Monin-Obukhov Length

One of the measures of the planetary boundary layer is the Monin-Obukhov length (abbreviated "L" ). This parameter is a rough measure of the height at which turbulence is generated more by buoyancy than by wind shear. The M-O length is a fundamental scaling quantity in surface layer theory. Roughly speaking, it is a measure of the relative importance of mechanical and thermal forcing on atmospheric turbulence. When L is large and negative, mechanical forces dominate over thermal forces. On a windy day with little sunshine, L might have a value of -150 m. When L is small and negative, for example, -10 m, the turbulence is driven by convection. At night, when L is positive, the temperature stratification tends to suppress the mechanical generation of turbulence. The Monin-Obukhov length scale has applications in boundary layer modeling and in quality control.

The Monin-Obukhov length is typically used to determine the wind speed profile in the stable surface layer. Meteorologists, as a standard, measure the wind speed profile at a height of 10m. Monin-Obukhov lengths are calculated by many air quality models, given several variables. A detailed description of this calculation, and how it is used in determining the windspeed profile in the stable surface layer, is provided along with a Monin-Obukhov and wind speed profile calculator.

The Monin-Obukhov length is a key component of the Monin-Obukhov similarity hypothesis which states that surface layer quantities, when properly nondimensionalized, become universal functions of z/L where z is the height above ground (in meters) and L is the Monin-Obukhov length. The Monin-Obukhov length scale, L, is a fundamental scaling quantity in surface layer theory. Roughly speaking, it is a measure of the relative importance of mechanical and thermal forcing on atmospheric turbulence.

As we shall describe later, newer air quality models (such as AERMOD) use the Monin-Obukhov Similarity Theory to characterize turbulence and other PBL processes. Turbulence is produced by two primary mechanisms: wind shear and buoyancy. There are equations for many PBL parameters, such as the friction velocity, convective velocity, and the Monin-Obukhov Length, that are solved iteratively by the model.

The friction velocity is a measure of the shear contribution to turbulence. The convective velocity is a measure of the contribution due to buoyancy. The theoretical height at which these two scales become equal is known as the Monin-Obukhov Length.

The Monin-Obukhov length is also an objective measure of stability in the atmosphere. A positive value indicates stable conditions, while a negative value indicates unstable (convective) conditions. The larger the magnitude of the number, the weaker the relevant stability (ie. -5 is very unstable while -100 would only be slightly unstable).