Forcing Factors Affecting Sea Level Changes at the Coast

Abstract

We review the characteristics of sea level variability at the coast focussing on how it differs from the variability in the nearby deep ocean. Sea level variability occurs on all timescales, with processes at higher frequencies tending to have a larger magnitude at the coast due to resonance and other dynamics. In the case of some processes, such as the tides, the presence of the coast and the shallow waters of the shelves results in the processes being considerably more complex than offshore. However, ‘coastal variability’ should not always be considered as ‘short spatial scale variability’ but can be the result of signals transmitted along the coast from 1000s km away. Fortunately, thanks to tide gauges being necessarily located at the coast, many aspects of coastal sea level variability can be claimed to be better understood than those in the deep ocean. Nevertheless, certain aspects of coastal variability remain under-researched, including how changes in some processes (e.g., wave setup, river runoff) may have contributed to the historical mean sea level records obtained from tide gauges which are now used routinely in large-scale climate research.

1 Introduction

Sea level variability at the coast can be similar to, or differ from, that in the neighbouring deep ocean, depending on location and timescale. For example, large spatial- and temporal-scale changes, such as a rise in mean sea level (MSL) due to climate change, might be expected to be similar, to first order at least, at the coast and in the ocean nearby.¹

However, there are many processes which introduce sea level variability with shorter spatial scales, or which result in a coastal modification in the character of the larger-scale variability. These processes occur primarily due to coastal waters being shallow (by definition) and coastlines having complicated shapes and features such as estuaries and harbours. In addition, the coast provides one of the boundaries (the other being the continental shelf edge) which result in dynamical changes in the ocean circulation and thereby in the sea level variability observed over larger spatial scales. Runoff from rivers introduces another source of sea level variability from the landward side.

As one example, Fig. 1 (from Vinogradov and Ponte 2011) shows the correlation between monthly means of sea level measured at the coast by tide gauges and in the nearby ocean by satellite altimetry. The correlation is far from perfect and (leaving aside for the moment any questions of data imprecision) indicates that there are processes at work resulting in differences in sea level variability between coast and ocean, even on monthly timescales. This means that coastal processes need to be identified and understood as far as possible, partly so that they can be studied in their own right, and partly so that they can be clearly separated from the large-scale, climate-related signals.

Fig. 1

Correlations between IB-corrected monthly mean sea levels measured at the coast by tide gauges and sea levels recorded by satellite altimetry in the nearby deep ocean over the period 1993–2008. Locations with correlations statistically indistinguishable from zero at 95% confidence level are shown as open circles. From Vinogradov and Ponte (2011)

In fact, there are many such coastal processes, operating at different timescales, for which in many cases the physics responsible is well understood. Many occur across the short spatial scales of the shelf (e.g., storm surges) or even shorter (e.g., harbour seiches), and timescales much shorter than the monthly and annual timescales of interest in climate studies. Others can occur on quite large spatial scales along the coast and on longer timescales. Examples include the trapped Kelvin waves along the Pacific coast associated with the El Niño–Southern Oscillation (ENSO) (Enfield and Allen 1980; Pugh and Woodworth 2014), or the long-distance correlations of sea level (or sub-surface pressure) along the shelf and slope (Hughes and Meredith 2006). Table 1 provides a list of such processes, while Fig. 2 demonstrates schematically the space and timescales of many of them.

Table 1 A highly schematic list of processes which contribute to sea level variability at the coast, in approximate order of timescale

Fig. 2

A schematic overview of processes contributing to sea level variability at the coast indicating the space and timescales involved. Note that Table 1 contains a fuller list of processes than those shown here. Very high frequency processes with timescales less than 1 min (wind waves, swash, etc.) are not included. See Hughes et al. (2019) for a detailed review of different types of coastal trapped waves

The following sections of this paper discuss a number of forcing factors of coastal sea level variability. The first one refers to the tides, which are the dominant signal in sea level variability along all coastlines and which span a wide range of timescales. We then move to a discussion of a number of other processes, ordered approximately in terms of timescale instead of possible importance (magnitude), although sometimes processes again span different timescales, so the reader will have to be aware that such a division is not straightforward. We consider processes responsible for extreme sea levels, as well as MSL, extremes being of particular interest at the coast.

However, it can be appreciated that, while there are many processes, there is only one ocean, so changes in depth introduced by one process necessarily introduce modifications to others. For example, there are interactions between tides and storm surges in coastal waters, due to both processes modifying the instantaneous depth. In addition, the generally deeper coastal waters arising from a rise in global MSL will result in an increase in tidal wavelengths and modification of patterns of tidal variability. Such interactions between processes are discussed in detail by Idier et al. (2019).

2 Tides

There is one topic that arises in a discussion of nearly every timescale: the tides (Pugh and Woodworth 2014). The dominant half-daily and daily periods of tidal variability are obvious, but tidal periods range from much shorter to very much longer than these. At shorter periods, compound tides such as M₄ (period 6.21 h) reach 25 cm at places like Dover, UK, and higher overtides such as M₁₂ (2.07 h) or higher are often detectable and are sometimes even needed for precise predictions. At longer periods, the astronomical tides are all relatively small and sea level variability at these timescales is usually dominated by non-tidal processes, yet the impact of tides on long-term properties of extreme water levels can be pronounced; important tidal periodicities for extreme high water include fortnightly, 4.4 years and 18.6 years, and these will be referred to below. On even longer timescales, short period (semidiurnal and diurnal) tides are found to respond to long-term changes in the oceanic medium, seasonally in particular, but also at longer periods, even secular, leading to tentative connections between tides and climate.

Considerable progress has been made in recent years in modelling the tides of the deep ocean (Stammer et al. 2014), and Ray and Egbert (2017) have summarised major recent research progress in determining the energy budgets of the barotropic tides and in the transmission of internal tides across ocean basins (Zhao et al. 2016). Where internal tides break on a distant coast many days later, they can result in increased seiche activity on timescales typical of the shelf or harbour (e.g., Wijeratne et al. 2010).

The ocean tides are largely generated in the deep ocean. However, their transition to the shelves and to the coast results in their amplification, partly through resonance depending on the shape of the coast and depth of coastal waters, and the generation of higher harmonics of their main frequencies. As a result, many difficulties remain in parameterising the more complex tides which occur near the coast (Ray et al. 2011). Figure 3a provides a demonstration of the complexity of the tide at one coastal location (Eastport, Maine, NE USA). The main semidiurnal and diurnal lines to the left of the spectrum, and a number of others, are now represented well in global ocean tide models (e.g., FES2014 2018). However, it can be appreciated that a major challenge remains to parameterise spatially the many harmonics at frequencies higher than 2 cpd, and also the subtleties of variability and interaction hidden within the tidal cusps.

Fig. 3

a A sea level spectrum from Eastport, Maine, on the US NE Atlantic coast, highlighting the main tidal band. The dominant tidal constituent is the lunar semidiurnal M₂, but strong nonlinear compound tides appear at higher frequencies. Numerical labels denote tidal species, where each species n consists of multiple spectral lines clustering around n cycles per lunar day. The spectrum is obtained from four years of hourly spot readings from the Eastport tide gauge. The Nyquist frequency is therefore 12 cpd, so species 14 is aliased into lower frequencies. b The corresponding spectrum of bottom pressure (BP) obtained from a nearby deep-ocean buoy (2600 m depth, south of the New England shelf). The higher oceanic tide harmonics are much reduced, the peaks at 5, 7 and 9 cpd being due to atmospheric tides in the BP record

Figure 3b provides a contrasting spectrum obtained from a bottom pressure (BP) sensor on a Deep-ocean Assessment and Reporting of Tsunami (DART) buoy deployed at 2600 m depth just south of the New England shelf. Although the main semidiurnal and diurnal tides have similar amplitudes to those at Eastport, the higher tidal harmonics are either considerably weaker or absent, those at 5, 7 and 9 cpd in (b) being due to atmospheric tides in BP and not oceanic tides. One may also note the lower non-tidal background provided by a BP record compared to the sea level record of a conventional coastal tide gauge.

One subtlety to do with tidal variability concerns the apparent long-term changes in tidal amplitudes and phases along the coast; it is not yet known whether similar changes are occurring in the deep ocean. Of course, the tide changes over long timescales in response to changes in the orbit of the Moon (Green et al. 2017), and when coastlines and water depths change. However, the presently observed tidal changes (mostly during the past half-century) cannot be explained by simple arguments and constitute an important topic in tidal research (Hill 2016; Haigh et al. 2019).

3 High-Frequency to Daily Coastal Variability

Sub-daily oscillations of sea level near the coast are strongly controlled by bathymetry and local topography. Seiches provide examples of such oscillations. Seiches are a type of resonance in which the sea level oscillates at a natural period of an inlet, harbour, bay or continental shelf (Rabinovich 2010). They were observed first in lakes (Forel 1876) and have since been found to be present in almost all tide gauge records (e.g., Airy 1878). Even larger bodies of water such as the Adriatic Sea and Baltic experience seiches (Lisitzin 1974).

The physical characteristics of a seiche in a lake can be considered similar to that of a guitar string tied at both ends (i.e. a node at each end), while a seiche in a semi-enclosed basin such as a coastal inlet is analogous to a string tied (i.e. a node) at only one of its ends. Resonances can therefore occur with wavelengths twice the lake length in the former case, or four times the inlet length in the latter. Similarly, ‘quarter-wavelength seiches’ occur across continental shelves, with a node at the land end and an anti-node at the shelf edge. The frequency of a seiche is then given by its wavelength divided by $\sqrt {gh}$ where $g$ is acceleration due to gravity and $h$ is water depth. In the case of complicated coastal geometries, additional factors also play a role (Rabinovich 2010; Wiegel 1964; Wilson 1972).

Free oscillations of a natural system (their so-called natural resonant periods or ‘eigen-periods’) occur as a response to any external input of energy. In the case of coastal seiches, the forcing is normally in the form of long waves entering through the coastal basin mouth. These periods may be considered as a fundamental property of a particular location and are independent of the type of external forcing (see below). Natural basins generally oscillate with periods ranging between a few minutes and several hours, with amplitudes of centimetres to decimetres. However, at some locations and in some circumstances seiches can have amplitudes comparable to the tide. A maximum response will occur when an external forcing impinges on a basin mouth with a frequency corresponding to its eigen-frequencies. Seiche amplitudes may be then strongly amplified, and the currents associated with them and the resulting flooding inside the basin may cause serious damage to boats and harbour infrastructure. This is particularly the case when the amplification at resonance, characterised by the so-called quality factor Q, is particularly high. In basins with a high Q, generally those that are elongated and narrow, high levels of background seiche energy are also more likely to be present, even with a low level of external forcing (Rabinovich 2010).

There are several processes in nature which are able to generate oceanic long waves with periods matching the eigen-periods of basins and which are able to force them resonantly. Amongst them, tsunamis are probably the best-known phenomena. Tsunami wave properties are determined by the characteristics of the sea floor displacements (earthquakes) which generate them. They propagate as surface long waves with typical wavelengths of hundreds of kilometres and wave periods of up to an hour. The most energetic events affect the coast indiscriminately. However, less energetic tsunamis can also have a major impact where seiche frequencies match those of the tsunami itself, when a resonant coupling takes place and a seiche response is amplified at the local eigen-frequencies. As a consequence, there can be catastrophic consequences for harbours and bays with high Q-factors (Miller 1972; Rabinovich 1997; Rabinovich and Thomson 2007).

Seiches may also be forced by a number of other mechanisms, the most common processes being of atmospheric origin, either due to direct generation of long waves by pressure or wind forcing on the sea surface, or by transferring energy from low-frequency motions (storm surges) or high-frequency gravity waves (wind waves and swell) through nonlinear processes. The first mechanism is the most important because it is responsible for the generation of destructive seiche oscillations (meteotsunamis) all around the world (Defant 1961; Rabinovich and Monserrat 1996; Monserrat et al. 2006).

Destructive meteotsunamis are observed at certain locations in the world ocean where two mechanisms play a successive role: (1) the initial atmospheric energy is optimally transferred into the ocean through some specific resonant process, namely Proudman resonance (when atmospheric disturbance velocity equals the long wave phase speed of the ocean waves), Greenspan resonance (when atmospheric velocity matches that of edge wave modes, see below) or shelf resonance (when the atmospheric disturbance and associated generated ocean wave have periods and/or wavelengths equal to the resonant values for the shelf region); and (2) the generated long ocean waves approach the entrance of a bay or harbour and induce hazardous oscillations in the basin, exciting the basin seiche through harbour resonance (Monserrat et al. 2006).

Vilibić and Šepić (2017) demonstrated that many tide gauge records contain high-frequency variability on timescales from a few minutes to 2 h, which will include any energy due to seiches, although will not necessarily be exclusively due to seiches. They showed that such high-frequency variability, which is often not considered in studies of extreme sea levels based on hourly values from tide gauges, can contribute up to 50% of sea level extremes in some low-tidal areas.

Other high-frequency sea level oscillations can occur at the coast due to existence of the continental shelf, with the shelf characteristics (width and depth) playing a key role in determining their properties. For example, there are waves that travel along the coast or shelf and decay away from the coast: these include edge waves (periods of minutes to hours) and coastal trapped waves. The latter term usually applies to waves with periods longer than an inertial period and is at least partially dependent on the Earth’s rotation and vorticity dynamics. A summary of their properties may be found in Huthnance (1978), Huthnance et al. (1986), Huthnance (2001) and references therein. Kelvin waves, with an elevation maximum at the coast and the greatest offshore extent (no offshore nodes of elevation), span the frequency range from edge waves (super-inertial) to coastal trapped waves (sub-inertial). (A ‘mode-0’ barotropic Kelvin wave in an idealised (straight shelf) context can propagate at super-inertial frequencies without losing energy, as can internal Kelvin waves against a wall. Stratification makes little difference to the mode-0 Kelvin wave. Edge waves are exclusively super-inertial.)

The temporal and spatial scales of these waves depend mainly on the forcing (tides, weather, adjacent oceanic features) and the width of the continental shelf or slope, and on stratification for baroclinic waves. Modes with scales best matching the forcing tend to be favoured. Thus, tides propagating as Kelvin waves may have an amplitude of metres (e.g., Pugh and Woodworth 2014), while amplitudes of coastal trapped wave components are more typically 0.1 m. For example, weather- and oceanic-forced coastal trapped waves have magnitudes of typically 0.1 m, but extreme storm surges may be ± 1 m or more (e.g., Gönnert et al. 2001; Merrifield et al. 2013).

Hughes et al. (2019) discuss further the physical mechanisms for generation, propagation and decay of coastal trapped waves and their role in determining differences in sea level between deep-ocean, shelf and coast and in transmitting dynamical signals rapidly around the ocean.

4 Daily Coastal Sea Level Variability

In this section, we refer to several types of processes with meteorological forcing which result in sea level variability on timescales of several hours to several days (which we denote as ‘daily’). Some of these are well known and are described adequately in text books.

One of the most important meteorological forcings of sea level variability over the open ocean, as well near the coast, is variability in surface air pressure. The inverse barometer (IB) effect, whereby an increase of 1 mbar in air pressure results in approximately 1 cm decrease in sea level (to within approximately half a per cent), was discovered in Sweden by Nils Gissler (Roden and Rossby 1999). An historical example of the IB effect using data collected in 1842 is given in Fig. 4. Other historical examples from the early nineteenth century are discussed by Daussy (1831), Lubbock (1836) and Ross (1854). As the ocean takes some time to adjust to a new equilibrium (typically ~ 1 day), there is a transient ‘dynamic air pressure effect’ (e.g., Ponte et al. 1991). Within the spectrum of air pressure variability in some parts of the ocean, and consequently within that of sea level variability, are modes with particular periods. These include the Madden–Julian 5-day waves which are, in principle, global in scale but are most evident in the tropics where the overall magnitude of air pressure variability is less (Luther 1982; Woodworth et al. 1995). (These are not to be confused with the approximately 4-day equatorial-trapped waves discussed by Wunsch and Gill 1976.)

Fig. 4

Historical demonstration of the IB effect. Daily values of sea level (i.e. mean tide level, MTL) in 1842 at Port Louis, Falkland Islands (blue) together with daily values of sea level air pressure (SLP) (red), both measured by James Clark Ross. Air pressure values are shown inverted and their average adjusted to equal that in MTL. The MTL daily values are defined as the average of the average of high waters and average of low waters recorded each day. From Woodworth et al. (2010)

Wind stress is the shear force that the wind exerts on the ocean surface and is proportional to the square of the wind speed (Pugh and Woodworth 2014). Wind stress is a relatively more important forcing of sea level variability than air pressure in shallow-water areas, where increases in sea level gradients are proportional to wind stress divided by water depth. In addition, the coastal boundary acts to block wind-driven transport, leading to sea level elevation at the coast. As a result, coastal sea level variability on daily to monthly timescales departs significantly from an IB response to air pressure change (e.g., for the east coast of the UK, Thompson 1980; Woodworth 2018).

At times, the sea level changes resulting from a combination of air pressures and winds, called storm surges, can result in catastrophic flooding and loss of life. Depth-averaged (or barotropic) tides and storm surges can be modelled using the depth-averaged (2D) nonlinear shallow-water (NLSW) equations (Gönnert et al. 2001; WMO 2011; Pugh and Woodworth 2014; Piecuch et al. 2019). Such modelling schemes are used operationally in many countries (Flather 2000) and can be employed in delayed mode in research studies of coastal sea level variability (Carrère and Lyard 2003; Wakelin et al. 2003) and sea level extremes (Muis et al. 2016). Tides, winds and waves can also energise seiches (quasi-resonant modes of oscillation of sea level in inlets, bays, harbours and shelves, see Sect. 3) that can be superimposed on a storm surge and can consequently result in a higher measured extreme sea level.

An insight into waves is important for simulating accurately the daily variations in sea level in numerical models. Bottom friction coefficients used in barotropic modelling have been shown to depend on wave height (Madsen et al. 1988; Wolf 1999; Soulsby and Clarke 2005), although in practice such dependence is not usually taken into account. Nevertheless, this provides a further example of interaction between processes (tide-surge-wave) discussed by Idier et al. (2019).

The storm surges caused by tropical cyclones are different in character to those produced by higher latitude storms. Tropical storm surges tend to be of smaller spatial scale (~ 500 km rather than ~ 1000 km) and usually have a shorter duration (hours to days rather than several days), but are much larger in amplitude (sometimes 5–10 m rather than typically 2–3 m) (von Storch and Woth 2008). Extreme sea levels occur by the combination of surge and astronomical tide and clearly have their most extreme values when both tide and surge are large and coincide. Extreme sea levels are usually studied by techniques such as percentile analysis (Menéndez and Woodworth 2010). In strongly semi-diurnal tide regimes, the high percentiles have a perigean (~ 4.4 year) dependence, while in strongly diurnal tide regimes the high percentiles vary over the lunar nodal cycle (18.6 years) (Haigh et al. 2011).

Merrifield et al. (2013) made maps of mean annual maximum sea level (relative to annual mean MSL, thereby excluding consideration of interannual variability) at many locations round the world coastline, and also maps of the individual contributions to mean annual maximum sea level from either the tide, seasonal cycle in sea level or low and high-frequency variations. The low-frequency components were defined by timescales longer than approximately a month but less than seasonal, whereas high-frequency variations were identified using a running 1-month median filter. Mean annual maximum levels occur where tide and low-frequency components are both large, such as the coasts of the North East Pacific, North West European continental shelf and North West Australia, while high-frequency variability was shown to be relatively more important along the American Atlantic coast and in North West Europe and South Australia (see their Figs. 3, 4).

One concern arises from the fact that the largest extremes (and so the events with the most catastrophic flooding) might not be represented adequately in tide gauge data sets. This reservation applies particularly to extremes caused by tropical storms. By definition, these events are rare ones and, when they do occur, the highest sea level may not be located exactly at the gauge, but some distance away. Therefore, this type of event may not be sampled adequately, even in a record spanning many decades. Furthermore, some gauges may not be able to record very high sea levels, and during an energetic storm, a gauge might be destroyed and so the extreme may not be recorded. To some extent, this is a sampling issue that can be addressed by analysing the tide gauge data in combination with numerical ocean modelling (e.g., Haigh et al. 2014a, b).

Changes in MSL are a major driver of changes in extreme sea levels at interannual and longer timescales (Lowe et al. 2010; Menéndez and Woodworth 2010; Woodworth et al. 2011; Marcos and Woodworth 2017, 2018). For example, Fig. 5 shows that linear trends of annual 99th percentiles of total sea level since 1960 (these are a good approximation of annual extreme levels), and of skew surges over the same period, can be accounted for to a great extent by trends in MSL. However, MSL is not the only driver: analyses of high-frequency tide gauge records, once the effect of MSL has been removed, reveal variations in the storm surge contribution associated with changes in storminess on long timescales (Menéndez and Woodworth 2010; Marcos et al. 2015; Marcos and Woodworth 2017). The intensity and frequency of storm surge changes unrelated to MSL show regionally coherent patterns that have been linked to large-scale climate indices, such as the North Atlantic Oscillation (NAO) in the North Atlantic (Marcos et al. 2015; Wahl and Chambers 2015; Marcos and Woodworth 2017). Similar conclusions on MSL being a major, if not the only, driver of changes in extremes were obtained using a small number of very long tide gauge records starting in the mid-nineteenth century.

Fig. 5

a Linear trends of annual 99th percentiles of total sea level and b with median removed. c Linear trends of annual 99th percentiles of skew surges and d with median removed. Tide gauge data from 1960 to present are used. Black dots indicate where the trends are not significant. From Marcos and Woodworth (2018)

Semidiurnal and diurnal variations in meteorological forcings that can potentially lead to sea level variability are of particular interest in the tropics. For example, air pressure has a predominantly semidiurnal cycle throughout the tropics (Pugh and Woodworth 2014, Sect. 5.5), with an amplitude of more than 1 mbar, peaking at about 10:00 and 22:00 h local time. Small diurnal variations in wind speed occur in the synoptic trades (e.g., in the Caribbean, Cook and Vizy 2010) and are best measured in situ by ocean buoys well away from land. However, much larger diurnal cycles in wind speed are found in data from some coastal land stations. These occur due to local sea and land breeze effects, which at locations in the tropics can extend 10s of km from the coast (Miller et al. 2003; Gille et al. 2005), and can affect many physical and biological processes including the local ocean circulation (e.g., Walter et al. 2017) and conceivably sea level to some extent. Inevitably, the sea and land breezes are not represented well in the large-scale meteorological products that are used for storm surge modelling.

5 Examples of Processes Spanning Timescales

As a demonstration of the difficulty of drawing simple diagrams such as Fig. 2, with some processes spanning a range of timescales, this section considers the importance to sea level studies of ocean waves. Waves manifest themselves at the high-energy end of the instantaneous sea level spectrum, and yet it will be seen that through long-term changes in wave climate waves can also contribute to long-term changes in MSL. This section also considers river runoff as a further example of processes spanning timescales that can contribute to MSL variability.

5.1 Wave Setup

Tides, surges and MSL together make up the ‘still water level’ superimposed upon which there are ocean wind waves. Wind waves span a range of period typically 1–25 s (LeBlond and Mysak 1978). The wave field impinging on a given location at the coast is usually composed of waves of different origins, ages and periods. Part of that field will consist of locally generated waves with shorter periods, while waves with longer periods will partly comprise ocean swell that could have travelled 1000s of km from distant storms (Ardhuin et al. 2009). Distantly generated swell has been found to result in major impacts on coastlines far from its generation (e.g., Harangozo 1993; Hoeke et al. 2013).

Wind waves are of great practical importance to coastal protection (e.g., Roelvink et al. 2009). Wave energy flux is a key driver of coastal erosion and contributes significantly to the evolution of shorelines, for example through modification of beach profiles due to sea level rise (Bruun 1962). Wind waves also play a role in flooding through overflowing, overtopping and breaching of natural barriers (e.g., dunes) or flood defences (e.g., dykes). Coastal flooding impacts are different in character in each case. Overflowing refers to when the water level (which includes wave setup) exceeds the height of the barrier. In the case of overtopping, when the crests of the waves exceed the barrier height, water with high momentum pours intermittently onto the coastal land. When breaching occurs, even greater flooding can take place, as the original barrier is no longer effective.

In spite of their importance, waves are often ignored in sea level studies, especially when those studies are not focused on extreme events. As waves propagate into shallow water, wave amplitudes increase until the waves become unstable and break (Dodet et al. 2019, in review). Breaking and wave dissipation raise water levels in the surf zone in a process known as wave setup (Fig. 6). The reduction in wave energy due to breaking leads to a radiation stress gradient, with momentum transferred from waves to the water column (Longuet-Higgins and Stewart 1962; Bowen et al. 1968; Holman and Sallenger 1985; Dean and Walton 2009; Pugh and Woodworth 2014). Assuming steady-state conditions, the radiation stress gradient is balanced by higher water levels at the shore. Wave setup is proportional to the offshore significant wave height and can contribute to elevated water levels that are an appreciable fraction (20–30%) of the incident deep water significant wave height. The magnitude of setup can be estimated if one has either measured or modelled wave data and has knowledge of coastal bathymetry (e.g., Stockdon et al. 2006; Dietrich et al. 2009; Melet et al. 2016; Marsooli and Lin 2018; Pedreros et al. 2018). Spatial gradients in wave setup, due, for example, to variations in breaker height, can cause local circulations such as rip currents. Characteristic periods of wave setup are tens of the dominant incident wind-wave periods (O(1 min)). However, it is modulated on longer timescales through its dependence on the height, period and direction of incident waves and on the still water level (Idier et al. 2019, in review).

Fig. 6

Adapted from Melet et al. (2018)

Schematic of processes contributing to total water level changes at the coast. The mean sea level derived from radar altimetry data includes contributions from ocean thermal expansion and ocean circulation, transfer of water from land to ocean due to mass loss from glaciers and the Arctic and Antarctic ice sheets, as well as from land water storage changes (pictograms on the right, top to bottom). Sea level variability from tides and coastal processes including storm surges due to air pressure effects and wind setup, as well as wave setup and swash are superimposed on the larger-scale changes. Vertical land movements are denoted by VLM. The rotation of the depression (D) applies to the northern hemisphere.

Wave setup is a particular concern for island shorelines that are otherwise protected from wave energy by coral reefs (Vetter et al. 2010; Becker et al. 2014; Hoeke et al. 2015; Buckley et al. 2018). At these locations, wave setup can be the largest single non-tidal contributor to extreme water levels (Merrifield et al. 2014).²

Because tide gauges are usually located in large protected harbours, where wave breaking is limited, wave setup in most cases will be negligible in tide gauge records, although notable exceptions can occur (e.g., Thompson and Hamon 1980; Aucan et al. 2012). In these cases, it can be appreciated that, although wave events and wave setup occur on the ‘daily’ timescale, wave setup will inevitably contribute to MSL variability on seasonal and even interannual timescales. Consequently, there is a possibility in some cases of contamination of existing long-term MSL records by variations in wave setup in the past, and the character of that contamination might change again if wave climate changes in the future (Melet et al. 2018, discussed in Aucan et al. 2019 and Melet et al. 2019). For example, in the Arctic, wave climate will depend on future sea ice conditions (Stopa et al. 2016). A further technical issue is that tide gauge measurements, whatever the technique employed, can be affected to some extent by waves (e.g., see discussion of wave effects on radar tide gauge data in Intergovernmental Oceanographic Commission, IOC 2016).

Before leaving waves, we can refer to a further process called ‘swash’ (Fig. 6). Wave swash is the oscillation in shoreline position due to wave propagation onto upper parts of the beach. It plays an important role in shaping the coastline through sediment transport, and in flooding through overtopping and breaching. Wave runup is defined as the combination of wave setup and swash, with setup being the mean component of runup averaged over some time window, and swash therefore having zero contribution to sea level over that window. On wave-exposed, open-coast beaches, wave runup can reach several metres during extreme events (Kennedy et al. 2016; Poate et al. 2016) and at times wave energy can cause significant modifications to the coast (e.g., Cox et al. 2018). Like setup, the importance of swash is site dependent, being determined by the height, period and direction of the incident waves. Therefore, it is modulated at low frequencies in a similar way to wave setup. However, unlike setup, it does not contribute to variability in what we refer to usually as ‘sea level’.

5.2 River Runoff

A process with a similar potential contribution to coastal sea level measurement across a wide range of timescales is freshwater runoff from rivers (Durand et al. 2019, in review). The process is known to contribute to signals of the order of centimetres in sea level variability on daily timescales for some rivers in Europe, with plumes extending ~10 km from the river mouth (e.g., Laiz et al. 2014). Gómez-Enri et al. (2017) have suggested that such discharges of small rivers can be detected as sea surface height anomalies in coastal altimeter data. Runoff will undoubtedly be a much larger factor in large river deltas. For example, Wijeratne et al. (2008) pointed to the large (~1 m) seasonal cycle in MSL in the Ganges Delta, although it is not clear whether this is due to only runoff per se, or also to an associated thermosteric contribution (Fabien Durand, private communication; Neetu et al. 2012). Meade and Emery (1971) suggested a link between runoff and interannual variability in MSL at US tide gauges, a link which has been confirmed by recent research (Piecuch et al. 2018). The most extreme contribution from runoff is probably that associated with the Amazon River (e.g., Korosov et al. 2015), where the spreading of the river plume can be traced for distances larger than a 1000 km from its mouth. A climate model simulation by Jahfer et al. (2015) has shown that Amazon runoff can impact climate and sea level in a much broader sense, by contributing to the strength of the Atlantic Meridional Overturning Circulation (AMOC).

6 Seasonal Variability in Coastal Sea Level

The seasonal cycle is one of the most important non-tidal components of sea level records, especially in the mid- to high latitudes.³ Seasonal variability in sea level is forced by a variety of mechanisms, including atmospheric pressure and winds, precipitation, river runoff, ice melting, ocean circulation changes and variations in steric height. The latter, driven by expansion/contraction of the water column above the seasonal thermocline in response to heat flux exchanges with the atmosphere, is the dominant contributor in most oceanic regions (Gill and Niller 1973).

The mean seasonal sea level cycle at the coast was investigated by Tsimplis and Woodworth (1994) using a data set of 1043 tide gauges distributed globally around the world coastlines. They reported high spatial variability in the annual and the semi-annual signals with annual amplitudes reaching several decimetres along some parts of the coast. However, coastal seasonal oscillations may significantly differ from those in the open ocean (Vinogradov and Ponte 2010). While in the deep ocean the annual cycle is driven by steric changes and the large-scale wind field (Chen et al. 2000; Vinogradov et al. 2008), near the coast other factors, such as local wind patterns, rivers or seasonal upwelling/downwelling, become dominant (Middleton and Cirano 1999; Middleton 2000). In general, annual amplitudes are larger along the coasts and over continental shelves due to the impact of these coastal processes. Seasonal changes in the atmospheric forcing also induce variability at these timescales in higher-frequency processes such as storm surges, which result in larger extremes of sea level during the winter season (Menéndez and Woodworth 2010; Merrifield et al. 2013; Marcos and Woodworth 2017). The same applies for offshore wave conditions as a result of the seasonality in storminess and thereby in the propagation of swell waves (e.g., Semedo et al. 2011). Seasonal changes in wave height, period and direction are more pronounced in extratropical regions, and highest in the Northern Hemisphere (Young 1999). As a result, wave setup also contributes to seasonal water level changes at the coast (Melet et al. 2016).

The major constituents of the ocean tide also display seasonality. For example, Pugh and Vassie (1976, 1992) demonstrated that the amplitude of the predominant M₂ constituent along North Sea coasts varies through the year by several per cent and is a maximum in summer. This variation is due to a well-developed thermocline in summer and a well-mixed water column during winter (Müller 2012; Gräwe et al. 2014). Similar variations have been observed in other shelf areas (e.g., Yellow Sea, Kang et al. 1995, and the Canadian Pacific, Foreman et al. 1995). As far as we know, such studies have not been made on a global basis. However, inspection of the Admiralty Tide Tables (UK Hydrographic Office, UKHO 2017) and other tidal databases shows evidence for similar seasonality in other shelf areas. One suspects that it is not so apparent at deep-ocean islands where tidal amplitudes anyway tend to be smaller than in continental shelf areas.

Despite the seasonal sea level cycle often being considered as a steady signal, many studies have reported significant temporal changes in seasonality. Interannual to multidecadal variability has been related to changes in atmospheric pressure and wind fields (e.g., Plag and Tsimplis 1999, in the North and Baltic Seas; Marcos and Tsimplis 2007, in Southern Europe; Torres and Tsimplis 2012, in the Caribbean Sea) which, in turn, are linked to climate indices such as NAO. They have also been associated with variability in ocean currents, especially where these are strong (e.g., in the NW Pacific (Feng et al. 2015) or western Atlantic (Calafat et al. 2018)), or to changes in large-scale forcing patterns in steric height or sea surface temperature (SST) (Wahl et al. 2014). The study of Amiruddin et al. (2015) made use of both tide gauge and altimeter data from the South China Sea, finding significant differences between the coastal seasonal cycle and that of the nearby deeper ocean. Both types of data have also been applied to studies of the coastal seasonal cycle on a quasi-worldwide basis by Etcheverry et al. (2015), finding differences of ~ 2 cm between data types in the observed amplitudes of the annual cycle of MSL.

7 Interannual and Decadal Sea Level Variability

7.1 Importance of Climate Modes to Interannual Variability

Climate modes are large-scale patterns of coherent variability in meteorological or oceanographic parameters such as air pressure or SST, with the amplitude of the variability represented by a mode index. Since these parameters, and additional ones associated with them (e.g., winds), are known to be forcings of sea level variability (e.g., see Sect. 4 for discussion of wind forcing), it is unsurprising that large-scale patterns of variability in mean and extreme sea levels similar to the climate modes have also been observed (e.g., Menéndez and Woodworth 2010). Han et al. (2017a, b, 2018a, b) have already provided an overview of ocean modes, with a focus on the Pacific and Indian Oceans. We comment below on the importance of such modes from the primary perspective of coastal sea level.

The modes have large impacts on coastal oceans by means of forcing by local winds associated with them and by remote influence from the ocean interior. For example, surface winds associated with the El Niño–Southern Oscillation (ENSO) and Indian Ocean Dipole (IOD), discussed below, induce eastward-propagating equatorial Kelvin waves; upon arriving at the eastern boundary, the energy subsequently propagates poleward as coastal trapped waves, affecting sea level in a long distance along the coastlines of the eastern Pacific (e.g., Enfield and Allen 1980) and eastern Indian Ocean, respectively.

ENSO is the best-known climate mode, consisting of a coupled atmospheric and oceanic oscillatory mode that originates in the tropical Pacific and acts on typical timescales of 5–7 years. ENSO ‘warm events’ are characterised by both a lowering of sea level air pressure and a weakening of the easterly trade winds over the eastern tropical Pacific, allowing an area of anomalously high SST to spread eastwards, accompanied by a shift in the main area of convection from Indonesia to the central Pacific (Rasmussen and Carpenter 1982). This reduces upwelling, deepens the thermocline and increases sea levels at the eastern boundary. In contrast, ‘cold events’ or ‘La Niña’ episodes are associated with anomalously low SST in the central and eastern Pacific and warmer surface waters to the western Pacific, which strengthens the easterly trade winds, increasing upwelling at the eastern margins. In both warm and cold events, sea level anomalies are transmitted polewards along the Pacific coast of the Americas in the form of coastal trapped Kelvin waves (Enfield and Allen 1980; Pugh and Woodworth 2014). Recently, Merrifield and Thompson (2018) have pointed to differences in ENSO climatology between the pre-1970 period, when ENSO variability was relatively low, and post-1970 when it was greater. The effects of ENSO are widespread, and ENSO influences have been identified in MSL variability along both the Pacific and Atlantic coastlines of the USA (Hamlington et al. 2015), while Marcos and Woodworth (2017) noted an ENSO influence on wintertime extreme sea levels along the US Atlantic coast.

In polar regions, annular climate modes dominate atmospheric variability, reflecting the meridional pressure contrast between a mid-latitude ring of high pressure and a polar low, which determines the strength of the westerlies in each hemisphere. In the Southern Hemisphere, Hall and Visbeck (2002) proposed the existence of a large-scale oceanic response to the Southern Annular Mode (SAM) or Antarctic Oscillation (AAO), describing how a positive state SAM index (associated with stronger eastward wind stress) would increase equatorward Ekman transport, coastal divergence and upwelling along the Antarctic coast, generating a simultaneous lowering of coastal sea levels and increased outcropping of isopycnals at the sea surface, and resulting in both a barotropic and a baroclinic response in circumpolar transport. Observational studies using sub-surface pressure (sea level corrected for the IB effect) from Southern Ocean coastal tide gauge and bottom pressure recorders have substantiated this, identifying a virtually instantaneous large-scale coherent and inverse sea level response to subseasonal variability of the SAM at coastal locations (Aoki 2002; Hughes et al. 2003; Meredith et al. 2004, Woodworth et al. 2006, Hibbert et al. 2010), with covariability having been shown to hold for interannual timescales in some studies (Hughes et al. 2003; Meredith et al. 2004, Hibbert et al. 2010).

The Northern Hemisphere counterpart to the SAM, the Northern Annular Mode (NAM) or Arctic Oscillation (AO), is characterised by centres of low air pressure over the Arctic and higher pressure over the North Pacific and central North Atlantic oceans. There is a close correspondence between this pattern and that of the NAO which is focused on the Icelandic Low and the Azores High, and it is usually agreed that the NAO is a regional expression of the NAM (Thompson and Wallace 1998; Cohen and Barlow 2005).

Modelling studies of the Arctic Ocean suggest that coastal sea levels respond to periodic reversals of the ocean circulation (i.e. cyclonic or anticyclonic) (Proshutinsky and Johnson 1997; Proshutinsky et al. 2002; Dukhovsky et al. 2004), depending on the phase of the NAM (Newton et al. 2006; Proshutinsky et al. 2007). However, Häkkinen and Geiger (2000) reported the existence of two separate modes of sea surface height variability: one related to the NAM and a second associated with the NAO. Hughes and Stepanov (2004) used a barotropic model referenced to tide gauge observations, finding evidence of a highly coherent (but not dominant) Arctic Ocean sea level mode at interannual timescales that was associated with both the NAO and NAM. They concluded that variability of these atmospheric patterns caused changes in the eastward wind stress of atmospheric flows from the Atlantic, altering onshore Ekman flow and sea levels along the Arctic coast. These results are largely supported by observational studies (Dvorkin et al. 2000; Pavlov 2001, Proshutinsky et al. 2004; Richter et al. 2012; Calafat et al. 2013). Correlations between sea level and NAO/NAM decrease travelling east from the Norwegian Sea (Dvorkin et al. 2000; Calafat et al. 2013).

At lower latitudes, on the Eastern US coast, associations between the NAO and coastal sea levels have also been established (e.g., Andres et al. 2013), though it is unclear whether this arises from the dynamic effects of NAO-related variability on regional wind stress and air pressure (Andres et al. 2013; Ezer et al. 2013; Kenigson et al. 2018), or whether ocean heat anomalies associated with the NAO modulate the strength of the Atlantic Meridional Overturning Circulation, AMOC (Häkkinen 2000; McCarthy et al. 2015), or alternatively from some combination of the two (Goddard et al. 2015). Here, sea levels have been shown to exhibit a negative poleward gradient, with elevated sea levels in the vicinity of the subtropical gyre to the south of Cape Hatteras, and lower sea levels to the north in the colder waters of the sub-polar gyre. Variability in this sea level gradient has been strongly associated with heat exchange between the two gyres forcing changes in the AMOC, such that positive heat anomalies advected to the sub-polar gyre inhibit the AMOC (Bingham and Hughes 2009; Yin et al. 2009).

On the eastern boundary of the North Atlantic, a large-scale coherent sea level signal has been noted, which is highly correlated with the NAO at decadal timescales and which has been attributed to the association of the NAO with regional wind changes and to a lesser extent with air pressure (Wakelin et al. 2003; Miller and Douglas 2007; Calafat et al. 2012). The latter study noted that the region of coherent variability was largely confined to the continental shelf, postulating that along-shore winds force sea level anomalies that propagate polewards as coastal trapped waves (see below).

The Quasi-Biennial Oscillation (QBO) (Angell and Korshover 1964) describes a periodic reversal in the predominant direction (easterly or westerly) of the equatorial stratospheric winds that occurs approximately every 14 months. The phase of this is determined by upward fluxes of westerly and easterly momentum supplied by equatorially trapped Kelvin waves and Rossby-gravity waves, respectively (Lindzen and Holton 1968; Holton and Lindzen 1972), generating alternate wind regimes that gradually propagate downwards, dissipating at the tropopause. Unlike the climate modes discussed so far, the QBO is a stratospheric phenomenon, and, intuitively, a connection to sea level would be unexpected. However, Andrew et al. (2006) noted a statistically significant relationship between QBO index and sea level from altimetry in the tropical South Atlantic, but was unable to establish a dynamical explanation. Hibbert et al. (2010) identified an extratropical sea level response to the QBO along the coast of Antarctica, which was ascribed to modulation of the westerlies by the poleward focusing of planetary wave activity during an easterly QBO phase.

There is also an important intraseasonal mode of tropical atmospheric variability called the Madden–Julian Oscillation (MJO) (Madden and Julian 1971). The MJO is characterised by the generation and eastward propagation of coupled atmospheric deep convection and precipitation anomalies on timescales of 30–100 days (Xie and Arkin 1997), but most commonly 40–50 days (Madden and Julian 1994). These eastward-propagating systems typically originate in the Indian Ocean and are discernible in observations of zonal wind and precipitation (Zhang 2005). Oliver and Thompson (2010) performed a global analysis of altimeter data, validated using tide gauge sea levels, and established three key regions of strong connection between sea level and the MJO, the most significant of which was found to be the equatorial region and eastern boundary of the Pacific. It was suggested that zonal winds induced sea level anomalies that propagate eastwards along the equator and then polewards in both hemispheres along the coast of the Americas in the form of coastal trapped waves. Along the coast of Sumatra, a similar mechanism was proposed, but in this case, the poleward-propagating waves were thought to be accompanied by westward-travelling Rossby waves. In contrast, sea level setup by MJO-related onshore winds was the underlying mechanism in the Gulf of Carpentaria. Matthews and Meredith (2004) identified a sea level response to the MJO on the Antarctic coast, which was attributed to the development of an extratropical atmospheric wave train.

Similar large-scale patterns to those of variability in coastal MSL associated with climate modes have also been observed in extreme sea levels (Menéndez and Woodworth 2010; Marcos et al. 2009; Talke et al. 2014; Marcos et al. 2015; Wahl and Chambers 2016). For example, a strong wintertime dependence of MSL and storm surge elevations on the NAO has been noted on the NW European shelf (Wakelin et al. 2003; Woodworth et al. 2007; Marcos and Woodworth 2017). Interannual changes in wind-wave height, period and direction are also influenced by climate modes (e.g., Semedo et al. 2011; Stopa and Cheung 2014 and references therein). Wave-driven processes in the coastal zone are therefore also directly dependent on large-scale teleconnection patterns such as ENSO, SAM and PDO (Pacific Decadal Oscillation), with remote responses of wave setup and runup through the propagation of swell across ocean basins (and, in turn, as noted above, wave setup can contribute to coastal sea level, Melet et al. 2018). Similarly, rates of coastal erosion will be affected by the variability in storm surges, MSL and wave direction and energy flux, and consequently will have a dependence on climate modes. Such an association between coastal erosion and ENSO has been observed on Pacific coasts (Barnard et al. 2015).

7.2 Decadal Sea Level Variability

Decadal variability can perhaps be claimed to be more important than interannual variability in some respects, owing to the longer periods being more comparable to the lengths of sea level records, and thereby being a determining factor in obtaining reliable secular sea level trends. Two of the main climate modes that exhibit energetic decadal timescale variability are the Pacific Decadal Oscillation (Mantua and Hare 2002) and the Indian Ocean Dipole (IOD) (Saji and Yamagata 2003). (In fact, the PDO also has an energetic interannual component. However, it has proportionally more decadal energy than ENSO modes.)

The PDO occurs in the same ocean areas as ENSO (primarily the Pacific), but on longer timescales, as reflected in Pacific SST north of 20°N. The IOD is a quasi-periodic oscillation of SST between the western and eastern tropical Indian Ocean, which impacts significantly on the regional monsoonal weather. Major IOD events occur less frequently than ENSO ones, but the two phenomena are clearly linked components of the climate system.

Although these two decadal indices are defined in terms of SST, they are also reflected in similar regional patterns of sea level change. For example, Merrifield and Thomson (2018) (see also Hamlington et al. 2016) pointed to a shift in PDO index and trade wind fields between 1993–2011 and 2012–2016 which manifests itself in patterns of sea level change of opposite sign in the two periods (Fig. 7). Reviews of Indian Ocean decadal variability, including discussion of the IOD and sea level, are given by Han et al. (2014, 2018a, b).

Fig. 7

Adapted from Merrifield and Thompson (2018)

Sea surface height (SSH) trends from a 1993 to 2011 and b from 2012 to 2016 based on Aviso gridded SSH data. These patterns in SSH trends are similar to those in sea surface temperatures, these two periods being times of decreasing and increasing PDO index, respectively.

All of these decadal signals are regional, or even basin scale, in extent, rather than being particularly coastal. Nevertheless, the temperature and sea level variability associated with them can result in coastal impacts in, for example, coral bleaching or flooding of low-lying coral islands (e.g., Dunne et al. 2012).

Finally, one can mention that the nodal astronomical tide will contribute to variability in MSL. If this has a magnitude comparable to its equilibrium expectations, then it will be at the centimetre level or less at most locations (Woodworth 2012). Occasionally, larger nodal signals are reported in analyses of tide gauge data (e.g., Baart et al. 2012). However, these anomalous findings are mostly likely due to localised sea level variability (e.g., in river estuaries), or to genuine ocean variability with a similar period that is not adequately separable from the nodal tide in a short record.

8 Coastal Circulation Dynamics and Sea Level

The dynamics of the coastal ocean circulation are controlled by, amongst other things, bathymetry and the shape of the coastal boundaries. The dynamics introduces differences in sea level variability observed both along-shore and between the coast and deep ocean. These dynamics are discussed in detail by Hughes et al. (2019). However, for present purposes, we can point to three important aspects which are demonstrated in many studies: (1) the relative importance to sea level variability of atmospheric forcing, in particular wind stress, in shallow shelf seas, (2) the benefit of taking (1) into account when looking for longer-term trends in sea level variability, and (3) the sea level responses to forcing propagate along the shelf and slope, primarily cyclonically around an ocean basin (i.e. in the sense of Kelvin waves).

Dynamical processes along continental shelves have been investigated most intensively along the Atlantic coast of North America, where there is interesting dynamics related to the Gulf Stream, and high-quality tide gauge and meteorological data sets are available (e.g., Thompson and Mitchum 2014; Frederiske et al. 2017). The latter found a strong correlation between coastal sea level and decadal steric variability in the sub-polar gyre which is probably caused by variability in the Labrador Sea that is propagated southward. They cite theory and modelling literature regarding coastal trapped waves as an explanation of the findings from their analysis of sea level measurements showing this propagation. The steric signal explains the majority of the observed decadal sea level variability. Much other research has focused on differences in variability north and south of Cape Hatteras and between shelf and deep ocean (Woodworth et al. 2014, 2017a; McCarthy et al. 2015), interannual variability north of the Cape being largely wind-driven over the shelf (Andres et al. 2013; Piecuch et al. 2016; Kenigson et al. 2018), while that to the south is controlled more by fluctuations in the Gulf Stream. As a result, coastal sea level variability, especially in the north, has little correspondence to that in the nearby deep ocean (Fig. 8). In addition, balances between the forces of bottom and lateral friction, which are larger where the flow is faster, and sea level gradient, result in along-shore tilts in sea level being smaller than in the deep ocean. In this situation, the sea level variations observed at the coast are said to be insulated from those in deeper ocean by the shelf (Fig. 9) (Higginson et al. 2015).

Fig. 8

Correlations of detrended annual mean values of sea level from altimeter data over 1993–2009 with those at a point on the shelf to the east of Cape Cod (42°N, 69°W). Sea level on the shelf can be seen to vary differently from that in the ocean. From Woodworth et al. (2014)

Fig. 9

(left) Mean dynamic topography (MDT) (in m) from the HYbrid Coordinate Ocean Model (HYCOM) data-assimilative ocean model. The magenta and green lines show the smoothed location of the 200 m and 2000 m isobaths, respectively. (right) MDT along the coastline (black) and along the 200 m (magenta) and 2000 m (green) isobaths, plotted against latitude. Note that the Gulf Stream signal in green is much attenuated on the shelf. From Higginson et al. (2015)

Links have been made between changes in the strength of the overturning circulation and sea level gradients on the US coast (Bingham and Hughes 2009; Yin et al. 2009; Yin and Goddard 2013). Consequently, the high rates of sea level rise (‘accelerations’) observed in recent years at stations in the Middle Atlantic Bight have been interpreted in terms of overturning changes (Sallenger et al. 2012; Boon 2012) with possible additional Greenland and Antarctic mass loss changes (Davis and Vinogradova 2017). Other links have been made between coastal sea level gradients, the strength of the Gulf Stream circulation and climate indices including the NAO (McCarthy et al. 2015) and the Atlantic Multidecadal Oscillation (AMO), an index defined by Atlantic sea surface temperatures (Kenigson and Han 2014). Most recently, Domingues et al. (2018) suggested two processes at work: warming of the Florida Current in the south, and air pressure changes in the north.

Sea level variability on the eastern boundary of the North Atlantic has been shown to be controlled largely by along-shore wind stress (Calafat et al. 2012). It is not known at present what the across-shelf spatial scale of such variability is, and so whether it can be considered ‘coastal’. Nevertheless, one can suggest that it is due to a first-mode coastal trapped wave. Such a coastal trapped wave has the form of a Kelvin wave confined to the shelf, if the shelf width exceeds the barotropic radius of deformation at that location, and with the wind stress having a spatial scale exceeding the shelf width. There will be an along-shelf flow in the same sense across the whole shelf, with a node (zero) of elevation near the shelf break (Huthnance 1992). In the North Sea, Dangendorf et al. (2014) found that local atmospheric forcing mainly initiates MSL variability on timescales up to a few years; the IB effect being important in the northern North Sea, and wind stress in the shallower southern North Sea which is susceptible to storm surges. On decadal timescales, MSL variability was found to mainly reflect steric changes, which are largely forced remotely. They found evidence for a coherent signal extending between the Canary Islands and the Norwegian shelf, supporting the theory that along-shore wind forcing along the eastern boundary of the North Atlantic may cause coastal trapped waves that propagate thousands of kilometres along the continental slope. Similarly, Thompson et al. (2014) emphasised the need to account for atmospheric forcing and especially wind stress along North East Pacific coasts. They found that along-shore wind stress and local wind-stress curl are less important than (remote) equatorial forcing, the response to which propagates northwards.

Some general points can be made on the importance of along-shore winds based on the above literature. In the idealised context of uniform forcing and straight uniform shelf and slope, an along-shore wind tends to accelerate along-shore flow against bottom friction. The Coriolis force sets up cross-shelf transport which affects sea surface elevation at the coast relative to offshore (on the scale of the Rossby radius of deformation, or the shelf width if less). This sea surface slope balances the accelerating along-shore flow geostrophically, if bottom friction is relatively weak. Stronger friction tends to align the surface slope with the wind stress and limit the flow magnitude. Non-uniform or time-dependent forcing and non-uniform shelves result in propagating wave responses, so that the influence of the forcing extends over wave decay distances (greater for wide shelves and weak friction). Responses around very large islands may be considered in the same way. However, islands of much smaller scale than the forcing will experience an approximate averaging of the surrounding oceanic sea level.

Returning to the Pacific, the ENSO-related coastal sea levels along the American coast have already been referred to above. On the western side of the North Pacific, the Kuroshio Extension (KuE) provides the western boundary current of the subtropical gyre and is the Pacific counterpart of the Gulf Stream after separation at Cape Hatteras. As for the case of the Gulf Stream, interannual to decadal fluctuations of the KuE can have large impacts on coastal sea level variability.

Sasaki et al. (2014) have researched sea level variability along the coasts of Japan, primarily on decadal timescales. The first empirical orthogonal function (EOF) mode of sea level variability in the KuE region had previously been shown to describe well the meridional displacements of the KuE on decadal timescales (e.g., Taguchi et al. 2007). Sasaki et al. (2014) found that northward shifts of the KuE jet and the Kuroshio Current southeast of Japan are accompanied by higher sea levels at the coast. The decadal variability of the KuE latitude is mainly induced by westward-propagating, wind-forced Rossby waves from the eastern North Pacific (Qiu and Chen 2005; Yasuda and Sakurai 2006). These waves are concentrated along the KuE jet axis as jet-trapped Rossby waves. The resulting sea level changes along the Japan coast were found to be spatially variable, with large values along the south-eastern coast that are directly influenced by the jet-trapped Rossby waves, and also on the west coast, but small values north of the KuE jet. This is because any wind-induced Rossby waves will be trapped along the KuE axis (Sasaki et al. 2013). Hence, the area north of the KuE becomes a shadow zone which an incoming Rossby wave does not enter (Sasaki et al. 2014). Instead, a wind-forced coastal wave is one of the causes of interannual coastal sea level variability north of the KuE (e.g., Nakanowatari and Ohshima 2014). Kourafalou et al. (2015) described a case study, from the perspective of ocean forecasting, of an event in September 2011 that caused flooding in southern Japan. Sea level anomalies of ~30 cm were observed that resulted from the passage of coastal trapped waves induced by short-term fluctuations of the Kuroshio around 34°N, 140°E.

Sasaki et al. (2014) stress the importance of understanding the dynamical reasons for such variability in order to reliably predict future sea level changes. In a later modelling study of Japan sea level variability over 1906–2010, Sasaki et al. (2017) further pointed to the need to understand natural variability on decadal timescales for understanding future regional sea level change.

Another interesting feature is the bimodality of the Kuroshio path south of Japan. That changes between a straight path (along the south coast of Japan) and a large-meander path (away from the coast) on interannual to decadal timescales. This path variability induces sea level changes of about 10 cm along the south coast of Japan (Kawabe 1988; Usui et al. 2011). The Kuroshio transport, which is determined by the large-scale wind, is a key factor in determining the Kuroshio path (e.g., Tsujino et al. 2013). Its transport in the East China Sea has been found to be highly correlated with the PDO (Andres et al. 2009). The variability of the Kuroshio transport also causes coastal sea level change in the upstream region, such as along the coasts of Taiwan (Chang and Oey 2011) and Philippines (e.g., Zhuang et al. 2013).

Elsewhere in the Pacific and Indian Oceans, there has long been evidence for wind-driven coastal trapped waves along Australian coasts, mostly on monthly timescales. These include the coastal trapped waves on the south coast forced by strong westerly winds and the wide shelf, on the west coast that propagate southwards, and on the east coast propagating north (White et al. 2014 and references therein).

One interesting dynamical aspect of near-coastal sea level (or sub-surface pressure, SSP) variability concerns coherence of variability in SSP on intraseasonal timescales (timescales less than a year and not including the regular seasonal cycle) over great distances along the shelf and slope around continental boundaries (Hughes and Meredith 2006). The existence of such coherence, investigated first using altimeter data, has since been verified with ocean models (Roussenov et al. 2008; Hughes et al. 2018, 2019) and demonstrates that ‘coastal’ (or at least ‘shelf slope’) variability need not always be ‘short spatial scale’.

With regard to sea levels on island coasts, we can mention the important role of eddies in the dynamics of the global ocean circulation. Open-ocean eddies have been found to be responsible for decimetric signals in some sea level records from ocean islands. For example, Mitchum (1995) relates 90-day oscillations at Wake Island (western Pacific) to Rossby waves propagating westwards (possibly from eddies generated by flow impinging on Hawaii). As Wake Island is very small and at latitude < 20°, it is expected to show the surface oscillations of the arriving Rossby waves. Modelled differences between coastal sea levels observed at islands and in the open ocean (Williams and Hughes 2013) show poor correlation for islands surrounded by ocean in which a large fraction of steric variability is at frequencies and wavelengths lacking baroclinic Rossby wave propagation. This is more likely at higher latitudes, so that coherence between island and open-ocean sea level decreases away from the Equator, until at yet higher latitudes the steric signal decreases and coherence increases once again.

Finally, on a similarly small spatial scale, one can refer to coastal bays and estuaries and their interaction with larger-scale dynamics that is sometimes reflected in sea level. For example, Feng and Li (2010) discussed the flushing of coastal bays in Louisiana due to the passage of cold fronts. This process takes place on timescales of less than 40 h and results in sea level changes of ~ 25 cm. On longer timescales, the strong winds and air pressure variations which are important to the coastal dynamics on shelves and the large-scale ocean circulation discussed above can result in particularly energetic (several decimetre) sub-tidal sea level variability in bays and estuaries. Examples for the American coast are discussed by Salas-Monreal and Valle-Levinson (2008) and Waterhouse and Valle-Levinson (2010).

9 Long-Term Changes in MSL

A major consequence of climate change is sea level rise resulting from changes in the density of sea water (steric effect) and from water mass transfer from land to the ocean from melting glaciers, ice sheets and groundwater storage changes (Church et al. 2013). Analysis of the first years of altimeter data suggested that MSL might be rising at a greater rate near to the coast than in the nearby deeper ocean (Holgate and Woodworth 2004) although such a difference was not considered significant by others (White et al. 2005; Prandi et al. 2009), and, as far as we are aware, there is at present no evidence for such differences.

As the depths of coastal waters increase, then many of the processes mentioned above will change:

• Tidal wavelengths will increase, and tidal patterns over the continental shelves will change. In fact, coastal tides are already known to be changing (e.g., Woodworth 2010; Haigh et al. 2019) for reasons that are not well understood. Sea level rise will result in further changes to the tides (e.g., Devlin et al. 2017; Idier et al. 2017; Pickering et al. 2017);

• Storm surge spatial gradients and magnitudes will reduce because of their dependence on 1/depth (Pugh and Woodworth 2014);

• Changes to tides and surges imply changes to extreme sea levels;

• Ocean waves break when entering water with depths ~ 2.6 times the wave amplitude (Dean and Walton 2009). As the MSL rises, waves with greater height and larger periods will impinge on coastal zones, with associated changes in wave setup and runup (Chini et al. 2010). This will cause amplified potential flooding impacts (Arns et al. 2017);

• Climate change may result in modifications to large-scale climate patterns (ENSO, NAO, etc.) and associated wind fields (and also heat content), resulting in regional changes in MSL and extreme sea level (Kirtman et al. 2013).

In addition to changes due to the depth of coastal waters, coastal sea level could also be affected by other changes in response to climate change including:

• Changes in regional patterns of atmospheric surface pressure and winds;

• Changes in ocean circulation (e.g., strengthening/weakening of coastal currents and of upwelling/downwelling);

• Changes in wind fields also imply further changes in wind waves and, therefore, in changes in wave setup, runup and overtopping.

Trends in surface winds have been observed over the last few decades, with notably a strengthening of the westerlies in the Southern Ocean and of the trade winds in the Pacific (e.g., Young et al. 2011; Swart and Fyfe 2012; Takahashi and Watanabe 2016). Climate change projections for the twenty-first century indicate significant changes in annual mean wave conditions over large ocean regions, notably with increased wave energy in the Southern Ocean that will impact remote regions through northward swell propagation (Hemer et al. 2013). Wave-driven contributions to water level at the coast could, therefore, exhibit trends in response to climate change over parts of the global ocean (Melet et al. 2018), which could lead to important coastal impacts. Long-term changes in wave direction may also induce changes in wave refraction and diffraction patterns, in along-shore current and associated sediment transport due to non-normal wave incidence. Together with changes in wave energy, they could result in altered patterns of beach erosion/accretion, and position and orientation of the shoreline.

All of these aspects of sea level variability are linked in various ways. In particular, trends observed in extreme sea levels in tide gauge records have been found to be related to trends in local MSL (see Sect. 4). Therefore, a gradual increase in MSL can thereby rapidly increase the frequency and severity of coastal flooding (Sweet and Park 2014). It has been estimated that 10 to 20 cm of sea level rise expected by 2050 will more than double the frequency of extreme events in the tropics (Vitousek et al. 2017). Extreme wave energy fluxes are projected to increase during this century implying potentially amplified impacts on the coast (Mentaschi et al. 2017). The many interactions between the various processes mentioned above are discussed in greater detail by Idier et al. (2019).

10 Vertical Land Movements at the Coast

Vertical land motion contributes to relative sea level change observed by tide gauges at the coast, which can therefore differ from a change in sea level in the open ocean observed by altimetry. In other words, the ocean volume could remain unchanged, and yet sea level changes and coastal impacts could be observed due to vertical land motion only. As a matter of fact, the vertical position of the land surface at the coast (measured relative to the centre of the Earth) could be changing as much as the position of the sea surface itself, sometimes by a factor of ten or more. For instance, coastal subsidence in excess of a centimetre per year has been observed at Manila, Philippines (Raucoules et al. 2013), due to sub-surface anthropogenic activities and at Grand Isle, Louisiana (Törnqvist et al. 2008; Kolker et al. 2011), due to a combination of natural and anthropogenic processes, whereas coastal uplift up to a centimetre per year has been observed in Fennoscandia (Kierulf et al. 2014) or at Hudson Bay (Sella et al. 2007) due to ice mass unloading from the last deglaciation and glacial isostatic adjustment (GIA). What is more, ignoring vertical land motion, especially in active tectonic regions, can result in mistakes in attributing the reasons for sea level change and thereby in adoption of strategies for protecting populations and assets against coastal flooding (Ballu et al. 2011). Therefore, vertical land motion deserves as much attention as climate change in coastal sea level studies.

In fact, there are many phenomena that can cause vertical land motion, operating at different time and spatial scales (Fig. 2 and Table 1), resulting both from natural processes (e.g., GIA, tectonics and sediment compaction) and from anthropogenic activities (e.g., groundwater depletion, dam building or settling of landfill in urban areas) over a broad range of space and timescales. GIA is the most widely known phenomenon, operating globally at decadal to millennia timescales for which geodynamic models are available on a global basis (e.g., Peltier et al. 2015). This geological process includes deformational, gravitational and rotational effects due to the waxing and waning of the great ice sheets. It is essential to know the rheology of the Earth’s interior and the histories of the ice sheets in order to predict accurately the viscoelastic response of the solid Earth and the resulting rates of vertical land movement (crustal displacement). There are important differences in such geodynamic modelling if the melting of land ice relates to the late Pleistocene ice sheets or to the present-day ice sheets, although the calculations are based on the same physics. For instance, the rheological behaviour of the Earth’s interior can be approximated to that of an elastic body for short (decade to century) contemporary timescales of melting (Tamisiea and Mitrovica 2011; Riva et al. 2017; Spada 2017).

Water mass redistributions on the Earth’s surface, and the associated loading of the solid Earth, can also result in significant vertical land motion. These include natural processes such as non-tidal atmospheric, oceanic and continental water mass loading variations, operating at interannual to decadal timescales with vertical displacements of the order of a mm/year (Santamaría-Gómez and Mémin 2015). To a lesser extent (at the level of 0.5 mm/year over multidecadal timescales), anthropogenic activities associated with water impoundment behind dams (Fiedler and Conrad 2010) and groundwater depletion (Veit and Conrad 2016) can also be important.

Earthquakes are instantaneous co-seismic vertical displacements of the Earth’s surface. However, the earthquakes themselves are only one aspect of a set of tectonic processes within the earthquake deformation cycle. That cycle consists of steady interseismic motion that can last for years, decades or longer, punctuated by the instantaneous displacements during the earthquakes themselves. Following the earthquakes, there will be a postseismic relaxation during which deformation will occur lasting months to years before reverting to steady interseismic motion. For example, Ballu et al. (2011) reported a steady interseismic subsidence of the order of a cm/year at Torres Islands, Vanuatu, in between the magnitude Mw 7.8 earthquakes of 1997 and 2009. Those two earthquakes resulted in sudden vertical displacements of several hundreds of millimetres (subsidence of 500–1000 mm in 1997 and uplift of about 200 mm in 2009). These vertical displacements in land level thereby translated into abrupt coastal sea level changes in the opposite direction (sea level rise in the case of land subsidence and sea level fall in the case of land uplift). One may note that in this case study the interseismic vertical land motion (~ 1 cm/year) was three times larger than the rise of global MSL observed during the satellite altimetry era. Hence, it can be seen that such geological processes can play major roles in magnifying coastal risks from sea level change at such locations.

Prediction of the epochs and magnitudes of co-seismic and postseismic displacements are still beyond the present-day means of geophysical modelling. However, some progress has recently been accomplished regarding the interseismic motion. Smith-Konter et al. (2014) used a 3-D elastic/viscoelastic earthquake cycle model of the San Andreas Fault System, and identified in the sea level records along the California coastline the tectonic signals associated with the flexure of the elastic plate caused by bending moments at the ends of the locked faults. Unfortunately, such estimates of tectonic vertical land motion are not yet readily available for regions outside California.

Magma flow and pressure in active volcanoes, whether associated with tectonic plate boundaries or hot spots, can cause large inflation/deflation ground deformation events over days to months, and sometimes even longer periods. For example, at Socorro Island, part of a shield volcano located 200 km west of the Pacific coast of Mexico, Cazenave et al. (1999) observed a large post-eruptive 30 cm subsidence of the island during the 3 years following a submarine volcanic eruption in 1993.

In delta regions, land subsidence occurs naturally through sediment compaction when water is lost from interstitial spaces caused by the weight of overlying sediment or through rearrangement of sediment particles (Törnqvist et al. 2008). Observed rates of deltaic subsidence over the last few decades range from 3 to 100 mm/year. For instance, average subsidence rates of 4–6 mm/year have been reported for the Ganges–Brahmaputra Delta (Brown and Nicholls 2015) with much larger rates up to 10–20 mm/year in densely populated areas. This includes an estimated long-term contribution from sediment loading and sea level rise during the Holocene amounting to 1.1–1.7 mm/year, depending on the values for lithospheric thickness and Earth mantle viscosity considered (Karpytchev et al. 2018). These are all significant rates of vertical land movement when compared to the 3 mm/year rate of global MSL rise observed by satellite altimetry over the same time span. In highly populated delta areas, the extraction of groundwater, oil and gas that fill pore spaces can significantly exacerbate, and sometimes dominate, the rate of compaction and resulting subsidence (Kolker et al. 2011).

Locally, all contributions to sea level changes are important, whether arising from oceanic or vertical land motion processes. The factors controlling relative sea level differ from one coastline to another, and oceanic effects may not be the largest. In some coastal regions of the world, vertical land motion clearly dominates. In other areas, they might be of the same order of magnitude as oceanic (climate) factors (Wöppelmann and Marcos 2016). There is a clear need for measurements by modern geodetic techniques that provide accurate estimates of vertical land motion, which underlie the observed relative sea level changes, for application to sustainable management plans for the coast. This is why the new implementation plan of the international Global Sea Level Observing System (GLOSS) programme (see Marcos et al. 2019) calls for an important upgrade to its core network by requesting the installation of continuous Global Navigation Satellite System (GNSS) stations at tide gauges. GNSS will thereby measure the local vertical land movement of whatever origin. Figure 10 provides a demonstration of how trends of MSL measured by different tide gauges can be made more regionally consistent when GNSS information is employed to measure vertical land movements. The modern geodetic techniques are also required to place the tide gauge data into the same geocentric reference frame as for the altimeter data as required for altimeter calibration studies (Mitchum 2000; IOC 2016).

Fig. 10

Time series of annual MSL from (left) tide gauge records, and (right) GNSS-adjusted tide gauge records in (top) N Europe, (middle) NW America and (bottom) Gulf of Mexico. MSL data are from the Permanent Service for Mean Sea Level (PSMSL, https://psmsl.org), while GNSS information was acquired using the ULR6a solutions of the Système d’Observation du Niveau des Eaux Littorales (SONEL, http://www.sonel.org). The time series are displayed with arbitrary offsets for presentation purposes. Units mm. RMS indicates the root-mean-square of the trends shown in each panel

11 Human Influences on Coastal Sea Level Variability

A full discussion of modifications in coastal sea level variability, which occur due to human intervention in coastal processes via coastal engineering, is outside the scope of this paper. However, several examples may be mentioned in order to demonstrate that there can indeed be such man-made impacts.

It is well known that the amplitudes and phases of tides in harbours and lagoons can be altered by engineering to their inlets, thereby altering the tidal prism. Similarly, both natural and anthropogenic changes in the sedimentation of coastal lagoons affect the tide (Araújo et al. 2008). Dredging in river estuaries will tend to lower low waters but leave high waters relatively unchanged, with a consequent increase in tidal range (Siefert 1982). Coastal engineering can affect the tides (de Boer et al. 2011), and schemes such as beach nourishment, which modify near-shore gradients, will modify wave setup and overtopping (Dean 1991). Similarly, a rise in MSL (which in itself could be said to be man-made) will modify the vertical profiles of some coastlines (Bruun 1962). MSL records exist which demonstrate the effect of human-induced sedimentation in coastal embayments (e.g., Manila), or the consequences of submergence due to ground water pumping (e.g., Bangkok, Shanghai), leading to anomalous local rates of relative sea level rise (see examples in Pugh and Woodworth 2014).

These examples demonstrate that the history of any changes to the area around a tide gauge station can be reflected in its record, as can relocations of recording within a large harbour, or changes in tide gauge technology.

12 Conclusions

We have shown that there are many processes which result in coastal sea level variability, operating on timescales from seconds to centuries and on spatial scales from local to global. Many of the processes (summarised in Table 1) are understood well (in principle at least), such as tides and surges, although some remain relatively little researched and under-represented in sea level studies. In fact, there are others that have not been included here as they are not particularly coastal in character. Compendiums such as Pugh and Woodworth (2014) and Cazenave and Stammer (2017) provide more information on some of them, while several are discussed in greater detail in other papers in this volume. The scientific aim must be to be able to understand and model as many of these processes as possible.

We have also shown that each process will depend on the others to some extent due to the associated changes in water depth. It has also been shown that it is mistake to think that coastal sea level variability always has a ‘local’ forcing (although it often does), given that there are also for instance processes that result in signals trapped by and propagating along the continental shelves.

Some questions for consideration in future research are:

• How well can ocean models of various kinds reproduce the time series of sea level variability observed at the coast by tide gauges and offshore by altimetry (i.e. understanding the differences akin to those shown in Fig. 1)? Models will inevitably perform well for some regions and timescales, but less well for others (e.g., Chepurin et al. 2014; Becker et al. 2016; Meyssignac et al. 2017). In particular, models that are capable of reproducing coastal sea level variability observed to date will provide confidence in projecting future coastal sea level change (Ponte et al. 2019).

• Concerning our knowledge of tides at the coast, users of satellite altimetry in the deep ocean have grown accustomed to having reliable tide models that account for that dominant component of variability in their data. However, when altimetry is applied to the near-coastal zones, the existing models are less reliable and must be developed to greater complexity with many additional constituents. Deep-water versus shallow-water spectra (Fig. 3) readily convey the challenges of modelling coastal tides. In addition, a better determination and understanding is required of secular and other low-frequency changes in coastal tides that have been observed (this question relates to the need for ‘data archaeology’ mentioned below).

• With regard to waves, how much are historical MSL records contaminated by wave setup and can any contributions be modelled efficiently and so removed from the records? This question applies especially to composite records obtained from gauges at different locations within a bay or port. Should there be a comprehensive global coastal wave monitoring network to collect the data needed to assess the setup contribution to MSL? How will the wave setup contribution change in the future if wave climate changes?

• Similarly, how much have historical MSL records been contaminated by contributions from river runoff, and therefore misrepresent open-ocean conditions?

• There are several important questions in geodesy. How well can models of the solid Earth predict the motion (primarily vertical) of geodetic benchmarks at the coast over decadal to century timescales, specifically at tide gauges? Also, can the terrestrial reference frame be implemented in an accurate and stable manner in order to predict accurately the positions and motions of geodetic stations? Geophysical modelling and space geodesy observations have suggested that we should target vertical land motion predictability at the level of 0.1 mm/year over decadal to century timescales (Blewitt et al. 2010).

• In climate research, what mechanisms have been responsible for past changes in extreme levels (other than changes in MSL) and how might forcings and extremes change in the future? In particular, how will the extremely damaging storm surges associated with tropical cyclones change?

• In coastal modelling, because atmospheric forcing (and in particular wind stress) is relatively important in shallow shelf seas, there are challenges (1) to remove its shorter-term effects on coastal sea levels when estimating longer-term trends, and (2) to separate its longer-term effect from open-ocean sea level trends as drivers of coastal sea level change. Additionally, (3) as discussed in Sect. 8, because responses to forcing propagate along the shelf and slope, with forms and speed dependent on the shelf and slope topography, there is a need for models to be developed with sufficient resolution and ‘upstream’ extent over the distance in which the propagating signals decay. An additional challenge relates to modelling in greater detail the sea level variability around islands (including any surrounding shelves) located at different latitudes and with different sizes (larger and smaller than the baroclinic deformation radius) to understand where models and measurements differ.

Progress cannot be made with these and many other questions to do with sea level variability without access to the best, and most complete, observational and modelling data sets, as discussed further by Ponte et al. (2019). One may note:

• It is essential that the global network of tide gauges and other essential in situ data sets be completed and analysed in combination with satellite altimeter data sets (Roemmich et al. 2017). The global tide gauge network is currently challenged with maintaining many existing stations and installing new ones where required. Where appropriate, GNSS-reflection tide gauges may be more suitable than conventional techniques (Larson et al. 2017). In addition, there is a need for continuous monitoring of vertical land motion at tide gauges, requiring the installation of permanent GNSS stations at as many tide gauges as possible, and as near as possible to the tide gauges, and the undertaking of regular levelling campaigns between the tide gauge benchmarks and GNSS benchmarks (Woodworth et al. 2017b). See also discussion of this topic in Marcos et al. (2019) and Ponte et al. (2019).

• It is important also to extend the historical coastal sea level data set via a programme in ‘data archaeology’ (Bradshaw et al. 2015) and the use of ‘proxy’ (geological) data sets (e.g., Barlow et al. 2014).

• High-frequency (timescales ~ 1 h or less) sea level variability due to seiches, meteotsunamis and other high-frequency processes are frequently under-represented in sea level studies (Vilibić and Šepić 2017), and yet contribute to the extreme sea levels which are of great research interest and importance to coastal dwellers. In particular, an important objective should be to derive via barotropic modelling a global data set of seiche climatology.

• Similarly, it is highly desirable that barotropic tide-surge modelling, presently providing typically hourly values of modelled sea level on a global grid back to the mid-twentieth century, be extended back to the mid-nineteenth century using newly available reanalysis wind fields (Compo et al. 2011). Such model data sets would have many applications in understanding sea level variability.

• Access to new sets of coastal altimetry data, uncontaminated by reflections from the altimeter footprint over land and with improved geophysical corrections, should illuminate to a greater extent the reasons for differences between coastal and ocean sea level variability (Vignudelli et al. 2011; Cipollini et al. 2012, 2017; Birol et al. 2017). However, in our opinion, these data sets will never be a substitute for tide gauges in the coastal zone, given their temporal resolution and accuracy. The continuity of both in situ and space-based instrumentation is essential for a proper monitoring and understanding changes in sea level. The several techniques in combination will thereby enable us to understand as well as possible the evolution of coastal zones (Cazenave et al. 2017).