Monin-Obukhov length

Another stability parameter often used in micrometeorology is the Monin-Obukhov length... 

Interpretation of the Monin-Obukhov Length L with Respect to Atmospheric Stability... 

The Monin-Obukhov length L is not a parameter that is routinely measured. Colder (1972), however, established a relation between the stability classes of Pasquill, the roughness height zo (see Section VII,B), and L. The results of his investigation are shown in Fig. 4. Alternatively, the local wind speed and cloud cover measurements are used to estimate the Pasquill stability class (Table IV). In addition, Colder developed a nonogram for relating the gradient Richardson number R-, to the more easily determined bulk Richardson number / (, ... 

Fig. 4. Relationship between Monin-Obukhov length L and roughness height Zo for various Pasquill stability classes. From Myrup and Ranzieri (1976).

The Monin-Obukhov length L can also be estimated from conventional meteorological data by first evaluating the parameter a (Fulle, 1975) ... 

From the definition of the Monin-Obukhov length, shear production of turbulence is confined to a layer of height of the order of L. Under convective conditions, then, we expect... 

Fig. 6. Variation of the power law index p with surface roughness and Monin-Obukhov length L (a) z = 10 m (b) z = 30 m. From Huang (1979).

This latter result can be expressed in terms of the friction velocity u, and the Monin-Obukhov length L as... 

Stability parameters (Monin-Obukhov length, Deardorff convective velocity... 

The stability of the atmosphere is clearly a major influence on the dispersion of a smoke-plume. If the plume comprised a CWA rather than a harmless tracer, then the atmospheric stability would have an important effect on the extent of the downwind hazard area and on the concentrations of agent experienced within that hazard area. Atmospheric stability can be determined by direct observation - as in Figures 1-5 -or by estimation of the Monin-Obukhov length-scale, L (m), which is a height proportional to the height above a surface at which thermal effects first dominate shear (momentum) effects (Pasquill, 1962), as defined in Equation (1) ... 

By definition the Monin-Obukhov length is the height at which the production of turbulence by both mechanical and buoyancy forces is equal. The parameter L, like the flux Richardson number, provides a measure of the stability of the surface layer. As we discussed, when Rf > 0 and therefore according to (16.69) L > 0 the atmosphere is stable. On the other hand, when the atmosphere is unstable, Rf < 0 and then L < 0. Because of the inverse relationship between Rf and L, an adiabatic atmosphere corresponds to very small (positive or negative) values of Rf and to very large (positive or negative) values of L. Typical values of L for different atmospheric stability conditions are given in Table 16.2. 

Use of the equations derived in this section requires estimation of the Monin-Obukhov length L. A number of approaches are available, including the profile and gradient methods using available measurements (Arya 1999). The simplest approach based on the Pasquill stability classes will be discussed in the next section. 

The Monin-Obukhov length L is not a parameter that is routinely measured. Recognizing the need for a readily usable way to define atmospheric stability based on routine observations, Pasquill (1961) proposed a discrete atmospheric stability classification scheme that was later modified by Turner (1969). The scheme relies on observations of near-surface (10 m) wind, solar radiation, and cloudiness. If these... 

Estimation of the Monin-Obukhov Length Estimate L for an agricultural area with windspeed at 10m equal to 2.5ms 1 and solar flux 500 Wm 2. 

The variables on which Fy and F, are assumed to depend are the friction velocity u, the Monin-Obukhov length L, the Coriolis parameter /, the mixed-layer depth zt, the convective velocity scale w, the surface roughness z.a, and the height of pollutant release above the ground h.s... 

We note that Myrup and Ranzieri chose the mixed-layer depth z, as the characteristic vertical lengthscale, whereas Shir uses the Ekman layer height, u /f. (Since L = oo under neutral conditions, the Monin-Obukhov length cannot be used as a characteristic length scale.)... 

We see that L is simply the height above the ground at which the production of turbulence by both mechanical and buoyancy forces is equal. The Monin-Obukhov length, like / /, provides a measure of the stability of the surface layer, that is (see Table 16.2),... 

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