 21 Sep 2022
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Tidal Harmonics Boundary
 Updated on 21 Sep 2022
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A tidal boundary is a headtime 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 surge  Sstart(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 occurs  Yrise(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 headtime 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.
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 steadystate 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 tideraising 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 semidiurnal constituents.
The contribution of every tidal constituent may be expressed as:
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 tidalraising 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
Semidiurnal Constituents
Name  Description  Hourly Speed (°)  Flood Modeller Unit Code 
M_{2}  Principal lunar constituent  28.98  M2 
S_{2}  Principal solar constituent  30.00  S2 
N_{2}  Allow for the changes in the Moon's distance due to its elliptic orbit round the Earth  28.44  N2 
L_{2}  L2 
 
K_{2}  Allow for the effect of the declination of the Sun and Moon and of changes in the Sun's distance  30.08  K2 
T_{2}  T2 

Diurnal Constituents
Name  Description  Hourly Speed (°)  Flood Modeller Unit Code 
K_{1}  Allow for the effect of the Moon's declination  15.04  K1 
O_{1}  O1 
 
K_{1}  Allow for the effect of the Sun's declination 


P_{1}  P1 
 
Q_{1}  Allow for the effect of changes in the Moon's distance on K1 and O1  13.40  Q1 
M_{1}  M1 
 
J_{1}  J1 

Quarterdiurnal Constituents
Name  Description  Hourly Speed (°)  Flood Modeller Unit Code 
M_{4}  First shallow water harmonic of M2 with a speed twice that of M2  57.98  M4 
MS_{4}  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 
p_{1} 
 14.92  PI1 
2N_{2} 
 27.90  2N2 
µ_{2} 
 27.97  MU2 
u_{2} 
 28.51  NU2 
M_{3} 
 43.48  M3 
M_{6} 
 86.95  M6 
2MS_{6} 
 87.97  2MS6 
2SM_{6} 
 88.98  2SM6 
M_{8} 
 115.94  M8 
The storm surge component, S, is given by:
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:
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]) y is the current simulation time (as year, including factional part, e.g. 1992.5 denotes 0000hrs, 2^{nd} 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 i^{th} surge (hours from start of run)
sdur(i) = i^{th} Surge duration (hours)
samp(i) = i^{th} Surge amplitude (m)
spower(i) = i^{th} Surge cosine power (unitless)
x_{0 }= 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)
[1] This (repeatable) line must occur at least once
[2] This (repeatable) line is absent if nrises=0