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 sub-diurnal 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 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.