Tidal Harmonics Boundary
    • 21 Sep 2022
    • 6 Minutes to read
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    Tidal Harmonics Boundary

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    Article summary

    A tidal boundary is a head-time boundary which can be used as an alternative to a Head Time Boundary unit, by using numerical methods based upon the Admiralty Tide Tables and the Constituent Harmonics of the tide for a given location and date.

    Data

    Field in Data Entry Form

    Description

    Name in Datafile

    Boundary Unit Label

    Node label at boundary

    Label

    Override date with event time

    Tick to use date/time from event file

    tidbdy_dates

    Hour

    start hour of the tidal predictions in decimal on the 24 hour clock

    hour

    Day/Month

    start date of the tidal predictions as day and month (eg for 21 July enter 2107)

    idat

    Year

    start year of the tidal predictions (eg 1995)

    iy

    Mean Sea Level

    Mean Sea Level for the location, including the Seasonal Correction taken from Admiralty Tide Tables, vol II. (mAD)

    x0

    Harmonic Code

    Constituent name

    ifharm

    Amplitude

    Amplitude of Constituent (m)

    amp

    Phase Lag Constant

    Phase lag constant (°)

    phase

    Include Surge

    Tick if required

     

    Start Time

    Surge start time (hours from start of run) of ith surgeSstart(i)

    Duration

    ith Surge duration (hours)Sdur(i)

    Amplitude

    ith Surge amplitude (m)Samp(i)

    Cosine Power

    ith Surge cosine power (dimensionless)Spower(i)

    Year

    Year from which the jth rate of rose occursYrise(j)

    MSL rise

    Rate of rise of mean sea level (mm/yr [in/yr, US])Rrise(j)

    Theory and Guidance

    The Tidal Harmonics Boundary calculates the tide levels at a specified time and location from a set of up to 28 tidal constituents derived from the Admiralty Tide Tables (time zone referenced by Greenwich Mean Time (GMT)). The calculations are based on the Admiralty method of Tidal Prediction which uses the harmonic constants and table of tide angles and factors documented in the Admiralty Tide Tables.

    In many estuaries, tidal properties can be an important factor to both the hydrodynamics and the water quality. A representation of the tides is therefore required if an understanding of the system is to be gained. A tidal wave can be represented mathematically by a combination of sinusoidal curves of varying phase and amplitude, namely the tidal constituents.

    A tidal boundary is a head-time boundary which can either be generated by analyzing field data and entering the data as a Head Time Boundary, or by using numerical methods based upon the Admiralty Tide Tables and the Constituent Harmonics of the tide for a given location and date.

    From version 4.0 onwards, it is possible to specify a varying mean sea level rate rise, to enable long term simulations to take into account sea level rise scenarios.

    The time at which the tidal boundary is effective from may be specified in the Tidal Boundary (TIDBDY) unit itself, although it is preferable to set this in the event file by using real ("Absolute") times in the run forms interface. An option is available in the TIDBDY form ("Override date with event time") to toggle this option. If checked, the date/time is obtained from the event file. The recommendation to use event times is made so that the TIDBDY unit will not need changing if the simulation date/time changes.

    When loading a data file into the Flood Modeller interface which contains a Tidal Boundary with the date/time set in the TIDBDY form, a warning dialogue box appears suggesting that the user uses an event date/time instead. There is also an option on this dialogue box to switch this warning off. The first such TIDBDY unit in the data file is highlighted, although it is then left to the user to change the field if desired.

    RiverNodesimagesTidalBdyMsg.jpg

    Note: If "Event Times" are chosen, but no Absolute times are set in the event file, the times used will revert to those specified in the TIDBDY unit by default.

    The Tidal Boundary unit is also compatible with the steady-state runs, although will use a single value, corresponding to the tide level at the real time equivalent to the time of simulation.

    Equations

    The total tide-raising force may be expressed as the sum of a number of cosine curves of different amplitude and frequency. The amplitude and phase of the contributory factors to tidal motion are known as tidal constituents, the principal of which are called M2 and S2 , relating to synodic tides of the Moon and Sun respectively; the subscript 2 indicates that they are both semi-diurnal constituents.

    The contribution of every tidal constituent may be expressed as:

    h = fA.cos((E + u) - g)

    (1)

    where:

    h = the height relative to mean sea level.

    f = the mean amplitude modification factor due to the variation of the Moon's and/or Sun's orbit.

    A = the mean amplitude

    E = the tidal-raising force calculated for any time on the Greenwich meridian.

    u = the increase in phase due to the variation of the Moon's and/or Sun's orbit.

    g = the phase lag constant.

    The quantities A and g form the tidal constants for a particular location. The tidal level at any particular time and location is given by the sum of the above expression derived for each tidal constituent.

    Table of Major Harmonic Constituents

    Semi-diurnal Constituents

    Name

    Description

    Hourly Speed (°)

    Flood Modeller Unit Code

    M2

    Principal lunar constituent

    28.98

    M2

    S2

    Principal solar constituent

    30.00

    S2

    N2

    Allow for the changes in the Moon's distance due to its elliptic orbit round the Earth

    28.44

    N2

    L2

    L2

     

    K2

    Allow for the effect of the declination of the Sun and Moon and of changes in the Sun's distance

    30.08

    K2

    T2

    T2

     

    Diurnal Constituents

    Name

    Description

    Hourly Speed (°)

    Flood Modeller Unit Code

    K1

    Allow for the effect of the Moon's declination

    15.04

    K1

    O1

    O1

     

    K1

    Allow for the effect of the Sun's declination

     

     

    P1

    P1

     

    Q1

    Allow for the effect of changes in the Moon's distance on K1 and O1

    13.40

    Q1

    M1

    M1

     

    J1

    J1

     

    Quarter-diurnal Constituents

    Name

    Description

    Hourly Speed (°)

    Flood Modeller Unit Code

    M4

    First shallow water harmonic of M2 with a speed twice that of M2

    57.98

    M4

    MS4

    Shallow water constituent produced by the interaction of M2 and S2, with speed equal to sum of speeds of M2 and S2

    58.98

    MS4

    Other Constituents

    Name

    Description

    Hourly Speed (°)

    Flood Modeller Unit Code

    Sa

     

    0.041

    SA

    SSa

     

    0.082

    SSA

    Mm

     

    0.544

    MM

    MSf

     

    1.015

    MSF

    Mf

     

    1.098

    MF

    p1

     

    14.92

    PI1

    2N2

     

    27.90

    2N2

    µ2

     

    27.97

    MU2

    u2

     

    28.51

    NU2

    M3

     

    43.48

    M3

    M6

     

    86.95

    M6

    2MS6

     

    87.97

    2MS6

    2SM6

     

    88.98

    2SM6

    M8

     

    115.94

    M8

    The storm surge component, S, is given by:

    TidalBoundaryStormSurgeEqn

    (2)

    where:

    samp = surge amplitude (m)

    time = current model time (hrs)

    sstart = surge start time (hrs from start of run)

    sdur = surge duration (hrs)

    spower = surge cosine power

    From version 4.0 onwards, it is possible to model more than one surge, with differing parameters, during a simulation.
    Thus the water level at the Tidal Harmonics Boundary is given by:

    tidalimage11

    (3)

    where:

    H = Water level (mAD [ft, US])

    h = tidal component (m [ft,US])

    S = surge component (m [ft, US])

    X0 = Initial Mean Sea Level for the location (m AD [ft,US])

    tidalimage12

    y  is  the current simulation time (as year, including factional part, e.g. 1992.5 denotes 0000hrs, 2nd July 1992),

     yo,i is the year from which rate rise i applies,

     ri is the MSL rate rise i (m/yr [ft/yr, US]),

    and the sum is performed over all i such that y >  yo,i

    Datafile Format

    LINE 1 - Keywords 'TIDBDY'

    LINE 2 - Label

    LINE 3 – z, nsurges, nrises

    LINE 4.1 to LINE 4.nsurges [1] - sstart(i), sdur(i), samp(i), spower(i)

    LINE 5 - x0

    LINE 6 - hour, idat, iy, tidbdy_dates

    LINE 7 - nh

    LINE 8.1 to LINE 8.nh - ifharm, amp, phase

    LINE 9.1 to LINE 9.nrises [2] – yrise(i), rrise(i)

    Note: line 8 has a format width of 4 characters for ifharm and 10 characters for amp and phase (ie a4,2f10)

    where

    Label = Node label at boundary

    z = Sea Bed Elevation (mAD) (not used in calculations)

    nsurges – number of surges to be modelled during the simulation

    nrises – number of different rate of sea level rises during the simulation

    sstart(i) = Surge start time of ith surge (hours from start of run)

    sdur(i) = ith Surge duration (hours)

    samp(i) = ith Surge amplitude (m)

    spower(i) = ith Surge cosine power (unitless)

    x= Mean Sea Level for the location, including the Seasonal Correction taken from Admiralty Tide Tables, vol II. (mAD)

    hour = start hour of the tidal predictions in decimal on the 24 hour clock

    idat = start date of the tidal predictions as day and month (eg for 21 July enter 2107)

    iy = start year of the tidal predictions (eg 1995)

    tidbdy_dates = 'EVENT' if times are to be taken from the ief file, if present; anything else, e.g. blank, if times are to be taken from the TIDBDY unit

    nh = number of harmonics to be included

    ifharm = Constituent name (left justified within a field width of 4 characters)

    amp = Amplitude of Constituent (m)

    phase = Phase lag constant (°)

    yrise(i) – year from which the isea level rate rise occurs

    rrise(i) - isea level rate rise (mm/yr)
    RiverNodesimagesTidalHarBDyData.gif
    [1] This (repeatable) line must occur at least once
    [2] This (repeatable) line is absent if nrises=0


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