Unstable lapse rate

As long as A > r, the parcel continues to rise. Similarly, a parcel of air cooler than the surrounding air will continue to descend if its rate of adiabatic heating is less than the lapse rate in the atmosphere. Since vertical motion is enhanced by buoyancy, if A > F the atmosphere is called unstable. Lapse rates A for which A > F are called superadiabatic. 

When the actual temperature-decline-with-altitude is greater than 9.8°C/1000 m, the atmosphere is unstable, the Cj s become larger, and the concentrations of poUutants lower. As the lapse rate becomes smaUer, the dispersive capacity of the atmosphere declines and reaches a minimum when the lapse rate becomes positive. At that point, a temperature inversion exists. Temperature inversions form every evening in most places. However, these inversions are usuaUy destroyed the next morning as the sun heats the earth s surface. Most episodes of high poUutant concentrations are associated with multiday inversions. 

From the viewpoint of air pollution, both stable surface layers and low-level inversions are undesirable because they minimize the rate of dilution of contaminants in the atmosphere. Even though the surface layer may be unstable, a low-level inversion will act as abarrier to vertical mixing, and contaminants will accumulate in the surface layer below the inversion. Stable atmospheric conditions tend to be more frequent and longest in persistence in the autumn, but inversions and stable lapse rates are prevalent at all seasons of the year. 

If the potential temperature decreases with height, the atmosphere is unstable- If the potential temperature increases with height, the atmosphere is stable. The average lapse rate of the atmosphere is about 6.5°C/km that is, the potential temperature increases with height and the average state of the atmosphere is stable. 

Conversely, if the actual measured lapse rate is greater than 9.8°C/1000 m, a parcel of air displaced upward from its initial height becomes warmer than its surroundings and therefore tends to rise (Fig. 4-6b). If pushed downward, the parcel becomes colder than its surroundings and therefore tends to keep sinking. In this case, buoyant forces amplify any initial upward or downward movement of the air parcel, thus creating an unstable atmosphere. 

FIGURE 4-10 Emission of pollutants from a smokestack, a typical continuous source, under a variety of meteorological conditions. The dry adiabatic lapse rate is represented as a dashed line and the actual measured lapse rate as a solid line in the left panels. Vertical mixing is strongest when the adiabatic lapse rate is less than the actual measured lapse rate and the atmosphere is unstable (top). Weak lapse is a term used to express the existence of a stable atmosphere, which results in less vigorous vertical mixing. An inversion, in the third panel from the top and in part of the last three panels, results in a very stable atmospheric layer in which relatively little vertical mixing occurs (Boubel et al, 1994). 

The lapse rate in the PBL is unstable and vertical motion leads to the transport of significant amounts of energy upward, due to the buoyancy of air that has been in contact with the surface. A mixed layer forms up to a height where static stability of the air forms a barrier to thermally induced upward motion. This extreme occurs practically daily over the arid areas of the world and the barrier to upward mixing is often the tropopause itself. On the average in midlatitudes, the unstable or mixed layer is typically 1-2 km deep. 

An important factor in determining the extent of air pollution in urban areas is whether the atmosphere is stable (poor mixing, accumulation of pollutants) or unstable (good mixing and dispersion of pollutants). Whether the atmosphere is stable or unstable depends on how the temperature profile (the so-called lapse rate) in the atmosphere near ground level compares with the adiabatic lapse rate. The adiabatic lapse... 

FIGURE 16.2 Temperature profiles for (a) an unstable atmosphere and (b) a stable atmosphere. The dry adiabatic lapse rate is also shown. 

If the environmental lapse rate lies between the dry and moist values, then the stability of the atmosphere depends on whether the rising air is saturated. When an air parcel is not saturated, then the dry adiabatic lapse rate is the relevant reference state and the atmosphere is stable. For a saturated air parcel inside a cloud, the moist adiabatic rate is the applicable criterion for comparison and the atmosphere is unstable. Therefore a cloudy atmosphere is inherently less stable than the corresponding dry atmosphere with the same lapse rate. 

Thus a cloudy atmosphere is inherently less stable than a dry atmosphere, and a stable situation with reference to the dry adiabatic lapse rate may actually be unstable for upward displacements of a saturated air parcel. 

FIGURE 4 Examples of absolutely stable, conditionally unstable, and absolutely unstable environmental lapse rates (solid lines) relative to the dry and moist adiabatic process lapse rates (dashed lines) experienced by parcels of air displaced vertically from point A. Parcels follow the dry (DD) and moist (MM) adiabatic process curves. 

Now consider temperature profile UU. When an air parcel at point A is displaced adiabatically upward (downward) along DD or MM, it becomes increasingly warmer (colder) than the environment and continues to rise (sink). Thus environmental lapse rate UU is said to be absolutely unstable because a parcel of air continues to ascend or descend once it has been displaced either moist or dry adiabatically from its equilibrium level. 

It is possible for an environmental lapse rate to be both stable and unstable, depending on whether or not the air parcel is saturated. Profile CC is said to be conditionally unstable because it is stable for dry adiabatic processes but unstable for moist adiabatic processes. 

An additional aspect of the vertical distribution of pheromone has been considered by Schal (1982). The odor dispersion models discussed in this chapter all assume that the mean wind flow is horizontal. The occurrence of buoyant or convective transport of odors is treated by increasing the rate of dispersion to that characteristic of unstable conditions. On the relatively small scale of odor communication this description may not be adequate. Schal demonstrated that air currents at night beneath a Costa Rican rain forest move predominantly upward in response to a substantial lapse rate. He found that male cockroaches of various species positioned themselves in trees at levels above that of pheromone producing females of the same species. 

The dry adiabatic lapse rate is a fixed rate, entirely independent of ambient air temperature. A parcel of dry air moving upward in the atmosphere, then, will always cool at the rate of 9.8°C/1000 m, regardless of its initial temperature or the temperature of the surroimding air. When the ambient lapse rate exceeds the adiabatic lapse rate, the ambient rate is said to be superadiabatic, and the atmosphere is highly unstable. When the two lapse rates are exactly equal, the atmosphere is said to be neutral. When the ambient lapse rate is less than the dry adiabatic lapse rate, the ambient lapse rate is termed sub-adiabatic, and the atmosphere is stable. 

The basis for the prediction system is as follows. Convection cells of sufficient strength arise only if the lower atmosphere is (sufficiently) unstable. The criterion for this is that the adiabatic lapse rate (rate of decrease in temperature from the sea surface upward) exceeds some threshold, the value of which depends on the moisture content because of its consequence for possible cloud formation. In case the lapse rate is smaller than 5.5 to 7.5°C/km, the lower atmosphere is stable here 6.5C/km is used as a representative critical value. Between approximately 10°C/km and (say) 6.5°C/km, it is conditionally unstable (depending on the moisture content), and a temperature lapse rate larger than 10°C/km results in an unstable atmosphere. Prediction of the lapse rate and moisture content using multi-layered atmospheric models is part of routine weather forecast systems. This, therefore, also allows operational prediction of the occurrence of significant seiche events on a routine basis, just like common weather prediction. 

If the lapse rate of the atmosphere is less than the adiabatic lapse rate, for example, -15°C/km, a rising air parcel will be accelerated upward by buoyancy, and likewise, a sinking air parcel will be accelerated downward. In this case the atmosphere is called unstable, since any initial vertical motion results in positive feedback and acceleration in the same direction. Conversely, if the lapse rate of the atmosphere is greater than the adiabatic lapse rate, for example —5°C/km, a rising air parcel will be propelled back downward, and a sinking air parcel will be propelled upward. In such a case the atmosphere is called stable, since any initial vertical motion is dampened. Stable conditions with very little vertical mixing are especially encountered during a temperature inversion, when temperature increases with altitude and thus the lapse rate is positive. 

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