Wave Runup & Freeboard Calculator
Reservoir wave-runup analysis for embankment dams: wind setup, significant wave height (SPM 1984 shallow-water formulas), wave period, Iribarren breaker classification, and runup R per Hunt/Saville with surface-roughness reduction. Returns total required freeboard above maximum design pool.
Wind setup S = U²·F/(1400·d) per Sibul / Saville (US units, mph, mi, ft → ft). Wave height and period from SPM 1984 shallow-water formulas. Runup uses Hunt's R/Hs = ξ for plunging waves with surface-type reduction γ_r.
Wind setup formulas
Sibul / Saville's empirical relation S = U²·F/(1400·d) gives wind setup in feet for U in mph, F in miles, and d_avg in feet. In SI: S = U²·F·c, with c = 1.16×10⁻⁶ for U in m/s, F in km, d in m, S in m. Both reduce to S ≈ τ·F/(γw·d) with the wind shear stress τ proportional to U². For very deep reservoirs (d > 100 ft) wind setup is negligible.
Wave height and period (SPM 1984)
The Shore Protection Manual shallow-water relations:
$$ \frac{gH_{m0}}{U^2} = 0.283\,\tanh\!\left[0.530\!\left(\frac{gd}{U^2}\right)^{0.75}\right]\,\tanh\!\left[\frac{0.00565\,(gF/U^2)^{0.5}}{\tanh[0.530(gd/U^2)^{0.75}]}\right] $$
$$ \frac{gT_p}{U} = 7.54\,\tanh\!\left[0.833\!\left(\frac{gd}{U^2}\right)^{0.375}\right]\,\tanh\!\left[\frac{0.0379\,(gF/U^2)^{1/3}}{\tanh[0.833(gd/U^2)^{0.375}]}\right] $$
Surface-roughness reduction γ_r
| Slope surface | γ_r |
|---|---|
| Smooth concrete, asphalt-paved | 1.00 |
| Single-layer cellular concrete blocks | 0.65 |
| Two-layer riprap on granular filter | 0.55 |
| Single-layer riprap, dumped | 0.65 |
| Grass-lined embankment | 0.85 |
| Asphalt or fabric mat | 0.85 |
Worked example
Example — small high-hazard embankment dam
References: USACE EM 1110-2-1420 (1997). Hydrologic Engineering Requirements for Reservoirs. USACE EM 1110-2-1100 (2002). Coastal Engineering Manual. Saville, T. (1962). Wave Runup on Composite Slopes. ASCE Trans. Hunt, I.A. (1959). Design of Sea-Walls and Breakwaters. ASCE J. Waterways & Harbors Div. Sibul, O.J. (1955). Laboratory Study of the Generation of Wind Waves in Shallow Water. USACE BEB Tech. Memo 72.
Related tools
- Riprap sizing — size the upstream slope-protection layer
- Reservoir routing — find max pool elevation during IDF
- Gravity dam stability — wave loads on concrete dams