Doc #12 — NZ Tide Tables: Precomputed 50+ Years

COMPUTED DATA: NZ TIDE TABLES

View the computed NZ Tide Tables for 2026–2030 → — High and low water times and heights for Auckland, Wellington, and Nelson, generated from LINZ harmonic constants using a 5-constituent harmonic prediction model. This sample demonstrates the approach; operational tables should use all 25–30 published constituents for higher accuracy.

View the Mathematical Reference Tables → — Logarithms and trigonometric functions needed for manual tide computation as a fallback (see Section 8 of this document).

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RECOMMENDED ACTIONS

Immediate (Days 1–7) — Phase 1

1. Download and archive LINZ harmonic constants for all NZ standard ports and tidal difference data for all secondary ports. These are published on the LINZ website and in the NZ Nautical Almanac (a separate publication from the astronomical nautical almanac of Doc #10). Store on multiple physical media.³
2. Download tidal prediction software. The Python library utide implements harmonic tidal prediction and analysis.⁴ Also archive the UK National Oceanography Centre’s TidePy or the NOAA pytides library as alternatives. Archive all source code and dependencies, including the Python interpreter itself and the NumPy/SciPy numerical libraries these tools depend on. Without these dependencies, the tidal prediction libraries will not run.
3. Locate and secure all existing printed NZ tide tables — at ports, on vessels, in LINZ offices, in harbour masters’ offices, and in maritime training institutions. Current published tables cover only 1–2 years ahead and serve as validation references.
4. Identify tidal computation personnel. Any programmer with basic signal processing knowledge can implement harmonic prediction from documented algorithms. LINZ tidal scientists (based in Wellington) are the primary experts; university oceanographers at the University of Auckland, University of Otago, and NIWA are secondary sources.⁵

Short-term (Days 7–21) — Phase 1

5. Validate computation against published LINZ predictions. Cross-check computed tides for all standard ports against LINZ published predictions for the current year. Agreement within 5 minutes for time and 0.05 m for height confirms correct implementation.⁶
6. Compute the complete 50-year dataset for all standard and secondary ports.
7. Format for printing. Generate print-ready output organised by port and year.

Medium-term (Days 21–90) — Phase 1

8. Print and distribute. Priority: major commercial and fishing ports first, then regional ports, then archive copies. Coordinate with overall printing schedule (Doc #5).
9. Print tidal stream atlases for Cook Strait, Foveaux Strait, and Hauraki Gulf approaches.

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1. WHAT TIDE TABLES CONTAIN

1.1 Daily predictions

A standard tide table provides, for each day of the year at each port:

• Times of high water (typically two per day, approximately 12 hours 25 minutes apart)
• Heights of high water in metres above chart datum
• Times of low water (typically two per day)
• Heights of low water in metres above chart datum

Some days have only one high water or one low water (diurnal inequality), particularly at ports where diurnal constituents are significant relative to semidiurnal ones.⁷

1.2 Chart datum

All heights are referenced to chart datum, which in NZ is defined as Lowest Astronomical Tide (LAT) — the lowest tide level that can be predicted under average meteorological conditions. This means all predicted heights are positive or zero under normal conditions. Actual water levels can fall below chart datum during unusually low tides combined with high atmospheric pressure.⁸

1.3 What tide tables do not predict

Tide tables predict the astronomical tide only. They do not account for:

• Storm surge — wind and atmospheric pressure effects that can raise or lower water levels by 0.3–1.0 m or more in NZ waters⁹
• Tsunami — seismic sea waves
• River flood effects — in estuarine ports
• Long-period oscillations (seiches) in enclosed harbours

Mariners must understand that actual water levels may differ from predicted levels, particularly during storms. This limitation should be printed on every page of the tide tables.

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2. HARMONIC TIDAL PREDICTION

2.1 Principle

The tide at any location is the sum of periodic components driven by the gravitational attraction of the moon and sun. Each component (called a harmonic constituent) has:

• A known frequency, determined by the orbital mechanics of the Earth-Moon-Sun system
• An amplitude (in metres), specific to each port, determined by local geography
• A phase (in degrees), specific to each port, representing the time lag between the astronomical forcing and the local tidal response

The prediction formula is:

h(t) = Z₀ + Σ [Aₙ × fₙ × cos(ωₙt + Vₙ + uₙ - gₙ)]

where Z₀ is the mean water level above chart datum, Aₙ is the amplitude of constituent n, fₙ is a nodal modulation factor (varies with the 18.61-year lunar nodal cycle), ωₙ is the angular speed of constituent n, Vₙ is the astronomical argument at the time origin, uₙ is a nodal correction to the phase, and gₙ is the phase lag (Greenwich epoch) for constituent n at that port.¹⁰

2.2 Principal constituents

The following table lists the constituents most significant for NZ tidal prediction, in approximate order of importance.¹¹

Constituent	Symbol	Period (hours)	Description
Principal lunar semidiurnal	M2	12.421	Dominant constituent at most NZ ports
Principal solar semidiurnal	S2	12.000	Sun’s semidiurnal gravitational effect
Larger lunar elliptic	N2	12.658	Effect of moon’s elliptical orbit
Luni-solar declinational	K2	11.967	Combined lunar-solar declination effect
Luni-solar diurnal	K1	23.934	Diurnal effect of lunar-solar declination
Principal lunar diurnal	O1	25.819	Moon’s diurnal gravitational effect
Principal solar diurnal	P1	24.066	Sun’s diurnal gravitational effect
Larger lunar elliptic diurnal	Q1	26.868	Diurnal elliptic effect
Shallow water overtide	M4	6.210	Harmonic of M2, significant in shallow harbours
Shallow water compound	MS4	6.103	Compound tide, significant in estuaries

For most NZ ports, M2 alone accounts for 60–80% of the total tidal range. The combination of M2, S2, N2, K1, and O1 typically captures over 95% of the predictable tidal signal.¹²

2.3 Nodal modulation

The amplitudes and phases of tidal constituents are modulated by the 18.61-year cycle of the regression of the lunar nodes (the points where the moon’s orbit crosses the ecliptic). This modulation affects M2 amplitude by approximately ±4% and O1 amplitude by approximately ±19%. The nodal factors f and u are computed from the longitude of the lunar ascending node at the date of prediction — a calculation requiring standard astronomical formulas but no iterative or approximate methods.¹³

For a 50-year tide table, correct handling of the nodal cycle is essential. Tables computed without nodal corrections will show systematic errors that grow and shrink on an 18.61-year cycle, with maximum errors of 0.1–0.2 m at ports with large tidal ranges.

2.4 Number of constituents required

LINZ publishes harmonic constants for approximately 25–30 constituents per standard port.¹⁴ For prediction accuracy matching published LINZ tables (within 5 minutes in time, 0.05 m in height), all published constituents should be used. Using only the 5–8 principal constituents produces predictions accurate to approximately 15–20 minutes in time and 0.1–0.2 m in height — adequate for most practical navigation but noticeably less precise than published tables.¹⁵

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3. NZ STANDARD AND SECONDARY PORTS

3.1 Standard ports

LINZ designates the following as standard ports, for which full harmonic constants are published and daily predictions are computed directly.^{16 17}

Standard Port	Region	Mean Spring Range (m)	Mean Neap Range (m)	Tidal Character
Marsden Point (Whangārei)	Northland	2.0	1.5	Semidiurnal
Auckland (Waitematā)	Auckland	2.8	2.0	Semidiurnal
Tauranga	Bay of Plenty	1.6	1.2	Semidiurnal
Gisborne	East Cape	1.4	1.0	Semidiurnal
Napier	Hawke’s Bay	1.6	1.2	Semidiurnal
Wellington	Wellington	1.1	0.8	Semidiurnal
Nelson	Tasman Bay	3.7	2.6	Semidiurnal
Westport	West Coast	2.5	1.7	Semidiurnal
Lyttelton	Canterbury	2.1	1.3	Semidiurnal
Timaru	South Canterbury	1.9	1.3	Semidiurnal
Port Chalmers (Dunedin)	Otago	1.7	1.3	Semidiurnal
Bluff	Southland	2.1	1.5	Semidiurnal
Picton	Marlborough Sounds	1.4	1.1	Semidiurnal

Note: The exact list of LINZ standard ports has varied across editions of the NZ Nautical Almanac. The above reflects the principal ports for which full harmonic analysis has been conducted. Some editions include additional standard ports (e.g., New Plymouth, Onehunga). The AI facility should use the most current LINZ data available at the time of computation.¹⁸

All NZ ports are predominantly semidiurnal — the tide rises and falls twice daily, with the two daily highs and two daily lows at similar but not identical heights. The diurnal inequality (difference between successive highs or successive lows) is generally small compared to the semidiurnal range, though it varies geographically.

3.2 Secondary ports

Secondary ports are locations where tidal predictions are derived from a nearby standard port by applying time and height differences. LINZ publishes tidal difference data for approximately 200 secondary ports around NZ’s coastline.¹⁹

For each secondary port, the published differences are:

• Time difference for HW — minutes to add to or subtract from the standard port’s HW time
• Time difference for LW — minutes to add to or subtract from the standard port’s LW time
• Height ratio for HW — multiply the standard port’s HW height by this factor
• Height ratio for LW — multiply the standard port’s LW height by this factor
• Height correction for mean level — added to account for differences in mean sea level

Example: If a secondary port’s data states “HW +25 min, LW +35 min, HW height ×0.85, LW height ×0.90” relative to Auckland, then when Auckland’s high water is predicted at 14:30 with height 3.2 m, the secondary port’s high water is predicted at 14:55 with height 2.72 m.

For the 50-year tide tables, the recommended approach is:

• For major secondary ports (approximately 30–50 ports with significant commercial or fishing activity): compute full predictions using the secondary port’s own harmonic constants where available, or apply differences to the standard port predictions.
• For remaining secondary ports: print the difference data alongside the standard port tables, allowing users to compute local predictions by hand. This dramatically reduces printing volume while preserving coverage.

3.3 Notable NZ tidal characteristics

Nelson: Has the largest tidal range of any major NZ port (spring range approximately 3.7 m) due to the resonant geometry of Tasman Bay and the Golden Bay embayment.²⁰

Wellington: Has a comparatively small tidal range (spring range approximately 1.1 m). Wellington Harbour’s tides are complicated by the interaction between Cook Strait tidal flows and harbour oscillations. The tide gauge at Queens Wharf is the longest-running continuous tidal record in NZ, dating from 1944.²¹

Kaipara Harbour: NZ’s largest harbour by area. Tidal flows through the entrance are very strong (up to 5 knots on spring tides) and the bar is one of NZ’s most dangerous harbour entrances. Tidal predictions for Kaipara must be accompanied by strong warnings about the entrance conditions.²²

Cook Strait: Not a port, but the tidal regime is important for inter-island navigation. The oceanic tidal waves arriving at the Tasman Sea (western) and Pacific Ocean (eastern) entrances of the strait are significantly out of phase, driving strong tidal streams through the strait (Section 5). Wellington and Nelson have similar M2 phases (~174° and ~179° respectively — see Appendix A) but differ in tidal range and compound tidal behaviour due to differing shallow-water effects and bay geometries.²³

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4. SAMPLE TIDE TABLE ENTRIES

4.1 Standard port format

The following illustrates the format for one month of predictions at a standard port. Values are representative of Auckland’s tidal characteristics.

AUCKLAND (WAITEMATĀ) — MARCH 2030
Times in NZST (UT +12:00). Heights in metres above Chart Datum (LAT).

Day   HW Time  Ht(m)   LW Time  Ht(m)   HW Time  Ht(m)   LW Time  Ht(m)
 1 Sa  02:18   3.1      08:41   0.6      14:42   3.0      21:03   0.7
 2 Su  03:04   3.0      09:28   0.7      15:31   2.9      21:52   0.8
 3 Mo  03:55   2.8      10:22   0.9      16:27   2.7      22:48   0.9
 4 Tu  04:54   2.6      11:24   1.0      17:33   2.6      23:53   1.0
 5 We  06:02   2.5      —        —       12:32   1.1      18:45   2.6
 6 Th  00:58   1.0      07:10   2.5      13:36   1.0      19:48   2.7
 7 Fr  01:57   0.9      08:08   2.6      14:29   0.9      20:39   2.8
 8 Sa  02:46   0.8      08:55   2.8      15:14   0.8      21:23   3.0
 9 Su  03:28   0.6      09:36   2.9      15:54   0.6      22:03   3.1
10 Mo  04:07   0.5      10:14   3.1      16:32   0.5      22:41   3.2  ●
  ...
15 Sa  07:35   2.7      01:14   1.1      20:04   2.6      13:42   1.1
  ...
25 Tu  04:14   0.4      10:22   3.2      16:38   0.4      22:50   3.3  ○
  ...
31 Mo  03:48   3.1      10:08   0.5      16:12   3.1      22:29   0.6

● = New Moon    ○ = Full Moon
Spring tides: approximately days 10–12 and 25–27
Neap tides: approximately days 3–5 and 18–20

Notes on format:

• Each day has up to four entries: two high waters and two low waters
• On some days, a high or low water may fall just before or after midnight, creating apparent gaps (see day 5 in the example)
• Moon phase symbols help users anticipate spring and neap tides
• All times are in NZ Standard Time for convenience; a note on the page specifies the UT offset and the need to adjust for NZ Daylight Time when applicable

4.2 Secondary port format

SECONDARY PORT: RAGLAN                    Standard Port: AUCKLAND
Time differences:   HW +0h 10m    LW +0h 15m
Height factors:     HW × 0.89     LW × 0.92
Mean level diff:    +0.02 m

Apply these corrections to the Auckland predictions on the facing page.
Example: Auckland HW 02:18 at 3.1 m → Raglan HW 02:28 at 2.76 m

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5. TIDAL STREAMS

5.1 Cook Strait

Cook Strait is NZ’s most important tidal stream area. The oceanic tidal waves arriving at the Tasman Sea (western) and Pacific Ocean (eastern) entrances are significantly out of phase, creating a hydraulic head difference that drives strong tidal currents through the strait.²⁴

• Maximum spring stream rates: 3–4 knots in the narrows between Cape Terawhiti and the Brothers Islands; locally up to 5 knots in restricted passages²⁵
• Stream direction: Generally northward during the flood (Wellington rising tide) and southward during the ebb, but the pattern is complex and varies across the width of the strait
• Timing: The stream turns approximately 1–2 hours before high and low water at Wellington, but varies with location within the strait

The tide tables should include a Cook Strait tidal stream atlas — a series of 13 charts (one for each hour relative to high water at Wellington) showing stream direction and rate across the strait. This format, standard in Admiralty tidal stream atlases, allows mariners to plan passage timing to use favourable streams and avoid adverse ones.²⁶

5.2 Foveaux Strait

Foveaux Strait separates Stewart Island/Rakiura from the South Island. Tidal streams are significant:

• Maximum spring stream rates: 2–3 knots, locally stronger near reefs and islands²⁷
• Stream direction: Generally eastward on the flood and westward on the ebb
• Importance: Essential for fishing vessels and for any future coastal trade route to Bluff. Foveaux Strait is also known for sudden weather changes and confused seas when tidal stream opposes wind — the tide tables should note this hazard.

5.3 Hauraki Gulf

The Hauraki Gulf approaches to Auckland are commercially critical:

• Tidal streams through the Rangitoto and Motuihe channels reach 1–2 knots on springs²⁸
• Kaipara Harbour entrance (north of Auckland, technically outside the gulf): tidal streams to 5 knots, extremely dangerous bar — vessel entry should be timed strictly by tide tables²⁹
• Tauranga entrance: Moderate streams (1–2 knots) but a narrow entrance requiring tidal awareness³⁰

5.4 Tidal stream atlas format

For each major strait or harbour approach, the atlas should contain:

• Thirteen hourly charts (HW -6 through HW +6 at the reference port)
• Stream arrows showing direction and rate (in knots) at spring and neap tides
• Reference port clearly stated (e.g., “Hours before/after HW Wellington”)
• Interpolation guidance for rates between springs and neaps

Total tidal stream atlas pages: approximately 13 pages per area × 3–5 areas = 40–65 pages. These are the same for all years (tidal stream patterns do not change) and need to be printed only once.

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6. COMPUTATION AND VERIFICATION

6.1 Software implementation

The harmonic prediction computation can be implemented in any programming language with floating-point arithmetic and trigonometric functions. The core algorithm is:

1. For the target date/time, compute the astronomical arguments (Vₙ) for each constituent from standard formulas based on the date (year, month, day, hour)
2. Compute the nodal factors (fₙ, uₙ) from the longitude of the lunar ascending node
3. For each constituent, compute the contribution: Aₙ × fₙ × cos(ωₙt + Vₙ + uₙ - gₙ)
4. Sum all contributions and add Z₀ (mean level) to get the predicted height
5. Search for maxima and minima (high and low waters) by evaluating the prediction at short intervals (e.g., every 6 minutes) and refining

The angular speeds (ωₙ) and the formulas for astronomical arguments are tabulated in standard references.^{31 32} The port-specific data (Aₙ and gₙ for each constituent, plus Z₀) come from the LINZ harmonic constants.

Estimated computation time: Computing 50 years of predictions for all standard ports (evaluating the tidal function at 6-minute intervals, searching for turning points) takes approximately 1–4 hours on a modern laptop. This is longer than the astronomical almanac computation (Doc #10) because of the large number of ports and the iterative search for high/low water times, but well within the capability of any functioning computer with the required software.

6.2 Verification procedures

Cross-check against LINZ published predictions: For all standard ports, compare computed predictions against published LINZ predictions for the current and recent years. Acceptable accuracy: within 5 minutes for time of high/low water, within 0.05 m for height.³³

Cross-check against historical tide gauge records: LINZ and NIWA maintain tide gauge records for many NZ ports, some extending back decades. Compare hindcast predictions (computed tides for past dates) against actual recorded tide gauge data. Discrepancies exceeding 0.1 m consistently suggest errors in the harmonic constants or the computation method.

Internal consistency checks:

• Spring tides (highest predicted tides) should occur within 1–2 days of new and full moon
• Neap tides (lowest range) should occur near first and third quarter moon
• The predicted tidal range should agree with the known mean spring and neap ranges for each port (Section 3.1)
• The long-term mean water level should remain approximately constant (no trend across the 50-year dataset, unless sea level rise is deliberately incorporated)

6.3 Sea level rise consideration

Over a 50-year prediction period, sea level rise is potentially significant. Current estimates for NZ are approximately 3–5 mm per year, implying a rise of 15–25 cm by 2076 under pre-war projections.³⁴ Post-nuclear-war sea level change is harder to predict — nuclear winter cooling could temporarily reduce thermal expansion and slow ice melt, partially offsetting the long-term trend.

Recommendation: Compute tide tables without a sea level rise adjustment, but include a note on each table stating that actual water levels may be higher than predicted by an amount that increases over the decades. Print a correction table showing estimated additional height per decade. This approach keeps the prediction method clean (pure harmonic prediction) while informing users of the likely systematic error.

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7. PAGE COUNT AND PRINTING REQUIREMENTS

7.1 Estimated pages

Component	Pages	Notes
Standard port predictions (13 ports × 50 years × 2 pages/port-year)	~1,300	Two pages per port per year (6 months per page)
Major secondary ports (40 ports × 50 years × 1 page/port-year)	~2,000	One page per port per year
Secondary port difference tables	~40	Approximately 200 secondary ports, printed once
Tidal stream atlases	~65	Printed once; same for all years
Introduction, instructions, worked examples	~20	Printed once per set
Constituent tables and computation methods	~15	Printed once; fallback for manual recomputation
Total per complete set	~3,440

If printing is further constrained, the 40 major secondary ports can be omitted (users apply differences to standard port tables manually), reducing the total to approximately 1,440 pages per set — still substantial but significantly less than the full version.

7.2 Binding and organisation

Recommended organisation:

• By port, in decade volumes. Each major port gets a booklet covering 10 years (approximately 20 pages per port per decade). A harbour master receives the booklet for their port; a vessel carries booklets for its intended ports of call.
• Alternative: annual volumes by region. One volume per year covering all ports in a region (e.g., Auckland and Hauraki Gulf, Wellington and Cook Strait, Canterbury and Otago). Approximately 30–40 pages per regional volume per year.

The tidal stream atlases, secondary port difference tables, and instruction pages are bound separately as a permanent companion volume (approximately 120–140 pages), unchanged across the 50-year period.

7.3 Print run

Copy purpose	Quantity	Notes
National Archive	3 sets	Geographically separated (Wellington, Auckland, Christchurch)
Major commercial ports	13 sets	One per standard port
Regional fishing ports	20–30 sets	Major fishing ports and marinas
Offshore-capable vessels	30–50 sets	Vessels expected to navigate coastally
Maritime training institutions	5 sets	Navigation schools
Reserve stock	10–20 sets	Replacement and future vessels
Total	~80–120 sets

At approximately 3,400 pages per complete set, total printing is approximately 272,000–408,000 pages. This is comparable to the nautical almanac printing requirement (Doc #10) and must be coordinated with the overall printing schedule (Doc #5).

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8. MANUAL COMPUTATION FALLBACK

8.1 Computing tides by hand

If computers become unavailable before the 50-year tables are fully computed, tidal predictions can be computed manually from harmonic constants. The process for one day at one port, using the principal 5–8 constituents:

1. Look up the astronomical arguments for each constituent on the target date (requires tables of astronomical arguments, which should be printed as part of this document)
2. For each constituent, compute: Aₙ × fₙ × cos(ωₙt + Vₙ + uₙ - gₙ) at 1-hour intervals through the day
3. Sum all constituent contributions plus Z₀ at each hour
4. Identify the times and heights of high and low water from the resulting curve

Labour estimate: A skilled human computer, using pre-computed tables of astronomical arguments and trigonometric tables (Doc #14 in the catalog), can complete one day’s prediction for one port in approximately 30–60 minutes. One year for one port requires approximately 180–360 hours — roughly 5–9 person-weeks of full-time work. Covering 13 standard ports for one year requires approximately 65–120 person-weeks. This is laborious but feasible, and is essentially how tide tables were produced before electronic computers.³⁵

8.2 Why 50 years of precomputation matters

The manual computation labour estimate demonstrates why precomputing 50 years while computers are functional is so valuable. The computer does in hours what would take human computers years. Every year of precomputed tables saved is a year that human labour can be directed to other recovery tasks.

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9. CRITICAL UNCERTAINTIES

Uncertainty	Impact if unfavourable	Mitigation
LINZ harmonic constants may not be downloaded in time	Cannot compute predictions for any port without its constants	Download immediately; also record constants from any printed NZ Nautical Almanac editions held in NZ
Harmonic constants may be inaccurate for ports with limited tidal records	Predictions less accurate at some secondary ports	Use standard ports as primary reference; flag secondary ports with known limited data
Long-period sea level change (either from global warming or nuclear winter cooling)	Predictions systematically high or low in later decades	Include sea level correction note on all tables (Section 6.3)
Harbour geometry may change (earthquake, tsunami, sedimentation, sea wall construction)	Harmonic constants become invalid for affected port	Note that after major earthquakes or coastal changes, local tide observations should be used to re-derive constants; print the methodology for doing so
Printing capacity may be insufficient for full secondary port coverage	Fewer ports covered; some users must compute from differences	Print standard ports first, major secondary ports second; include difference tables for all remaining ports
Shallow water effects may not be captured by published constituents	Predictions less accurate in estuarine and shallow-water ports	Note affected ports; users should add safety margins

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10. CROSS-REFERENCES

Document	Relationship
Doc #5 — Printing Strategy	Printing schedule and consumable allocation for tide table production
Doc #10 — Nautical Almanac	Astronomical data for navigation; tide tables complement the almanac for inshore work
Doc #11 — Sight Reduction Tables	Part of the navigation reference set alongside tide tables
Doc #13 — NZ Coastal Pilot	Harbour approaches and hazards; tide tables provide the timing data
Doc #14 — Mathematical Tables	Trigonometric tables needed for manual tide computation fallback
Doc #138 — Sailing Vessel Design	The vessels that will use these tide tables for harbour entry
Doc #138 — Celestial Navigation	Offshore navigation counterpart to the inshore navigation supported by tide tables
Doc #139 — Coastal Trading Network	The trade network that depends on safe harbour entry and passage timing

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11. PRINT FORMAT AND DISTRIBUTION RECOMMENDATIONS

11.1 Print specifications

• Paper: Standard 80 gsm minimum. Archive copies on heavier acid-free stock if available.
• Font: Monospaced, minimum 8 point for numerical tables. Column headers in bold.
• Layout: Two pages per port per year (6 months per page), with port name, year, and time zone reference on every page.
• Laminated quick-reference cards: For each major port, a single laminated A4 card showing the current year’s spring/neap tide times, tidal stream summary, and harbour entry guidance. These cards are intended for bridge use on vessels and for display at port offices.

11.2 Distribution priority

1. Wellington, Auckland, Lyttelton, Tauranga, Bluff — the five ports most likely to be critical for inter-island and coastal trade
2. All remaining standard ports — within 30 days
3. Major fishing ports — Greymouth, Kaikōura, Ahipara, Whitianga, Riverton
4. Maritime training institutions — for navigator training (Doc #138, #159)
5. Archive copies — three complete sets in geographically separated secure storage

11.3 Companion materials

Every set of tide tables should be accompanied by:

• The tidal stream atlas for the user’s region
• The secondary port difference tables
• A one-page instruction sheet explaining how to read the tables and apply secondary port corrections
• A note on the limitations of tidal prediction (storm surge, actual vs. predicted levels)

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APPENDIX A: HARMONIC CONSTANTS — REPRESENTATIVE VALUES

The following table shows representative harmonic constants for selected NZ standard ports (principal constituents only). These values are approximate and are provided to illustrate the data format. The AI facility must use the most current LINZ-published values for actual prediction.^{36 37}

Auckland (Waitematā)

Constituent	Amplitude (m)	Phase g (°)
Z₀ (mean level)	1.74	—
M2	1.07	255
S2	0.21	289
N2	0.21	237
K1	0.07	175
O1	0.04	151

Wellington

Constituent	Amplitude (m)	Phase g (°)
Z₀ (mean level)	0.75	—
M2	0.44	174
S2	0.07	219
N2	0.09	154
K1	0.06	021
O1	0.04	350

Nelson

Constituent	Amplitude (m)	Phase g (°)
Z₀ (mean level)	2.15	—
M2	1.44	179
S2	0.29	215
N2	0.28	160
K1	0.07	352
O1	0.04	322

Note on the M2 phase values: The M2 phase at Auckland (~255°) versus Wellington (~174°) and Nelson (~179°) illustrates the out-of-phase tidal relationship across Cook Strait — the approximately 76° phase difference between Auckland and Wellington corresponds to roughly a 2.5-hour time offset in the M2 constituent, while Wellington and Nelson are nearly in phase for M2 but their compound tidal behaviour differs due to differences in other constituents and shallow-water effects.³⁸

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APPENDIX B: ASTRONOMICAL ARGUMENT TABLES

For manual tide computation, the astronomical arguments V₀+u for each constituent must be evaluated for the target date. These arguments depend on six astronomical variables (typically denoted h, s, p, N, p₁, and T in tidal notation), which are linear functions of time computed from the date.³⁹

These tables should be computed and printed for the entire 50-year period at monthly intervals (600 entries per variable). The tables occupy approximately 10–15 pages and enable manual prediction without any computer — a critical fallback resource.

The formulas for the astronomical variables as functions of Julian date, the angular speeds of all standard constituents, and the nodal factor equations should all be printed in full as part of this appendix. This ensures that even if all pre-printed tables and all computers are lost, a person with mathematical training can reconstruct the prediction from first principles using only this document, a calendar, and trigonometric tables (Doc #14 in the catalog).

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FOOTNOTES

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1. Pugh, D.T. and Woodworth, P.L., Sea-Level Science: Understanding Tides, Surges, Tsunamis and Mean Sea-Level Changes, Cambridge University Press, 2014. The standard modern reference for tidal science and prediction methodology. Chapters 3–4 cover harmonic analysis and prediction in detail. Also: Schureman, P., Manual of Harmonic Analysis and Prediction of Tides, US Coast and Geodetic Survey Special Publication No. 98, 1958 (revised). The classic reference for tidal harmonic methods, still widely used.↩︎

2. Land Information New Zealand (LINZ), “Tides and Tidal Streams.” LINZ publishes harmonic constants, tidal predictions, and secondary port data for NZ waters. Published in the annual New Zealand Nautical Almanac (not to be confused with the astronomical nautical almanac of Doc #10) and available digitally. https://www.linz.govt.nz/products-services/tides-and-tida...↩︎

3. Land Information New Zealand (LINZ), “Tides and Tidal Streams.” LINZ publishes harmonic constants, tidal predictions, and secondary port data for NZ waters. Published in the annual New Zealand Nautical Almanac (not to be confused with the astronomical nautical almanac of Doc #10) and available digitally. https://www.linz.govt.nz/products-services/tides-and-tida...↩︎

4. Codiga, D.L., “Unified Tidal Analysis and Prediction Using the UTide Matlab Functions,” Technical Report 2011-01, Graduate School of Oceanography, University of Rhode Island, 2011. The utide Python port is available on PyPI. Also: pytides (Python tidal prediction library) and TidePy from the National Oceanography Centre, Southampton.↩︎

5. NIWA (National Institute of Water and Atmospheric Research) maintains NZ’s principal expertise in coastal oceanography and tidal science. NIWA operates tide gauges and conducts tidal analysis. https://niwa.co.nz/. University of Auckland’s School of Environment and University of Otago’s Department of Marine Science also have relevant expertise.↩︎

6. LINZ publishes accuracy standards for NZ tidal predictions: predictions at standard ports are expected to agree with observed tides to within 10–15 minutes in time and 0.1 m in height under normal meteorological conditions. Predictions computed from the same harmonic constants should match LINZ published values more closely (within 5 minutes and 0.05 m), with any differences attributable to rounding or minor algorithmic variations. Source: LINZ Hydrographic Authority standards.↩︎

7. Pugh, D.T. and Woodworth, P.L., Sea-Level Science: Understanding Tides, Surges, Tsunamis and Mean Sea-Level Changes, Cambridge University Press, 2014. The standard modern reference for tidal science and prediction methodology. Chapters 3–4 cover harmonic analysis and prediction in detail. Also: Schureman, P., Manual of Harmonic Analysis and Prediction of Tides, US Coast and Geodetic Survey Special Publication No. 98, 1958 (revised). The classic reference for tidal harmonic methods, still widely used.↩︎

8. Chart datum in NZ is Lowest Astronomical Tide (LAT), adopted by LINZ in accordance with International Hydrographic Organization (IHO) standards. LAT is defined as the lowest tide level predictable under average meteorological conditions and any combination of astronomical conditions. Source: LINZ Chart Datum information. https://www.linz.govt.nz/products-services/tides-and-tida...↩︎

9. Storm surge in NZ waters is typically 0.2–0.5 m for moderate storms, occasionally reaching 0.8–1.0 m during severe cyclones. The largest recorded storm surge in NZ was approximately 0.9 m during Cyclone Giselle (Wahine storm) in April 1968. Source: Goring, D.G., “Extreme Sea Levels in the Wellington Region,” NIWA Client Report, 2000.↩︎

10. Pugh, D.T. and Woodworth, P.L., Sea-Level Science: Understanding Tides, Surges, Tsunamis and Mean Sea-Level Changes, Cambridge University Press, 2014. The standard modern reference for tidal science and prediction methodology. Chapters 3–4 cover harmonic analysis and prediction in detail. Also: Schureman, P., Manual of Harmonic Analysis and Prediction of Tides, US Coast and Geodetic Survey Special Publication No. 98, 1958 (revised). The classic reference for tidal harmonic methods, still widely used.↩︎

11. The International Hydrographic Organization (IHO) lists over 300 harmonic constituents with known frequencies. In practice, 25–60 constituents are sufficient for most port predictions. The five principal constituents (M2, S2, N2, K1, O1) capture the majority of the tidal signal at most locations. Source: IHO Standards for Hydrographic Surveys (S-44); also Pugh and Woodworth (note 1), Table 4.1.↩︎

12. The International Hydrographic Organization (IHO) lists over 300 harmonic constituents with known frequencies. In practice, 25–60 constituents are sufficient for most port predictions. The five principal constituents (M2, S2, N2, K1, O1) capture the majority of the tidal signal at most locations. Source: IHO Standards for Hydrographic Surveys (S-44); also Pugh and Woodworth (note 1), Table 4.1.↩︎

13. Pugh, D.T. and Woodworth, P.L., Sea-Level Science: Understanding Tides, Surges, Tsunamis and Mean Sea-Level Changes, Cambridge University Press, 2014. The standard modern reference for tidal science and prediction methodology. Chapters 3–4 cover harmonic analysis and prediction in detail. Also: Schureman, P., Manual of Harmonic Analysis and Prediction of Tides, US Coast and Geodetic Survey Special Publication No. 98, 1958 (revised). The classic reference for tidal harmonic methods, still widely used.↩︎

14. Land Information New Zealand (LINZ), “Tides and Tidal Streams.” LINZ publishes harmonic constants, tidal predictions, and secondary port data for NZ waters. Published in the annual New Zealand Nautical Almanac (not to be confused with the astronomical nautical almanac of Doc #10) and available digitally. https://www.linz.govt.nz/products-services/tides-and-tida...↩︎

15. LINZ publishes accuracy standards for NZ tidal predictions: predictions at standard ports are expected to agree with observed tides to within 10–15 minutes in time and 0.1 m in height under normal meteorological conditions. Predictions computed from the same harmonic constants should match LINZ published values more closely (within 5 minutes and 0.05 m), with any differences attributable to rounding or minor algorithmic variations. Source: LINZ Hydrographic Authority standards.↩︎

16. Land Information New Zealand (LINZ), “Tides and Tidal Streams.” LINZ publishes harmonic constants, tidal predictions, and secondary port data for NZ waters. Published in the annual New Zealand Nautical Almanac (not to be confused with the astronomical nautical almanac of Doc #10) and available digitally. https://www.linz.govt.nz/products-services/tides-and-tida...↩︎

17. LINZ, New Zealand Nautical Almanac, published annually. Contains tide tables for standard ports, secondary port differences, and tidal stream information for NZ waters. The standard port list and harmonic constants are updated periodically as new tidal analysis becomes available.↩︎

18. LINZ, New Zealand Nautical Almanac, published annually. Contains tide tables for standard ports, secondary port differences, and tidal stream information for NZ waters. The standard port list and harmonic constants are updated periodically as new tidal analysis becomes available.↩︎

19. Land Information New Zealand (LINZ), “Tides and Tidal Streams.” LINZ publishes harmonic constants, tidal predictions, and secondary port data for NZ waters. Published in the annual New Zealand Nautical Almanac (not to be confused with the astronomical nautical almanac of Doc #10) and available digitally. https://www.linz.govt.nz/products-services/tides-and-tida...↩︎

20. Nelson’s large tidal range is due to the near-resonant geometry of Tasman Bay and Golden Bay, which amplify the M2 tidal constituent. The enclosed bay geometry creates a standing wave pattern that increases tidal range toward the head of the bay. Source: Walters, R.A., Goring, D.G., and Bell, R.G., “Ocean Tides Around New Zealand,” New Zealand Journal of Marine and Freshwater Research, 35:567–579, 2001.↩︎

21. The Queens Wharf tide gauge in Wellington Harbour has been operating since 1944 and is NZ’s longest continuous tidal record. It is maintained by LINZ and provides the reference data for Wellington’s harmonic constants. Source: LINZ; Hannah, J., “An Updated Analysis of Long-Term Sea Level Change in New Zealand,” Geophysical Research Letters, 31, 2004.↩︎

22. Kaipara Harbour is NZ’s largest harbour by area (approximately 947 km²). The tidal prism (volume of water exchanged each tide) is enormous, creating powerful tidal streams at the entrance. The Kaipara bar has claimed over 100 vessels and is one of NZ’s most dangerous navigational hazards. Source: Heath, R.A., “A Review of the Physical Oceanography of the Seas Around New Zealand,” New Zealand Journal of Marine and Freshwater Research, 19:79–124, 1985.↩︎

23. Cook Strait tidal dynamics: the tides on the Tasman Sea (west) and Pacific Ocean (east) sides of NZ are driven by different components of the oceanic tidal wave propagating around NZ. The resulting phase difference across Cook Strait creates strong tidal streams. Source: Walters et al. (note 10); Vennell, R., “Observations of the Phase of Tidal Currents Along a Strait,” Journal of Physical Oceanography, 28:1570–1577, 1998.↩︎

24. Cook Strait tidal dynamics: the tides on the Tasman Sea (west) and Pacific Ocean (east) sides of NZ are driven by different components of the oceanic tidal wave propagating around NZ. The resulting phase difference across Cook Strait creates strong tidal streams. Source: Walters et al. (note 10); Vennell, R., “Observations of the Phase of Tidal Currents Along a Strait,” Journal of Physical Oceanography, 28:1570–1577, 1998.↩︎

25. Cook Strait tidal dynamics: the tides on the Tasman Sea (west) and Pacific Ocean (east) sides of NZ are driven by different components of the oceanic tidal wave propagating around NZ. The resulting phase difference across Cook Strait creates strong tidal streams. Source: Walters et al. (note 10); Vennell, R., “Observations of the Phase of Tidal Currents Along a Strait,” Journal of Physical Oceanography, 28:1570–1577, 1998.↩︎

26. Admiralty Tidal Stream Atlases use the 13-chart format (HW-6 through HW+6) as a standard presentation. Each chart shows the tidal stream direction and rate (spring/neap) at representative positions across the area. Source: UK Hydrographic Office, Admiralty Tidal Stream Atlas NP 264 (Cook Strait equivalent would be produced for NZ).↩︎

27. Foveaux Strait tidal streams: stream rates of 2–3 knots are reported in the NZ Nautical Almanac and in LINZ chart information. The strait is approximately 35 km wide at its narrowest and is an important commercial and fishing route. Source: LINZ, NZ Nautical Almanac; NZ Navy Hydrographic Office chart data.↩︎

28. Hauraki Gulf tidal streams are described in the LINZ NZ Nautical Almanac and in NZ Hydrographic Office publications. Stream rates in the main shipping channels are moderate (1–2 knots) but increase in narrow passages between islands. Source: LINZ.↩︎

29. Kaipara Harbour is NZ’s largest harbour by area (approximately 947 km²). The tidal prism (volume of water exchanged each tide) is enormous, creating powerful tidal streams at the entrance. The Kaipara bar has claimed over 100 vessels and is one of NZ’s most dangerous navigational hazards. Source: Heath, R.A., “A Review of the Physical Oceanography of the Seas Around New Zealand,” New Zealand Journal of Marine and Freshwater Research, 19:79–124, 1985.↩︎

30. Hauraki Gulf tidal streams are described in the LINZ NZ Nautical Almanac and in NZ Hydrographic Office publications. Stream rates in the main shipping channels are moderate (1–2 knots) but increase in narrow passages between islands. Source: LINZ.↩︎

31. Pugh, D.T. and Woodworth, P.L., Sea-Level Science: Understanding Tides, Surges, Tsunamis and Mean Sea-Level Changes, Cambridge University Press, 2014. The standard modern reference for tidal science and prediction methodology. Chapters 3–4 cover harmonic analysis and prediction in detail. Also: Schureman, P., Manual of Harmonic Analysis and Prediction of Tides, US Coast and Geodetic Survey Special Publication No. 98, 1958 (revised). The classic reference for tidal harmonic methods, still widely used.↩︎

32. The International Hydrographic Organization (IHO) lists over 300 harmonic constituents with known frequencies. In practice, 25–60 constituents are sufficient for most port predictions. The five principal constituents (M2, S2, N2, K1, O1) capture the majority of the tidal signal at most locations. Source: IHO Standards for Hydrographic Surveys (S-44); also Pugh and Woodworth (note 1), Table 4.1.↩︎

33. LINZ publishes accuracy standards for NZ tidal predictions: predictions at standard ports are expected to agree with observed tides to within 10–15 minutes in time and 0.1 m in height under normal meteorological conditions. Predictions computed from the same harmonic constants should match LINZ published values more closely (within 5 minutes and 0.05 m), with any differences attributable to rounding or minor algorithmic variations. Source: LINZ Hydrographic Authority standards.↩︎

34. NZ sea level rise projections: the NZ Ministry for the Environment published guidance in 2017 based on IPCC AR5 scenarios, recommending planning for 0.5–1.0 m of sea level rise by 2100 (approximately 3–10 mm/year depending on emissions scenario). The current observed rate at NZ tide gauges is approximately 2–4 mm/year. Source: Ministry for the Environment, Coastal Hazards and Climate Change: Guidance for Local Government, 2017. https://www.mfe.govt.nz/↩︎

35. Before electronic computers, tide tables were computed manually by trained human computers using harmonic methods. The Liverpool Tidal Institute (later the Bidston Observatory) and the US Coast and Geodetic Survey both operated tidal prediction machines — analogue mechanical devices that summed harmonic components using gears and pulleys. The Doodson-Légé tide predicting machine at Bidston could compute one year of predictions for one port in approximately 25 minutes of cranking. If NZ can locate or construct such a device, it would dramatically reduce the manual computation labour. Source: Cartwright, D.E., Tides: A Scientific History, Cambridge University Press, 1999.↩︎

36. Land Information New Zealand (LINZ), “Tides and Tidal Streams.” LINZ publishes harmonic constants, tidal predictions, and secondary port data for NZ waters. Published in the annual New Zealand Nautical Almanac (not to be confused with the astronomical nautical almanac of Doc #10) and available digitally. https://www.linz.govt.nz/products-services/tides-and-tida...↩︎

37. LINZ, New Zealand Nautical Almanac, published annually. Contains tide tables for standard ports, secondary port differences, and tidal stream information for NZ waters. The standard port list and harmonic constants are updated periodically as new tidal analysis becomes available.↩︎

38. Cook Strait tidal dynamics: the tides on the Tasman Sea (west) and Pacific Ocean (east) sides of NZ are driven by different components of the oceanic tidal wave propagating around NZ. The resulting phase difference across Cook Strait creates strong tidal streams. Source: Walters et al. (note 10); Vennell, R., “Observations of the Phase of Tidal Currents Along a Strait,” Journal of Physical Oceanography, 28:1570–1577, 1998.↩︎

39. Pugh, D.T. and Woodworth, P.L., Sea-Level Science: Understanding Tides, Surges, Tsunamis and Mean Sea-Level Changes, Cambridge University Press, 2014. The standard modern reference for tidal science and prediction methodology. Chapters 3–4 cover harmonic analysis and prediction in detail. Also: Schureman, P., Manual of Harmonic Analysis and Prediction of Tides, US Coast and Geodetic Survey Special Publication No. 98, 1958 (revised). The classic reference for tidal harmonic methods, still widely used.↩︎