Earth rotation and global change. Clark R. Wilson. Introduction. Theory and Connections with Geodetic Problems

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1 REVIEWS OF GEOPHYSICS, SUPPLEMENT, PAGES , JULY 1995 U.S. NATIONAL REPORT TO INTERNATIONAL UNION OF GEODESY AND GEOPHYSICS Earth rotation and global change Clark R. Wilson Department of Geological Sciences, Center for Space Research, and Institute for Geophysics The University of Texas, Austin Introduction Variations in the rotation of the Earth include changes in the rate of rotation (altering the Length of the Day, LOD), in orientation of the rotation axis relative to a terrestrial frame (Polar Motion, PM) and in orientation relative to a celestial frame due to external torques (Nutation and Precession). Variations occur over a wide range of time scales, from hours to the age of the Earth. Scientific interest in and understanding of Earth rotation variations have proceeded rapidly over the last several decades due, in large part, to enormous improvements in observations by space geodetic means, including satellite laser ranging (SLR), very long baseline interferometry (VLBI), lunar laser ranging (LLR), and satellite positioning methods, especially the global positioning system (GPS). The study of the Earth's rotation is a mature interdisciplinary field, and extensive reviews of many aspects of the field are contained in the AGU monographs 'Contributions of Space Geodesy to Geodynamics' (Smith and Turcotte, 1993). Articles by Eubanks (1993), Dickey (1993), Hide and Dickey (1991), and monographs by Lambeck (1988,1980) and Munk and Mac Donald (1960) provide excellent background material on these problems, as well. The reader may also wish to review other IUGG Report articles in this series on related subjects, specifically those on the global gravity field, VLBI technology, satellite orbit dynamics, and GPS. It is now virtually certain that air and water cause most observed PM and LOD variations at periods of a few years and less, excluding tidal variations in LOD due to the long period solid Earth tides (McCarthy and Luzum, 1993; Robertson et al, 1993). Thus, PM and LOD variations measure changes in global integrals of air and water mass distribution and momentum. The purpose of this article is to review the contributions that PM and LOD observations can make to understanding atmospheric, oceanic, and hydrologic system variations. The discussion is divided into three parts: a review of the relationships among air and water distribution and motion, Earth rotation changes and other geodetic problems; discussion of changes at periods of a few years and less; followed by discussion of changes at longer periods. Theory and Connections with Geodetic Problems The geographic coordinate system is defined by the set of three mutually orthogonal basis vectors (ei, e2, e3). ei and e2 are in the equatorial plane with ei intersecting the Greenwich meridian, e2 intersecting the 90 East meridian, and e 3 intersecting the geographic north pole. Quantities with subscripts Copyright 1995 by the American Geophysical Union. Paper number 95RG /95/95RG-00104$l , 2, and 3 are components along these axes. Earth rotation variations are excited by the motion of air and water as they exchange angular momentum with the solid Earth, while conserving absolute angular momentum within the Earth system. The linearized Liouville equations, expressing this conservation of angular momentum are, following Gross (1992), and Barnes et al, (1983) [1.00]AI(t)/(C-A) + [1.43] h(t)/q(c-a) = (i/a c )(dm(t)/dt)+m(t) (1) [.7]AI 3 (t)/c + h 3 (t)/(qc) = -m 3 (t) (2) with the usual convention that (mi, m2, 1 + m 3 )Q is the rotation vector of the Earth as reported by the International Earth Rotation Service (IAU,1993), Q is the mean angular velocity, and the quantities (mi, m2, m 3 ) are all small dimensionless numbers of the order of 10"^ or so. In simple terms, equation (1) describes the Chandler Wobble (free Eulerian nutation) of the Earth when motion of matter causes the greatest moment of inertia (principal) axis to be displaced from the rotation axis. A similar wobble is readily seen in a poorly thrown toy disk (Frisbee) when rotation and principal axes are misaligned. Similarly, equation 2 describes changes in the Earth's spin rate as axial angular momentum is exchanged between the solid Earth and various constituents in the Earth system, such as the atmosphere or oceans. The very simple form of equation (1) comes from the use of complex notation to describe polar motion, in which the real axis is identified with the Greenwich meridian and the imaginary axis with 90 degrees East longitude. In this notation, m is the quantity (mi + i m2). Other terms in (1) and (2) are: relative angular momentum in the Earth system due to winds and currents described by the vector (hi, h2, h 3 ); the complex quantity h = (hi + ih2); the polar moment of inertia of the Earth, C, and the equatorial moment of inertia A, excluding the fluid core, which is assumed uncoupled from the mantle; the complex quantity Al =(AIi 3 + ial2 3 ) which describes fluctuations in products of inertia associated with the (ei,e 3 ) plane (AIi 3 )? and the (e2,e 3 ) plane, (Al2 3 ); AI 3, which describes changes in the moment of inertia about e 3 ; finally, a c is 27cF(l+i/2Q), the complex Chandler Wobble frequency with F near.843 cycles per year (cpy) and Q, the dimensionless quality factor, near 175. Alternative expressions for the left hand side can be given in terms of torques applied by air and water to the Earth. There are a few interesting remarks to be made concerning equations (1) and (2), pertaining to underlying theory, and connections with other geodetic problems. First, the left hand side of (1) has only recently been shown to be valid for polar motion observations reported in terms of the celestial ephemeris pole (Eubanks, 1993; Gross, 1992; Brzezinski, 1992; Brzezinski and Capitaine, 1993). 225

2 226 WILSON: EARTH ROTATION AND GLOBAL CHANGE Second, (1) does not apply to PM near retrograde frequencies of 1 cycle per day (cpd), close to the free core nutation frequency. Such motion is best treated as nutation, (Herring and Dong, 1994; Watkins and Eanes, 1994; Sovers et al, 1993; Gross, 1993). Third, quantities in brackets [] reflect the loading response of the Earth, with numerical values dependent upon an adopted physical model. These values may also be frequency dependent. In principle, they may be experimentally obtained, given accurate observations of quantities on both left and right hand sides, but this is difficult given available observations of the atmosphere and oceans (Chao, 1994). Fourth, the complex Chandler frequency is also dependent upon the physical properties of the Earth. Current estimates of F = cpy and Q = 175 were obtained assuming that the excitation process is random, Gaussian, and stationary (Jeffreys, 1940;Wilson and Vicente, 1990). Kuehne et al (1993) have shown that the excitation is actually not stationary, showing strong seasonal variance fluctuations. Thus, improved estimates of a c should be possible, and continue to be of interest as a measure of global rheology at a frequency well below the seismic band. Fifth, the inertia terms on the left hand side of (1) and (2) are proportional to changes in the spherical harmonic coefficients of the global gravity field, commonly called the Stokes coefficients. In particular, those in (1) are proportional to the degree 2-order 1 coefficients, and in (2) to the degree 2-order zero (zonal) Stokes coefficient. Therefore, estimating inertia changes which cause Earth rotation variations is a subset of a more general problem of current interest, estimating time variations in the Earth's gravity field and center of mass (Chao and Au, 1991; Mitrovica and Peltier, 1993; Peltier, 1994; Nerem et al, 1993; Trupin et al, 1990; Trupin, 1993; Chen et al, 1994; Dong et al, 1994; Vigue et al, 1992). One of the principal data types used in the gravity field problem is SLR observations of geodetic satellites (Gutierrez and Wilson, 1987). This makes SLR important to Earth rotation studies in two separate ways, by providing accurate observations of the right hand side of (1) and (2), as is now routine, and by providing estimates of the inertia tensor terms on the left hand side, which is a promise for the future. In the case of LOD (equation 2), the prospects for success are excellent, because changes in even zonal Stokes coefficients perturb the precession rate of the satellite node (Lambeck, 1988, Chapter 6). On the other hand, SLR data are unlikely to provide direct estimates of AI(t) at short periods because changes in the tesseral (non zonal) spherical harmonics do not perturb satellite orbital elements in a simple way. However, changes in AI(t) may be inferred from PM at long periods, because in this limit m(t) becomes directly proportional to AI(t). This is a consequence of the rate term dm/dt becoming small, and the likelihood that relative motion contributions, h(t), also diminish at long periods. Sixth, there is a developing synergy between geodetic technology and global numerical models of the atmosphere, oceans, and hydrologic cycle. The same air and water loads causing PM and LOD changes are now recognized as a major contributor to non-tidal, non-tectonic displacements at geodetic observatories (vandam and Herring, 1994; Blewitt, 1994; vandam et al, 1994). Another air-water connection to geodetic positioning is via GPS- and VLBI-determined delay corrections for tropospheric water vapor (MacMillan and Ma, 1994). With the impending proliferation of GPS receivers world-wide, these corrections should provide useful measures of atmospheric water vapor for assimilation into global hydrologic and atmospheric models. Thus, global summaries of air and water distribution, now used to explain PM and LOD changes, will eventually improve the space geodetic methods by which PM and LOD are observed, and, in turn, will benefit from new water vapor data provided by the geodetic stations. PM and LOD at Periods Less Than a Few Years The spectrum of LOD variations at periods of a few years and less shows a continuum of variations with peaks at the seasonal frequencies (1, 2, 3...cpy) (Hide and Dickey, 1991). Thus, it is natural to analyze LOD change as a broad-band process, with separate treatment of purely harmonic seasonal components. On the other hand, in addition to seasonal components, the spectrum of PM is sharply peaked at the Chandler frequency, a feature which has historically been interpretted to mean (e.g. Runcorn et al, 1990) that PM near the Chandler frequency requires special explanation. In fact, the excellent signal to noise level provided by modern data permits PM be analyzed over a continuum of periods extending from hours to decades. Digital signal processing problems associated with the narrow-band character of PM data can be resolved via a simple linear filter to remove the resonant amplification at the Chandler frequency (Jeffreys, 1940; Wilson, 1985). To understand the excitation sources of Earth rotation variations, one compares observed LOD and PM time series with global gridded numerical model or data time series giving atmospheric, oceanic, and hydrologic mass and momentum quantities on the left hand side of (1) or (2). The following is a summary of the results obtained from studies of this type. Ocean tides are the apparent cause of semidiurnal and diurnal tidal PM and LOD, based upon the reasonably good agreement between observations and numerical ocean tide model predictions of PM and LOD. (Brosche et al, 1991; Watkins and Eanes, 1994; Herring and Dong, 1994, Sovers et al, 1993; Gross, 1993; Dickman, 1993). Ocean tides also contribute to longer period variations in LOD dominated by the solid body tides (Nam and Dickman, 1990). Additional diurnal or subdiurnal non-tidal PM and LOD variations may be atmospherically driven, as deduced from four-per-day samples of numerical general circulation models (Salstein, 1994). Further understanding of the atmosphere's role at hourly time scales should develop as sub-daily observations of LOD and PM become routinely available from GPS data (Lichten et al, 1992). At daily and longer time scales, a combination of atmospheric, oceanic, and ground water sources appears to force PM, although many details are uncertain. There is some problem in accounting for the full variance of observed PM, but the correlation of PM with meteorological observations and models is quite convincing (Chao and Au, 1991; Chao and O'Connor, 1988; Chao, 1993; Gross and Lindqwister, 1992: King and Agnew, 1991; Kuehne and Wilson, 1991; Preisig, 1992; Kuehne et al, 1993). The motion and mass distribution of the oceans are a poorly-determined yet potentially significant part of both PM and LOD excitations. The ocean mass contribution consists of two parts, a response to barometric pressure forcing, an inverted barometer response in the static limit, and all other changes driven by winds, density variations, etc. An inverted barometer response appears to be a good assumption at periods of a few days and longer (Dickman, 1988; vandam and

3 WILSON: EARTH ROTATION AND GLOBAL CHANGE 227 Wahr, 1993; Wunsch, 1991; Fu, 1994, Hoar and Wilson, 1994), but other oceanic contributions are virtually unconstrained. Only a small amount of water (a few centimeters over ocean basins dimensions) is required to account for the missing PM excitation, with a somewhat larger amount needed to explain interannual LOD changes (Dickey et al, 1994a,b). Coastal tide gauge data seem poorly suited to estimate basin scale changes (Trupin and Wahr, 1992), but centimeter-level load changes have been observed in the open ocean using bottom pressure gauges (Luther et al, 1990; Eubanks et al, 1993). In place of observations, numerical ocean models have been used to estimate contributions to PM, LOD and related gravity field changes (Ponte, 1994; Ponte and Gutzler, 1991; Steinberg et al, 1994). Unfortunately, currents which produce centimeter-level mass redistribution are tiny when compared with the largely divergence-less currents of the general circulation. Thus, mass redistribution effects that are of interest in earth rotation problems are second-order in oceanic general circulation models. An additional difficulty is that these numerical models often do not conserve mass on a global scale (S. Nerem, personal communication, 1994). The atmosphere is the principal excitation source for LOD variations up to periods of a few years, with excellent agreement in amplitude and phase at periods from a few weeks to more than a year (Dickey et al, 1991; Dickey et al, 1992a; Dickey et al, 1992b; Salstein et al, 1993; Eubanks, 1991; Eubanks, 1993; Freedman et al, 1994). Transfer of angular momentum occurs by both mountain and surface friction torques, but mountain torques may dominate (Salstein and Rosen, 1994; Salstein, 1994). Interannual variations known to be associated with the El Nino-Southern Oscillation events are not fully explained (Rosen, et al, 1990; Rosen, 1993; Dickey et al, 1994a,b), and correlation between atmospheric and LOD observations diminishes at periods shorter than about 15 days (Hide and Dickey, 1991). The results summarized above confirm that air and water are the cause of virtually all PM and LOD changes at periods shorter than a few years, but many details of mass and momentum exchange among the three constituents, earth, air, and water, remain unknown or poorly understood. Numerical models of the climate and oceans will play a central role in understanding PM and LOD variations, and the processes of mass and momentum exchange. Conversely, Earth rotation observations should contribute to numerical model development by providing global measures of momentum and mass redistribution over a continuum of short to long time scales. LOD and PM at Longer Periods At periods longer than a few years, extending to many tens of years, the so-called 'decadal variations', the sources of excitation for both LOD and PM are more enigmatic. The difficulty is that at these periods other effects may be important, including visco-elastic behavior such as post-glacial rebound, and exchange of angular momentum with the fluid core. In particular, it has become common to invoke the core as the major cause of decadal LOD changes. Although some climatic forcing of long period LOD has been recognized, (Salstein and Rosen, 1986; Eubanks, 1993), it is uncertain at what time scale air and water become less important than the core. Unfortunately, the role of the core remains largely unqualified because it is too remote to be easily observed. A further difficulty in assessing the air/water role at long periods is that the torques required to cause decadal LOD variations are utterly insignificant when compared with those applied by the atmosphere at shorter time scales (Hide and Dickey, 1991). This means that atmospheric/oceanic torques of geodetic significance are of second-order importance in general circulation studies. Quantification of momentum budgets among Earth, air, and water reservoirs is thus lacking at long periods. The requirements for progress in this field coincide completely with the central problems of global climate change. Long period PM is conveniently divided into a linear drift, probably a post-glacial rebound effect (Wu and Peltier, 1984) plus irregular motions with periods of years to decades. The postglacial rebound effect provides some constraint on ice loading and rheological models of the earth, (Peltier and Jiang, 1994) but surface geodetic measurements are likely to be perhaps more effective in constraining the time and space distributions of recent glacial ice loads (Mitrovica et al, 1994). Neglecting the core, it is likely that the irregular decadal PM superimposed on the drift is forced by long term variations in water mass distribution, although the details remain obscure. Decadal PM is clearly polarized along the same longitude that would result from a global rise or fall in sealevel (Chao and O'Connor, 1988). However, the implied sealevel variations, ten or so centimeters over decades, are larger than those inferred from coastal tide gauges (Eubanks, 1993; Wilson, 1993). Storage in terrestrial water reservoirs is a likely contributor, but only surface storage has been accessible to observation. However, the potential contribution of surface reservoirs, alone, is surprisingly large (Chao, 1988). World-wide, subsurface (aquifer) water storage exceeds that in surface reservoirs and may be more important (Kuehne and Wilson, 1991). Another aspect of terrestrial water storage is the balance of water stored in glacial ice. At the present time, earth rotation variations (both PM and LOD), coupled with SLR-determined gravity field changes, provide better constraints on ice balance than do field observations by glaciologists (Trupin, 1993). This condition will probably persist until the development of remote sensing methods for ice sheet monitoring (Schutz and Zwally, 1993). Summary The significance of the study of Earth rotation variations in modern geophysics is four-fold: Modern space-geodetic Earth rotation observations provide access to globally integrated properties of the Earth system (total absolute angular momentum of air and water) over a range of periods. These observations provide not only a unique measure of long period fluctuations, normally thought of as global change, but also of the temporal continuum of such variations to periods as short as a few hours. The nature of Earth rotation changes as integral measures of variability is unusual. Most surface and many satellite remote sensing observations of the Earth system record variations at isolated locations and times. Only a few measurements, including variations in the Stokes coefficients and Earth rotation changes, offer genuinely global measures. Earth rotation studies are interdisciplinary, requiring the application and development of technology, theory, and observational programs in a variety of fields. Excellent space geodetic data are the product of many independent efforts, including: international cooperation; military-driven programs on positioning and laser tracking; fundamental radio astron-

4 228 WILSON: EARTH ROTATION AND GLOBAL CHANGE omy of extra-gallactic objects; and the civilian space program. The task of interpretting these data belongs to a multitude of scientists: theorists interested in the physical properties of the Earth; oceanographers interested in fundamental and military aspects of the seas; atmospheric scientists interested in basic and applied (forecasting) problems, and hydrologists and glaciologists, addressing both fundamental and applied problems. Earth rotation studies are intimately connected to those of the gravity field, with again, both fundamental and applied (orbit prediction) aspects. Beyond these interconnections, Earth rotation research will also contribute to understanding global climate change, which connects all fundamental and applied earth and life sciences. Earth rotation studies, by their global nature and significance in national security, time keeping, reference frames and positioning, require the convergence and international cooperation of scientists, societies, and cultures. The founding of the International Latitude Service at the end of the last century, and the continuing tradition of international cooperation and organization in the International Earth Rotation Service (and related activities) demonstrate that this science is able to transcend national and cultural boundaries in times of overwhelming political global change. Acknowledgments. This review was prepared with support from NASA Grant NAGW-3131, and with additional support from the Geology Foundation of the University of Texas. References Barnes, R., R. Hide, A. White, and C. Wilson, Atmospheric angular momentum functions, length-of-day changes and polar motion, Proc. R. Soc. Lond., A387, 31-73, Blewitt, G. Atmospheric Loading Effects and GPS Time-Averaged Vertical Positions, Eos Trans. AGU, 75, 16, 104, Brzezinski, A., Polar motion excitation by variations of the effective angular momentum function: considerations concerning deconvolution problem, Manuscripta Geodetica, 17, 3-20, Brzezinski, A. and N. Capitaine, The Use of the Precise Observations of the Celestial Ephemeris Pole in the Analysis of Geophysical Excitation of Earth Rotation, J. Geophys. Res., 98, , Brosche, P., J. Wunsch, J. Campbell, and H. Schuh, Ocean tide effects on Universal Time detected by VLB I, Astron. Astrophys., 245, , Chao, B. F., Excitation of the Earth's Polar Motion due to Mass Variations in Major Hydrological Reservoirs. J. Geophys. Res., 93, ,1988. Chao, B.F., Excitation of Earth's Polar Motion by Atmospheric Angular Momentum Variations, , Geophys.. Res. Lett, Chao, B.F., Transfer Function for Length-of-Day Variations: Inference for Earth Dynamics, Eos Trans. AGC/,75,16,111, Chao, B. F., and A. Y. Au, Atmospheric Excitation of the Earth's Annual Wobble: , J. Geophys. Res., 96, , Chao, B.F. and A. Y. Au, Temporal Variation of the Earth's Low Degree Zonal Gravitational Field Caused by Atmospheric Mass Redistribution: , J. Geophys. Res, 96, ,1991. Chao, B., F. and W. P. O'Connor, Effect of a uniform sea-level change on the Earth's rotation and gravitational field, Geophys. J., R. astr. Soc., , Chao, B. F., and W. P. O'Connor, Global surface water-induced seasonal variations in the Earth's rotation and gravitational field, Geophys. J. R. astr. Soc, 94, , Chen, M.K., C.K. Shum, B.D., Tapley, and C.R. Wilson, Global Constraint on Modeling the Time Varying Gravitational Field from Analysis of SLR to Geodetic Satellites, Eos Trans. AGU, 75,16,114, Dickey, J.O., M. Ghil, and S.L. Marcus, Extratropical Aspects of the Day Oscillation in Length of Day and Atmospheric Angular Momentum, /. Geophys. Res., 96, , Dickey, J.O., S. L. Marcus, J. A. Steppe, and R. Hide, The Earth's Angular Momentum Budget on Subseasonal Time Scales, Science, 255, , Dickey, J.O., S.L. Marcus, T.M. Eubanks, and R. Hide, Climate Studies via Space Geodesy: Relationships Between ENSO and Interannual Length-of-Day Variations, 'Fluxes of Matter Between Global Climate Subsystems, American Geophysical Union Monograph, 1994a. Dickey, J.O., S.L. Marcus, R. Hide, T.M. Eubanks, and D.H. Boggs, Angular momentum exchange among the solid Earth, atmosphere and oceans: A case study of the El Nino event, J. Geophys. Res., 99, B12, , Dickey, J.O., S. L. Marcus, and R. Hide, Global Propagation of Interannual Fluctuations in Atmospheric Angular Momentum, Nature, 357, ,1992. Dickey, J.O., Atmospheric Excitation of the Earth's Rotation: Progress and Prospects via Space Geodesy, in Contributions of Space Geodesy to Geodynamics: Earth Dynamics, D. Smith and D. Turcotte, eds., American Geophysical Union Monograph, Geodynamics Series, v. 24, Dickman, S. Theoretical investigation of the Inverted Barometer hypothesis, /. Geophys. Res., 93, , Dickman, S. Dynamic Ocean Tide Effects on Earth Rotation, Geophys. J. Int., 112, , Dong,D., J.O. Dickey, and R.S. Gross, Variations of the Earth's gravity field for from LAGEOS, Eos Trans. AGU, 75,16,114, Eubanks, T. M., Interactions between the atmosphere, oceans and crust: possible oceanic signals in Earth rotation, in The Orientation of the Planet Earth as Observed by Modern Space Techniques, M. Feissel, ed. Pergamon, Eubanks, T. M. Variations in the Orientation of the Earth, in Contributions of Space Geodesy to Geodynamics: Earth Dynamics, D. Smith and D. Turcotte, eds., American Geophysical Union Monograph, Geodynamics Series, v. 24, Eubanks, T.M., D.S. Luther, H.O. Mofjeld, F.I. Gonzalez, and A.D. Chave, Geodetic Observability of Deep Sea Bottom Pressure Changes in the Pacific, Eos Trans. AGU, Eubanks, T.M., Fluid Normal Modes and Rapid Variations in the Rotation of the Earth, IUGG Assembly, Vienna, Program with abstracts, Eubanks, T.M., Global Warming Signals in Earth Rotation, Eos Trans. AGU, 74,43,181,1993. Freedman, A.P., J.A. Steppe, J.O. Dickey, T.M. Eubanks, and L.-Y. Sung, The short-term prediction of universal time and length of day using atmospheric angular momentum, J. Geophys. Res, 90, , Fu, L.L., A Progress Report of the Results from the Topex/Poseidon Mission, Eos Trans. AGU, 75,107, Gross, R. S., Correspondence betweeen Theory and Observations of Polar Motion, Geophys. J. Int., 109, , Gross, R. S., The Effect of Ocean Tides on the Earth's Rotation as Predicted by the Results of an Ocean Tide Model, Geophys. Res. Lett., 20, , Gross, R. S., and U. Lindqwister, Atmospheric Excitation of Polar Motion during the GIG91 Measurement Campaign, Geophys. Res. Lett., 19, , Herring, T. and D. Dong, Measurement of Diurnal and Semidiurnal rotational variations and tidal parameters of the Earth, J. Geophys. Res., 99, B9, Hide, R., and J. O. Dickey, Earth's variable rotation, Science, 253, , Hoar, T., and C. R. Wilson, Geosat Observations of sea level response to barometric pressure forcing, Geophys. Res. Lett., 27,23, , Gutierrez, R., and C. R. Wilson, Seasonal air and water mass redistribution effects on Lageos and Starlette, Geophys. Res. Lett., 14, , International Astronomical Union, Report of the IAU Commission 19- Earth Rotation , IAU Transaction, XXII A, Jeffreys, H., 1940, The variation of latitude, Monthly Notices R.. astr. Soc. 100, 139, King, N.E. and D.C. Agnew, How Large is the Retrograde Annual Wobble?, Geophys. Res Lett. 18, 9, , Kuehne, J., and C. R. Wilson, Terrestrial Water Storage and Polar Motion, J. Geophys. Res., 96, , Kuehne, J., S. Johnson, and C. R. Wilson, Atmospheric Excitation of Nonseasonal Polar Motion, J. Geophys. Res., 98, , 1993.

5 WILSON: EARTH ROTATION AND GLOBAL CHANGE 229 Lambeck, K., The Earth's Variable Rotation, Cambridge University Press, Cambridge, Lambeck, K., Geophysical Geodesy, Oxford Science Publications, Clarendon Press, Oxford, Lichten, S.M., S. L. Marcus, and J. O. Dickey, Sub-Daily Resolution of Earth Rotation Variations with Global Positioning System Measurements, Geophys. Res. Lett., 19, , Luther, D.S., A.D. Chave, J.H. Filloux, and P.F. Spain, Evidence for Local and Nonlocal Barotropic Responses to Atmospheric Forcing during Bempex, Geophys. Res. Lett., 17, , MacMillan, D.S., and C. Ma, Evaluation of very long baseline interferometry atmospheric modeling improvements, J. Geophys. Res. 99, , McCarthy, D.D. and B.J. Luzum, An analysis of tidal variations in the length of day, Geophys. J. Int., 114, , Mitrovica, J.X., J.L. Davis, and I.I. Shapiro, A spectral formalism for computing three-dimensional deformations due to surface loads, 2, Present-day glacial isostatic adjustment, J. Geophys. Res, 90, , Mitrovica, J.X. and W.R. Peltier, Present-Day Secular Variations in the Zonal Harmonics of the Earth's Geopotential, J. Geophys. Res., 98, , Munk, W., H. and G.J.F. MacDonald, The Rotation of the Earth, Cambridge University Press, Cambridge, Nam, Y. S., and S. R. Dickman, Effects of Dynamic long-period ocean tides on changes in Earth's rotation rate, J. Geophys. Res., 95, , Nastula, J., A. Korsun, B. Kolaczek, W. Kosek, and W. Hozakowski, Variations of the Chandler and annual wobbles of polar motion in and their prediction, Manuscripta Geodaetica, 18, , Nerem, R.S., B.F. Chao, A.Y. Au, J.C. Chan, S.M. Klosko, N.K. Pavlis, and R.G. Williamson, Temporal Variations of the Earth's Gravitational Field from Satellite Laser Ranging to Lageos, Geophys. Res. Lett., 20,1, , Peltier, W.R., Ice Age Paleotopography, Science, 265, , Peltier, W.R. and Xianhua Jiang, The Precession Constant of the Earth: Variations through the ice age, Geophys. Res. Lett.,21,21, , Ponte, R.M., Barotropic Motions and the Exchange of Angular Momentum Between the Oceans and the Solid Earth, J. Geophys. Res., 95, , Ponte, R.M., Understanding the relation between wind- and pressuredriven sea level variability, /. Geophys. Res., 99, , Ponte, R. M., and D. S. Gutzler, The Madden-Julian Oscillation and the Angular Momentum Balance in a Barotropic Ocean Model, J. Geophys. Res., 96, , Preisig, J.R., Polar motion, atmospheric angular momentum excitation and earthquakes - correlations and significance, Geophys. J. Int., 108, , Robertson, D.S., J.R. Ray, and W.E. Carter, Tidal variations in UT1 observed with very long baseline interferometry, J. Geophys. Res., 99, , 1994 Rosen, R.D., The Axial Momentum Balance of the Earth and its Fluid Envelope, Surveys in Geophysics, 14, 1-29, Rosen, R.D., D. A. Salstein, and T. M. Wood, Discrepancies in the Earth-Atmosphere Angular Momentum Budget, J. Geophys. Res., 95, , Runcorn, S.K., et al., The Excitation of the Chandler Wobble, Surveys in Geophysics, 9, , Salstein, D. A., D.M. Kann, A.J. Miller, and R. D. Rosen, The Sub-bureau for Atmospheric Angular Momentum of the International Earth Rotation Service: A meteorological data center with geodetic applications, Bull. Am. Met. Soc, 74, 67-80, Salstein, D.A. and R.D. Rosen, Earth Rotation as a Proxy for Interannual Variability in Atmospheric Circulation, 1860-Present, J. Climate and Applied Meteorology, 25, 12, , Salstein, D. and R. Rosen, Topographic Forcing of the Atmosphere and a Rapid Change in the Length of Day, Science, 264, , Salstein, D.A., Atmospheric Forcing of Earth Rotation During the January 1994 Intensive Campaign, Eos Trans. AGU, 75, 111, Schutz, B. E. and J.H. Zwally, Geosciences Laser Altimeter System (GLAS): A Spaceborne Laser Altimeter for Ice Sheet Mass Balance Applications, Eos Trans. AGU, 74, 181, Smith, D.E. and D. Turcotte, editors, Contributions of Space Geodesy to Geodynamics, American Geophysical Union, Geodynamics Series, v. 23, 24, 25, Sovers, O.J., C.S. Jacobs, and R.S. Gross, Measuring Rapid Ocean Tidal Earth Orientation Variations With Very Long Baseline Interferometry, J. Geophys. Res., 98, , Steinberg, D.J., J.A. Marshall, N. Pavlis, B.F. Chao, The Role of Global Wind-Driven Ocean Circulation in the Earth's Angular Momentum Budget and Time Varying Gravity Field, Eos Trans. AGU, 75, 16, 115, Trupin, A.S., and J. M. Wahr, Spectroscopic analysis of global tide gauge sea level data, Geophys. J. Int., 108, 1-15, Trupin, A. S., M. F. Meier, and J. M. Wahr, Effect of melting glaciers on the Earth's rotation and gravitational field: , Geophys. J. Int., 100, , Trupin, A.S., Effects of polar ice on the Earth's rotation and gravitational potential, Geophys. J. Int., 113, , vandam, T.M. and T.A. Herring, Detection of atmospheric pressure loading using very long baseline interferometry measurements, J. Geophys. Res, 99, , vandam, T.M. and J. Wahr, The atmospheric load response of the ocean determined using Geosat altimeter data, Geophys. J. Int, 113, 1-16, Vigue, Y., S. M. Lichten, G. Blewitt, M.B. Helfin, and R. P. Malla, Precise Determination of Earth's Center of Mass Using Measurements from the Global Positioning System, Geophys. Res Lett., 19, 14, , Watkins, M. and R. Eanes, Diurnal and Semidiurnal variations in Earth orientation Determined from LAGEOS Laser Ranging, /. Geophys. Res., 99, B9, , Wilson, C.R. Contribution of Water Mass Redistribution to Polar Motion Excitation, in Smith, D.E. and D. Turcotte, editors, Contributions of Space Geodesy to Geodynamics, American Geophysical Union, Geodynamics Series, v. 24, Wilson, C.R., Discrete Polar Motion Equations, Geophys. J. R. astr. Soc, 80, , Wilson, C. R. and Vicente, R. O., Maximum Liklelihood Estimates of Polar Motion parameters in Variations in Earth Rotation, McCarthy and Carter eds., American Geophysical Union Geophysical Monograph 59, , Wilson, C.R. and R. Haubrich, Meteorological Excitation of the Earth's Wobble, Geophys. J. R. astr. Soc, 46, , Wu, P. and W.R. Peltier, Pleistocene deglaciation and the Earth's rotation: a new analysis, Geophys. J. R. astr. Soc. 76, , Wunsch, C, Global-Scale Sea Surface Variability from Combined Altimetric and Tide Gauge Measurements, J. Geophys. Res., 96, , C. R. Wilson, Department of Geological Sciences, University of Texas at Austin, Austin, TX ( clarkw@maestro.geo.utexas.edu) (Received June 10, 1994; accepted November 21, 1994)