Harmonic constants

Harmonic constants

Harmonic constants are created by analysis of regular water level readings taken by automated tide stations like the one pictured here. A tide station whose predictions trace directly to harmonic constants that were derived from water level readings for that same station is called a reference station.

Corrections

A subordinate station is a tide station whose predictions are obtained by applying corrections to the predictions generated for a reference station, i.e., a station for which we have good harmonic constants. The words 'corrections,' 'differences,' and 'offsets' are used interchangeably.

While harmonic constants can be hard to get, you should be able to get offsets with relative ease from a local boating magazine, chartbook, yacht club, or marine authority.

There are many different flavors of offsets for subordinate stations. At this time, XTide supports all commonly appearing flavors except for the Admiralty one that has different height differences depending on the time of month. The following rare and freakish sorts are not supported: those that use different offsets depending on whether the flood at the reference station crossed some threshold; those that rely on more than one reference station; those that use different offsets for higher high or low water versus lower high or low water; currents that use a regular tide station as reference, or vice-versa.

Some putative sets of harmonic constants for subordinate stations were created by mangling the constants of a reference station to approximate the results of applying corrections. Such mangled data only junk up the database and should be avoided.

Adding subordinate stations using tideEditor

If you find suitable offsets, you can add them to harmonics.tcd using the tideEditor program available from http://www.flaterco.com/xtide/files.html#extras. There are two other ways to do it, as described below under "Importing batches of harmonic constants and offsets," but tideEditor is most expedient for the non-expert.

First, always make a backup copy of whatever you are about to modify.

TideEditor version 1.4 takes the name of the file to modify as the command-line argument.

bash-3.1$ tideEditor whatever.tcd

When you start tideEditor, you get a map of the world. Point at the location where you want to add a subordinate station and right click.

You will get a prompt asking "Will the new station be a reference station or a subordinate station?" Choose Subordinate.

You will get a prompt saying "Please select the new reference station." Use the pull-down list to select the reference station and click OK.

You will then get a window with the tabs General, Verbiage and Offsets, initially showing General. On the General tab, the Reference Station, Latitude and Longitude fields will be pre-filled based on your previous actions. If you don't know the correct latitude and longitude, just estimate the coordinates as best you can.

The other fields that you MUST fill in are as follows:

Station Name: Enter the name of the new subordinate station.

Time Zone: Use the pull-down to set the time zone (select the major city for the applicable region). The timezone attribute is only used to choose the time zone in which to render output for the location. In the majority of cases this will be the same as for the reference station.

Level Units: Select feet or meters for tides, knots for currents.

All other fields on the General and Verbiage tabs are optional. Descriptions of the other fields are obtainable using the question mark tool thingy).

The Offsets tab has the following fields.

Minimum Time Add. The time adjustment for low tide / max ebb. It is expressed as an integer that is hours times 100 plus minutes, so for 0:20 (negative 0 hours, 20 minutes) you would write 20, and for 1:40 (positive 1 hour, 40 minutes) you would write 140. If you don't have this, leave it blank.

Minimum Level Add. A value, in the units identified by Level Units, that is added to the tide level or current velocity predicted at low tide or max ebb. If you don't have this, leave it blank.

Minimum Level Multiply. A multiplier for the tide level or current velocity predicted at low tide or max ebb. If you don't have this, leave it blank.

Maximum Time Add, Level Add, and Level Multiply are analogous, but correspond to high tide / max flood.

Flood Begins. Another kind of "Time Add" used only by currents to adjust the time of the slack preceding a flood. If you don't have this, leave it blank. If it got initialized to zero, make it blank.

Ebb Begins. Analogous to Flood Begins.

Notations used to describe corrections will vary:

NotationTranslation

0:20Time Add 20

1 23Time Add 123

*1.07Level Multiply 1.07

+0.4Level Add 0.4

(*0.65+0.3)Level Multiply 0.65, Level Add 0.3

If you were not given separate corrections for max and min, set both the max and min values to whatever you got. For example, if you get

Head Harbor, Isle au Haut -0:20 (Portland)

then you should set both Minimum Tide Add and Maximum Time Add to 20.

Special cases:

If you don't get slack offsets (floodbegins, ebbbegins) for a current station, OMIT those fields! When slack offsets are omitted, XTide will interpolate a reasonable value. But if you specify zero, you get zeroeven if that's unreasonable with respect to the specified max and min.

If your reference station is in a different time zone, you may need to alter the time offsets to REMOVE compensation for the time zone difference. NOAA had a practice of including the time zone differential in the offsets, but in XTide, the offsets are independent of the time zone.

When finished, click OK. When you quit tideEditor, your new station will be saved in the updated TCD file.

Adding reference stations using tideEditor

To add a reference station with tideEditor, the general process is similar to adding a subordinate station, but the data to enter are more obscure and there are more opportunities for the non-expert to get stuck.

When you get the prompt asking "Will the new station be a reference station or a subordinate station?" choose Reference.

Instead of "Offsets," the third tab in the dialog is now "Constituents."

Datum Description. Choose Mean Lower Low Water or whatever is the description of the datum that you have received. If you don't know, you can proceed without setting it.

Datum Value. Enter the datum (sometimes known as Z0) in the level units that were specified on the first tab.

Meridian. This is a fixed offset from UTC to which the amplitudes of the harmonic constants were calibrated. Opportunity for trouble: You have to know the right answer for the data that you received. Sometimes it will be local standard time for the location; sometimes it will be zero. The format is hours times 100 plus minutes, with positive values being east of Greenwich and negative values west.

Amplitude and Epoch for many constituents. Scroll down to see all of the constituents that are supported by the harmonics file. Opportunity for trouble: Different countries sometimes use different names for the same constituents, or worse yet, use the same names for different constituents. XTide's naming scheme is just yet another one that had to deal with these ambiguities and conflicts. For the technical definitions of the constituents used in XTide's default harmonics files, refer to the Congen package.

Importing batches of harmonic constants and offsets

All pretense of user-friendliness stops here. If you want to do large numbers of stations without lots of manual data entry, you have two options, both of which require a higher level of computer literacy than is demanded by tideEditor.

1. The good way is to install Harmbase 2 and either write an import procedure for your data format or convert your data into one of the formats that it can already import. Harmbase 2 uses PostgreSQL to manage the data and merely exports to the TCD format.

2. The evil way is to convert your data into the legacy .txt and .xml file formats that XTide used in the bad old days and then use tcd-utils to convert that to TCD.

Deriving harmonic constants from water level data

Anyone with a Linux PC, enough determination to install Octave, enough skill to convert data from one format to another, and enough dataat least a year's worth of hourly water level measurementsshould be able to derive harmonic constants using the Harmgen package. Harmgen produces results in the form of an SQL insert statement that loads the new station into Harmbase 2 using XTide's constituent naming scheme. Those with sufficient background and a reason to do it can change the constituent set, but the new constituent definitions must be harmonized between Harmbase and Harmgen.

There is no added complication from multi-year time serieses. Harmgen accounts for the equilibrium arguments and node factors for each year and minimizes the error across the entire span of the time series.

Under the best of circumstances, predictions from harmonic constants derived this way can be expected to differ from authoritative predictions by 20 minutes or so. But if the authorities are using a nonharmonic method of tide predictionor if you messed upthe discrepancies could be worse. It is up to you to do quality assurance.

Details on the operation of Harmgen can be found in that package's README file.

List of web sites with traceable data

This list is probably neither complete nor current. These are just the data sources that have been brought to my attention. Links valid as of 2012-02-26.

Harmonic constants:

Italy: I had this link, but I can't find anything there now. Maybe here?

National Ocean Service: Some locations outside of U.S. jurisdiction have historically been included along with the U.S. data.

Norway (simplified harmonic constants only) [*]

Spain

Water level data:

Canada

Spain

U.K.

University of Hawai`i Sea Level Center (see also here or here)

* "Simplified" harmonic constants just omit all but the 6 or 7 most significant constituents, which limits the accuracy that can be achieved for predictions. If simplified harmonic constants are to be used, it is a good idea to enable constituent inference in XTide.

Current Constants: Tidal current relations that re-main practically constant for any particular locality. Current constants are classified as harmonic and non-harmonic. The harmonic constants consist of the am plitudes and epochs of the harmonic constituents, and the non-harmonic constants include the velocities and intervals derived directly from the current observations.

Harmonic Constants: The amplitudes and epochs of the harmonic constituents of the tide or tidal current at any place.Harmonic Analysis: The mathematical process by which the observed tide or tidal current at any place is separated into basic harmonic constituentsHarmonic Analyzer: A machine designed for the resolution of a periodic curve into its harmonic constituents. Now performed by electronic digital computerHarmonic Prediction: Method of predicting tides and tidal currents by combining the harmonic constituents into a single tide curve. The work is usually performed by electronic digital computerA harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency, i.e. if the fundamental frequency is f, the harmonics have frequencies 2f, 3f, 4f, . . . etc. The harmonics have the property that they are all periodic at the fundamental frequency, therefore the sum of harmonics is also periodic at that frequency. Harmonic frequencies are equally spaced by the width of the fundamental frequency and can be found by repeatedly adding that frequency. For example, if the fundamental frequency is 25 Hz, the frequencies of the harmonics are: 50 Hz, 75 Hz, 100 Hz etcEpoch: (1) Also known as phase lag. Angular retardation of the maximum of a constituent of the observed tide (or tidal current) behind the corresponding maximum of the same constituent of the theoretical equilibrium tide. It may also be defined as the phase difference between a tidal constituent and its equilibrium argument. As referred to the local equilibrium argument, its symbol is 6. When referred to the corresponding Greenwich equilibrium argument, it is called the Greenwich epoch and is represented by G. A Greenwich epoch that has been modified to adjust to a particular time meridian for convenience in the prediction of tides is represented by g or by 6N. The relations between these epochs may be expressed by the following formula: G = 6 + pl, g = 6N = G as / 15 in which L is the longitude of the place and S is the longitude of the time meridian, these being taken as positive for west longitude and negative for east longitude; p is the number of constituent periods in the constituent day and is equal to 0 for all long-period constituents, 1 for diurnal constituents, 2 for semidiurnal constituents, and so forth; and a is the hourly speed of the constituent, all angular measurements being expressed in degrees. (2) As used in tidal datum determination, it is a 19-year cycle over which tidal height observations are meaned in order to establish the various datums. As there are periodic and apparent secular trends in sea level, a specific 19-year cycle (the National Tidal Datum Epoch) is selected so that all tidal datum determinations throughout the United States, its territories, Commonwealth of Puerto Rico, and Trust Territory of the Pacific Islands, will have a common reference. See National Tidal Datum Epoch.National Tidal Datum Epoch: The specific l9-year period adopted by the National Ocean Service as the official time segment over which tide observations are taken and reduced to obtain mean values (e.g., mean lower low water, etc.) for tidal datums. It is necessary for standardization because of periodic and apparent secular trends in sea level. The present National Tidal Datum Epoch is 1960 through 1978. It is reviewed annually for possible revision and must be actively considered for revision every 25 years.

where Hn is an amplitiude in metres, gn is a phase lag on the Equilibrium Tide at Greenwich in degrees, n is an angular speed and t is time.

Except where indicated to the contrary, all harmonic constants listed are based on observations lasting for at least one month. All times of predictions calculated by DP560 are in the same Zone Time as the harmonic constants, Charges in Zone time are clearly annotated on the relevant pages. All predicted heights are given in meters above Charts Datum, which is taken as the datum of depths on the latest edition of the largest scale Admiralty Chart. In the British Isles, Chart Datum at all ports is approximately the level of Lowest Astronomical Tide (LAT). All metric charts of these waters are referred to this Datum. Predictions calculated by DP560 using the harmonic constants herein are valid for average meteorological conditions. It follows, therefore, that when such conditions are not average the actual tides may differ from those predicted. Under extreme conditions these differences can be very large. Users of this publication and of DP560 are asked to keep the United Kingdom Hydrographic Office informed of any inaccuracies noted and are invited to make suggestions for the improvement of the two publications. ISBN: 978-0-70--772-1309.

The World Geodetic System is a standard for use in cartography, geodesy, and navigation. It comprises a standard coordinate frame for the Earth, a standard spheroidal reference surface (the datum or reference ellipsoid) for raw altitude data, and a gravitational equipotential surface (the geoid) that defines the nominal sea level.

The latest revision is WGS 84 (dating from 1984 and last revised in 2004), which was valid up to about 2010.[1][citation needed] Earlier schemes included WGS 72, WGS 66, and WGS 60. WGS 84 is the reference coordinate system used by the Global Positioning System.

A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair (0,0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.

The coordinate origin of WGS 84 is meant to be located at the Earth's center of mass; the error is believed to be less than 2 cm.[2]The WGS 84 meridian of zero longitude is the IERS Reference Meridian,[3] 5.31 arc seconds or 102.5 metres (336.3 ft) east of the Greenwich meridian at the latitude of the Royal Observatory.[4][5]The WGS 84 datum surface is an oblate spheroid (ellipsoid) with major (transverse) radius a = 6378137 m at the equator and flattening f = 1/298.257223563.[6] The polar semi-minor (conjugate) radius b then equals a times (1f), or 6356752.3142 m.[6]Presently WGS 84 uses the EGM96 (Earth Gravitational Model 1996) geoid, revised in 2004. This geoid defines the nominal sea level surface by means of a spherical harmonics series of degree 360 (which provides about 100 km horizontal resolution).[7] The deviations of the EGM96 geoid from the WGS 84 reference ellipsoid range from about 105 m to about +85 m.[8] EGM96 differs from the original WGS 84 geoid, referred to as EGM84.

The Unified WGS Solution, as stated above, was a solution for geodetic positions and associated parameters of the gravitational field based on an optimum combination of available data. The WGS 72 ellipsoid parameters, datum shifts and other associated constants were derived separately. For the unified solution, a normal equation matrix was formed based on each of the mentioned data sets. Then, the individual normal equation matrices were combined and the resultant matrix solved to obtain the positions and the parameters.

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Crossing the Demerara River via the Demerara Harbour Bridge

The Demerara River is a river in eastern Guyana that rises in the central rainforests of the country and flows to the north for 346 kilometres until it reaches the Atlantic Ocean. Georgetown, Guyana's largest seaport and capital, is situated on the east bank of the river's mouth. The Demerara's estuary is narrow and the flowrate is rapid. This scouring action maintains a 5-6 metre deep direct channel to the ocean. The river's deep brown color is primarily the result of the massive quantities of silt carried from upriver by the powerful currents. So powerful are these currents, that the ocean retains the Demerara's brown color for a considerable distance out to sea.

The Demerara's width and depth allow oceangoing vessels to navigate up to Linden (105 km from the mouth), while smaller vessels may reach up to Malali (245 km from the mouth). Beyond Malali, numerous rapids make further upstream travel impossible.

A floating bridge, the Demerara Harbour Bridge, crosses the river 4 miles south of Georgetown from Peter's Hall, East Bank Demerara to Schoon Ord, West Bank Demerara.

Tributaries of the Demerara River include the Haiama River, Kuruabaru River, Haiakwa Creek and Haianari Creek.

The islands Inver, Borselem, and Biesen are found 15 to 20 miles from the mouth. Borselem was once the location of the Dutch capital of Demerara.

A Dutch colony of the same name (see Demerara) was situated along the river's banks. The colony founded the sugarcane industry that continues to thrive today. Sugar from this industry is used to make the widely exported El Dorado Rum [1]. Bauxite is also mined around the Demerara, and Linden is a major export centre