to changes in the gyre circulation and shifts in the ACC. Similar distinct east-west changes are seen between SST and SSH variability (Fig. 8) for the North Atlantic where an east (increase) -west (decrease) pattern emerges that can be influence from a combination of gyre strength (e.g., a weakened Gulf Stream), the declining AMOC strength and variability and the northeastward shifts in the westerly wind driven NAO and future evolution in ocean eddies. The combination of these complex mechanisms makes it challenging to attribute changes in SSH variability to only one key mechanism. However, it is likely that the MPI-GE and its given resolution are associated with atmospherically forced variability and it changes under climate forcing.

Most importantly, our results suggest that sea level extremes (computed as 99th percentiles) shift toward higher values than those expected from the pure change of the mean, which is linked primarily to changes in sea level variability. We diagnosed regional changes of the 99th percentiles as well as global mean that increase by 16cm for RCP4.5 and by 24cm for RCP8.5, respectively, suggesting increased high-end sea level extremes for warmer climate conditions. This serves as vital information for coastal adaptions under climate change.

Following from here, a caveat in our statistical SSH analysis arise from uncertainties in the simulated sea surface height changes. Since this model configuration is run at low resolution without resolving ocean eddies and smaller scale dynamics, not all processes affecting sea level are included in the model, such as storm surges and tides. This impacts the model’s response to forcing changes in dynamically active regions such as the Gulf Stream or the ACC southeast of Australia. Concerning eddies, it is vital to note that recent high resolution simulations from Beech et al. (2022) predicts poleward intensification in eddy activity; albeit, with mixed results regionally. But one also needs to consider that the existing internal variability in the 100-member ensemble will be model specific and may be different when using another set of model ensembles. It therefore appears vital that our analysis gets repeated with different large ensemble results, but also with eddy-resolving models to either confirm that they are robust or identify their sensitivity to additional physics.

Even though large ensembles are limited to coarse resolution models, our study sheds light on implications on regional areas. The potential implications for coastal regions suggest increases in SSH seen from the widening of the PDF tails, and increased variability along Western and North Pacific as well as Eastern North Atlantic. As we see SSH variability increase in these regions, they will be prone to enhanced high-end sea level values due to internal ocean (eddy) variability that would be superimposed to a global mean SSH increase. Assuming that eddy variability would increase in the same way as we see the large variability to change here, natural variability can be a significant cause of enhanced high-end sea level variability around the ocean. To verify this, in the future we need large ensembles based on eddy resolving climate models. It is vital to consider that many model ensemble outputs are needed to detect and attribute various statistics as being influenced by internal variability or distinguished as a forced response.

Acknowledgments

This study was funded in part by the Deutsche Forschungsgemeinschaft (DFG) under the SPP 1889 “Sealevel” and by the Germany’s Excellence Strategy -EXC 2037’ CLICCS- Climate, Climatic Change, and Society’- Project Number: 390683824. Contribution to the Center für Erdsystemforschung und Nachhaltigkeit (CEN) of Universität Hamburg. The simulations were performed at the Deutsches Klimarechenzentrum (DKRZ).

Funding

Competing Interests

The authors declare they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data Availability Statement

Information on the Max Planck Institute Grand Ensemble (MPI-GE) outputs used in this study can be found and downloaded from the website (https://www.mpimet.mpg.de/en/grand-ensemble/).

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published 07 Oct, 2023

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Long-term climate change impacts on regional Sea Level Statistics analyzed from the MPI-ESM Large Ensemble Simulation

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Journal Publication

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Abstract

Figures

1 Introduction

2 Method

2.1 The MPI Grand Ensemble

2.2 Statistical Analysis

3 Regional Ssh Statistics And Its Changes

4 Sea Level Variability Change Mechanism

4.1 North Atlantic

4.2 Southern Ocean

5 Concluding Remarks

Declarations

References

Status:

Journal Publication

Version 1