Harmonic Analysis of Water Level - Revision history

127.0.0.1: The LinkTitles extension automatically added links to existing pages (https://github.com/bovender/LinkTitles).

2022-10-21T09:25:35Z

The LinkTitles extension automatically added links to existing pages (<a target="_blank" rel="nofollow noreferrer noopener" class="external free" href="https://github.com/bovender/LinkTitles">https://github.com/bovender/LinkTitles</a>).

← Older revision		Revision as of 09:25, 21 October 2022
Line 3:		Line 3:
	* General Information		* General Information
	* Main Constituents of Tides		* Main Constituents of Tides
	* Shallow Water Constituents of Tides		* [[Shallow water\|Shallow Water]] Constituents of Tides
	* Tidal Harmonic Analysis		* Tidal Harmonic Analysis
	* Fortnightly (Phase) Inequality		* Fortnightly (Phase) Inequality
Line 13:		Line 13:
	==General Information==		==General Information==

	The tide is caused by the attraction of the Sun and the Moon on the oceans, and the rotation of the Earth. The precise pattern at any particular spot along the coast depends strongly on the shape of the coastline and on the profile of the seafloor nearby. Furthermore, in shallow seas, bays and estuaries co-oscillating tides and resonance contribute to a large amount to the final shape of the tides. The tides at any specific location are essentially impossible to calculate theoretically even though the generating gravitational forces are very precisely known.		The tide is caused by the [[attraction]] of the Sun and the Moon on the oceans, and the rotation of the Earth. The precise pattern at any particular spot along the coast depends strongly on the shape of the coastline and on the profile of the seafloor nearby. Furthermore, in shallow seas, bays and estuaries co-oscillating tides and resonance contribute to a large amount to the final shape of the tides. The tides at any specific location are essentially impossible to calculate theoretically even though the generating gravitational forces are very precisely known.

	[[File: Bombay.png]]		[[File: Bombay.png]]
Line 41:		Line 41:
	[[File:Tides_animation.png\|thumb\|Freezed frame from the animation ''Entstehung der Gezeiten'' (in German), see accompanying link next to ''Animation''.]]		[[File:Tides_animation.png\|thumb\|Freezed frame from the animation ''Entstehung der Gezeiten'' (in German), see accompanying link next to ''Animation''.]]

	Gravitational as well as centrifugal forces cause tidal forces on Earth. Some significant causes as well as phenomena are explained in the following animation as well as on the poster:		Gravitational as well as centrifugal forces cause tidal forces on Earth. Some significant causes as well as phenomena are explained in the following [[ANIMATION\|animation]] as well as on the poster:
	* animation [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/tides/tides.mp4 ''Entstehung der Gezeiten''] (in German, 325 MB, MP4 file format), and		* [[ANIMATION\|animation]] [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/tides/tides.mp4 ''Entstehung der Gezeiten''] (in German, 325 MB, MP4 file format), and
	* poster [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/tides/tides.pdf ''Gezeiten - Entstehung und Phänomene''] (in German, 18 MB, PDF file format).		* poster [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/tides/tides.pdf ''Gezeiten - Entstehung und Phänomene''] (in German, 18 MB, PDF file format).
	You can find more of BAWs videos on [https://av.getinfo.de/ AV-Portal TIB] in Hannover (search there for BAW). All videos are marked using a ''Digital Object Identifier'' (DOI). Therefore videos can be as easily cited as common text publications. DOI for this video is [http://dx.doi.org/10.5446/15182 http://dx.doi.org/10.5446/15182].		You can find more of BAWs videos on [https://av.getinfo.de/ AV-Portal TIB] in Hannover (search there for BAW). All videos are marked using a ''Digital Object Identifier'' (DOI). Therefore videos can be as easily cited as common text publications. DOI for this video is [http://dx.doi.org/10.5446/15182 http://dx.doi.org/10.5446/15182].
Line 48:		Line 48:
	==Main Constituents of Tides==		==Main Constituents of Tides==

	Any main constituent of the tides is written using a capital letter and an index number which is appended to it. Index numbers 1 and 2 make it easy to distinguish between diurnal and semidiurnal tides. For example the [[#Short Tide Glossary\|M2-tide]] is the principal semidiurnal lunar constituent. Low frequencies are marked in a different way (e.g. f, mf, sa).		Any main constituent of the tides is written using a capital letter and an [[index]] number which is appended to it. [[Index]] numbers 1 and 2 make it easy to distinguish between diurnal and semidiurnal tides. For example the [[#Short Tide Glossary\|M2-tide]] is the principal semidiurnal lunar constituent. Low frequencies are marked in a different way (e.g. f, mf, sa).

	{\| border="1" cellpadding="2" cellspacing="0"		{\| border="1" cellpadding="2" cellspacing="0"
Line 109:		Line 109:
	==Shallow Water Constituents of Tides==		==Shallow Water Constituents of Tides==

	Besides the astronomically dominated main constituents in shallow marginal or coastal seas additional frequencies do occur. The shallow water constituents are also called compound tides and overtides. They are mainly a results of the nonlinear dynamic processes which are present in the physics governing the motion of water, namely		Besides the astronomically dominated main constituents in shallow marginal or coastal seas additional frequencies do occur. The [[shallow water]] constituents are also called compound tides and overtides. They are mainly a results of the nonlinear dynamic processes which are present in the physics governing the motion of water, namely

	# dependence of the celerity of a tidal wave on the actual water depth;		# dependence of the celerity of a tidal wave on the actual [[water depth]];
	# nonlinear bottom friction;		# nonlinear bottom friction;
	# advection of momentum.		# advection of momentum.
Line 120:		Line 120:

	[http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/pdf/river-de.pdf Graphical representation] of the influence of river flow on dissipation (with German text only). This graphical representation is also available in [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/eps/river-de1.eps Encapsulated PostScript format].		[http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/pdf/river-de.pdf Graphical representation] of the influence of river flow on dissipation (with German text only). This graphical representation is also available in [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/eps/river-de1.eps Encapsulated PostScript format].
	The shallow water constituents are described using a combination of numbers and letters which are indicating the composition (linear combination of one or more main constituents) and frequency of the constituent.		The [[shallow water]] constituents are described using a combination of numbers and letters which are indicating the composition (linear combination of one or more main constituents) and frequency of the constituent.

	The following table gives an overview over the most significant shallow water constituents of tides and their composition (e.g. compund tides like MSN2 or overtides like M4 and S4).		The following table gives an [[overview]] over the most significant [[shallow water]] constituents of tides and their composition (e.g. compund tides like MSN2 or overtides like M4 and S4).

	{\| border="1" cellpadding="2" cellspacing="0"		{\| border="1" cellpadding="2" cellspacing="0"
	! colspan="3"\|table with selected shallow water constituents of tides		! colspan="3"\|table with selected [[shallow water]] constituents of tides
	\|-		\|-
	!Abbreviation		!Abbreviation
Line 199:		Line 199:

	For any spot along the coast or in the open sea only the periods or frequencies of the constituents of the tides are known. Amplitude as well as phase are not known a priori. Measured tidal records as well as results from numerical siumulations can be used to determine amplitude and phase. This procedure is called Tidal Harmonic Analysis. Normally long tidal records are needed to determine amplitude and phase for a larger number of constituents with high accuracy.		For any spot along the coast or in the open sea only the periods or frequencies of the constituents of the tides are known. Amplitude as well as phase are not known a priori. Measured tidal records as well as results from numerical siumulations can be used to determine amplitude and phase. This procedure is called Tidal Harmonic Analysis. Normally long tidal records are needed to determine amplitude and phase for a larger number of constituents with high accuracy.
	If we know amplitudes und phase of the tidal constituents at a specific location we can perform a forecast of sea level with a Tidal Harmonic Synthesis, a summation of all known constituents.		If we know amplitudes und phase of the tidal constituents at a specific location we can perform a [[forecast]] of sea level with a Tidal Harmonic Synthesis, a summation of all known constituents.

	[[File: Kelvin.png]]		[[File: Kelvin.png]]
Line 215:		Line 215:

	==Diurnal Inequality==		==Diurnal Inequality==
	The difference in height of the two high waters or of the two low waters of each tidal day is called diurnal inequality; also, the difference in speed between the two flood tidal currents or the two ebb currents of each tidal day. The difference changes with the declination of the Moon and, to a lesser extent, with the declination of the Sun. In general, the inequality tends to increase with increasing declination, either north or south, and to diminish as the Moon approaches the Equator.		The difference in height of the two high [[waters]] or of the two low [[waters]] of each tidal day is called diurnal inequality; also, the difference in speed between the two [[flood]] tidal currents or the two ebb currents of each tidal day. The difference changes with the declination of the Moon and, to a lesser extent, with the declination of the Sun. In general, the inequality tends to increase with increasing declination, either north or south, and to diminish as the Moon approaches the Equator.

	The amplitudes of the constituents M2, S2, K1 and O1 can be used to calculate the form ratio F = (K1 + O1)/(M2 + S2) which leads to the following subdivisions:		The amplitudes of the constituents M2, S2, K1 and O1 can be used to calculate the form ratio F = (K1 + O1)/(M2 + S2) which leads to the following subdivisions:
Line 228:		Line 228:
	The calculation and graphic display of amplitude and phase for a reasonable number of tidal constituents contributes to a large amount for an improved understanding of the tide induced dynamic processes in coastal seas and estuaries.		The calculation and graphic display of amplitude and phase for a reasonable number of tidal constituents contributes to a large amount for an improved understanding of the tide induced dynamic processes in coastal seas and estuaries.

	*A comparison between tide records and numerically calculated results (see also [[Mathematical Models for Coastal Areas and Estuaries\|mathematical models]]) can be made based on amplitudes and phases derived by means of a tidal harmonic analysis for a reasonable number of tidal constituents. This is a nice instrument in the verification process of a numerical model for a specific area. Deviations in amplitude and phase can be precisely quantified.		*A comparison between tide records and numerically calculated results (see also [[Mathematical Models for Coastal Areas and Estuaries\|mathematical models]]) can be made based on amplitudes and phases derived by means of a tidal harmonic analysis for a reasonable number of tidal constituents. This is a nice instrument in the verification process of a numerical [[model]] for a specific area. Deviations in amplitude and phase can be precisely quantified.
	*Spatial variations of the tidal spectrum within an area of investigation are caused by topographic effects, nonlinear physical processes, resonance and reflexion. The interpretation of the spatial variations can be used to identify single processes and may contribute to an improved understanding of the natural system.		*Spatial variations of the tidal spectrum within an area of investigation are caused by topographic effects, nonlinear physical processes, resonance and reflexion. The interpretation of the spatial variations can be used to identify single processes and may contribute to an improved understanding of the natural system.
	*Changes in relative phase and amplitude ratio between two constituents (e.g. between the M2-constituent and the corresponding overtides M4, M6 and M8) can be related to the asymmetry of the tide. Very often residual processes of water-, salt- and sediment-transport are closely linked to hydrodynamic asymmetries. Relationships between transport and hydrodynamic processes can be claryfied.		*Changes in relative phase and amplitude ratio between two constituents (e.g. between the M2-constituent and the corresponding overtides M4, M6 and M8) can be related to the asymmetry of the tide. Very often residual processes of water-, salt- and sediment-transport are closely linked to hydrodynamic asymmetries. Relationships between transport and hydrodynamic processes can be claryfied.
Line 236:		Line 236:
	[http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/pdf/m60_10-de.pdf Graphical representation] of superposition of M2 and M6 tide (with German text only). This graphical representation is also available in [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/eps/m60_10-de1.eps Encapsulated PostScript format].		[http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/pdf/m60_10-de.pdf Graphical representation] of superposition of M2 and M6 tide (with German text only). This graphical representation is also available in [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/eps/m60_10-de1.eps Encapsulated PostScript format].

	[http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/pdf/double-de.pdf Graphical representation] of superposition of M2 and M4 or M6 tide in situations where double high- or low-waters occur (with German text only). This graphical representation is also available in [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/eps/double-de1.eps Encapsulated PostScript format].		[http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/pdf/double-de.pdf Graphical representation] of superposition of M2 and M4 or M6 tide in situations where double high- or low-[[waters]] occur (with German text only). This graphical representation is also available in [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/eps/double-de1.eps Encapsulated PostScript format].

	'''An automatic tidal harmonic analysis for the above shown constituents is carried through by the computer programs [[FRQWF]] and [[NCANALYSE]]. A tidal harmonic synthesis at single stations is done by the computer program [[FRQ2ZEITR]].'''		'''An automatic tidal harmonic analysis for the above shown constituents is carried through by the computer programs [[FRQWF]] and [[NCANALYSE]]. A tidal harmonic synthesis at single stations is done by the computer program [[FRQ2ZEITR]].'''

Ak3glang: skewness result variables added

2021-03-11T13:00:17Z

skewness result variables added

← Older revision		Revision as of 13:00, 11 March 2021
Line 276:		Line 276:
	''No example figures available yet''. <br />		''No example figures available yet''. <br />
	Analysis program: [[NCANALYSE]].		Analysis program: [[NCANALYSE]].
			===Skewness===
			Skewness (sum over all contributions of tidal constituents) according to [https://www.researchgate.net/publication/256682174_The_contribution_to_tidal_asymmetry_by_different_combinations_of_tidal_constituents Song (2011), Eq. 16] from amplitude, phase and frequency of tidal constituents.<br />
			<!-- [[Example figures: Difference of phase for various tidal constituents]]. <br /> -->
			''No example figures available yet''. <br />
			Analysis program: [[NCANALYSE]].
			===Skewness for pairs and triplets===
			Skewness for all pairs and triplets of suitable tidal constituents according to [https://www.researchgate.net/publication/256682174_The_contribution_to_tidal_asymmetry_by_different_combinations_of_tidal_constituents Song (2011), Eq. 20 and Eq. 21] from amplitude, phase and frequency of contributing tidal constituents.<br />
			<!-- [[Example figures: Difference of phase for various tidal constituents]]. <br /> -->
			''No example figures available yet''. <br />
			Analysis program: [[NCANALYSE]].
	==Short Tide Glossary==		==Short Tide Glossary==

imported>Lang Guenther: category "tidal constituents" added

2016-08-10T09:22:28Z

category "tidal constituents" added

← Older revision		Revision as of 09:22, 10 August 2016
Line 1:		Line 1:
	[[de: Harmonische Analyse des Wasserstands]]		[[de: Harmonische Analyse des Wasserstands]]
			[[Category:Tidal Constituents]]
	* General Information		* General Information
	* Main Constituents of Tides		* Main Constituents of Tides

imported>Lang Guenther: /* Motivation to Perform a Tidal Harmonic Analysis */ section on computational results added

2016-07-28T07:04:20Z

Motivation to Perform a Tidal Harmonic Analysis: section on computational results added

← Older revision		Revision as of 07:04, 28 July 2016
Line 238:		Line 238:

	'''An automatic tidal harmonic analysis for the above shown constituents is carried through by the computer programs [[FRQWF]] and [[NCANALYSE]]. A tidal harmonic synthesis at single stations is done by the computer program [[FRQ2ZEITR]].'''		'''An automatic tidal harmonic analysis for the above shown constituents is carried through by the computer programs [[FRQWF]] and [[NCANALYSE]]. A tidal harmonic synthesis at single stations is done by the computer program [[FRQ2ZEITR]].'''

			==Computational results of a tidal harmonic analysis==
			The ''Least Square Fit Method'' (LSQF) is used to perform a tidal harmonic analysis.
			Within programs [[FRQWF]] and [[NCANALYSE]] different routines of the software package
			[http://www.netlib.org/lapack/ LAPACK] are used for this purpose.

			For any tidal constituent the following quantities are computed.
			===Amplitude===
			Amplitude of a tidal constituent.<br />
			<!-- [[Example figures: Amplitude of various tidal constituents]]. <br /> -->
			''No example figures available yet''. <br />
			Analysis programs: [[FRQWF]] and [[NCANALYSE]].
			===Phase===
			Phase of a tidal constituent.<br />
			<!-- [[Example figures: Phase of various tidal constituents]]. <br /> -->
			''No example figures available yet''. <br />
			Analysis programs: [[FRQWF]] and [[NCANALYSE]].
			===Amplitude error===
			Error with respect to amplitude of a tidal constituent computed using the LSQF method.<br />
			<!-- [[Example figures: Error with respect to amplitude for various tidal constituents]]. <br /> -->
			''No example figures available yet''. <br />
			Analysis program: [[NCANALYSE]].
			===Phase error===
			Error with respect to phase of a tidal constituent computed using the LSQF method.<br />
			<!-- [[Example figures: Error with respect to phase for various tidal constituents]]. <br /> -->
			''No example figures available yet''. <br />
			Analysis program: [[NCANALYSE]].
			===Amplification of amplitude===
			Amplification of amplitude of a tidal constituent with respect to the amplitude computed at a reference location.<br />
			<!-- [[Example figures: Amplification of amplitude for various tidal constituents]]. <br /> -->
			''No example figures available yet''. <br />
			Analysis program: [[NCANALYSE]].
			===Phase difference===
			Difference of phase of a tidal constituent with respect to the phase computed at a reference location.<br />
			<!-- [[Example figures: Difference of phase for various tidal constituents]]. <br /> -->
			''No example figures available yet''. <br />
			Analysis program: [[NCANALYSE]].

	==Short Tide Glossary==		==Short Tide Glossary==

imported>Lang Guenther: /* Motivation to Perform a Tidal Harmonic Analysis */ program NCANALYSE added

2016-07-28T06:22:32Z

Motivation to Perform a Tidal Harmonic Analysis: program NCANALYSE added

← Older revision		Revision as of 06:22, 28 July 2016
Line 237:		Line 237:
	[http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/pdf/double-de.pdf Graphical representation] of superposition of M2 and M4 or M6 tide in situations where double high- or low-waters occur (with German text only). This graphical representation is also available in [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/eps/double-de1.eps Encapsulated PostScript format].		[http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/pdf/double-de.pdf Graphical representation] of superposition of M2 and M4 or M6 tide in situations where double high- or low-waters occur (with German text only). This graphical representation is also available in [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/pre_postpr/eps/double-de1.eps Encapsulated PostScript format].

	'''An automatic tidal harmonic analysis for the above shown constituents is carried through by the computer ~~program~~ [[FRQWF]]. ~~This program also analyses single time series of water level.'''<br />~~		'''An automatic tidal harmonic analysis for the above shown constituents is carried through by the computer programs [[FRQWF]] and [[NCANALYSE]]. A tidal harmonic synthesis at single stations is done by the computer program [[FRQ2ZEITR]].'''
	~~'''~~A tidal harmonic synthesis at single stations is done by the computer program [[FRQ2ZEITR]].'''

	==Short Tide Glossary==		==Short Tide Glossary==

imported>Lang Guenther: /* Generation of tides */ remark about DOI

2015-04-15T22:07:44Z

Generation of tides: remark about DOI

← Older revision		Revision as of 22:07, 15 April 2015
Line 43:		Line 43:
	* animation [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/tides/tides.mp4 ''Entstehung der Gezeiten''] (in German, 325 MB, MP4 file format), and		* animation [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/tides/tides.mp4 ''Entstehung der Gezeiten''] (in German, 325 MB, MP4 file format), and
	* poster [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/tides/tides.pdf ''Gezeiten - Entstehung und Phänomene''] (in German, 18 MB, PDF file format).		* poster [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/tides/tides.pdf ''Gezeiten - Entstehung und Phänomene''] (in German, 18 MB, PDF file format).
			You can find more of BAWs videos on [https://av.getinfo.de/ AV-Portal TIB] in Hannover (search there for BAW). All videos are marked using a ''Digital Object Identifier'' (DOI). Therefore videos can be as easily cited as common text publications. DOI for this video is [http://dx.doi.org/10.5446/15182 http://dx.doi.org/10.5446/15182].

	==Main Constituents of Tides==		==Main Constituents of Tides==

imported>Lang Guenther: freezed frame added in section "generation of tides"

2014-08-25T06:38:10Z

freezed frame added in section "generation of tides"

← Older revision		Revision as of 06:38, 25 August 2014
Line 37:		Line 37:

	==Generation of tides==		==Generation of tides==

			[[File:Tides_animation.png\|thumb\|Freezed frame from the animation ''Entstehung der Gezeiten'' (in German), see accompanying link next to ''Animation''.]]

	Gravitational as well as centrifugal forces cause tidal forces on Earth. Some significant causes as well as phenomena are explained in the following animation as well as on the poster:		Gravitational as well as centrifugal forces cause tidal forces on Earth. Some significant causes as well as phenomena are explained in the following animation as well as on the poster:

imported>Lang Guenther: section on "generation of tides" added

2014-08-22T11:15:05Z

section on "generation of tides" added

← Older revision		Revision as of 11:15, 22 August 2014
Line 35:		Line 35:

	An infinite number of harmonics and linear combinations of the fundamental frequencies can be observed in tidal signals. The Earths rotation causes a doubling of the frequencies which is related to the presence of two tidal bulges travelling around the world (a simplified view). Due to the large differences in the periods of the fundamental frequencies tides do contain usually also very close lying frequencies which are responsible for modulations of the range of the tides (e.g. the spring neap cycle).		An infinite number of harmonics and linear combinations of the fundamental frequencies can be observed in tidal signals. The Earths rotation causes a doubling of the frequencies which is related to the presence of two tidal bulges travelling around the world (a simplified view). Due to the large differences in the periods of the fundamental frequencies tides do contain usually also very close lying frequencies which are responsible for modulations of the range of the tides (e.g. the spring neap cycle).

			==Generation of tides==

			Gravitational as well as centrifugal forces cause tidal forces on Earth. Some significant causes as well as phenomena are explained in the following animation as well as on the poster:
			* animation [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/tides/tides.mp4 ''Entstehung der Gezeiten''] (in German, 325 MB, MP4 file format), and
			* poster [http://www.baw.de/downloads/wasserbau/mathematische_verfahren/tides/tides.pdf ''Gezeiten - Entstehung und Phänomene''] (in German, 18 MB, PDF file format).

	==Main Constituents of Tides==		==Main Constituents of Tides==

imported>Spohr Susanne at 10:57, 11 October 2010

2010-10-11T10:57:17Z

← Older revision		Revision as of 10:57, 11 October 2010
Line 1:		Line 1:
	[[de: Harmonische Analyse des Wasserstands]]		[[de: Harmonische Analyse des Wasserstands]]
	~~[[Category: Tidal Harmonic Analysis]]~~
	* General Information		* General Information
	* Main Constituents of Tides		* Main Constituents of Tides

imported>BAWiki 1 at 10:21, 15 June 2010

2010-06-15T10:21:27Z

← Older revision		Revision as of 10:21, 15 June 2010
Line 192:		Line 192:
	If we know amplitudes und phase of the tidal constituents at a specific location we can perform a forecast of sea level with a Tidal Harmonic Synthesis, a summation of all known constituents.		If we know amplitudes und phase of the tidal constituents at a specific location we can perform a forecast of sea level with a Tidal Harmonic Synthesis, a summation of all known constituents.

	[[:File:Kelvin.png\|The Tide Predicter was designed in 1873 by Kelvin]], based on a suggestion of Beauchamp Tower's for summing several trigonometric functions with independent periods. This machine was exhibited at the South Kensington Museum in 1876. It is designed to sum the M2, S2, N2, K1, O1, K2, L2, P1, M4 and MS4 constituents, in that order reading from the left.		[[File: Kelvin.png]]

			The Tide Predicter was designed in 1873 by Kelvin, based on a suggestion of Beauchamp Tower's for summing several trigonometric functions with independent periods. This machine was exhibited at the South Kensington Museum in 1876. It is designed to sum the M2, S2, N2, K1, O1, K2, L2, P1, M4 and MS4 constituents, in that order reading from the left.
	See also: KELVIN (= Sir William Thomson, Baron Kelvin), The tidal gauge, tidal harmonic analyser, and tide predicter, in Kelvin, Mathematical and Physical Papers (Volume VI), Cambridge 1911, pp 272-305. [From the Minutes of the Proceedings of the Institution of Civil Engineers, March 11, 1882.]		See also: KELVIN (= Sir William Thomson, Baron Kelvin), The tidal gauge, tidal harmonic analyser, and tide predicter, in Kelvin, Mathematical and Physical Papers (Volume VI), Cambridge 1911, pp 272-305. [From the Minutes of the Proceedings of the Institution of Civil Engineers, March 11, 1882.]