Firstly a brief introduction to why AAM is important. A more technical background follows.
Why do we study AAM?
For about a century, the rotation of the Earth has been known to vary by small but measurable amounts. Some of the observed changes have long been recognised as being due to the exchange of angular momentum between the solid Earth and the atmosphere. With the advent of modern astronomical techniques and global atmospheric analyses it has become possible to make detailed assessments of the extent to which fluctuations in AAM are responsible for the observed changes in the length of the day (LOD) and instantaneous position of the Earth's pole of rotation.
AAM and its effect on the Earth's rotation is important for a variety of reasons. Geophysicists would like to be able to allow for the atmosphere's contribution to the Earth's motion so that they can study other effects, such as that of the Earth's liquid core. Atmospheric analyses and forecasts may also be used to improve the determination and prediction of changes in the Earth's orientation in space, which is of increasing importance to the space agencies. Finally, fluctuations in AAM can give information about the large scale behaviour of the atmosphere.
Taken largely from Salstein. D.A., Kann,D.M., Miller, A.J. and Rosen, R.D. "The Sub-Bureau for Atmospheric Angular Momentum of the International Earth Rotation Service (IERS): A meteorological data center with geodetic applications." Bulletin of the American Meteorological Society, Vol. 74, No. 1, January 1993.
Angular momentum is a three-dimensional quantity that in the absence of external torques is conserved: it is therefore a fundamental measure of the state of any closed system. Numerous studies have examined the balance of angular momentum within the earth system, involving all parts of the planet, including its atmosphere, oceans, solid shell (crust and mantle), and core. It is the atmosphere, though, that is most variable, exchanging relatively large proportions of its momentum with the solid earth below, compared with the other components. Indeed, on a wide range of time scales between several days and years, considerable agreement exists between changes in the angular momentum of the atmosphere and those of the solid earth, which are evident as small but important changes in the rotation of the planet.
Variations in the axial component of the earth orientation vector, and hence the rotation rate, are reckoned by geodesists as variations in "universal time," or its derivative, the length of day (LOD). Variations in its two equatorial components indicate movements in the position of the earth's pole relative to its crust, a wobble of the planet. Historically, both LOD changes and polar motions were determined from conventional astronomical measurements. In recent years, however, a number of sophisticated space geodetic techniques have supplanted the older optical methods to produce well-resolved and highly accurate values of earth orientation. The scientific need for monitoring changes in earth rotation relates to understanding a number of geophysical processes involving the planet's interior structure, as well as its enveloping oceans and atmosphere. Precise knowledge of the earth's orientation is also important for purposes of navigation, especially in the tracking of interplanetary spacecraft.
It has been recognized since at least the time of Starr (1948) that the angular momentum of the atmosphere need not remain constant and that exchanges with the underlying planet can occur. The variable nature of atmospheric momentum indicates that momentum transfer is intimately linked to the subtle changes that occur in the earth's orientation. The topic of the earth's variable rotation has been reviewed in a number of comprehensive books and papers including those of Munk and MacDonald (1960) and Lambeck (1980), who provide a theoretical basis as well as earlier observational evidence of various forcing terms. Oort (1989), Hide and Dickey (1991), Herring (1991) and Rosen (1993) discuss recent geophysical views and results using modern observing systems.
A formal derivation of the dynamic relation between the atmosphere and solid earth was developed by Barnes et al (1983). Their expressions for the atmospheric excitation functions for changes in earth orientation involve both motion terms represented by volume integrals of winds (W), and mass terms, represented by surface integrals of pressure (P).
The three EAAM functions (X1, X2, X3 - here X should be read as chi) formulated by Barnes et al (1983), can be regarded as the components of the atmospheric angular momentum (AAM) vector. To be more precise, they form a pseudo-vector because the equatorial components of AAM are multiplied by C / (C - A) to form X1 and X2 (where C is the polar moment of inertia of the whole earth and A is the corresponding equatorial moment of inertia). Their formulation includes Love numbers which paramterize the effect of the lack of rigidity of the Earth on its response to atmospheric forcing.
The first two functions, X1 and X2, are the equatorial components and are associated with the excitation of polar motion. The axial component X3 is associated with changes in LOD. The formulas relating earth-orientation parameters and these excitation terms are described in detail in Barnes et al (1983). Briefly, the equatorial relationships involve a transfer function between pole position and its two excitation terms X1 and X2 consisting of a convolution with the earth's free mode (a strong oscillation in polar motion with a 14-month period, discovered by Chandler in the nineteenth century). Less complicated is the axial relationship, in which changes in LOD are merely proportional to the excitation X3.
Significant variations in all three components of the excitation functions occur on many scales. The axial component, X3w, proportional to the relative atmospheric angular momentum due to zonal winds, varies by as much as 100% seasonally, essentially doubling between Northern Hemisphere summer and winter due to the strong annual cycle of the jet stream in that hemisphere. The resulting change between seasonal extremes in LOD can be as much as 2 ms ( Rosen and Salstein 1983). Furthermore, X3w is well correlated with LOD on time scales varying between several days and years ( Rosen et al 1990; Dickey et al 1992b). (The X3P term, related to meridional transports of mass that change the atmosphere's polar moment of inertia, appears to be of lesser importance than the X3w term on most time scales.) Shorter, intraseasonal momentum fluctuations on the 40-60-day time scale are mirrored in the LOD signal as well ( Langley et al 1981 ). Changes in LOD on longer, interannual time scales have been related to the El Ni&ntildeo-Southern Oscillation phenomenon, due to the strong wind anomalies associated with ENSO events (e.g., Salstein and Rosen 1986; Dickey et al 1992a). Some evidence also exists for a signal of the stratospheric quasi-biennial oscillation in the LOD series ( Chao 1989).
With regard to the equatorial components of earth orientation, the strongest signal contains variations on the order of 10 m in pole position, occurring at the resonant 14-month Chandler period, but a suitable explanation for its maintenance against dissipation is not yet available. In contrast, shorter variations of polar motion have been more clearly identified with specific geophysical causes. Earth wobble has a strong annual component associated in part with both groundwater storage and the atmosphere ( Kuehne and Wilson 1991; Chao 1988). On intraseasonal time scales, motions of the pole occur with a magnitude of about 60 cm. The evidence for atmospheric pressure forcing of these rapid polar motions is strong ( Eubanks et al 1988) and contributions from wind may play a role as well ( Gross and Lindqwister 1992).
The degree to which changes in the mass distribution of the global ocean impact LOD changes and polar motion is an important unknown. A zero-order approach to dealing with the problem is to not involve the ocean at all by assuming it rigid. A relatively simple alternative is to assume a state of static ocean equilibrium with the overlying atmosphere, the so-called inverted barometer (IB) hypothesis ( Gill and Niiler 1973). Simply stated, under IB conditions, any change in air mass over the ocean will depress the water surface below areas of high atmospheric pressure and raise sea level beneath low pressure areas. The ocean water so displaced has the same mass as that part of the atmosphere greater than its mean value over the ocean, with an approximate equivalence of 1 mb of atmospheric pressure to 1 cm of sea level. Because of oceanic mass redistribution under IB conditions, the solid earth below the ocean will not be affected by local changes of atmospheric pressure, but rather by the mean change of surface air pressure over the entire ocean. The sensitivity of the pressure excitation terms to the introduction of an IB model is comparable to the terms themselves; however, the degree to which the IB response occurs, and reduces the importance of the pressure variations over the ocean, is still under investigation. Therefore, it has become the general practice to calculate the excitation terms assuming both a non-IB and a pure IB response of the oceans. In fact, though, some sort of dynamic, intermediate, ocean response to variation in atmospheric pressure is perhaps most likely and the object of current research using both analytic means ( Dickman 1988) and modelling approaches ( Ponte et al 1991 ).