Umbrella Cloud Spread Radius
Balance uniform-thickness axisymmetric umbrella intrusion volume into radius, excluding wind shear, entrainment and sedimentation; not a mapped ash footprint or aviation warning.
Description
An umbrella cloud spreads laterally near its atmospheric intrusion level.
An umbrella cloud spreads laterally near its atmospheric intrusion level. Volume added to a layer of fixed thickness increases its plan area.
Balance uniform-thickness axisymmetric umbrella intrusion volume into radius, excluding wind shear, entrainment and sedimentation; not a mapped ash footprint or aviation warning.
When to use Umbrella Cloud Spread Radius
Use this tool to balance uniform-thickness axisymmetric umbrella intrusion volume into radius, excluding wind shear, entrainment and sedimentation; not a mapped ash footprint or aviation warning.
Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.
How to use Umbrella Cloud Spread Radius and understand its results
- Gather the relevant observations and fitted model parameters. Use the stated units and time basis; keep paired observations aligned.
- Enter initialUmbrellaRadiusM, intrusionVolumeFluxM3PerSecond, elapsedSeconds, umbrellaLayerThicknessM using the field table and calculation rules, then run the tool.
- Read modelUmbrellaRadiusM, addedCloudAreaM2. 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 |
|---|---|---|---|
| initialUmbrellaRadiusM | Initial umbrella radius m | number | Required |
| intrusionVolumeFluxM3PerSecond | Intrusion volume flux m3 per second | number | Required |
| elapsedSeconds | Elapsed seconds | number | Required |
| umbrellaLayerThicknessM | Umbrella layer thickness m | number | Required |
Use positive layer thickness and nonnegative initial radius, flux and seconds. Divide added volume by thickness, then add that area to the initial circular cloud area.1
radius = sqrt(initial radius² + volume flux × time/(π × thickness)) Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.
| Output field | Meaning | Value type |
|---|---|---|
| modelUmbrellaRadiusM | Model umbrella radius m | number |
| addedCloudAreaM2 | Added cloud area m2 | number |
{
"input": {
"initialUmbrellaRadiusM": 10,
"intrusionVolumeFluxM3PerSecond": 3.141592653589793,
"elapsedSeconds": 100,
"umbrellaLayerThicknessM": 1
},
"output": {
"modelUmbrellaRadiusM": 14.142135623730951,
"addedCloudAreaM2": 314.1592653589793
}
}Limitations and assumptions
Uniform axisymmetric geometry excludes wind, entrainment and sedimentation; radius is a model scenario rather than an ash footprint.
Numbers and computed results must be finite; overflow produces an error. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.
Alternative or Complementary methods
Use Plume Mass Flux Buoyancy Estimate: Estimate signed heat-derived plume buoyancy flux using supplied source/ambient heat properties; neglects particle loading, moisture and momentum, retaining negatively buoyant thermal scenarios. For a complementary task, use Eruption Column Height Estimation: Predict a calibrated power-law eruption column height above vent and datum elevation; coefficient units follow supplied exponent and no wind/eruption-style-independent plume law is guaranteed.
References
-
Umbrella Cloud Spread Radius — tool.io
Similar or alternative tools
- Plume Mass Flux Buoyancy Estimate
Estimate signed heat-derived plume buoyancy flux using supplied source/ambient heat properties; neglects particle loading, moisture and momentum, retaining negatively buoyant thermal scenarios.
- Eruption Column Height Estimation
Predict a calibrated power-law eruption column height above vent and datum elevation; coefficient units follow supplied exponent and no wind/eruption-style-independent plume law is guaranteed.