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DWR Wave Buoy Data Interpreter (Hs, Hmax, Tz, Tp, Direction)

Interpret Directional Waverider buoy records and test Hmax against the rogue wave threshold.

Last reviewed by the myCalculator Editorial Team

Input Parameters

m
m
s
s
°
min

Calculation Results

Wave Statistics Verdict
Above Rayleigh expectation but within normal statistics
Hmax / Hs Ratio
1.82 (rogue threshold 2.00)
Sea Character
Swell-dominated — organised, long-crested
WMO Sea State
5 — Rough
Significant Wave Height (Hs)
2.8 m
Maximum Wave (Hmax)
5.1 m
Rayleigh Expected Hmax
4.68 m over 265 waves
Estimated Crest Height
3.06 m above still water
Zero-Crossing Period (Tz)
6.8 s
Peak Period (Tp)
11.5 s
Tz / Tp Ratio
0.591 — spectral bandwidth indicator
Wave Steepness
0.0388 — Moderate — typical mixed sea
Wave Direction
210° (SSW) — coming from
Wavelength at Tp
206.5 m
Wave Celerity at Tp
17.96 m/s (34.9 kts)
Waves in Record
265 over 30 min
Summary: This DWR record shows Hs 2.8 m with Hmax 5.1 m — a ratio of 1.82 against a Rayleigh expectation of 4.68 m. Above Rayleigh expectation but within normal statistics. The Tz/Tp ratio of 0.591 indicates swell-dominated from 210° (SSW).
Step-by-Step Calculation Solution
1.Directional Waverider (DWR) buoys report Hs, Hmax, Tz, Tp and direction per record.
2.Hmax/Hs = 5.1 / 2.8 = 1.82
3.N = Record / Tz = 1800 / 6.8 = 265 waves
4.Rayleigh Expected Hmax = Hs x sqrt(ln(N)/2) = 2.8 x 1.67 = 4.68 m
5.Rogue criterion: Hmax/Hs > 2.0 — not exceeded
6.Tz/Tp = 6.8 / 11.5 = 0.591 — Swell-dominated
7.Steepness = 2 pi Hs / (g Tz²) = 0.0388 — Moderate — typical mixed sea
8.L = gTp²/(2 pi) = 206.5 m | C = L/Tp = 17.96 m/s
9.Hs is the mean of the highest one-third of waves, equal to 4 x sqrt(m₀).

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Formula & How DWR Wave Buoy Data Interpreter (Hs, Hmax, Tz, Tp, Direction) Works

Mathematical Formula
Rogue if Hmax/Hs > 2.0 | Expected Hmax = Hs√(ln N / 2) | Steepness = 2πHs / gTz²

Directional Waverider buoys report a standard set of parameters each record, and the relationships between them reveal the character of the sea. The Hmax to Hs ratio tests whether the largest wave was statistically ordinary or abnormal — the accepted rogue wave definition is a ratio above 2.0. The Tz to Tp ratio separates locally generated wind sea, which is broad-banded with the two periods close together, from long-travelled groundswell, where a long peak period sits well above the zero-crossing period.

How to Calculate DWR Wave Buoy Data Interpreter (Hs, Hmax, Tz, Tp, Direction) (Step-by-Step)
  1. Enter Significant Wave Height Hs (m) (m): Input your target parameter value.
  2. Enter Maximum Wave Height Hmax (m) (m): Input your target parameter value.
  3. Enter Zero-Crossing Period Tz (s) (s): Input your target parameter value.
  4. Enter Peak Period Tp (s) (s): Input your target parameter value.
  5. Enter Mean Wave Direction (° from) (°): Input your target parameter value.
  6. Enter Record Length (minutes) (min): Input your target parameter value.
  7. Apply Formula: Calculate using Rogue if Hmax/Hs > 2.0 | Expected Hmax = Hs√(ln N / 2) | Steepness = 2πHs / gTz².
  8. Review Results: View exact computed answers, metrics, and worked mathematical proofs.
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Frequently Asked Questions (FAQs)

What qualifies as a rogue wave?

The accepted definition is a single wave whose height exceeds twice the significant wave height of the surrounding sea state. The Draupner wave of 1995 recorded a ratio above 2.2 and confirmed such waves occur more often than early models predicted.

How do I tell wind sea from swell in buoy data?

Compare Tz with Tp. A ratio above 0.85 indicates a broad-banded local wind sea, while a ratio below 0.7 means a narrow-banded swell that has travelled from a distant storm.

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