Monin-Obukhov Similarity Theory
Also known as: Monin-Obukhov, Similarity theory, Monin-Obukhov length scale
Monin-Obukhov similarity theory is a fundamental framework in boundary layer meteorology that describes how wind speed, temperature, and humidity vary with height near the surface. Published in 1954, it shows that normalized vertical profiles depend on a single dimensionless parameter—the Monin-Obukhov stability parameter—which quantifies the balance between mechanical turbulence and buoyant convection.
Key highlights
- Theoretically grounded in dimensional analysis and scaling arguments; similarity framework is robust and widely applicable
- Enables prediction of profiles throughout the surface layer from measurements at one or few heights
- Universality of similarity functions simplifies parameterization in numerical models
- Successfully reproduces observed profiles across diverse environments (land, ocean, ice, vegetation)
Intuition
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How it works
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When to use it
Use Monin-Obukhov similarity theory for extrapolating wind and temperature measurements to different heights, for interpretation of surface-layer observations, for validation of land-surface and boundary-layer parameterizations in models, and for estimating fluxes from limited profile data.
Strengths & limitations
- Theoretically grounded in dimensional analysis and scaling arguments; similarity framework is robust and widely applicable
- Enables prediction of profiles throughout the surface layer from measurements at one or few heights
- Universality of similarity functions simplifies parameterization in numerical models
- Successfully reproduces observed profiles across diverse environments (land, ocean, ice, vegetation)
- Assumes quasi-steady-state, horizontally homogeneous, and flat-terrain conditions; violations in complex terrain or during rapid weather changes introduce errors
- Similarity functions are empirically derived with scatter; coefficients vary among published formulations
- Application limited to the surface layer (approximately lowest 10% of boundary layer); does not apply above this height
- Assumes vertical gradients of momentum and heat are co-linear; not always valid, especially in strongly stable conditions
Common pitfalls
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Applications
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Frequently asked
What is the Monin-Obukhov length and what does it represent physically?
The Monin-Obukhov length (L) is a length scale that represents the height at which buoyancy production of turbulent kinetic energy equals shear production. When L is small, buoyancy dominates (unstable); when L is large, shear dominates (stable). At neutral conditions, L approaches infinity.
What are neutral, unstable, and stable conditions?
Neutral conditions occur when the lapse rate equals the adiabatic rate; turbulence is driven by wind shear alone. Unstable conditions have stronger heating from below, enhancing buoyant turbulence. Stable conditions suppress turbulent mixing, reducing wind shear effects.
How do universal similarity functions differ between stability conditions?
In neutral conditions, the wind profile follows the logarithmic law. In unstable conditions, the profile is more curved due to enhanced mixing. In stable conditions, the profile is very steep because turbulence is suppressed. Different polynomial or exponential functions capture these shapes.
Can Monin-Obukhov theory predict temperature profiles?
Yes, the theory extends to temperature and humidity. The potential temperature gradient is parameterized using the same stability parameter, though the universal functions for heat differ from those for momentum.
Sources
- 1.Monin, A. S., & Obukhov, A. M. (1954). Basic laws of turbulent mixing in the ground layer of the atmosphere. Tr. Akad. Nauk SSSR, 24, 163-187.
- 2.Paulson, C. A. (1970). The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer. Journal of Applied Meteorology, 9(6), 857-861.
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Cite this page
ScholarGate. (2026, June 3). Monin-Obukhov Similarity. ScholarGate. https://scholargate.app/meteorology/monin-obukhov-similarity