Reply to: Parker A. Comment on “Low-frequency sea level variation and its correlation with climate events in the Pacific”

First, we would like to thank Parker for his discussion and comments on our work. Parker’s main concern [1] is that the sea level is oscillating with important multi-decadal periodicities but absolutely not positively accelerating. He also argued that the global mean sea level (GMSL) acceleration computed by Jin et al. [2] seemed too large. His similar concern had also appeared in the comment of local sea level rise on Long Island, New York [3]. The most important difference between these two commented papers is that the former computes the sea level acceleration globally, while the latter locally. Parker quoted both, individual tide gauges and the time series of GMSL by satellite radar altimeter from the University of Colorado CU Sea Level Research Group. Individual tide-gauge records with enough length and quality can be used to compute the local sea level accelerating trend. However, the length should be longer than 60 years [4] to avoid large oscillations due to long-term tidal effects, which has also been confirmed by Parker himself [5]. As we known, individual tide-gauge records only represent the mean sea level variation within localized area. Parker presented the sea level records of several tide gauges in his Figure 1. The length of sea level time series are all longer than 100 years, and the 2nd order coefficients computed from the time series have both positive and negative values. The results show the largest positive acceleration in San Francisco, CA of +0.007 mm/a, and the largest negative acceleration in Honolulu, HI of 0.006 mm/a. These phenomena demonstrate that the local sea levels are accelerating or decelerating in different sea areas. Nevertheless, the GMSL accelerating trend is still unknown from his Figure 1. Either by tide gauges, or by satellite radar altimetry, many researches have achieved the conclusion that regional mean sea level trends are geographically dependent. Woodworth et al. [6] had pointed out that most of the tide-gauge data from Europe and North America display evidence for a positive acceleration, but the magnitude of the acceleration varies between stations. There are also a few of stations which display negative accelerations. From the most recent results published by AVISO (http://www.aviso.oceanobs.com/ en/news/ocean-indicators/mean-sea-level/) and that shown in Figure 1, we can see large difference, especially between eastern and western parts of the Pacific Ocean. Another fact is that the magnitude of the acceleration/deceleration depends on the time period of observations. For comparison, we select the tide gauges whose periods are longer then 60 years from the Revised Local Reference (RLR) dataset provided by PSMSL (http://www.psmsl.org/ data/obtaining/) [7], and remove the tide gauges whose spare time is greater then 30% to ensure the stability. Then considering the seasonal signals, the sea level records on each selected tide gauge are fitted by the following linear regression model: 2 cos(2 ) sin(2 ) cos(4 )