The increasingly dominant role of climate change on length of day variations

Fig. 1 shows our computed barystatic LOD changes for 1900 to 2100. We also show the linear rate (i.e., secular trend) of LOD change and its SD in separate intervals of 20 y. These linear trends are obtained by weighted least-squares, with weights inversely proportional to the squared uncertainties in the data. The individual contributions to the LOD from AIS, GrIS, global glaciers, and Terrestrial Water Storage (TWS) are shown in Fig. 2.

The climate-induced rate of LOD change has varied considerably throughout the 20th century, between 0.31 $\pm$ 0.03 ms/cy (1960 to 1980) and 1.00 $\pm$ 0.04 ms/cy (1920 to 1940) (Fig. 1B and SI Appendix, Tables 1 and 2). These fluctuations reflect the variable rates of global surface temperature change, ice melting, TWS change, and sea level rise that have occurred in the 20th century (30). Melting of global glaciers and GrIS both contribute approximately equally to the positive LOD trend, with AIS playing a secondary, though not negligible, role. The LOD signal from TWS is comparatively weaker, contributing to a small negative LOD trend, mainly due to dam impoundment (31).

An accelerating trend in LOD is seen after around 2000, owing to accelerating rates of glaciers and ice sheet melting and associated sea level rise. Our computed rate of LOD change of 1.33 $\pm$ 0.03 ms/cy during the past two decades is significantly higher than at any time in the 20th century. Fig. 2 reveals that this recent acceleration in LOD is caused by melting of GrIS and AIS, whereas the contribution from global glaciers has remained broadly constant since 1960 (22). These results show, through their effect on the LOD, that the pole-to-equator mass transport from climate change in the past two decades has been unprecedented compared to that of the previous 100 y.

The projections of LOD changes until 2100 are based on the emission scenarios from the Representative Concentration Pathways (RCP) 2.6 and 8.5. Using these rather outdated scenarios instead of the Shared Socioeconomic Pathways (SSP) is constrained by the different available projections of AIS and GrIS mass balance provided in refs. 32 and 33, respectively. We use the multimodel ensemble approach, where the unique projections of various institutions are used to compute the mean and SD of LOD variations. This gives us the future LOD evolution and its uncertainty for both RCP 2.6 and RCP 8.5 separately.

The LOD predictions for the two RCP scenarios differ significantly (Fig. 1). In the low emission scenario, the projection of the rate of LOD change remains close to 1.00 ms/cy in the next few decades and decelerates toward the end of the 21st century. In the high emission scenario, the LOD rate continues to increase and reaches a value as high as 2.62 $\pm$ 0.79 ms/cy by 2080 to 2100. Such a large rate would surpass the rate of 2.40 $\pm$ 0.01 ms/cy from tidal friction (18). It is difficult to anticipate which of the two RCP scenarios is the better representation of future climate change. It might be reasonable to expect that the LOD variations in the next few decades may lie somewhere in between the rates suggested by each of these two extreme scenarios.

Fig. 2 shows the individual barystatic contributions to the LOD projections. Even though AIS does not significantly contribute to LOD in the 20th century, its impact is projected to be increasingly more important in the 21st century because of the rapid melting in the Amundsen Sea Sector and the associated rise in global sea level (34, 35). TWS projections exhibit only a minor effect on LOD. However, it is interesting to observe the change in trend at around 2005 from negative to positive. This implies that the negative LOD trend from dam impoundment is compensated and overtaken by the cumulative depletion in the water content of rivers, lakes, wetlands, soil, and canopies due to climate change which collectively result in a rise of sea level (36). Groundwater extraction is expected to rise significantly due to severe water scarcity in a warming climate (37), which will eventually contribute to the rise in sea level and a positive LOD trend.

Our computed climate-induced LOD change from 1900 to 2018 is much weaker than the decadal LOD changes caused by core–mantle angular momentum exchange. Given the large uncertainty in core flow models (38), it is challenging to extract this signal directly from the record of LOD observations (SI Appendix). In order to confirm our computed signal, we turn our attention to the changes in ${\text{J}}_2$ induced by these barystatic processes; the latter are directly related to the LOD changes that they produce (Eq. 6 in Materials and Methods). Fig. 3A shows the temporal variations of ${\text{J}}_2$ based on Satellite Laser Ranging (SLR) data, computed in the same manner as in refs. 39 and 40, and from which the effect of the 18.6 y tide is removed. In the same Figure, we also show our computed barystatic prediction. Note that our prediction only provides annually averaged estimates, and we cannot resolve the observed seasonal fluctuations in ${\text{J}}_2$. However, annual estimates are well resolved and our focus here is on the interannual changes. Fig. 3A shows that barystatic processes lead to an increase in ${\text{J}}_2$, which is accelerating upward markedly after 2000. Fig. 3B shows the contribution of individual processes. Global glaciers and GrIS are responsible for the largest change in ${\text{J}}_2$, although all processes, including TWS, contribute significantly to the post-2000 increase.

Our prediction differs from the observed ${\text{J}}_2$ in Fig. 3A in that it only contains the contribution from barystatic processes. The observed ${\text{J}}_2$ also includes a linear trend induced by GIA and other processes. This includes decadal pressure changes at the core–mantle boundary induced by core flows, although the amplitude of this signal is expected to be small, of the order of ${10}^{-11}$ (41). To isolate the GIA signal, we subtract our barystatic prediction from the SLR observations. The remaining signal (Fig. 3C) is well approximated by a linear trend on top of which seasonal fluctuations occur.

The conclusions that can be drawn from these results are many-fold. First, they show that the pole-to-equator mass transport from climate change is the dominant contributor to the upward acceleration in ${\text{J}}_2$ observed in recent decades. Second, it demonstrates that this mass transport is well resolved in the barystatic models that we have used. By extension, this validates our predictions of LOD changes made on the basis of these models. Moreover, although the role of climate change on the upward acceleration of ${\text{J}}_2$ has been noted before (40, 42–44), we can now accurately separate the different contributions to this acceleration.

The linear trend in Fig. 3C captures the GIA contribution to ${\text{J}}_2$. A linear fit to this signal gives $(-4.6\pm 0.6)\times {10}^{-11}$ y${}^{-1}$ which corresponds to a LOD trend of $-$0.80 $\pm$ 0.10 ms/cy. This constitutes an independent recovery of the GIA contribution to the rates of change of both ${\text{J}}_2$ and LOD. We assert that GIA models must be consistent with these rates which, in turn, provides an important constraint for the viscosity profile of the mantle (19, 20, 45). We note that the ${\text{J}}_2$ rate that we recover is consistent with that predicted on the basis of the ensemble average from a large number of GIA models (46) (SI Appendix).

The sustained increase in sea level in the 20th century and its accelerating trend after 2000 is connected to climate warming since the start of the industrial revolution (30). Prior to 1800, sea level fluctuated with a timescale of a few hundred years, with no clear trend (47). This implies that barystatic processes did not contribute significantly to the longer term secular LOD trend of $+$1.72 $\pm$ 0.03 ms/cy over the past three millennia derived from the eclipse record (5). This past, long-term secular LOD trend must therefore be dominated by tidal friction and GIA. Indeed, the sum of tidal friction ($2.40\pm 0.01$ ms/cy)(18) and our estimate of the GIA trend ($-$0.80 $\pm$ 0.10 ms/cy) gives a secular trend of $+$1.60 $\pm$ 0.10 ms/cy, and within error bars, this matches the observed secular trend (Fig. 4). This budget closure provides further support for the GIA trend that we recover and, by extension, for the climate-induced LOD changes computed in Fig. 1.

Core–mantle coupling causes LOD fluctuations of a few ms at decadal (11, 12) to millennial (21) timescales. Because the latter may not be properly averaged out over the past three millennia, they may contribute a residual signal to the observed secular trend; this contribution has been suggested to be as high as 0.4 to 0.6 ms/cy (20). The good match of the observed secular LOD trend by the sum of tidal friction and the GIA rate of $-$0.80 $\pm$ 0.10 ms/cy suggests that the residual contribution from core flow, under this scenario, is limited to approximately $+$0.1 ms/cy.

Over the course of Earth’s geological evolution, tidal friction by the moon has been the dominant cause of the secular decrease in the rate of Earth’s rotation and increase in LOD. The waxing and waning of large continental ice sheets and associated viscous mantle adjustment to the Quaternary glaciations over the past 2.5 My induced 10-to-100 kyr fluctuations in LOD (45). Based on reconstructed climate-driven surface mass models, combined with ${\text{J}}_2$ observations, we infer a present-day rate of LOD change from ongoing GIA since the end of the last glaciation of $-$0.80 $\pm$ 0.10 ms/cy.

We have computed the pole-to-equator mass transport since 1900 and shown that it has contributed to a rate of LOD change that hovered between 0.3 and 1.0 ms/cy during the 20th century. This is mostly caused by the melting of global glaciers and the Greenland Ice Sheet, with the melting of the Antarctic Ice Sheet playing a secondary but not negligible role. With the accelerating rate of ice melting since 2000, the climate-induced LOD change has increased to a rate of 1.33 $\pm$ 0.03 ms/cy in the past two decades, therefore not only compensating for the negative LOD trend due to the ongoing GIA, but overtaking it.

This present-day rate is likely higher than at any time in the past few thousand years (47) and, as we have shown, it is projected to remain approximately at a level of 1.00 ms/cy for the next few decades even if greenhouse gas emissions are severely curbed. If, however, greenhouse gas emissions continue to rise, the increase in atmospheric and oceanic warming and associated ice melting will lead to a much higher rate of climate-induced LOD change, perhaps even surpassing the rate of 2.40 ms/cy from tidal friction, and thereby becoming the most important contribution to the long-term LOD variations. The impacts of ongoing surface climate change are far reaching, both on land and in the oceans (22). As we have illustrated here, the mass transport that it causes is also impacting the whole of planet Earth, by changing its oblateness and slowing its rotation rate. This, in turn, affects precise time keeping (44).

The acknowledgement here is adapted from https://zenodo.org/record/3939037 and https://zenodo.org/record/3940766, as a requirement for using the data. The following are acknowledged: 1) Climate and Cryosphere effort for providing support for Ice Sheet Model Intercomparison Project 6 (ISMP6) through sponsoring of workshops, hosting the ISMIP6 website and wiki, and promoting ISMIP6. 2) World Climate Research Program, for coordinating and promoting Coupled Model Intercomparison Project 5 (CMIP5) and CMIP6 through Working Group on Coupled Modelling. 3) Climate modeling groups for producing and making available their model output. 4) The Earth System Grid Federation (ESGF) for archiving the CMIP data and providing access. 5) The University at Buffalo for ISMIP6 data distribution and upload. 6) Multiple funding agencies who support CMIP5 and CMIP6 and ESGF. 7) ISMIP6 steering committee. 8) The ISMIP6 model selection group. 9) ISMIP6 dataset preparation group. We also acknowledge http://grace.jpl.nasa.gov for providing ${\text{J}}_2$ time series. Part of the research was conducted at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration (NASA) and funding support from the NASA Sea-level Change Team, Earth Surface and Interior Focus Area and Cryosphere Sciences Program. M.D. is supported by Discovery grant RGPIN-2018-05796 from Natural Sciences and Engineering Research Council of Canada (NSERC/CRSNG) of Canada.