Benoa, Bali
Mixed, mainly semidiurnal- Period
- 01 Jan 2026 — 01 Agu 2026212 days
- Datum
- Nol sensor stasiun (bukan MSL)
- gaps
- 6988 jam
- Source
- IOC Sea Level Station Monitoring Facility (UNESCO/IOC & VLIZ)
Source, licence and datum notes
IOC menyajikan data mentah terhadap nol sensor masing-masing stasiun. Tinggi di sini tidak merujuk MSL, LAT, maupun chart datum.
Licence: Akses terbuka dengan kewajiban sitasi (VLIZ/IOC, DOI 10.14284/482)
Flanders Marine Institute (VLIZ); Intergovernmental Oceanographic Commission (IOC) (2026): Sea level station monitoring facility. https://www.ioc-sealevelmonitoring.org — DOI 10.14284/482
Not for navigationThe official Indonesian tide tables are published by Pushidrosal.
The chart
The record
- Observed the water level the gauge actually recorded
- Predicted what the fitted constituents say it should be
- Residual the difference — weather, wind and instrument trouble
The rest is held out and predicted. Shorten the window and constituents start dropping out — the same Rayleigh criterion, moved by the window rather than by the length of the record.
Result
Request refused
S2 and K2 cannot be separated on a record of 141.3 days.
- S2 and K2 differ by only 0.0821°/h: separating them needs a record of 182.6 days, and 141.3 are available.
- K1 and P1 differ by only 0.0821°/h: separating them needs a record of 182.6 days, and 141.3 are available.
Record length: 141.3 days · Length required: 182.6 days
What follows is the largest set this window can still support: M2, S2, N2, K1, O1, Q1, M4, MS4.
- Condition number κ
- 1.45good
- Residual RMS
- 0.2020 m
- Mean level Z₀
- 6.8442 m
- Record length
- 141.3 days
Unexplained, over the fitted part
0.2020m
Mean distance between the black line and the blue one, over the part used to fit.
Unexplained, over the held-out part
0.2554m
Over the part deliberately not seen while fitting. This is the real test.
Constituents
Harmonic constituents
| Constituent | Amplitude H (m) | Phase g (°) | Lag (h) | Speed (°/h) | Period (h) | Nodal factor f | Nodal correction u (°) |
|---|---|---|---|---|---|---|---|
| M2255.555 | 0.6240±0.0051 | 51.3±0.5 | 1.77 | 28.984104 | 12.421 | 0.9659 | 0.79 |
| S2273.555 | 0.4032±0.0050 | 108.7±0.7 | 3.62 | 30.000000 | 12.000 | 1.0000 | 0.00 |
| K1165.555 | 0.2476±0.0045 | 358.8±1.0 | 23.86 | 15.041069 | 23.934 | 1.1068 | 2.86 |
| O1145.555 | 0.1647±0.0042 | 343.5±1.5 | 24.63 | 13.943036 | 25.819 | 1.1728 | -3.23 |
| N2245.655 | 0.1083±0.0051 | 28.2±2.7 | 0.99 | 28.439730 | 12.658 | 0.9659 | 0.79 |
| Q1135.655 | 0.0446±0.0042 | 325.4±5.4 | 24.29 | 13.398661 | 26.868 | 1.1728 | -3.23 |
| M4455.555 | 0.0105±0.0053 | 202.3±29.1 | 3.49 | 57.968208 | 6.210 | 0.9329 | 1.57 |
| MS4473.555 | 0.0061±0.0051 | 281.2±47.9 | 4.77 | 58.984104 | 6.103 | 0.9659 | 0.79 |
H is half the height of that constituent’s wave; g is how late it arrives behind the Moon or Sun, and the column beside it says the same thing in hours — g divided by the constituent’s speed. f and u are the 18.6-year corrections, applied and still shown.
The ± figure is one standard error, taken from the diagonal of the solve’s covariance matrix. It assumes the record’s noise is independent from hour to hour, and tidal residuals are not: weather lasts for days, so neighbouring hours are wrong in the same direction. The true uncertainty is larger than what is printed here — by how much, this site does not compute.
A property of the place, or of these months?
The same numbers, four different stretches of the record
This whole site rests on one claim: that amplitude and phase are properties of the place — what a coastline does to the same forcing. But every number above came from one particular stretch of 2026. Here the record is cut into 4 equal, non-overlapping pieces and each is fitted on its own. Where an amplitude barely moves between them it is behaving like a property of the harbour. Where it swings, the record is doing the work rather than the place.
- Stretch 1 01 Jan 2026 — 23 Feb 2026
- Stretch 2 23 Feb 2026 — 17 Apr 2026
- Stretch 3 17 Apr 2026 — 09 Jun 2026
- Stretch 4 09 Jun 2026 — 01 Agu 2026
| Constituent | Mean H (m) | Lowest — highest | Swing | Phase swing |
|---|---|---|---|---|
| M2 | 0.6472 | 0.6144 — 0.6731 | 9% | ±2.0° |
| S2 | 0.3684 | 0.2762 — 0.4827 | 56% | ±20.3° |
| K1 | 0.2607 | 0.1957 — 0.2988 | 40% | ±12.3° |
| O1 | 0.1648 | 0.1555 — 0.1725 | 10% | ±3.1° |
| N2 | 0.1198 | 0.1049 — 0.1375 | 27% | ±8.2° |
| Q1 | 0.0434 | 0.0383 — 0.0513 | 30% | ±10.2° |
| M4 | 0.0100 | 0.0074 — 0.0154 | 81% | ±39.5° |
| MS4 | 0.0078 | 0.0066 — 0.0089 | 29% | ±48.7° |
One constituent, from the start
How M2 came out of this record
The table above is the answer. This is the route to it, in this record’s own numbers — nothing simplified or rounded for the example.
- Step 1 — Where the Moon and Sun are. Every constituent has six Doodson numbers saying how many times each astronomical element enters its angle. For M2 they are 2 0 0 0 0 0, so its equilibrium argument is V(t) = 2τ. The element polynomials are from Meeus, Astronomical Algorithms (2nd ed.), chapters 22 and 47.
τ = mean lunar time · s = the Moon’s mean longitude · h = the Sun’s mean longitude · p = lunar perigee · N = the Moon’s ascending node · p′ = solar perigee.
Step 2 — Two columns, hour by hour. cos(V + u) and sin(V + u) are evaluated at every sample in the record. These are M2’s two columns of the design matrix; four consecutive hours of this record:
How M2 came out of this record Time (UTC) V(t)° cos(V+u) sin(V+u) M2’s share (m) Recorded (m) 12 Mar 2026 14:00 UTC 204.47 -0.9044 -0.4268 -0.5414 6.6980 12 Mar 2026 15:00 UTC 233.46 -0.5843 -0.8115 -0.6019 6.7090 12 Mar 2026 16:00 UTC 262.44 -0.1179 -0.9930 -0.5116 6.7330 12 Mar 2026 17:00 UTC 291.43 0.3781 -0.9258 -0.2932 6.7710 - Step 3 — Least squares picks one pair of numbers. The solve looks for the a and b that bring Σ (a·cos + b·sin) as close to the record as it can get, for every constituent at once. For M2 it returned a = 0.3766 and b = 0.4705. The last column above is a·cos + b·sin: what M2 alone contributes at that hour.
- Step 4 — Two lines of trigonometry. The pair (a, b) is amplitude and phase in another form: H = √(a² + b²) ÷ f = 0.6240 m, and g = atan2(b, a) = 51.3°. Exactly the numbers on M2’s row above. The division by f takes out the 18.6-year nodal correction, so the constant does not depend on which year you happened to observe.