Wave Base, Shoaling & Depth of Closure Calculator
Calculate wave base, shoaling coefficient and the Hallermeier depth of closure for coastal design.
Last reviewed by the myCalculator Editorial Team
Input Parameters
The Hallermeier He(12h) parameter — the wave height exceeded 12 hours a year.
Calculation Results
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Formula & How Wave Base, Shoaling & Depth of Closure Calculator Works
Orbital motion under a wave decays exponentially with depth, becoming negligible at about half the deep-water wavelength — the wave base. Shoreward of that, the wave feels the seabed, slows, shortens and steepens, with the shoaling coefficient describing the height change. The Hallermeier depth of closure marks the seaward limit of significant annual profile change and is the standard boundary used to define beach nourishment and coastal structure design envelopes. Worked example: a 9 second wave has a deep-water wavelength of 1.56 × 9² = 126 m, so the wave base is about 63 m. Below that depth the water is hardly disturbed by the wave. In 15 m of water the same wave feels the bottom, slows, shortens and steepens, which is how shoaling begins. This is why seabed features inshore have a strong effect on wave height and why waves refract toward the shore.
- Enter Deep-Water Wave Height (m) (m): Input your target parameter value.
- Enter Wave Period (s) (s): Input your target parameter value.
- Enter Local Water Depth (m) (m): Input your target parameter value.
- Enter Hs Exceeded 12 Hours per Year (m) (m): Input your target parameter value.
- Apply Formula: Calculate using
Wave Base = L₀/2 | Ks = √(Cg₀/Cg) | dc = 1.75 He - 57.9 (He² / gTe²). - Review Results: View exact computed answers, metrics, and worked mathematical proofs.
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Frequently Asked Questions (FAQs)
What is wave base?
The depth at which orbital motion becomes negligible, conventionally half the deep-water wavelength. Below it the seabed is undisturbed by that wave, which is why storm swell reworks sediment far deeper than local wind chop.
What is the depth of closure used for?
It defines the seaward limit of the active profile for beach nourishment design, coastal structure siting and sediment budget calculations. Beyond it, annual bed level change is negligible.
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