Minimum time span of TOPEX/Poseidon, Jason-1 and Jason-2 global altimeter data to detect a significant trend and acceleration in sea level change

The present study aims to estimate a minimum time span of the global mean sea level time series (from TOPEX/Poseidon, Jason-1 and Jason-2 satellite altimetry) which is sufficient to detect a statistically meaningful trend in global sea level variation. In addition, the objective of this paper is also to seek a minimum time span required to detect a significant acceleration in sea level change.Detecting a trend is based upon the Cox\textendashStuart statistical test. In order to make the analysis representative a stepwise procedure is proposed. The input global mean sea level time series is divided into shorter data sets (blocks) of dissimilar lengths. First, a length of block is chosen and the test is performed for the first truncated time series of a fixed length. Subsequently, the block is moved one step forward in each iteration. This produces the dissimilar data sets of the same length. The procedure is repeated for blocks of greater lengths and for each step the Cox\textendashStuart test is applied. The procedure makes the inference independent of the starting data epoch. Considering the set S = 0.002, 0.004, \textellipsis , 0.1 of significance levels, the test is applied to compute the probability of trend detection. Detecting an acceleration is based on the same procedure, however, applied to the differenced global mean sea level time series.We infer that the trend in the global mean sea level time series (January 1993\textendashApril 2010) corrected for the global isostatic adjustment can be detected for all significance levels from the set S with the probability close to 1 after 110 satellite cycles (approximately 2.99 years). The corresponding estimate based on the data without correcting for the global isostatic adjustment is equal to 114 satellite cycles (approximately 3.09 years). Over the majority of the study period it is impossible to detect any acceleration in sea level rise. However, for the time spans of approximately 400 and 500 satellite cycles an acceleration may be detected with probability of approximately 0.4. These specific time spans correspond to the periods with reduced rates of sea level change.