Mixing height calculator form
Use morning sounding temperatures, an afternoon surface maximum, and optional transport details to estimate daytime mixing depth.
Example data table
| Scenario | Morning surface | Max surface | Level 1 | Level 2 | Level 3 | Wind | Estimated mixing height |
|---|---|---|---|---|---|---|---|
| Sample daytime case | 17 °C | 24 °C | 300 m / 15 °C | 900 m / 10 °C | 1500 m / 7 °C | 4.2 m/s | About 1,979 m |
| Stronger heating case | 16 °C | 28 °C | 400 m / 14 °C | 1100 m / 9 °C | 1800 m / 5 °C | 5.5 m/s | About 2,960 m |
Formula used
1) Rising parcel temperature
Tp(z) = Tmax - Γdz
The parcel starts at the forecast or observed afternoon surface maximum. It cools upward with the dry adiabatic lapse rate, Γd = 9.8 K/km.
2) Environmental layer line
Te(z) = Ti + m(z - zi)
Each sounding layer is treated as a straight segment. The slope m comes from the temperatures and heights of adjacent sounding levels.
3) Mixing height condition
Tp(z) = Te(z)
The mixing height is the first altitude where the rising parcel is no longer warmer than the environment. That intersection estimates the convective mixing top.
4) Optional transport metrics
VC = U × H and V = A × H
Ventilation coefficient uses wind speed U. Mixed air volume multiplies surface area A by mixing height H.
This approach is useful for screening and planning. It does not replace a full boundary-layer model, remote sensing profile, or regulatory dispersion run.
How to use this calculator
- Enter the morning surface temperature and the expected afternoon maximum temperature.
- Enter three sounding heights and their matching environmental temperatures.
- Select the temperature and altitude units used in your observations.
- Optionally add transport wind speed to estimate the ventilation coefficient.
- Optionally add an area value to estimate the total mixed air volume.
- Press the calculate button. The result block appears above the form.
- Review the graph, lapse rates, and solver note before using the estimate.
- Use the CSV or PDF buttons to export the result summary.
Frequently asked questions
1) What is mixing height?
Mixing height is the depth of the atmosphere where surface emissions and heat are actively blended by turbulence. A deeper layer usually allows better vertical dilution of pollutants, smoke, dust, and heat released near the ground.
2) Why does afternoon maximum temperature matter?
Daytime heating creates buoyant parcels. A warmer surface maximum gives the parcel more energy, so it can rise higher before matching the surrounding air temperature. That generally increases the estimated daytime mixing depth.
3) Why are sounding temperatures needed?
The sounding profile describes how environmental temperature changes with height. The calculator compares the rising parcel against that profile. Without the temperature structure aloft, there is no defensible way to estimate where buoyant mixing stops.
4) What does the graph show?
The graph overlays two lines: the environmental temperature profile and the dry adiabatic parcel path. Their first intersection marks the estimated mixing height. This visual check helps confirm whether the result comes from measured layers or extrapolation.
5) What is the ventilation coefficient?
The ventilation coefficient is wind speed multiplied by mixing height. It combines vertical dilution depth with horizontal transport strength. Larger values usually indicate better atmospheric dispersion conditions for many screening-level air quality applications.
6) When should I trust extrapolated results less?
Use extra caution when the parcel and environmental profile do not intersect within the measured sounding range. Extrapolated results depend on the last observed slope staying valid above the highest level, which may not reflect real inversions or profile curvature.
7) Can this calculator replace a full dispersion model?
No. This tool is a practical estimator for screening, planning, education, and quick sensitivity checks. Regulatory work or high-stakes forecasting may need richer meteorological data, turbulence schemes, remote sensing, and full dispersion modeling.
8) What inputs most strongly affect the result?
The largest drivers are surface heating, the lapse rate structure aloft, and any capping inversion. Stronger heating tends to raise the parcel line, while stable layers or inversions usually lower the mixing top and limit dispersion.