In previous studies, the northern hemisphere of the Earth is considered to be in compression while the southern one is in expansion. In this study, based on three different methods, we calculate average vertical variations of the two hemispheres from velocity field data under the ITRF2008 (International Terrestrial Reference Frame 2008) solution. Results show that the northern hemisphere is in expansion at the rate about 1 mm/yr, while the compression rate of the southern hemisphere is one order smaller than the expansion rate of the northern one. After the post glacial rebound effect is subtracted, results show that the expansion and compression rates of the northern and southern hemispheres are 0.46 mm/yr and -0.19 mm/yr, respectively. Transformation between the velocity fields under ITRF2008 and ITRF2000 can explain why different authors have different conclusions about the expansion/compression pattern of one hemisphere or the other. Anyway, the entire Earth is expanding at a rate about 0.2 mm/yr, and this estimation coincides with results of our previous studies. The mean variation rates of the radii at different latitudes have been calculated.

The fluctuation characteristics and excitations of the intradecadal changes in the length-of-day variation (∆LOD) were thought to be related to the secular variations in the core geomagnetic field and hence help to constrain the magnetic field strength in the core as well as to understand the mechanism driving the Earth's core-mantle interactions (e.g., R. S. Gross, 2015; Mound & Buffett, 2006). Two periodic signals have been detected from the ∆LOD in the intradecadal period band (i.e., the 5-10 years period band), an approximately six year oscillation (SYO, e.g., Holme & de Viron, 2013; Liao & Greiner-Mai, 1999) and an approximately 8.5 years oscillation (EYO, Ding, 2019). Their fluctuation characteristics are thought to help determine their possible mechanism (e.g., Gillet et al., 2010), but the fluctuation characteristics of these two signals are still controversial. Liao and Greiner-Mai (1999) first found a nearly stable ∼5.8 years oscillation in the 1970-1990 ∆LOD (see their Figure 5a) and suggested that the Southern Oscillation Index may have had some correlation with it. Abarca del Rio et al. (2000) also showed that the 6-7 years oscillation had no stable decreasing trend in the 1900-2000 time span (see their Figures 3 and 5), and its fluctuation characteristic was similar to a

<p>We propose a new approach for testing the gravitational redshift based on frequency signals transmission between a spacecraft and a ground station. By a combination of one uplink signal and two downlink signals, the gravitational redshift can be tested at about 6.5×10<sup>-6</sup> level for a GNSS satellite (the signals’ frequencies are about 1.2~1.6 GHz), and about 2.2×10<sup>-6</sup> level for the International Space Station (the signals’ frequencies are up to 14.7 GHz), under the assumption that the clock accuracy is about 10<sup>-17</sup> level. For better desinged cases the accuracy of gravitational redshift test can be improved to several parts in 10<sup>-8</sup> level (the signals’ frequencies are about 8~12 GHz). Compared to the scheme of Gravity Probe-A (GP-A) experiment conducted in1976, the new approach does not require any onboard signal transponders, and the frequency values of the three links can be quite arbitrarily given. As the hardware requirement is reduced, a number of spacecrafts could be chosen as candidates for a gravitational redshift experiment. This approach could also be used in gravitational potential determination, which has prospective applications in geodesy. This study is supported by National Natural Science Foundation of China (NSFC) (grant Nos. 42030105, 41721003, 41631072, 41874023, 41804012), Space Station Project (2020)228, and Natural Science Foundation of Hubei Province(grant No. 2019CFB611).</p>