Variable Vertical Land Motion Over the 20th Century Inferred at Tide Gauges

Variable Vertical Land Motion Over the 20th Century Inferred at Tide Gauges | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Physical Sciences - Article Variable Vertical Land Motion Over the 20th Century Inferred at Tide Gauges Sönke Dangendorf, Julius Oelsmann, Jerry Mitrovica, Torbjorn Tornqvist, and 6 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6024708/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted You are reading this latest preprint version Abstract Vertical land motion (VLM) is a key driver of relative sea-level (RSL) changes in coastal areas. Rates of VLM can vary in time due to both anthropogenic (e.g., subsurface fluid extraction) and natural (e.g., sediment compaction, volcano-tectonic activity) processes. However, such nonlinear behavior has not been included in 20th century sea-level budgets or in sea-level projections due to a lack of long-term observations over relevant temporal and spatial scales. Here, we use a probabilistic reconstruction of large-scale climate-related sea level (CSL) from 1900 to 2021 to estimate VLM at a global set of tide gauge stations. We interpret differences between CSL and tide-gauge records (CSL-TG) primarily in terms of VLM and argue that the CSL-TG residuals quantify previously overlooked temporal variations in VLM primarily related to subsurface fluid withdrawal, seismic, and volcanic activity. We demonstrate that decadal variations in the resulting regional RSL trends can be an order of magnitude larger than variations due to CSL, introducing misestimates of up to ~ 75 mm yr − 1 in sea level projections based on linear extrapolations. Our variable VLM estimates provide new constraints on geophysical models of anthropogenic and volcano-tectonic crustal motions and pave the way for more robust, site-specific sea-level projections. Earth and environmental sciences/Environmental sciences/Environmental impact Earth and environmental sciences/Natural hazards Earth and environmental sciences/Ocean sciences/Physical oceanography Earth and environmental sciences/Solid Earth sciences/Seismology Figures Figure 1 Figure 2 Figure 3 Figure 4 Introduction Sea-level rise threatens hundreds of millions of people in low-lying coastal regions worldwide 1 – 3 , increasing flood risk and other related hazards 4 , 5 . Coastal areas are also prone to land subsidence: current estimates indicate that over the past two decades coastal residents experienced on average four times faster rates than due to climate-related sea level (CSL) rise alone 6 . A multitude of natural and anthropogenic factors cause land to subside or uplift 7 – 9 . Natural factors, including glacial isostatic adjustment (GIA), sediment compaction, aseismic creep, volcanic activity and earthquakes drive vertical land motion (VLM) in coastal areas 9 , 10 . However, anthropogenic activities such as groundwater pumping, oil and gas withdrawal, land reclamation or artificial drainage of wetland or urban areas also drive VLM and have become the dominant causes of rapid changes in RSL rates in many densely populated coastal zones 9 , 11 – 13 . Having a solid observation-based understanding of the overall mechanisms, magnitudes, and scales of VLM is therefore critical for producing useful future coastal sea-level projections. The Global Navigation Satellite System (GNSS) and Interferometric Synthetic Aperture Radar (InSAR) currently monitor VLM in time and space, but these data have only been available for 10 to 30 years and they do not always capture the full VLM signal 14 . Despite this short record length, the inferred VLM rates have been extrapolated under the assumption that current rates apply to past and future sea-level periods 8 , 13 , 15 . Tide-gauge records, which measure sea level relative to a stable reference point, have also been used to constrain VLM. However, the VLM signal in tide-gauge records should be separated from changes due to ocean dynamics and thermal expansion, the inverted barometer effect, and present-day barystatic gravitational, rotational, and deformational fingerprints 16 – here collectively termed CSL. To isolate these VLM effects, past studies corrected tide gauge records of interest using nearby, tectonically stable reference stations 17 – 20 . This technique has several drawbacks. It assumes that nearby stations exist and have sufficiently long records, that they share a similar CSL signal and have no datum shifts, and tectonic activity has not precluded identifying stable sites. These drawbacks can generally be overcome by replacing reference stations with altimetry-based sea-surface height measurements, the so-called altimetry-minus-tide gauge (ALT-TG) technique 21 . Ref. 22 recently jointly assessed ALT-TG and GNSS based estimates at a global scale to reveal substantial nonlinear VLM signals in response to several different processes including fluid withdrawals, and post-seismic activity. However, the short altimetry record limits the assessment to the period after 1995, leaving any analogous signals at lower frequencies and/or earlier in the 20th century unexplored. Here we use a globally resolved sea-level reconstruction from 1900 to 2021 3 to isolate the CSL signal ( Methods ). We argue that differences between CSL signals and tide-gauge records are largely related to VLM. Compared to other approaches (GNSS, InSAR, ALT-TG), our method provides longer-term VLM estimates extending back to 1900. The method is also free of assumptions commonly made with the reference station technique. We apply this approach to 633 tide-gauge records included in the Permanent Service for Mean Sea Level (PSMSL) ‘Revised Local Reference’ database. At each tide gauge site, the observations are subtracted from the nearby CSL reconstruction (CSL-TG) such that the sign of the resulting residual indicates the sense of VLM (negative for subsidence and positive for uplift) ( Methods ). We account for potential shifts in tide gauge observations using change point analysis ( Extended Data Fig. 1 , Methods ). We also adjust the data for the fact that tide gauge records are affected by local ocean processes that may not be fully observed by satellite altimetry and, hence, not represented in the CSL reconstruction ( Extended Data Fig. 2 , Methods ). Establishing vertical land motion estimates at tide gauges We first calculate linear trends in CSL-TG time series as a measure of VLM rates over the period 1993 to 2021 for all records with at least 75% data coverage (370 of the 633 records, Fig. 1 a). Rate patterns are characterized by regional post-glacial uplift signals in formerly glaciated centers including Scandinavia and Hudson Bay, while large subsidence signals are, for instance, prevalent in river deltas with active sediment compaction and/or fluid extraction along the northern Gulf of Mexico and South Asia. To quantify consistency between CSL-TG-based VLM estimates and other approaches, we compare our CSL-TG rates to three other VLM trend datasets (ALT-TG, and two different GNSS datasets). The CSL-TG trends correlate nearly perfectly with ALT-TG estimates (coefficient of determination of R 2 ~ 0.99) with differences of 0.1 ± 0.43 mm yr - 1 (median ± root mean square) ( Extended Data Fig. 3 a), a result that is unsurprising since the leading spatial patterns from satellite altimetry have been used as a prior in the CSL reconstruction. We also compare our VLM rate estimates to two independent GNSS-based products: University of La Rochelle (ULR) 23 and the Nevada Geodetic Laboratory (NGL) 24 . ULR estimates are developed specifically for sea-level assessments at tide gauges. Of their 601 GNSS sites, 65 are in close vicinity (< 5 km) to the tide gauge sites ( Methods ). The corresponding pairs of CSL-TG and GNSS estimates of VLM are highly correlated (R 2 ~ 0.83) and we detect no systematic bias (-0.05 ± 1.07 mm yr - 1 , Extended Data Fig. 3 b). The error of 1.07 mm yr - 1 is lower than those previously reported for ALT-TG/GNSS comparisons 25 , 26 , which can partly be explained by the stricter distance criterion adopted here (5 km vs. 50 km in ref. 25). NGL provides interpolated VLM estimates along the entire global coastline (Fig. 1 a) together with quality classification metrics for each site 24 . Here, we only consider locations that are classified as ‘good’ ( Methods ), which results in an overlapping set of 156 sites. We find similar statistics as for ULR (R 2 = 0.85; trend differences of -0.06 ± 1.07 mm yr - 1 ) ( Extended Data Fig. 3 c). These comparisons suggest that the multidecadal trends in CSL-TG time series are primarily due to VLM. We also note that our estimates are likely conservative (i.e., the accuracy is higher than reported here) since the GNSS datasets used for validation are based on different and varying observation periods (usually after 2000) and sometimes interpolated to the location of interest. Variability in estimated vertical land motion rates We next consider whether the CSL-TG time series show variable rates over time. We calculate linear trends over the preceding period from 1964 to 1992 and subtract them from the trends for 1993 to 2021. Of the 204 records that fulfill the 75% data availability criteria over both periods, 107 show statistically significant differences (probability P > = 0.95, Methods ) (Fig. 1 b, c). Median absolute differences are usually on the order of 1 mm yr - 1 but can become as large as 24.6 mm yr - 1 (Ayukawa, Japan). Significant differences can be found along major subduction zones in the Indo-Pacific region and the Mediterranean, but also in areas previously reported to be influenced by subsurface fluid withdrawals (e.g., Gulf of Mexico 19 , U.S. east coast 27 , and Southeast Asia 6 ). A cluster of significant differences of ~-1 to 2 mm yr - 1 is also found in the Baltic Sea. Nonlinear GIA effects may play a partial role 28 , although they are expected to be an order of magnitude smaller than the differences reported here. Generally, the trend differences in Fig. 1 b, c demonstrate that rates of VLM have not been constant over time at ~ 50% of the sites investigated here. For a more detailed view of variable VLM rates, Fig. 2 shows four examples that represent a range of behaviors found in CSL-TG time series. Eight additional examples are provided in Extended Data Figs. 4 and 5. Bangkok, Thailand (Fig. 2 a) and Venice, Italy (Fig. 2 b) are locations where rapid subsidence due to groundwater and gas withdrawals was later moderated through mitigation measures 20 , 29 , 30 . Bangkok experienced ~ 1 cm yr - 1 of post-seismic subsidence following the 2004 Sumatra earthquake off Indonesia 31 , 32 . Pago Pago, American Samoa, and the east coast of Japan were subject to strong seismic effects. The complex 2009, magnitude 8.1 Samoa-Tonga megathrust and normal earthquake increased local subsidence rates due to the constructive interference between the two earthquake sources 33 , which doubled the rate of RSL rise (Fig. 2 c, CSL-TG and ALT-TG time series). Japan’s 2011, magnitude 9 Tōhoku earthquake induced a devastating tsunami and widespread VLM 34 , 35 . The CSL-TG based VLM estimates suggest co-seismic subsidence of up to 1 m and decadal time scale post-seismic uplift, features that match the amplitude and time scale of GNSS measurements near the tide gauge of Ofunato, Japan (Fig. 2 d). A spatially and temporally broader global picture of potential nonlinearities in VLM emerges when we estimate the standard deviation of decadal rates in the CSL-TG time series ( Methods , Fig. 3 a). The largest standard deviations are found in deltaic regions (e.g., Nile, Hooghly, Mississippi), the Arctic Ocean, and along subduction zones in the Indo-Pacific, the Caribbean Sea, and the Mediterranean Sea. Deltaic regions often show variable VLM rates due to compaction and increased anthropogenic activity over the 20th century 36 – 38 . In the Arctic Ocean, several factors may play a role, including ocean dynamic effects from large river flows 39 possibly not captured by our corrections ( Methods ) due to the sparse stream gauge records in this region 40 , increasing permafrost subsidence 41 , or uncertainties in the ice histories describing the barystatic fingerprints in CSL 3 , 42 . Locations in subduction zones, however, show the largest variability in the rates, likely because of the influence of co- and post-seismic VLM, whose onset typically occurs more abruptly with a slower elevation change for months to years after the megathrust earthquake (Fig. 2 c, d; Extended Data Fig. 4 a, c, d) as compared to more steady changes associated with compaction and fluid extraction (Fig. 2 a, b). To further consider the potential impact of major earthquakes, we use the USGS earthquake catalog to identify 167 tide gauges that may have been close enough (within 4°) to be influenced by earthquakes of magnitude 7+ ( Methods ). These locations are characterized by higher standard deviations in decadal CSL-TG rates (Fig. 3 a inset); the median at sites impacted by seismic activity is 4.2 mm yr - 1 , which is significantly higher than the median of 3.2 mm yr - 1 at other sites, based on a Kolmogorov-Smirnow (KS) test ( Methods ). Additional areas with higher uncertainties are tide gauges near active volcanoes (e.g., Fig. 2 c, Extended Data Fig. 4 c, d, and Extended Data Fig. 5b ). This underpins the importance of further assessing the impacts of co- and post-seismic deformations at tide gauge sites and their utility in studies of fault behavior and Earth rheology. Increased RSL variability due to variable VLM rates Nonlinear VLM rates are often comparable to or larger than CSL rates, particularly on decadal and longer time scales. For example, the tide gauge record at Grand Isle, Louisiana (Fig. 3 b), shows rates of RSL that peaked in the 1970s at ~ 30 mm yr - 1 concurrent with oil and gas extraction 19 , while CSL rates peaked over the past ~ 15 years at 10 mm yr -1 43, 44 . A similar picture emerges at the global scale. CSL rates calculated at all tide gauges range between − 7 and 11.8 mm yr - 1 (95% CIs) with a median rate of 1.9 mmyr - 1 (Fig. 3 c). In contrast, RSL rates have a wider and significantly (P > 0.99, KS test) different distribution ranging from − 14.4 to 16.2 mm yr - 1 (median rate of 1.50 mm yr - 1 ) for sites that are unimpacted by major earthquakes and − 16.2 to 19 mm yr - 1 (median rate of 1.79 mm yr - 1 ) for seismically active sites. Assuming that VLM is a linear process (i.e., adding linear VLM estimates to CSL), as is current practice for projections, leads to wider rate distributions than for CSL alone (-10.9 to 11.8 mm yr - 1 for sites unaffected by seismic activity and − 11.1 to 15 mm yr - 1 for affected sites) but still falls significantly (P > 0.99) below the reported range for nonlinear VLM. The skewed distribution of RSL rates further underscores the importance of nonlinear VLM. For instance, at Kōzu Shima, a seismically and volcanically active site 45 , RSL rates reach up to ~ 6 times greater than the largest observed CSL rate (183.1 mm yr - 1 vs. 28.8 mm yr - 1 ) at the same site (Kōzu Shima, Japan). The variable VLM rates can undermine the current practice of linearly extrapolating past rates into the future 2 , 13 , 15 . To provide an analogous estimate on how nonlinear VLM influences predictions, Fig. 4 a maps the maximum absolute differences when estimating linear VLM from any given past 13-year period to predict the following 13-year period (the average length of available GNSS records in the ULR dataset 23 ) using two rolling windows of the entire observational record at each site. The maximum absolute difference averaged over all sites is 5.7 mm yr - 1 , but they can become as large as 74.9 mm yr - 1 at seismically active sites (Fig. 4 b). As expected, the spatial pattern of differences largely resembles the spatial pattern of rate variations in Fig. 3 a (R 2 = 0.63). Implications for sea-level science Our results have significant implications for instrumental sea-level reconstructions and projections and associated coastal adaptation and mitigation efforts. Sea-level reconstructions have been thought of as highly uncertain with respect to their local variability and trends 46 , and therefore more of a tool for improving the sampling of the ocean when calculating the global mean values rather than a complementary source of information along the coast. We show that the residual mismatch between sea-level reconstructions and tide gauge measurements can reveal processes that contribute importantly to observed changes but have not yet been assimilated into the reconstruction framework, including nonlinear VLM (Fig. 2 ), datum shifts ( Extended Data Fig. 1 ), and near-coastal processes not captured by satellite altimetry ( Extended Data Fig. 2 ). The CSL-TG methodology emphasizes these processes that are otherwise overshadowed by large-scale CSL in raw tide gauge data. This detection, in turn, offers opportunities to better understand these processes and incorporate them as corrections in instrumental sea-level reconstruction procedures as is done, for instance, in temperature reconstructions for urban heat island effects 47 , and may ultimately help reconcile existing differences between individual reconstructions 48 , 49 . For sea-level projections, our results emphasize that the current practice of linearly extrapolating historical VLM 13 , 15 may misestimate the associated sea-level hazards (Fig. 4 ). Major metropolitan hubs, including Tokyo, Venice, and Shanghai have reduced fluid extraction-related subsidence using mitigation policies like pumping regulations 50 – 52 . Similarly, in South Louisiana, onshore hydrocarbon production and associated nonlinear VLM have waned since the 1970s 19 (Fig. 3 b, Extended Data Fig. 4 a). Properly capturing those historic VLM nonlinearities is necessary to understand the underlying processes and develop process-based hydro-geological models that feature local-scale policy scenarios 53 , 54 . Such models are ultimately needed to improve sea-level projections, assess impacts 6 , and optimize adaptation and mitigation measures 55 . The CSL-TG dataset provides a global benchmark against which past mitigation strategies and newly developed subsidence models can be compared. This utility also extends to co- and post-seismic VLM. The CSL-TG differential provides constraints on the temporal and spatial scales of co- and post-seismic subsidence and motivates studies of fault slip and post-seismic relaxation 33 , 56 , elucidating earthquake and volcanic processes 18 , 32 , 57 and consequently improving associated sea-level projections 58 and hazard adaptation strategies. Finally, we note that data from many deltaic regions are not currently featured in global databases such as PSMSL even though such records often exist but either have not yet been digitized 59 or are often not openly shared local authorities 38 . In addition, the extraction of VLM from CSL-TG (and GNSS) may often only capture a fraction of the total subsidence signal in depositional settings, where tide gauges are tied to benchmarks anchored at depths 60 below the shallow strata dominated by sediment compaction 61 , 62 . Our results underscore the spatial, temporal, and vertical complexity of VLM in such regions and should motivate efforts to close these data and knowledge gaps. Methods Tide Gauge Data . We use annual tide-gauge records from the Permanent Service for Mean Sea Level (PSMSL) ‘Revised Local Reference’ database 63 , which provides sea-level records referenced to a consistent datum. From the initial 1,556 tide-gauge records we only select those that provide at least 30 years of data. We discard data from sites farther than 100 kilometers from the closest altimetry/reconstruction grid point. These criteria reduce the dataset to 633 records. Climatic Sea Level (CSL) Reconstruction . To determine CSL we use the recent sea-level reconstruction by ref. 3. The reconstruction is generated by applying a Kalman Smoother to tide-gauge records in combination with prior information on contributions from barystatic self-gravitation, rotation, and deformation fingerprints 64 associated with present-day redistribution of water and ice; sterodynamic sea level (estimated from 10 leading modes of variability from satellite altimetry); GIA; and the inverse barometer effect. The reconstruction is consistent with satellite altimetry, tide gauges, and independent steric height datasets 3 and furnishes global gridded estimates of CSL change over the period 1900 to 2021. Here, we use CSL from the reconstruction with GIA removed. We note that the barystatic sea level fingerprints are defined in terms of RSL and therefore contain the associated deformational contribution 65 . Therefore, when we compare CSL-TG rates to VLM trends from GNSS data, we first adjust the GNSS data so as not to double count these deformational effects (see below). Near-Coastal Processes . The CSL-TG time series reflect processes that are not modelled by the CSL reconstruction but measured by tide gauges. This includes not only VLM but also coastal ocean-dynamic sea-level signals, for example, excited by local winds and river discharge, which are characterized by short offshore decorrelation length scales 66 , 67 . While they can influence RSL measured by tide gauges at the coast, these processes may not be observed by satellite altimetry, given data uncertainties near the coast, and hence may not be represented in the CSL reconstruction. To estimate these effects and separate them from nonlinear VLM in the CSL-TG residuals, we use a stepwise regression model that uses linearly detrended river discharge and near-coastal wind stresses as predictors and linearly detrended CSL-TG time series as the predictand 68 – 70 . For river discharge, we use stream gauge records compiled from the Global Streamflow Indices and Metadata Archive (GSIM) 40 , which is a collection of more than 30,000 monthly average (and extreme) records worldwide covering the period 1900 to 2015. For the U.S. stream gauges within GSIM, we extended data to 2021 with data from the United States Geological Survey (USGS). Then, we compute annual averages from the monthly average records to be consistent with the CSL-TG methodology. We desire to adjust tide-gauge records for river discharge effects. Ideally, this should be performed using outputs from dedicated physical models, in a similar fashion as done for the other components that contribute to sea-level change. However, such models do not currently exist, because of a lack of global gridded river discharge datasets needed as model forcing and because running such a model for a long enough period at sufficiently high spatial resolution to resolve the relevant physics is computationally prohibitive. Given these realities, we developed a statistical approach to estimate river discharge effects on tide gauge records in the presence of sparse and gappy stream gauge data. Our approach assumes that (i) discharge-driven sea-level changes are proportional to discharge itself, (ii) the streamflow process is characterized by spatial scales on the order of drainage basins or larger 71 , 72 , and (iii) discharge may influence tide-gauge records locally in the proximity of a river mouth. The assumptions are imperfect, and our approach may overlook or underemphasize time lags between forcing and response, important river effects on smaller sub-basin scales, and more remote river effects on tide-gauge records downstream along open coastlines. Despite these caveats, our approach is nevertheless useful. Adjusting CSL-TG data for river discharge effects (determined as described immediately below) can substantially reduce variance in CSL-TG records, demonstrating that our river discharge estimates are informative predictors of CSL-TG. For these reasons, and until which time model solutions along the lines described above become available, this approach represents the state of the art. Future studies could take steps forward towards more robust estimates by quantifying the skill and uncertainty associated with this approach (e.g., through high-resolution regional pseudo data experiments). We use a three-step approach to estimate river effects on a tide gauge record. First, we identify all stream gauges and rivers within a surrounding grid box of 4° surrounding the tide gauge. This criterion was chosen to balance data availability in data-sparse regions and computation time in data-rich regions. Individual rivers can feature multiple stream-gauge records with different record lengths, mean values, and variances. Thus, second, we produce one representative discharge time series for each river using an approach similar to the one described in ref. 71. Their method involved (1) obtaining multiple stream gauge records along a given river, (2) log-transforming and removing the mean from each record, (3) averaging the resulting series together ignoring any data gaps, (4.) adding back the previously removed mean values, (5) exponentiating the now-complete time series to convert back to discharge units, and (6) taking the most downstream data record as the representative series ( Extended Data Fig. 6a ). Third, we perform a probabilistic principal component analysis over all standard-normalized river indices within the 4° box around the tide gauge. This approach enables the calculation of principal components even in the presence of data gaps 73 . The leading principal component in our assessment is used as a regional river index that is representative of river discharge variability in the corresponding box. We illustrate this approach for the case of the Washington, DC, tide gauge record in Extended Data Fig. 6 . Within the 3° box there are 307 stream gauge records with distinct means and variances ( Extended Data Fig. 6a ). However, when their discharge time series are log-transformed and standardized ( Extended Data Fig. 6c ), the records are significantly correlated with one another and with the tide gauge record ( Extended Data Fig. 6b ). This supports our argument that the first principal component is representative of common variability shared by stream gauges within a 4° box ( Extended Data Fig. 6c ). Furthermore, the most downstream record within the Potomac River, on which the Washington, DC, tide gauge is located, is highly correlated with the principal component-based index from the 4° box over their overlapping period (R 2 = 0.82). Similar results were identified within other river systems around the world, suggesting that this approach is usefully applied in the context of our global assessment. For wind stress, we use zonal and meridional wind stress from the 20th century reanalysis dataset v3 covering 1900 to 2015 74 and the NCEP-NCAR Reanalysis 1 covering 1948 to 2021 75 . Since neither reanalysis covers the full 1900–2021 study period, we used wind stresses from the 20th century reanalysis for 1900–2015 and the NCEP-NCAR reanalysis for 2016–2021. Note that we offset the NCEP-NCAR reanalysis to have the same time mean value and standard deviation as the 20th century reanalysis over the period 2011–2015. As with the stream gauges, we select zonal and meridional wind stress from a box of 3° around the respective tide gauge. We note that the specific choice of the grid box size does not appreciably alter the results because wind stresses are typically characterized by large-scale atmospheric patterns at this temporal scale. We calculate principal components from all wind stress time series to reduce dimensionality and select sufficient leading modes that \(\:\ge\:95\%\) of the wind stress variance within the box is explained. The stepwise regression model is then built by using the linearly-detrended leading principal components of zonal and meridional wind stress, and, if available over at least 75% of the tide gauge record, the linearly detrended river discharge index as predictors and the linearly detrended CSL-TG time series as the predictand. The estimated regression coefficients are then applied to non-detrended predictors, selected by the stepwise algorithm, to include trends into the final estimate. Large nonlinear VLM signals can influence the estimation of regression coefficients. Therefore, we build three different regression models, one over the entire period, and two over two equally sized sub-periods. We then visually inspect each record and the associated estimates of near-coastal processes. If regression coefficients and the associated estimates of near-coastal processes show large differences between different sub-periods, we either select the regression model built over a nearly linear period of CSL-TG or entirely discard the estimate of near-coastal processes (sometimes required in tectonically highly active regions such as Japan). We also note that due to the temporal availability of stream gauge records in the GSIM database, the approach of estimating river effects on tide gauges can only be made from 1900 to 2015 (except for U.S. stream gauges which were updated with NOAA data), i.e., missing the last six years of our study period (2016–2021). Thus, CSL-TG time series with river discharge effects removed outside the U.S. only cover the period 1900–2015. An example of the modelled near-coastal processes at Washington, DC, is shown in Extended Data Fig. 2 a. The tide gauge is situated more than 200 km upstream along the Potomac River, which discharges into Chesapeake Bay. River discharge is the leading near-coastal process in this case. Together with winds, it explains 60% of the variability in the Washington, DC, CSL-TG time series. Thus, removing those signals substantially reduces interannual variability in the CSL-TG time series. On average (median), near-coastal processes explain ~ 53% of the variability in CSL-TG time series worldwide ( Extended Data Fig. 2 b), though their influence is usually limited to interannual timescales. Data for VLM Comparison . We compare three VLM datasets to our CSL-TG estimates: ALT-TG as well as GNSS from ULR 23 and NGL 24 . The ALT-TG estimates are based on satellite altimetry data from AVISO distributed through the Copernicus Marine Environment Monitoring Service (CMEMS) (Copernicus Climate Change Service, Climate Data Store, 2018). We use satellite altimetry data on the same spatial grid as the reconstruction and as re-gridded by ref. 3. The inverted barometer correction is added back to the raw sea-surface height data, and the deformation component of the present-day barystatic sea-level changes (from the CSL reconstruction based on ref 63) is also added. Thus, CSL-TG and ALT-TG estimates provide VLM estimates that include GIA and other geological, tectonic or human processes but exclude deformation through surface loading by present-day land ice and hydrology. The ULR-based GNSS estimates were produced within the third International GNSS Service reprocessing campaign. These data are available near tide gauges with a median station record length of 13.1 years and robust uncertainty estimates based on correlated noise 23 . Even though ULR focuses on VLM estimates near tide gauges, there are only 65 locations where the GNSS station is within 5 km of the tide gauge location. VLM varies over short spatial scales, but since GNSS stations are seldom precisely co-located with tide gauges a distance criterion was chosen that allows enough GNSS stations to satisfy it. The NGL VLM dataset is also based on GNSS, but it uses a much larger number of uniformly processed GNSS records that are interpolated to all locations on the Earth’s land surface 24 . Each estimate is provided with an uncertainty that considers the number of GNSS observations used for interpolation, the distance of each GNSS observation to the grid point of interest, the uncertainty of the trend estimates, and the spatial variability of trend estimates 24 . Here, we follow the recommendation of ref. 24 and only consider locations that are classified as ‘good’, which results in 153 overlapping sites. To avoid double counting the VLM effects related to present-day surface loading through ice and hydrology (which is explicitly modelled by the reconstruction as CSL), we remove the deformational contribution since 1993 from GNSS estimates. We also add the GIA sea-surface height component from the weighted Kalman smoother-determined GIA fields to the GNSS estimates 77 . We use raw GNSS time series for comparison purposes in Fig. 2 and Extended Data Figs. 4 , and 5. The associated GNSS time series were downloaded from the NGL website ( http://geodesy.unr.edu/index.php ). For the time series, the annual deformational component of surface loading through ice and hydrology was temporally interpolated onto the times of the weekly GNSS observations and subsequently subtracted. The GIA sea-surface height component was added in a similar fashion as for the linear GNSS estimates above. The groundwater extraction data for Bangkok (Fig. 2 a) 30 as well as the benchmark compilation (based on a combination of historical leveling data, GNSS, and InSAR) at Venice (Fig. 2 b) 20 were not publicly available. Therefore, both records were digitized from the original publications using online digitization software Automeris ( https://apps.automeris.io/wpd4/ ). Earthquake database . We use the global ANSS Comprehensive Earthquake Catalog from the USGS ( https://earthquake.usgs.gov/earthquakes/search/ ). We search for earthquakes with magnitude 7 or larger. From the respective database we then search for earthquakes within 4° of a tide gauge that overlap temporally with available sea-level measurements. Change point Detection . The CSL-TG differential does not solely reflect nonlinear VLM but may also feature abrupt and unphysical change points (e.g., through unaccounted datum shifts and benchmark issues) in tide gauge records 77 . To test the extent to which CSL-TG time series are affected by change points, we apply two different change point detection algorithms 78 , 79 and visual inspection. The first change point approach, DiscoTimeS 78 , estimates a variable number of change points, discontinuities (i.e., offsets at the respective change point), piecewise trends of the individual elements, noise properties (AR1 noise) and their uncertainties. The second, a change point detection algorithm from ref. 79, provides the number, location, and probability of potential change points with associated uncertainties based on piecewise regression models. Both change points algorithms provide change points not only indicative of datum shifts but also sometimes related to major earthquakes. Since the latter corresponds to the nonlinear VLM that we seek to resolve, we visually screen each site with significant change points identified by one or both approaches. If a shift aligns with a known earthquake, we keep the CSL-TG time series as is. If we find no indication for an earthquake and related co-seismic VLM and/or find notes on potential, yet unaccounted for datum shifts in the PSMSL documentation, we correct the CSL-TG time series for the associated change point. This procedure may omit smaller magnitude earthquakes associated with volcanic eruptions and dike intrusions that may be accompanied by significant VLM 80 . We identify 30 sites with significant datum shifts not connected to earthquakes, many of which are noted in the PSMSL database but not accounted for due to missing benchmark information ( Extended Data Fig. 1 ). To illustrate the effect this has on our results, we compare the resulting linear trends to GNSS estimates from NGL 23 . Before their correction, large biases exist between both products (0.06 ± 4.14 mm yr - 1 ). After the change point correction, biases are reduced to 0.09 ± 1.4 mm yr - 1 , a value much closer to statistics reported from the validation sites. Linear and Nonlinear Trends . Linear trends are calculated using ordinary least squares regression under the assumption that the residuals are normally distributed and can be described by an autoregressive process of order 1 81 . To test whether trends calculated from 1993 to 2021 and 1964 to 1992 in Fig. 1 b, c are statistically significant, we perform a Monte-Carlo experiment. We estimate the linear long-term trend in CSL-TG at each location and the associated variance and lag 1 autocorrelation parameter g of the residual noise. To avoid inflated values of the variance and the autocorrelation parameter g due to large nonlinear trends or sudden shifts, we estimate the parameters of moving 10-year boxes and subsequently calculate the mean over all parameter values. We then create 1000 random series as pseudo-observations, add the linear long-term trend, estimate trends over the same sub-periods, and calculate the associated trend differences. If an observed difference is larger than 95% of the trend differences in the Monte-Carlo experiment, the difference is considered statistically significant. Nonlinear trends are calculated using Singular Spectrum Analysis (SSA) 82 , 83 . SSA is a nonparametric spectral estimation approach that uses lagged copies of the time series that are used to define coordinates in a phase space to approximate a nonlinear trend. The number of lagged copies is called the embedding dimension. Here the embedding dimension is set to 5, which extracts decadal signals from the associated time series. The SSA tool used here applies time series padding at the ends of the series using the minimum roughness criterium. Uncertainties are modelled using an autoregressive process of order 1. Statistical tests . We use a non-parametric Kolmogorov-Smirnov test (KS-test) to assess whether two different samples of RSL rates, or RSL rate standard deviations, belong to the same probability distribution. The KS-test quantifies the maximal distance between two distributions. The null hypothesis assumes that two samples share the same reference probability distribution. This null hypothesis is rejected if the probability that the two samples share the same reference probability becomes smaller than 5%. Declarations Data availability . The tide gauge data used in this study is publicly available from the Permanent Service of Mean Sea Level (https://www.psmsl.org/), while the GRD fingerprints and VLM estimates at individual locations are accessible from the ref. 64. The CSL reconstruction is publicly available under: https://doi.org/10.5281/zenodo.10621070. All data used in the study is available under: https://doi.org/10.5281/zenodo.14866331 Code availability . All codes to produce the papers results are publicly available under: https://doi.org/10.5281/zenodo.14866331 Acknowledgements: S.D., T.W., C.G.P., and P.T. acknowledge the NASA grant 80NSSC20K1241 and J.X.M. the MacArthur Foundation. S.D. also acknowledges David and Jane Flowerree for their endowment funds. Correspondence : Correspondence and requests should for materials should be addressed to S.D. Author contributions: S.D. designed and performed the research and wrote the first draft of the paper. J.O. ran the DiscoTimeS algorithm and supported the evaluation of GNSS data. W.C. updated the GSIM database with USGS stream gauges for the period after 2015. C.G.P. and R.C gave advice on the implementation of the river discharge correction. J.X.M., J.O. and C.E. helped with the interpretation of seismic events. T.E.T. provided advice on the interpretation of nonlinear subsidence in depositional areas. All authors shared ideas and contributed to the writing of the manuscript. 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In AGU fall meeting abstracts (Vol. 2001, pp. V42C-1037). Additional Declarations There is NO Competing Interest. Supplementary Files ExtendedDataFigures.docx Cite Share Download PDF Status: Under Review Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6024708","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Physical Sciences - Article","associatedPublications":[],"authors":[{"id":421396580,"identity":"faa4de8c-36bd-4b2b-a723-27aee7fadf2f","order_by":0,"name":"Sönke Dangendorf","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABAElEQVRIiWNgGAWjYFCCBDDJ2MDA+ODABwYGGYgoG1FamA0Pzkhg4CFJi/FhHmK0yLcnP3v4peKObL/0YYbDtj8O8/DPbj7A8KHsME4tBmeemRvLnHlmPLMvmeFwTsJhHok7xxIYZ5zDo0UiwUxasu1w4oYz/AfAWhhu5Bgw87bh1iI/I/2btOQ/kBZmhsMWQC3yN/I/MP/FowVoppnkxwaoFgagFoMbOQzMjHi0GJx5UybNcOyw8cweZoaDPWnpPIY30gwO9pxLx+2w9vRtkj9qDsv28zAzf/hhYy0ndyP54YMfZda4HQYEzDzoIgfwqgcCxh+EVIyCUTAKRsHIBgDMLV2APKo1JgAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0002-3679-5234","institution":"Tulane University","correspondingAuthor":true,"prefix":"","firstName":"Sönke","middleName":"","lastName":"Dangendorf","suffix":""},{"id":421396581,"identity":"52ab6c78-d244-4c9e-be73-7f8ee0a7d629","order_by":1,"name":"Julius Oelsmann","email":"","orcid":"","institution":"Tulane University","correspondingAuthor":false,"prefix":"","firstName":"Julius","middleName":"","lastName":"Oelsmann","suffix":""},{"id":421396582,"identity":"d8b071bc-26ef-4cd9-8758-33cc73768efd","order_by":2,"name":"Jerry Mitrovica","email":"","orcid":"","institution":"Harvard University","correspondingAuthor":false,"prefix":"","firstName":"Jerry","middleName":"","lastName":"Mitrovica","suffix":""},{"id":421396583,"identity":"d21033d6-372c-4544-9e2c-884cff875918","order_by":3,"name":"Torbjorn Tornqvist","email":"","orcid":"https://orcid.org/0000-0002-1563-1716","institution":"Tulane University","correspondingAuthor":false,"prefix":"","firstName":"Torbjorn","middleName":"","lastName":"Tornqvist","suffix":""},{"id":421396584,"identity":"0b1672c3-eb5b-43d4-ab28-bd2d4c77b91a","order_by":4,"name":"Christopher Piecuch","email":"","orcid":"https://orcid.org/0000-0001-7973-7328","institution":"Woods Hole Oceanographic Institution","correspondingAuthor":false,"prefix":"","firstName":"Christopher","middleName":"","lastName":"Piecuch","suffix":""},{"id":421396585,"identity":"d89749b4-3531-4cdf-9a5e-a29aa29511b4","order_by":5,"name":"Roger Creel","email":"","orcid":"","institution":"WHOI","correspondingAuthor":false,"prefix":"","firstName":"Roger","middleName":"","lastName":"Creel","suffix":""},{"id":421396586,"identity":"0d08bd0f-282a-4747-8d77-b45270dcd8c3","order_by":6,"name":"William Coronel","email":"","orcid":"","institution":"Tulane University","correspondingAuthor":false,"prefix":"","firstName":"William","middleName":"","lastName":"Coronel","suffix":""},{"id":421396587,"identity":"058e131b-5345-41b2-b5ac-dae5c50f093e","order_by":7,"name":"Philip thompson","email":"","orcid":"https://orcid.org/0000-0002-0875-4208","institution":"University of Hawai'i at Mānoa","correspondingAuthor":false,"prefix":"","firstName":"Philip","middleName":"","lastName":"thompson","suffix":""},{"id":421396588,"identity":"17a2cada-0b5f-4cf4-a2a2-3cab05c293fa","order_by":8,"name":"Cynthia Ebinger","email":"","orcid":"https://orcid.org/0000-0002-6211-3399","institution":"Tulane University","correspondingAuthor":false,"prefix":"","firstName":"Cynthia","middleName":"","lastName":"Ebinger","suffix":""},{"id":421396589,"identity":"4f956237-ffda-4baa-bbc2-833d43e29afc","order_by":9,"name":"Thomas Wahl","email":"","orcid":"https://orcid.org/0000-0003-3643-5463","institution":"University of Central Florida, USA","correspondingAuthor":false,"prefix":"","firstName":"Thomas","middleName":"","lastName":"Wahl","suffix":""}],"badges":[],"createdAt":"2025-02-13 16:15:22","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6024708/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6024708/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":78745764,"identity":"c7162e1c-d57c-49be-bee5-3f186c82723c","added_by":"auto","created_at":"2025-03-18 10:30:08","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":116979,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eLinear VLM from the climatic sea-level reconstruction minus tide gauge observations of RSL (i.e., CSL-TG) and changes in linear estimates over time. a\u003c/strong\u003e VLM trends estimated from CSL-TG (circles with black edges) over the period 1993 to 2021 versus the GNSS-based coastal VLM product from NGL\u003csup\u003e24\u003c/sup\u003e (colored squares). Locations discussed throughout the paper are highlighted by arrows. \u003cstrong\u003eb\u003c/strong\u003e Differences between linear VLM estimates for the period 1993 to 2021 (\u003cstrong\u003ea\u003c/strong\u003e) and the preceding period from 1964 to 1992. Black circles indicate statistically significant trend differences (P\u0026gt;0.95, \u003cstrong\u003eMethods\u003c/strong\u003e). Note that trends for the two periods have only been calculated if at least 75% of data coverage was available. For the trend differences in (\u003cstrong\u003eb\u003c/strong\u003e) this leaves 204 records. \u003cstrong\u003ec\u003c/strong\u003e Scatter plot of the CSL-TG based linear VLM estimates for the two different periods. Black circles indicate pairs with significant differences (P\u0026gt;0.95). The black dashed line represents the 1:1 line, i.e. a perfect linear relationship. The grey shading shows the 99% confidence interval of the median global uncertainty retrieved from GNSS based estimates from NGL.\u003c/p\u003e","description":"","filename":"Figure1.png","url":"https://assets-eu.researchsquare.com/files/rs-6024708/v1/e98b3d73ad07aaafdf3d4677.png"},{"id":78745056,"identity":"c53df97b-ee98-428e-89dd-c52150d5b433","added_by":"auto","created_at":"2025-03-18 10:22:08","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":92713,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eExamples of nonlinear VLM from the climatic sea-level reconstruction minus tide gauge observations (i.e., CSL-TG) at selected sites\u003c/strong\u003e. Nonlinear VLM at Bangkok, Thailand (\u003cstrong\u003ea\u003c/strong\u003e), Venice, Italy (\u003cstrong\u003eb\u003c/strong\u003e), Pago Pago, American Samoa (\u003cstrong\u003ec\u003c/strong\u003e), and the east coast of Japan (\u003cstrong\u003ed\u003c/strong\u003e). Insets show tide gauge and satellite altimetry observations in comparison to CSL. CSL-TG differences are shown with their uncertainties as error bars and nonlinear trend with decadal smoothing applied. In (\u003cstrong\u003ea\u003c/strong\u003e), a digitized groundwater extraction record from ref. 30 is shown in yellow for comparison. The record has been scaled to have the same mean and variance as VLM. In (\u003cstrong\u003eb\u003c/strong\u003e), we added a digitized version of GNSS, InSAR, and leveling benchmarks from ref. 20 in yellow. In (\u003cstrong\u003ec\u003c/strong\u003e) and (\u003cstrong\u003ed\u003c/strong\u003e), GNSS records from NGL in the vicinity of the tide gauge are shown for validation.\u003c/p\u003e","description":"","filename":"Figure2.png","url":"https://assets-eu.researchsquare.com/files/rs-6024708/v1/e0c524048c8f201339d72520.png"},{"id":78745052,"identity":"6465e539-6f90-4948-95a1-5bfd053ad572","added_by":"auto","created_at":"2025-03-18 10:22:08","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":92205,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eVariability in the rates of nonlinear VLM and their impact on RSL.\u003c/strong\u003e \u003cstrong\u003ea \u003c/strong\u003e\u0026nbsp;Standard deviation of the CSL-TG rates derived from a Singular Spectrum Analysis (SSA) with 10 yr-smoothing. Grey dots represent sites that have experienced major earthquakes during their observational period. The inset shows the corresponding empirical distributions for seismic and non-seismic sites. \u003cstrong\u003eb\u003c/strong\u003e Rates of CSL and RSL at Grand Isle, Louisiana. \u003cstrong\u003ec\u003c/strong\u003e Empirical distributions of CSL and RSL at seismic and non-seisimic sites. Dots represent all observed rates over the respective sites. The transparent rectangle represents 95% confidence intervals and the vertical bar represents the median.\u003c/p\u003e","description":"","filename":"Figure3.png","url":"https://assets-eu.researchsquare.com/files/rs-6024708/v1/1e05950a671c865593ef15b1.png"},{"id":78746174,"identity":"1a331075-028e-4775-b76b-ae1bf674da71","added_by":"auto","created_at":"2025-03-18 10:38:08","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":38078,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003ePrediction differences due to variable rates of vertical land motion (VLM).\u003c/strong\u003e \u003cstrong\u003ea \u003c/strong\u003eShown is the maximum prediction difference, when using any past 13-year period to linearly predict the following future 13-year period. The rates have been calculted using two rolling 13-year windows. The period of 13 year has been chosen based on the average length of GNSS records in ULR\u003csup\u003e23\u003c/sup\u003e. \u003cstrong\u003eb\u003c/strong\u003e The associated maxumum prediction difference distributions for seismic and non-seismic sites.\u003c/p\u003e","description":"","filename":"Figure4.png","url":"https://assets-eu.researchsquare.com/files/rs-6024708/v1/360bb7a0b74b15b9d240b59d.png"},{"id":78746960,"identity":"a011f212-2ef2-4fe4-9bbe-d499564cbbe3","added_by":"auto","created_at":"2025-03-18 10:46:09","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1934248,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6024708/v1/1a760758-b283-4dcb-8788-0799c07f5f5c.pdf"},{"id":78745054,"identity":"f268d74c-0746-419f-9db2-54ec88f6a5ae","added_by":"auto","created_at":"2025-03-18 10:22:08","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":1894641,"visible":true,"origin":"","legend":"","description":"","filename":"ExtendedDataFigures.docx","url":"https://assets-eu.researchsquare.com/files/rs-6024708/v1/552b84e6296ac712f46c4870.docx"}],"financialInterests":"There is \u003cb\u003eNO\u003c/b\u003e Competing Interest.","formattedTitle":"Variable Vertical Land Motion Over the 20th Century Inferred at Tide Gauges","fulltext":[{"header":"Introduction","content":"\u003cp\u003eSea-level rise threatens hundreds of millions of people in low-lying coastal regions worldwide\u003csup\u003e\u003cspan additionalcitationids=\"CR2\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e, increasing flood risk and other related hazards\u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. Coastal areas are also prone to land subsidence: current estimates indicate that over the past two decades coastal residents experienced on average four times faster rates than due to climate-related sea level (CSL) rise alone\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. A multitude of natural and anthropogenic factors cause land to subside or uplift\u003csup\u003e\u003cspan additionalcitationids=\"CR8\" citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. Natural factors, including glacial isostatic adjustment (GIA), sediment compaction, aseismic creep, volcanic activity and earthquakes drive vertical land motion (VLM) in coastal areas\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e. However, anthropogenic activities such as groundwater pumping, oil and gas withdrawal, land reclamation or artificial drainage of wetland or urban areas also drive VLM and have become the dominant causes of rapid changes in RSL rates in many densely populated coastal zones\u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan additionalcitationids=\"CR12\" citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. Having a solid observation-based understanding of the overall mechanisms, magnitudes, and scales of VLM is therefore critical for producing useful future coastal sea-level projections.\u003c/p\u003e \u003cp\u003eThe Global Navigation Satellite System (GNSS) and Interferometric Synthetic Aperture Radar (InSAR) currently monitor VLM in time and space, but these data have only been available for 10 to 30 years and they do not always capture the full VLM signal\u003csup\u003e\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e. Despite this short record length, the inferred VLM rates have been extrapolated under the assumption that current rates apply to past and future sea-level periods\u003csup\u003e\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e,\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. Tide-gauge records, which measure sea level relative to a stable reference point, have also been used to constrain VLM. However, the VLM signal in tide-gauge records should be separated from changes due to ocean dynamics and thermal expansion, the inverted barometer effect, and present-day barystatic gravitational, rotational, and deformational fingerprints\u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e \u0026ndash; here collectively termed CSL. To isolate these VLM effects, past studies corrected tide gauge records of interest using nearby, tectonically stable reference stations\u003csup\u003e\u003cspan additionalcitationids=\"CR18 CR19\" citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. This technique has several drawbacks. It assumes that nearby stations exist and have sufficiently long records, that they share a similar CSL signal and have no datum shifts, and tectonic activity has not precluded identifying stable sites. These drawbacks can generally be overcome by replacing reference stations with altimetry-based sea-surface height measurements, the so-called altimetry-minus-tide gauge (ALT-TG) technique\u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. Ref. 22 recently jointly assessed ALT-TG and GNSS based estimates at a global scale to reveal substantial nonlinear VLM signals in response to several different processes including fluid withdrawals, and post-seismic activity. However, the short altimetry record limits the assessment to the period after 1995, leaving any analogous signals at lower frequencies and/or earlier in the 20th century unexplored.\u003c/p\u003e \u003cp\u003eHere we use a globally resolved sea-level reconstruction from 1900 to 2021\u003csup\u003e3\u003c/sup\u003e to isolate the CSL signal (\u003cb\u003eMethods\u003c/b\u003e). We argue that differences between CSL signals and tide-gauge records are largely related to VLM. Compared to other approaches (GNSS, InSAR, ALT-TG), our method provides longer-term VLM estimates extending back to 1900. The method is also free of assumptions commonly made with the reference station technique. We apply this approach to 633 tide-gauge records included in the Permanent Service for Mean Sea Level (PSMSL) \u0026lsquo;Revised Local Reference\u0026rsquo; database. At each tide gauge site, the observations are subtracted from the nearby CSL reconstruction (CSL-TG) such that the sign of the resulting residual indicates the sense of VLM (negative for subsidence and positive for uplift) (\u003cb\u003eMethods\u003c/b\u003e). We account for potential shifts in tide gauge observations using change point analysis (\u003cb\u003eExtended Data\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e, \u003cb\u003eMethods\u003c/b\u003e). We also adjust the data for the fact that tide gauge records are affected by local ocean processes that may not be fully observed by satellite altimetry and, hence, not represented in the CSL reconstruction (\u003cb\u003eExtended Data\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e, \u003cb\u003eMethods\u003c/b\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e\n\u003ch3\u003eEstablishing vertical land motion estimates at tide gauges\u003c/h3\u003e\n\u003cp\u003eWe first calculate linear trends in CSL-TG time series as a measure of VLM rates over the period 1993 to 2021 for all records with at least 75% data coverage (370 of the 633 records, Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea). Rate patterns are characterized by regional post-glacial uplift signals in formerly glaciated centers including Scandinavia and Hudson Bay, while large subsidence signals are, for instance, prevalent in river deltas with active sediment compaction and/or fluid extraction along the northern Gulf of Mexico and South Asia. To quantify consistency between CSL-TG-based VLM estimates and other approaches, we compare our CSL-TG rates to three other VLM trend datasets (ALT-TG, and two different GNSS datasets). The CSL-TG trends correlate nearly perfectly with ALT-TG estimates (coefficient of determination of R\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e\u0026thinsp;~\u0026thinsp;0.99) with differences of 0.1\u0026thinsp;\u0026plusmn;\u0026thinsp;0.43 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e (median\u0026thinsp;\u0026plusmn;\u0026thinsp;root mean square) (\u003cb\u003eExtended Data\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea), a result that is unsurprising since the leading spatial patterns from satellite altimetry have been used as a prior in the CSL reconstruction.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWe also compare our VLM rate estimates to two independent GNSS-based products: University of La Rochelle (ULR)\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e and the Nevada Geodetic Laboratory (NGL)\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. ULR estimates are developed specifically for sea-level assessments at tide gauges. Of their 601 GNSS sites, 65 are in close vicinity (\u0026lt;\u0026thinsp;5 km) to the tide gauge sites (\u003cb\u003eMethods\u003c/b\u003e). The corresponding pairs of CSL-TG and GNSS estimates of VLM are highly correlated (R\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e\u0026thinsp;~\u0026thinsp;0.83) and we detect no systematic bias (-0.05\u0026thinsp;\u0026plusmn;\u0026thinsp;1.07 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e, \u003cb\u003eExtended Data\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb). The error of 1.07 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e is lower than those previously reported for ALT-TG/GNSS comparisons\u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e, which can partly be explained by the stricter distance criterion adopted here (5 km vs. 50 km in ref. 25). NGL provides interpolated VLM estimates along the entire global coastline (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003ea) together with quality classification metrics for each site\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. Here, we only consider locations that are classified as \u0026lsquo;good\u0026rsquo; (\u003cb\u003eMethods\u003c/b\u003e), which results in an overlapping set of 156 sites. We find similar statistics as for ULR (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.85; trend differences of -0.06\u0026thinsp;\u0026plusmn;\u0026thinsp;1.07 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e) (\u003cb\u003eExtended Data\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec). These comparisons suggest that the multidecadal trends in CSL-TG time series are primarily due to VLM. We also note that our estimates are likely conservative (i.e., the accuracy is higher than reported here) since the GNSS datasets used for validation are based on different and varying observation periods (usually after 2000) and sometimes interpolated to the location of interest.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003eVariability in estimated vertical land motion rates\u003c/h2\u003e \u003cp\u003eWe next consider whether the CSL-TG time series show variable rates over time. We calculate linear trends over the preceding period from 1964 to 1992 and subtract them from the trends for 1993 to 2021. Of the 204 records that fulfill the 75% data availability criteria over both periods, 107 show statistically significant differences (probability P\u0026thinsp;\u0026gt;\u0026thinsp;=\u0026thinsp;0.95, \u003cb\u003eMethods\u003c/b\u003e) (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb, c). Median absolute differences are usually on the order of 1 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e but can become as large as 24.6 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e (Ayukawa, Japan). Significant differences can be found along major subduction zones in the Indo-Pacific region and the Mediterranean, but also in areas previously reported to be influenced by subsurface fluid withdrawals (e.g., Gulf of Mexico\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e, U.S. east coast\u003csup\u003e\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e, and Southeast Asia\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e). A cluster of significant differences of ~-1 to 2 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e is also found in the Baltic Sea. Nonlinear GIA effects may play a partial role\u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e, although they are expected to be an order of magnitude smaller than the differences reported here. Generally, the trend differences in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb, c demonstrate that rates of VLM have not been constant over time at ~\u0026thinsp;50% of the sites investigated here.\u003c/p\u003e \u003cp\u003eFor a more detailed view of variable VLM rates, Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows four examples that represent a range of behaviors found in CSL-TG time series. Eight additional examples are provided in \u003cb\u003eExtended Data\u003c/b\u003e Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and 5. Bangkok, Thailand (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea) and Venice, Italy (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb) are locations where rapid subsidence due to groundwater and gas withdrawals was later moderated through mitigation measures\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e,\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. Bangkok experienced\u0026thinsp;~\u0026thinsp;1 cm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e of post-seismic subsidence following the 2004 Sumatra earthquake off Indonesia\u003csup\u003e\u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e,\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. Pago Pago, American Samoa, and the east coast of Japan were subject to strong seismic effects. The complex 2009, magnitude 8.1 Samoa-Tonga megathrust and normal earthquake increased local subsidence rates due to the constructive interference between the two earthquake sources\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e\u003c/sup\u003e, which doubled the rate of RSL rise (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec, CSL-TG and ALT-TG time series). Japan\u0026rsquo;s 2011, magnitude 9 Tōhoku earthquake induced a devastating tsunami and widespread VLM\u003csup\u003e\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e34\u003c/span\u003e,\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e. The CSL-TG based VLM estimates suggest co-seismic subsidence of up to 1 m and decadal time scale post-seismic uplift, features that match the amplitude and time scale of GNSS measurements near the tide gauge of Ofunato, Japan (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ed).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eA spatially and temporally broader global picture of potential nonlinearities in VLM emerges when we estimate the standard deviation of decadal rates in the CSL-TG time series (\u003cb\u003eMethods\u003c/b\u003e, Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea). The largest standard deviations are found in deltaic regions (e.g., Nile, Hooghly, Mississippi), the Arctic Ocean, and along subduction zones in the Indo-Pacific, the Caribbean Sea, and the Mediterranean Sea. Deltaic regions often show variable VLM rates due to compaction and increased anthropogenic activity over the 20th century\u003csup\u003e\u003cspan additionalcitationids=\"CR37\" citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. In the Arctic Ocean, several factors may play a role, including ocean dynamic effects from large river flows\u003csup\u003e\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e possibly not captured by our corrections (\u003cb\u003eMethods\u003c/b\u003e) due to the sparse stream gauge records in this region\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e, increasing permafrost subsidence\u003csup\u003e\u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e, or uncertainties in the ice histories describing the barystatic fingerprints in CSL\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e,\u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e42\u003c/span\u003e\u003c/sup\u003e. Locations in subduction zones, however, show the largest variability in the rates, likely because of the influence of co- and post-seismic VLM, whose onset typically occurs more abruptly with a slower elevation change for months to years after the megathrust earthquake (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec, d; \u003cb\u003eExtended Data\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea, c, d) as compared to more steady changes associated with compaction and fluid extraction (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea, b).\u003c/p\u003e \u003cp\u003eTo further consider the potential impact of major earthquakes, we use the USGS earthquake catalog to identify 167 tide gauges that may have been close enough (within 4\u0026deg;) to be influenced by earthquakes of magnitude 7+ (\u003cb\u003eMethods\u003c/b\u003e). These locations are characterized by higher standard deviations in decadal CSL-TG rates (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea inset); the median at sites impacted by seismic activity is 4.2 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e, which is significantly higher than the median of 3.2 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e at other sites, based on a Kolmogorov-Smirnow (KS) test (\u003cb\u003eMethods\u003c/b\u003e). Additional areas with higher uncertainties are tide gauges near active volcanoes (e.g., Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ec, \u003cb\u003eExtended Data\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ec, d, and \u003cb\u003eExtended Data Fig.\u0026nbsp;5b\u003c/b\u003e). This underpins the importance of further assessing the impacts of co- and post-seismic deformations at tide gauge sites and their utility in studies of fault behavior and Earth rheology.\u003c/p\u003e \u003c/div\u003e\n\u003ch3\u003eIncreased RSL variability due to variable VLM rates\u003c/h3\u003e\n\u003cp\u003eNonlinear VLM rates are often comparable to or larger than CSL rates, particularly on decadal and longer time scales. For example, the tide gauge record at Grand Isle, Louisiana (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb), shows rates of RSL that peaked in the 1970s at ~\u0026thinsp;30 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e concurrent with oil and gas extraction\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e, while CSL rates peaked over the past ~\u0026thinsp;15 years at 10 mm yr\u003csup\u003e-1 43,\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e. A similar picture emerges at the global scale. CSL rates calculated at all tide gauges range between \u0026minus;\u0026thinsp;7 and 11.8 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e (95% CIs) with a median rate of 1.9 mmyr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ec). In contrast, RSL rates have a wider and significantly (P\u0026thinsp;\u0026gt;\u0026thinsp;0.99, KS test) different distribution ranging from \u0026minus;\u0026thinsp;14.4 to 16.2 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e (median rate of 1.50 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e) for sites that are unimpacted by major earthquakes and \u0026minus;\u0026thinsp;16.2 to 19 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e (median rate of 1.79 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e) for seismically active sites. Assuming that VLM is a linear process (i.e., adding linear VLM estimates to CSL), as is current practice for projections, leads to wider rate distributions than for CSL alone (-10.9 to 11.8 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e for sites unaffected by seismic activity and \u0026minus;\u0026thinsp;11.1 to 15 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e for affected sites) but still falls significantly (P\u0026thinsp;\u0026gt;\u0026thinsp;0.99) below the reported range for nonlinear VLM. The skewed distribution of RSL rates further underscores the importance of nonlinear VLM. For instance, at Kōzu Shima, a seismically and volcanically active site\u003csup\u003e\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e, RSL rates reach up to ~\u0026thinsp;6 times greater than the largest observed CSL rate (183.1 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e vs. 28.8 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e) at the same site (Kōzu Shima, Japan).\u003c/p\u003e \u003cp\u003eThe variable VLM rates can undermine the current practice of linearly extrapolating past rates into the future\u003csup\u003e\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e,\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. To provide an analogous estimate on how nonlinear VLM influences predictions, Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea maps the maximum absolute differences when estimating linear VLM from any given past 13-year period to predict the following 13-year period (the average length of available GNSS records in the ULR dataset\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e) using two rolling windows of the entire observational record at each site. The maximum absolute difference averaged over all sites is 5.7 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e, but they can become as large as 74.9 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e at seismically active sites (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003eb). As expected, the spatial pattern of differences largely resembles the spatial pattern of rate variations in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003ea (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.63).\u003c/p\u003e\n\u003ch3\u003eImplications for sea-level science\u003c/h3\u003e\n\u003cp\u003eOur results have significant implications for instrumental sea-level reconstructions and projections and associated coastal adaptation and mitigation efforts. Sea-level reconstructions have been thought of as highly uncertain with respect to their local variability and trends\u003csup\u003e\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e\u003c/sup\u003e, and therefore more of a tool for improving the sampling of the ocean when calculating the global mean values rather than a complementary source of information along the coast. We show that the residual mismatch between sea-level reconstructions and tide gauge measurements can reveal processes that contribute importantly to observed changes but have not yet been assimilated into the reconstruction framework, including nonlinear VLM (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), datum shifts (\u003cb\u003eExtended Data\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), and near-coastal processes not captured by satellite altimetry (\u003cb\u003eExtended Data\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The CSL-TG methodology emphasizes these processes that are otherwise overshadowed by large-scale CSL in raw tide gauge data. This detection, in turn, offers opportunities to better understand these processes and incorporate them as corrections in instrumental sea-level reconstruction procedures as is done, for instance, in temperature reconstructions for urban heat island effects\u003csup\u003e\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e\u003c/sup\u003e, and may ultimately help reconcile existing differences between individual reconstructions\u003csup\u003e\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e,\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFor sea-level projections, our results emphasize that the current practice of linearly extrapolating historical VLM\u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e may misestimate the associated sea-level hazards (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). Major metropolitan hubs, including Tokyo, Venice, and Shanghai have reduced fluid extraction-related subsidence using mitigation policies like pumping regulations\u003csup\u003e\u003cspan additionalcitationids=\"CR51\" citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e\u003c/sup\u003e. Similarly, in South Louisiana, onshore hydrocarbon production and associated nonlinear VLM have waned since the 1970s\u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003eb, \u003cb\u003eExtended Data\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003ea). Properly capturing those historic VLM nonlinearities is necessary to understand the underlying processes and develop process-based hydro-geological models that feature local-scale policy scenarios\u003csup\u003e\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e,\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e\u003c/sup\u003e. Such models are ultimately needed to improve sea-level projections, assess impacts\u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e, and optimize adaptation and mitigation measures\u003csup\u003e\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e\u003c/sup\u003e. The CSL-TG dataset provides a global benchmark against which past mitigation strategies and newly developed subsidence models can be compared. This utility also extends to co- and post-seismic VLM. The CSL-TG differential provides constraints on the temporal and spatial scales of co- and post-seismic subsidence and motivates studies of fault slip and post-seismic relaxation\u003csup\u003e\u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e33\u003c/span\u003e,\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e\u003c/sup\u003e, elucidating earthquake and volcanic processes\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e,\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e\u003c/sup\u003e and consequently improving associated sea-level projections\u003csup\u003e\u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e\u003c/sup\u003e and hazard adaptation strategies. Finally, we note that data from many deltaic regions are not currently featured in global databases such as PSMSL even though such records often exist but either have not yet been digitized\u003csup\u003e\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e\u003c/sup\u003e or are often not openly shared local authorities\u003csup\u003e\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e. In addition, the extraction of VLM from CSL-TG (and GNSS) may often only capture a fraction of the total subsidence signal in depositional settings, where tide gauges are tied to benchmarks anchored at depths\u003csup\u003e\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e\u003c/sup\u003e below the shallow strata dominated by sediment compaction\u003csup\u003e\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e,\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e\u003c/sup\u003e. Our results underscore the spatial, temporal, and vertical complexity of VLM in such regions and should motivate efforts to close these data and knowledge gaps.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e \u003cb\u003eTide Gauge Data\u003c/b\u003e. We use annual tide-gauge records from the Permanent Service for Mean Sea Level (PSMSL) \u0026lsquo;Revised Local Reference\u0026rsquo; database\u003csup\u003e\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e\u003c/sup\u003e, which provides sea-level records referenced to a consistent datum. From the initial 1,556 tide-gauge records we only select those that provide at least 30 years of data. We discard data from sites farther than 100 kilometers from the closest altimetry/reconstruction grid point. These criteria reduce the dataset to 633 records.\u003c/p\u003e \u003cp\u003e \u003cb\u003eClimatic Sea Level (CSL) Reconstruction\u003c/b\u003e. To determine CSL we use the recent sea-level reconstruction by ref. 3. The reconstruction is generated by applying a Kalman Smoother to tide-gauge records in combination with prior information on contributions from barystatic self-gravitation, rotation, and deformation fingerprints\u003csup\u003e\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e\u003c/sup\u003e associated with present-day redistribution of water and ice; sterodynamic sea level (estimated from 10 leading modes of variability from satellite altimetry); GIA; and the inverse barometer effect. The reconstruction is consistent with satellite altimetry, tide gauges, and independent steric height datasets\u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e and furnishes global gridded estimates of CSL change over the period 1900 to 2021. Here, we use CSL from the reconstruction with GIA removed. We note that the barystatic sea level fingerprints are defined in terms of RSL and therefore contain the associated deformational contribution\u003csup\u003e\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e\u003c/sup\u003e. Therefore, when we compare CSL-TG rates to VLM trends from GNSS data, we first adjust the GNSS data so as not to double count these deformational effects (see below).\u003c/p\u003e \u003cp\u003e \u003cb\u003eNear-Coastal Processes\u003c/b\u003e. The CSL-TG time series reflect processes that are not modelled by the CSL reconstruction but measured by tide gauges. This includes not only VLM but also coastal ocean-dynamic sea-level signals, for example, excited by local winds and river discharge, which are characterized by short offshore decorrelation length scales\u003csup\u003e\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e,\u003cspan citationid=\"CR67\" class=\"CitationRef\"\u003e67\u003c/span\u003e\u003c/sup\u003e. While they can influence RSL measured by tide gauges at the coast, these processes may not be observed by satellite altimetry, given data uncertainties near the coast, and hence may not be represented in the CSL reconstruction. To estimate these effects and separate them from nonlinear VLM in the CSL-TG residuals, we use a stepwise regression model that uses linearly detrended river discharge and near-coastal wind stresses as predictors and linearly detrended CSL-TG time series as the predictand\u003csup\u003e\u003cspan additionalcitationids=\"CR69\" citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e70\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFor river discharge, we use stream gauge records compiled from the Global Streamflow Indices and Metadata Archive (GSIM)\u003csup\u003e\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e\u003c/sup\u003e, which is a collection of more than 30,000 monthly average (and extreme) records worldwide covering the period 1900 to 2015. For the U.S. stream gauges within GSIM, we extended data to 2021 with data from the United States Geological Survey (USGS). Then, we compute annual averages from the monthly average records to be consistent with the CSL-TG methodology. We desire to adjust tide-gauge records for river discharge effects. Ideally, this should be performed using outputs from dedicated physical models, in a similar fashion as done for the other components that contribute to sea-level change. However, such models do not currently exist, because of a lack of global gridded river discharge datasets needed as model forcing and because running such a model for a long enough period at sufficiently high spatial resolution to resolve the relevant physics is computationally prohibitive. Given these realities, we developed a statistical approach to estimate river discharge effects on tide gauge records in the presence of sparse and gappy stream gauge data. Our approach assumes that (i) discharge-driven sea-level changes are proportional to discharge itself, (ii) the streamflow process is characterized by spatial scales on the order of drainage basins or larger\u003csup\u003e\u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e,\u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e72\u003c/span\u003e\u003c/sup\u003e, and (iii) discharge may influence tide-gauge records locally in the proximity of a river mouth. The assumptions are imperfect, and our approach may overlook or underemphasize time lags between forcing and response, important river effects on smaller sub-basin scales, and more remote river effects on tide-gauge records downstream along open coastlines. Despite these caveats, our approach is nevertheless useful. Adjusting CSL-TG data for river discharge effects (determined as described immediately below) can substantially reduce variance in CSL-TG records, demonstrating that our river discharge estimates are informative predictors of CSL-TG. For these reasons, and until which time model solutions along the lines described above become available, this approach represents the state of the art. Future studies could take steps forward towards more robust estimates by quantifying the skill and uncertainty associated with this approach (e.g., through high-resolution regional pseudo data experiments).\u003c/p\u003e \u003cp\u003eWe use a three-step approach to estimate river effects on a tide gauge record. First, we identify all stream gauges and rivers within a surrounding grid box of 4\u0026deg; surrounding the tide gauge. This criterion was chosen to balance data availability in data-sparse regions and computation time in data-rich regions. Individual rivers can feature multiple stream-gauge records with different record lengths, mean values, and variances. Thus, second, we produce one representative discharge time series for each river using an approach similar to the one described in ref. 71. Their method involved (1) obtaining multiple stream gauge records along a given river, (2) log-transforming and removing the mean from each record, (3) averaging the resulting series together ignoring any data gaps, (4.) adding back the previously removed mean values, (5) exponentiating the now-complete time series to convert back to discharge units, and (6) taking the most downstream data record as the representative series (\u003cb\u003eExtended Data Fig.\u0026nbsp;6a\u003c/b\u003e). Third, we perform a probabilistic principal component analysis over all standard-normalized river indices within the 4\u0026deg; box around the tide gauge. This approach enables the calculation of principal components even in the presence of data gaps\u003csup\u003e\u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e73\u003c/span\u003e\u003c/sup\u003e. The leading principal component in our assessment is used as a regional river index that is representative of river discharge variability in the corresponding box.\u003c/p\u003e \u003cp\u003eWe illustrate this approach for the case of the Washington, DC, tide gauge record in \u003cb\u003eExtended Data Fig.\u0026nbsp;6\u003c/b\u003e. Within the 3\u0026deg; box there are 307 stream gauge records with distinct means and variances (\u003cb\u003eExtended Data Fig.\u0026nbsp;6a\u003c/b\u003e). However, when their discharge time series are log-transformed and standardized (\u003cb\u003eExtended Data Fig.\u0026nbsp;6c\u003c/b\u003e), the records are significantly correlated with one another and with the tide gauge record (\u003cb\u003eExtended Data Fig.\u0026nbsp;6b\u003c/b\u003e). This supports our argument that the first principal component is representative of common variability shared by stream gauges within a 4\u0026deg; box (\u003cb\u003eExtended Data Fig.\u0026nbsp;6c\u003c/b\u003e). Furthermore, the most downstream record within the Potomac River, on which the Washington, DC, tide gauge is located, is highly correlated with the principal component-based index from the 4\u0026deg; box over their overlapping period (R\u003csup\u003e2\u003c/sup\u003e\u0026thinsp;=\u0026thinsp;0.82). Similar results were identified within other river systems around the world, suggesting that this approach is usefully applied in the context of our global assessment.\u003c/p\u003e \u003cp\u003eFor wind stress, we use zonal and meridional wind stress from the 20th century reanalysis dataset v3 covering 1900 to 2015\u003csup\u003e74\u003c/sup\u003e and the NCEP-NCAR Reanalysis 1 covering 1948 to 2021\u003csup\u003e75\u003c/sup\u003e. Since neither reanalysis covers the full 1900\u0026ndash;2021 study period, we used wind stresses from the 20th century reanalysis for 1900\u0026ndash;2015 and the NCEP-NCAR reanalysis for 2016\u0026ndash;2021. Note that we offset the NCEP-NCAR reanalysis to have the same time mean value and standard deviation as the 20th century reanalysis over the period 2011\u0026ndash;2015. As with the stream gauges, we select zonal and meridional wind stress from a box of 3\u0026deg; around the respective tide gauge. We note that the specific choice of the grid box size does not appreciably alter the results because wind stresses are typically characterized by large-scale atmospheric patterns at this temporal scale. We calculate principal components from all wind stress time series to reduce dimensionality and select sufficient leading modes that \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\ge\\:95\\%\\)\u003c/span\u003e\u003c/span\u003e of the wind stress variance within the box is explained.\u003c/p\u003e \u003cp\u003eThe stepwise regression model is then built by using the linearly-detrended leading principal components of zonal and meridional wind stress, and, if available over at least 75% of the tide gauge record, the linearly detrended river discharge index as predictors and the linearly detrended CSL-TG time series as the predictand. The estimated regression coefficients are then applied to non-detrended predictors, selected by the stepwise algorithm, to include trends into the final estimate. Large nonlinear VLM signals can influence the estimation of regression coefficients. Therefore, we build three different regression models, one over the entire period, and two over two equally sized sub-periods. We then visually inspect each record and the associated estimates of near-coastal processes. If regression coefficients and the associated estimates of near-coastal processes show large differences between different sub-periods, we either select the regression model built over a nearly linear period of CSL-TG or entirely discard the estimate of near-coastal processes (sometimes required in tectonically highly active regions such as Japan). We also note that due to the temporal availability of stream gauge records in the GSIM database, the approach of estimating river effects on tide gauges can only be made from 1900 to 2015 (except for U.S. stream gauges which were updated with NOAA data), i.e., missing the last six years of our study period (2016\u0026ndash;2021). Thus, CSL-TG time series with river discharge effects removed outside the U.S. only cover the period 1900\u0026ndash;2015. An example of the modelled near-coastal processes at Washington, DC, is shown in \u003cb\u003eExtended Data\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea. The tide gauge is situated more than 200 km upstream along the Potomac River, which discharges into Chesapeake Bay. River discharge is the leading near-coastal process in this case. Together with winds, it explains 60% of the variability in the Washington, DC, CSL-TG time series. Thus, removing those signals substantially reduces interannual variability in the CSL-TG time series. On average (median), near-coastal processes explain\u0026thinsp;~\u0026thinsp;53% of the variability in CSL-TG time series worldwide (\u003cb\u003eExtended Data\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb), though their influence is usually limited to interannual timescales.\u003c/p\u003e \u003cp\u003e \u003cb\u003eData for VLM Comparison\u003c/b\u003e. We compare three VLM datasets to our CSL-TG estimates: ALT-TG as well as GNSS from ULR\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e and NGL\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. The ALT-TG estimates are based on satellite altimetry data from AVISO distributed through the Copernicus Marine Environment Monitoring Service (CMEMS) (Copernicus Climate Change Service, Climate Data Store, 2018). We use satellite altimetry data on the same spatial grid as the reconstruction and as re-gridded by ref. 3. The inverted barometer correction is added back to the raw sea-surface height data, and the deformation component of the present-day barystatic sea-level changes (from the CSL reconstruction based on ref 63) is also added. Thus, CSL-TG and ALT-TG estimates provide VLM estimates that include GIA and other geological, tectonic or human processes but exclude deformation through surface loading by present-day land ice and hydrology. The ULR-based GNSS estimates were produced within the third International GNSS Service reprocessing campaign. These data are available near tide gauges with a median station record length of 13.1 years and robust uncertainty estimates based on correlated noise\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. Even though ULR focuses on VLM estimates near tide gauges, there are only 65 locations where the GNSS station is within 5 km of the tide gauge location. VLM varies over short spatial scales, but since GNSS stations are seldom precisely co-located with tide gauges a distance criterion was chosen that allows enough GNSS stations to satisfy it. The NGL VLM dataset is also based on GNSS, but it uses a much larger number of uniformly processed GNSS records that are interpolated to all locations on the Earth\u0026rsquo;s land surface\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. Each estimate is provided with an uncertainty that considers the number of GNSS observations used for interpolation, the distance of each GNSS observation to the grid point of interest, the uncertainty of the trend estimates, and the spatial variability of trend estimates\u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. Here, we follow the recommendation of ref. 24 and only consider locations that are classified as \u0026lsquo;good\u0026rsquo;, which results in 153 overlapping sites. To avoid double counting the VLM effects related to present-day surface loading through ice and hydrology (which is explicitly modelled by the reconstruction as CSL), we remove the deformational contribution since 1993 from GNSS estimates. We also add the GIA sea-surface height component from the weighted Kalman smoother-determined GIA fields to the GNSS estimates\u003csup\u003e\u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e77\u003c/span\u003e\u003c/sup\u003e. We use raw GNSS time series for comparison purposes in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e and \u003cb\u003eExtended Data\u003c/b\u003e Figs.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, and 5. The associated GNSS time series were downloaded from the NGL website (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttp://geodesy.unr.edu/index.php\u003c/span\u003e\u003cspan address=\"http://geodesy.unr.edu/index.php\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). For the time series, the annual deformational component of surface loading through ice and hydrology was temporally interpolated onto the times of the weekly GNSS observations and subsequently subtracted. The GIA sea-surface height component was added in a similar fashion as for the linear GNSS estimates above.\u003c/p\u003e \u003cp\u003eThe groundwater extraction data for Bangkok (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003ea)\u003csup\u003e\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e as well as the benchmark compilation (based on a combination of historical leveling data, GNSS, and InSAR) at Venice (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003eb)\u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e were not publicly available. Therefore, both records were digitized from the original publications using online digitization software Automeris (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://apps.automeris.io/wpd4/\u003c/span\u003e\u003cspan address=\"https://apps.automeris.io/wpd4/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003cb\u003eEarthquake database\u003c/b\u003e. We use the global ANSS Comprehensive Earthquake Catalog from the USGS (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://earthquake.usgs.gov/earthquakes/search/\u003c/span\u003e\u003cspan address=\"https://earthquake.usgs.gov/earthquakes/search/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). We search for earthquakes with magnitude 7 or larger. From the respective database we then search for earthquakes within 4\u0026deg; of a tide gauge that overlap temporally with available sea-level measurements.\u003c/p\u003e \u003cp\u003e \u003cb\u003eChange point Detection\u003c/b\u003e. The CSL-TG differential does not solely reflect nonlinear VLM but may also feature abrupt and unphysical change points (e.g., through unaccounted datum shifts and benchmark issues) in tide gauge records\u003csup\u003e\u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e77\u003c/span\u003e\u003c/sup\u003e. To test the extent to which CSL-TG time series are affected by change points, we apply two different change point detection algorithms\u003csup\u003e\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e78\u003c/span\u003e,\u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e79\u003c/span\u003e\u003c/sup\u003e and visual inspection. The first change point approach, DiscoTimeS\u003csup\u003e\u003cspan citationid=\"CR78\" class=\"CitationRef\"\u003e78\u003c/span\u003e\u003c/sup\u003e, estimates a variable number of change points, discontinuities (i.e., offsets at the respective change point), piecewise trends of the individual elements, noise properties (AR1 noise) and their uncertainties. The second, a change point detection algorithm from ref. 79, provides the number, location, and probability of potential change points with associated uncertainties based on piecewise regression models. Both change points algorithms provide change points not only indicative of datum shifts but also sometimes related to major earthquakes. Since the latter corresponds to the nonlinear VLM that we seek to resolve, we visually screen each site with significant change points identified by one or both approaches. If a shift aligns with a known earthquake, we keep the CSL-TG time series as is. If we find no indication for an earthquake and related co-seismic VLM and/or find notes on potential, yet unaccounted for datum shifts in the PSMSL documentation, we correct the CSL-TG time series for the associated change point. This procedure may omit smaller magnitude earthquakes associated with volcanic eruptions and dike intrusions that may be accompanied by significant VLM\u003csup\u003e\u003cspan citationid=\"CR80\" class=\"CitationRef\"\u003e80\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eWe identify 30 sites with significant datum shifts not connected to earthquakes, many of which are noted in the PSMSL database but not accounted for due to missing benchmark information (\u003cb\u003eExtended Data\u003c/b\u003e Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). To illustrate the effect this has on our results, we compare the resulting linear trends to GNSS estimates from NGL\u003csup\u003e\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. Before their correction, large biases exist between both products (0.06\u0026thinsp;\u0026plusmn;\u0026thinsp;4.14 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e). After the change point correction, biases are reduced to 0.09\u0026thinsp;\u0026plusmn;\u0026thinsp;1.4 mm yr\u003csup\u003e-\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e, a value much closer to statistics reported from the validation sites.\u003c/p\u003e \u003cp\u003e \u003cb\u003eLinear and Nonlinear Trends\u003c/b\u003e. Linear trends are calculated using ordinary least squares regression under the assumption that the residuals are normally distributed and can be described by an autoregressive process of order 1\u003csup\u003e81\u003c/sup\u003e. To test whether trends calculated from 1993 to 2021 and 1964 to 1992 in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003eb, c are statistically significant, we perform a Monte-Carlo experiment. We estimate the linear long-term trend in CSL-TG at each location and the associated variance and lag 1 autocorrelation parameter g of the residual noise. To avoid inflated values of the variance and the autocorrelation parameter g due to large nonlinear trends or sudden shifts, we estimate the parameters of moving 10-year boxes and subsequently calculate the mean over all parameter values. We then create 1000 random series as pseudo-observations, add the linear long-term trend, estimate trends over the same sub-periods, and calculate the associated trend differences. If an observed difference is larger than 95% of the trend differences in the Monte-Carlo experiment, the difference is considered statistically significant.\u003c/p\u003e \u003cp\u003eNonlinear trends are calculated using Singular Spectrum Analysis (SSA)\u003csup\u003e\u003cspan citationid=\"CR82\" class=\"CitationRef\"\u003e82\u003c/span\u003e,\u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e83\u003c/span\u003e\u003c/sup\u003e. SSA is a nonparametric spectral estimation approach that uses lagged copies of the time series that are used to define coordinates in a phase space to approximate a nonlinear trend. The number of lagged copies is called the embedding dimension. Here the embedding dimension is set to 5, which extracts decadal signals from the associated time series. The SSA tool used here applies time series padding at the ends of the series using the minimum roughness criterium. Uncertainties are modelled using an autoregressive process of order 1.\u003c/p\u003e \u003cp\u003e \u003cb\u003eStatistical tests\u003c/b\u003e. We use a non-parametric Kolmogorov-Smirnov test (KS-test) to assess whether two different samples of RSL rates, or RSL rate standard deviations, belong to the same probability distribution. The KS-test quantifies the maximal distance between two distributions. The null hypothesis assumes that two samples share the same reference probability distribution. This null hypothesis is rejected if the probability that the two samples share the same reference probability becomes smaller than 5%.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e. The tide gauge data used in this study is publicly available from the Permanent Service of Mean Sea Level (https://www.psmsl.org/), while the GRD fingerprints and VLM estimates at individual locations are accessible from the ref. 64. The CSL reconstruction is publicly available under: https://doi.org/10.5281/zenodo.10621070. All data used in the study is available under: https://doi.org/10.5281/zenodo.14866331 \u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCode availability\u003c/strong\u003e. All codes to produce the papers results are publicly available under: https://doi.org/10.5281/zenodo.14866331 \u003c/p\u003e\u003cp\u003e\u003cstrong\u003eAcknowledgements:\u0026nbsp;\u003c/strong\u003eS.D., T.W., C.G.P., and P.T. acknowledge the NASA grant 80NSSC20K1241 and J.X.M. the MacArthur Foundation. S.D. also acknowledges David and Jane Flowerree for their endowment funds.\u003c/p\u003e\n\u003cstrong\u003eCorrespondence\u003c/strong\u003e: Correspondence and requests should for materials should be addressed to S.D.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions:\u0026nbsp;\u003c/strong\u003eS.D. designed and performed the research and wrote the first draft of the paper. J.O. ran the DiscoTimeS algorithm and supported the evaluation of GNSS data. W.C. updated the GSIM database with USGS stream gauges for the period after 2015. C.G.P. and R.C gave advice on the implementation of the river discharge correction. J.X.M., J.O. and C.E. helped with the interpretation of seismic events. T.E.T. provided advice on the interpretation of nonlinear subsidence in depositional areas. All authors shared ideas and contributed to the writing of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests:\u0026nbsp;\u003c/strong\u003eThe authors declare no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eOppenheimer, M., Glavovic, B., Hinkel, J., van de Wal, R., Magnan, A. K., Abd-Elgawad, A., ... \u0026amp; Sebesvari, Z. (2019). Sea level rise and implications for low lying islands, coasts and communities.\u003c/li\u003e\n\u003cli\u003eFox-Kemper, B., Hewitt, H. T., Xiao, C., A\u0026eth;algeirsd\u0026oacute;ttir, G., Drijfhout, S. S., Edwards, T. L., ... \u0026amp; Yu, Y. (2021). Ocean, cryosphere and sea level change. Climate change 2021: the physical science basis. Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change. \u003cem\u003eP. Zhai, editor;, A. 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In \u003cem\u003eAGU fall meeting abstracts\u003c/em\u003e (Vol. 2001, pp. V42C-1037).\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nature-portfolio","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"","title":"Nature Portfolio","twitterHandle":"","acdcEnabled":false,"dfaEnabled":false,"editorialSystem":"ejp","reportingPortfolio":"","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-6024708/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6024708/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e \u003cb\u003eVertical land motion (VLM) is a key driver of relative sea-level (RSL) changes in coastal areas. Rates of VLM can vary in time due to both anthropogenic (e.g., subsurface fluid extraction) and natural (e.g., sediment compaction, volcano-tectonic activity) processes. However, such nonlinear behavior has not been included in 20th century sea-level budgets or in sea-level projections due to a lack of long-term observations over relevant temporal and spatial scales. Here, we use a probabilistic reconstruction of large-scale climate-related sea level (CSL) from 1900 to 2021 to estimate VLM at a global set of tide gauge stations. We interpret differences between CSL and tide-gauge records (CSL-TG) primarily in terms of VLM and argue that the CSL-TG residuals quantify previously overlooked temporal variations in VLM primarily related to subsurface fluid withdrawal, seismic, and volcanic activity. We demonstrate that decadal variations in the resulting regional RSL trends can be an order of magnitude larger than variations due to CSL, introducing misestimates of up to ~\u0026thinsp;75 mm yr\u003c/b\u003e \u003csup\u003e \u003cb\u003e\u0026minus;\u0026thinsp;1\u003c/b\u003e \u003c/sup\u003e \u003cb\u003ein sea level projections based on linear extrapolations. Our variable VLM estimates provide new constraints on geophysical models of anthropogenic and volcano-tectonic crustal motions and pave the way for more robust, site-specific sea-level projections.\u003c/b\u003e\u003c/p\u003e","manuscriptTitle":"Variable Vertical Land Motion Over the 20th Century Inferred at Tide Gauges","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-03-18 10:22:03","doi":"10.21203/rs.3.rs-6024708/v1","editorialEvents":[],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"nature-geoscience","isNatureJournal":true,"hasQc":false,"allowDirectSubmit":false,"externalIdentity":"ngeo","sideBox":"Learn more about [Nature Geoscience](http://www.nature.com/ngeo/)","snPcode":"","submissionUrl":"","title":"Nature Geoscience","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"ejp","reportingPortfolio":"Nature Research","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"bff30e8a-6634-476c-a565-1f042600cc8a","owner":[],"postedDate":"March 18th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[{"id":44919565,"name":"Earth and environmental sciences/Environmental sciences/Environmental impact"},{"id":44919566,"name":"Earth and environmental sciences/Natural hazards"},{"id":44919567,"name":"Earth and environmental sciences/Ocean sciences/Physical oceanography"},{"id":44919568,"name":"Earth and environmental sciences/Solid Earth sciences/Seismology"}],"tags":[],"updatedAt":"2025-04-24T13:01:16+00:00","versionOfRecord":[],"versionCreatedAt":"2025-03-18 10:22:03","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-6024708","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-6024708","identity":"rs-6024708","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}