Gaussian Puff Dispersion Calculator

Formula Used

This calculator uses a 3D Gaussian puff model for an instantaneous release. The puff center moves with the wind: x0 = u·t, so the along-wind offset is dx = x − u·t.

• Q is the released mass (g).
• σx, σy, σz are dispersion standard deviations (m).
• The exp(−(z+H)²/(2σz²)) term is the ground-reflection image (optional).

How to Use This Calculator

1. Enter the released mass Q, wind speed u, and time t.
2. Set receptor coordinates (x,y,z) and release height H.
3. Choose a dispersion method: stability-based estimation or manual σ values.
4. Pick output units and enable ground reflection if appropriate.
5. Click Calculate to see the result above the form.
6. Use the CSV/PDF buttons to export the computed report.

Example Data Table

Example values below are computed using the same model and stability-based sigmas.

Note: This is a simplified screening model. For regulatory work, use site-approved dispersion tools and meteorology.

Professional Article

1) What Gaussian Puff Dispersion Represents

A Gaussian puff describes a short, instantaneous emission released into a moving atmosphere. Instead of assuming a steady plume, the model tracks a “packet” of contaminant as it travels downwind and spreads in three dimensions. This approach is widely used for screening-level assessments of accidental releases, odor events, or brief process upsets where the emission duration is small compared with transport time.

2) Key Inputs and Their Physical Meaning

The release mass Q controls total material available in the puff. Wind speed u advects the puff center to x0 = u·t, while receptor coordinates (x,y,z) define where concentration is evaluated. The effective height H represents the release elevation and any buoyant rise you choose to include.

3) Dispersion Parameters σx, σy, and σz

The standard deviations σx, σy, and σz quantify the puff’s spread along-wind, crosswind, and vertically. Larger sigma values produce lower peak concentrations and broader time/space influence. When σx is small, the arrival is sharper in time at a fixed receptor; when it is larger, the signal is smoother and more persistent.

4) Stability Class and Typical Ranges

Atmospheric stability reflects turbulence intensity. Unstable conditions (Class A–C) often occur under strong solar heating and promote rapid mixing, increasing sigmas and reducing peaks. Neutral conditions (Class D) are common in overcast or windy weather. Stable conditions (Class E–F) occur at night with weak winds, yielding smaller sigmas and potentially higher concentrations near the centerline.

5) Ground Reflection and Near-Surface Impacts

Many screening models include a reflection (image) term that mirrors the puff across the ground. This represents a no-flux boundary at the surface and can increase predicted concentrations near the ground compared with a free-space solution. Turn it off when modeling an elevated receptor far above the surface or when another boundary treatment is preferred.

6) Timing, dx, and Interpreting the Peak

The factor dx = x − u·t determines whether the puff center is upstream, directly over, or downstream of the receptor. Concentrations are highest when dx ≈ 0, meaning the center has reached the receptor distance at that time. If you are exploring worst-case timing, sweep t around t ≈ x/u while holding other parameters fixed.

7) Units, Reporting, and Exporting

The core computation returns g/m³, then converts to mg/m³ or µg/m³ for air-quality style reporting. The CSV/PDF exports capture inputs, sigma values, the computed offset dx, and the final concentration, supporting clear documentation of scenario assumptions.

8) Practical Use Cases and Limitations

Use this calculator for quick comparisons: assessing how stability, wind speed, or release height changes peak impacts at a receptor. Because sigmas are simplified screening estimates, results should be treated as indicative rather than definitive. For compliance or emergency response planning, confirm with site meteorology, terrain, and approved dispersion modeling procedures.

FAQs

1) When should I use a puff model instead of a plume model?

Use a puff model for short releases or changing conditions. A steady plume suits continuous emissions with stable wind and turbulence. Puff modeling better represents transient peaks and arrival timing.

2) What time t gives the maximum concentration at a fixed x?

Peak concentration typically occurs near t ≈ x/u because the puff center aligns with the receptor. Spread parameters and reflection can shift the peak slightly, so test nearby times.

3) Why does stability class affect the result so strongly?

Stability controls turbulence and mixing. Unstable air increases dispersion (larger sigmas) and lowers peaks. Stable air reduces mixing (smaller sigmas), often raising centerline concentrations for the same release.

4) What should I choose for σx if I do not know it?

A common screening choice is σx = σy. If you have time-series observations, increase σx to broaden the signal or decrease it for sharper timing. Manual σx is best when justified.

5) Does ground reflection always increase concentration?

Near the ground, reflection often increases predicted values because it adds an image contribution. For receptors well above the release height or in free-space assumptions, the difference may be small.

6) Can I model deposition or chemical reactions with this calculator?

No. This calculator treats the contaminant as conservative and non-depositing. Deposition, decay, or chemistry requires additional terms or specialized models with appropriate parameters and validation.

7) How accurate are the built-in sigma estimates?

They are screening approximations intended for quick comparisons, not final design. Local terrain, urban roughness, and site meteorology can change dispersion significantly. Use manual sigmas or approved tools for formal studies.