Wave Setup Superelevation Surf Zone

Integrate steady wave-stress setup increments over supplied interval depths relative to the offshore start; neglects setup feedback on depth, currents and breaking closures.

Description

Wave radiation-stress changes can raise or lower mean water level.

Wave radiation-stress changes can raise or lower mean water level. Integrating that balance gives setup relative to a chosen offshore start.

Integrate steady wave-stress setup increments over supplied interval depths relative to the offshore start; neglects setup feedback on depth, currents and breaking closures.

When to use Wave Setup Superelevation Surf Zone

Use this tool to integrate steady wave-stress setup increments over supplied interval depths relative to the offshore start; neglects setup feedback on depth, currents and breaking closures.

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 Wave Setup Superelevation Surf Zone 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 crossShoreDistancesM, radiationStressesNPerM, intervalWaterDepthsM, waterDensityKgPerM3, gravityMPerSecondSquared using the field table and calculation rules, then run the tool.
Read setupAnomaliesM. 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
crossShoreDistancesM	Cross shore distances m	list of number	Required
radiationStressesNPerM	Radiation stresses n per m	list of number	Required
intervalWaterDepthsM	Interval water depths m	list of number	Required
waterDensityKgPerM3	Water density kg per m3	number	Required
gravityMPerSecondSquared	Gravity m per second squared	number	Required

Align increasing cross-shore stations and stresses with one positive depth per interval and positive density/gravity. Begin at zero anomaly and accumulate signed increments.^[1]

Paired lists must be nonempty and have equal lengths. Each sequence checked for increasing order must contain at least two strictly increasing values.

setup increment = −stress difference/(density × gravity × interval depth)

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
setupAnomaliesM	Setup anomalies m	list of number

json

{
  "input": {
    "crossShoreDistancesM": [
      0,
      10,
      20
    ],
    "radiationStressesNPerM": [
      100,
      80,
      40
    ],
    "intervalWaterDepthsM": [
      2,
      1
    ],
    "waterDensityKgPerM3": 1000,
    "gravityMPerSecondSquared": 10
  },
  "output": {
    "setupAnomaliesM": [
      0,
      0.001,
      0.005
    ]
  }
}

Limitations and assumptions

Depth is held fixed; currents, feedback and breaking closures are excluded.

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 Radiation Stress Flux SX: Compute monochromatic linear-wave shore-normal and cross radiation stresses with caller group/phase ratio and incident angle; no surf-zone closure is assumed. For a complementary task, use Runup Stockdon Total: Evaluate the empirical Stockdon 2006 general-beach R2 formulation and add supplied still water; not a dune overtopping probability, tsunami model or guaranteed maximum.

References

Wave Setup Superelevation Surf Zone — tool.io

Similar or alternative tools

Radiation Stress Flux SX
Compute monochromatic linear-wave shore-normal and cross radiation stresses with caller group/phase ratio and incident angle; no surf-zone closure is assumed.
Runup Stockdon Total
Evaluate the empirical Stockdon 2006 general-beach R2 formulation and add supplied still water; not a dune overtopping probability, tsunami model or guaranteed maximum.