A comparison of methods to estimate vertical land motion trends from GNSS and altimetry at tide gauge stations

Tide gauge (TG) records are affected by vertical land motion (VLM), causing them to observe relative instead of geocentric sea level. VLM can be estimated from global navigation satellite system (GNSS) time series, but only a few TGs are equipped with a GNSS receiver. Hence, (multiple) neighboring GNSS stations can be used to estimate VLM at the TG. This study compares eight approaches to estimate VLM trends at 570 TG stations using GNSS by taking into account all GNSS trends with an uncertainty smaller than 1 mmyr(-1) within 50 km. The range between the methods is comparable with the formal uncertainties of the GNSS trends. Taking the median of the surrounding GNSS trends shows the best agreement with differenced altimetrytide gauge (ALT-TG) trends. An attempt is also made to improve VLM trends from ALT-TG time series. Only using highly correlated along-track altimetry and TG time series reduces the SD of ALT-TG time series by up to 10 %. As a result, there are spatially coherent changes in the trends, but the reduction in the root mean square (RMS) of differences between ALT-TG and GNSS trends is insignificant. However, setting correlation thresholds also acts like a filter to remove problematic TG time series. This results in sets of ALT-TG VLM trends at 344-663 TG locations, depending on the correlation threshold. Compared to other studies, we decrease the RMS of differences between GNSS and ALT-TG trends (from 1.47 to 1.22mmyr(-1)), while we increase the number of locations (from 109 to 155), Depending on the methods the mean of differences between ALT-TG and GNSS trends vary between 0.1 and 0.2mmyr(-1). We reduce the mean of the differences by taking into account the effect of elastic deformation due to present-day mass redistribution. At varying ALT-TG correlation thresholds, we provide new sets of trends for 759 to 939 different TG stations. If both GNSS and ALT-TG trend estimates are available, we recommend using the GNSS trend estimates because residual ocean signals might correlate over long distances. However, if large discrepancies (> 3mmyr(-1)) between the two methods are present, local VLM differences between the TG and the GNSS station are likely the culprit and therefore it is better to take the ALT-TG trend estimate. GNSS estimates for which only a single GNSS station and no ALT-TG estimate are available might still require some inspection before they are used in sea level studies.