Mixing Height Calculator

Stable scaling (turbulence vs. stratification)

z_i = C · (u* / N)

• u* is friction velocity (m/s), a measure of near‑surface turbulent stress.
• N is the Brunt–Väisälä frequency (1/s), describing static stability.
• C is a dimensionless coefficient (site‑dependent).

Computing N from a potential temperature gradient

N = √[(g/θ₀) · (dθ/dz)]

• g ≈ 9.80665 m/s²
• θ₀ is a representative potential temperature (K)
• dθ/dz is the potential temperature gradient (K/m)

Neutral rotational scaling (Earth rotation limit)

z_i = C · (u* / |f|),   f = 2Ω sinφ

• Ω ≈ 7.292115×10⁻⁵ s⁻¹ is Earth’s rotation rate.
• φ is latitude (degrees).

Capping inversion option

If a strong inversion caps turbulence, the mixing height is often close to the inversion base height.

1. Pick a method that matches your data: stable, neutral, or capped.
2. Enter u* from surface fluxes (or an estimate from wind and roughness).
3. For stable cases, either enter N directly or compute it using θ₀ and dθ/dz.
4. For neutral scaling, provide latitude to compute the Coriolis parameter.
5. Click Calculate Mixing Height to see results above the form.
6. Use the CSV or PDF buttons to download a record of your run.

Tip: If your site has a known calibration, adjust C to match observations.

Values are illustrative and depend on local conditions.

1) Why mixing height matters

Mixing height is the effective depth of the turbulent layer that dilutes heat, moisture, and pollutants. A deeper layer generally reduces near‑surface concentrations, while a shallow layer can trap emissions and increase exposure during calm, stable periods.

2) Stable boundary layers and typical ranges

Stable conditions often occur at night when the ground cools and turbulence weakens. In many locations, stable mixing heights can be tens to a few hundreds of meters, especially under light winds. The stable scaling option links depth to friction velocity and atmospheric stability through u* and N.

3) Neutral conditions and rotation effects

Near‑neutral conditions are common with stronger winds or cloudy skies that limit surface cooling. When buoyancy effects are small, Earth’s rotation helps set an upper scale through the Coriolis parameter f. The neutral option uses latitude to compute f = 2Ωsinφ and estimates mixing height with u*/|f|.

4) Using a capping inversion from profiles

Soundings, lidar, and profilers often show a sharp temperature or potential temperature jump that caps turbulence. If the inversion is strong, the mixing height is frequently close to the inversion base. This option is practical for operational air‑quality workflows that already ingest profile products.

5) Inputs you should measure carefully

Friction velocity u* comes from surface stress and responds to roughness, wind speed, and stability. The Brunt–Väisälä frequency N reflects stratification and can be derived from potential temperature gradients. Small changes in these terms can shift mixing height noticeably.

6) Choosing coefficients C

The coefficient C is dimensionless and represents site and regime behavior. Values around 0.2–0.5 are often used for stable scaling, while 0.2–0.4 is common for neutral rotational scaling. If you have local observations, tune C so computed heights match observed layers.

7) Interpreting results for decisions

Use mixing height as an order‑of‑magnitude indicator, not a single “true” depth. Compare runs across methods to bracket uncertainty: stable scaling for nocturnal stability, neutral scaling for windy conditions, and inversion‑capped depth when profile evidence is strong.

8) Quality checks and common pitfalls

Watch for unrealistic inputs: near‑zero N implies weak stability and can inflate stable estimates, while very small f near the equator can produce large neutral values. Always review units, keep gradients consistent, and validate against local observations when available.

1) What is a typical mixing height during the day?

Daytime convective mixing heights often range from about 1,000 to 2,500 meters, depending on surface heating, moisture, and wind. Coastal or cloudy conditions may keep values lower.

2) Why can mixing height be very small at night?

Nighttime surface cooling increases stability and suppresses turbulence. With weak winds, the turbulent layer can shrink to tens or a few hundreds of meters, trapping pollutants close to the ground.

3) Which method should I choose in this calculator?

Use stable scaling when stratification is clearly stable, neutral scaling when buoyancy is weak and winds are stronger, and inversion‑cap when a profile shows a strong, well‑defined capping inversion.

4) What does friction velocity u* represent?

u* is a turbulence scale related to surface stress. Higher u* usually indicates stronger mechanical mixing from wind interacting with surface roughness and can increase estimated mixing height.

5) How do I get Brunt–Väisälä frequency N?

You can input N directly from a profile product, or compute it using a potential temperature gradient. Positive dθ/dz indicates stable stratification, producing a real, positive N.

6) Why does latitude matter for neutral scaling?

Latitude sets the Coriolis parameter f, which represents rotational influence on atmospheric flow. Smaller |f| generally allows larger rotational length scales, increasing the neutral mixing height estimate.

7) Are these results suitable for regulatory reporting?

They are best used as supportive estimates and screening values. For formal reporting, compare against local observations or approved meteorological models, and document inputs, coefficients, and the selected regime.