Pierson Moskowitz Significant Height
Integrate a caller-parameter Pierson–Moskowitz omega^-5 spectrum analytically over full and finite frequency bands; reference wind-height convention is caller calibrated, not a measured buoy-spectrum alias.
Description
The Pierson–Moskowitz form represents a calibrated wind-wave spectrum.
The Pierson–Moskowitz form represents a calibrated wind-wave spectrum. Its full-band and finite-band variances yield different significant heights.
Integrate a caller-parameter Pierson–Moskowitz omega^-5 spectrum analytically over full and finite frequency bands; reference wind-height convention is caller calibrated, not a measured buoy-spectrum alias.
When to use Pierson Moskowitz Significant Height
Use this tool to integrate a caller-parameter Pierson–Moskowitz omega^-5 spectrum analytically over full and finite frequency bands; reference wind-height convention is caller calibrated, not a measured buoy-spectrum alias.
Gather the water, wave, current or profile observations and any supplied calibration constants. Confirm units and the stated coordinate and pressure conventions.
How to use Pierson Moskowitz Significant Height and understand its results
- Gather the water, wave, current or profile observations and any supplied calibration constants. Confirm units and the stated coordinate and pressure conventions.
- Enter referenceWindSpeedMPerSecond, gravityMPerSecondSquared, pmAlpha, pmBeta, frequencyBandHz, frequencyWindCoefficient using the field table and calculation rules, then run the tool.
- Read fullSpectrumSignificantHeightM, bandSignificantHeightM, peakPeriodSeconds. The explanation below defines the units, signs, ordering and any flags or placeholder values.
- If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.
| Input field | Meaning | Value type; see rules below | Requirement |
|---|---|---|---|
| referenceWindSpeedMPerSecond | Reference wind speed m per second | number | Required |
| gravityMPerSecondSquared | Gravity m per second squared | number | Required |
| pmAlpha | Pm alpha | number | Required |
| pmBeta | Pm beta | number | Required |
| frequencyBandHz | Frequency band hz | list of number | Required |
| frequencyWindCoefficient | Frequency wind coefficient | number | Required |
Use positive wind, gravity and spectral parameters with two increasing nonnegative Hz bounds. Derive the angular-frequency scale, analytically integrate full and bounded variance and report both heights plus peak period.1
m0 = alpha × gravity²/(4beta × frequency scale⁴); height = 4sqrt(m0) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| fullSpectrumSignificantHeightM | Full spectrum significant height m | number |
| bandSignificantHeightM | Band significant height m | number |
| peakPeriodSeconds | Peak period seconds | number |
{
"input": {
"referenceWindSpeedMPerSecond": 10,
"gravityMPerSecondSquared": 1,
"pmAlpha": 0.01,
"pmBeta": 1,
"frequencyBandHz": [
0,
0.015915494309189534
],
"frequencyWindCoefficient": 1
},
"output": {
"fullSpectrumSignificantHeightM": 20,
"bandSignificantHeightM": 12.130613194252662,
"peakPeriodSeconds": 66.43659586683667
}
}Limitations and assumptions
Wind-height convention and coefficients are caller-calibrated; this is not a measured buoy spectrum.
Numbers and computed results must be finite; overflow produces an error. Numeric lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Significant Height Spectral Moment: Integrate a supplied one-sided elevation PSD by trapezoidal spectral moments, returning Hm0 and Tm02; missing frequency bands are not extrapolated and buoy-heave aliases excluded. For a complementary task, use Wave Age Young Mature Classifier: Screen c_phase/u_star wave age using supplied wind and air-side drag, with caller phase classes; this convention is not c/U10 and does not identify fetch-limited growth by itself.
References
-
Pierson Moskowitz Significant Height — tool.io
Similar or alternative tools
- Significant Height Spectral Moment
Integrate a supplied one-sided elevation PSD by trapezoidal spectral moments, returning Hm0 and Tm02; missing frequency bands are not extrapolated and buoy-heave aliases excluded.
- Wave Age Young Mature Classifier
Screen c_phase/u_star wave age using supplied wind and air-side drag, with caller phase classes; this convention is not c/U10 and does not identify fetch-limited growth by itself.