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Simplified Harmonic Method – height of tide from harmonic constants

The Simplified Harmonic Method of Tidal Prediction from the Admiralty Tide Tables works out the height of tide at any time directly from the harmonic constants of a port, with no standard port and no tidal curve. NauticTools2 follows forms A and B line by line and calculates the values of Table VII itself.

• Part III
• Harmonic constants
• M2 · S2 · K1 · O1
• Table VII
• Forms A and B
• Hourly heights

What is the Simplified Harmonic Method?

The tide can be described as the sum of individual oscillations, the constituents. At a given port each has its own amplitude H and phase g: the harmonic constants of Part III of the Tide Tables. The simplified method takes the four main constituents M2, S2, K1 and O1 plus two shallow-water terms. Table VII supplies the astronomical values for each day that place the oscillations at the time required.

When do you need it?

• Ports in Part III: for many ports the Tide Tables give only harmonic constants, not daily predictions.
• Where the standard curves do not apply: the Tide Tables call for the method with shallow-water corrections (f4, F4, f6, F6) and with a duration of rise or fall outside 5 to 7 hours.
• Teaching and checking: every line of the forms is visible and can be compared with a calculation by hand.

The working

• ML – mean level of the port (Z₀, or the value from Table VI for ports marked w)
• Seasonal – seasonal correction
• K1, O1 – contributions of the diurnal constituents
• R – contribution of the semidiurnal constituents, as a vector of M2 and S2
• D4, D6 – shallow-water terms

1. Form A (lines 1–16)

   Applies to the whole day: mean level, A1 and A2 from Table VII, the hourly rates p/24, A1 + g and the factors F.

2. Form B (lines 17–40)

   Works out the height for one time: angle θ, Ft, the contributions of the constituents, the semidiurnal vector R and the shallow-water terms. Line 40 is the sum.

3. Hourly heights

   As note 1 of the instructions recommends, the tool also calculates the hours from T−3 h to T+3 h. This shows the course of the tide around the time required.

Worked example

This example is included in NauticTools2 as “Example (ATT Instructions)”, together with examples for Bermuda and Dover.

What to watch out for

• Table VII: the app calculates the values itself. Compared with the printed table they differ at most in the last digit (1° or 0.01). It does not overwrite values you enter yourself. If they no longer fit the date, the calculation is blocked until they do.
• Mark w: with large fortnightly variations, the mean level from Table VI applies instead of Z₀. The tool shows how many days the chosen day lies before or after springs.
• Mark v: with large seasonal variations, Part III gives monthly values of H or g. Enter the value for the month in the calculation.
• Seasonal correction: the field is pre-filled from the seasonal changes under ATT Ports. If there is no matching range, a red note appears.
• Rounding: with “Round intermediate values as in the book” ticked, every line is rounded as on the form. Without it the tool calculates without intermediate rounding.

How it works in NauticTools2

1. Choose or add a port

   In the Simplified Harmonic Method tile, choose a port or add one with ＋: name, number from Part III, time zone, Z₀, the constants H and g for M2, S2, K1 and O1, and f4/F4 and f6/F6. The same list is under ATT Ports in the SHM ports tab. Where Part III shows ⊙, leave the field empty.

2. Enter date and time

   The time is the zone time of the port. Table VII fills itself in from the date. It is laid out as in the book, one row per day and columns A and F for each constituent.

   

3. Calculate

   The height at time T is at the top, followed by forms A and B and the hourly heights, with the time required highlighted.

   

4. Save and print

   Port, date, time, Table VII and the daily values are saved. The printout contains the inputs, the result, both forms and the hourly heights.

Report to print

Every calculation can be printed as a report or saved as a PDF. Page 1 holds the inputs, the result and the hourly heights, page 2 forms A and B.

View the example report as a PDF ›

Frequently asked questions

Do I need the printed Table VII?

No. NauticTools2 calculates the values from the date. Compared with the book they differ at most in the last digit. You can still enter your own values from the book.

How accurate is the Simplified Harmonic Method?

It is an approximation with four main constituents and two shallow-water terms. Results can differ from official predictions by a few centimetres to decimetres.

How does it differ from Tides ATT?

Tides ATT works from a standard port through differences and tidal curves. The Simplified Harmonic Method needs neither and uses the harmonic constants of the port itself.

Not for navigation: the Simplified Harmonic Method is an approximation with four main constituents and two shallow-water terms. Results can differ from official predictions by a few centimetres to decimetres. For navigation, the official tide tables are authoritative.

Related tools

• Tides ATT – tidal predictions with standard and secondary ports
• Tides BSH – height of tide by the method of the German BSH tide tables
• Depth of Water – depth of water from charted depth and height of tide