Harmonic Analysis of Current Velocity - Revision history

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

2022-10-21T10:21:24Z

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← Older revision		Revision as of 10:21, 21 October 2022
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	=Motivation=		=Motivation=

	For almost any location within an estuary the current velocity can be decomposed into a periodic part driven by the tides (astronomical and shallow water tides) as well as a non-periodic part driven by river runoff, meteorological effects as well as local topographic features.		For almost any location within an [[estuary]] the current velocity can be decomposed into a periodic part driven by the tides (astronomical and [[shallow water]] tides) as well as a non-periodic part driven by river [[runoff]], meteorological effects as well as local topographic features.

	[[File:Tidal_current_ellipse_definition.png\|200px\|thumb\|right\|defintion of tidal ellipse]]		[[File:Tidal_current_ellipse_definition.png\|200px\|thumb\|right\|defintion of tidal ellipse]]
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	==Residual Current Velocity (Vres)==		==Residual Current Velocity (Vres)==

	Residual current velocity (computed from tidal constituent analysis) within the period of data analysis.		Residual current velocity (computed from tidal constituent analysis) within the [[period of data analysis]].
	This quantity describes the non-tidal (or non-periodc) contribution. It mainly depends on river flow,		This quantity describes the non-tidal (or non-periodc) contribution. It mainly depends on river flow,
	meteorology and local topographic details, but is also dependent to some extent on the number of tidal		meteorology and local topographic details, but is also dependent to some extent on the number of tidal
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	==Flow Duration Asymmetry (Skewness FDA)==		==Flow Duration Asymmetry (Skewness FDA)==

	This parameter describes differences in the flow velocities around flood slack compared to those around ebb slack. Positive values indicate smaller velocities around flood slack. Please notice that a residual current is neglected in the formulas used.		This parameter describes differences in the flow velocities around [[flood]] slack compared to those around ebb slack. Positive values indicate smaller velocities around [[flood]] slack. Please notice that a residual current is neglected in the formulas used.

	===Skewness FDA===		===Skewness FDA===
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	==Flow Velocity Asymmetry (Skewness FVA)==		==Flow Velocity Asymmetry (Skewness FVA)==

	This parameter describes differences between maximum flood current and ebb current velocities. Positive values indicate larger flood current velocities. Please notice that a residual current is taken into account in the formulas used.		This parameter describes differences between maximum [[flood]] current and ebb current velocities. Positive values indicate larger [[flood]] current velocities. Please notice that a residual current is taken into account in the formulas used.

	===Skewness FVA===		===Skewness FVA===

Ak3glang: description for skewness FDA and skewness FVA added

2021-04-20T15:12:19Z

description for skewness FDA and skewness FVA added

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 Phase (in dgree) of minimum current velocity for a tidal constituent. Restricted range -180 to 180 degree.
 <!-- [[Example figure: Phase of maximum current velocity]]. <br /> -->
 ----

Ak3glang: range for phase of max. and min. velocity modified

2021-02-11T16:42:52Z

range for phase of max. and min. velocity modified

← Older revision		Revision as of 16:42, 11 February 2021
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	===Phase of maximum Current Velocity===		===Phase of maximum Current Velocity===

	Phase (in dgree) of maximum current velocity for a tidal constituent. Restricted range 0 to 180 degree.		Phase (in dgree) of maximum current velocity for a tidal constituent. Restricted range -180 to 180 degree.
	<!-- [[Example figure: Phase of maximum current velocity]]. <br /> -->		<!-- [[Example figure: Phase of maximum current velocity]]. <br /> -->

	===Phase of minimum Current Velocity===		===Phase of minimum Current Velocity===

	Phase (in dgree) of minimum current velocity for a tidal constituent. Restricted range 0 to 180 degree.		Phase (in dgree) of minimum current velocity for a tidal constituent. Restricted range -180 to 180 degree.
	<!-- [[Example figure: Phase of maximum current velocity]]. <br /> -->		<!-- [[Example figure: Phase of maximum current velocity]]. <br /> -->

Ak3glang: description for phase of maximum|minimum current velocity added

2021-02-11T12:37:11Z

description for phase of maximum|minimum current velocity added

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 * -1.0 : circular current velocity in mathematical negative direction (clockwise).
 <!-- [[Example figure: Eccentricity of tidal constituent velocity ellipse]]. <br /> -->
 ----

Ak3spohr: replaced Tidal_current_ellipse_definition.gif by Tidal_current_ellipse_definition.png

2019-12-16T14:39:35Z

replaced Tidal_current_ellipse_definition.gif by Tidal_current_ellipse_definition.png

← Older revision		Revision as of 14:39, 16 December 2019
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	For almost any location within an estuary the current velocity can be decomposed into a periodic part driven by the tides (astronomical and shallow water tides) as well as a non-periodic part driven by river runoff, meteorological effects as well as local topographic features.		For almost any location within an estuary the current velocity can be decomposed into a periodic part driven by the tides (astronomical and shallow water tides) as well as a non-periodic part driven by river runoff, meteorological effects as well as local topographic features.

	[[File:Tidal_current_ellipse_definition.~~gif~~\|200px\|thumb\|right\|defintion of tidal ellipse]]		[[File:Tidal_current_ellipse_definition.png\|200px\|thumb\|right\|defintion of tidal ellipse]]
	For each tidal constituent the tip of the current velocity vector describes an ellipse, the tidal ellipse (see accompanying figure). Within each period of the respective tidal constituent a full rotation is executed. Characteristic parameters for a tidal ellipse are semi major axis, semi minor axis, inclination of tidal ellipse as well as its eccentricity. In dependence on eccentricity the ellipse degenerates either to a circle (eccentricity +1.0 or -1.0) or a straight line (eccentricity 0.0). The beforementioned parameters are well suited to describe the tidal influence on current velocity.		For each tidal constituent the tip of the current velocity vector describes an ellipse, the tidal ellipse (see accompanying figure). Within each period of the respective tidal constituent a full rotation is executed. Characteristic parameters for a tidal ellipse are semi major axis, semi minor axis, inclination of tidal ellipse as well as its eccentricity. In dependence on eccentricity the ellipse degenerates either to a circle (eccentricity +1.0 or -1.0) or a straight line (eccentricity 0.0). The beforementioned parameters are well suited to describe the tidal influence on current velocity.

Ak3spohr: replaced File by Media in link to document Zihang.pdf

2019-12-16T14:11:21Z

replaced File by Media in link to document Zihang.pdf

← Older revision		Revision as of 14:11, 16 December 2019
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	Basic informations on ''Tidal Harmonic Analysis'' are presented in [[Harmonic Analysis of Water Level]].		Basic informations on ''Tidal Harmonic Analysis'' are presented in [[Harmonic Analysis of Water Level]].
	The methods used to compute various ellipse parameters using program [[NCANALYSE]] are described in more detail in publication		The methods used to compute various ellipse parameters using program [[NCANALYSE]] are described in more detail in publication
	~~<!--~~ [[~~File~~:zhigang_xu_2000_ellipse_parameters_conversion.pdf]] ~~-->~~.		[[Media:zhigang_xu_2000_ellipse_parameters_conversion.pdf\|zhigang_xu_2000_ellipse_parameters_conversion.pdf]].

	The computational procedure is as follows (number of equation with reference to Zhigang Xu (2000) given in brackets):		The computational procedure is as follows (number of equation with reference to Zhigang Xu (2000) given in brackets):

Ak3glang: File zhigang_xu_2000_ellipse_parameters_conversion.pdf commented

2019-12-16T12:16:41Z

File zhigang_xu_2000_ellipse_parameters_conversion.pdf commented

← Older revision		Revision as of 12:16, 16 December 2019
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	Basic informations on ''Tidal Harmonic Analysis'' are presented in [[Harmonic Analysis of Water Level]].		Basic informations on ''Tidal Harmonic Analysis'' are presented in [[Harmonic Analysis of Water Level]].
	The methods used to compute various ellipse parameters using program [[NCANALYSE]] are described in more detail in publication		The methods used to compute various ellipse parameters using program [[NCANALYSE]] are described in more detail in publication
	[[File:zhigang_xu_2000_ellipse_parameters_conversion.pdf]].		<!-- [[File:zhigang_xu_2000_ellipse_parameters_conversion.pdf]] -->.

	The computational procedure is as follows (number of equation with reference to Zhigang Xu (2000) given in brackets):		The computational procedure is as follows (number of equation with reference to Zhigang Xu (2000) given in brackets):

imported>Lang Guenther: text for characteristic parameters introduced

2016-08-12T09:25:23Z

text for characteristic parameters introduced

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 =Basic Concepts=
-Basic informations on  ''Tidal Harmonic Analysis'' are presented in [[Harmonic Analysis of Water Level]]. The methods used to compute various ellipse parameters using program [[NCANALYSE]] are described in more detail in publication [[File:zhigang_xu_2000_ellipse_parameters_conversion.pdf]].
+Basic informations on  ''Tidal Harmonic Analysis'' are presented in [[Harmonic Analysis of Water Level]].
 =Definition of Characteristic Numbers=
-====Residual Tidal Constituent Velocity (Vres)====
+The Least Square Fit Method (LSQF) is used to compute amplitude and phase for the u- and v-component of current velocity.
-Residual value of current velocity (computed from harmonic analysis) within the period of data analysis.<br />
+For this purpose program [[NCANALYSE]] makes use of methods available within the software package LAPACK.
-The residual is computed for permanently wet locations only.<br />
-<!-- [[Example figures: residual current velocity (computed from harmonic analysis)]]. <br /> -->
+All quantities are computed for permanently wet areas only.
-==Amplitude of Tidal Constituent Velocity==
+Semi minor axis of a tidal constituent. Gives minimum current velocity within one period for the tidal constituent.
-==Phase of Tidal Constituent Velocity==
+===Inclination (direction) of Major Axis===
-==Error in Amplitude of Tidal Constituent Velocity==
+Gives the (mathematically positive) direction (-180.0 to 180.0 degree) of the semi major axis for a tidal constituent velocity.
-==Error in Phase of Tidal Constituent Velocity==
+===Inclination (direction) of Minor Axis===
-==Semi Major Axis of Tidal Constituent Ellipse==
+Gives the (mathematically positive) direction (-180.0 to 180.0 degree) of the semi minor axis for a tidal constituent velocity.
-==Semi Minor Axis of Tidal Constituent Ellipse==
+===Eccentricity of Tidal Ellipse===
-==Eccentricity of Tidal Constituent Ellipse==
+Eccentricity is defined as the ratio between semi minor and semi major axis of a tidal ellipse. Special cases are:
 ----

imported>Lang Guenther: /* Motivation */ text added

2016-08-10T14:15:37Z

Motivation: text added

← Older revision		Revision as of 14:15, 10 August 2016
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	=Motivation=		=Motivation=

			For almost any location within an estuary the current velocity can be decomposed into a periodic part driven by the tides (astronomical and shallow water tides) as well as a non-periodic part driven by river runoff, meteorological effects as well as local topographic features.

			[[File:Tidal_current_ellipse_definition.gif\|200px\|thumb\|right\|defintion of tidal ellipse]]
			For each tidal constituent the tip of the current velocity vector describes an ellipse, the tidal ellipse (see accompanying figure). Within each period of the respective tidal constituent a full rotation is executed. Characteristic parameters for a tidal ellipse are semi major axis, semi minor axis, inclination of tidal ellipse as well as its eccentricity. In dependence on eccentricity the ellipse degenerates either to a circle (eccentricity +1.0 or -1.0) or a straight line (eccentricity 0.0). The beforementioned parameters are well suited to describe the tidal influence on current velocity.

	=Basic Concepts=		=Basic Concepts=

imported>Lang Guenther: first text version, incomplete

2016-08-10T13:24:22Z

first text version, incomplete

New page

[[de:Harmonische Analyse der Strömung]]
[[Category:Tidal Constituents]]

=Motivation=

=Basic Concepts=

Basic informations on ''Tidal Harmonic Analysis'' are presented in [[Harmonic Analysis of Water Level]]. The methods used to compute various ellipse parameters using program [[NCANALYSE]] are described in more detail in publication [[File:zhigang_xu_2000_ellipse_parameters_conversion.pdf]].

=Definition of Characteristic Numbers=

====Residual Tidal Constituent Velocity (Vres)====
Residual value of current velocity (computed from harmonic analysis) within the period of data analysis.<br />
The residual is computed for permanently wet locations only.<br />


==Amplitude of Tidal Constituent Velocity==

==Phase of Tidal Constituent Velocity==

==Error in Amplitude of Tidal Constituent Velocity==

==Error in Phase of Tidal Constituent Velocity==

==Semi Major Axis of Tidal Constituent Ellipse==

==Semi Minor Axis of Tidal Constituent Ellipse==

==Eccentricity of Tidal Constituent Ellipse==

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back to [[Analysis of Calculated Results]]
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[[Overview]]