Earth rotation changes since −500 CE driven by ice mass variations

Highlights

• Ancient eclipse records constrain changes in Earth's rotation rate and clock error.

• There is a departure of the clock error from the predicted quadratic trend.

• 11 eclipse records drive the inferred millennial scale variability in clock error.

• Common Era ice mass flux can partially explain the deviation in the records since 700 CE.

• Ice mass flux cannot explain the variability in clock error prior to 700 CE.

Abstract

We predict the perturbation to the Earth's length-of-day (LOD) over the Common Era using a recently derived estimate of global sea-level change for this time period. We use this estimate to derive a time series of “clock error”, defined as the difference in timing of two clocks, one based on a theoretically invariant time scale (terrestrial time) and one fixed to Earth rotation (universal time), and compare this time series to millennial scale variability in clock error inferred from ancient eclipse records. Under the assumption that global sea-level change over the Common Era is driven by ice mass flux alone, we find that this flux can reconcile a significant fraction of the discrepancies between clock error computed assuming constant slowing of Earth's rotation and that inferred from eclipse records since 700 CE. In contrast, ice mass flux cannot reconcile the temporal variability prior to 700 CE.

Introduction

Ancient eclipse observations compiled from Babylonian, Chinese, European, and Arab sources provide the primary constraint on changes in the Earth's rotation rate over the past 3000 yr of Earth history (Stephenson and Morrison, 1984, Stephenson and Morrison, 1995, Stephenson, 1997, Stephenson, 2003). Analyses of these records have yielded a relatively continuous time series since ∼−700 CE of the clock error ($\mathrm{\Delta }\mathrm{T}$; Fig. 1A), defined as the difference in the timing of an eclipse as measured using timescales that are theoretically-invariant (terrestrial time, TT) or fixed to Earth rotation (universal time, UT). A cubic spline fit through the time series (Stephenson and Morrison, 1995, Stephenson, 1997, Stephenson, 2003) indicates that the clock error accumulates to $\sim 18000\text{s}$, or 5 hr, by −500 CE (Fig. 1A, black line). The first derivative of this spline fit yields the change in the rotation period, or length-of-day (LOD; Fig. 1B, black line). Note that the fit to $\mathrm{\Delta }\mathrm{T}$ in Fig. 1A is constrained to reach a minimum at 1820 CE, when LOD in the TT timescale is precisely 86400 s, and thus changes in the LOD are estimated relative to this date (the black line in Fig. 1B is zero at 1820 CE). All numerical calculations described below will be referenced to the same date.

The clock error monotonically increases as one moves back in time from ∼1820 CE, reflecting a shorter rotation period, or LOD, relative to the value over the past few centuries (Fig. 1B). Stephenson and Morrison (1995) and Stephenson, 1997, Stephenson, 2003 characterized the clock error as the combination of a quadratic background trend (Fig. 1A, green line) and a millennial timescale oscillation of $\sim 1000\text{s}$ around this trend (green line in Fig. 2A). In this case, the change in the LOD comprises a linear background trend of ∼1.7 ms/century (cy) (∼40 ms since −500 CE; green line, Fig. 1B) and a millennial timescale oscillation with peak-to-peak amplitude of 10 ms (green line in Fig. 2B).

Tidal dissipation produces a significant slowing of the Earth's rotation over time (Lambeck, 2005). Modern satellite geodetic and lunar laser-ranging measurements imply a rate of change of LOD due to this dissipation mechanism of 2.3 ms/cy (Christodoulidis et al., 1988, Williams and Dickey, 2003). If one assumes that the dissipation rate has remained constant since −500 CE, then the red lines in Figs. 1A–B show the clock error and the change in LOD associated with tidal dissipation over this period, respectively. This quadratic signal in Fig. 1A (red line) is often termed the “tidal parabola”.

The differences between the time series of the clock error and LOD estimated from the ancient eclipse record and the associated signals due to tidal dissipation are shown in Fig. 2 (red lines). The secular trends in these curves (or the black minus red lines in Figs. 1A, B) are characterized by a clock error that grows to $\sim 5400\text{s}$, or ∼1.5 hr, at −500 CE and a change in LOD of ∼0.6 ms/cy. These reflect a non-tidal acceleration of the Earth's rate of rotation, and they have been widely associated with a poleward shift of mass from ongoing glacial isostatic adjustment (GIA) in consequence of the last deglaciation phase of the ice age, which ended ∼5 ka (Stephenson and Morrison, 1984, Stephenson and Morrison, 1995, Stephenson, 1997, Stephenson, 2003, Sabadini et al., 1982, Wu and Peltier, 1984, Vermeersen et al., 1997, Mitrovica et al., 2006), or a combination of GIA and angular momentum exchange between flows in the Earth's outer core and rocky mantle (i.e., core–mantle coupling) (Mitrovica et al., 2015).

The origin of the millennial time scale oscillations in the time series (Fig. 2, green lines), remains enigmatic, and serves as the sole focus of the present study. There have been arguments that these oscillations arise either from core–mantle coupling (Stephenson, 2003, Dumberry and Bloxham, 2006) and/or ice volume changes affecting global sea level (Stephenson, 2003). However, the inferred departure of the clock error from a simple quadratic form is driven by a relatively small set of untimed solar eclipse observations (Stephenson, 1997) (Fig. 3), each of which is subject to a suite of error sources (Stephenson, 1997, Steele and Ptolemy, 2005). (The term “untimed” refers to eclipse observations in which the occurrence of an eclipse was recorded but not the duration; in such cases, timing of the event may be bounded by knowledge of the location of the observation and the nature of the solar eclipse, i.e., total, annular, or partial (Stephenson, 1997).)

Fig. 3 shows the constraint on clock error implied by these observations relative to the best fitting quadratic form. The eleven records have dates of −708 CE, −180 CE, −135 CE, 454 CE, 761 CE, 1133 CE, 1147 CE, 1178 CE, 1221 CE, 1267 CE, and 1361 CE, and the individual constraints imply a minimum departure from the best-fit quadratic of $+439\text{s}$, 0 s, 0 s, $+365\text{s}$, −167 s, −293 s, −194 s, −118 s, −112 s, −108 s, and −133 s, respectively (Stephenson, 1997). The consistency in the seven observations spanning the period 761–1361 CE in Fig. 3 suggests that a departure of the clock error from the best-fit quadratic over this period is relatively robust. However, it is clear that the spline fit adopted in Stephenson and Morrison, 1995, Stephenson, 1997, Stephenson, 2003 (Figs. 1A and 3) may be overestimating the maximum discrepancy of the clock error from a quadratic form within this time interval. The departure from the quadratic form of the observations at both −708 CE and 454 CE is of opposite sign, and it drives the trends in the spline fit for the periods prior to −250 CE and from 0–500 CE, respectively (Fig. 3). In this case, the spline fit may be overestimating the peak amplitude of the millennial scale oscillation prior to 500 CE. For these reasons, we focus in the analysis below on the individual constraints shown in Fig. 3 rather than the millennial time scale signature inferred from the spline fit through these observations.

During the last decade, high-resolution records of local sea-level changes over the last 3 kyr have become available, Kemp et al. (2011) and these have recently been analyzed within a statistical framework (Kopp et al., 2016) to isolate signals associated with ongoing GIA, global sea-level changes, and regional dynamic effects (e.g., ocean circulation changes). The global sea-level changes, which include contributions from ice mass fluctuations and ocean thermal expansion, show an oscillation in sea level of amplitude $\sim 0.1\text{m}$ with several major peaks in the interval 400–1000 CE and minima at (for example) approximately −200 CE, 1100 CE, and 1400 CE (Fig. 4). The curve is also characterized by an exceptionally rapid sea-level rise commencing in the late 19th century (Fig. 4). This bound on the global sea-level variation is consistent, in terms of amplitude, with an earlier published bound based on a less extensive data set (Lambeck et al., 2014) and with a high-resolution sea-level curve from the equatorial Pacific (Woodroffe et al., 2012). Moreover, the global sea-level fall after ∼1000 CE correlates with a $\sim 0.2\text{C}$ decline in global mean temperature seen over the same period (Marcott et al., 2013). We note that typical rates of long-term sea-level rise on Fig. 4 (e.g., from −180 CE to 360 CE) are ∼0.2 mm/yr, nearly an order of magnitude smaller than the rate over the past few decades (Church et al., 2013) (see also Kopp et al., 2016).