Unstable atmosphere

Critical GLC s can usually be calculated based on a unstable atmosphere, thus enabling the designer to determine a worst case scenario. For any given day, typical atmospheric stabihty data can usually be obtained from a local weather bureau, or may be estimated from the so-called Pasquill chart for the appropriate Atmospheric Stability Class (refer to Table 1). 

The air-mass thunderstorm is the least severe of all thunderstorms. In its simplest form, an air-mass thunderstorm grows as a single cell when solar radiation heats the surface air in an unstable atmosphere. Its life cycle lasts around 30 minutes. Towering cumulus clouds are formed as in-cloud updrafts push moisture upward. The tower may reach a height about five times the diameter of the cloud base in the growth phase. 

Heavy-gas effects at the source are more important if the cloud s potential energy is larger than the turbulent kinetic energy generated by the surrounding air. Therefore, heavy-gas effects are more important at low wind speeds and stable atmospheric conditions than at high wind speeds and neutral or unstable atmospheric conditions. 

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. 

If a waste source emits a gas with a buoyancy flux of 50m /s, and the wind averages 4m/s, find the plume rise at a distance of 750 m downward from a stack that is 50 m high under unstable atmospheric conditions. Use the equation proposed by Briggs. 

Figure 2 shows the typical shape of a smoke-plume in an unstable atmosphere. In this case, there is a vertical temperature gradient such that... 

Meteorology the use of appropriate wind vectors to steer drift away from susceptible areas, awareness of the dangers of strongly stable and unstable atmospheric conditions and the selection of low-wind velocities for placement application. 

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

Case 1. If m(0 > 0, then qz > 0 and Rf < 0. For this case, positive values of n tend to be associated with positive values of 0 and vice versa. This case corresponds to an unstable atmosphere (decreasing potential temperature with height). If an air parcel moves upward because of a positive fluctuation in its velocity u v it rises to a region of lower potential temperature. However, the air parcel temperature changes adiabatically during this small rapid fluctuation, and its potential temperature remains constant. As a result, the air parcel potential temperature will exceed the potential temperature of its surroundings and will cause a positive potential temperature fluctuation 0 in its new position. 

Finally, for an unstable atmosphere, Benoit (1977) derived the following approximate relationship after integration of (16.80) ... 

Standard deviations that fix the calculated spread of the Gaussian plume. The more unstable models predict more rapid dispersion. While they may not be suitable for worst-case scenarios, these models are important in real-time modeling. They provide less drastic but more realistic projections. A moderately unstable atmosphere ( D stability ) is assigned a horizontal dispersion coefficient twice as great as a stable atmosphere. Greater instability, or A stability, increases the horizontal dispersion coefficient by another factor of 3. The vertical dispersion coefficients increase even more as the atmosphere becomes less stable. The applied factors are not constant but vary with conditions. The end result is that downwind centerline concentrations may be reduced by factors greater than 100 in progressing from F to A stability. 

The Richardson number is a turbulence indicator and also an index of stability. Meteorologists classify atmospheric stability in the surface layer as unstable, neutral, and stable. Strongly negative Richardson numbers indicate that convection predominates, winds are weak, and there is a strong vertical motion characteristic of an unstable atmosphere. Smoke leaving a source spreads rapidly vertically and horizontally. As mechanical turbulence increases, the Richardson number approaches zero, and the... 

FIGURE 2 A diagram indicating the various similarity regions in the unstable atmospheric boundary layer. The indicated scaling parameters are defined in the text. [After Fig. 1 in Holtslag, A. A. M., and Nieuwstadt, F. T. M. (1986). Boundary-Layer Meteorol. 36, 201-209.]... 

Paulson, C. A. 1970. The Mathematical Representation of Wind Speed and Temperature Profiles in the Unstable Atmospheric Surface Layer, Journal of Applied Meteorology, vol. 9, pp. 857-861. 

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. 

Fig. 8.6. The bars indicate the observed temperature difference between the surface sea water at AUK and the air at 925 hPa level at Ekofisk for January till March 1999. Top panel all days bottom panel days of occurrence of a cold front that moved from the North Sea toward the Dutch coast. Straight dashed lines critical temperature difference for an unstable atmosphere based on average elevation of 925 hPa. Wiggly curves values of the critical temperature difference for an unstable atmosphere from day to day, based on an observed elevation of 925 hPa.

The bottom panel shows that an unstable atmosphere is found during a munber of potentially seiche-prone cold-front situations, correctly predicting a seiche-episode. All the seiche events that occurred in this time interval are correctly predicted (no misses). A stable atmosphere is found during most other days indicated in the bottom panel and no convection cells are expected during these days (regardless of the availability of moisture in the air), which agrees with the fact that no seiche events occurred. 

For neutral and unstable atmospheres, the time integrated concentration (E) at ground level can be expressed by Sutton s equation, as follows ... 

Similarly, the air concentration for neutral and unstable atmospheres can be expressed by ... 

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