Introduction

It has long been theorized that the Earth's rate of rotation has been slowly decreasing through time. However, only recently have apparent accelerations been discovered. Growth lines in fossil bivalves have been shown to record the number of days between full moons (the synodic month). From such information, the rate of paleorotation can be derived. Direct measurement of the Earth's rotation over the past 120 years has shown that accelerations and decelerations also occur on a shorter period. The goal of this review is to examine the paleorotation record, evaluate causes of variability, and discuss the climatic consequences of variable rotation.


Determination of the Earth's Rotation History

Direct measurements
To determine the length of day (LOD) using the stars, the time elapsed between two consecutive transits of a star across a meridian (through the rotation axis) must be measured precisely [Lambeck, 1980]. Early measurements of the elapsed time were made using the universal time scale (mean solar time). Changes in the LOD are small (millisecond range), therefore, measurements must be averaged over several days and between several locations. With the advent of high precision pendulum clocks at the turn of the century, seasonal variations in the LOD were discovered [Lambeck, 1980]. Quartz crystal clocks of the 1940's to 1950's contributed to the discovery of possible monthly variations in LOD [Lambeck, 1980]. Since 1955, workers have used cesium atomic clocks to record daily fluctuations [O'Hora, 1975]. Decade fluctuation measurements (measured every 10 years) of LOD date back to the seventeenth century.

Indirect measurements
Pre-seventeenth century estimates of LOD involve the use of "paleontological clocks." As corals, molluscs, and stromatolites grow, they record environmental factors such as the alternation between night and day, and the tides. The growth behavior of bivalves has received the most attention, because they record the cleanest signal [Berry and Barker, 1975]. Figure 1 shows how the growth lines of a modem bivalve correlate with tidal predictions. Barker [1964] observed fine-scale clustering of growth lines in modem bivalves approximately every 15 or 29-30 lines, depending on the species. He suggested that these clusterings were related to the synodic month (full moon to full moon). Counting the number of lines between the tighter groups results in an estimate of the number of days in a synodic month. Because bivalves are preserved relatively well in the geologic record, estimates of the number of days per month can be determined through time. The number of days per month can be easily converted into rotation rate.

Rotation History

Phanerozoic
Figure 2 shows the variation in the number of days per synodic month over the last 500 million years. One interpretation of the data is a simple linear decrease in the rate of Earth rotation, the scatter being caused by experimental error. Alternatively, lines may be fit through linear sections [Creer, 1975]. The outcome of the latter interpretation is that there are apparent accelerations of the Earth's angular velocity between approximately 420 and 365 Ma, and 55 and 220 Ma. Possible causes for these variations will be discussed in a later section.

The Last 120 Years
Direct measurements of the LOD also show accelerations and decelerations [Muller and Stephenson, 1975]. Figure 3 shows the variation in the LOD over the last 120 years.

Causes of Variable Rotation

Because the available data show variation that spans durations differing by orders of magnitude, there must be at least two causes for the observed changes. Both are postulated to stem from the outer core-lower mantle boundary. Topography on this boundary, possibly caused by descending subducted oceanic crust, is thought to play a major role in the behavior of the Earth's geomagnetic field [Butler, 1992]. The geomagnetic field as measured at the surface, therefore, may reflect conditions at the core-mantle boundary. The portion of the geomagnetic field most affected by topography is the non-dipole field. The migration and intensity fluctuations of the non-dipole field are thought to be the causes of geomagnetic reversals and secular variation [Butler, 1992]. Topography at the core-mantle boundary may control the migration of the non-dipole field.  The time-averaged location of the non-dipole field is thought to be the cause of "polarity bias" (Figure 4) [Jacobs, 1984]. Therefore, the changes in polarity bias (which appear to be sharp) likely reflect changes in topography at the core-mantle boundary (perhaps due to a redistribution of oceanic trenches).  Creer [1975] made a tentative correlation between changes in polarity bias and changes in rotation rates (compare times labeled 1-4 in Figures 2 and 4). Creer [1975] explained the accelerations as resulting from conservation of angular momentum. A decrease in the moment of inertia perpendicular to the spin axis (as a result of mass transfer due to topographic changes) will result in an increase in the Earth's angular velocity.

The non-dipole field also controls secular variation of the geomagnetic field on a much shorter time scale (~10,000 years) [Butler, 1992]. Courtillot et al. [1982] correlated (correlation coefficient of ~0.8) the modern rotation record with secular variation of geomagnetic declination measured over the same period of time (Figure 5). The geomagnetic fluctuations preceded the LOD curve by approximately 10 years. These authors proposed that torque produced by electromagnetic coupling between the outer core and the lower mantle may result in accelerations or decelerations. The degree of coupling may be related to the rate of change of the non-dipole field.

In addition to correlating LOD with secular variation, Courtillot et al. [1982] correlated changes in the LOD with the mean global temperature record for the past 120 years (Figure 6). Unfortunately, little is known about global temperature throughout most of the Phanerozoic. These authors obtained a correlation coefficient of 0.85 and observed that temperature variation lagged behind LOD change by 5 years. Geomagnetic secular variation and the LOD, therefore, have the potential to be used as a predictive tool for future changes in global temperature [Courtillot et al., 1982; Rozelot and Spaute, 1990]. It is impressive that LOD variations on the order of microseconds can result in temperature variations on the order of tenths of degrees. It should, however, be recognized that the temperature record may not reflect rotation variations at all. Yet, intuitively, it is easy to accept that circulation of the outer core, mantle, lithosphere, and atmosphere are interrelated. A model of the Earth's energy budget may aid in proving causality.

Conclusions

The Earth's rate of rotation has varied through time. Variable rotation over the last 120 years has been reasonably well correlated with global temperature variations [Courtillot et al., 1982]. If there is indeed a rotation component to global temperature, paleorotation rates estimated from growth lines in fossil bivalves could possibly be used in an Earth energy budget model in order to help constrain Phanerozoic paleotemperature variations. Direct measurements of LOD and secular variation may aid in predicting future changes in global temperature. More high quality data are required to adequately test the hypothesis that circulation of the core, mantle, lithosphere, and atmosphere are interrelated.


Acknowledgements- Special thanks to Dr. Andrew Warnock for insightful conversations.  This project received funding from the Department of Climate Change undergraduate research fund.

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