S U M M A R YGreen's functions of the indirect effects of atmospheric loading is formulated taking into account the effect of the atmospheric thickness. This is a modification of the classic paper by Farrell that formulated the indirect effects of ocean loading by approximating the loading mass as a thin layer. Atmospheric loading differs from ocean loading in the ways in which gravitational attraction and pressure act. In the case of ocean loading, because both the gravitational attraction and the pressure can be considered to arise from the mass located at the surface of the Earth, the effects of both are treated together and are included in the load Love numbers defined for the problem. In the case of atmospheric loading, if the atmospheric thickness is taken into account, because the mass is distributed over a large elevation and the pressure is exerted at the surface of the Earth, defining a set of load Love numbers including both effects of gravitational attraction and pressure is no longer possible. In this paper, the indirect effects of gravitational attraction and pressure of atmospheric loading are formulated separately by introducing load Love numbers for each of them respectively. Asymptotic expressions of the various load Love numbers one order of magnitude more accurate than those given be Farrell are obtained by searching for the asymptotic solutions of their governing ordinary-differential equations. These are used to improve the convergence of the Legendre sums in the various Green's functions. We find that the consideration of the atmospheric thickness has a negligible effect when compared with the simple thin-layer approximation.

S U M M A R YAbout 10 yr of TOPEX/Poseidon (T/P) altimetry data have been used to compute time series of lake levels at six inland lakes in China. To verify our T/P data processing strategy, the T/P-derived lake levels at Bosten Lake (west China) and Lake Huron (north America) were compared with lake gauge records: good agreement is found between the T/P and the gauge results. Wavelet spectra indicate annual and interannual variations of these lake levels, which are also sensitive to climate variability. At the interannual timescale, the lake levels of Hulun (north China), Bosten (west China) and Ngangzi (east Tibet) are correlated with precipitation and El Niño Southern Oscillation (ENSO); in particular, they all respond to the 1997-1998 El Niño. The Bosten lake level has increased monotonically since 1993 due to the increased temperature on Tianshan Mountain, which feeds water into this lake. The lake levels of Hongze and Gaoyou (east China) show minor decreasing trends. The lake level of La'nga (west Tibet) decreased steadily from 1993 to 2001, with a total drop of 4 m. The Ngangzi lake level decreased from 1993 January to 1997 December, but after the peak of the 1997-1998 El Niño the slope was reversed and the lake level has increased monotonically since then. An example given at Bosten Lake shows that waveform contamination over Chinese lakes affects the quality of T/P-derived lake levels and retracking is necessary to mitigate the problem.

[1] The inner core wobble and the free inner core nutation are studied. A simple Earth model is adopted to derive all the results analytically. As new results over earlier work, the formulas of the frequencies of these two modes taking into account of the rotation rate and the obliquity of the inner core relative to the mantle are obtained. The formula for the inner core wobble is also used to study the inner core rotation relative to the mantle under some other assumptions.