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Global sea level provides an important indicator of the state of the warming climate, but changes in regional sea level are most relevant for coastal communities around the world. With improvements to the sea-level observing system, the knowledge of regional sea-level change has advanced dramatically in recent years. Satellite measurements coupled with in situ observations have allowed for comprehensive study and improved understanding of the diverse set of drivers that lead to variations in sea level in space and time. Despite the advances, gaps in the understanding of contemporary sea-level change remain and inhibit the ability to predict how the relevant processes may lead to future change. These gaps arise in part due to the complexity of the linkages between the drivers of sea-level change. Here we review the individual processes which lead to sea-level change and then describe how they combine and vary regionally. The intent of the paper is to provide an overview of the current state of understanding of the processes that cause regional sea-level change and to identify and discuss limitations and uncertainty in our understanding of these processes. Areas where the lack of understanding or gaps in knowledge inhibit the ability to provide the needed information for comprehensive planning efforts are of particular focus. Finally, a goal of this paper is to highlight the role of the expanded sea-level observation network-particularly as related to satellite observations-in the improved scientific understanding of the contributors to regional sea-level change.

The long‐wavelength correction (LWC) of SWOT data is intended to reduce errors related to the stability of the SWOT antenna and its attitude in orbit. The algorithms used to compute the LWC utilize SWOT KaRIn sea surface‐height (SSH) measurements and additional data, and the LWC may absorb geophysical SSH into the correction. Different LWC algorithms are used on the L2 and L3 SWOT products, which are analyzed here during the 1 day repeat (Cal/Val) mission phase lasting approximately 100 days. During this mission phase the SSH anomaly (SSHA) computed using the L3 LWC is much more realistic than the L2 LWC, as shown here by comparing spatial statistics of the L2 and L3 products. The L3 LWC algorithm is nonlinear insofar as it depends on second‐order statistics of the SSHA and multi‐satellite SSHA differences, making it difficult to quantify the extent to which it could absorb baroclinic tidal signals. To overcome this difficulty, a proxy L3 LWC algorithm is developed which mimics the L3 LWC but is strictly linear in the SSHA. The proxy LWC is applied to both idealized waveforms and to the predicted internal tide available on the products, and it is found to absorb 1% or less of the signal variance, leading to corresponding pointwise errors of 10% or less. Because the errors are at longer wavelengths and are significantly smaller amplitude than internal tide signals, the LWC impact on the measurement and interpretation of internal tides with SWOT is expected to be negligible in most applications. Plain Language Summary: In order to make the SWOT data useful for studies of sea level associated with horizontal length scales of roughly 100 km and larger, it is necessary to compute a correction which aligns the measured SSH with independent data from other satellite missions. The correction is implemented with a type of data‐driven spatial low‐pass filter; however, the data‐driven character of this filter means that it is nonlinear and its response cannot be characterized using standard techniques of linear filter analysis. In this paper a linear approximation of the long‐wavelength correction is developed which is amenable to standard linear analysis techniques. Using this linear approximation, the extent to which the long‐wavelength correction may absorb signals of interest arising from the baroclinic tides is quantified. It is found that the filter response is generally below 1% of the signal variance, which ought to be negligible in most studies of tides using data during the Cal/Val mission phase. Key Points: The long‐wavelength correction has the potential to remove geophysical signals of interestThe correction is implemented as a nonlinear data‐driven filter, making it difficult to characterize its response using linear techniquesA linear approximation of the filter is developed here and used to characterize the response to baroclinic tides in the open ocean [ABSTRACT FROM AUTHOR]

Through the implementation of a streaming filter, output of numerical ocean simulations can be band‐pass filtered at tidal frequencies while the model is running, yielding time series of sinusoidal motions consisting of tidal signals in the filter's target frequency band. The filtering algorithm is developed from a system of two ordinary differential equations that represents the motion of a damped harmonic oscillator. The filter's response to a broadband input signal is unity at its target frequency but vanishes toward the low and high frequency limits. The decay of the filter response is controlled by a dimensionless parameter, which determines the filter's bandwidth. As a result, the filter allows signals within a small frequency band around its target frequency to pass through, while blocking signals outside of its target frequency band. In this work, the filtering algorithm is implemented into the barotropic solver of the Modular Ocean Model version 6 (MOM6) for determining the instantaneous tidal velocities of the semi‐diurnal and diurnal tides. Utilizing the filters, the frequency‐dependent internal wave drag is applied to the semi‐diurnal and diurnal frequency bands separately. The simulation results suggest that the performance of the algorithm is consistent with the filter transfer function in Fourier space. Potential applications of the algorithm also include de‐tiding the model output for nested regional ocean models, especially those for the purpose of operational forecasting. Plain Language Summary: In this work, we developed a computationally efficient algorithm for detecting tidal signals from the instantaneous model output, without needing to harmonically analyze the entire time series of model output. This is achieved through the construction of a streaming filter, which takes the instantaneous model output as the input and returns a time series consisting of tidal motions at its target frequency band as the output, in a process that effectively allows signals within its target frequency band to pass through and blocks signals outside of its target frequency band. Unlike the conventional harmonic analysis, the band‐pass filtering process does not require information from any of the previous or future time steps. The filtering algorithm is implemented and validated in a global ocean model. The filters can be utilized to parameterize frequency‐dependent internal wave drag, as demonstrated in this work, and to remove tidal signals from the model output, which has potential application in regional ocean forecasting systems. Key Points: The streaming band‐pass filter can detect sinusoidal motions at tidal frequencies from the instantaneous model outputThe filtering algorithm is computationally efficient and is capable of capturing the temporal variation of tidal signalsThe filters can be utilized to parameterize frequency‐dependent internal wave drag and to de‐tide model output [ABSTRACT FROM AUTHOR]

Internal tides (ITs) play a critical role in ocean mixing, and have strong signatures in ocean observations. Here, global IT sea surface height (SSH) in nadir altimetry is compared with an ocean forecast model that assimilates de‐tided SSH from nadir altimetry. The forecast model removes IT SSH variance from nadir altimetry at skill levels comparable to those achieved with empirical analysis of nadir altimetry. Accurate removal of IT SSH is needed to fully reveal lower‐frequency mesoscale eddies and currents in altimeter data. Analysis windows of order 30–120 days, made possible by the frequent (hourly) outputs of the forecast model, remove more IT SSH variance than longer windows. Forecast models offer a promising new approach for global internal tide mapping and altimetry correction. Because they provide information on the full water column, forecast models can also help to improve understanding of the underlying dynamics of ITs. Plain Language Summary: Tidal flow over topographic features on the seafloor generates vertical displacements along the interfaces of ocean layers that have different densities. These vertical displacements at tidal frequencies are known as internal tides. Internal tide displacements are largest well below the sea surface, but also display a sea surface height (SSH) signature that is large enough to be measured by satellite altimeters. Removing internal tide signals from satellite altimeter SSH allows for a more accurate accounting of non‐tidal features, including slowly evolving ocean currents and eddies, that are also measured by altimeters. Here, we show that supercomputer ocean forecast simulations of the global internal tide field are able to remove internal tide SSH from satellite altimeter measurements with a skill level that is comparable to the skill of internal tide SSH removal based upon analysis of the satellite altimeter data itself. Thus, forecast models offer a complementary method for this important task. In addition, forecast models provide information on the entire ocean water column, not just the sea surface. Finally, the hourly outputs of forecast models allow for a greater variety of tidal analysis record lengths than can be achieved with altimeter outputs, which report sea surface height fields much less frequently. Key Points: Global ocean forecast models can accurately simulate both long‐term (phase‐locked) internal tides and their short‐term modulationsOcean forecast models offer a useful complement to empirical models for mapping internal tides and correcting altimetry for internal tidesIn regions of strong internal tides, optimal variance reduction in nadir altimetry is attained through short‐term tidal analyses (∼60 days) [ABSTRACT FROM AUTHOR]

Harmonic analysis of time series from 20 years of MODIS-Aqua ocean color observations (2002–2022) is conducted to identify periodic variability of near-surface chlorophyll (Chl- a) inferred from ocean color. As they are based on satellite imagery, the Chl- a observations are characterized by significant gaps in both spatial and temporal coverage due to the masking of clouds in the images. Results yield a coherent picture of surface Chl- a associated with the time mean, annual and semiannual cycles, and spring-neap tidal variability. Spring-neap variability is heterogeneous and associated with regions of significant baroclinic tides as well as coastal regions with strong tidal currents. The observations provide another line of evidence for the significant contribution of ocean tides to mixing in the Indonesian Seas. [ABSTRACT FROM AUTHOR]