Bottom Friction in a Baroclinic Ocean: Influences on Sea Level and Slope Currents

Sea-level measurements along the western coast of the Americas have shown that there is a strong signal at ENSO frequencies (approximately 2π/2 yr−1 to 2π/5 yr−1) that propagates poleward at about 40 to 90 cm s−1. This ENSO sea level signal must be associated with ENSO coastal currents, but because adequate interannual current time series are unavailable, the structure and strength of these currents are not known. Coastal ENSO currents must be fundamentally affected by bottom topography and bottom friction, but previous theory has not taken these effects into account. A near-boundary numerical model with realistic bottom friction, stratification, and shelf and slope topography was therefore constructed to study ENSO coastal flow. (i) At ENSO frequencies, previous results for models with no bottom topography and no bottom friction suggest that sea level should not propagate poleward. With realistic bottom friction and bottom topography coastal sea level propagates poleward at speeds similar to those observed. A simple mechanism based on the effect of bottom friction on offshore propagating geostrophic alongshore flow explains why coastal poleward alongshore propagation occurs. Calculations also show that the depths of the 20°C and 15°C isotherms also propagate poleward at approximately the observed speeds. (ii) Sea levels change little across the shelf and slope at lower latitudes and slowly decrease in amplitude alongshore due to bottom friction. The small sea level change across the shelf and slope implies that the long sea level records available are useful for analysing the nearby deep ocean variability. (iii) Lower-order deep-sea vertical modes incident at the equator are rapidly scattered mainly by bottom friction into other (higher) vertical modes. Scattering has two main effects. Those vertical modes equatorward of their critical latitudes propagate offshore as Rossby waves interfere with each other and produce a complicated deep-sea velocity field, especially at low latitudes where most of the vertical modes are propagating offshore. Those vertical modes poleward of their critical latitudes only exist as coastally trapped motion and give rise to a trapped ENSO jet over the continental slope. This jet has an amplitude peak of order 20 cm s−1 and is trapped within about 500 m of the bottom. The jet core is approximately 180° out of phase with near-surface currents over the continental shelf and slope. Therefore, during (say) the El Niño part of the ENSO cycle when the sea level is high and the near-surface flow over the continental shelf and slope tends to be poleward, the flow in the jet core tends to be equatorward. Present observations are inadequate to prove or disprove the existence of this ENSO continental slope jet. Due to bottom friction, the alongshore velocity decreases shoreward of the shelf break and is negligible at the coast. (iv) Critical latitudes for vertical modes change when the coastline angle changes and so motion near the boundary is affected by coastline angle. When the coastline is less meridional, coastal sea level and the 20°C and 15°C isotherm depths propagate poleward more rapidly (although still at approximately the observed speeds). The ENSO jet has its maximum amplitude nearer the equator. (v) In the biologically important top 100 m or so of the ocean alongshore particle displacements seaward of the shelf can be ∼1000 km. Interannual near-surface alongshore currents over the continental shelf and slope lead coastal sea level by several months.

Coastal sea level changes in Europe from GPS, tide gauge, satellite altimetry and GRACE, 1993–2011

An historical objective analysis of subsurface temperature and salinity was carried out on a monthly basis from 1945 to 2003 using the latest observational databases and a sea surface temperature analysis. In addition, steric sea level changes were mainly examined using outputs of the objective analyses. The objective analysis is a revised version of Ishii et al. and is available at 16 levels in the upper 700 m depth. Artificial errors in the previous analysis during the 1990s have been worked out in the present analysis. The steric sea level computed from the temperature analysis has been verified with tide gauge observations and TOPEX/Poseidon sea surface height data. A correction for crustal movement is applied for tide gauge data along the Japanese coast. The new analysis is suitable for the discussion of global warming. Validation against the tide gauge reveals that the amplitude of thermosteric sea level becomes larger and the agreement improves in comparison with the previous analysis. A substantial part of local sea level rise along the Japanese coast appears to be explained by the thermosteric effect. The thermal expansion averaged in all longitudes from 60°S to 60°N explains at most half of recent sea level rise detected by satellite observation during the last decade. Considerable uncertainties remain in steric sea level, particularly over the southern oceans. Temperature changes within MLD make no effective contribution to steric sea level changes along the Antarctic Circumpolar Current. According to statistics using only reliable profiles of the temperature and salinity analyses, salinity variations are intrinsically important to steric sea level changes in high latitudes and in the Atlantic Ocean. Although data sparseness is severe even in the latest decade, linear trends of global mean thermosteric and halosteric sea level for 1955 to 2003 are estimated to be 0.31 ± 0.07 mm/yr and 0.04 ± 0.01 mm/yr, respectively. These estimates are comparable to those of the former studies.

Estimation of steric sea level variations from combined GRACE and Jason-1 data

Sea level has risen significantly in the recent decades and is expected to rise further based on recent climate projections. Ocean reanalyses that synthetize information from observing networks, dynamical ocean general circulation models, and atmospheric forcing data offer an attractive way to evaluate sea level trend and variability and partition the causes of such sea level changes at both global and regional scales. Here, we review recent utilization of reanalyses for steric sea level trend investigations. State-of-the-science ocean reanalysis products are then used to further infer steric sea level changes. In particular, we used an ensemble of centennial reanalyses at moderate spatial resolution (between 0.5 × 0.5 and 1 × 1 degree) and an ensemble of eddy-permitting reanalyses to quantify the trends and their uncertainty over the last century and the last two decades, respectively. All the datasets showed good performance in reproducing sea level changes. Centennial reanalyses reveal a 1900–2010 trend of steric sea level equal to 0.47 ± 0.04 mm year−1, in agreement with previous studies, with unprecedented rise since the mid-1990s. During the altimetry era, the latest vintage of reanalyses is shown to outperform the previous ones in terms of skill scores against the independent satellite data. They consistently reproduce global and regional upper ocean steric expansion and the association with climate variability, such as ENSO. However, the mass contribution to the global mean sea level rise is varying with products and its representability needs to be improved, as well as the contribution of deep and abyssal waters to the steric sea level rise. Similarly, high-resolution regional reanalyses for the European seas provide valuable information on sea level trends, their patterns, and their causes.

Satellite radar altimetry is often considered to be the most succesful spaceborne remote sensing technique ever. Satellite radar altimeters were designed for static geodetic and ocean dynamics applications. The goal of the geodetic mission phases, which have a dense ground-track spacing, is primarily to acquire information about the marine gravity field. This enables the estimation of mean dynamic topography (geographical sea surface height patterns due to ocean currents) and deep-ocean bathymetry. The primary goal of the oceanographic mission phases is to gain information about time-varying currents and ocean dynamics. TOPEX/Poseidon is the first altimetry mission to reveal sea surface height variations related to ocean dynamics as the El Nino Southern Oscillation (ENSO). During the mission it became clear that secular changes in sea level could also be monitored. Already in 1995, Nerem (1995) computed a Global Mean Sea Level (GMSL) time series from the TOPEX/Poseidon data. Currently, the GMSL record spans 26 years, in which TOPEX/Poseidon time series is extended with the Jason-1a2a3 observations. The estimated secular trend of GMSL over the altimetry era is approximately 3 mm yr−1. The succes of the TOPEX/Poseidon mission spawned the Argo project with the deployment of the first floats in the year 2000. One argued that Argo would support the future Jason missions in separating changes into the two components (density and mass) of sea level. The Argo project aims to estimate temperature and salinity over a depth of 2000 meter using floats, which enable the estimation of density or steric sea level changes. By subtracting the steric signal from the absolute sea level measured by Jason (steric-corrected altimetry), the second component of sea level changes, mass, is estimated. The launch of the Gravity Recovery And Climate Experiment (GRACE) satellites in 2002 made it possible to independently validate oceanic mass variations. If the sum of the mass and steric components equals total sea level within the uncertainties, the sea level is said to be closed. Besides these two oceanic components, ocean bottom deformation or Vertical Land Motion (VLM) also affects the sea level observed by altimeters. Over the open ocean VLM signals are generally small after a correction for Glacial Isostatic Adjustment (GIA), but near large mass variations they might become significant. Additionally, tide-gauge records are affected by VLM changes, because they are connected to land. Therefore they measure sea level relative to the sea floor, while the satellite altimeters observe the absolute variations. To bring tide gauges in the same reference frame as the altimeters, corrections for VLM have to be applied, which is usually done with nearby Global Navigation Satellite System (GNSS) data...

Modeled steric and mass-driven sea level change caused by Greenland Ice Sheet melting

Since 1993, the global mean sea level (GMSL) has been rising at a rate of about 3 mm/a detected by multi-satellite radar altimetry. The spaceborne gravimetry satellite, Gravity Recovery and Climate Experiment (GRACE), has been monitoring Earth’s surface water mass variations since 2002. La Nina and El Nino events induces inter-annual variations of the GMSL manifest in ocean mass and steric sea level changes, linked with corresponding changes in land water cycle. Here we study the GMSL inter-annual variations and global land water mass changes integrating satellite altimetry, GRACE and Argo data, 2010–2016, during which strong La Nina and El Nino events occurred. First, we quantify the evolutions of GMSL during the study time period. The results show that during the 2010–2011 La Nina episode, the GMSL dropped rapidly to 7.6 mm, with the ocean mass and the steric sea level decreased to 5.1 mm and to 1.8 mm, respectively. GMSL then increased to 19.2 mm, with ocean mass increased to 12.3 mm during 2011–2013. From 2013 to 2014, the steric GMSL increased by 2.1 mm, and the ocean mass variations dropped by 2.3 mm, thus the total GMSL remains nearly unchanged. During the strong 2014–2016 El Nino, ocean mass variations increased by 13.1 mm and contributed over 90% of GMSL change, which rises up by 15.1 mm. Next, we analyze land water mass changes in four regions, namely Australia and Southeast Asia, South America, North America, Antartica and Greenland, and investigate their linkage to the GMSL inter-annual variations. Here, we used the Forward Modelling (FM) method for GRACE data post-processing to reduce signal leakage problem to estimate land water storage mass changes. The results show that during the 2014–2016 El Nino episode, the global ocean mass increasing is mainly due to the total land water storage decreasing in Australia and Southeast Asia, South America, and Antartica and Greenland. The inter-annual variations of global ocean mass variation during 2003–2016 is closely linked with the land water storage changes from Australia and Southeast Asia and the South America regions, which are strongly affected by La Nina and El Nino events. During 2003–2016, the ice ablations from the Antartica and Greenland ice sheets directly contributed to GMSL rising, as opposed to the land water mass increase in the North America region, which has a negative effect on GMSL trend. Finally, we estimated the GMSL, ocean mass and steric sea level trends at 3.4±0.4, 2.1±0.3, and 1.1±0.2 mm/a, respectively during 2003–2016, and 6.5±1.2, 4.1±1.0, and 1.9±0.4 mm/a, respectively during 2010–2016. We concluded that the ocean mass variation contributed to the GMSL trend two times larger than that of the steric sea level contribution during these two time periods. However the ocean mass variation is roughly equivalent to the steric sea level variation during 2003–2010.

During the winter of 2013–2014, the averaged tide gauge (TG) coastal sea level (CSL) anomaly north of 40°N was a record low of −107 mm for the period of 1948–2016. Statistical analysis indicates that this large drop was a once-in-a-century event and closely related to an unusual ocean warming event known as “The Blob”. The Blob developed in the NE Pacific during the winter of 2013–2014. Both the Blob and record-low CSL can be attributed to wind changes associated with an unusually high sea level pressure (SLP) pattern over the NE Pacific. The anomalous local longshore winds induced by the positive SLP anomalies caused strong offshore Ekman transport along the coast of NE Pacific, thereby leading to the record-low CSL. In addition, the steric sea level changes also contributed a significant part (17%) to the record-low CSL. The Pacific Decadal Oscillation (PDO), as the primary variability mode in the NE Pacific on decadal time scales, did not contribute to the emergence of this extreme CSL event.

Regional sea level prediction plays a vital role in understanding the impacts of climate change and guiding the design of coastal infrastructure. Sea level rise is mainly driven by two primary factors: barystatic sea level change, caused by the melting of ice sheets, glaciers, and run-off of terrestrial water, and by steric sea level change, resulting from the expansion of seawater due to temperature and salinity changes. The former can be monitored from the Gravity Recovery and Climate Experiment (GRACE) and GRACE Follow-On missions, and the latter is commonly calculated based on ocean salinity and temperature models. In this study, satellite altimetry was used to observe relative sea level changes spanning from May 2002 to April 2023. Specifically, barystatic sea level changes were derived using Mass Concentration (Mascon) solutions, while the steric height was estimated through the Ocean Physics Reanalysis model. According to the sea level budget equation, the total sea level change aligns closely with the combined contributions of barystatic and steric sea level components, validating the consistency of the data and methodology.Machine learning has become increasingly significant in climate research in recent years. It enables the analysis of large and complex datasets that exceed human processing capabilities. Among the machine learning techniques, the Long Short-Term Memory (LSTM) model is particularly effective for the time series prediction due to its ability to capture long-term dependencies and patterns through its gated mechanisms. LSTM models excel at handling trends, seasonality, and noise in data, making them ideal for understanding the temporal dynamics of sea level changes and predicting future values.In this research, we applied a CNN-LSTM model to predict total, barystatic, and steric sea level changes. The model leverages the feature extraction capabilities of convolutional neural networks (CNNs) combined with the sequential learning strengths of LSTM. The results of this study provide valuable insights into the contributions of mass and steric components to regional sea level changes. By predicting these signals, this research enhances our understanding of the mechanisms driving the sea level rise, offering the critical information for climate change mitigation and coastal adaptation planning.

Understanding global sea level variations and exploring their causes hold significant importance for future climate change predictions and the sustainable development of mankind, with the steric sea level (SSL) variations being one of the primary contributors to these changes. Here, we utilize four types of temperature and salinity products (i.e., EN4, IAP, SODA, and GDCSM) to investigate the spatiotemporal characteristics of global SSL changes from 1980 to 2020. We also explore the relationship between SSL changes and the El Niño-Southern Oscillation (ENSO) phenomenon. The findings reveal a rising trend of 0.64–0.97 mm/a in global SSL over the past 40 years, and the annual amplitudes of SSL time series are within the range of 0–50 mm. The SSL trend at a depth of 0–100 m exerts the greatest influence on the overall trend. The ENSO phenomenon has an obvious influence on sea level changes both in the equatorial Pacific region and global scale. The changes in the global sea level (GSL) associated with ENSO are primarily caused by changes in SSL. This study benefits the understanding of SSL changes and their connection to climate change, serves as a reference for comprehensively assessing sea level change mechanisms using diverse datasets and remote sensing technology, and further provides a scientific basis for the sustainable development of mankind in coastal areas.

In comparison with the number of tide gauges measuring in-situ sea-level change along the Northern Hermisphere coastlines, the Southern Hemisphere has a poor spatial distribution of stations. For example, along the South American Atlantic coastline, only 12 tide gauges are registered at the Permanent Service for Mean Sea-level (PSMSL), of which only two have been updated in the last three years. While satellite altimetry can be used to provide data in locations where there is no in-situ data, estimating coastal sea-level change using altimetry data is challenging due to the distortion of the satellite signal close to the land. Consequently, sea-level change along the South American Atlantic coastline is still poorly understood. Here, we fill this gap by using coastal altimetry products together with a new network of tide gauges deployed along the coast of Brazil (by the SIMCosta project). Via a sea-level budget analysis, we look at the regional drivers of sea-level change along the coast. Recently, a large effort has been put towards developing algorithms that improve the accuracy of standard radar altimetry in coastal regions. Here, we compare both a coastal altimetry product (XTRACT/ALES) and a standard altimetry product (from CMEMS) to the local tide gauges. Previous studies have shown that, for some regions, coastal sea level is driven by open ocean sea-level change ( e.g., Dangendorf et al, 2021). Following this approach, we use clusters of coherent sea-level variability (Camargo et al., 2022), extracted with a network detection algorithm (delta-Maps), that extend to the open ocean, as proxies of the drivers of sea-level change along the coast.  The northern part of the study region, covering the Amazon Plateau, has a good match between the coastal altimetry-observed sea-level change and the sum of the drivers. The sum of the drivers and coastal altimetry trends also match, considering the uncertainty bars, for the most southern part, covering the Patagonian Shelf. For the other regions, we find a large difference between the coastal altimetry-observed sea-level change and the sum of the drivers. Thus, it is possible that these regions cover large-scale features, which are not strongly correlated with coastal sea level. ReferencesCamargo, C. M. L., Riva, R. E. M., Hermans, T. H. J., Schütt, E. M., Marcos, M., Hernandez-Carrasco, I., and Slangen, A. B. A.: Regionalizing the Sea-level Budget With Machine Learning Techniques, EGUsphere [preprint, accepted], https://doi.org/10.5194/egusphere-2022-876, 2022. Dangendorf, S., Frederikse, T., Chafik, L., Klinck, J. M., Ezer, T., & Hamlington, B. D.: Data-driven reconstruction reveals large-scale ocean circulation control on coastal sea level. Nature Climate Change, 11, 514-520. https://doi.org/10.1038/s41558-021-01046-1, 2021.

We investigate sea level change and variability in some areas of the Arctic region over the 1950–2009 period. Analysis of 62 long tide gauge records available during the studied period along the Norwegian and Russian coastlines shows that coastal mean sea level (corrected for Glacial Isostatic Adjustment and inverted barometer effects) in these two areas was almost stable until about 1980 but since then displayed a clear increasing trend. Until the mid‐1990s, the mean coastal sea level closely follows the fluctuations of the Arctic Oscillation (AO) index, but after the mid‐to‐late 1990s the co‐fluctuation with the AO disappears. Since 1995, the coastal mean sea level (average of the Norwegian and Russian tide gauge data) presents an increasing trend of ∼4 mm/yr. Using in situ ocean temperature and salinity data down to 700 m from three different databases, we estimated the thermosteric, halosteric and steric (sum of thermosteric and halosteric) sea level since 1970 in the North Atlantic and Nordic Seas region (incomplete data coverage prevented us from analyzing steric data along the Russian coast). We note a strong anti‐correlation between the thermosteric and halosteric components both in terms of spatial trends and regionally averaged time series. The latter show a strong change as of ∼1995 that indicates simultaneous increase in temperature and salinity, a result confirmed by the Empirical Orthogonal Function decomposition over the studied region. Regionally distributed steric data are compared to altimetry‐based sea level over 1993–2009. Spatial trend patterns of observed (altimetry‐based) sea level over 1993–2009 are largely explained by steric patterns, but residual spatial trends suggest that other factors contribute, in particular regional ocean mass changes. Focusing again on Norwegian tide gauges, we then compare observed coastal mean sea level with the steric sea level and the ocean mass component estimated with GRACE space gravimetry data and conclude that the mass component has been increasing since 2003, possibly because of the recent acceleration in land ice melt.

We show that steric sea-level varies with a period of 18.6 years along the western European coast. We hypothesize that this variation originates from the modulation of semidiurnal tides by the lunar nodal cycle and associated changes in ocean mixing. Accounting for the steric sea level changes in the upper 400 m of the ocean solves the discrepancy between the nodal cycle in mean sea level observed by tide gauges and the theoretical equilibrium nodal tide. Namely, by combining the equilibrium tide with the nodal modulation of steric sea level, we close the gap with the observations. This result supports earlier findings that the observed phase and amplitude of the 18.6-year cycle do not always correspond to the equilibrium nodal tide. This finding allows to better filter natural variability when estimating the current rate of sea level rise along the European coast. Practical applications include the detection of an acceleration of sea level rise and the comparison between tide gauge and satellite observations with sea level projections.

Closure of the global mean sea level (GMSL) budget is essential to understand the causes of GMSL rise. Accounting for the recent progress in observing and estimating of GMSL, steric sea level and ocean mass changes, this study assesses the budget for the GMSL trend and acceleration for the three key observational eras of 1960-2021, 1993-2023 and 2005-2023. For 1960-2021, the trend of GMSL is 1.86 ± 0.34 mm yr-1, closely matching the sum of contributions of 1.88 ± 0.13 mm yr-1, with most dominant contributions coming from steric height change and glacier melting. The observed GMSL acceleration of 0.072 ± 0.005 mm yr-2 for 1960-2021 matches contributions of 0.066 ± 0.005 mm yr-2 and is dominated by steric height change. From 1993 to 2023, the GMSL rise of 3.27 ± 0.06 mm yr-1 also aligns with contributions of 3.22 ± 0.15 mm yr-1. The acceleration of observed GMSL is 0.078 ± 0.013 mm yr-2 for this period, which is supported by the acceleration inferred from sum of contributions of 0.072 ± 0.004 mm yr-2. For 2005-2023, the observed GMSL acceleration is 0.084 ± 0.006 mm yr-2, mainly driven by steric sea level change at 0.083 ± 0.016 mm yr-2. Although the acceleration within three periods is consistent, the driver changes depend on the periods. This study reconciles the observed GMSL trend and acceleration with the sum of contributors since 1960, highlighting the importance of adequate data processing and bias corrections.