Drivers of sea level variability using neural networks

Maldives, a South Asian small island nation in the northern part of the Indian Ocean is extremely vulnerable to the impacts of Sea Level Rise (SLR) due to its low altitude from the mean sea level. This artricle attempts to estimate the recent rates of SLR in Maldives during different seasons of the year with the help of existing tidal data recorded in the Maldives coast. Corresponding Sea Surface Temperature (SST) trends, utilizing reliable satellite climatology, have also been obtained. The relationships between the SST and mean sea level have been comprehensively investigated. Results show that recent sea level trends in the Maldives coast are very high. At Male, the capital of the Republic of Maldives, the rising rates of Mean Tidal Level (MTL) are: 8.5, 7.6, and 5.8 mm/year during the postmonsoon (October-December), Premonsoon (March-May) and southwest monsoon (June-September) seasons respectively. At Gan, a station very close to the equator, the increasing rate of MTL is maximum during the period from June to September (which is 6.2 mm/year). These rising trends in MTL along the Maldives coast are certainly alarming for this small developing island nation, which is hardly one meter above the mean sea level. Thus there is a need for careful monitoring of future sea level changes in the Maldives coast. The trends presented are based on the available time-series of MTL for the Maldives coast, which are rather short. These trends need not necessarily reflect the long-term scenario. SST in the Maldives coast has also registered significant increasing trend during the period from June to September. There are large seasonal variations in the SST trends at Gan but SST and MTL trends at Male are consistently increasing during all the seasons and the rising rates are very high. The interannual mode of variation is prominent both in SST as well as MTL. Annual profile of MTL along the Maldives coast is bimodal, having two maxima during April and July. The April Mode is by far the dominant one. The SST appears to be the main factor governing the sea level variations along the Maldives coast. The influence of SST and sea level is more near the equatorial region (i.e., at Gan). There is lag of about two months for the maximum influence of SST on the sea level. The correlation coefficient between the smoothed SST and mean tidal level at Gan with lag of two months is as high as ~ +0.8, which is highly significant. The corresponding correlation coefficients at Male with the lags of one and two months are +0.5 and +0.3, respectively. Thus, the important finding of the present work for the Maldives coast is the dominance of SST factor in sea level variation, especially near the region close to the equator.

The UNEP in its regional seas program in 1989 has included Pakistan in a group of countries which are vulnerable to the impact of rising sea level. If the present trend of sea level rise (SLR) at Karachi continues, in the next 50 years the sea level rise along the Pakistan Coast will be 50 mm (5 cm). Since the rising rates of sea level at Karachi are within the global range of 1-2 mm/year, the trends may be treated as eustatic SLR. Historical air temperature and sea surface temperature (SST) data of Karachi also show an increasing pattern and an increasing trend of about 0.67°C has been registered in the air temperature over the last 35 years, whereas the mean SST in the coastal waters of Karachi has also registered an increasing trend of about 0.3°C in a decade. Sindh coastal zone is more vulnerable to sea level rise than Baluchistan coast, as uplifting of the coast by about 1-2 mm/year due to subduction of Indian Ocean plate is a characteristic of Baluchistan coast. Within the Indus deltaic creek system, the area nearby Karachi is more vulnerable to coastal erosion and accretion than the other deltaic region, mainly due to human activities together with natural phenomena such as wave action, strong tidal currents, and rise in sea level. Therefore, The present article deals mainly with the study of dynamical processes such as erosion and accretion associated with sea level variations along the Karachi coast and surrounding Indus deltaic coastline. The probable beach erosion in a decade along the sandy beaches of Karachi has been estimated. The estimates show that 1.1 mm/year rise in sea level causes a horizontal beach loss of 110 mm per year. Therefore, coast eroded with rise in sea level at Karachi and surrounding sandy beaches would be 1.1 m during a period of next 10 years. The northwestern part of Indus delta, especially the Gizri and Phitti creeks and surrounding islands, are most unstable. Historical satellite images are used to analyze the complex pattern of sediment movements, the change in shape of coastline, and associated erosion and accretion patterns in Bundal and Buddo Islands. The significant changes in land erosion and accretion areas at Bundal and Buddo Islands are evident and appear prominently in the images. A very high rate of accretion of sediments in the northwestern part of Buddo Island has been noticed. In the southwest monsoon season the wave breaking direction in both these islands is such that the movement of littoral drift is towards west. Erosion is also taking place in the northeastern and southern part of Bundal Island. The erosion in the south is probably due to strong wave activities and in the northeast is due to strong tidal currents and seawater intrusion. Accretion takes place at the northwest and western parts of Bundal Island. By using the slope of Indus delta, sea encroachment and the land area inundation with rising sea level of 1 m and 2 m have also been estimated.

Sea-level variability in the South China Sea was investigated based on satellite altimetry, tide-gauge data, and temperature and salinity climatology. The altimetric sea-level results clearly reveal three distinct amphidromes associated with the annual cycle. The annual sea level is higher in fall/winter in the coast and shelf region and lower in summer/fall in the central sea, agreeing well with independent tide-gauge data. Averaged over the deep basin (bottom depth > 2,000 m), the annual cycle can be approximately accounted for by the steric height relative to 700 db. Significant interannual sea-level change is observed from altimetry and tide-gauge data. The interannual and longer-term sea-level variability in the altimetric data is negatively correlated (significant at the 95% confidence level) with the El Nino - Southern Oscillation (ENSO), attributed in part to the steric height change. The altimetric sea-level rise rate is 1.0 cm/year for the period from 1993 to 2001, which is consistent with the rate derived from coastal tide-gauge data and approximately accountable for by the steric height calculated relative to 700 db. The tide-gauge sea-level (steric height) rise rate of 1.05 (0.9) cm/year from 1993 to 2001 is much larger than that of 0.22 (0.12) cm/year for the period from 1979 to 2001, implying the sensitivity to the length of data as a result of the decadal variability. Potential roles of the ENSO in the interannual and longer-term sea-level variability are discussed in terms of regional manifestations such as the ocean temperature and salinity.

Sea level variations along the coasts of Sumatra and Java were investigated to determine the coastal upwelling signal that is linked to local sea surface temperature (SST) variability. We used Indonesian tidal station data together with satellite SST data and atmospheric reanalysis data. The sea level variations along the southern coast of Java have a significant coherence with remote wind, local wind, and local SST variations, with an intraseasonal time scale of 20–50 days. Assuming that a coastal upwelling signal would appear as a sea level drop (SLD), we focused on intraseasonal‐scale SLD events in the data. Significant upwelling signals are frequently observed during both the boreal summer and winter. To evaluate the impact of the coastal upwelling on local SST, we examined statistical relationships between sea level and SST variations. The results demonstrated that events that occurred during April–August were associated with local SST cooling. The horizontal distribution of the SST cooling was analogous with annual mean SST, suggesting the importance of intraseasonal‐scale coastal upwelling in forming the climatic conditions of the southeastern tropical Indian Ocean.

Projections of global sea-level rise into the future have become more pessimistic over the past five years or so. A global rise by more than one metre by the year 2100 is now widely accepted as a serious possibility if greenhouse gas emissions continue unabated. That is witnessed by the scientific assessments that were made since the last IPCC report was published in 2007. The Delta Commission of the Dutch government projected up to 1.10 m as a 'high-end' scenario (Vellinga et al 2009). The Scientific Committee on Antarctic Research (SCAR) projected up to 1.40 m (Scientific Committee on Antarctic Research 2009), and the Arctic Monitoring and Assessment Programme (AMAP) gives a range of 0.90–1.60 m in its 2011 report (Arctic Monitoring and Assessment Programme 2011). And recently the US Army Corps of Engineers recommends using a 'low', an 'intermediate' and a 'high' scenario for global sea-level rise when planning civil works programmes, with the high one corresponding to a 1.50 m rise by 2100 (US Army Corps of Engineers 2011).

Variations of the 10‐day‐averaged sea level extracted from TOPEX/POSEIDON (T/P) altimeter data are examined from October 1992 to February 1995. Data are corrected from instrumental drifts, and recent precise orbit and ocean tide corrections are used. When data from the less accurate first eight cycles are excluded and atmospheric pressure effects are not corrected, the 10‐day mean sea level varies by 5.0 mm rms. Its variations can be described by a 4.1±1 mm/yr drift, a small annual signal of 2.7 mm amplitude and a residual signal of 3.5 mm rms amplitude, and Gaussian statistics close to formal error estimates. The mean sea level rise is difficult to explain by drifts of geophysical corrections, though the case for the wet tropospheric correction and that for the orbit are uncertain. Pressure effects should be corrected relative to the global pressure averaged over the ocean. The latter shows a seasonal signal of 1 cm amplitude and apparent fluctuations of 30‐ to 70‐day periods. These fluctuations could result from errors in the atmospheric pressure fields, but they seem to be mostly related to large regional pressure evolutions. Evidence is also found for a sampling effect by the T/P orbit of pressure signals at shorter than 10‐day periods. Pressure effects on sea level are then assumed to be an inverse barometer relative to 10‐day global atmospheric pressure over the ocean, which allows analysis of the geographical repartition of the mean sea level evolution due to other effects. The mean sea level rise is comparable in the northern (4.2±2.5 mm/yr) and southern (3.7±1.9 mm/yr) hemispheres. It seems mostly related to interannual variations of the tropical ocean (41% of the global signal) and of the northern hemisphere subtropical gyres (30% of the global signal); residual noise on these regional values seems inversely proportional to the square root of the number of data points in each area. The hemispheric seasonal pressure variation relative to the globally averaged pressure over the ocean is less than 3 mm amplitude; in our calculation it is implicitely assumed that it induces a small interhemispheric water mass exchange. The amplitudes of the seasonal hemispheric sea level variations are 27 and 18 mm in the northern and southern hemispheres, respectively. These amplitudes are very close to being inversely proportional to the ocean surface in each hemisphere. The maxima of sea level in these hemispheres are reached in the last weeks of September and March, respectively. At subpolar latitudes, semiannual components are observed in each hemisphere, which are consistent with those of sea surface temperature.

Melting of the land-based ice and warming of the oceans around the world has resulted in acceleration of the pace of global mean sea level rise. Higher mean sea level causes more frequent extreme sea levels. This forces coastal cities urgently to do major preparedness and adaptation measures. In Finland, preparedness for coastal flooding hazards is relevant even though protection given by the post-glacial land uplift is helpful. This is especially true on the Finnish southern coast, where mean sea level rise is foreseen and increase of probability of high sea levels within the 21st century is expected (Pellikka et al., 2023, 2018). In the Finnish coastal area, the extreme sea level estimates are used e.g. to support infrastructure planning, flood maps and safe operation of nuclear power plants. On a short timescale, sea level variations are driven on the Finnish coast by storm surges, wind induced oscillations within the bays, and tides (playing a minor role). On the long-term side, global mean sea level rise, land uplift and the water inflow and outflow in the Danish straits (which change the total amount of Baltic Sea water) are the main factors controlling the sea level behaviour. In this presentation, a study aiming at improving extreme sea level estimates in Finland will be illustrated. Tentative results on how different sampling techniques and extrapolation approaches affect the probability estimates of coastal floods will be presented. Altogether 90 years of observations from the 13 Finnish tide gauges are analysed. We apply two different well-known sampling methods (Block Maxima and Peak Over Threshold) to the high tail of the sea level distribution and investigate which extrapolation function belonging to the family of Generalized Extreme Value (GEV) distribution matches best to the Finnish tide gauge observations. The results will be grouped into four coastal regions in Finland: the Gulf of Finland and Archipelago Sea in the south, and the Bothnian Sea and Bay of Bothnia in the west.   Pellikka, H., Johansson, M. M., Nordman, M., and Ruosteenoja, K., 2023: Probabilistic projections and past trends of sea level rise in Finland, Nat. Hazards Earth Syst. Sci., 23, 1613–1630, https://doi.org/10.5194/nhess-23-1613-2023 Pellikka, H., Leijala, U., Johansson, M. M., Leinonen, K., Kahma, K. K., 2018: Future probabilities of coastal floods in Finland, Continental Shelf Research, 157, 32-42, https://doi.org/10.1016/j.csr.2018.02.

In this study, we apply probabilistic estimates of mean sea level (MSL) rise and a sub-set of regional climate model ensemble simulations to force a numerical model of the southern North Sea, downscaling projected sea level variability to the Elbe estuary that serves as a prototype for an industrialised meso-tidal estuary. The specific forcing combination enables a localised projection of future estuarine hydrodynamics accounting for the spread of projected global sea level rise and the spread of the regional climate projection due to internal variability. Under the applied high-emission scenario, the Elbe estuary shows high decadal rates of mean water level (MWL) rise beyond 19 mm y-1, increase in the tidal range of up to 14 mm y-1 and increase in extreme water levels of up to 18 mm y-1. The bandwidth of the estuarine response is also high. For example, the range of average monthly extreme water levels is up to 0.57 m due to the spread of projected global sea level rise, up to 0.58 m due to internal variability whereas seasonal range attains 1.99 m locally. In the lower estuary, the spread of projected global sea level rise dominates over internal variability. Internal variability, represented by ensemble spread, notably impacts the range of estuarine water levels and tidal current asymmetry in the shallow upper estuary. This area demonstrates large seasonal fluctuations of MWLs, the M2 tidal amplitude and monthly extreme water levels. On the monthly and inter-annual time scales, the MWL and M2 amplitude reveal opposite trends, indicative of a locally non-linear response to the decadal MSL rise enforced at the open boundary. Overall, imposed by the climate projections decadal change and MSL rise enhance the horizontal currents and turbulent diffusivities whereas internal variability locally mitigates sea level rise–driven changes in the water column. This work establishes a framework for providing consistent regionalised scenario-based climate change projections for the estuarine environment to support sustainable adaptation development.

Measuring very low frequency sea level variations using satellite altimeter data

Internal waves generated by the interaction of the surface tides with topography are known to propagate long distances and lead to observable effects such as sea level variability, ocean currents, and mixing. In an effort to describe and predict these waves, the present work is concerned with using geographically distributed data from satellite altimeters and drifting buoys to estimate and map the baroclinic sea level associated with the M2, S2, N2, K1, and O1 tides. A new mapping methodology is developed, based on a mixed L1/L2-norm optimization, and compared with previously developed methods for tidal estimation from altimeter data. The altimeter and drifter data are considered separately in their roles for estimating tides and for cross-validating estimates obtained with independent data. Estimates obtained from altimetry and drifter data are found to agree remarkably well in regions where the drifter trajectories are spatially dense; however, heterogeneity of the drifter trajectories is a disadvantage when they are considered alone for tidal estimation. When the different data types are combined by using geodetic mission altimetry to cross validate estimates obtained with either exact-repeat altimetry or drifter data, and subsequently averaging the latter estimates, the estimates significantly improve on the previously published HRET8.1 model, as measured by their utility for predicting sea level and surface currents in the open ocean. The methodology has been applied to estimate the annual modulations of M2, which are found to have much smaller amplitudes compared to those reported in HRET8.1, and suggest that the latter estimates of these tides were not reliable. Significance Statement The mechanical and thermodynamic forcing of the ocean occurs primarily at very large scales associated with the gravitational perturbations of the sun and moon (tides), atmospheric wind stress, and solar insolation, but the frictional forces within the ocean act on very small scales. This research addresses the question of how the large-scale tidal forcing is transformed into the smaller-scale motion capable of being influenced by friction. The results show where internal waves are generated and how they transport energy across ocean basins to eventually be dissipated by friction. The results are useful to scientists interested in mapping the flows of mechanical energy in the ocean and predicting their influences on marine life, ocean temperature, and ocean currents.

Continental groundwater loss during the past century has elevated sea level by up to ~25 mm. The mass unloading associated with this depletion locally uplifts Earth's solid surface and depresses the geoid, leading to slower relative sea level rise near areas of significant groundwater loss. We computed spatial variations in sea level using a model of the solid Earth's response to estimates of groundwater depletion during the past century and find large negative deviations of ~0.4 mm/yr along the coastlines of western North America and southern Asia. This approximately corresponds to the difference between rates of sea level rise measured by tide gauges in these regions since 1930 and average rates inferred from global reconstructions. Groundwater‐induced regional variations in sea level can be larger than those due to postglacial rebound and interseismic deformation and should become increasingly important in the future as both groundwater depletion and sea level rise accelerate.

A major problem which is envisaged in the course of man-made climate change is sea-level rise. The global aspect of the thermal expansion of the sea water likely is reasonably well simulated by present day climate models; the variation of sea level, due to variations of the regional atmospheric forcing and of the large-scale oceanic circulation, is not adequately simulated by a global climate model because of insufficient spatial resolution. A method to infer the coastal aspects of sea level change is to use a statistical "downscaling" strategy: a linear statistical model is built upon a multi-year data set of local sea level data and of large-scale oceanic and/or atmospheric data such as sea-surface temperature or sea-level air-pressure. We apply this idea to sea level along the Japanese coast. The sea level is related to regional and North Pacific sea-surface temperature and sea-level air pressure. Two relevant processes are identified. One process is the local wind set-up of water due to regional low-frequency wind anomalies; the other is a planetary scale atmosphere-ocean interaction which takes place in the eastern North Pacific.

Forecasting sea level is crucial, especially in areas located at the interface between land and ocean, as it can facilitate early and appropriate actions to reduce environmental, social, and economic damages caused by high sea levels. Sea level forecasting is used to estimate the accuracy in successfully addressing emergency situations due to floods. This research discusses a new approach to forecasting sea level using Long Short-Term Memory (LSTM) equipped with Attention mechanisms. The research focuses on the application of this method in a case study in Jakarta, Indonesian, with the aim of improving the accuracy and reliability of sea level forecasting. The importance of sea level predictions lies in their ability to contribute to flood risk mitigation in the coastal areas of Jakarta. By using the LSTM with Attention method, this research aims to address the complexity of patterns in sea level time series data, so that the prediction results can serve as a more reliable basis for disaster risk management decisions. The LSTM with Attention method is designed to model complex patterns in sea level time series data. Experiments were conducted using sea level datasets in Jakarta obtained through the Sea Level Station Monitoring Facility (SLSMF). The analysis process is divided into two parts: training data and testing data. This research compares the performance of the LSTM with Attention method with two other methods, namely RNN and LSTM, to evaluate prediction accuracy over a 3-month period from June to August 2023. The results show that the LSTM method outperforms RNN and LSTM with Attention in forecasting sea levels. Qualitative and quantitative evaluations using R2 and RMSE confirm the superiority of LSTM. This research also involves long-term predictions for periods of 3, 5, 7, 10, and 14 days ahead, providing further insights into the model's ability to anticipate changes in sea level.

The rise and fall of mean sea level are non-uniform around the global oceans. Their long-term regional trend and variability are intimately linked to the fluctuations and changes in the climate system. In this study, geographical patterns of sea level change derived from altimetric data over the period 1993-2015 were partitioned into large-scale oscillations allied with prevailing climatic factors after an empirical orthogonal function analysis. Taking into account the El Niño–Southern Oscillation (ENSO) and the Pacific Decadal Oscillations (PDO), the sea level change deduced from the multiple regression showed a better estimate than the simple linear regression thanks to significantly larger coefficients of determination and narrower confidence intervals. Regional patterns associated with climatic factors varied greatly in different basins, notably in the eastern and western regions of the Pacific Ocean. The PDO exhibited a stronger impact on long-term spatial change in mean sea level than the ENSO in various parts of the Indian and Pacific Oceans, as well as of the subtropics and along the equator. Further improvements in the signal decomposition technique and physical understanding of the climate system are needed to better attain the signature of climatic factors on regional mean sea level.

Sea level variability off East China has been investigated based primarily on 10 years of Ocean Topography Experiment (TOPEX)/Poseidon altimetry data. The altimetric annual harmonic has a magnitude of 10 to 30 cm in amplitude and is highest in summer, agreeing well with independent tide-gauge data. After the inverse barometer effect is removed, the annual sea level cycle can be approximately accounted for by the steric height variation. Significant interannual sea level change was also observed from altimetry and tide-gauge data, with a range of ∼10 cm. The interannual and longer-term sea level variability in the altimetric data are negatively correlated (significant at the 95% confidence level) with the Pacific decadal oscillation (PDO), attributed in part to steric height change. The altimetric sea level rise rate is 0.64 cm yr−1 for the period from 1992 to 2002, consistent with the tide-gauge rate of 0.6 cm yr−1. These values are much larger than the rate of 0.24 cm yr−1 observed at the same tide gauges but for the period from 1980 to 2002, implying the sensitivity to the length of data as a result of the decadal variability. The potential role of the PDO in the interannual and longer-term sea level variability is discussed in terms of regional manifestations such as the ocean temperature and salinity and the Kuroshio transport.