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Tidal range
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Tidal range is the difference in height between high tide and low tide. Tides are the rise and fall of sea levels caused by gravitational forces exerted by the Moon and Sun, by Earth's rotation and by centrifugal force caused by Earth's progression around the Earth-Moon barycenter. Tidal range depends on time and location.
Larger tidal range occur during spring tides (spring range), when the gravitational forces of both the Moon and Sun are aligned (at syzygy), reinforcing each other in the same direction (new moon) or in opposite directions (full moon). The largest annual tidal range can be expected around the time of the equinox if it coincides with a spring tide. Spring tides occur at the second and fourth (last) quarters of the lunar phases.
By contrast, during neap tides, when the Moon and Sun's gravitational force vectors act in quadrature (making a right angle to the Earth's orbit), the difference between high and low tides (neap range) is smallest. Neap tides occur at the first and third quarters of the lunar phases.
Tidal data for coastal areas is published by national hydrographic offices.[1] The data is based on astronomical phenomena and is predictable. Sustained storm-force winds blowing from one direction combined with low barometric pressure can increase the tidal range, particularly in narrow bays. Such weather-related effects on the tide can cause ranges in excess of predicted values and can cause localized flooding. These weather-related effects are not calculable in advance.
Mean tidal range is calculated as the difference between mean high water (i.e., the average high tide level) and mean low water (the average low tide level).[2]
Geography
[edit]
The typical tidal range in the open ocean is about 1 metre (3 feet) – mapped in blue and green at right. Mean ranges near coasts vary from near zero to 11.7 metres (38.4 feet),[4] with the range depending on the volume of water adjacent to the coast, and the geography of the basin the water sits in. Larger bodies of water have higher ranges, and the geography can act as a funnel amplifying or dispersing the tide.[5]
The world's largest mean tidal range of 11.7 metres (38.4 feet) occurs in the Bay of Fundy, Canada (more specifically, at Burntcoat Head, Nova Scotia).[4][6] The next highest, of 9.75 metres (32.0 feet), is at Ungava Bay, also in Canada,[4][7] and the next, of 9.60 metres (31.5 feet), in the Bristol Channel, between England and Wales.[4] The highest predicted extreme (not mean) range is 17.0 metres (55.8 feet), in the Bay of Fundy.[7] The maximum range in the Bristol Channel is 15 metres (49 feet).[8] The fifty coastal locations with the largest ranges worldwide are listed by the National Oceanic and Atmospheric Administration of the United States.[4]
Some of the smallest tidal ranges occur in the Mediterranean, Baltic, and Caribbean Seas. A point within a tidal system where the tidal range is almost zero is called an amphidromic point.
Classification
[edit]The tidal range has been classified[9] as:
- Micro-tidal – when the tidal range is lower than 2 metres (6'6¾").
- Meso-tidal – when the tidal range is between 2 metres and 4 metres (6'6¾" and 13'1½").
- Macro-tidal – when the tidal range is higher than 4 metres (13'1½").
See also
[edit]- King tide, an informal term for an especially high spring tide
References
[edit]- ^ "Hydrographic and Oceanographic Agencies". Archived from the original on 2010-03-25. Retrieved 2010-01-17.
- ^ NOAA. "Tidal Datums". Retrieved 26 Mar 2019.
- ^ Picture credit: R. Ray, TOPEX/Poseidon: Revealing Hidden Tidal Energy GSFC, NASA. Redistribute with credit to R. Ray, as well as NASA-GSFC, NASA-JPL, Scientific Visualization Studio, and Television Production NASA-TV/GSFC
- ^ a b c d e NOAA. "FAQ Where are the highest tides?". Retrieved 20 Aug 2021.
- ^ NOAA. "It appears that the range of the tides gets larger the further the location from the equator. What causes this??". Retrieved 23 Oct 2020.
- ^ NOAA. "The highest tide in the world is in Canada". Retrieved 23 Oct 2020.
- ^ a b Charles T. O'Reilly, Ron Solvason, and Christian Solomon. "Resolving the world's largest tides", in J.A. Percy, A.J. Evans, P.G. Wells, and S.J. Rolston (Editors) 2005: The Changing Bay of Fundy: Beyond 400 years. Proceedings of the 6th Bay of Fundy Workshop, Cornwallis, Nova Scotia. Sackville, NB.
- ^ "Tidal range". SurgeWatch. University of Southampton / National Oceanography Centre / British Oceanography Data Centre.
- ^ Masselink, G.; Short, A. D. (1993). "The effect of tidal range on beach morphodynamics and morphology: a conceptual beach model". Journal of Coastal Research. 9 (3): 785–800. ISSN 0749-0208.
Tidal range
View on Grokipediafrom Grokipedia
The tidal range is the vertical difference in height between the high tide and the low tide at a specific coastal location, typically measured over a tidal cycle.[1] This phenomenon results from the gravitational interactions between the Earth, Moon, and Sun, which cause periodic rises and falls in sea level, with the Moon's influence being dominant due to its proximity. Tidal ranges can vary significantly, from less than 1 meter in some open ocean areas to over 16 meters in extreme cases, and are classified based on tidal patterns such as semidiurnal (two high and two low tides daily with roughly equal ranges), diurnal (one high and one low tide daily), or mixed.[2]
Tidal ranges are influenced by both astronomical and geographical factors. Astronomically, ranges increase during spring tides—when the Sun, Moon, and Earth align (at new or full moon)—producing greater gravitational pull, and decrease during neap tides when the Sun and Moon are at right angles, resulting in smaller ranges.[3] Additionally, the Moon's elliptical orbit causes higher ranges at perigee (closest approach) and lower at apogee, while Earth's orbital position relative to the Sun amplifies this during perihelion.[3] Geographically, coastal topography plays a crucial role: funnel-shaped bays amplify ranges through resonance, as seen in the Bay of Fundy between Canada’s New Brunswick and Nova Scotia, where the world's highest recorded tidal range reaches up to 16 meters (53 feet) due to the basin's shape, depth, and a 12-hour oscillation period matching the tidal cycle.[4] Other factors include shoreline configuration, estuary shapes, river outflows, wind patterns, and atmospheric pressure, which can modify local ranges by several meters during storms.[5] In contrast, the Pacific Ocean's vast size leads to generally smaller ranges compared to the Atlantic.[6]
The tidal range holds significant implications for coastal environments, human activities, and renewable energy. It shapes intertidal ecosystems by determining the extent of submersion and exposure, influencing biodiversity in zones like salt marshes and mudflats where species adapt to varying inundation periods.[7] For navigation, precise knowledge of tidal ranges is essential to avoid grounding in shallow waters or to time port operations, as variations affect water depths and currents.[8] In engineering, large ranges inform the design of harbors, bridges, and flood defenses, while in energy production, they enable tidal range technologies like barrages to harness the potential energy of water flow, with sites like the Bay of Fundy offering substantial hydroelectric potential equivalent to billions of cubic meters of water movement daily.[9] Overall, understanding tidal ranges is vital for mitigating coastal hazards, sustainable development, and climate adaptation amid rising sea levels.
Fundamentals
Definition
The tidal range refers to the vertical difference in sea level between consecutive high and low tides at a specific coastal location.[1] This metric captures the amplitude of the tidal oscillation over a single tidal cycle, typically spanning about 12 to 24 hours depending on the local tidal pattern.[10] Tidal range is commonly measured in meters or feet using tide gauges, which record continuous water level variations relative to a fixed benchmark on land.[10] In modern applications, satellite altimetry supplements these observations by providing global data on sea surface heights, from which tidal ranges can be derived through harmonic analysis.[11] The mean tidal range, a standardized value, is calculated as the difference between mean high water (the average of all high water heights over a 19-year epoch) and mean low water (the average of all low water heights over the same period).[12] Within the broader tidal cycle, the range connects high and low water levels, forming the basis for reference datums like mean high water and mean low water, which serve as benchmarks for nautical charting and coastal engineering.[12] These datums account for long-term averages to mitigate short-term variations, such as those during spring tides (larger ranges) or neap tides (smaller ranges).[3] The concept of tidal range emerged in 19th-century oceanography through systematic tide gauge observations, where researchers tabulated differences between high and low water heights to quantify tidal behavior.[13] This approach, pioneered in coastal monitoring efforts across Europe and North America, laid the foundation for modern tidal analysis.[14]Physical Causes
The tidal range, which measures the vertical difference between high and low tides, arises primarily from the gravitational attractions exerted by the Moon and the Sun on Earth's oceans. The Moon's gravitational pull is the dominant force due to its proximity to Earth, despite the Sun's much greater mass; the Moon is about 390 times closer to Earth than the Sun is, resulting in a tidal force approximately twice as strong as the Sun's, as tidal effects scale inversely with the cube of the distance between bodies.[15] These gravitational forces create a two-bulge system in Earth's oceans: one bulge forms on the side facing the Moon due to direct gravitational attraction pulling water toward it, while the second bulge appears on the opposite side because the centrifugal force from the Earth-Moon orbital motion exceeds the Moon's gravitational pull there, causing water to lag behind. Earth's rotation beneath these relatively stationary bulges (aligned with the Moon) produces the observed semidiurnal tidal cycle, with locations experiencing high tide twice daily as they pass through each bulge.[16] In the equilibrium tide theory, the shape of these ocean bulges is determined by the tidal potential, which describes the gravitational perturbation from the Moon (or Sun). The basic form of this potential at a point on or near Earth's surface is given by where is the gravitational constant, is the mass of the Moon (or Sun), is the distance from Earth's center to the Moon's (or Sun's) center, is the distance from Earth's center to the point (approximately Earth's radius), is the angle between the position vectors to the point and the Moon, and is the second-degree Legendre polynomial capturing the quadrupolar deformation. The equilibrium ocean surface aligns with equipotential surfaces of this potential plus Earth's own gravity, yielding theoretical tide heights of about 0.5 meters for the Moon alone.[17] The tidal range varies due to changes in the Moon's declination (its angular position relative to Earth's equator) and orbital alignments with the Sun. During new and full moons, when the Moon and Sun are aligned with Earth, their gravitational forces constructively interfere, producing spring tides with greater ranges; conversely, at quarter moons, the forces partially cancel, resulting in neap tides with smaller ranges. Declination effects further modulate this: maximum lunar declination (up to 28.5°) tilts the bulges away from the equator, reducing ranges at low latitudes and enhancing them at higher ones, while perigee (Moon's closest approach) amplifies forces by up to 20% compared to apogee.[18][3] Beyond equilibrium theory, dynamic effects in the oceans modify the tidal range through wave propagation and interactions with the seafloor. In shallow waters, where depth is much less than the tidal wavelength, friction and reduced wave speed (, with as depth) cause tidal energy to concentrate, amplifying amplitudes via shoaling—similar to how waves grow taller approaching a beach—and potentially exciting resonances in basins, leading to ranges several times the equilibrium value. These shallow-water distortions also generate higher harmonics (overtides) that further alter the tidal waveform.[19]Tidal Patterns and Classification
Types of Tidal Cycles
Tidal cycles refer to the periodic patterns of high and low tides over daily and monthly timescales, primarily driven by the gravitational forces from the Moon and Sun acting on Earth's oceans. These cycles determine the frequency and variability of tidal ranges experienced in coastal areas. The main types are classified based on the number of tides and their relative amplitudes within a lunar day, which lasts about 24 hours and 50 minutes.[2] Semidiurnal tides occur twice daily, featuring two high tides and two low tides of approximately equal heights each lunar day. This pattern results from the dominance of semidiurnal tidal constituents, such as the principal lunar semidiurnal tide (M2), which aligns with the Moon's orbital period.[2][20] Diurnal tides, in contrast, produce one high tide and one low tide per lunar day. They are characterized by the prevalence of diurnal tidal components, like the principal lunar diurnal tide (O1) and the principal solar diurnal tide (K1), which have periods close to 24 hours.[2][20] Mixed tides combine elements of both, typically manifesting as two unequal high tides and two unequal low tides per lunar day, with one high tide significantly higher than the other and one low tide notably lower. This mixed semidiurnal pattern arises when both semidiurnal and diurnal components are comparably strong, leading to irregular inequalities in tide heights.[2][21] The distribution of these daily tidal cycle types is influenced by factors such as basin geometry and latitude, with diurnal tides tending to dominate near the equator due to the equatorial alignment of diurnal forcing mechanisms.[22][21] Over monthly cycles, tidal ranges fluctuate due to changing alignments of the Sun, Moon, and Earth. Spring tides happen around the times of full moon and new moon, when the Sun and Moon's gravitational pulls reinforce each other, producing the greatest tidal range.[20][23] Neap tides occur during the first and third quarter moons, when the Sun and Moon are at right angles to each other, causing their tidal effects to partially counteract and resulting in the smallest tidal range. These monthly variations stem from the relative phases of the principal lunar semidiurnal (M2) and principal solar semidiurnal (S2) tidal constituents.[20][23]Range-Based Classification
The range-based classification of tidal regimes, primarily focused on the amplitude of the mean spring tidal range, provides a framework for understanding coastal dynamics and morphology. Introduced by J.L. Davies in 1964, this system categorizes shorelines into three principal classes: microtidal (less than 2 meters), mesotidal (2 to 4 meters), and macrotidal (greater than 4 meters).[24] These thresholds reflect the dominant role of tidal energy in shaping coastal features, with lower ranges indicating limited tidal influence on sediment movement and higher ranges promoting extensive intertidal zones and stronger currents.[25] Microtidal conditions, with ranges below 2 meters, are characteristic of open ocean coastlines and enclosed seas, where frictional dissipation reduces tidal amplitude, leading to wave-dominated morphologies.[26] Mesotidal ranges of 2 to 4 meters occur along moderate coastlines, balancing tidal and wave processes to form mixed sedimentary environments.[27] Macrotidal regimes, exceeding 4 meters, are prevalent in funnel-shaped estuaries, where basin geometry amplifies tides, resulting in tide-dominated landscapes with pronounced ebb and flood channels.[28] Subsequent refinements by Miles O. Hayes in 1979 incorporated wave-tide interactions, expanding Davies' model into a hydrodynamic classification that considers both mean spring tidal range and annual significant wave height to delineate tide-dominated, wave-dominated, and mixed-energy coasts.[25] This approach highlights how relative energy partitioning affects barrier island formation and inlet stability, with implications for erosion patterns and habitat distribution. For extreme cases, hypertidal regimes with ranges over 6 meters—often amplified to exceed 9 meters in resonant bays—represent specialized subsets of macrotidal systems, fostering unique ecological and geomorphic features due to intense tidal currents.[29] This amplitude-focused classification applies across tidal cycle types, such as semidiurnal patterns, where the range defines the vertical excursion between successive high and low waters.[26]Geographical Distribution
Global Variations
Tidal ranges exhibit significant latitudinal variations, with generally smaller amplitudes near the equator and larger ones at higher latitudes, primarily due to the interplay of the Coriolis force and continental basin geometries that channel tidal energy more effectively poleward.[30] The Coriolis parameter, which increases with latitude, deflects tidal waves, causing them to rotate around amphidromic points and concentrate energy in mid- to high-latitude coastal regions where landmasses like Eurasia and North America form resonant pathways.[31] This latitudinal gradient arises because equatorial regions experience minimal deflection, leading to more uniform dissipation of tidal energy across vast open oceans, whereas higher latitudes benefit from constructive interference in semi-enclosed basins.[32] Amphidromic systems further contribute to global variations by creating nodes of zero tidal amplitude at central points within ocean basins, from which tidal ranges radiate outward in concentric patterns.[33] These systems form due to the Earth's rotation, with co-tidal lines emanating from the amphidromic point and co-range lines forming irregular circles where amplitude increases with distance from the node, often reaching maxima at basin edges.[34] In the Northern Hemisphere, rotation occurs counterclockwise around these points, enhancing range gradients in regions like the North Atlantic, while Southern Hemisphere systems rotate clockwise, influencing Pacific and Indian Ocean margins differently.[31] Continental shelves and coastal convergence amplify tidal ranges through shallow-water effects and geometric funneling, particularly for semi-diurnal tides.[35] As tidal waves propagate onto shelves, decreasing water depth slows the wave speed, causing crests to bunch up and increase amplitude, with amplification factors up to 60% from shelf break to coast in some systems.[36] Convergence in narrowing coastal geometries further enhances this, as tidal energy is conserved while the wavefront narrows, leading to heightened ranges in shelf seas compared to adjacent deep oceans.[31] Ocean basin resonance plays a key role in spatial variations, where tidal periods align with natural oscillation modes of the basin, amplifying ranges in responsive geometries.[37] For instance, the North Sea acts as a quarter-wave resonator for the semi-diurnal M2 tide, with its length approximating one-quarter of the tidal wavelength, resulting in pronounced amplification toward the southern and eastern coasts.[38] Global tide models such as TPXO illustrate these patterns, revealing average tidal ranges of 1-2 m across much of the Pacific Ocean, contrasted with higher values often exceeding 2 m in the Atlantic and its approaches, reflecting basin-scale differences in resonance and shelf interactions.[39][9]Notable Examples
The Bay of Fundy in Canada exhibits one of the world's largest tidal ranges, reaching up to 16 meters at its head, primarily due to resonant amplification within its funnel-shaped basin that concentrates incoming tidal waves.[4][9] These extreme tides have been documented in historical records dating back to early European explorations in the 17th century, with systematic measurements confirming the range's consistency over time.[40] In the United Kingdom, the Severn Estuary experiences a maximum tidal range of approximately 15 meters during spring tides, driven by the narrowing channel that funnels Atlantic waters and generates a prominent tidal bore—a standing wave that propagates upstream.[41][42] This site represents a classic macrotidal environment, second only to certain North American bays in global scale.[43] The Gulf of California features predominantly diurnal tidal cycles, with ranges up to 10-12 meters in its northern reaches during spring tides, influenced by the region's mixed tidal regime and coastal topography that enhances local variations.[2][44] Conversely, the Mediterranean Sea exemplifies minimal tidal ranges, typically less than 1 meter and averaging around 0.4 meters, owing to its semi-enclosed nature and limited open-ocean fetch that dampens incoming tidal energy.[45][9] Ungava Bay, Canada, is a contender for having one of the world's highest tidal ranges, with historical records from 1953 indicating up to 16.6 meters at Leaf Basin and recent analyses (post-2020) suggesting around 16.3 meters, due to resonant effects in Hudson Strait. As of 2025, this places it in dispute with the Bay of Fundy for the global record, with ongoing efforts to verify and recognize the measurements.[46][47][48][49]Influences and Applications
Environmental and Coastal Impacts
The extent of the intertidal zone, which spans the area between high and low tide marks, is directly proportional to the tidal range, creating broader habitats in areas with larger ranges that support diverse assemblages of flora and fauna. In mesotidal regions (tidal ranges of 2–4 m), such as parts of the U.S. East Coast, extensive salt marshes develop within these zones, where vegetation like Spartina alterniflora stabilizes sediments and fosters high biodiversity through stratified plant communities adapted to varying inundation levels.[50] Greater tidal ranges enhance marsh stability by expanding the elevational window for vegetation growth, allowing for richer microbial, invertebrate, and bird populations that thrive in the dynamic wetting-drying cycles.[50] This zonation promotes ecological resilience, with lower intertidal areas hosting algae and mobile crustaceans, while upper zones support desiccation-tolerant species like barnacles and periwinkles. In macrotidal environments (tidal ranges exceeding 4 m), such as those along the coasts of northern Europe and eastern Canada, intense erosion and deposition processes dominate, resulting in highly dynamic shorelines and expansive mudflats that reshape rapidly over tidal cycles. During flood tides in extremely shallow waters (depths <0.2 m), elevated bed shear stress—up to twice that of deeper stages—drives significant erosion, mobilizing fine sediments and preventing permanent stabilization.[51] Conversely, ebb tides favor net accretion as reduced shear allows suspended particles to settle, forming thick mudflat layers that serve as foraging grounds for shorebirds and support microbial mats essential for nutrient cycling.[51] These alternating forces contribute to migratory shorelines, where mudflats can advance or retreat by meters per tide, influencing long-term coastal morphology without human intervention.[52] Tidal range-induced salinity fluctuations profoundly shape ecosystems in mangroves and estuaries, creating sharp gradients that dictate habitat zonation and species distribution. In estuarine mangroves, such as those in the Gulf of Mexico, larger tidal ranges amplify incursions of saline seawater into freshwater-dominated areas, causing daily salinity swings of 10–30 ppt that favor salt-tolerant species like Rhizophora mangle in seaward zones and less tolerant Avicennia germinans inland.[53] These variations promote vertical stratification, with propagules sorting by density in response to salinity density gradients, leading to distinct bands of mangrove forest that enhance overall habitat diversity for fish nurseries and epibenthic invertebrates.[54] In broader estuarine settings, such zonation supports food webs by providing refugia during low-salinity floods and saline stress periods. Climate change exacerbates these impacts through sea-level rise, which can modify tidal ranges by altering coastal bathymetry and increasing inundation frequencies in intertidal habitats. According to IPCC AR6 assessments, global mean sea-level rise is projected to reach 0.28–0.55 m by 2100 under low-emission scenarios (SSP1-1.9) and 0.63–1.01 m under high-emission scenarios (SSP5-8.5), relative to 1995–2014 levels, potentially compressing intertidal zones and shifting salinity regimes in marshes and mangroves.[55] This rise could amplify erosion in macrotidal areas and submerge low-elevation salt marshes, reducing their extent by 20–50% in vulnerable regions without compensatory sediment supply.[55] High tidal ranges also create biodiversity hotspots by concentrating nutrients and prey through intense mixing, as exemplified in the Bay of Fundy, where ranges up to 16 m sustain over 2,000 species including the endemic mud piddock clam (Barnea truncata) and critical habitats for endangered North Atlantic right whales.[56] The fundy's tidal fronts aggregate plankton, supporting unique benthic communities like horse mussel reefs and sponge fields, which harbor species such as the giant Melananchora elliptica sponge, underscoring the role of extreme ranges in fostering exceptional ecological productivity.[56]Human Uses and Engineering
Tidal ranges have been exploited for power generation through barrages that impound water during high tides and release it through turbines to produce electricity, particularly in sites with mean spring tidal ranges exceeding 5 meters. The La Rance Tidal Power Station in Brittany, France, operational since November 1966 and managed by Électricité de France (EDF), represents the pioneering example of this technology, featuring 24 reversible bulb turbines with a total installed capacity of 240 MW.[57] This facility has demonstrated long-term reliability, generating approximately 500 GWh annually by harnessing a tidal range of approximately 8 meters.[58] In macrotidal environments, where tidal ranges surpass 4 meters, navigation and port infrastructure face significant challenges from fluctuating water depths and sediment transport, often requiring regular dredging to maintain safe channels. For example, in the Severn Estuary with its extreme 12-15 meter spring tides, ports such as Avonmouth undergo frequent dredging to combat siltation from tidal currents, ensuring accessibility for large vessels despite the natural scouring that keeps the main channel deep.[59] Lock systems further mitigate these issues by isolating vessels from rapid tidal changes, enabling controlled transit between tidal estuaries and inland waterways, as seen in various European ports adapting to high-range conditions.[60] Large tidal ranges exacerbate flood risks during storm surges, prompting engineered defenses to protect coastal populations and infrastructure. The Thames Barrier in London, completed in 1982, serves as a critical example, closing to block tidal surges amplified by the estuary's 7-meter-plus spring tidal range, having prevented over 200 flooding events to date.[61] Such structures use hydraulic gates to hold back water levels up to 10.2 meters above mean sea level, combining predictive modeling with mechanical reliability to safeguard urban areas.[62] Tidal flats in mesotidal zones, characterized by ranges of 2-4 meters, offer productive habitats for aquaculture and fishing, particularly shellfish cultivation that benefits from periodic exposure and submersion. These intertidal areas facilitate oyster and clam farming by providing nutrient-rich sediments and natural filtration, as exemplified in Puget Sound where shellfish operations on mudflats and eelgrass beds yield significant commercial harvests.[63] Traditional fishing also thrives here, with low tides exposing flats for hand-gathering or raking of bivalves, supporting local economies in regions like the U.S. Pacific Northwest.[64] Contemporary engineering advancements leverage tidal ranges through stream generators that capture kinetic energy from currents without full barrages, enabling deployment in moderate-to-high range sites. Devices like Orbital Marine Power's O2 turbine, a 2 MW floating system installed at Scotland's MeyGen array since 2021, operate in areas with strong tidal currents associated with tidal ranges of several meters to produce reliable baseload power with minimal environmental footprint. As of November 2025, Orbital Marine Power is expanding to sites like Nova Scotia's Bay of Fundy with O2-X turbines.[65][66] Accurate tidal predictions, essential for these and other applications, employ harmonic analysis models that resolve observed water levels into constituent sinusoids for forecasting, as standardized by NOAA protocols using least-squares fitting of up to 37 components.[67]References
- https://www.coastalwiki.org/wiki/Coriolis_and_tidal_motion_in_shelf_seas
- https://www.coastalwiki.org/wiki/Ocean_and_shelf_tides