Hi seden, you are having trouble understanding the paper? It does have a lot of science in it and can be hard for the layperson to follow though it's far from being one of the more difficult papers to read.
Anyway, for the period before satellites, the authors used the information from analyses of tidal gauges. Post satellite they used information from satellites as well as analyses of data from tidal gauges.
Here is what they say in the abstract:
We review the sea-level and energy budgets together from 1961, using recent and updated estimates of all terms. From 1972 to 2008, the observed sea-level rise (1.8 ± 0.2 mm yr-1 from tide gauges alone and 2.1 ± 0.2mm yr-1 from a combination of tide gauges and altimeter observations) agrees well with the sum of contributions (1.8 ± 0.4 mm yr-1) in magnitude and with both having similar increases in the rate of rise during the period.
And from page 4 of the article, where they go into more detail:
We use an estimate of global averaged sea level from Church and White [2011]. From 1993 to 2009, they estimated global-averaged sea level with satellite altimeter data using standard techniques. For the period from 1961, they ‘reconstructed’ sea level using coastal and island tide gauges of 8and empirical orthogonal functions of sea level calculated with satellite altimeter data. Fiedler and Conrad [2010] indicate that there can be an important impact on tide-gauge data from terrestrial loading and gravitational changes resulting from dam storage. However, for the large number of tide gauges used here (over 200), we estimate the impact of this correction (which we include) on global mean sea level is only about 0.05 mm yr-1. Similar corrections for changes in the cryosphere are smaller, at least until recently. The satellite and the in situ sea-level time series have also been corrected for glacial isostatic adjustment [Davis and Mitrovica, 1996; M. Tamisiea, personal communication, 2004] so that the sea-level estimates are a measure of changes in ocean volume
Collecting and analysing data is what scientists do. It's not hypothetical nor is it fictitious - it's what they refer to as empirical. Anyone can make careful observations and interpret and analyse them. It's hard slog and requires careful work though. Perhaps the notion is too fantastic for you to contemplate. (Personal incrdulity is a recognised logical fallacy.)
Hope that helps. Let me know if you need anything else explained and I'll do my best to help you out.
