F. R. Stephenson

Bio: F. R. Stephenson is an academic researcher from Durham University. The author has contributed to research in topics: Earth's rotation & Eclipse. The author has an hindex of 14, co-authored 40 publications receiving 841 citations. Previous affiliations of F. R. Stephenson include University of Liverpool & University of Newcastle.

Long-Term Fluctuations in the Earth's Rotation: 700 BC to AD 1990

Abstract: Records of solar and lunar eclipses in the period 700 BC to AD 1600, originating from the ancient and medieval civilizations of Babylon, China, Europe and the Arab world, are amassed and critically appraised for their usefulness in answering questions about the long-term variability of the Earth’s rate of rotation. Results from previous analyses of lunar occupations in the period AD 1600-1955.5, and from high-precision data in AD 1955.5-1990, are included in the dataset considered in this paper.

Long-term changes in the rotation of the Earth: 700 B.C. to A.D. 1980

Abstract: Occultations of stars by the Moon, and solar and lunar eclipses are analysed for variations in the Earth’s rotation over the past 2700 years. Although tidal braking provides the dominant, long-term torque, it is found that the rate of rotation does not decrease uniformly as would be expected if tidal friction were the only mechanism affecting the Earth’s rotation. There are also non-tidal changes present that vary on timescales ranging from decades to millennia. The magnitudinal and temporal behaviour of these non-tidal variations are evaluated in this paper.

Historical Values of the Earth's Clock Error Δ and the Calculation of Eclipses:

Abstract: Numerous observations of the Moon, Sun and planets are recorded in ancient and medieval history. These observations which include many eclipses and lunar and planetary conjunctions frequently attract the interest of historians of astronomy. If the positions of the Moon and Sun (and to a lesser extent the planets) in the historical past are to be computed with high precision, it is usually necessary to make satisfactory allowance for the effect of variations in the Earth's rate of rotation, or, equivalently, the length of the day (LOD). Long-term variations in the LOD are mainly produced by lunar and solar tides, but other causes such as the continuing rise of land that was glaciated during the last ice-age are also significant. Although actual changes in the LOD amount to only a few hundredths of a second over several thousand years, the cumulative effect (known as ~T) of these minute changes can be very large. For instance, the estimated value of ~T at the epoch 1000 B.C. is as much as 7 hours. During this interval, the Moon can change position by nearly 4°. It is therefore a matter of concern that at present there appears to be a degree of confusion and misapprehension among historians of astronomy over the choice of values of ~T that should be used in making retrospective computations of lunar and solar positions. Accurate knowledge of the value of ~T is often crucial in assessing the local circumstances of solar eclipses. Neglect of variations in the Earth's spin rate would materially affect the calculated positions of where these phenomena could be seen on the Earth's surface. In this paper we shall try to elucidate the necessary procedures and in particular draw attention to several important points regarding ~T in the calculation of solar eclipses. We shall place special emphasis on three specific issues: the adopted time-scale, the importance of tidal friction in the ephemeris of the Moon, and the enumeration of ~T at various epochs in the past.

Measurement of the Earth's rotation: 720 BC to AD 2015

Abstract: New compilations of records of ancient and medieval eclipses in the period 720 BC to AD 1600, and of lunar occultations of stars in AD 1600–2015, are analysed to investigate variations in the Earth’s rate of rotation. It is found that the rate of rotation departs from uniformity, such that the change in the length of the mean solar day (lod) increases at an average rate of +1.8 ms per century. This is significantly less than the rate predicted on the basis of tidal friction, which is +2.3 ms per century. Besides this linear change in the lod, there are fluctuations about this trend on time scales of decades to centuries. A power spectral density analysis of fluctuations in the range 2–30 years follows a power law with exponent −1.3, and there is evidence of increased power at a period of 6 years. There is some indication of an oscillation in the lod with a period of roughly 1500 years. Our measurements of the Earth’s rotation for the period 720 BC to AD 2015 set firm boundaries for future work on post-glacial rebound and core–mantle coupling which are invoked to explain the departures from tidal friction.

Fundamentals of Geophysics

Abstract: This enduringly popular undergraduate textbook has been thoroughly reworked and updated, and now comprises twelve chapters covering the same breadth of topics as earlier editions, but in a substantially modernized fashion to facilitate classroom teaching. Covering both theoretical and applied aspects of geophysics, clear explanations of the physical principles are blended with step-by-step derivations of the key equations and over 400 explanatory figures to explain the internal structure and properties of the planet, including its petroleum and mineral resources. New topics include the latest data acquisition technologies, such as satellite geophysics, planetary landers, ocean bottom seismometers, and fibre optic methods, as well as recent research developments in ambient noise interferometry, seismic hazard analysis, rheology, and numerical modelling - all illustrated with examples from the scientific literature. Student-friendly features include separate text boxes with auxiliary explanations and advanced topics of interest; reading lists of foundational, alternative, or more detailed resources; end-of-chapter review questions and an increased number of quantitative exercises. Completely new to this edition is the addition of computational exercises in Python, designed to help students acquire important programming skills and develop a more profound understanding of geophysics.

Postglacial variations in the level of the sea: Implications for climate dynamics and solid‐Earth geophysics

Abstract: Throughout the latter half of the Pleistocene epoch of Earth history, beginning ∼900 kyr ago, the climate system has been dominated by an intense oscillation between full glacial and interglacial conditions. During each glacial stage, global sea level fell by ∼120 m on average, as extensive ice sheets formed and thickened on the surfaces of the continents at high northern (primarily) and southern latitudes. Within each cycle this glaciation phase lasted ∼90 kyr and was followed by a much more rapid deglaciation event which terminated after ∼10 kyr and which returned the system to the interglacial state. The period of the canonical glacial cycle has remained very close to 100 kyr since its inception in mid-Pleistocene time. Because of the magnitude of the mass that was redistributed over the surface of the Earth during each such glacial cycle and because of the viscoelastic nature of the rheology of the planetary mantle, these shifts in surface mass load induced variations in the shape of the planet that have been indelibly transcribed into the geological record of sea level variability. Indeed, the geological, geophysical, and even astronomical signatures of this process, which is continuing today, are now being measured with unprecedented precision using the methods of space geodesy and have thereby begun to provide important new scientific insight and understanding, both of the interior of the solid Earth and of the climate system variability with which the ice ages themselves are associated. In this article my purpose is to bring together, in a single review, an assessment of where we currently stand scientifically with regard to understanding both of these aspects of the ice ages. Although the discussion will not address in any detail the fascinating issue of ice age climate, since this topic is sufficiently complex of itself to require a detailed review of its own, I will nevertheless attempt to briefly summarize the current state of understanding of the physical processes that are responsible for the occurrence of the ice age cycle, by way of providing a more complete context in which to appreciate the main lines of argument that will be developed.

Present‐day sea level change: Observations and causes

Abstract: We investigate climate-related processes causing variations of the global mean sea level on interannual to decadal time scale. Wc focus on thermal expansion of the oceans and continental water mass balance. We show that during the 1990s where global mean sea level change has been measured by Topex/Poseidon satellite altimetry. thermal expansion is the dominant contribution to the observed 2.5 mm/yr sea level rise. For the past decades, exchange of water between continental reservoirs and oceans had a small, but not totally negligible contribution (about 0.2 mm/yr) to sea level rise. For the last four decades, thermal contribution is estimated to about 0.5 mm/yr, with a possible accelerated rale of thermosteric rise during the 1990s. Topex/Posei don shows an increase in mean sea level of 2.5 mm/yr over the last decade, a value about two times larger than reported by historical tide gauges. This would suggest that there has been significant acceleration of sea level rise in the recent past, possibly related to ocean warming.

Deceleration in the Earth's oblateness

Abstract: [1] For over three decades, satellite laser ranging (SLR) has recorded the global nature of the long-wavelength mass change within the Earth system. Analysis of the most recent time series of 30 day SLR-based estimates of Earth's dynamical oblateness, characterized by the gravitational degree-2 zonal spherical harmonic J2, indicates that the long-term variation of J2 appears to be more quadratic than linear in nature. The superposition of a quadratic and an 18.6 year variation leads to the “unknown decadal variation” reported by Cheng and Tapley (2004). Although the primary trend is expected to be linear due to global isostatic adjustment, there is an evident deceleration (J¨2=18±1×10−13/yr2) in the rate of the decrease in J2 during the last few decades, likely due to changes in the rate of the global mass redistribution from melting of the glaciers and ice sheets as well as mass changes in the atmosphere and ocean.

Radial profile of mantle viscosity: Results from the joint inversion of convection and postglacial rebound observables

Abstract: We present new inferences of the radial profile of mantle viscosity that simultaneously fit long-wavelength free-air gravity harmonics associated with mantle convection and a large set of decay times estimated from the postglacial uplift of sites within previously glaciated regions (Hudson Bay, Arctic Canada, and Fennoscandia). The relative sea level variation at these latter sites is constrained by age-height pairs obtained by geological survey, rather than the subjective trends which are commonly used in glacial isostatic adjustment (GIA) studies. Our viscosity inferences are generated using two approaches. First, we adopt a relative viscosity profile which is known to provide a good fit to the free-air gravity harmonics and determine an absolute scaling which yields a best fit to the GIA decay time constraints. Second, we perform an iterative, nonlinear, joint inversion of the two data sets. In both cases our inferred profiles are characterized by a significant increase of viscosity (∼2 orders of magnitude), with depth, to values of ∼1022 Pa s in the bottom half of the lower mantle. The new viscosity profiles are shown to satisfy constraints based on the postglacial uplift of both Fennoscandia (the classic Haskell [1935] number) and Hudson Bay which have commonly been invoked to argue for an isoviscous mantle. Furthermore, the models are used to predict a set of long-wavelength signatures of the GIA process. These include predictions of GIA-induced variations in (1) the length-of-day over the late Holocene period; (2) the Earth's precession constant and obliquity over the last 2.6 Myr; and (3) the present-day zonal harmonics of the geopotential, Jl(l≤7). The predictions (1) and (3) bound the late Holocene (and ongoing) mass flux between the large polar ice sheets (Greenland and Antarctic) and the global oceans to small values (≤0.4 mm/yr equivalent eustatic sea level rise).