## Results
### Comparison with Fremantle
Both the MSL and the GPS position results from SONEL are shown in Figure 10. The figure also presents the periodogram of the oscillations about the parabolic trend, for the case of the PSMSL RLR with gaps filled. The periodogram clearly shows a 60-years periodicity, as well as a 13-years periodicity. Then, there is another, but smaller, periodicity of about 24 years. Similar oscillations are expected in Aden, Karachi, and Mumbai. Trends like Fremantle, where the absolute sea levels are not rising, are expected in Aden, Mumbai, and Karachi, where a lack of subsidence may translate to a lack of sea level rise. Recent past subsidence of parts of the Perth Basin has most probably been caused by increased groundwater extraction for domestic and agricultural use [30; 31]. This may explain the positive sea level acceleration of Fremantle, rated at +0.00571 mm/yr\({}^{2}\). Compared to Fremantle, the acceleration of Aden is a huge +0.0164 mm/yr\({}^{2}\) in the PSMSL RLR data and it is +0.0038 mm/yr\({}^{2}\) in the data realigned. The acceleration of Karachi is a huge +0.0642 mm/yr\({}^{2}\) in the PSMSL RLR data and it is still exceptionally large at +0.0510 mm/yr\({}^{2}\) in the data realigned. The acceleration in Mumbai is +0.0068 mm/yr\({}^{2}\) in the PSMSL RLR data and it is +0.0076 mm/yr\({}^{2}\) in the data realigned. Figure 11 presents a comparison of the MSL of Fremantle and Aden (a) and their differences (b), plus a comparison of the MSL of Fremantle and Karachi (c) and their differences (d). The offsets of the Aden segmented record 1933-1937 and 1956-1957 were tested for similarity with Fremantle. As Fremantle had the largest relative sea level rise, the difference in the MSL in Fremantle and Aden increased at a rate of 0.7065 mm/yr. At the offsets, in between 1933-1937, and in between 1956-1957, there were two suspicious \"jumps\" towards more negative values. The offsets of the Karachi segmented record 1920-1937, 1948-1957, and 1995-2007, were tested for similarity with Fremantle. As Fremantle and Karachi had a close relative sea level rise, the difference in the MSL in Fremantle and Karachi was about constant (it only increased at a rate of 0.0987 mm/yr.). At the offsets between 1948-1957 and 1995-2007, there were two suspicious \"jumps\" towards more negative values. The breakpoint alignment technique may be applied to the Fremantle tide gauge record, modified by introducing the gaps of Aden or Karachi (Mumbai is affected to a lesser extent by gaps). Figure 12 presents the analysis of the Fremantle MSL records, with the same gaps as Aden. With data from 1916 to 2013 (the common time window of the two tide gauges), there were four segments and three gaps to consider. The first three segments had in Aden a very close linear trend, from \(-0.78\) to \(+0.49\) mm/yr, which, considering the noticeably brief time windows of 18, 20, and 13 years, indicates the presence of small oscillations over these time windows. Also, the noticeably short last segment, less than a decade long, had a linear trend of \(-3.02\) mm/yr. In the case of Fremantle, with the same gaps as Aden (Figure 12b), the difference in the trends for the first three segments was much larger, from \(+0.11\) to \(+4.88\) mm/yr, reflecting much larger oscillations over these time windows. The noticeably short last segment of trend \(+14.21\) mm/yr confirms this impression. The breakpoint alignment technique may supply satisfactory results only in specific cases, where the segments are long enough, and there are no strong oscillations over the time window to bias the linear trends. Figure 11: _Cont._  
Figure 11: Comparison of the MSL of Fremantle and Aden (**a**) and their differences (**b**). Comparison of the MSL of Fremantle and Karachi (**c**) and their differences (**d**).