Technical Disclaimer

This utility is a "Crude Model" intended for educational and visualization purposes. It solves simplified hydrodynamic equations on a 5-minute grid. It does not account for local meteorological effects (storm surge), complex estuary shapes below 9km resolution, or precise harmonic constituents derived from observation. Do not use for navigation.

The Move to First-Principles Simulation

Most tide utilities rely on static look-up tables. We took a novel approach: simulating the Earth's oceans as a fluid dynamic system in real-time.

1. Global Bathymetry Grid

To predict tides anywhere on Earth without a database of ports, we first had to model the shape of the ocean floor. We utilize the ETOPO5 / TerrainBase dataset, a 5-minute global elevation grid.

Binary Compression

The original 37MB text dataset was converted into a highly optimized 16-bit Signed Integer Binary format. This allows our engine to perform random-access lookups for any coordinate on the globe in under 0.05 milliseconds.

9.3 Million Points

The grid contains 9,331,200 unique data points, covering the entire planet from North Pole to South Pole. This allows detection of continental shelves, deep ocean trenches, and shallow bays.

2. Hydrodynamic Amplification

Tides in the deep ocean are microscopic (less than 0.5 meters). They only become dangerous "tides" when they hit the coast. Our engine simulates this using Green's Law of fluid dynamics.

As a wave travels from deep water to shallow water, its velocity decreases, but its energy flux must remain constant. This forces the amplitude (height) to increase.

$$ H_{local} = H_{deep} \times \left( \frac{h_{deep}}{h_{local}} \right)^{\frac{1}{4}} $$

Where $H$ is wave height and $h$ is water depth. Our engine applies a Resonance Multiplier for depths shallower than 250m to simulate the "sloshing" effect seen on continental shelves.

3. Rotary Tide Physics (Amphidromic Systems)

Newton's Equilibrium Theory predicts a simple "bulge" dragging East-to-West. However, in the real world, the Coriolis Effect causes tidal waves to rotate around zero-points called Amphidromic Nodes.

Our engine simulates this behavior using Wave Superposition. Instead of a linear progression, the local water height is the sum of waves radiating from six major synthetic nodes:

North Atlantic (CCW)

South Atlantic (CW)

North Pacific (CCW)

South Pacific (CW)

Indian Ocean (CW)

Southern Ocean (CW)

For every pixel, the engine calculates the Azimuthal Phase Angle ($\phi$) relative to the nearest nodes and sums their influence, weighted by a Gaussian distance decay. This creates the organic "Pinwheel" rotation visible on the map.

$$ \eta_{total} = \sum_{i=1}^{6} A_i \cdot e^{-dist^2} \cdot \cos(\omega t - \phi_{rotary}) $$

Interference Patterns By summing multiple rotary waves, we recreate the complex interference patterns (standing waves) found in the mid-Pacific and Atlantic, without using any pre-recorded harmonic data.

Lunitidal Friction We compute the friction-induced delay based on wave celerity $ c = \sqrt{gh} $. Waves travel at ~700 km/h in the deep ocean but slow to ~30 km/h on the coast, creating a predictable phase lag.