Climate-Induced Polar Motion: 1900–2100

Abstract

It has been demonstrated that the motion of the Earth's rotational pole with respect to the crust—termed polar motion—is increasingly influenced by barystatic processes, that is, continental-ocean mass redistribution due to melting of polar ice sheets, global glaciers, and variations in terrestrial water storage. However, how these processes might impact polar motion in the $${21}^{\text{st}}$$ century is not known. Here we investigate this problem under various climatic scenarios, namely, Representative Concentration Pathways (RCP) and Shared Socioeconomic Pathways. We show that the climate-induced polar motion is sensitive to the choice of climatic scenario; under the optimistic RCP2.6, the rotational pole might wander by $${\sim} $$12 m with respect to 1900, whereas under the pessimistic RCP8.5 by more than twice as much ($${\sim} $$27 m). The most important contributor is the melting of polar ice sheets (Greenland and, to a lesser degree, Antarctica), followed by melting of global glaciers, and variations in terrestrial water storage.

Key Points

• We investigate the climate-induced polar motion under various pessimistic and optimistic climatic scenarios up to 2100

• We show that by 2100, the rotational pole may have wandered $${\sim} $$27 m relative to its position in 1900

• We discuss some of the consequences of this climate-induced polar motion

Plain Language Summary

The rotation axis of the Earth moves relative to the crust, a phenomenon that is known as polar motion. Recent studies have provided evidence of the increasing influence of Earth surface mass redistribution on the polar motion. Due to melting of polar ice sheets (Greenland and Antarctica), global glaciers, and variations in land hydrology, a large-scale continental-ocean mass redistribution happens—collectively known as barystatic processes—that causes perturbations in the Earth's rotation axis and induces polar motion. Here we analyze this climate-induced polar motion from 1900 to the end of 2100 under optimistic and pessimistic climatic scenarios. We show the dependence of the derived polar motion on the climatic scenario, demonstrating that by 2100, under the pessimistic scenario, the Earth's rotation axis might be displaced by $${\sim} $$27 m relative to its position in 1900. The primary contributor is the melting of the Greenland ice sheet, followed by the melting of the Antarctic ice sheet and global glaciers, and variations in terrestrial water storage. Our results shed light on the planetary-scale influence of the present-day climate change and provide new insights into the impact of climate-induced Earth rotation variations on, for instance, the accuracy of positing in space.

1 Introduction

The term polar motion refers to the movements of the Earth's rotation axis exhibited across the crust (Gross, 2015). These movements span all measurable time scales, from subdaily to geological. Short periods up to the Chandler wobble (period of $${\sim} $$433 days) are dominated by high-frequency atmospheric and oceanic processes (Gross, 2000) and long periods (longer than the Chandler wobble) by climate, core, and mantle dynamics (Kiani Shahvandi et al., 2024a).

Over the last decade, with the availability of satellite gravimetry data (e.g., Landerer et al., 2020), evidence has emerged that highlights the growing influence of ongoing climatic variations on polar motion. In this context, climate refers to the so-called barystatic processes (Gregory et al., 2019), that is, the continental-ocean mass redistribution due to the melting of polar ice sheets, global glaciers, and variations in terrestrial water storage (TWS). Adhikari and Ivins (2016) demonstrated that TWS is the cause of the quasi-decadal oscillations in the observed polar motion record. This was followed by a series of studies confirming the role of TWS on polar motion variations (e.g., Deng et al., 2021; Seo et al., 2023). A comprehensive analysis of the causes of polar motion is provided in Kiani Shahvandi et al. (2024a), where the individual contributions of climate, mantle, core, and seismic processes are analyzed. One of the most prominent conclusions of the mentioned study is that barystatic processes account for $${\sim} $$90% of the interannual and multidecadal variations in polar motion. Together with a subtle contribution from the core, these processes explain the long-sought origin of the so-called Markowitz wobble (period of $${\sim} $$30 years). Aside from TWS, the melting of polar ice sheets (Greenland and Antarctica) and global glaciers significantly contributes to polar motion. However, the range of the analysis in this study was limited to 1900–2018, leaving the future contribution of the barystatic processes to polar motion unexplored (i.e., up to the end of the $${21}^{\text{st}}$$ century). Understanding the future evolution of polar motion is important in various fields in the Earth sciences, including sea-level change caused by pole tide, as well as the reduction in the predictability of Earth rotation parameters, which are important quantities for the transformation between terrestrial and celestial coordinate systems and as such, essential for spacecraft navigation and orientation of deep space telescopes (Gross, 2015). The latter is particularly important; considering the uncertain state of the climate in the $${21}^{\text{st}}$$ century, it is necessary to analyze the problem under various climatic scenarios.

In this study, our focus is on the analysis of polar motion caused by individual barystatic processes. Our setup is similar to that of Kiani Shahvandi et al. (2024b), which investigates the variations of length of day under different climatic scenarios. An important point to note is that our focus is on the analysis of the path of the rotational pole caused by barystatic processes, rather than comparing the derived results with astrometric and space-geodetic observations of polar motion, which has been investigated thoroughly in previous studies (Adhikari & Ivins, 2016; Kiani Shahvandi et al., 2024a).

The rest of the paper is organized as follows. First, in Section 2, we describe the data and the methodology that we have used in our analysis. Then, in Section 3, we present and thoroughly analyze the main results. Finally, in Section 4, we provide the conclusions and outlook of the study.

2 Data and Methodology

The data used in this study can be categorized into two ranges: 1900–2018 and 2019–2100. For the former range we adopt the results of Kiani Shahvandi et al. (2024a) that are based on mass variations in polar ice sheets, global glaciers, variations in TWS, and their associated sea-level change (cf. Frederikse et al., 2020, which, as mentioned in Section 1 are demonstrated to explain the majority of observed polar motion record in the range 1900–2018). Whereas for the latter range we compute the polar motion using the sea-level equation on a rotating Earth (Milne & Mitrovica, 1998) and available projections for individual barystatic processes. These projections all have a temporal resolution of 1 year and include:

• Greenland and Antarctic ice sheets provided by various institutions from dedicated campaigns (Goelzer et al., 2020b; Seroussi et al., 2020b), and under Representative Concentration Pathways (RCP, van Vuuren et al., 2011) RCP2.6 and RCP8.5 scenarios,

• global glaciers provided by Randolph Glacier Inventory (RGI 7.0 Consortium, 2023) under RCP2.6, RCP4.5, RCP8.5, as well as Shared Socioeconomic Pathways (SSP, Meinshausen et al., 2020) SSP126, SSP245, SSP370, and SSP585,

• TWS under SSP126, SSP370, and SSP585 provided by Pokhrel et al. (2021).

Note that for individual barystatic processes there are different projections that are unavailable for others. However, based on the available projections and for reasons of consistency, we compute the total barystatic processes only for the RCP2.6 and RCP8.5 scenarios, although we present all the mentioned projections for each individual process. Note that since these two scenarios represent roughly the lower and upper bounds of climatic variations in the $${21}^{\text{st}}$$ century, the derived polar motion series represents the plausible range of paths that the Earth's rotational pole might take under the influence of barystatic processes.

For the analysis of contributions of Greenland and Antarctic ice sheets, we follow a multimodel ensemble approach, where the average of the individual projections by different institutions in the dedicated campaigns (Goelzer et al., 2020b; Seroussi et al., 2020b) is computed for both RCP2.6 and RCP8.5. The spread of these projections determines the uncertainty in the form of standard deviation. For TWS, we compute the average over all three scenarios, because all these projections exhibit similar behavior and their magnitude is smaller than other barystatic processes (we have demonstrated this in Figure 5). A crucial point to mention is that these TWS projections lack the quasi-decadal variability available in the range 1900–2018, since they are primarily focused on the trends observed in TWS under climate change (cf. Pokhrel et al., 2021). This implies that unlike the results in the range 1900–2018 where all the TWS components are considered (i.e., natural variability, dam impoundment, ground water depletion), the mentioned TWS projections are less accurate. Therefore, this shortcoming should be taken into account when analyzing the contribution of TWS based on these projections. Note also that for each climatic scenario mentioned for global glaciers and TWS, a series of so-called experiments are available, where the parameters of the models based on which these projections are computed are varied to give a reasonable range for the spread of these projections. Hence, the standard deviation across these experiments determines the uncertainty under each climatic scenario.

With the aforementioned data sets we are able to compute a continuous time series for both components of polar motion (denoted by $${x}_{p}$$ and $${y}_{p}$$, along the Greenwich meridian and 90$${}^{\circ}$$W, respectively) in the range 1900–2100 and with a temporal resolution of 1 year, using Equation 1a-1d (the sea-level equation):

$$$\begin{array}{r}\hfill L(\theta ,\lambda ,t)=H(\theta ,\lambda ,t)\mathcal{C}(\theta ,\lambda )+S(\theta ,\lambda ,t)\mathcal{O}(\theta ,\lambda ),\end{array}$$$ (1a)

$$$\begin{array}{r}\hfill {\psi }_{13}(t)=-\frac{4\pi {R}^{4}}{\sqrt{15}}{L}_{21}(t),\qquad {\psi }_{23}(t)=-\frac{4\pi {R}^{4}}{\sqrt{15}}{L}_{22}(t),\end{array}$$$ (1b)

$$$\begin{array}{r}\hfill \begin{array}{rl}\hfill & {\chi }_{1}(t)=\frac{1}{C-A}{\psi }_{13}(t)+\frac{1}{{\Omega }(C-A)}\frac{d}{dt}{\psi }_{23}(t),\hfill \\ \hfill & {\chi }_{2}(t)=\frac{1}{C-A}{\psi }_{23}(t)-\frac{1}{{\Omega }(C-A)}\frac{d}{dt}{\psi }_{13}(t),\hfill \end{array}\end{array}$$$ (1c)

$$$\begin{array}{r}\hfill \begin{array}{rl}\hfill & p\frac{d{x}_{p}}{dt}+q\frac{d{y}_{p}}{dt}+{x}_{p}=\frac{{k}_{s}}{{k}_{s}-{k}_{2}}\left(1+{k}_{2}^{\prime }\right){\chi }_{1}(t),\hfill \\ \hfill & q\frac{d{x}_{p}}{dt}-p\frac{d{y}_{p}}{dt}-{y}_{p}=\frac{{k}_{s}}{{k}_{s}-{k}_{2}}\left(1+{k}_{2}^{\prime }\right){\chi }_{2}(t),\hfill \end{array}\end{array}$$$ (1d)

in which $$L$$ is the so-called loading function based on spherical colatitudes and longitudes $$(\theta ,\lambda )$$ and time $$t$$; $$H$$ and $$S$$ are, respectively, the continental and oceanic mass redistributions (with mask functions $$\mathcal{C}$$ and $$\mathcal{O}$$, respectively); $${L}_{21}$$ and $${L}_{22}$$ are the coefficients of the spherical harmonic expansion of the loading function; $$R$$ is the radius of the Earth, $${\Omega }$$ is the mean rotation rate of the Earth, while $$C-A$$ is the difference between polar and mean-equatorial moments of inertia; the constants $$p$$ and $$q$$ assume the values $$p=0.2027$$, $$q=68.9135$$, and $${k}_{s}=0.942$$, $${k}_{2}=0.3055$$, and $${k}_{2}^{\prime }=-0.30$$ are the degree two secular, tidal, and load Love numbers, respectively. We note that the coefficients $$p,q$$ as appearing the Liouville equation above are based on the Chandler wobble period of 433 days with quality factor of 179 (as recommended by Gross, 2015). Note also that $${L}_{21}(t)$$ and $${L}_{22}(t)$$ are computed as in Equation 2a-2b:

$$$\begin{array}{r}\hfill {L}_{2i}(t)=\frac{1}{4\pi }{\int }_{{\Sigma }}L(\theta ,\lambda ,t){y}_{2i}(\theta ,\lambda )d{\Sigma },\quad i=1,2,\end{array}$$$ (2a)

$$$\begin{array}{r}\hfill {y}_{2i}(\theta ,\lambda )=\sqrt{\frac{5}{3}}{P}_{21}(\cos \,\theta )\left({\delta }_{1i}\,\cos \,\lambda +{\delta }_{2i}\,\sin \,\lambda \right),\end{array}$$$ (2b)

where $$d{\Sigma }$$ represents the surface element of a unit sphere (denoted by $${\Sigma }$$), and $${y}_{2i}$$ is the fully normalized spherical harmonic function based the degree 2 order 1 Legendre function $${P}_{21}(\cos \,\theta )$$ and the Kronecker delta denoted by $$\delta $$.

Although the computed polar motion components are based on an elastically compressible rotating Earth (Adhikari et al., 2016), we have been able to confirm the negligible role of viscoelasticity on the time scale of interest here, as pointed out by Kiani Shahvandi et al. (2024b), although on longer time scales (such as millennial) it needs to be considered in modeling (cf. Kiani Shahvandi et al., 2024c). Finally, we note that all the results are presented with respect to the mean in the range 2002–2018, as proposed in Frederikse et al. (2020) and followed in other studies (Kiani Shahvandi et al., 2024a, 2024b).

3 Results and Discussion

In Figure 1 we display the polar motion driven by barystatic processes (i.e., the cumulative contribution of the melting of polar ice sheets, global glaciers, and variations in TWS). The individual contributions for the Greenland ice sheet, Antarctic ice sheet, global glaciers, and TWS are shown in Figures 2-5, respectively. These are presented in the unit of milliarcseconds (mas), which is equivalent to $${\sim} $$3.09 cm on the Earth's surface.

Figure 1

Polar motion driven by barystatic processes. Panels (a) and (b) are for $${x}_{p}$$ and $${y}_{p}$$, respectively. The polar view of this polar motion is shown in panel (c), together with the 2D coordinate system defining polar motion. An example of the pole tide in the year 2100 and under RCP8.5 is shown in panel (d). The unit in panels (a) and (b) is mas, meters in panel (c), and millimeters in panel (d). The shaded areas around the solid lines show the uncertainties at the level of one standard deviation. Note that results in the range 2019–2100 are based on two climatic scenarios RCP2.6 and RCP8.5.

Figure 2

Polar motion driven by the melting of the Greenland ice sheet. Panels (a) and (b) are for $${x}_{p}$$ and $${y}_{p}$$, respectively. The unit is mas. The shaded areas around the solid lines show the uncertainties at the level of one standard deviation. The results in the range 2019–2100 are based on two climatic scenarios RCP2.6 and RCP8.5.

Figure 3

Polar motion driven by the melting of the Antarctic ice sheet. Panels (a) and (b) are for $${x}_{p}$$ and $${y}_{p}$$, respectively. The unit is mas. The shaded areas around the solid lines show the uncertainties at the level of one standard deviation. The results in the range 2019–2100 are based on two climatic scenarios RCP2.6 and RCP8.5.

Figure 4

The polar motion driven by the melting of global glaciers. Panels (a) and (b) are for $${x}_{p}$$ and $${y}_{p}$$, respectively. The unit is mas. The shaded areas around the solid lines show the uncertainties at the level of one standard deviation. The results in the range 2019–2100 are based on seven climatic scenarios: RCP2.6, RCP4.5, RCP8.5, SSP126, SSP245, SSP370, and SSP585.

Figure 5

The polar motion driven by the variations in TWS. Panels (a) and (b) are for $${x}_{p}$$ and $${y}_{p}$$, respectively. The unit is mas. The shaded areas around the solid lines show the uncertainties at the level of one standard deviation. The results in the range 2019–2100 are based on three climatic scenarios: SSP126, SSP370, and SSP585.

According to Figure 1, the path of the future rotational pole exhibits a westward drift compared to its relatively stable, trendless path during the $${20}^{\text{th}}$$ century. Under the RCP2.6 scenario, the direction of this westward drift is more westward (longitudes $${\ge} 45{}^{\circ}$$W) than that based on RCP8.5. According to Figure 4, this is due to the shift of the rotational pole to the west due to a decrease in the melting of Eastern Hemispheric glaciers (including Himalayan) under stringently reduced greenhouse gas emissions stipulated by RCP2.6. Under RCP8.5, the significant melting of the Antarctic ice sheet drives the rotational pole eastward to a greater extent, such that the direction of the rotational pole would mainly be toward longitudes $${\le} 30{}^{\circ}$$W. As suggested by Kiani Shahvandi et al. (2024b), this is potentially due to the rapid melting of the Amundsen Sea Sector (Feldmann & Levermann, 2015), which would be amplified under increased atmospheric greenhouse gas emissions and surface temperatures. The magnitude of the climate-induced polar motion drift under RCP8.5 relative to 1900 is around 27.4 m, while it is around 12 m under RCP2.6. These estimates are also in agreement with the global mean sea-level rise caused by barystatic processes, with varying rates ranging from a few mm per year (under RCP2.6) to more than 10 cm per year (under RCP 8.5). We note that both the melting of global glaciers and variations in TWS will likely drive the rotational pole eastward (cf. Figures 4 and 5), but the magnitude of these drifts is smaller compared to that resulting from the melting of Antarctic ice sheet under RCP8.5. Among the TWS components (which include natural variability, dam impoundment, and groundwater depletion, Frederikse et al., 2020), the sustained depletion of groundwater particularly in the Eastern Hemisphere and in regions such as the Indian subcontinent (Rodell et al., 2009; Wada et al., 2012) is the likely cause of the eastward drift of the rotational pole caused by TWS variations.

From Figures 2-5, the individual contributions of barystatic processes can be discerned. The major contribution arises from the melting of the Greenland ice sheet, which, due to its geographical location, spatial coverage, and melting pattern, has a characteristic sea-level fingerprint (Coulson et al., 2022). Therefore, the melting of Greenland ice sheet drives a nearly symmetrical polar motion, meaning that both $${x}_{p}$$ and $${y}_{p}$$ exhibit similar behavior, resulting in a westward drift toward approximately 45$${}^{\circ}$$W. Under both RCP8.5 and RCP2.6 the aforementioned contribution drives the rotational pole westward, although the effect is more than twice as large for RCP8.5 compared to RCP2.6. Consistent with the observed nonlinearity of the Greenland ice sheet evolution initiated at the onset of the industrial era (Trusel et al., 2018), the polar motion drift is nonlinear, with increasing rates under RCP8.5 and decreasing rates under RCP2.6 in the coming decades of the $${21}^{\text{st}}$$ century.

Under the RCP8.5 scenario, the next significant contribution is from the melting of the Antarctic ice sheet, representing an eastward drift. The rates and directions for the $${20}^{\text{th}}$$ century are consistent with those reported in previous studies (Adhikari et al., 2018). This contribution is considerably smaller under RCP2.6, comparable or even less prominent than that from the melting of global glaciers under the same climatic scenario. In the $${21}^{\text{st}}$$ century, similar to the case of the Greenland ice sheet, the drifts that result from the melting of Antarctic ice sheet and global glaciers exhibit nonlinear behavior. Under the RCP8.5 the rate is higher compared to the rest of the scenarios, although for global glaciers most of the scenarios (aside from RCP2.6) are similar. Although the influence of melting of global glaciers under RCP2.6 is different from the rest of the scenarios, there is large uncertainty surrounding these estimates, representing the complex interconnection between the available greenhouse gases in the atmosphere, surface temperatures, and the melting of global glaciers (e.g., Rounce et al., 2023).

The smallest contribution comes from variations in TWS, which although being the plausible cause of the quasi-decadal oscillations in the polar motion record (Adhikari & Ivins, 2016; Kiani Shahvandi et al., 2024a), represents only a small eastward trend, likely due to the aforementioned depletion of groundwater offsetting the natural TWS variability (Frederikse et al., 2020). The mentioned trend arising from TWS mainly has a linear form in the $${21}^{\text{st}}$$ century, but shows strong variations in the $${20}^{\text{th}}$$ century. In the entire 1900–2100 period covered by this study, the calculated TWS trend has an average magnitude of $${\sim} $$0.25 mas/year and direction toward $${\sim} 53{}^{\circ}$$E. This trend has significantly different magnitude and direction if we choose a subset of the 1900–2100 interval, such as the range 1993–2010, in which case the magnitude is $${\sim} $$1.4 mas/year and roughly toward 60$${}^{\circ}$$E, comparable to those reported in Seo et al. (2023) and in general agreement with the original estimates by Adhikari and Ivins (2016) for the range 2003–2015. Hence, our results not only represent a wider view of the climate-induced polar motion by using an extended study period (1900–2100), but they also confirm the findings of previous studies if a subset of this period is considered. However, as mentioned in Section 2, these TWS projections might not capture all the relevant TWS components, as evidenced in the lack of quasi-decadal variations in the reconstructed polar motion in the range 2019–2100. Nevertheless, they provide valuable insights into the possible changes in the path of the rotational pole caused by variations in terrestrial hydrology.

The results presented in this paper have considerable implications. For one, since the $${x}_{p}$$ component is more strongly affected by barystatic processes than $${y}_{p}$$, the long-range predictability (forecasting horizons longer than a year) of $${x}_{p}$$ is lower, as reported in studies that utilize mathematical prediction models (Kiani Shahvandi et al., 2022, 2023; Kur et al., 2024). Under increased global warming the shorter periods such as those close to—or shorter than—the Chandler wobble might also be affected (Xu et al., 2024), in which case the medium-range (seasonal) predictability of polar motion is reduced as well. Since prediction of polar motion is crucial for applications such as spacecraft navigation and orientation of deep-space telescopes (because of the role of polar motion in connecting terrestrial and celestial coordinate systems; Gross, 2015), the reduced predictability of polar motion under climate change might impact the operational accuracy of such applications. As another implication, the resulting pole tide due to the significant shifts in polar motion in the $${21}^{\text{st}}$$ century might decrease the accuracy of the recovery of the Earth's gravitational field from satellite gravimetry (Wahr et al., 2015). In addition, these shifts might induce measurable global deformations in the Earth, which based on our results (an example for the year 2100 is given in Figure 1d) and the pole tide-based formulation of Wahr (1985), could reach a value of $${\sim} $$2.8 cm in the radial direction and in the mid-latitudes. These deformations might be coupled with the impact of barystatic processes, amplifying the consequences of sea-level change particularly in mid-latitude coastal areas. Finally, the climate-induced pole tide might result in global gravity variations, which based on the estimates in this paper (and using the relations in Wahr, 1985) can assume values of $${\sim} $$5–12 µGal in mid-latitudes, detectable by currently available superconducting gravimeters and potentially providing a source of information for studies probing mantle dynamics (e.g., Ding & Chao, 2017).

4 Conclusions and Outlook

We have analyzed the climatic contributions to polar motion over the period of 1900–2100 under various climatic scenarios. Our results show the dependence of the climate-induced polar motion to the climatic scenario, with polar motion potentially subject to a $${\sim} $$27-m shift relative to 1900 under the pessimistic RCP8.5 scenario. The melting of the Greenland ice sheet is the major contributor to this shift, although the contributions of the Antarctic ice sheet, global glaciers, and TWS are also significant. The path of the rotational pole will be different under the optimistic RCP2.6 scenario, representing a westward drift of $${\sim} $$12 m relative to 1900. However, we note that both RCP2.6 and RCP8.5 represent rather extreme scenarios, and the evolution of polar motion remains uncertain due to the challenges in predicting climate trends (especially TWS) in the coming decades of the $${21}^{\text{st}}$$ century. Our results, however, provide estimates on the possible evolution of polar motion under climate change, along with the potential consequences for positioning in space, Earth surface deformation, and sea-level change.

Finally, it is noteworthy that even though the focus of this paper is on climate-induced polar motion, other contributors—particularly Glacial Isostatic Adjustment (GIA)—could also affect polar motion significantly. The comparison between the magnitudes of GIA and climate-induced polar motion (Figure S1 in Supporting Information S1) reveals that the latter could surpass the former mainly under RCP8.5 climate scenario, implying that polar motion will be dominated by modern climate change. Therefore, when analyzing polar motion and its long-term predictions, both the GIA climatic effects should be considered. For the utmost accuracy, however, the role of core dynamics and seismic processes can also be taken into account, as demonstrated in previous studies (Kiani Shahvandi et al., 2024a).

Acknowledgments

We are grateful to all the data providers whose data we used in this study. We are grateful to Surendra Adhikari for his initial helpful guidance. Open access charges provided by ETH Zurich.

Conflict of Interest

The authors declare no conflicts of interest relevant to this study.

Open Research

Data Availability Statement

The projection data can be accessed as follows: (a) Antarctic and Greenland ice sheets on Seroussi et al. (2020a), and Goelzer et al. (2020a), respectively; (b) global glaciers on RGI 7.0 Consortium (2023); (c) terrestrial water storage variations on Gosling et al. (2025).