Equilibrium Beach Profile Dean Parameter
Fit Dean h=A x^(2/3) through the supplied shoreline origin by depth-residual least squares; not a universal grain-size lookup or free-origin profile fit.
Description
Dean's equilibrium profile describes depth increasing with offshore distance to the two-thirds power.
Dean's equilibrium profile describes depth increasing with offshore distance to the two-thirds power. The origin must be fixed before fitting.
Fit Dean h=A x^(2/3) through the supplied shoreline origin by depth-residual least squares; not a universal grain-size lookup or free-origin profile fit.
When to use Equilibrium Beach Profile Dean Parameter
Use this tool to fit Dean h=A x^(2/3) through the supplied shoreline origin by depth-residual least squares; not a universal grain-size lookup or free-origin profile fit.
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 Equilibrium Beach Profile Dean Parameter 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 offshoreDistancesM, positiveWaterDepthsM using the field table and calculation rules, then run the tool.
- Read fittedDeanParameterMToOneThird, rootMeanSquaredDepthResidualM. 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 |
|---|---|---|---|
| offshoreDistancesM | Offshore distances m | list of number | Required |
| positiveWaterDepthsM | Positive water depths m | list of number | Required |
Align positive offshore distances and positive depths from the supplied shoreline origin. Fit through zero by depth-residual least squares and return A in m^(1/3) and depth RMSE.1
Paired lists must be nonempty and have equal lengths.
A = Σ depth × distance^(2/3)/Σ distance^(4/3) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| fittedDeanParameterMToOneThird | Fitted dean parameter m to one third | number |
| rootMeanSquaredDepthResidualM | Root mean squared depth residual m | number |
{
"input": {
"offshoreDistancesM": [
1,
8,
27
],
"positiveWaterDepthsM": [
2,
8,
18
]
},
"output": {
"fittedDeanParameterMToOneThird": 2.0000000000000004,
"rootMeanSquaredDepthResidualM": 2.5639502485114184e-16
}
}Limitations and assumptions
No free-origin fit or universal grain-size lookup is performed.
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 Closure Depth Hallermeier Formula: Evaluate a caller-coefficient Hallermeier closure-depth screen using the wave height exceeded for the caller selected duration; empirical applicability and wave statistic selection remain external. For a complementary task, use Beach Nourishment Fill Volume: Integrate measured target-minus-existing profile fill on supplied stations and length, then account for retention; target cuts error rather than silently crediting cut volume as nourishment.
References
-
Equilibrium Beach Profile Dean Parameter — tool.io
Similar or alternative tools
- Closure Depth Hallermeier Formula
Evaluate a caller-coefficient Hallermeier closure-depth screen using the wave height exceeded for the caller selected duration; empirical applicability and wave statistic selection remain external.
- Beach Nourishment Fill Volume
Integrate measured target-minus-existing profile fill on supplied stations and length, then account for retention; target cuts error rather than silently crediting cut volume as nourishment.