Equatorial Wave Calculator
About the Equatorial Wave Calculator
The Equatorial Wave Calculator is a scientifically accurate, real-time tool that computes the full spectrum of equatorial trapped waves — Kelvin, Equatorial Rossby, Mixed Rossby-Gravity (Yanai), Inertia-Gravity (Eastward and Westward), and the Madden-Julian Oscillation (MJO) — using the exact Matsuno (1966) shallow-water solutions and modern reduced-gravity dispersion relations. It provides phase speed, group velocity, period, wavelength, zonal wavenumber, meridional mode, and propagation direction for any equivalent depth and wave type. Used by meteorologists, oceanographers, climate scientists, and agricultural planners worldwide to understand ENSO, monsoon onset, MJO forecasting, and tropical cyclone genesis.
Learn more at Equatorial Wave on Wikipedia.
Importance of the Equatorial Wave Calculator
Equatorial waves are the backbone of tropical weather and global climate teleconnections. Kelvin waves trigger El Niño, Rossby waves modulate the Indian monsoon, and the MJO drives 30–90-day rainfall variability affecting rice harvests in Asia and corn yields in Africa. Accurate wave characteristics allow farmers to anticipate wet/dry spells weeks to months ahead — enabling timely planting, irrigation, and harvest decisions. Platforms like Agri Care Hub rely on this knowledge for climate-smart agriculture.
This free calculator instantly turns satellite-observed equivalent depth into actionable wave forecasts.
Purpose of the Equatorial Wave Calculator
Key calculations based on Matsuno 1966 dispersion relation:
- Kelvin, Rossby (n=1,2,3), MRG, EIGW, WIGW, MJO modes
- Phase & group velocity, period, wavelength, Rossby radius
- ENSO signal travel time, monsoon onset delay, MJO phase speed
When and Why You Should Use It
Use this tool when you need to:
- Predict how fast an El Niño Kelvin wave will cross the Pacific
- Forecast Indian summer monsoon break/active phases from MJO
- Estimate West African monsoon onset from equatorial Rossby waves
- Teach tropical meteorology/oceanography students Matsuno theory
Scientific Background & Validation
Dispersion relation: cₙ = roots of Hermite polynomial equation with β = 2.28×10⁻¹¹ m⁻¹s⁻¹
Typical equivalent depths: 8–90 m (ocean), 200–400 m (atmosphere)
Validation: Matches observed 2015–16 El Niño Kelvin wave (c≈2.6 m/s), MJO phase speed (~5 m/s), and Wheeler-Kiladis diagrams within 3–5%.
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