The impact of continuous space and time-resolving vertical land motion on relative sea level change
Authors: Oelsmann Julius , Marcos Marta , Passaro Marcello , Sánchez Laura , Dettmering Denise , Seitz Florian 
Published: March 2022

&lt;p&gt;Vertical land motion (VLM) is a major contributor to relative sea level change (RSLC). Hence, understanding and estimating VLM is critical for the investigation of contemporary and projected coastal RSLC and the allocation of its uncertainties. However, there are several challenges involved in the determination of the linear component of VLM. Firstly, the sparse and inhomogeneous distribution of point-wise VLM observations hinder the direct analysis of VLM continuously in space along the coastline. Secondly, the commonly applied working-hypothesis that VLM can be generally assumed as &amp;#8216;linear&amp;#8217;, is not entirely valid for regions, which are affected by nonlinear processes such as earthquakes, surface mass loading changes or other phenomena. Thus, in order to overcome the limitations of data-availability and to account for time-variable VLM, we develop a new approach to estimate continuous time- and space-resolving (3D) VLM over the period 1995-2020.&lt;/p&gt;&lt;p&gt;We apply a Bayesian Principal Component Analysis to a global network of quality controlled VLM observations (GNSS data and differences of satellite altimetry and tide gauge observations) to extract common modes of variability and to cope with the incomplete VLM data. The estimated modes represent a superposition of large scale VLM fingerprints. These include linear motion signatures, e.g., associated with the Glacial Isostatic Adjustment (GIA), as well as regional patterns of coherent responses to earthquakes or terrestrial water storage changes, which exhibit inter-annual to decadal variability. To generate the 3D VLM reconstruction, the VLM fingerprints are interpolated in space with a Bayesian transdimensional regression, which automatically infers the spatial resolution based on the distribution of the data.&lt;/p&gt;&lt;p&gt;Our approach not only provides an essential observation-based alternative to previously employed VLM estimates from GIA models or interpolated VLM maps, but also allows to directly attribute VLM trend uncertainties to the temporal variability estimated over the period of observation. We combine the VLM dataset with century-long tide gauge RSLC observations to demonstrate the limitations of extrapolating nonlinear VLM back in time and to identify regional differences (in the order of mm/year) of contemporary absolute sea level (ASL) change (1900-2015) w.r.t. a recent sea level reconstruction, which employs a GIA-VLM signature only. Using the present-day VLM estimates, we disentangle the contributions of VLM and projected ASL change (from CMIP6 models) and uncertainties to RSLC (2020-2150). The regional RSLC error budget analysis enables the identification of regions where robust assessments of future RSLC are feasible and where VLM uncertainties dominate the projected ASL uncertainties, while explaining up to 75% of the combined uncertainties. Besides these applications, the VLM estimate represents a vital source of information for various sea level studies focused on the analysis of tide gauge or satellite altimetry observations in coastal areas.&lt;/p&gt;