Coastal Water Level

Coastal water is a showcase of the highly dynamic processes associated with the continuous rise and fall of water elevations – in symmetry and asymmetry. Apart from the undulations people see when sitting on a coastline – the best quantitative depiction of the showcase is revealed in time-series measurements of Water Level (WL) in many gaging stations that dot coastal waterfronts. The coastal zone WL on our Seashore – are driven by many – from regular Ocean Waves and Surf Zone activities to the episodic forcing of Storm Surge, Tsunami and Coastal Responses to Tsunami.
The Natural World of Coastal Water working under the canopy of the Gravitational Force Field or GFF is a superimposition of 5 other major Force Fields – the strengths of which vary in time and space. As described in the Force Fields in a Coastal System – they are: Metocean Force Field or MOFF; Extraterrestrial Force Field or ETFF; Land Drainage Force Field or LDFF; Heat Exchange Force Field or HEFF; and the Frontal Wave Force Field or FWFF.
All these force fields have different magnitudes and scales of variation. Depending on what dominates a certain scenario – a water body responds by displaying its flow characteristics transformation dynamics. Effects of MOFF, ETFF, LDFF and FWFF are highlighted in this essay. The role of HEFF in WL changes is not so much of a significance like others, therefore not discussed.
Linearity, Non-linearity, Spectromatic and Turbulent compositions of water motion with its characteristic Wave Asymmetry and associated Coastal Ocean Currents – in areas from Coastal River Delta and Coastal Inlets to the contiguous ocean – generate many other processes and activities on alluvial seabeds that include: Sediment Transport, Longshore Sand Transport and Sedimentation, among others.
In the presence of coastal structures – such as Breakwaters, Flood Barriers and others – more activities follow – such as Wave Loads on Vertical Piles, Wave Structure Interactions and Scour, Forces on Structures—thereby causing Motion on Moored Ships and Propwash in harbors.
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With this, let us attempt to see in brief terms – how the interesting dynamics of WL change works in the coastal zone. The processes related to this changes are described from the viewpoints of Force Fields - and the pasted image is created from that perspective. My long experience in coastal engineering as well as my publications and teaching lecture notes, together with several pieces posted in WIDECANVAS – helped me drawing up this essay.
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1. The Hydraulics of Coastal Water
The WL rise and fall is a visual manifestation of the dynamic interactions between potential energy (proportional to the mass of the water column) and kinetic energy (proportional to water density and the mean flow velocity squared). The dynamic interactions between the two – a result of the changes in depth and topographical configuration – is superbly demonstrated in the fluid flow Bernoulli Equation (Daniel Bernoulli, 1700 – 1782). This equation is a simplification of the elaborate Navier-Stokes Equation (French engineer Claude-Louis Navier, 1785 – 1836; and British mathematician George Gabriel Stokes, 1819 – 1903) and Newton’s Law of motion (Isaac Newton, 1642 – 1727). The Seabed Roughness of Coastal Waters shows the practical interpretations and significance of different terms in the Navier-Stokes Equation - further in the Natural Equilibrium and Water Modeling essays.
Bernoulli Equation representing steady approximation of long-wave transformation – is a clear depiction of the equilibrium correspondence between the potential energy or static pressure – and the kinetic energy or dynamic pressure in a frictionless flow. In other words – when flow velocity becomes high, the water level is lowered and vice versa.
ETFF
The regular rise and fall of coastal WL represents a superposition or phase-addition of multiple forcing factors – among them ETFF is overwhelmingly dominant. The undulation manifests itself in semi-diurnal (like in North America East coast), diurnal (like in Gulf of Mexico coasts) and mixed tides (like in North America West coast). The different tidal types are the results of interactions between the forced ocean tide and the coastal zone topographical factors. Diurnal tides are usually low in amplitude.
The fortnightly spring and neap tides responding to the waxing and waning phases of moon – is another regular forcing added on top of the daily tide. Tide is a predictable quantity. Harmonic analyses of measured tidal heights at a certain station are used to determine constituents and arguments of the moon-sun phases and forces – which are then used to predict future tide at that station. That’s how regional and global tide tables are produced and published – to help all navigators and different works in coastal waters, ports and harbors.
As highlighted in Ocean Waves – the coastal tide resulting from the circumnavigating ocean tide that traverses close behind the trio of the Sun-Moon-Earth phase – goes through the transformation processes of shoaling, funneling, amplification-or-weakening, and near-resonance amplification in the coastal zone. The phenomenon and processes of near-resonance amplification are demonstrated in my 2006 Tsunami Modeling paper. In especial coastal configurations, amplifications give birth to coastal overtides and compound tides (demonstrated in my 1991 COPEDEC-PIANC paper – Fourier Spectral analyses of time-series water levels showed how some harmonics were amplified, others were weakened in simultaneous observations along the Bangladesh coast).
Coastal WL displays a Gaussian bell-shaped curve – a symmetric distribution about the mean (more in Uncertainty Propagation in Wave Loadings). As demonstrated in The World of Numbers and Chances – such a distribution helps one to find the exceedence probability of WL for a certain height. As discussed further later, this probability is very useful to engineer the crest or the top elevation of a coastal structure.
Apart from WL descriptions as such – local WL variations do occur in different frequencies, amplitudes and phases, in particular when MOFF, LDFF and FWFF dominate the regional hydrodynamics. Nature of these force fields and consequences are described in the Force Fields in a Coastal System essay – with the following descriptions heavily relying on what were written there.
MOFF
Apart from generating surface wave activities (see Wave Hindcasting), MOFF actions display one of the devastating Ocean’s Fury on coastal WL – the Storm Surge – a virtually troughless wave crest that flood coastal low lands – propagating onto coastal inlets and estuaries. It is the combined effects of wind setup, wave setup and inverse barometric rise of WL (the phenomenon of reciprocal rise in water level in response to atmospheric pressure drop). MOFF effects are modulated by tidal activities and phases on a rather daily basis – accentuating or attenuating WL. In terms of the storm surge – the devastating disasters occur when the peak surge rides on high tide (the superimposition of tide and storm surge is known as Storm Tide).
The wind setup contribution to WL-rise in most coastal water bodies – occurs during the periods of Strong Breeze and Gale Force winds (see Beaufort Wind Scale) – and during the passing episodes of winter storms and landward monsoons. They are measurable when the predicted tide is separated from the measured WL. Such setups and seiche (standing wave-type basin oscillation responding to different forcing and disturbances) are visible in WL records of many British Columbia tide gages.
When Hurricane-scale cyclonic wind fields dominate a certain area – wind-setup and set-down turn into surge waves attaining the dynamics of a FWFF. The surge waves are characterized by high surge on the right side of the propagating storm in the Northern Sphere – with the negative surge on the left side. Affected by coastal topography – spectacular Sea Level Blow Out or emptying of water-basins could occur on the left side. A storm surge period scaling in order of days – causes devastating effects together with heavy rainfall – during the passage of a slow moving Hurricane than a fast moving one.
Storms are accompanied by high wave activities, consequently wave setups are caused by breaking waves. Wave setup is the super elevation of the mean WL at the shoreline – this elevation rises from the low set-down at the wave breaker line. A model simulating the likeness of Hurricane FRANCES and JEANNE on Florida coast – that generated a 4.0 m high significant wave height having a peak spectral wave period of 14 second – the modeled wave setup was estimated to be about 1.2 meter, or about 30% of the wave height.
LDFF
This force field is a minor contributor to coastal WL changes. It particularly affects the deltaic estuaries (Coastal River Delta) and the contiguous coastal ocean when high river stage wet season or storm season freshwater flow debouches into open water. Apart from the freshwater discharge volume – the density difference between the incoming flow and the ambient saline water – distorts local tide causing the mean water level to rise in the affected area.
Seasonality of the freshwater outflow has a substantial influence on the river-mouth hydrodynamics – from pushing the freshwater front out into the sea during the high-flow period – to the modification of tidal wave – to letting salt-water to intrude into the lower river reaches during the lean-flow period. All these are manifested in WL changes.
FWFF
In the Force Fields in a Coastal System, I have tried to explain how FWFF works – in particular during the windstorm and tsunami episodes when depth-induced wave-breaking occurs. The same happens with tidal bores and in Surf Zone processes.
FWFF is characterized by wave energy propagating in the supercritical flow regime. As visibly spectacular in tsunami and tidal bores – a wave with such a high speed could propagate upstream, and cross and overtake obstacles and transports huge load of debris and sediments. As a consequence of and immediately following the passing of the wave-front – the WL is raised.
Tidal bores form during spring tides when the range is the highest. With the combined affects of shoaling and funneling – the propagating tide becomes highly asymmetric so much so that at a certain time maintaining the wave-form becomes unsustainable – the result is the breaking of the accumulated pressures – giving birth to tidal bores.
Like all waves, a small tsunami in deep water shoals to monstrous waves as it propagates into the shallow water. After breaking, Tsunami Run-ups flood coastal lands with enormous inbound and outbound speeds causing havoc and destruction. The arrival of Tsunami crest is preceded by the huge draw down or Sea Level Suck Out associated with the Tsunami trough. This phenomenon sucks out things from the shore out into the sea—exposing shoreline features – leaving many aquatic lives stranded in air.
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2. Measuring Water Surface Elevation
The WL is a depiction of the depth of the column of water – with or without the propagation of energy through it. How to have a quantitative measure of this water? The vertical measures of the column – are known as Depth when measured from top to bottom; and Height when measured from bottom to top. There have been enormous progress in hydrographic and oceanographic instrumentation of data collection- the following is only a basic snapshot. 
Depth measurements range from the past techniques of using marked vertical rods or strings – to the use of modern echosounder transducer probes immersed at a certain depth. Some echosounders also come with dual frequency option to determine the thickness of seabed fluid-mud layer, if present.
A remarkable breakthrough in mapping the seafloor – is obtained by applying simultaneous use of multiple beam echosounder or sonar. The 2015 NOAA Newsletter Version says: Multibeam sonar has several transducers that allow a large swath of area to be surveyed at once making surveying much faster and more accurate . . . The swath width is determined by the depth of the seafloor being surveyed. The ping is emitted in a fan shape outward from the transmitter. The farther away the object the more area there is for the sound to echo off. The sonar pings several times per second which, with the speed of the boat, determines the horizontal resolution of the images created.
A pressure sensor immersed at a certain location of the water column – yields the height of water above that sensor. On most occasions, the adjustment and tuning of the sensor registration frequency – allows one to measure both water and wave parameters.
Among others, remote sensing technology is gradually replacing the traditional methods of hydrographic data collection. Two of them are highlighted – Lidar and Satellite Altimetry.
LIDAR – the Light Detection and Ranging method uses light in the form of a pulsed laser to remotely measure distances from an airborne platform to the object – to map the reflecting land surfaces and underwater topography. A Lidar device consists of a laser, a scanner, and a specialized GPS to collect geospatial data. To avoid moisture absorption – a surface topographic Lidar typically uses a near-infrared laser to map the land on cloud-free days and nights – while a bathymetric Lidar uses water-penetrating green radiation to map seafloor elevations. In both the cases, the travel time taken by emission and reception along with the speed of the used laser beams – is used to calculate distance. More in NOAA Lidar Technology and Applications and USGS Lider Base.
Satellite Altimetry – according to a NOAA article, satellite radar altimeters measure the ocean surface height (sea level) by measuring the time it takes a radar pulse to make a round-trip from the satellite to the sea surface and back. NOAA ongoing research shows that – the same principle can be used to estimate deep ocean floor elevations based on the principle that a seabed height difference can change the water surface elevations. The approach is complemented by employing multi-beam echosounders.
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As outlined before, gaging stations installed in different waterfront locations – are used to serve many purposes, the most important of which is to measure water elevation with respect to a common vertical Datum. When bathymetry is related to the same vertical datum – seabed level appears – shown as positive for submerged seabed below the datum and negative as a drying height above the datum.
What are the common datums used to determine coastal water elevation? Let us have a brief overview of them. A coastal engineer or a scientist comes across two vertical datum types – the Geodetic Datum and the Hydrographic or Chart Datum.
Geodetic Datum.
In North America, the Geodetic Datum is known as the North American Vertical Datum of 1988 (or NAVD88) – it replaced the formerly used National Geodetic Vertical Datum of 1929 (or NGVD29). While the conversion between the historical and presently used geodetic datums – varies spatially – USGS suggests this conversion: NGVD29 = NAVD88 – 3.6 ft (1.1 m), with an accuracy of (plus or minus) 0.5 ft. It means the NAVD plane is lower than NGVD. For example, if NGVD at a certain location is 1.0 m, the NAVD in that location would be 2.1 m. In coastal Washington State close to Canada border, NAVD plane is 1.23 m lower than NGVD. NGVD is approximately close to Mean Sea Level (MSL), but they are not exactly the same.
Hydrographic or Tidal Datum.
Tidal datums are based on the average of observations over a 19-year period – the so-called Metonic Cycle or NTDE (National Tidal Datum Epoch). This period is applied in defining: MSL (the arithmetic mean of hourly heights observed over the NTDE period); MLLW (Mean Lower Low Water; the arithmetic mean of the lower low water levels of the tide observed over the NTDE period); and MLW (Mean Low Water; the arithmetic mean of the low water heights observed over the NTDE period). The datum of Tide Tables and the bathymetric charts is MLLW on the West Coast (a mixed tidal regime). On the East Coast it is MLW (a semi-diurnal tidal regime). More in the NOAA Datum Definition. The MLW or MLLW are used to reduce and refer the measured depths and Tide Tables to Chart Datum.
In North America, the traditional horizontal or georeference system was based on NAD83 or WGS84. With the advances in instrumentation, particularly GPS, some limitations and errors of the system have become evident. GPS is a three-part system: satellites, ground stations, and receivers. The trio works by some georeferenced ground stations monitoring the satellites to determine their locations. A receiver uses the signals from the satellites to locate its position in the referred system. The new georeference system in North America is called ITRF or the International Terrestrial Reference Frame.
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3. Sea Level Rise and Consequences
How does Warming Climate going to affect coastal water level? Answer to this question is addressed in Sea Level Rise and Sea Level Rise Consequences. According to the 2021 IPCC - AR6, present rate of global mean sea level rise is 3.2 to 4.2 mm/year. In regional to global scales, the primary factors responsible for Sea level Rise (SLR) are attributable to: (1) melting of continental and polar ice masses; (2) reduction in ocean water density and resulting expansion; (3) ocean circulation responsible for distributing heat and dissolved substances; (4) isostatic rebound of the coastal landmass resulting from melting and regression of glaciers; (5) uplift or subsidence due to tectonic activity; (6) soft sediment consolidation and subsidence; and (6) ocean-atmosphere interaction.
SLR is a slow process from an engineering point of view – yet, all low-lying coastal lands, waterfront engineering interventions and structures are vulnerable to its influence and effects. The vulnerability becomes clear if we consider the highlighted Force-Fields – which are going to become more forceful both in terms of intensity and frequency. This means planning and design factors and methods including design Standards and Codes would require redefinition and re-visitation to examine their adequacy to withstand the enhanced forces. The associated increase of Risks has a far reaching implication in all areas of coastal activities including the low-lying lands subjected to heavy rainfall and drainage flows.
One reason is the depth-limited filtering of wave actions – for a certain depth only waves smaller than about 4/5th of water depth could pass on to the shore without breaking. Therefore, as the water level rises with SLR, the number of waves propagating on to the shore would increase.
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4. Water Level and Coastal Structure
WL associated factors of inundation, runup and overtopping (green and spray) – constitute some of the pressing issues in planning and designing of coastal structures (more in Flood Barrier Systems).
Still Water Level (SWL) together with the actions of a certain design wave – is used to design the top elevation of a coastal structure. Depending on location and importance, the raised WL caused by episodes of storm surge or tsunami is added to determine the Design Water Level (DWL). The determined top elevation is further fitted with a safety freeboard (the height of the structure above DWL) to minimize or eliminate the incidences of wave overtopping. Considering the structure type and installations - a Risk Analysis may be warranted to design final structure dimensions and risk implications.
Large vertical-face coastal structures – are required to be fitted with wave absorption measures to minimize wave-structure interactions, reflection and turbulence. Placing frontal stone ripraps is one of the methods to absorb incident wave energy as well as to prevent structure toe scour. Such structures are usually aligned in mild outer bends to avoid inviting concentration of wave energy or wave focusing. More on coastal structures are in Civil Engineering on Our Seashore.
Further in: USACE EM 110-2-1100 (Part VI series); USACE EM 1110-2-1415; USACE EM 1110-2-1913; Storm Surge Analysis and Design Water Level Determinations, USACE EM 1110-2-1412; USACE, Hurricane and Storm Damage Risk Reduction System Design Guidelines; and the 2008 TUDelft (VSSD) Breakwater and Closure Dams (2nd ed).
In Breakwater engineering – the vertical height of the structure is designed differently according to WL and wave loading considerations. According to CIRIA (1991): Zone I – the bottom foundational zone below the level of Mean Low Water (MLW); the Zone II – the tidal zone from MLW to the Mean High Water (MHW), loading on this zone is very frequent and determines the longterm structural stability; the Zone III – the higher high water zone from MHW to the design level, wave attack on this zone is less frequent but of high impact; and the top Zone IV subjected to the effects of runup and overtopping.
As in Wave Structure Interactions & Scour, Overtopping discharge rate is directly proportional to the incident wave height and period, but inversely to the freeboard. To give an idea: for a 1 m high freeboard, 2 to 1 sloped structure – a 1-m high wave with periods of 6-s and 15-s would have an overtopping discharge of 0.10 and 0.82 m^2/s per meter width of the crest, respectively. If the freeboard is lowered to 0.5 m, the same waves will cause overtopping of 0.26 and 1.25 m^2/s/m.
In maritime port engineering – the determination of an appropriate COPE gets attention. Cope refers to top edge level of a quay or jetty adjacent to a berth. To understand the methods of determining Cope, one can consult: JW Gaythwaite 2004, Design of Marine Facilities for the Berthing, Mooring, and Repair of Vessels, ASCE Press, 2nd ed.; CA Thoresen 2003 Port designer’s handbook, Thomas Telford; and Y Goda 2000, Random Seas and Design of Maritime Structures, World Scientific.
The optimum level of a cope can be selected by determining the risk of flooding together with an economic analysis. A low cope may be appropriate at berths exclusively used by small crafts. At cargo berths within an impounded dock the ground surface should be at least 1.5 m above the working water level. For berthing in open water harbor or exposed location, a statistical analysis can best be prepared to determine the level of the frequency of high water levels and wave heights.
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This is the 82nd essay in WIDECANVAS – and is dedicated to a healthy ocean and coastal water – vital for our collective prosperity and sustaining a balance between Nature and a neat social cohabitation. It is in everyone’s interest that global awareness prevails – for a harmonious sensible management, in harnessing coastal and ocean resources – and in engineering interventions. It is a belated post to honor the World Oceans Day – the June 8th of each year.
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The Koans of this piece:
In a un-interrupted Natural world of interdependence and harmonious plays of the Fluid, Solid and Life Systems – how can anyone miss seeing the balancing acts of the rise and fall of wave dynamics in everything.
Why wasting energy and resources to identify oneself and things as Conservative or non-Conservative through the media-articulated divisive lenses – how about something different – something that can be termed as being Realist, Simple, Right, Beneficial and Inclusive.

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- by Dr. Dilip K. Barua, 4 October 2024

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