Tides

Predict → Check → Explain

The core tide lab. Everything in this module has been building to it.

Prerequisites: What causes tides, The lunar day, Spring and neap.

Time: 45 minutes, plus a return visit if you are observing in person.

The question

What tide do you think it will be at this time, where you are?

Do not look anything up yet. That is the whole point of the exercise.

Step 1: Assemble what you know

Write these down:

1. The time and date you are asking about
2. Your location, or a tide station you have chosen from data/
3. The Moon's phase: moonfield phase
4. When the Moon crosses your meridian: moonfield moon, the transit time

moonfield phase --no-art
moonfield moon

Step 2: Predict, in writing, before checking anything

Write down, on paper or in a file:

The reasoning line is the most important one. In a month you will not remember what you were thinking, and "I was wrong" is far less useful than "I was wrong because I assumed high water coincides with the Moon overhead."

Being wrong here is expected. It is not a failure state; it is the data.

Step 3: What the simple model says

moonfield tide rough

ROUGH TIDE ESTIMATE -- FOR LEARNING ONLY, NOT FOR NAVIGATION
============================================================

Brighton (50.8225N, 0.1372W)
Time: 2026-08-16 13:00 BST  (2026-08-16 12:00 UTC)

The sky right now
-----------------
  - Moon crosses your meridian at 16:04 BST
  - between springs and neaps
  - Relative range factor: 1.09 (1.00 is the Moon alone; 1.46 at springs, 0.54 at neaps)
  - Lunitidal interval in use: 0.00 hours

Predicted events
----------------
  > Sun 16 Aug 16:04 BST  HIGH  (Moon overhead)
    Sun 16 Aug 22:16 BST  LOW   (quarter cycle after Moon overhead)
    Mon 17 Aug 04:26 BST  HIGH  (Moon underfoot)

Compare with your prediction. Did you agree with the model?

Note what the model has assumed: high water arrives exactly when the Moon is overhead. Hold that thought.

Step 4: Check reality

Now, and only now, get real data.

If you live near tidal water, find your nearest official tide station:

Better still: go and look. Photograph the same spot every hour for six hours. That is a real observation, and it beats any table.

If you do not live near tidal water, use a supplied dataset:

docs/04-tides/data/brest-2026-08.csv        Brest, France: textbook semidiurnal
docs/04-tides/data/hilo-2026-08.csv         Hilo, Hawaii: mixed tides
docs/04-tides/data/fremantle-2026-08.csv    Fremantle, Australia: diurnal, tiny range
docs/04-tides/data/burntcoat-2026-08.csv    Bay of Fundy: 16 m range

Each has published high and low water times. Read the header; it says where the numbers came from.

Step 5: Quantify the discrepancy

Do not eyeball it. Get a number.

Use your own observed high waters if you have them. If you do not yet, this repository ships real published tide tables you can borrow: the three times below are actual high waters at Brest, taken from data/brest-2026-08.csv.

moonfield tide compare --lat 48.383 --lon -4.495 --timezone UTC \
    --date "2026-08-16T12:00:00Z" \
    --observed 2026-08-16T04:06 \
    --observed 2026-08-16T16:32 \
    --observed 2026-08-17T04:56

Comparison
----------
  Observed               Model predicted         Model error
  2026-08-16 04:06       2026-08-16 03:00          1.09 h early
  2026-08-16 16:32       2026-08-16 15:22          1.15 h early
  2026-08-17 04:56       2026-08-17 03:45          1.18 h early

What the difference is telling you
----------------------------------
Average model error: -1.14 hours
Spread across your samples: 0.09 hours

Read those two summary numbers carefully, because they are the whole point of the step. The model is off by more than an hour every time, and it is off by almost exactly the same amount every time. An error that large would be alarming if it were random. An error that consistent is barely an error at all: it is a missing constant, sitting there waiting to be measured.

Step 6: Explain

Now the real work. Answer these in writing:

Was the error consistent or scattered?

Consistent: every prediction off by roughly the same amount, in the same direction. That is not noise. A steady offset is a missing constant, and a missing constant is fixable.

Scattered: the error varies between tides. A single constant will not fix that; something more structural is wrong.

If consistent: you have measured the lunitidal interval

The lunitidal interval is the characteristic lag at your port between the Moon crossing your meridian and high water actually arriving. It exists because the tidal bulge is not a rigid thing that rides under the Moon; it is a wave, and waves take time to travel across a shelf and up an estuary.

It is a property of the place, not of the sky. It cannot be computed from astronomy. It has to be measured.

Feed yours back in:

moonfield tide rough --lat 48.383 --lon -4.495 --interval 1.14

Then compare again. The error should mostly vanish, because you have just handed the model the one number it could never have worked out for itself.

You have just calibrated a physical model with local measurements. That is the lesson.

If scattered: something structural is missing

Likely causes:

• A strong diurnal component. Your coast has a once-daily as well as a

twice-daily tide, so consecutive highs are genuinely unequal. Hilo shows this.

• Shallow-water distortion. In shallow water the crest travels faster than

the trough, so the rise and fall take unequal times.

• Weather. A deep low-pressure system raises sea level by roughly 1 cm per

millibar. Onshore wind piles water up. A storm surge can exceed the astronomical tide entirely.

• Resonance. If your basin's natural period is near 12.4 hours, the tide is

amplified enormously and its phase is set by the basin, not the Moon.

What information was missing?

The most useful question in the lab. The two-bulge model knows about the Moon, the Sun and your latitude. It does not know:

• The shape of your coastline
• The depth of the water
• The natural period of your basin
• Friction
• Today's weather

Which of these do you think matters most where you are?

Step 7: Compare four coastlines

Run the same lab against all four supplied datasets. They behave completely differently:

Same physics. Same Moon. Four completely different answers.

That is the most important observation in this module.

Four things that are not the same

The lab forces a distinction that is easy to blur:

A tide table is not an observation. It is a very good model, fitted to years of measurements at that specific station. Even it can be half a metre out in a storm.

Checkpoint

• I made a written prediction before checking anything
• I compared it against an authoritative source
• I quantified the discrepancy rather than eyeballing it
• I can say whether my error was consistent or scattered
• I know what a lunitidal interval is and why it cannot be computed
• I fed a measured interval back in and saw the error shrink
• I can name three things the model does not know about my coast
• I can distinguish model prediction, published prediction, and observation

Try it yourself

1. Run the lab for all four supplied stations. Rank them by how badly the model

does, and explain the ranking.

1. Find the lunitidal interval for a port near you. Is it published anywhere?
2. Predict a week of tides using only your measured interval. Check them.
3. Find a day when a storm made a real tide differ from its published

prediction. How big was the surge?

1. Compare a spring high water with a neap high water. Is the ratio the ~1.3/0.7

the model predicted?

Questions to think about

• The two-bulge model is physically correct and practically useless. How can

both be true at once?

• If harmonic analysis needs a year of measurements at every station, what

happens at a coast nobody has ever instrumented?

• Your calibrated model now works for one port. What would it take to make it

work for the next port along the coast?

• Where else in life do you use a model whose local calibration you have never

checked?

Go deeper

• Why local tides are hard
• moonfield tide explain: the full ten-step walkthrough
• Read src/moonfield/tides.py, the model and its stated limits

Next: Why local tides are hard.