Lapse rates

For one mole of an ideal gas, dH = Cp dT + Md p, where Cp is the constant pressure heat capacity per mole. Now the adiabatic condition implies that  

Another way of expressing the way temperature varies in the vertical direction involves the concept of potential temperature, 6. Potential temperature is defined as the temperature a parcel of air would reach if brought adiabatically from its existing temperature and pressure to a standard pressure, Pq. Hence  

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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. 

Fig. 8. Characteristic plume patterns where (--) represents dry-adiabatic lapse rate and (—), air (a) fanning (b) fumigation (c) lofting and (d) looping.

Lapse Rate and Atmospheric Stability Apart from mechanical interference with the steady flow of air caused by buildings and other obstacles, the most important fac tor that influences the degree of turbulence and hence the speed of diffusion in the lower air is the varia-... 

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. 

FIG. 25-4 Stability criteria with measured lapse rate. 

ADIABATIC LAPSE RATE ATMOSPHERIC LAPSE RATE... 

FIG. 25-5 Characteristic lapse rates under inversion conditions. 

FIG. 25-6 Lapse-rate characteristics of atmospheric-diffusion transport of stack emissions. 

Thus air cools as it rises and warms as it descends. Since we have assumed an adiabatic process, -ATIAz defines the dry adiabatic process lapse rate, a constant equal to 0.0098 K/m, is nearly 1 K/lOO m or 5.4°F/1000 ft. 

If an ascending air parcel reaches saturation, the addition of latent heat from condensing moisture will partially overcome the cooling due to expansion. Therefore, the saturated adiabatic lapse rate (of cooling) is smaller than y. ... 

Comparing the temperature of this parcel to that of the surrounding environment (Fig. 17-6), it is seen that in rising from 100 to 300 m, the parcel undergoes the temperature change of the dry adiabatic process lapse rate. The dashed line is a dry adiabatic line or dry adiabat. Suppose that... 

Fig. 17-6. Temperature of a parcel of air forced to rise 200 m compared to the superadiabatic environmental lapse rate. Since the parcel is still warmer than the environment, it will continue to rise.

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. 

Fig. 17-8. Effect of forced mixing (dashed) on the environmental subadiabatic lapse rate (solid). Note the formation of an inversion at the top of the mixed layer.

Fig. 19-4. Vertical expansion of continuous plumes related to vertical temperature structure, The dashed lines correspond to the dry adiabatic lapse rate for reference.

Temperature change with altitude has great influence on the motion of air pollutants. For example, inversion conditions result in only limited vertical mixing. The amount of turbulence available to diffuse pollutants is also a function of the temperature profile. The decrease of temperature with altitude is known as the lapse rate. The normal or standard lapse rate in the United States is -3.5" F/1,000 ft. An adiabatic lapse rate has a value of -5.4" F/1,000 ft. Temperature as a function of altitude is expressed by the following equation ... 

If the sphere of air mass moves upward in an adiabatic process but in an atmosphere with a subadiabatic lapse rate, the sphere follows a temperature change given by the adiabatic slope but when it arrives at point Zj, it is at a lower temperature than its surroundings, but at the same pressure. As a result, it is heavier than the surroundings and tends to fall back to its original position. This condition is called stable. In a stable atmosphere pollutants will only slowly disperse, and turbulence is suppressed. 

Vertical temperature gradient The lapse rate (rate of decrease in temperature with increases in height) must be taken into account because it affects the final height to which a buoyant plume rises. 

The vertical temperature gradient (the lapse rate) is usually not monitored by routine meteorological observation, and it, too, must be approximated from estimates of solar insolation, solar angle, and differential heating due to uneven cloud cover. For purposes of diffusion analyses, the lapse rate is usually approximated by a constant. 

The atmospheric stability class The lapse rate SfYJdz)... 

Adiabatic lapse rate The adiabatic temperature change that takes place with height of a rising (or falling) parcel of air, approximately -1 C/100 m. 

Inversion The condition that occurs when the lapse rate is positive, i.e, temperature rises with height at a rate greater than the adiabatic lapse rate 3 °C per 300 m. In these conditions stagnant air pollution builds up and is trapped under this layer. 

Lapse rate The rate of temperature increase with height. 

Stability Type Potential Temperature Lapse Rate, (K/lOO m) AG/Az... 

The lapse rate in the PBL is imstable 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 mid-latitudes, the imstable or mixed PBL is typically 1-2 km deep. 

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