Disclosure
Method
What is computed, from which record, by what means, and how much is left unexplained.
The astronomy
Each constituent’s equilibrium argument is computed from the Doodson formulation over six astronomical arguments: mean lunar time τ, the mean longitude of the Moon s, of the Sun h, of lunar perigee p, of the ascending node N, and of perihelion p′. The polynomials are from Meeus, Astronomical Algorithms (2nd ed.), chapters 22, 25 and 47.
Constituent speeds are derived from the rates of change of those six elements — not one frequency is written into the code as a literal. The test pnpm test:astro checks them against Schureman’s published tables (1958) to 1e-6 °/h.
The nodal corrections f and u follow Schureman’s compact series as presented in Pugh (1987) table 4:2, evaluated at the centre of the fit window. Their values are shown in the constituent table rather than folded silently into the constants.
The fit
The sea level model is η(t) = Z₀ + Σ f·H·cos(V(t) + u − g). It is linear in the pair (a, b) = f·H·(cos g, sin g), so solving it is ordinary least squares. The normal matrix AᵀA is diagonalised by cyclic Jacobi rotation, which yields the solution, the singular values of A, and the condition number κ = σmax/σmin together.
κ is a required part of the result, not an optional diagnostic. The thresholds: κ < 10 good, < 100 fair, < 1000 marginal, anything beyond that poor.
The Rayleigh criterion is enforced before the solve. Two constituents can only be separated once the record reaches T = 360° / |σᵢ − σⱼ|; where it does not, the request is refused, naming the conflicting pair and the record length required. There is no path that returns unstable amplitudes as though they were results.
The constituent set
The standard set requested at every station: M2, S2, N2, K2, K1, O1, P1, Q1, M4, MS4. Every constituent this project defines:
A Doodson number is six digits saying how many times each astronomical element enters the constituent’s angle: τ s h p N p′, each offset by +5 so that negative coefficients still fit in one digit. M2 = 255.555 means 2τ and nothing else — twice mean lunar time, that is all it is. The constituent’s speed is derived from those six numbers rather than read from a frequency table. Doodson 1921; the printed form as in Schureman 1958, SP 98.
| Constituent | Doodson | Speed (°/h) | Period (h) | What it is |
|---|---|---|---|---|
| Sa | 056.555 | 0.0410686 | 8765.813 | Solar annual — seasonal, largely not gravitational |
| Ssa | 057.555 | 0.0821373 | 4382.906 | Solar semi-annual |
| Mm | 065.455 | 0.5443747 | 661.309 | Lunar monthly — the perigee cycle |
| Mf | 075.555 | 1.0980330 | 327.859 | Lunar fortnightly — declinational |
| Q1 | 135.655 | 13.3986609 | 26.868 | Larger lunar elliptic diurnal |
| O1 | 145.555 | 13.9430356 | 25.819 | Principal lunar diurnal |
| P1 | 163.555 | 14.9589314 | 24.066 | Principal solar diurnal |
| K1 | 165.555 | 15.0410686 | 23.934 | Luni-solar declinational diurnal |
| 2N2 | 235.755 | 27.8953548 | 12.905 | Second-order lunar elliptic |
| MU2 | 237.555 | 27.9682085 | 12.872 | Lunar variational |
| N2 | 245.655 | 28.4397295 | 12.658 | Larger lunar elliptic semidiurnal |
| NU2 | 247.455 | 28.5125832 | 12.626 | Larger lunar evectional |
| M2 | 255.555 | 28.9841042 | 12.421 | Principal lunar semidiurnal — usually the largest |
| S2 | 273.555 | 30.0000000 | 12.000 | Principal solar semidiurnal — M2’s spring-neap partner |
| K2 | 275.555 | 30.0821373 | 11.967 | Luni-solar declinational semidiurnal |
| MN4 | 445.655 | 57.4238338 | 6.269 | Shallow water, M2 interacting with N2 |
| M4 | 455.555 | 57.9682085 | 6.210 | Fourth harmonic of M2 — tidal asymmetry |
| MS4 | 473.555 | 58.9841042 | 6.103 | Shallow water, M2 interacting with S2 |
| M6 | 655.555 | 86.9523127 | 4.140 | Sixth harmonic of M2 |
The records, and what they produced
| Station | Period | days | gaps | Datum | κ | Residual RMS |
|---|---|---|---|---|---|---|
| Ambon, Maluku | 01 Jan 2026 — 01 Agu 2026 | 212 | 19 (38 h) | ioc-sensor-zero | 1.52 | 0.1516 m |
| Benoa, Bali | 01 Jan 2026 — 01 Agu 2026 | 212 | 69 (88 h) | ioc-sensor-zero | 1.53 | 0.1855 m |
| Bitung, Sulawesi Utara | 01 Jan 2026 — 01 Agu 2026 | 212 | 27 (707 h) | ioc-sensor-zero | 1.65 | 0.0758 m |
| Kolinamil, Pelabuhan Jakarta | 10 Jan 2026 — 31 Jul 2026 | 202 | 68 (740 h) | ioc-sensor-zero | 1.46 | 0.0856 m |
| Padang, Sumatera Barat | 01 Jan 2026 — 01 Agu 2026 | 212 | 13 (33 h) | ioc-sensor-zero | 1.52 | 0.0825 m |
| Sabang, Aceh | 01 Jan 2026 — 01 Agu 2026 | 212 | 64 (79 h) | ioc-sensor-zero | 1.53 | 0.0887 m |
| Semarang, Jawa Tengah | 01 Jan 2026 — 01 Agu 2026 | 212 | 36 (42 h) | ioc-sensor-zero | 1.52 | 0.1749 m |
| Surabaya, Jawa Timur | 01 Jan 2026 — 01 Agu 2026 | 212 | 78 (91 h) | ioc-sensor-zero | 1.52 | 0.0976 m |
The residual is observation minus model. It holds weather, surge and everything the harmonic model does not explain, and its RMS is the honest measure of the fit. It is never hidden or smoothed.
The Admiralty method
The Admiralty scheme here projects the record onto each constituent’s argument one at a time, then infers K2 from S2 (ratio 0.27) and P1 from K1 (ratio 0.331) using the classical inference relations. It is not a reproduction of the printed NP 159 tabulation with its filtering multipliers, and every constant is marked as directly determined or inferred.
Data sources and licensing
IOC Sea Level Station Monitoring Facility (UNESCO/IOC & VLIZ) (enabled)
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
Data disajikan apa adanya tanpa kendali mutu, sesuai disclaimer resmi fasilitas; sitasi wajib dan sudah dicantumkan pada setiap tampilan.
University of Hawaii Sea Level Center (unverified)
Caldwell, P. C., M. A. Merrifield, P. R. Thompson (2015), Sea level measured by tide gauges from global oceans, NOAA NCEI, doi:10.7289/V5V40S7W
Portal UHSLC melampirkan syarat atribusi per negara yang ditetapkan operator pemilik alat; untuk stasiun Indonesia operator itu BIG, dan syaratnya belum diverifikasi. Adapter tersedia, gerbang lisensi menutupnya.
Badan Informasi Geospasial (unverified)
Syarat redistribusi rekaman stasiun maupun produk Model Pasut belum diverifikasi. Tidak ada data BIG dalam repositori ini.