Ocean lab

Tides — pick a NOAA CO-OPS station (a common one, its id, or search the 1,300+ stations with harmonic constants), a start date and a number of days. The tool fetches the station’s harmonic constituents and datums and computes the tide itself:

Waves — linear (Airy) wave theory for any depth: the dispersion relation ω² = gk·tanh(kh) is solved exactly (Newton’s method), giving wavelength, phase and group speed, the deep, intermediate or shallow regime, energy E = ρgH²/8 and power E·c_g per metre of crest, the Miche and depth-limited (H = 0.78 h) breaking heights, shoaling K_s = √(c_g0/c_g) and refraction over straight parallel contours (Snell’s law). The chart follows the wave from deep water to where it breaks. Wind waves grows a sea from wind speed, fetch and duration with the Shore Protection Manual (USACE 1984) deep-water equations (JONSWAP-based): fetch-limited, duration-limited or fully developed.

Seawater (TEOS-10) — practical salinity, in-situ temperature and pressure give Absolute Salinity, Conservative Temperature, potential temperature, in-situ and potential density (σ₀ to σ₄), α, β, sound speed, the freezing point and depth. The functions are a port of GSW-C, the TEOS-10 Gibbs SeaWater toolbox (75-term density polynomial). The T–S diagram draws σ₀ isopycnals; import a CTD cast as CSV (or use the demo cast) to plot it there and as profiles of Θ, S_A, σ₀ and sound speed, with the sound-speed minimum (the SOFAR channel).

Currents — the Coriolis parameter f = 2Ω·sin φ, β, the inertial period 2π/|f|, wind stress (Large and Pond drag), Ekman transport τ/(ρf) at 90° to the wind, Ekman depth and surface current (empirical, from Stewart’s Introduction to Physical Oceanography, or from an eddy viscosity), an animated Ekman spiral, and the geostrophic current from a sea-surface slope.

Buoys — NOAA National Data Buoy Center realtime observations for a station: significant wave height, dominant and average period, wave and wind direction, wind and gust, water and air temperature. NDBC’s files can’t be read by a web page directly (no CORS headers), so live data comes through the gitwebsite app’s companion; without it the tab shows a recorded sample from buoy 46026 off San Francisco.

TEOS-10: every check value in GSW-C’s gsw_check_data.h (version 3.05) for the functions used — CT from t, t and θ from CT, ρ, specific volume, σ₀, α, β, sound speed, freezing point, z ↔ p, S_R — agrees to within GSW’s own tolerance.

Tides: for San Francisco, Boston and Pensacola (17–18 Oct 2026) the hourly heights agree with NOAA’s predictions to within 2 cm (RMS about 1 cm), high and low water times within 10 minutes; the constituent speeds match NOAA’s listed speeds and M2’s node factor swings between 0.963 and 1.038 over the nodal cycle, as Schureman tabulates.

Waves: h/L against the h/L₀ table of the Shore Protection Manual (Appendix C), deep and shallow limits, and the shoaling minimum K_s = 0.913.

Ekman depths against Stewart’s Table 9.2 (75 m at 15° and 45 m at 45° for a 5 m/s wind).

No storm surge, wind set-up, river flow or pressure effects — astronomical tide only, like any tide table. Constituents beyond NOAA’s standard 37 are skipped. Subordinate stations (with offsets rather than harmonic constants) aren’t supported.

Absolute Salinity needs the SAAR atlas (a large data file); here S_A = S_R + the δS_A you enter (0 by default). Not for the Baltic (its own composition).

Waves are linear and monochromatic over straight, parallel contours; no friction, diffraction or wave–current interaction. Wind-wave growth is the 1984 SPM method in deep water; expect ±20%.

Ekman theory assumes steady wind, constant eddy viscosity and deep water, and fails near the equator.

NDBC data is provisional and the buoy may be adrift or off station; check NDBC’s station page.