Judge atmospheric stability from temperature gradients and wind shear. Choose gradient or bulk inputs wisely. Save your outputs with clean CSV and PDF files.
These rows demonstrate typical values and outcomes.
| Method | g | θ | Thermal term | Shear term | Ri | Interpretation |
|---|---|---|---|---|---|---|
| Gradient | 9.80665 | 300 | dθ/dz = 0.010 K/m | du/dz = 0.020 s⁻¹, dv/dz = 0.010 s⁻¹ | 0.654 | Stable; reduced turbulence |
| Gradient | 9.80665 | 290 | dθ/dz = -0.005 K/m | |dU/dz| = 0.020 s⁻¹ | -0.423 | Unstable; convection likely |
| Bulk | 9.80665 | 300 | Δθ = 2 K over Δz = 100 m | ΔU = 5 m/s | 0.131 | Shear can sustain mixing |
A common critical value is near 0.25. Negative values suggest buoyant instability. Larger positive values indicate stronger stability and weaker turbulence.
The Richardson number (Ri) is a stability index comparing buoyancy to wind shear. It is dimensionless because stratification and shear are expressed as rates. When buoyancy dominates, vertical motion is resisted and turbulence weakens. When shear dominates, mixing increases, even in slightly stable layers.
The gradient form uses local derivatives, such as dθ/dz and du/dz, making it suitable for profile data from towers, radiosondes, or model levels. The bulk form uses layer differences, Δθ, ΔU, and Δz, and is useful when only two heights are available or when averaging over a mixed layer.
Many applications use a critical value near Ri ≈ 0.25. Values below this often indicate shear-driven turbulence can persist. Values above it imply increasing suppression of turbulence and stronger stratification control. Negative Ri occurs when dθ/dz is negative, suggesting buoyant instability and convection potential.
In near-surface daytime conditions, Ri is frequently near zero or negative due to convective heating. At night, stable stratification can push Ri above 0.25, especially with weak winds. In elevated inversions, Ri may exceed 1, indicating very stable conditions where waves and intermittent mixing dominate.
In oceans and lakes, Ri helps evaluate shear instabilities in thermoclines and haloclines. Large positive Ri typically corresponds to a sharp density gradient that resists mixing. Smaller Ri suggests shear from currents, tides, or wind forcing can overcome stratification, enhancing nutrient transport and heat exchange.
Because shear appears squared in the denominator, small errors in ΔU or derivatives can strongly affect Ri. Confirm consistent units: θ in kelvin, z in meters, and velocity in m/s. If shear is close to zero, Ri becomes undefined or extremely large, so treat results as diagnostic rather than absolute.
Negative Ri indicates unstable stratification; mixing can be buoyancy-driven even without strong wind shear. Very large positive Ri indicates strong stability; turbulence is suppressed and transport may occur through waves, drainage flows, or localized shear layers. Always pair Ri with context such as surface fluxes and terrain effects.
Start by choosing the method that matches your measurements. Enter a representative θ for the layer, then supply either derivatives or layer differences. Review the regime label and note the 0.25 reference threshold. Save multiple rows, then export CSV for analysis and PDF for documentation in field reports.
1) What does a Richardson number below 0.25 imply?
It suggests shear is strong enough to maintain turbulence despite stable stratification. Mixing is more likely, and eddy transport can persist in boundary layers or shear zones.
2) Why can the calculator return an undefined result?
Ri divides by the squared shear term. If shear is zero, missing, or extremely small, the denominator collapses and the computed value becomes invalid or numerically unstable.
3) Should I use gradient or bulk Richardson number?
Use gradient Ri when you have vertical derivatives from a detailed profile. Use bulk RiB when you have two-level measurements or want a layer-averaged stability estimate.
4) Why is potential temperature used instead of air temperature?
Potential temperature removes pressure effects and better represents buoyancy changes with height. That makes Ri more consistent across elevations and pressure levels, especially in atmospheric applications.
5) What does a negative Richardson number mean?
Negative Ri indicates unstable stratification, usually from a negative dθ/dz. Buoyancy-driven convection is possible, and turbulence can occur even with modest wind shear.
6) Can Ri be used in oceans and lakes?
Yes. Replace θ with an appropriate density-related variable, and use current shear and density stratification. The same stability logic applies to thermoclines and haloclines.
7) How many decimals should I report?
For field summaries, three decimals is usually sufficient. Keep more precision when comparing model levels or performing sensitivity checks, especially when Ri is near 0.25.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.